Finite Group Databasebeta

← #17198700

Subgroups — #17198700

Order 4352.

2314 conjugacy classes of subgroups.

The subgroup lattice has 1570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763394C211yesmaximal, characteristic
2#14531971C211yesmaximal, characteristic, complemented
3#14531944C211yesmaximal, characteristic, complemented
4#14531934C211yesmaximal, characteristic, complemented
5#14531911C211yesmaximal, characteristic, complemented
6#14531902C211yesmaximal, characteristic, complemented
7#14531902C211yesmaximal, characteristic, complemented
8#14531893C211yesmaximal, characteristic, complemented
9#14531854C211yesmaximal, characteristic, complemented
10#14531814C211yesmaximal, characteristic, complemented
11#14531782C211yesmaximal, characteristic, complemented
12#14531768C211yesmaximal, characteristic, complemented
13#14531732C211yesmaximal, characteristic, complemented
14#14531722C211yesmaximal, characteristic, complemented
15#14531635C211yesmaximal, characteristic, complemented
16#14531635C211yesmaximal, characteristic, complemented
17#14531595C211yesmaximal, characteristic, complemented
18#14531581C211yesmaximal, characteristic, complemented
19#14531550C211yesmaximal, characteristic, complemented
20#14531545C211yesmaximal, characteristic, complemented
21#14531493C211yesmaximal, characteristic, complemented
22#14531485C211yesmaximal, characteristic, complemented
23#14531470C211yesmaximal, characteristic, complemented
24#14531470C211yesmaximal, characteristic, complemented
25#14531439C211yesmaximal, characteristic, complemented
26#14531439C211yesmaximal, characteristic, complemented
27#14531425C211yesmaximal, characteristic, complemented
28#14531311C211yesmaximal, characteristic, complemented
29#14531300C211yesmaximal, characteristic, complemented
30#14531226C211yesmaximal, characteristic, complemented
31C17×#2375C211yesmaximal, characteristic, complemented
32#11763394C4116yescomplemented
33C2×#10587565C2211yescharacteristic
34C2×#10587565C2211yescharacteristic
35C2×#10587622C2211yescharacteristic
36C2×#10587571C2211yescharacteristic
37C2×#10587569C2211yescharacteristic
38C2×#10587621C2211yescharacteristic
39C2×#10587564C2211yescharacteristic
40C2×#10587625C2211yescharacteristic
41C2×#10587625C2211yescharacteristic
42C2×#10587624C2211yescharacteristic
43C2×#10587639C2211yescharacteristic
44C2×C4×Dic34C2211yescharacteristic, complemented
45C2×D4×Dic17C2211yescharacteristic
46C2×D4×Dic17C2211yescharacteristic
47C2×D4×Dic17C2211yescharacteristic
48C2×#10587567C2211yescharacteristic
49C2×#10587567C2211yescharacteristic
50C2×#10587567C2211yescharacteristic
51C2×#10587567C2211yescharacteristic, complemented
52C2×#10587563C2211yescharacteristic
53C2×#10587563C2211yescharacteristic
54C2×#10587563C2211yescharacteristic, complemented
55C22×C22⋊Dic17C2211yescharacteristic
56C22×C22⋊Dic17C2211yescharacteristic
57C22×C22⋊Dic17C2211yescharacteristic
58C2×C42×D17C2211yescharacteristic, complemented
59#11762714C2211yescharacteristic, complemented
60#11762713C2211yescharacteristic, complemented
61#11762713C2211yescharacteristic, complemented
62#11762712C2211yescharacteristic
63#11762709C2211yescharacteristic
64#11762709C2211yescharacteristic
65#11762709C2211yescharacteristic
66#11762709C2211yescharacteristic
67#11762709C2211yescharacteristic, complemented
68#11762707C2211yescharacteristic, complemented
69#11762706C2211yescharacteristic, complemented
70#11762704C2211yescharacteristic, complemented
71#11762704C2211yescharacteristic, complemented
72#11762704C2211yescharacteristic, complemented
73#11762704C2211yescharacteristic, complemented
74#11762703C2211yescharacteristic
75#11762703C2211yescharacteristic
76#11762703C2211yescharacteristic
77#11762703C2211yescharacteristic
78#11762703C2211yescharacteristic
79#11762703C2211yescharacteristic
80#11762703C2211yescharacteristic
81#11762703C2211yescharacteristic
82#11762703C2211yescharacteristic, complemented
83#11762703C2211yescharacteristic, complemented
84#11762703C2211yescharacteristic, complemented
85#11762702C2211yescharacteristic
86#11762702C2211yescharacteristic
87#11762701C2211yescharacteristic, complemented
88#11762700C2211yescharacteristic, complemented
89#11762700C2211yescharacteristic, complemented
90#11762698C2211yescharacteristic, complemented
91#11762697C2211yescharacteristic
92#11762697C2211yescharacteristic
93#11762697C2211yescharacteristic
94#11762697C2211yescharacteristic
95#11762697C2211yescharacteristic
96#11762697C2211yescharacteristic
97#11762697C2211yescharacteristic
98#11762697C2211yescharacteristic
99#11762697C2211yescharacteristic, complemented
100#11762696C2211yescharacteristic, complemented
