Finite Group Databasebeta

← #17195276

Subgroups — #17195276

Order 4352.

2834 conjugacy classes of subgroups.

The subgroup lattice has 1628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763281C211yesmaximal, characteristic
2#14531727C211yesmaximal, characteristic, complemented
3#14531725C211yesmaximal, characteristic, complemented
4#14531723C211yesmaximal, characteristic, complemented
5#14531719C211yesmaximal, characteristic, complemented
6#14531716C211yesmaximal, characteristic, complemented
7#14531714C211yesmaximal, characteristic, complemented
8#14531712C211yesmaximal, characteristic, complemented
9#14531708C211yesmaximal, characteristic, complemented
10#14531647C211yesmaximal, characteristic, complemented
11#14531645C211yesmaximal, characteristic, complemented
12#14531643C211yesmaximal, characteristic, complemented
13#14531639C211yesmaximal, characteristic, complemented
14#14531636C211yesmaximal, characteristic, complemented
15#14531634C211yesmaximal, characteristic, complemented
16#14531632C211yesmaximal, characteristic, complemented
17#14531628C211yesmaximal, characteristic, complemented
18#14531417C211yesmaximal, characteristic, complemented
19#14531412C211yesmaximal, characteristic, complemented
20#14531411C211yesmaximal, characteristic, complemented
21#14531410C211yesmaximal, characteristic, complemented
22#14531395C211yesmaximal, characteristic, complemented
23#14531358C211yesmaximal, characteristic
24#14531227C211yesmaximal, characteristic, complemented
25#14531224C211yesmaximal, characteristic, complemented
26#14531220C211yesmaximal, characteristic, complemented
27D17×#386C211yesmaximal, characteristic
28D17×#385C211yesmaximal, characteristic, complemented
29#14531136C211yesmaximal, characteristic, complemented
30C2×C4×#63227C211yesmaximal, characteristic, complemented
31C17×#2290C211yesmaximal, characteristic, complemented
32C22×D4×D17C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34#11763281C4116yescomplemented
35C2×C4×D68C2211yescharacteristic
36C2×D4×Dic17C2211yescharacteristic
37C2×#10587579C2211yescharacteristic
38C2×C4×C22⋊D17C2211yescharacteristic
39C2×C4×C22⋊D17C2211yescharacteristic
40C2×#10587567C2211yescharacteristic
41C2×#10587567C2211yescharacteristic
42C2×#10587578C2211yescharacteristic
43C2×#10587578C2211yescharacteristic, complemented
44C2×#10587558C2211yescharacteristic
45C2×#10587558C2211yescharacteristic, complemented
46C2×#10587563C2211yescharacteristic, complemented
47C2×C4⋊C4×D17C2211yescharacteristic, complemented
48C2×C4⋊C4×D17C2211yescharacteristic, complemented
49C22×#63227C2211yescharacteristic
50C22×#63227C2211yescharacteristic
51C22×#63227C2211yescharacteristic
52C2×C22⋊C4×D17C2211yescharacteristic
53C2×C22⋊C4×D17C2211yescharacteristic
54C2×C22⋊C4×D17C2211yescharacteristic
55C2×C22⋊C4×D17C2211yescharacteristic
56C2×C22⋊C4×D17C2211yescharacteristic
57C2×C22⋊C4×D17C2211yescharacteristic
58C22×C4×Dic17C2211yescharacteristic, complemented
59#11762703C2211yescharacteristic, complemented
60#11762703C2211yescharacteristic, complemented
61#11762702C2211yescharacteristic, complemented
62#11762702C2211yescharacteristic, complemented
63#11762701C2211yescharacteristic, complemented
64#11762701C2211yescharacteristic, complemented
65#11762700C2211yescharacteristic, complemented
66#11762700C2211yescharacteristic, complemented
67#11762700C2211yescharacteristic, complemented
68#11762700C2211yescharacteristic, complemented
69#11762699C2211yescharacteristic, complemented
70#11762699C2211yescharacteristic, complemented
71#11762697C2211yescharacteristic, complemented
72#11762697C2211yescharacteristic, complemented
73#11762696C2211yescharacteristic, complemented
74#11762696C2211yescharacteristic, complemented
75#11762695C2211yescharacteristic, complemented
76#11762695C2211yescharacteristic, complemented
77#11762694C2211yescharacteristic, complemented
78#11762694C2211yescharacteristic, complemented
79#11762693C2211yescharacteristic, complemented
80#11762693C2211yescharacteristic, complemented
81#11762693C2211yescharacteristic, complemented
82#11762693C2211yescharacteristic, complemented
83#11762692C2211yescharacteristic, complemented
84#11762692C2211yescharacteristic, complemented
85#11762690C2211yescharacteristic, complemented
86#11762690C2211yescharacteristic, complemented
87#11762689C2211yescharacteristic
88#11762689C2211yescharacteristic
89#11762688C2211yescharacteristic
90#11762688C2211yescharacteristic
91#11762687C2211yescharacteristic
92#11762687C2211yescharacteristic
93#11762687C2211yescharacteristic
94#11762687C2211yescharacteristic
95#11762686C2211yescharacteristic
96#11762686C2211yescharacteristic
97#11762685C2211yescharacteristic
98#11762685C2211yescharacteristic
99#11762685C2211yescharacteristic
100#11762685C2211yescharacteristic
101#11762684C2211yescharacteristic, complemented
102#11762684C2211yescharacteristic, complemented
103#11762683C2211yescharacteristic
104#11762683C2211yescharacteristic
105#11762683C2211yescharacteristic
106#11762683C2211yescharacteristic
107#11762682C2211yescharacteristic, complemented
108#11762682C2211yescharacteristic, complemented
109#11762681C2211yescharacteristic, complemented
110#11762681C2211yescharacteristic, complemented