101#11762696C2211yescharacteristic, complemented
102#11762696C2211yescharacteristic, complemented
103#11762694C2211yescharacteristic, complemented
104#11762694C2211yescharacteristic, complemented
105#11762693C2211yescharacteristic, complemented
106#11762693C2211yescharacteristic, complemented
107#11762692C2211yescharacteristic, complemented
108#11762692C2211yescharacteristic, complemented
109#11762691C2211yescharacteristic, complemented
110#11762691C2211yescharacteristic, complemented
111#11762691C2211yescharacteristic, complemented
112#11762689C2211yescharacteristic
113#11762689C2211yescharacteristic
114#11762689C2211yescharacteristic
115#11762688C2211yescharacteristic, complemented
116#11762686C2211yescharacteristic
117#11762686C2211yescharacteristic
118#11762685C2211yescharacteristic
119#11762685C2211yescharacteristic
120#11762685C2211yescharacteristic
121#11762685C2211yescharacteristic
122#11762685C2211yescharacteristic, complemented
123#11762684C2211yescharacteristic
124#11762684C2211yescharacteristic
125#11762683C2211yescharacteristic, complemented
126#11762681C2211yescharacteristic
127#11762681C2211yescharacteristic
128#11762681C2211yescharacteristic
129#11762681C2211yescharacteristic
130#11762681C2211yescharacteristic
131#11762681C2211yescharacteristic
132#11762681C2211yescharacteristic, complemented
133#11762680C2211yescharacteristic, complemented
134#11762680C2211yescharacteristic, complemented
135#11762678C2211yescharacteristic, complemented
136#11762676C2211yescharacteristic, complemented
137#11762671C2211yescharacteristic, complemented
138#11762670C2211yescharacteristic
139#11762670C2211yescharacteristic
140#11762667C2211yescharacteristic
141#11762667C2211yescharacteristic
142#11762667C2211yescharacteristic, complemented
143#11762667C2211yescharacteristic, complemented
144#11762666C2211yescharacteristic, complemented
145C4⋊C4×Dic17C2211yescharacteristic, complemented
146C4⋊C4×Dic17C2211yescharacteristic, complemented
147C4⋊C4×Dic17C2211yescharacteristic, complemented
148C4×#63225C2211yescharacteristic, complemented
149C4×#63225C2211yescharacteristic, complemented
150C4×#63225C2211yescharacteristic, complemented
151C4×#63225C2211yescharacteristic, complemented
152C4×C4⋊Dic17C2211yescharacteristic, complemented
153#11762660C2211yescharacteristic, complemented
154C22⋊C4×Dic17C2211yescharacteristic
155C22⋊C4×Dic17C2211yescharacteristic
156C22⋊C4×Dic17C2211yescharacteristic
157C22⋊C4×Dic17C2211yescharacteristic
158C22⋊C4×Dic17C2211yescharacteristic
159C22⋊C4×Dic17C2211yescharacteristic
160C22⋊C4×Dic17C2211yescharacteristic
161C22⋊C4×Dic17C2211yescharacteristic
162C22⋊C4×Dic17C2211yescharacteristic
163C22⋊C4×Dic17C2211yescharacteristic
164C22⋊C4×Dic17C2211yescharacteristic, complemented
165C4×C22⋊Dic17C2211yescharacteristic, complemented
166C4×C22⋊Dic17C2211yescharacteristic, complemented
167#11762656C2211yescharacteristic, complemented
168#11762656C2211yescharacteristic, complemented
169#11762654C2211yescharacteristic, complemented
170#11762654C2211yescharacteristic, complemented
171#11762654C2211yescharacteristic, complemented
172C2×#10587502C2211yescharacteristic, complemented
173C2×C17×#120C2211yescharacteristic
174C17×#390C2211yescharacteristic
175C17×#390C2211yescharacteristic
176C17×#390C2211yescharacteristic
177C17×#388C2211yescharacteristic
178C17×#388C2211yescharacteristic
179C17×#388C2211yescharacteristic
180C17×#388C2211yescharacteristic
181C17×#388C2211yescharacteristic
182C17×#388C2211yescharacteristic
183C17×#386C2211yescharacteristic
184C17×#386C2211yescharacteristic
185C17×#386C2211yescharacteristic
186C17×#379C2211yescharacteristic
187C17×#379C2211yescharacteristic
188C25×C17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C22×C22⋊D17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C23×Dic17C2311yescharacteristic
198C23×Dic17C2311yescharacteristic
199C23×Dic17C2311yescharacteristic
200C23×Dic17C2311yescharacteristic
201C23×Dic17C2311yescharacteristic
202C23×Dic17C2311yescharacteristic
203C23×Dic17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C22×C4×D17C2311yescharacteristic
206C22×C4×D17C2311yescharacteristic
207C22×C4×D17C2311yescharacteristic
208C22×Dic34C2311yescharacteristic
209C17×#120C2×C418yescomplemented
210C2×C4⋊C4×C17C2311yescharacteristic
211C2×C4⋊C4×C17C2311yescharacteristic
212C2×C4⋊C4×C17C2311yescharacteristic
213C2×C22⋊C4×C17C2311yescharacteristic
214C2×C22⋊C4×C17C2311yescharacteristic
215C2×C22⋊C4×C17C2311yescharacteristic
216C2×C22⋊C4×C17C2311yescharacteristic
217C2×C22⋊C4×C17C2311yescharacteristic
218C2×C22⋊C4×C17C2311yescharacteristic
219C2×C22⋊C4×C17C2311yescharacteristic
220C2×C22⋊C4×C17C2311yescharacteristic
221C2×C22⋊C4×C17C2311yescharacteristic