111#11762680C2211yescharacteristic
112#11762680C2211yescharacteristic
113#11762680C2211yescharacteristic
114#11762680C2211yescharacteristic
115#11762677C2211yescharacteristic, complemented
116#11762676C2211yescharacteristic, complemented
117#11762676C2211yescharacteristic, complemented
118#11762676C2211yescharacteristic, complemented
119#11762675C2211yescharacteristic, complemented
120#11762674C2211yescharacteristic, complemented
121#11762673C2211yescharacteristic, complemented
122#11762673C2211yescharacteristic, complemented
123#11762672C2211yescharacteristic, complemented
124#11762671C2211yescharacteristic
125#11762671C2211yescharacteristic
126#11762671C2211yescharacteristic, complemented
127#11762671C2211yescharacteristic, complemented
128#11762670C2211yescharacteristic, complemented
129#11762669C2211yescharacteristic, complemented
130#11762668C2211yescharacteristic, complemented
131#11762668C2211yescharacteristic, complemented
132#11762668C2211yescharacteristic, complemented
133#11762667C2211yescharacteristic, complemented
134#11762666C2211yescharacteristic, complemented
135#11762666C2211yescharacteristic, complemented
136#11762666C2211yescharacteristic, complemented
137#11762664C2211yescharacteristic
138#11762664C2211yescharacteristic
139C4⋊C4×Dic17C2211yescharacteristic, complemented
140C4×#63225C2211yescharacteristic, complemented
141#11762660C2211yescharacteristic, complemented
142C22⋊C4×Dic17C2211yescharacteristic, complemented
143C22⋊C4×Dic17C2211yescharacteristic, complemented
144C22⋊C4×Dic17C2211yescharacteristic, complemented
145C4×#63227C2211yescharacteristic
146C4×#63227C2211yescharacteristic
147C4×#63227C2211yescharacteristic
148C4×#63227C2211yescharacteristic
149C4×#63227C2211yescharacteristic
150C4×#63227C2211yescharacteristic
151C4×#63227C2211yescharacteristic, complemented
152C4×#63227C2211yescharacteristic, complemented
153C4×#63227C2211yescharacteristic, complemented
154C4×#63227C2211yescharacteristic, complemented
155C4×#63227C2211yescharacteristic, complemented
156C4×#63227C2211yescharacteristic, complemented
157C4×#63227C2211yescharacteristic, complemented
158C4×C22⋊Dic17C2211yescharacteristic, complemented
159#11762656C2211yescharacteristic
160#11762656C2211yescharacteristic
161#11762656C2211yescharacteristic, complemented
162#11762656C2211yescharacteristic, complemented
163#11762656C2211yescharacteristic, complemented
164#11762655C2211yescharacteristic, complemented
165#11762654C2211yescharacteristic, complemented
166#11762654C2211yescharacteristic, complemented
167C2×#10587502C2211yescharacteristic, complemented
168C2×#10587502C2211yescharacteristic, complemented
169#95×D17C2211yescharacteristic
170#95×D17C2211yescharacteristic
171#95×D17C2211yescharacteristic, complemented
172#95×D17C2211yescharacteristic, complemented
173C2×C4×D4×C17C2211yescharacteristic
174C2×C17×#117C2211yescharacteristic, complemented
175C22×C42×C17C2211yescharacteristic, complemented
176C17×#388C2211yescharacteristic, complemented
177C17×#388C2211yescharacteristic, complemented
178C17×#387C2211yescharacteristic, complemented
179C17×#387C2211yescharacteristic, complemented
180C17×#386C2211yescharacteristic
181C17×#386C2211yescharacteristic
182C17×#385C2211yescharacteristic, complemented
183C17×#385C2211yescharacteristic, complemented
184C4×C4⋊C4×C17C2211yescharacteristic, complemented
185C4×C22⋊C4×C17C2211yescharacteristic, complemented
186C4×C22⋊C4×C17C2211yescharacteristic, complemented
187C17×#376C2211yescharacteristic, complemented
188C24×D17C2311yescharacteristic
189C24×D17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C23×Dic17C2311yescharacteristic
198C23×Dic17C2311yescharacteristic
199C23×Dic17C2311yescharacteristic
200C23×Dic17C2311yescharacteristic
201C2×D4×D17—24no—
202C2×D4×D17—24no—
203C2×D4×D17C2×C418yes—
204C22×D68C2311yescharacteristic
205C22×C4×D17—24no—
206C22×C4×D17—42no—
207C22×C4×D17—42no—
208C22×C4×D17C2311yescharacteristic
209C22×C4×D17C2311yescharacteristic
210C22×C4×D17C2311yescharacteristic
211C22×C4×D17C2311yescharacteristic
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C22×C4×D17C2311yescharacteristic
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C4×D4×C17C2×C418yescomplemented
222C17×#117—42no—
223C2×C4⋊C4×C17C2311yescharacteristic
224C2×C4⋊C4×C17C2311yescharacteristic
225C2×C4⋊C4×C17C2311yescharacteristic
226C2×C4⋊C4×C17C2311yescharacteristic
227C2×C4⋊C4×C17C2311yescharacteristic
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
236C2×C42×C17—42no—
237C2×C42×C17C2311yescharacteristic
238C2×C42×C17C2311yescharacteristic
239C2×C42×C17C2311yescharacteristic
240C2×C42×C17C2311yescharacteristic
241C2×C42×C17C2311yescharacteristic
242C2×C42×C17C2311yescharacteristic
243C2×C42×C17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252D4×Dic17C2×C418yescomplemented
253C4×C22⋊D17C2×C418yescomplemented
254C4×C22⋊D17C2×C418yescomplemented
255C2×#63227—24no—
256C2×#63227C2×C418yes—
257C2×#63227C2×C418yescomplemented
258C2×#63227C2311yescharacteristic
259C2×#63227C2311yescharacteristic
260C2×#63227C2311yescharacteristic
261C2×#63227C2311yescharacteristic
262C2×#63227C2311yescharacteristic
263C2×#63227C2311yescharacteristic
264C2×#63227C2311yescharacteristic
265C2×#63227C2311yescharacteristic
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×C4⋊Dic17C2311yescharacteristic
283C2×C4⋊Dic17C2311yescharacteristic
284C2×C4⋊Dic17C2311yescharacteristic
285C2×C4⋊Dic17C2311yescharacteristic
286C2×C4⋊Dic17C2311yescharacteristic
287C2×#63225C2311yescharacteristic
288C2×#63225C2311yescharacteristic
289C2×#63225C2311yescharacteristic
290C2×#63225C2311yescharacteristic
291C2×#63225C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×C4×Dic17—42no—
298C2×C4×Dic17C2311yescharacteristic
299C2×C4×Dic17C2311yescharacteristic
300C2×C4×Dic17C2311yescharacteristic
301C2×C4×Dic17C2311yescharacteristic
302C2×C4×Dic17C2311yescharacteristic
303C2×C4×Dic17C2311yescharacteristic
304C2×C4×Dic17C2311yescharacteristic
305C2×C4×Dic17C2311yescharacteristic
306C2×C4×Dic17C2311yescharacteristic
307C2×C4×Dic17C2311yescharacteristic
308C2×C4×Dic17C2311yescharacteristic
309C2×C4×Dic17C2311yescharacteristic
310C2×C4×Dic17C2311yescharacteristic
311#10587579C2×C418yescomplemented
312#10587578—42no—
313#10587578C2×C418yescomplemented
314C4⋊C4×D17—42no—
315C4⋊C4×D17—42no—
316#10587567C2×C418yescomplemented
317#10587567C2×C418yescomplemented
318C22⋊C4×D17—24no—
319C22⋊C4×D17—24no—
320C22⋊C4×D17—42no—
321C22⋊C4×D17—42no—
322C22⋊C4×D17C2×C418yes—
323C22⋊C4×D17C2×C418yescomplemented
324#10587563—42no—
325C4×D68C2×C418yescomplemented
326#10587558—42no—
327#10587558C2×C418yescomplemented
328C17×#95C2311yescharacteristic
329C17×#95C2311yescharacteristic
330C17×#95C2311yescharacteristic
331C17×#95C2311yescharacteristic
332C17×#95C2311yescharacteristic
333C17×#95C2311yescharacteristic
334C17×#95C2311yescharacteristic
335C17×#95C2311yescharacteristic
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338#10587502C2311yescharacteristic
339#10587502C2311yescharacteristic
340#10587502C2311yescharacteristic
341#10587502C2311yescharacteristic
342#10587502C2311yescharacteristic
343#10587502C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376C24×C17C2411yescharacteristic
377C24×C17C2411yescharacteristic
378C23×D17—22no—
379C23×D17—22no—
380C23×D17—41no—
381C23×D17—41no—
382C23×D17—41no—
383C23×D17—41no—
384C23×D17—41no—
385C23×D17—41no—
386C23×D17—41no—
387C23×D17—41no—
388C23×D17C22×C414yes—
389C23×D17C22×C414yes—
390C23×D17#4114yes—
391C23×D17#4114yes—
392C23×D17C2411yescharacteristic
393C23×D17C2411yescharacteristic
394C23×D17C2411yescharacteristic
395C2×D4×C17—22no—
396C2×D4×C17—22no—
397C2×D4×C17C22×C414yes—
398C22×C4×C17—22no—
399C22×C4×C17—22no—
400C22×C4×C17—22no—
401C22×C4×C17—22no—
402C22×C4×C17—41no—
403C22×C4×C17—41no—
404C22×C4×C17—41no—
405C22×C4×C17—41no—
406C22×C4×C17—41no—
407C22×C4×C17—41no—
408C22×C4×C17C22×C414yes—
409C22×C4×C17C22×C414yescomplemented
410C22×C4×C17C2411yescharacteristic
411C22×C4×C17C2411yescharacteristic
412C22×C4×C17C2411yescharacteristic
413C22×C4×C17C2411yescharacteristic
414C22×C4×C17C2411yescharacteristic
415C22×C4×C17C2411yescharacteristic
416C22×C4×C17C2411yescharacteristic
417C22×C4×C17C2411yescharacteristic
418C22×C4×C17C2411yescharacteristic
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C2×C22⋊D17—22no—
424C2×C22⋊D17—22no—
425C2×C22⋊D17—22no—
426C2×C22⋊D17—22no—
427C2×C22⋊D17C22×C414yes—
428C2×C22⋊D17C22×C414yes—
429C22×Dic17—22no—
430C22×Dic17—22no—
431C22×Dic17—41no—
432C22×Dic17—41no—
433C22×Dic17—41no—
434C22×Dic17—41no—
435C22×Dic17—41no—
436C22×Dic17—41no—
437C22×Dic17—41no—
438C22×Dic17—41no—
439C22×Dic17C22×C414yes—
440C22×Dic17C22×C414yescomplemented
441C22×Dic17C2411yescharacteristic
442C22×Dic17C2411yescharacteristic
443C22×Dic17C2411yescharacteristic
444C22×Dic17C2411yescharacteristic
445C22×Dic17C2411yescharacteristic
446C22×Dic17C2411yescharacteristic
447C22×Dic17C2411yescharacteristic
448C22×Dic17C2411yescharacteristic
449C22×Dic17C2411yescharacteristic
450C22×Dic17C2411yescharacteristic
451C22×Dic17C2411yescharacteristic
452C22×Dic17C2411yescharacteristic
453C22×Dic17C2411yescharacteristic
454D4×D17—232no—
455C2×D68—22no—
456C2×D68—22no—
457C2×D68C22×C414yes—
458C2×C4×D17—22no—
459C2×C4×D17—22no—
460C2×C4×D17—22no—
461C2×C4×D17—22no—
462C2×C4×D17—22no—
463C2×C4×D17—22no—
464C2×C4×D17—22no—
465C2×C4×D17—22no—
466C2×C4×D17—22no—
467C2×C4×D17—22no—
468C2×C4×D17—22no—
469C2×C4×D17—22no—
470C2×C4×D17—22no—
471C2×C4×D17—22no—
472C2×C4×D17—41no—
473C2×C4×D17—41no—
474C2×C4×D17—41no—
475C2×C4×D17—41no—
476C2×C4×D17—41no—
477C2×C4×D17—41no—
478C2×C4×D17—41no—
479C2×C4×D17—41no—
480C2×C4×D17—41no—
481C2×C4×D17—41no—
482C2×C4×D17—41no—
483C2×C4×D17—41no—
484C2×C4×D17—416no—
485C2×C4×D17—41no—
486C2×C4×D17—41no—
487C2×C4×D17—41no—
488C2×C4×D17—41no—
489C2×C4×D17—41no—
490C2×C4×D17—41no—
491C2×C4×D17—41no—
492C2×C4×D17—41no—
493C2×C4×D17C22×C414yes—
494C2×C4×D17C22×C414yes—
495C2×C4×D17C22×C414yes—
496C2×C4×D17C22×C414yescomplemented
497C2×C4×D17C22×C414yescomplemented
498C4⋊C4×C17—22no—
499C4⋊C4×C17—22no—
500C4⋊C4×C17—41no—
501C4⋊C4×C17—41no—
502C4⋊C4×C17C22×C414yescomplemented
503C22⋊C4×C17—22no—
504C22⋊C4×C17—22no—
505C22⋊C4×C17—22no—
506C22⋊C4×C17—22no—
507C22⋊C4×C17—41no—
508C22⋊C4×C17—41no—
509C22⋊C4×C17C22×C414yes—
510C22⋊C4×C17C22×C414yescomplemented
511C42×C17—22no—
512C42×C17—22no—
513C42×C17—41no—
514C42×C17—41no—
515C42×C17—41no—