222C2×C22⋊C4×C17C2311yescharacteristic
223C2×C22⋊C4×C17C2311yescharacteristic
224C2×C22⋊C4×C17C2311yescharacteristic
225C2×C22⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17C2311yescharacteristic
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C42×C17C2311yescharacteristic
232C2×C42×C17C2311yescharacteristic
233C2×C42×C17C2311yescharacteristic
234#10587639C2×C418yescomplemented
235C2×C22⋊Dic17—42no—
236C2×C22⋊Dic17—42no—
237C2×C22⋊Dic17C2×C418yescomplemented
238C2×C22⋊Dic17C2311yescharacteristic
239C2×C22⋊Dic17C2311yescharacteristic
240C2×C22⋊Dic17C2311yescharacteristic
241C2×C22⋊Dic17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258#10587625C2×C418yescomplemented
259#10587625C2×C418yescomplemented
260#10587624C2×C418yescomplemented
261#10587622C2×C418yescomplemented
262#10587621C2×C418yescomplemented
263D4×Dic17—42no—
264D4×Dic17—42no—
265D4×Dic17C2×C418yescomplemented
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×C4⋊Dic17C2311yescharacteristic
275C2×C4⋊Dic17C2311yescharacteristic
276C2×C4⋊Dic17C2311yescharacteristic
277C2×C4⋊Dic17C2311yescharacteristic
278C2×C4⋊Dic17C2311yescharacteristic
279C2×#63225C2311yescharacteristic
280C2×#63225C2311yescharacteristic
281C2×#63225C2311yescharacteristic
282C2×#63225C2311yescharacteristic
283C2×#63225C2311yescharacteristic
284C2×#63225C2311yescharacteristic
285C2×#63225C2311yescharacteristic
286C2×#63225C2311yescharacteristic
287C2×#63225C2311yescharacteristic
288C2×#63225C2311yescharacteristic
289C2×#63225C2311yescharacteristic
290C2×#63225C2311yescharacteristic
291C2×#63225C2311yescharacteristic
292C2×#63225C2311yescharacteristic
293C2×#63225C2311yescharacteristic
294C2×#63225C2311yescharacteristic
295C2×#63225C2311yescharacteristic
296C2×#63225C2311yescharacteristic
297C2×C4×Dic17C2311yescharacteristic
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
311C2×C4×Dic17C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314C2×C4×Dic17C2311yescharacteristic
315C2×C4×Dic17C2311yescharacteristic
316#10587571C2×C418yescomplemented
317#10587569C2×C418yescomplemented
318#10587567—42no—
319#10587567—42no—
320#10587567—42no—
321#10587567C2×C418yescomplemented
322#10587565C2×C418yescomplemented
323#10587565C2×C418yescomplemented
324#10587564C2×C418yescomplemented
325#10587563—42no—
326#10587563—42no—
327#10587563—42no—
328C42×D17—42no—
329C4×Dic34—42no—
330C17×#95C2311yescharacteristic
331C17×#95C2311yescharacteristic
332C17×#95C2311yescharacteristic
333C17×#95C2311yescharacteristic
334C17×#95C2311yescharacteristic
335C17×#95C2311yescharacteristic
336#10587502C2311yescharacteristic
337#10587502C2311yescharacteristic
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
370C24×C17—41no—
371C24×C17—41no—
372C24×C17—41no—
373C24×C17—41no—
374C24×C17—41no—
375C24×C17—41no—
376C24×C17C22×C414yes—
377C24×C17C2411yescharacteristic
378C24×C17C2411yescharacteristic
379C24×C17C2411yescharacteristic
380C24×C17C2411yescharacteristic
381C23×D17C2411yescharacteristic
382C2×D4×C17—41no—
383C2×D4×C17—41no—
384C2×D4×C17—41no—
385C2×D4×C17—41no—
386C2×D4×C17—41no—
387C2×D4×C17—41no—
388C2×D4×C17C22×C414yes—
389C2×D4×C17C22×C414yes—
390C2×D4×C17C22×C414yes—
391C22×C4×C17—41no—
392C22×C4×C17—41no—
393C22×C4×C17—41no—
394C22×C4×C17C2411yescharacteristic
395C22×C4×C17C2411yescharacteristic
396C22×C4×C17C2411yescharacteristic
397C22×C4×C17C2411yescharacteristic
398C22×C4×C17C2411yescharacteristic
399C22×C4×C17C2411yescharacteristic
400C22×C4×C17C2411yescharacteristic
401C22×C4×C17C2411yescharacteristic
402C22×C4×C17C2411yescharacteristic
403C22×C4×C17C2411yescharacteristic
404C22×C4×C17C2411yescharacteristic
405C2×C22⋊D17—41no—
406C2×C22⋊D17—41no—
407C2×C22⋊D17—41no—
408C2×C22⋊D17—41no—
409C2×C22⋊D17—41no—
410C2×C22⋊D17—41no—
411C2×C22⋊D17—41no—
412C2×C22⋊D17—41no—
413C2×C22⋊D17C22×C414yes—
414C2×C22⋊D17C22×C414yes—
415C2×C22⋊D17C22×C414yes—
416C2×C22⋊D17C22×C414yes—
417C22×Dic17—22no—
418C22×Dic17—22no—
419C22×Dic17—22no—
420C22×Dic17—41no—
421C22×Dic17—41no—
422C22×Dic17—41no—
423C22×Dic17—41no—
424C22×Dic17—41no—
425C22×Dic17—41no—
426C22×Dic17—41no—
427C22×Dic17—41no—
428C22×Dic17—41no—
429C22×Dic17—41no—
430C22×Dic17—41no—
431C22×Dic17—41no—
432C22×Dic17—41no—
433C22×Dic17—41no—
434C22×Dic17—41no—
435C22×Dic17—41no—
436C22×Dic17—41no—
437C22×Dic17—41no—
438C22×Dic17C22×C414yes—
439C22×Dic17C22×C414yes—
440C22×Dic17C22×C414yes—
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
454C22×Dic17C2411yescharacteristic
455C22×Dic17C2411yescharacteristic
456C2×C4×D17—22no—
457C2×C4×D17—22no—
458C2×C4×D17—41no—
459C2×C4×D17—41no—
460C2×C4×D17—41no—
461C2×C4×D17—41no—
462C2×C4×D17—41no—
463C2×C4×D17—41no—
464C2×C4×D17C22×C414yes—
465C2×Dic34—41no—
466C2×Dic34—41no—
467C2×Dic34C22×C414yes—
468C4⋊C4×C17—41no—
469C4⋊C4×C17—41no—
470C4⋊C4×C17—41no—
471C22⋊C4×C17—41no—
472C22⋊C4×C17—41no—
473C22⋊C4×C17—41no—
474C22⋊C4×C17—41no—
475C22⋊C4×C17—41no—
476C22⋊C4×C17—41no—
477C22⋊C4×C17—41no—
478C22⋊C4×C17—41no—
479C22⋊C4×C17—41no—
480C22⋊C4×C17—41no—
481C22⋊C4×C17—41no—
482C22⋊C4×C17—41no—
483C22⋊C4×C17—41no—
484C22⋊C4×C17—41no—
485C22⋊C4×C17—41no—
486C22⋊C4×C17C22×C414yes—
487C22⋊C4×C17C22×C414yes—
488C22⋊C4×C17C22×C414yes—
489C42×C17—41no—
490C42×C17—41no—
491C42×C17—41no—
492C22⋊Dic17—22no—
493C22⋊Dic17—22no—
494C22⋊Dic17—22no—
495C22⋊Dic17—22no—
496C22⋊Dic17—22no—
497C22⋊Dic17—41no—
498C22⋊Dic17—41no—
499C22⋊Dic17—41no—
500C22⋊Dic17—41no—
501C22⋊Dic17—41no—
502C22⋊Dic17—41no—
503C22⋊Dic17C22×C414yes—
504C22⋊Dic17C22×C414yes—
505C22⋊Dic17C22×C414yes—
506C22⋊Dic17C22×C414yes—
507C22⋊Dic17C22×C414yes—
508C22⋊Dic17C22×C414yes—
509C22⋊Dic17C22×C414yes—
510C22⋊Dic17C22×C414yes—
511C22⋊Dic17C22×C414yes—
512#63227—41no—
513#63227—41no—
514#63227—41no—
515#63227—41no—
516#63227—41no—
517#63227—41no—
518#63227C22×C414yes—
519#63227C22×C414yes—
520C4⋊Dic17—22no—
521C4⋊Dic17—41no—
522C4⋊Dic17—41no—
523C4⋊Dic17C22×C414yes—
524C4⋊Dic17C22×C414yes—
525#63225—22no—
526#63225—22no—
527#63225—41no—
528#63225—41no—
529#63225—41no—
530#63225—41no—
531#63225—41no—
532#63225—41no—
533#63225—41no—
534#63225—41no—
535#63225—41no—
536#63225—41no—
537#63225—41no—
538#63225—41no—
539#63225C22×C414yes—
540#63225C22×C414yes—
541#63225C22×C414yes—
542#63225C22×C414yes—
543C4×Dic17—22no—
544C4×Dic17—22no—
545C4×Dic17—22no—
546C4×Dic17—22no—
547C4×Dic17—22no—
548C4×Dic17—41no—
549C4×Dic17—41no—
550C4×Dic17—41no—
551C4×Dic17—41no—
552C4×Dic17—41no—
553C4×Dic17—41no—
554C4×Dic17—41no—
555C4×Dic17—41no—
556C4×Dic17—41no—
557C4×Dic17—41no—
558C4×Dic17—41no—
559C4×Dic17—41no—
560C4×Dic17C22×C414yes—
561C4×Dic17C22×C414yes—
562#34451—171nomaximal, Sylow
563C23×C17—21no—
564C23×C17—21no—
565C23×C17—21no—
566C23×C17—21no—
567C23×C17—21no—
568C23×C17—21no—
569C23×C17—21no—
570C23×C17—21no—
571C23×C17—21no—
572C23×C17—21no—
573C23×C17—21no—
574C23×C17—21no—
575C23×C17—21no—
576C23×C17—21no—
577C23×C17—21no—
578C23×C17—21no—
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—44no—
588C23×C17—44no—
589C23×C17—44no—
590C23×C17—82no—
591C23×C17—82no—
592C23×C17—82no—
593C23×C17—82no—
594C23×C17C23×C412yes—
595C23×C17C23×C412yes—
596C23×C17C23×C412yes—
597C23×C17C23×C412yes—
598C23×C17C2511yescharacteristic
599C22×D17—21no—
600C22×D17—21no—
601C22×D17—21no—
602C22×D17—21no—
603C22×D17—21no—
604C22×D17—21no—
605C22×D17C23×C412yes—
606D4×C17—44no—
607D4×C17—44no—
608D4×C17—44no—
609C2×C4×C17—21no—
610C2×C4×C17—21no—
611C2×C4×C17—21no—
612C2×C4×C17—21no—
613C2×C4×C17—21no—
614C2×C4×C17—21no—
615C2×C4×C17—21no—
616C2×C4×C17—21no—
617C2×C4×C17—21no—
618C2×C4×C17—21no—
619C2×C4×C17—21no—
620C2×C4×C17—21no—
621C2×C4×C17—21no—
622C2×C4×C17—21no—
623C2×C4×C17—21no—
624C2×C4×C17—21no—
625C2×C4×C17—21no—
626C2×C4×C17—21no—
627C2×C4×C17—21no—
628C2×C4×C17—21no—
629C2×C4×C17—21no—
630C2×C4×C17—21no—
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—82no—
640C2×C4×C17C23×C412yes—
641C2×C4×C17C23×C412yes—
642C2×C4×C17C23×C412yes—
643C22⋊D17—44no—
644C22⋊D17—44no—
645C22⋊D17—44no—
646C22⋊D17—44no—
647C2×Dic17—21no—
648C2×Dic17—21no—
649C2×Dic17—21no—
650C2×Dic17—21no—
651C2×Dic17—21no—
652C2×Dic17—21no—
653C2×Dic17—21no—
654C2×Dic17—21no—
655C2×Dic17—21no—
656C2×Dic17—21no—
657C2×Dic17—21no—
658C2×Dic17—21no—
659C2×Dic17—21no—
660C2×Dic17—21no—
661C2×Dic17—21no—
662C2×Dic17—21no—
663C2×Dic17—21no—
664C2×Dic17—21no—
665C2×Dic17—21no—
666C2×Dic17—21no—
667C2×Dic17—21no—
668C2×Dic17—21no—
669C2×Dic17—21no—
670C2×Dic17—21no—
671C2×Dic17—21no—
672C2×Dic17—21no—
673C2×Dic17—21no—
674C2×Dic17—21no—
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—44no—
684C2×Dic17—44no—
685C2×Dic17—44no—
686C2×Dic17—82no—
687C2×Dic17—82no—
688C2×Dic17—82no—
689C2×Dic17—82no—
690C2×Dic17—82no—
691C2×Dic17C23×C412yes—
692C2×Dic17C23×C412yes—
693C2×Dic17C23×C412yes—
694C2×Dic17C23×C412yes—
695C2×Dic17C23×C412yes—
696C2×Dic17C23×C412yes—
697C2×Dic17C23×C412yes—
698C2×Dic17H(5,𝔽2)12yes—
699C2×Dic17H(5,𝔽2)12yes—
700C4×D17—44no—
701C4×D17—44no—
702C4×D17—44no—
703Dic34—44no—
704C2×#538—171no—
705#2383—171no—
706#2378—171no—
707#2376—171no—
708#2375D1711yescharacteristic, complemented
709#2373—171no—
710#2373—171no—
711#2373—171no—
712#2372—171no—
713#2367—171no—
714#2362—171no—
715#2359—171no—
716#2358—171no—
717#2354—171no—
718#2353—171no—
719#2342—171no—
720#2342—171no—
721#2337—171no—
722#2335—171no—
723#2333—171no—
724#2333—171no—
725#2326—171no—
726#2325—171no—
727#2324—171no—
728#2324—171no—