516C42×C17—41no—
517C42×C17C22×C414yescomplemented
518C22⋊Dic17—22no—
519C22⋊Dic17—22no—
520C22⋊Dic17—41no—
521C22⋊Dic17—41no—
522C22⋊Dic17—41no—
523C22⋊Dic17—41no—
524C22⋊Dic17C22×C414yes—
525C22⋊Dic17C22×C414yescomplemented
526#63227—22no—
527#63227—22no—
528#63227—22no—
529#63227—22no—
530#63227—22no—
531#63227—22no—
532#63227—22no—
533#63227—22no—
534#63227—22no—
535#63227—22no—
536#63227—41no—
537#63227—41no—
538#63227—41no—
539#63227—41no—
540#63227—41no—
541#63227—41no—
542#63227C22×C414yes—
543#63227C22×C414yes—
544#63227C22×C414yes—
545#63227C22×C414yes—
546#63227C22×C414yes—
547#63227C22×C414yes—
548#63227C22×C414yescomplemented
549#63227C22×C414yescomplemented
550C4⋊Dic17—41no—
551C4⋊Dic17—41no—
552C4⋊Dic17—41no—
553C4⋊Dic17—41no—
554C4⋊Dic17C22×C414yescomplemented
555#63225—22no—
556#63225—22no—
557#63225—41no—
558#63225—41no—
559#63225—41no—
560#63225—41no—
561#63225—41no—
562#63225—41no—
563#63225C22×C414yescomplemented
564#63225C22×C414yescomplemented
565C4×Dic17—22no—
566C4×Dic17—22no—
567C4×Dic17—41no—
568C4×Dic17—41no—
569C4×Dic17—41no—
570C4×Dic17—41no—
571C4×Dic17—41no—
572C4×Dic17—41no—
573C4×Dic17—41no—
574C4×Dic17—41no—
575C4×Dic17C22×C414yescomplemented
576C4×Dic17C22×C414yescomplemented
577C4×Dic17C22×C414yescomplemented
578#34251—171nomaximal, Sylow
579C23×C17—21no—
580C23×C17—21no—
581C23×C17—21no—
582C23×C17—21no—
583C23×C17—21no—
584C23×C17—21no—
585C23×C17—21no—
586C23×C17—21no—
587C23×C17—21no—
588C23×C17—21no—
589C23×C17C23×C412yes—
590C23×C17C23×C412yes—
591C23×C17C2×#4112yes—
592C23×C17C2×#4112yes—
593C23×C17C2511yescharacteristic
594C22×D17—21no—
595C22×D17—21no—
596C22×D17—21no—
597C22×D17—21no—
598C22×D17—21no—
599C22×D17—21no—
600C22×D17—21no—
601C22×D17—21no—
602C22×D17—21no—
603C22×D17—21no—
604C22×D17—21no—
605C22×D17—21no—
606C22×D17—21no—
607C22×D17—21no—
608C22×D17—28no—
609C22×D17—44no—
610C22×D17—44no—
611C22×D17—44no—
612C22×D17—44no—
613C22×D17—44no—
614C22×D17—44no—
615C22×D17—44no—
616C22×D17—44no—
617C22×D17—82no—
618C22×D17—82no—
619C22×D17—82no—
620C22×D17—82no—
621C22×D17#117116yescomplemented
622C22×D17C23×C412yes—
623C22×D17C23×C412yes—
624C22×D17C23×C412yes—
625C22×D17C2×#4112yes—
626C22×D17C2×#4112yes—
627C22×D17C2×#4112yes—
628C22×D17C2×#4112yes—
629D4×C17—28no—
630C2×C4×C17—28no—
631C2×C4×C17—21no—
632C2×C4×C17—21no—
633C2×C4×C17—21no—
634C2×C4×C17—21no—
635C2×C4×C17—21no—
636C2×C4×C17—21no—
637C2×C4×C17—21no—
638C2×C4×C17—21no—
639C2×C4×C17—21no—
640C2×C4×C17—21no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—21no—
645C2×C4×C17—21no—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
648C2×C4×C17—21no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—21no—
662C2×C4×C17—21no—
663C2×C4×C17—44no—
664C2×C4×C17—44no—
665C2×C4×C17—44no—
666C2×C4×C17C23×C412yes—
667C2×C4×C17C23×C412yes—
668C2×C4×C17C23×C412yes—
669C2×C4×C17C23×C412yes—
670C2×C4×C17C23×C412yes—
671C2×C4×C17H(5,𝔽2)12yes—
672C2×C4×C17H(5,𝔽2)12yes—
673C22⋊D17—28no—
674C22⋊D17—28no—
675C2×Dic17—21no—
676C2×Dic17—21no—
677C2×Dic17—21no—
678C2×Dic17—21no—
679C2×Dic17—21no—
680C2×Dic17—21no—
681C2×Dic17—21no—
682C2×Dic17—21no—
683C2×Dic17—21no—
684C2×Dic17—21no—
685C2×Dic17—21no—
686C2×Dic17—21no—
687C2×Dic17—21no—
688C2×Dic17—21no—
689C2×Dic17—21no—
690C2×Dic17—21no—
691C2×Dic17—21no—
692C2×Dic17—21no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—21no—
704C2×Dic17—21no—
705C2×Dic17—21no—
706C2×Dic17—21no—
707C2×Dic17—21no—
708C2×Dic17—21no—
709C2×Dic17—44no—
710C2×Dic17—44no—
711C2×Dic17—44no—
712C2×Dic17—44no—
713C2×Dic17C23×C412yes—
714C2×Dic17C23×C412yes—
715C2×Dic17C23×C412yes—
716C2×Dic17C23×C412yes—
717C2×Dic17C23×C412yes—
718D68—28no—
719C4×D17—28no—
720C4×D17—44no—
721C4×D17—44no—
722C4×D17—44no—
723C4×D17—44no—
724C4×D17—44no—
725C4×D17—44no—
726C4×D17—44no—
727C4×D17—44no—
728C4×D17—82no—
729C4×D17—82no—
730C4×D17—82no—
731C4×D17—82no—
732C2×#518—171no—
733#2353—171no—
734#2353—171no—
735#2353—171no—
736#2353—171no—
737#2352—171no—
738#2352—171no—
739#2352—171no—
740#2352—171no—
741#2343—171no—
742#2343—171no—
743#2343—171no—
744#2343—171no—
745#2342—171no—
746#2342—171no—
747#2342—171no—
748#2342—171no—
749#2318—171no—
750#2318—171no—
751#2318—171no—
752#2318—171no—
753#2315—171no—
754#2308—171no—
755#2290—171no—
756#2290—171no—
757#2290—171no—
758#2290D1711yescharacteristic, complemented
759C2×#386—171no—
760C2×#385—171no—
761#2273—171no—
762C2×C4×C22⋊C4—171no—
763C22×C17—22no—
764C22×C17—22no—
765C22×C17—22no—
766C22×C17—22no—
767C22×C17—22no—
768C22×C17—22no—
769C22×C17—22no—
770C22×C17—22no—
771C22×C17—22no—
772C22×C17—41no—
773C22×C17—41no—
774C22×C17—41no—
775C22×C17—41no—
776C22×C17C2×#11714yes—
777C22×C17C24×C411yescharacteristic
778C22×C17C22×#4111yescharacteristic
779C22×C17C22×#4111yescharacteristic
780C22×C17C2×H(5,𝔽2)11yescharacteristic
781C22×C17C2×H(5,𝔽2)11yescharacteristic
782C22×C17#58511yescharacteristic
783C22×C17#58511yescharacteristic
784C2×D17—22no—
785C2×D17—22no—
786C2×D17—22no—
787C2×D17—22no—
788C2×D17—22no—
789C2×D17—22no—
790C2×D17—22no—
791C2×D17—22no—
792C2×D17—22no—
793C2×D17—22no—
794C2×D17—22no—
795C2×D17—22no—
796C2×D17—22no—
797C2×D17—22no—
798C2×D17—22no—
799C2×D17—416no—
800C2×D17—41no—
801C2×D17—41no—
802C2×D17—41no—
803C2×D17—41no—
804C2×D17—88no—
805C2×D17C2×#11714yes—
806C2×D17C2×#11714yes—
807C4×C17—22no—
808C4×C17—22no—
809C4×C17—22no—
810C4×C17—22no—
811C4×C17—22no—
812C4×C17—22no—
813C4×C17—22no—
814C4×C17—41no—
815C4×C17—41no—
816C4×C17—41no—
817C4×C17—41no—
818C4×C17—41no—
819C4×C17—41no—
820Dic17—22no—
821Dic17—22no—
822Dic17—22no—
823Dic17—22no—
824Dic17—22no—
825Dic17—41no—
826Dic17—41no—
827Dic17—41no—
828Dic17—41no—
829Dic17—41no—
830Dic17—41no—
831Dic17—41no—
832Dic17—41no—
833C23×D4—171no—
834C24×C4—171no—
835#518—1716no—
836C2×C4×D4—171no—
837C2×C4×D4—171no—
838C2×C4×D4—171no—
839C2×C4×D4—171no—
840C2×C4×D4—171no—
841C2×C4×D4—171no—
842C2×C4×D4—171no—
843C2×C4×D4C2×D1711yescharacteristic
844C2×#117—171no—
845C2×#117—171no—
846C2×#117—171no—
847C2×#117—171no—
848C2×#117—171no—
849C2×#117C2×D1711yescharacteristic, complemented
850C22×C4⋊C4—171no—
851C22×C4⋊C4—171no—
852C22×C22⋊C4—171no—
853C22×C22⋊C4—171no—
854C22×C22⋊C4—171no—
855C22×C22⋊C4—171no—
856C22×C22⋊C4—171no—
857C22×C22⋊C4—171no—
858C22×C22⋊C4—171no—
859C22×C22⋊C4—171no—
860C22×C22⋊C4—171no—
861C22×C42—171no—
862C22×C42C2×D1711yescharacteristic, complemented
863#388—171no—
864#388—171no—
865#388—171no—
866#388—171no—
867#388—171no—
868#388—171no—
869#388—171no—
870#388—171no—
871#388—171no—
872#388—171no—
873#388—171no—
874#388—171no—
875#388—171no—
876#388—171no—
877#388C2×D1711yescharacteristic, complemented
878#388C2×D1711yescharacteristic, complemented
879#387—171no—
880#387—171no—
881#387—171no—
882#387—171no—
883#387—171no—
884#387—171no—
885#387—171no—
886#387—171no—
887#387—171no—
888#387—171no—
889#387—171no—
890#387—171no—
891#387—171no—
892#387—171no—
893#387C2×D1711yescharacteristic, complemented
894#387C2×D1711yescharacteristic, complemented
895#386—171no—
896#386—171no—
897#386—171no—
898#386—171no—
899#386—171no—
900#386—171no—
901#386—171no—
902#386—171no—
903#386—171no—
904#386—171no—
905#386—171no—
906#386—171no—
907#386—171no—
908#386—171no—
909#386C2×D1711yescharacteristic
910#386C2×D1711yescharacteristic
911#385—171no—
912#385—171no—
913#385—171no—
914#385—171no—
915#385—171no—
916#385—171no—
917#385—171no—
918#385—171no—
919#385—171no—
920#385—171no—
921#385—171no—
922#385—171no—
923#385—171no—
924#385—171no—
925#385C2×D1711yescharacteristic, complemented
926#385C2×D1711yescharacteristic, complemented
927#383—171no—
928#383—171no—
929#383—171no—
930#383—171no—
931#382—171no—
932#382—171no—
933#382—171no—
934#382—171no—
935#381—171no—
936#381—171no—
937#381—171no—
938#381—171no—
939#381—171no—
940#381—171no—
941#380—171no—
942#380—171no—
943#380—171no—
944#380—171no—
945#380—171no—
946#380—171no—
947#380—171no—
948#380—171no—
949#379—171no—
950#379—171no—
951C4×C4⋊C4—171no—
952C4×C4⋊C4—171no—
953C4×C4⋊C4—171no—
954C4×C4⋊C4C2×D1711yescharacteristic, complemented
955C4×C22⋊C4—171no—
956C4×C22⋊C4—171no—
957C4×C22⋊C4—171no—
958C4×C22⋊C4—171no—
959C4×C22⋊C4—171no—
960C4×C22⋊C4—171no—
961C4×C22⋊C4—171no—
962C4×C22⋊C4—171no—
963C4×C22⋊C4—171no—
964C4×C22⋊C4—171no—
965C4×C22⋊C4—171no—
966C4×C22⋊C4—171no—
967C4×C22⋊C4—171no—
968C4×C22⋊C4—171no—
969C4×C22⋊C4—171no—
970C4×C22⋊C4—171no—
971C4×C22⋊C4—171no—
972C4×C22⋊C4—171no—
973C4×C22⋊C4—171no—
974C4×C22⋊C4—171no—
975C4×C22⋊C4—171no—
976C4×C22⋊C4—171no—
977C4×C22⋊C4C2×D1711yescharacteristic, complemented
978C4×C22⋊C4C2×D1711yescharacteristic, complemented
979#376—171no—
980#376—171no—
981#376—171no—
982#376C2×D1711yescharacteristic, complemented
983C2×#95—171no—
984C2×#95—171no—
985C2×#95—171no—
986C2×#95—171no—
987C2×#95—171no—
988C2×#95—171no—
989C2×C17—24no—
990C2×C17—42no—
991C2×C17C22×#11711yescharacteristic
992C2×C17C4×H(5,𝔽2)11yescharacteristic
993C2×C17C4×H(5,𝔽2)11yescharacteristic
994C2×C17#349011yescharacteristic
995C2×C17#349111yescharacteristic
996C2×C17#350511yescharacteristic
997C2×C17#350511yescharacteristic
998D17—24no—
999D17—24no—
1000D17—42no—
1001C25—171no—
1002C25—171no—
1003C22×D4—171no—
1004C22×D4—171no—
1005C22×D4—178no—
1006C22×D4—171no—
1007C22×D4—344no—
1008C22×D4—344no—
1009C22×D4C22×D1711yescharacteristic
1010C23×C4—171no—
1011C23×C4—171no—
1012C23×C4—171no—
1013C23×C4—171no—
1014C23×C4—171no—
1015C23×C4—171no—
1016C23×C4—171no—
1017C23×C4—171no—
1018C23×C4—171no—
1019C23×C4—171no—
1020C23×C4—171no—
1021C23×C4—171no—
1022C23×C4—171no—
1023C23×C4—171no—
1024C23×C4—171no—
1025C23×C4—171no—
1026C23×C4—171no—
1027C23×C4—344no—
1028C23×C4—682no—
1029C23×C4—682no—
1030C23×C4C22×D1711yescharacteristic
1031C23×C4C22×D1711yescharacteristic
1032C23×C4C22×D1711yescharacteristic
1033C23×C4C22×D1711yescharacteristic
1034C4×D4—178no—
1035C4×D4—178no—
1036C4×D4—178no—
1037C4×D4—178no—
1038C4×D4—178no—
1039C4×D4—178no—
1040C4×D4—178no—
1041C4×D4C4×D1718yescomplemented
1042#117—42no—
1043#117—178no—
1044#117—178no—
1045#117—682no—
1046#117—682no—
1047#117—682no—
1048C2×C4⋊C4—171no—
1049C2×C4⋊C4—171no—
1050C2×C4⋊C4—171no—
1051C2×C4⋊C4—171no—
1052C2×C4⋊C4—171no—
1053C2×C4⋊C4—171no—
1054C2×C4⋊C4—171no—
1055C2×C4⋊C4—171no—
1056C2×C4⋊C4—171no—
1057C2×C4⋊C4—171no—
1058C2×C4⋊C4—171no—
1059C2×C4⋊C4—171no—
1060C2×C4⋊C4—171no—
1061C2×C4⋊C4—171no—
1062C2×C4⋊C4—171no—
1063C2×C4⋊C4—682no—
1064C2×C4⋊C4—682no—
1065C2×C4⋊C4C22×D1711yescharacteristic
1066C2×C4⋊C4C22×D1711yescharacteristic