729#2321—171no—
730#2321—171no—
731#2319—171no—
732C4×#123—171no—
733C4×#121—171no—
734#2290—171no—
735C22×C17—22no—
736C22×C17—22no—
737C22×C17—22no—
738C22×C17—22no—
739C22×C17—22no—
740C22×C17—22no—
741C22×C17—22no—
742C22×C17—22no—
743C22×C17—22no—
744C22×C17—22no—
745C22×C17—22no—
746C22×C17—22no—
747C22×C17—41no—
748C22×C17—41no—
749C22×C17—41no—
750C22×C17—41no—
751C22×C17—41no—
752C22×C17—41no—
753C22×C17—41no—
754C22×C17—41no—
755C22×C17—41no—
756C22×C17—41no—
757C22×C17—41no—
758C22×C17—41no—
759C22×C17—41no—
760C22×C17—41no—
761C22×C17—41no—
762C22×C17—41no—
763C22×C17—88no—
764C22×C17C24×C411yescharacteristic
765C22×C17C2×H(5,𝔽2)11yescharacteristic
766C22×C17C2×H(5,𝔽2)11yescharacteristic
767C22×C17#58511yescharacteristic
768C22×C17#58511yescharacteristic
769C22×C17#58511yescharacteristic
770C22×C17#58511yescharacteristic
771C2×D17—22no—
772C2×D17—22no—
773C2×D17—22no—
774C2×D17—41no—
775C2×D17—41no—
776C2×D17—41no—
777C2×D17—41no—
778C4×C17—22no—
779C4×C17—22no—
780C4×C17—22no—
781C4×C17—41no—
782C4×C17—41no—
783C4×C17—41no—
784C4×C17—41no—
785C4×C17—41no—
786C4×C17—41no—
787C4×C17—41no—
788C4×C17—41no—
789Dic17—22no—
790Dic17—22no—
791Dic17—22no—
792Dic17—22no—
793Dic17—22no—
794Dic17—22no—
795Dic17—22no—
796Dic17—22no—
797Dic17—22no—
798Dic17—41no—
799Dic17—41no—
800Dic17—41no—
801Dic17—41no—
802Dic17—41no—
803Dic17—41no—
804#538—1716no—
805C2×#126—171no—
806C2×#126—171no—
807C2×#124—171no—
808C2×#124—171no—
809C2×#123—171no—
810C2×#123—171no—
811C2×C22⋊Q8—171no—
812C2×#121—171no—
813C2×#121—171no—
814C2×#121—171no—
815C2×#120—171no—
816C2×#120C2×D1711yescharacteristic
817C2×C4×Q8—171no—
818C2×C4×D4—171no—
819C2×C4×D4—171no—
820C2×C4×D4—171no—
821C2×C4×D4—171no—
822C2×C4×D4—171no—
823C2×C4×D4—171no—
824C2×C4×D4—171no—
825C2×#117—171no—
826C2×#117—171no—
827C2×#117—171no—
828C22×C22⋊C4—171no—
829C22×C22⋊C4—171no—
830C22×C22⋊C4—171no—
831C22×C42—171no—
832#391—171no—
833#391—171no—
834#391—171no—
835#390—171no—
836#390—171no—
837#390—171no—
838#390—171no—
839#390—171no—
840#390—171no—
841#390C2×D1711yescharacteristic
842#390C2×D1711yescharacteristic
843#390C2×D1711yescharacteristic
844#389—171no—
845#389—171no—
846#389—171no—
847#389—171no—
848#389—171no—
849#389—171no—
850#388—171no—
851#388—171no—
852#388—171no—
853#388—171no—
854#388—171no—
855#388—171no—
856#388—171no—
857#388—171no—
858#388—171no—
859#388—171no—
860#388—171no—
861#388—171no—
862#388—171no—
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#388C2×D1711yescharacteristic
877#388C2×D1711yescharacteristic
878#388C2×D1711yescharacteristic
879#388C2×D1711yescharacteristic
880#388C2×D1711yescharacteristic
881#388C2×D1711yescharacteristic
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#387—171no—
894#386—171no—
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#386C2×D1711yescharacteristic
906#386C2×D1711yescharacteristic
907#386C2×D1711yescharacteristic
908#385—171no—
909#385—171no—
910#385—171no—
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#384—171no—
921#383—171no—
922#381—171no—
923#381—171no—
924#381—171no—
925#380—171no—
926#380—171no—
927#380—171no—
928#380—171no—
929#380—171no—
930#379C2×D1711yescharacteristic
931#379C2×D1711yescharacteristic
932C4×C4⋊C4—171no—
933C4×C4⋊C4—171no—
934C4×C4⋊C4—171no—
935C4×C4⋊C4—171no—
936C4×C4⋊C4—171no—
937C4×C4⋊C4—171no—
938C4×C4⋊C4—171no—
939C4×C4⋊C4—171no—
940C4×C4⋊C4—171no—
941C4×C22⋊C4—171no—
942C4×C22⋊C4—171no—
943C4×C22⋊C4—171no—
944C4×C22⋊C4—171no—
945C4×C22⋊C4—171no—
946C4×C22⋊C4—171no—
947C4×C22⋊C4—171no—
948C4×C22⋊C4—171no—
949C4×C22⋊C4—171no—
950C4×C22⋊C4—171no—
951C4×C22⋊C4—171no—
952C4×C22⋊C4—171no—
953C4×C22⋊C4—171no—
954C4×C22⋊C4—171no—
955C4×C22⋊C4—171no—
956#376—171no—
957#376—171no—
958#376—171no—
959C2×#95—171no—
960C2×C17—42no—
961C2×C17—42no—
962C2×C17—42no—
963C2×C17—42no—
964C2×C17#342811yescharacteristic
965C2×C17C4×H(5,𝔽2)11yescharacteristic
966C2×C17C4×H(5,𝔽2)11yescharacteristic
967C2×C17#353311yescharacteristic
968C2×C17#354211yescharacteristic
969C2×C17#355111yescharacteristic
970C2×C17#356811yescharacteristic
971D17—42no—
972C25C22×D1711yescharacteristic
973C22×Q8—171no—
974C22×D4—171no—
975C22×D4—171no—
976C22×D4—171no—
977C22×D4—171no—
978C22×D4C22×D1711yescharacteristic
979C22×D4C22×D1711yescharacteristic
980C22×D4C22×D1711yescharacteristic
981C23×C4—171no—
982C23×C4—171no—
983C23×C4—171no—
984C23×C4—171no—
985C23×C4—171no—
986C23×C4—171no—
987C23×C4—171no—
988C23×C4—171no—
989C23×C4—171no—
990C23×C4—171no—
991C23×C4—171no—
992C23×C4C22×D1711yescharacteristic
993#126—178no—
994#126—178no—
995#124—178no—
996#124—178no—
997#123—178no—
998#123—178no—
999C22⋊Q8—178no—
1000#121—178no—
1001#121—178no—
1002#121—178no—