1067C2×C4⋊C4C22×D1711yescharacteristic
1068C2×C4⋊C4C22×D1711yescharacteristic
1069C2×C4⋊C4C22×D1711yescharacteristic
1070C2×C22⋊C4—171no—
1071C2×C22⋊C4—171no—
1072C2×C22⋊C4—178no—
1073C2×C22⋊C4—178no—
1074C2×C22⋊C4—171no—
1075C2×C22⋊C4—171no—
1076C2×C22⋊C4—171no—
1077C2×C22⋊C4—171no—
1078C2×C22⋊C4—171no—
1079C2×C22⋊C4—171no—
1080C2×C22⋊C4—171no—
1081C2×C22⋊C4—171no—
1082C2×C22⋊C4—178no—
1083C2×C22⋊C4—178no—
1084C2×C22⋊C4—171no—
1085C2×C22⋊C4—171no—
1086C2×C22⋊C4—171no—
1087C2×C22⋊C4—171no—
1088C2×C22⋊C4—171no—
1089C2×C22⋊C4—171no—
1090C2×C22⋊C4—171no—
1091C2×C22⋊C4—171no—
1092C2×C22⋊C4—171no—
1093C2×C22⋊C4—171no—
1094C2×C22⋊C4—171no—
1095C2×C22⋊C4—171no—
1096C2×C22⋊C4—171no—
1097C2×C22⋊C4—171no—
1098C2×C22⋊C4—171no—
1099C2×C22⋊C4—171no—
1100C2×C22⋊C4—171no—
1101C2×C22⋊C4—171no—
1102C2×C22⋊C4—171no—
1103C2×C22⋊C4—171no—
1104C2×C22⋊C4—171no—
1105C2×C22⋊C4—171no—
1106C2×C22⋊C4—344no—
1107C2×C22⋊C4—344no—
1108C2×C22⋊C4—344no—
1109C2×C22⋊C4—682no—
1110C2×C22⋊C4—682no—
1111C2×C22⋊C4C22×D1711yescharacteristic
1112C2×C22⋊C4C22×D1711yescharacteristic
1113C2×C22⋊C4C22×D1711yescharacteristic
1114C2×C22⋊C4C22×D1711yescharacteristic
1115C2×C22⋊C4C22×D1711yescharacteristic
1116C2×C22⋊C4C22×D1711yescharacteristic
1117C2×C22⋊C4C22×D1711yescharacteristic
1118C2×C22⋊C4C22×D1711yescharacteristic
1119C2×C42—42no—
1120C2×C42—171no—
1121C2×C42—171no—
1122C2×C42—171no—
1123C2×C42—171no—
1124C2×C42—171no—
1125C2×C42—171no—
1126C2×C42—171no—
1127C2×C42—171no—
1128C2×C42—171no—
1129C2×C42—171no—
1130C2×C42—171no—
1131C2×C42—171no—
1132C2×C42—171no—
1133C2×C42—682no—
1134C2×C42C22×D1711yescharacteristic
1135C2×C42C22×D1711yescharacteristic
1136C2×C42C22×D1711yescharacteristic
1137C2×C42C22×D1711yescharacteristic
1138C2×C42C22×D1711yescharacteristic
1139C2×C42C22×D1711yescharacteristic
1140C2×C42C22×D1711yescharacteristic
1141#95—171no—
1142#95—171no—
1143#95—171no—
1144#95—171no—
1145#95—171no—
1146#95—171no—
1147#95—171no—
1148#95—171no—
1149#95—171no—
1150#95—171no—
1151#95—171no—
1152#95—171no—
1153#95—171no—
1154#95—171no—
1155#95—171no—
1156#95—171no—
1157#95—171no—
1158#95—171no—
1159#95—171no—
1160#95—171no—
1161#95—171no—
1162#95—171no—
1163#95—171no—
1164#95—171no—
1165#95—171no—
1166#95—171no—
1167#95—171no—
1168#95—171no—
1169#95—171no—
1170#95—171no—
1171#95—171no—
1172#95—171no—
1173#95—171no—
1174#95—171no—
1175#95—171no—
1176#95—171no—
1177#95—171no—
1178#95—171no—
1179#95C22×D1711yescharacteristic
1180#95C22×D1711yescharacteristic
1181#95C22×D1711yescharacteristic
1182#95C22×D1711yescharacteristic
1183#95C22×D1711yescharacteristic
1184#95C22×D1711yescharacteristic
1185#95C22×D1711yescharacteristic
1186#95C22×D1711yescharacteristic
1187#95C22×D1711yescharacteristic
1188#95C22×D1711yescharacteristic
1189C17#3425111yescharacteristic, complemented, Sylow
1190C24—171no—
1191C24—171no—
1192C24—174no—
1193C24—174no—
1194C24—174no—
1195C24—171no—
1196C24—174no—
1197C24—342no—
1198C24—342no—
1199C24—681no—
1200C24—681no—
1201C24—681no—
1202C24—681no—
1203C24—681no—
1204C24—681no—
1205C24—681no—
1206C24—681no—
1207C24C23×D1711yescharacteristic
1208C24C23×D1711yescharacteristic
1209C2×D4—22no—
1210C2×D4—22no—
1211C2×D4—174no—
1212C2×D4—174no—
1213C2×D4—174no—
1214C2×D4—342no—
1215C2×D4—342no—
1216C2×D4—3432no—
1217C2×D4—342no—
1218C2×D4—342no—
1219C2×D4—342no—
1220C2×D4—342no—
1221C2×D4C2×C4×D1714yes—
1222C22×C4—22no—
1223C22×C4—22no—
1224C22×C4—22no—
1225C22×C4—22no—
1226C22×C4—41no—
1227C22×C4—41no—
1228C22×C4—41no—
1229C22×C4—41no—
1230C22×C4—41no—
1231C22×C4—41no—
1232C22×C4—171no—
1233C22×C4—171no—
1234C22×C4—171no—
1235C22×C4—171no—
1236C22×C4—171no—
1237C22×C4—174no—
1238C22×C4—174no—
1239C22×C4—174no—
1240C22×C4—174no—
1241C22×C4—174no—
1242C22×C4—174no—
1243C22×C4—174no—
1244C22×C4—171no—
1245C22×C4—171no—
1246C22×C4—171no—
1247C22×C4—171no—
1248C22×C4—171no—
1249C22×C4—171no—
1250C22×C4—171no—
1251C22×C4—171no—
1252C22×C4—342no—
1253C22×C4—342no—
1254C22×C4—342no—
1255C22×C4—342no—
1256C22×C4—342no—
1257C22×C4—342no—
1258C22×C4—342no—
1259C22×C4—342no—
1260C22×C4—342no—
1261C22×C4—342no—
1262C22×C4—342no—
1263C22×C4—342no—
1264C22×C4—342no—
1265C22×C4—342no—
1266C22×C4—342no—
1267C22×C4—342no—
1268C22×C4—681no—
1269C22×C4—681no—
1270C22×C4—681no—
1271C22×C4—681no—
1272C22×C4—681no—
1273C22×C4—681no—
1274C22×C4—681no—
1275C22×C4—681no—
1276C22×C4—681no—
1277C22×C4—681no—
1278C22×C4—681no—
1279C22×C4—681no—
1280C22×C4—681no—
1281C22×C4—681no—
1282C22×C4—681no—
1283C22×C4—681no—
1284C22×C4—681no—
1285C22×C4—681no—
1286C22×C4—681no—
1287C22×C4—681no—
1288C22×C4—6816no—
1289C22×C4—681no—
1290C22×C4—681no—
1291C22×C4—681no—
1292C22×C4—681no—
1293C22×C4—681no—
1294C22×C4—681no—
1295C22×C4—681no—
1296C22×C4—681no—
1297C22×C4C2×C4×D1714yes—
1298C22×C4C2×C4×D1714yescomplemented
1299C22×C4C23×D1711yescharacteristic
1300C22×C4C23×D1711yescharacteristic
1301C22×C4C23×D1711yescharacteristic
1302C22×C4C23×D1711yescharacteristic
1303C22×C4C23×D1711yescharacteristic
1304C22×C4C23×D1711yescharacteristic
1305C22×C4C23×D1711yescharacteristic
1306C22×C4C23×D1711yescharacteristic
1307C22×C4C23×D1711yescharacteristic
1308C22×C4C23×D1711yescharacteristic
1309C22×C4C23×D1711yescharacteristic
1310C22×C4C23×D1711yescharacteristic
1311C22×C4C23×D1711yescharacteristic
1312C4⋊C4—22no—
1313C4⋊C4—22no—
1314C4⋊C4—41no—
1315C4⋊C4—41no—
1316C4⋊C4—174no—
1317C4⋊C4—174no—
1318C4⋊C4—174no—
1319C4⋊C4—342no—
1320C4⋊C4—342no—
1321C4⋊C4—681no—
1322C4⋊C4—681no—
1323C4⋊C4—681no—
1324C4⋊C4—681no—
1325C4⋊C4—681no—
1326C4⋊C4—681no—
1327C4⋊C4—681no—
1328C4⋊C4—681no—
1329C4⋊C4—681no—
1330C4⋊C4—681no—
1331C4⋊C4C2×C4×D1714yescomplemented
1332C22⋊C4—22no—
1333C22⋊C4—22no—
1334C22⋊C4—22no—
1335C22⋊C4—22no—
1336C22⋊C4—41no—
1337C22⋊C4—41no—
1338C22⋊C4—174no—
1339C22⋊C4—174no—
1340C22⋊C4—174no—
1341C22⋊C4—174no—
1342C22⋊C4—174no—
1343C22⋊C4—174no—
1344C22⋊C4—174no—
1345C22⋊C4—174no—
1346C22⋊C4—174no—
1347C22⋊C4—174no—
1348C22⋊C4—342no—
1349C22⋊C4—342no—
1350C22⋊C4—342no—
1351C22⋊C4—342no—
1352C22⋊C4—342no—
1353C22⋊C4—342no—
1354C22⋊C4—342no—
1355C22⋊C4—342no—
1356C22⋊C4—342no—
1357C22⋊C4—342no—
1358C22⋊C4—342no—
1359C22⋊C4—342no—
1360C22⋊C4—681no—
1361C22⋊C4—681no—
1362C22⋊C4—681no—
1363C22⋊C4—681no—
1364C22⋊C4—681no—
1365C22⋊C4—681no—
1366C22⋊C4—681no—
1367C22⋊C4—681no—
1368C22⋊C4—681no—
1369C22⋊C4—681no—
1370C22⋊C4C2×C4×D1714yes—
1371C22⋊C4C2×C4×D1714yescomplemented
1372C42—22no—
1373C42—22no—
1374C42—41no—
1375C42—41no—
1376C42—41no—
1377C42—41no—
1378C42—174no—
1379C42—174no—
1380C42—174no—
1381C42—342no—
1382C42—342no—
1383C42—681no—
1384C42—681no—
1385C42—681no—
1386C42—681no—
1387C42—681no—
1388C42—681no—
1389C42—681no—
1390C42—681no—
1391C42C2×C4×D1714yescomplemented
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—172no—
1403C23—172no—
1404C23—172no—
1405C23—172no—
1406C23—172no—
1407C23—172no—
1408C23—1716no—
1409C23—172no—
1410C23—348no—
1411C23—341no—
1412C23—341no—
1413C23—341no—
1414C23—341no—
1415C23—341no—
1416C23—341no—
1417C23—341no—
1418C23—341no—
1419C23—341no—
1420C23—341no—
1421C23—341no—
1422C23—341no—
1423C23—341no—
1424C23—341no—
1425C23—684no—
1426C23—684no—
1427C23—684no—
1428C23—684no—
1429C23—684no—
1430C23—684no—
1431C23—684no—
1432C23—684no—
1433C23—1362no—
1434C23—1362no—
1435C23—1362no—
1436C23—1362no—
1437C23C22×C4×D1712yes—
1438C23C22×C4×D1712yes—
1439C23#41×D1712yes—
1440C23#41×D1712yes—
1441C23C24×D1711yescharacteristic
1442D4—28no—
1443D4—348no—
1444D4—348no—
1445D4—348no—
1446C2×C4—28no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—44no—
1480C2×C4—44no—
1481C2×C4—44no—
1482C2×C4—172no—
1483C2×C4—172no—
1484C2×C4—172no—
1485C2×C4—172no—
1486C2×C4—172no—
1487C2×C4—348no—
1488C2×C4—341no—
1489C2×C4—341no—
1490C2×C4—341no—
1491C2×C4—341no—
1492C2×C4—341no—
1493C2×C4—341no—
1494C2×C4—341no—
1495C2×C4—341no—
1496C2×C4—341no—
1497C2×C4—341no—
1498C2×C4—341no—
1499C2×C4—341no—
1500C2×C4—341no—
1501C2×C4—341no—
1502C2×C4—341no—
1503C2×C4—341no—
1504C2×C4—341no—
1505C2×C4—341no—
1506C2×C4—341no—
1507C2×C4—341no—
1508C2×C4—341no—
1509C2×C4—341no—
1510C2×C4—341no—
1511C2×C4—341no—
1512C2×C4—341no—
1513C2×C4—341no—
1514C2×C4—341no—
1515C2×C4—341no—
1516C2×C4—341no—
1517C2×C4—341no—
1518C2×C4—341no—
1519C2×C4—341no—
1520C2×C4—341no—
1521C2×C4—341no—
1522C2×C4—684no—
1523C2×C4—684no—
1524C2×C4—684no—
1525C2×C4—684no—
1526C2×C4—684no—
1527C2×C4—684no—
1528C2×C4—684no—
1529C2×C4—684no—
1530C2×C4—684no—
1531C2×C4—684no—
1532C2×C4—684no—
1533C2×C4—684no—
1534C2×C4—1362no—
1535C2×C4—1362no—
1536C2×C4—1362no—
1537C2×C4—1362no—
1538C2×C4C22×C4×D1712yes—
1539C2×C4C22×C4×D1712yes—
1540C2×C4C22×C4×D1712yes—
1541C2×C4C22×C4×D1712yes—
1542C2×C4C22×C4×D1712yes—
1543C2×C4#1058769112yes—
1544C2×C4#1058769612yes—
1545C22—22no—
1546C22—22no—
1547C22—22no—
1548C22—22no—
1549C22—22no—
1550C22—22no—
1551C22—22no—
1552C22—22no—
1553C22—22no—
1554C22—41no—
1555C22—41no—
1556C22—41no—
1557C22—41no—
1558C22—174no—
1559C22—174no—
1560C22—342no—
1561C22—342no—
1562C22—342no—
1563C22—342no—
1564C22—342no—
1565C22—342no—
1566C22—342no—
1567C22—342no—
1568C22—342no—
1569C22—342no—
1570C22—342no—
1571C22—342no—
1572C22—342no—
1573C22—342no—
1574C22—342no—
1575C22—6816no—
1576C22—681no—
1577C22—681no—
1578C22—681no—
1579C22—681no—
1580C22—1368no—
1581C22#117×D1714yes—
1582C22C23×C4×D1711yescharacteristic
1583C22C2×#41×D1711yescharacteristic
1584C22C2×#41×D1711yescharacteristic
1585C22C2×#1058769111yescharacteristic
1586C22C2×#1058769611yescharacteristic
1587C22#1176364511yescharacteristic
1588C22#1176364511yescharacteristic
1589C4—22no—
1590C4—22no—
1591C4—22no—
1592C4—22no—
1593C4—22no—
1594C4—22no—
1595C4—22no—
1596C4—41no—
1597C4—41no—
1598C4—41no—
1599C4—41no—
1600C4—41no—
1601C4—41no—
1602C4—342no—
1603C4—342no—
1604C4—342no—
1605C4—342no—
1606C4—342no—
1607C4—681no—
1608C4—681no—
1609C4—681no—
1610C4—681no—
1611C4—681no—
1612C4—681no—
1613C4—681no—
1614C4—681no—
1615C2—24no—
1616C2—42no—
1617C2—344no—
1618C2—344no—
1619C2—682no—
1620C2C2×#117×D1711yescharacteristic
1621C2C4×#1058769111yescharacteristic
1622C2C4×#1058769611yescharacteristic
1623C2#1454246711yescharacteristic
1624C2#1454247611yescharacteristic
1625C2#1454261211yescharacteristic
1626C2#1454261911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2290C2
socle, cosocleC23×C17C25
prime radicalC22×D4×D17C22
hypercenter#2290D17
hypocenterC17#34251
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2290

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14531727C2semidirect
3. #14531725C2semidirect