1003#120—178no—
1004#120C4×D1718yescomplemented
1005C4×Q8—682no—
1006C4×D4—178no—
1007C4×D4—178no—
1008C4×D4—682no—
1009C4×D4—682no—
1010C4×D4—682no—
1011C4×D4—682no—
1012C4×D4—682no—
1013#117—682no—
1014#117—682no—
1015#117—682no—
1016C2×C4⋊C4—171no—
1017C2×C4⋊C4—171no—
1018C2×C4⋊C4—171no—
1019C2×C4⋊C4—171no—
1020C2×C4⋊C4—171no—
1021C2×C4⋊C4—171no—
1022C2×C4⋊C4—171no—
1023C2×C4⋊C4—171no—
1024C2×C4⋊C4—171no—
1025C2×C4⋊C4—171no—
1026C2×C4⋊C4—171no—
1027C2×C4⋊C4—171no—
1028C2×C4⋊C4—171no—
1029C2×C4⋊C4—171no—
1030C2×C4⋊C4—171no—
1031C2×C4⋊C4—171no—
1032C2×C4⋊C4—171no—
1033C2×C4⋊C4—171no—
1034C2×C4⋊C4—171no—
1035C2×C4⋊C4—171no—
1036C2×C4⋊C4—171no—
1037C2×C4⋊C4—171no—
1038C2×C4⋊C4—171no—
1039C2×C4⋊C4C22×D1711yescharacteristic
1040C2×C4⋊C4C22×D1711yescharacteristic
1041C2×C4⋊C4C22×D1711yescharacteristic
1042C2×C22⋊C4—178no—
1043C2×C22⋊C4—171no—
1044C2×C22⋊C4—171no—
1045C2×C22⋊C4—171no—
1046C2×C22⋊C4—171no—
1047C2×C22⋊C4—171no—
1048C2×C22⋊C4—171no—
1049C2×C22⋊C4—171no—
1050C2×C22⋊C4—171no—
1051C2×C22⋊C4—171no—
1052C2×C22⋊C4—171no—
1053C2×C22⋊C4—171no—
1054C2×C22⋊C4—171no—
1055C2×C22⋊C4—171no—
1056C2×C22⋊C4—171no—
1057C2×C22⋊C4—171no—
1058C2×C22⋊C4—171no—
1059C2×C22⋊C4—171no—
1060C2×C22⋊C4—171no—
1061C2×C22⋊C4—171no—
1062C2×C22⋊C4—171no—
1063C2×C22⋊C4—171no—
1064C2×C22⋊C4—171no—
1065C2×C22⋊C4—171no—
1066C2×C22⋊C4—171no—
1067C2×C22⋊C4—171no—
1068C2×C22⋊C4—171no—
1069C2×C22⋊C4—171no—
1070C2×C22⋊C4—171no—
1071C2×C22⋊C4—682no—
1072C2×C22⋊C4—682no—
1073C2×C22⋊C4C22×D1711yescharacteristic
1074C2×C22⋊C4C22×D1711yescharacteristic
1075C2×C22⋊C4C22×D1711yescharacteristic
1076C2×C22⋊C4C22×D1711yescharacteristic
1077C2×C22⋊C4C22×D1711yescharacteristic
1078C2×C22⋊C4C22×D1711yescharacteristic
1079C2×C22⋊C4C22×D1711yescharacteristic
1080C2×C22⋊C4C22×D1711yescharacteristic
1081C2×C22⋊C4C22×D1711yescharacteristic
1082C2×C22⋊C4C22×D1711yescharacteristic
1083C2×C22⋊C4C22×D1711yescharacteristic
1084C2×C22⋊C4C22×D1711yescharacteristic
1085C2×C22⋊C4C22×D1711yescharacteristic
1086C2×C22⋊C4C22×D1711yescharacteristic
1087C2×C22⋊C4C22×D1711yescharacteristic
1088C2×C22⋊C4C22×D1711yescharacteristic
1089C2×C22⋊C4C22×D1711yescharacteristic
1090C2×C22⋊C4C22×D1711yescharacteristic
1091C2×C42—171no—
1092C2×C42—171no—
1093C2×C42—171no—
1094C2×C42—171no—
1095C2×C42—171no—
1096C2×C42—171no—
1097C2×C42—171no—
1098C2×C42—171no—
1099C2×C42—171no—
1100C2×C42—171no—
1101C2×C42—171no—
1102C2×C42—171no—
1103C2×C42—171no—
1104C2×C42—171no—
1105C2×C42—171no—
1106C2×C42—171no—
1107C2×C42—171no—
1108C2×C42—171no—
1109C2×C42—171no—
1110C2×C42—682no—
1111C2×C42C22×D1711yescharacteristic
1112C2×C42C22×D1711yescharacteristic
1113C2×C42C22×D1711yescharacteristic
1114#95—171no—
1115#95—171no—
1116#95—171no—
1117#95—171no—
1118#95—171no—
1119#95—171no—
1120#95—171no—
1121#95—171no—
1122#95—171no—
1123#95—171no—
1124#95—171no—
1125#95—171no—
1126#95—171no—
1127#95—171no—
1128#95—171no—
1129#95—171no—
1130#95—171no—
1131#95—171no—
1132#95—171no—
1133#95—171no—
1134#95—171no—
1135#95—171no—
1136#95—171no—
1137#95—171no—
1138#95—171no—
1139#95—171no—
1140#95—171no—
1141#95—171no—
1142#95—171no—
1143#95—171no—
1144#95—171no—
1145#95—171no—
1146#95—171no—
1147#95—171no—
1148#95C22×D1711yescharacteristic
1149#95C22×D1711yescharacteristic
1150#95C22×D1711yescharacteristic
1151#95C22×D1711yescharacteristic
1152#95C22×D1711yescharacteristic
1153#95C22×D1711yescharacteristic
1154C17#3445111yescharacteristic, complemented, Sylow
1155C24—41no—
1156C24—41no—
1157C24—41no—
1158C24—41no—
1159C24—41no—
1160C24—41no—
1161C24—171no—
1162C24C2×C4×D1714yes—
1163C24C23×D1711yescharacteristic
1164C24C23×D1711yescharacteristic
1165C24C23×D1711yescharacteristic
1166C24C23×D1711yescharacteristic
1167C2×Q8—174no—
1168C2×Q8—681no—
1169C2×Q8—681no—
1170C2×D4—41no—
1171C2×D4—41no—
1172C2×D4—41no—
1173C2×D4—41no—
1174C2×D4—41no—
1175C2×D4—41no—
1176C2×D4—174no—
1177C2×D4—174no—
1178C2×D4—174no—
1179C2×D4—174no—
1180C2×D4—681no—
1181C2×D4—681no—
1182C2×D4—681no—
1183C2×D4—681no—
1184C2×D4—681no—
1185C2×D4—681no—
1186C2×D4—681no—
1187C2×D4—681no—
1188C2×D4C2×C4×D1714yes—
1189C2×D4C2×C4×D1714yes—
1190C2×D4C2×C4×D1714yes—
1191C22×C4—41no—
1192C22×C4—41no—
1193C22×C4—41no—
1194C22×C4—171no—
1195C22×C4—171no—
1196C22×C4—171no—
1197C22×C4—171no—
1198C22×C4—171no—
1199C22×C4—171no—
1200C22×C4—171no—
1201C22×C4—171no—
1202C22×C4—171no—
1203C22×C4—174no—
1204C22×C4—174no—
1205C22×C4—174no—
1206C22×C4—174no—
1207C22×C4—171no—
1208C22×C4—171no—
1209C22×C4—171no—
1210C22×C4—171no—
1211C22×C4—171no—
1212C22×C4—171no—
1213C22×C4—342no—
1214C22×C4—342no—
1215C22×C4—342no—
1216C22×C4—342no—
1217C22×C4—342no—
1218C22×C4—681no—
1219C22×C4—681no—
1220C22×C4—681no—
1221C22×C4—681no—
1222C22×C4—681no—