4. #14531723C2semidirect
5. #14531719C2semidirect
6. #14531716C2semidirect
7. #14531714C2semidirect
8. #14531712C2semidirect
9. #14531708C2semidirect
10. #14531647C2semidirect
11. #14531645C2semidirect
12. #14531643C2semidirect
13. #14531639C2semidirect
14. #14531636C2semidirect
15. #14531634C2semidirect
16. #14531632C2semidirect
17. #14531628C2semidirect
18. #14531417C2semidirect
19. #14531412C2semidirect
20. #14531411C2semidirect
21. #14531410C2semidirect
22. #14531395C2semidirect
24. #14531227C2semidirect
25. #14531224C2semidirect
26. #14531220C2semidirect
28. D17×#385C2semidirect
29. #14531136C2semidirect
30. C2×C4×#63227C2semidirect
31. C17×#2290C2semidirect
34. #11763281C4semidirect
43. C2×#10587578C22semidirect
45. C2×#10587558C22semidirect
46. C2×#10587563C22semidirect
47. C2×C4⋊C4×D17C22semidirect
48. C2×C4⋊C4×D17C22semidirect
58. C22×C4×Dic17C22semidirect
59. #11762703C22semidirect
60. #11762703C22semidirect
61. #11762702C22semidirect
62. #11762702C22semidirect
63. #11762701C22semidirect
64. #11762701C22semidirect
65. #11762700C22semidirect
66. #11762700C22semidirect
67. #11762700C22semidirect
68. #11762700C22semidirect
69. #11762699C22semidirect
70. #11762699C22semidirect
71. #11762697C22semidirect
72. #11762697C22semidirect
73. #11762696C22semidirect
74. #11762696C22semidirect
75. #11762695C22semidirect
76. #11762695C22semidirect
77. #11762694C22semidirect
78. #11762694C22semidirect
79. #11762693C22semidirect
80. #11762693C22semidirect
81. #11762693C22semidirect
82. #11762693C22semidirect
83. #11762692C22semidirect
84. #11762692C22semidirect
85. #11762690C22semidirect
86. #11762690C22semidirect
101. #11762684C22semidirect
102. #11762684C22semidirect
107. #11762682C22semidirect
108. #11762682C22semidirect
109. #11762681C22semidirect
110. #11762681C22semidirect
115. #11762677C22semidirect
116. #11762676C22semidirect
117. #11762676C22semidirect
118. #11762676C22semidirect
119. #11762675C22semidirect
120. #11762674C22semidirect
121. #11762673C22semidirect
122. #11762673C22semidirect
123. #11762672C22semidirect
126. #11762671C22semidirect
127. #11762671C22semidirect
128. #11762670C22semidirect
129. #11762669C22semidirect
130. #11762668C22semidirect
131. #11762668C22semidirect
132. #11762668C22semidirect
133. #11762667C22semidirect
134. #11762666C22semidirect
135. #11762666C22semidirect
136. #11762666C22semidirect
139. C4⋊C4×Dic17C22semidirect
140. C4×#63225C22semidirect
141. #11762660C22semidirect
142. C22⋊C4×Dic17C22semidirect
143. C22⋊C4×Dic17C22semidirect
144. C22⋊C4×Dic17C22semidirect
151. C4×#63227C22semidirect
152. C4×#63227C22semidirect
153. C4×#63227C22semidirect
154. C4×#63227C22semidirect
155. C4×#63227C22semidirect
156. C4×#63227C22semidirect
157. C4×#63227C22semidirect
158. C4×C22⋊Dic17C22semidirect
161. #11762656C22semidirect
162. #11762656C22semidirect
163. #11762656C22semidirect
164. #11762655C22semidirect
165. #11762654C22semidirect
166. #11762654C22semidirect
167. C2×#10587502C22semidirect
168. C2×#10587502C22semidirect
171. #95×D17C22semidirect
172. #95×D17C22semidirect
174. C2×C17×#117C22semidirect
175. C22×C42×C17C22semidirect
176. C17×#388C22semidirect
177. C17×#388C22semidirect
178. C17×#387C22semidirect
179. C17×#387C22semidirect
182. C17×#385C22semidirect
183. C17×#385C22semidirect
184. C4×C4⋊C4×C17C22semidirect
185. C4×C22⋊C4×C17C22semidirect
186. C4×C22⋊C4×C17C22semidirect
187. C17×#376C22semidirect
221. C4×D4×C17C2×C4semidirect
252. D4×Dic17C2×C4semidirect
253. C4×C22⋊D17C2×C4semidirect
254. C4×C22⋊D17C2×C4semidirect
257. C2×#63227C2×C4semidirect
311. #10587579C2×C4semidirect
313. #10587578C2×C4semidirect
316. #10587567C2×C4semidirect
317. #10587567C2×C4semidirect
323. C22⋊C4×D17C2×C4semidirect
325. C4×D68C2×C4semidirect
327. #10587558C2×C4semidirect
409. C22×C4×C17C22×C4semidirect
440. C22×Dic17C22×C4semidirect
496. C2×C4×D17C22×C4semidirect
497. C2×C4×D17C22×C4semidirect
502. C4⋊C4×C17C22×C4semidirect
510. C22⋊C4×C17C22×C4semidirect
517. C42×C17C22×C4semidirect
525. C22⋊Dic17C22×C4semidirect
548. #63227C22×C4semidirect
549. #63227C22×C4semidirect
554. C4⋊Dic17C22×C4semidirect
563. #63225C22×C4semidirect
564. #63225C22×C4semidirect
575. C4×Dic17C22×C4semidirect
576. C4×Dic17C22×C4semidirect
577. C4×Dic17C22×C4semidirect
621. C22×D17#117semidirect
758. #2290D17semidirect
849. C2×#117C2×D17semidirect
862. C22×C42C2×D17semidirect
877. #388C2×D17semidirect
878. #388C2×D17semidirect
893. #387C2×D17semidirect
894. #387C2×D17semidirect
925. #385C2×D17semidirect
926. #385C2×D17semidirect
954. C4×C4⋊C4C2×D17semidirect
977. C4×C22⋊C4C2×D17semidirect
978. C4×C22⋊C4C2×D17semidirect
982. #376C2×D17semidirect
1041. C4×D4C4×D17semidirect
1189. C17#34251semidirect
1298. C22×C4C2×C4×D17semidirect
1331. C4⋊C4C2×C4×D17semidirect
1371. C22⋊C4C2×C4×D17semidirect
1391. C42C2×C4×D17semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117632812
#145317272
#145317252
#145317232
#145317192
#145317162
#145317142
#145317122
#145317082
#145316472
#145316452
#145316432
#145316392
#145316362
#145316342
#145316322
#145316282
#145314172
#145314122
#145314112
#145314102
#145313952
#145313582
#145312272
#145312242
#145312202
D17×#3862
D17×#3852
#145311362
C2×C4×#632272
C17×#22902
#3425117