1223C22×C4—681no—
1224C22×C4—681no—
1225C22×C4—681no—
1226C22×C4—681no—
1227C22×C4—681no—
1228C22×C4—681no—
1229C22×C4—681no—
1230C22×C4—681no—
1231C22×C4—681no—
1232C22×C4—681no—
1233C22×C4—681no—
1234C22×C4—681no—
1235C22×C4—681no—
1236C22×C4—681no—
1237C22×C4—681no—
1238C22×C4—681no—
1239C22×C4—681no—
1240C22×C4—681no—
1241C22×C4—681no—
1242C22×C4C23×D1711yescharacteristic
1243C22×C4C23×D1711yescharacteristic
1244C22×C4C23×D1711yescharacteristic
1245C22×C4C23×D1711yescharacteristic
1246C22×C4C23×D1711yescharacteristic
1247C22×C4C23×D1711yescharacteristic
1248C22×C4C23×D1711yescharacteristic
1249C22×C4C23×D1711yescharacteristic
1250C22×C4C23×D1711yescharacteristic
1251C22×C4C23×D1711yescharacteristic
1252C22×C4C23×D1711yescharacteristic
1253C4⋊C4—41no—
1254C4⋊C4—41no—
1255C4⋊C4—41no—
1256C4⋊C4—174no—
1257C4⋊C4—174no—
1258C4⋊C4—174no—
1259C4⋊C4—174no—
1260C4⋊C4—174no—
1261C4⋊C4—174no—
1262C4⋊C4—342no—
1263C4⋊C4—342no—
1264C4⋊C4—342no—
1265C4⋊C4—681no—
1266C4⋊C4—681no—
1267C4⋊C4—681no—
1268C4⋊C4—681no—
1269C4⋊C4—681no—
1270C4⋊C4—681no—
1271C4⋊C4—681no—
1272C4⋊C4—681no—
1273C4⋊C4—681no—
1274C4⋊C4—681no—
1275C4⋊C4—681no—
1276C4⋊C4—681no—
1277C4⋊C4—681no—
1278C4⋊C4—681no—
1279C22⋊C4—41no—
1280C22⋊C4—41no—
1281C22⋊C4—41no—
1282C22⋊C4—41no—
1283C22⋊C4—41no—
1284C22⋊C4—41no—
1285C22⋊C4—41no—
1286C22⋊C4—41no—
1287C22⋊C4—41no—
1288C22⋊C4—41no—
1289C22⋊C4—41no—
1290C22⋊C4—41no—
1291C22⋊C4—41no—
1292C22⋊C4—41no—
1293C22⋊C4—41no—
1294C22⋊C4—174no—
1295C22⋊C4—174no—
1296C22⋊C4—174no—
1297C22⋊C4—174no—
1298C22⋊C4—174no—
1299C22⋊C4—174no—
1300C22⋊C4—174no—
1301C22⋊C4—174no—
1302C22⋊C4—174no—
1303C22⋊C4—174no—
1304C22⋊C4—174no—
1305C22⋊C4—342no—
1306C22⋊C4—342no—
1307C22⋊C4—342no—
1308C22⋊C4—342no—
1309C22⋊C4—342no—
1310C22⋊C4—681no—
1311C22⋊C4—681no—
1312C22⋊C4—681no—
1313C22⋊C4—681no—
1314C22⋊C4—681no—
1315C22⋊C4—681no—
1316C22⋊C4—681no—
1317C22⋊C4—681no—
1318C22⋊C4—681no—
1319C22⋊C4—681no—
1320C22⋊C4—681no—
1321C22⋊C4—681no—
1322C22⋊C4C2×C4×D1714yes—
1323C22⋊C4C2×C4×D1714yes—
1324C22⋊C4C2×C4×D1714yes—
1325C42—41no—
1326C42—41no—
1327C42—41no—
1328C42—174no—
1329C42—174no—
1330C42—342no—
1331C42—342no—
1332C42—342no—
1333C42—342no—
1334C42—342no—
1335C42—681no—
1336C42—681no—
1337C42—681no—
1338C42—681no—
1339C42—681no—
1340C42—681no—
1341C42—681no—
1342C42—681no—
1343C42—681no—
1344C42—681no—
1345C42—681no—
1346C42—681no—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23—21no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—21no—
1364C23—21no—
1365C23—21no—
1366C23—21no—
1367C23—21no—
1368C23—21no—
1369C23—21no—
1370C23—21no—
1371C23—44no—
1372C23—44no—
1373C23—44no—
1374C23—82no—
1375C23—82no—
1376C23—82no—
1377C23—82no—
1378C23—172no—
1379C23—341no—
1380C23—341no—
1381C23—341no—
1382C23—341no—
1383C23—341no—
1384C23—341no—
1385C23C22×C4×D1712yes—
1386C23C22×C4×D1712yes—
1387C23C22×C4×D1712yes—
1388C23C22×C4×D1712yes—
1389C23C24×D1711yescharacteristic
1390Q8—684no—
1391D4—44no—
1392D4—44no—
1393D4—44no—
1394D4—684no—
1395D4—684no—
1396D4—684no—
1397D4—684no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—82no—
1429C2×C4—172no—
1430C2×C4—172no—
1431C2×C4—172no—
1432C2×C4—172no—
1433C2×C4—172no—
1434C2×C4—172no—
1435C2×C4—172no—
1436C2×C4—172no—
1437C2×C4—172no—
1438C2×C4—341no—
1439C2×C4—341no—
1440C2×C4—341no—
1441C2×C4—341no—
1442C2×C4—341no—
1443C2×C4—341no—
1444C2×C4—341no—
1445C2×C4—341no—
1446C2×C4—341no—
1447C2×C4—341no—
1448C2×C4—341no—
1449C2×C4—341no—
1450C2×C4—341no—
1451C2×C4—341no—
1452C2×C4—341no—
1453C2×C4—341no—
1454C2×C4—341no—
1455C2×C4—341no—
1456C2×C4—341no—
1457C2×C4—341no—
1458C2×C4—341no—
1459C2×C4—341no—
1460C2×C4—341no—
1461C2×C4—341no—
1462C2×C4—341no—
1463C2×C4—341no—
1464C2×C4—341no—
1465C2×C4—341no—
1466C2×C4—341no—
1467C2×C4—341no—
1468C2×C4—341no—
1469C2×C4—341no—
1470C2×C4—341no—
1471C2×C4—341no—
1472C2×C4—341no—
1473C2×C4—341no—
1474C2×C4—684no—
1475C2×C4—684no—
1476C2×C4—684no—
1477C2×C4—684no—
1478C2×C4—684no—
1479C2×C4—684no—
1480C2×C4—1362no—
1481C2×C4—1362no—
1482C2×C4—1362no—
1483C2×C4—1362no—
1484C2×C4—1362no—
1485C2×C4C22×C4×D1712yes—
1486C2×C4C22×C4×D1712yes—
1487C2×C4C22×C4×D1712yes—
1488C22—22no—
1489C22—22no—
1490C22—22no—
1491C22—22no—
1492C22—22no—
1493C22—22no—
1494C22—22no—
1495C22—22no—
1496C22—22no—
1497C22—22no—
1498C22—22no—
1499C22—22no—
1500C22—41no—
1501C22—41no—
1502C22—41no—
1503C22—41no—
1504C22—41no—
1505C22—41no—
1506C22—41no—
1507C22—41no—
1508C22—41no—
1509C22—41no—
1510C22—41no—
1511C22—41no—
1512C22—41no—
1513C22—41no—
1514C22—41no—
1515C22—41no—
1516C22—88no—
1517C22—342no—
1518C22—342no—
1519C22—342no—
1520C22—681no—
1521C22—681no—
1522C22—681no—
1523C22—681no—
1524C22C23×C4×D1711yescharacteristic
1525C22H(5,𝔽2)×D1711yescharacteristic
1526C22H(5,𝔽2)×D1711yescharacteristic
1527C22#1176364411yescharacteristic
1528C22#1176364411yescharacteristic
1529C22#1176364411yescharacteristic
1530C22#1176364411yescharacteristic
1531C4—22no—
1532C4—22no—
1533C4—22no—
1534C4—41no—
1535C4—41no—
1536C4—41no—
1537C4—41no—
1538C4—41no—
1539C4—41no—
1540C4—41no—
1541C4—41no—
1542C4—342no—
1543C4—342no—
1544C4—342no—
1545C4—342no—
1546C4—342no—
1547C4—342no—
1548C4—342no—
1549C4—342no—
1550C4—342no—
1551C4—681no—
1552C4—681no—
1553C4—681no—
1554C4—681no—
1555C4—681no—
1556C4—681no—
1557C2—42no—
1558C2—42no—
1559C2—42no—
1560C2—42no—
1561C2—682no—
1562C2#1454198211yescharacteristic
1563C2#1454198811yescharacteristic
1564C2#1454198811yescharacteristic
1565C2#1454295311yescharacteristic
1566C2#1454308911yescharacteristic
1567C2#1454320311yescharacteristic
1568C2#1454347811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2375C2
socle, cosocleC23×C17C25
prime radicalC2×#11763394C2
hypercenter#2375D17
hypocenterC17#34451
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2375

Complements

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

NH ≅ G/Ntype
2. #14531971C2semidirect
3. #14531944C2semidirect
4. #14531934C2semidirect
5. #14531911C2semidirect
6. #14531902C2semidirect
7. #14531902C2semidirect
8. #14531893C2semidirect
9. #14531854C2semidirect
10. #14531814C2semidirect
11. #14531782C2semidirect
12. #14531768C2semidirect
13. #14531732C2semidirect
14. #14531722C2semidirect
15. #14531635C2semidirect
16. #14531635C2semidirect
17. #14531595C2semidirect
18. #14531581C2semidirect
19. #14531550C2semidirect
20. #14531545C2semidirect
21. #14531493C2semidirect
22. #14531485C2semidirect
23. #14531470C2semidirect
24. #14531470C2semidirect
25. #14531439C2semidirect
26. #14531439C2semidirect
27. #14531425C2semidirect
28. #14531311C2semidirect
29. #14531300C2semidirect
30. #14531226C2semidirect
31. C17×#2375C2semidirect
32. #11763394C4semidirect
44. C2×C4×Dic34C22semidirect
51. C2×#10587567C22semidirect
54. C2×#10587563C22semidirect
58. C2×C42×D17C22semidirect
59. #11762714C22semidirect
60. #11762713C22semidirect
61. #11762713C22semidirect
67. #11762709C22semidirect
68. #11762707C22semidirect
69. #11762706C22semidirect
70. #11762704C22semidirect
71. #11762704C22semidirect
72. #11762704C22semidirect
73. #11762704C22semidirect
82. #11762703C22semidirect
83. #11762703C22semidirect
84. #11762703C22semidirect
87. #11762701C22semidirect
88. #11762700C22semidirect
89. #11762700C22semidirect
90. #11762698C22semidirect
99. #11762697C22semidirect
100. #11762696C22semidirect
101. #11762696C22semidirect
102. #11762696C22semidirect
103. #11762694C22semidirect
104. #11762694C22semidirect
105. #11762693C22semidirect
106. #11762693C22semidirect
107. #11762692C22semidirect
108. #11762692C22semidirect
109. #11762691C22semidirect
110. #11762691C22semidirect
111. #11762691C22semidirect
115. #11762688C22semidirect
122. #11762685C22semidirect
125. #11762683C22semidirect
132. #11762681C22semidirect
133. #11762680C22semidirect
134. #11762680C22semidirect
135. #11762678C22semidirect
136. #11762676C22semidirect
137. #11762671C22semidirect
142. #11762667C22semidirect
143. #11762667C22semidirect
144. #11762666C22semidirect
145. C4⋊C4×Dic17C22semidirect
146. C4⋊C4×Dic17C22semidirect
147. C4⋊C4×Dic17C22semidirect
148. C4×#63225C22semidirect
149. C4×#63225C22semidirect
150. C4×#63225C22semidirect
151. C4×#63225C22semidirect
152. C4×C4⋊Dic17C22semidirect
153. #11762660C22semidirect
164. C22⋊C4×Dic17C22semidirect
165. C4×C22⋊Dic17C22semidirect
166. C4×C22⋊Dic17C22semidirect
167. #11762656C22semidirect
168. #11762656C22semidirect
169. #11762654C22semidirect
170. #11762654C22semidirect
171. #11762654C22semidirect
172. C2×#10587502C22semidirect
209. C17×#120C2×C4semidirect
234. #10587639C2×C4semidirect
237. C2×C22⋊Dic17C2×C4semidirect
258. #10587625C2×C4semidirect
259. #10587625C2×C4semidirect
260. #10587624C2×C4semidirect
261. #10587622C2×C4semidirect
262. #10587621C2×C4semidirect
265. D4×Dic17C2×C4semidirect
316. #10587571C2×C4semidirect
317. #10587569C2×C4semidirect
321. #10587567C2×C4semidirect
322. #10587565C2×C4semidirect
323. #10587565C2×C4semidirect
324. #10587564C2×C4semidirect
708. #2375D17semidirect
1004. #120C4×D17semidirect
1154. C17#34451semidirect

Maximal subgroups

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

subgroupindex
C2×#117633942
#145319712
#145319442
#145319342
#145319112
#145319022
#145318932
#145318542
#145318142
#145317822
#145317682
#145317322
#145317222
#145316352
#145315952
#145315812
#145315502
#145315452
#145314932
#145314852
#145314702
#145314392
#145314252
#145313112
#145313002
#145312262
C17×#23752
#3445117