Finite Group Databasebeta

← #17195277

Subgroups — #17195277

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×#11763283C211yesmaximal, characteristic
2#14531725C211yesmaximal, characteristic, complemented
3#14531723C211yesmaximal, characteristic, complemented
4#14531723C211yesmaximal, characteristic, complemented
5#14531717C211yesmaximal, characteristic, complemented
6#14531716C211yesmaximal, characteristic, complemented
7#14531710C211yesmaximal, characteristic, complemented
8#14531708C211yesmaximal, characteristic, complemented
9#14531708C211yesmaximal, characteristic, complemented
10#14531646C211yesmaximal, characteristic, complemented
11#14531644C211yesmaximal, characteristic, complemented
12#14531640C211yesmaximal, characteristic, complemented
13#14531631C211yesmaximal, characteristic, complemented
14#14531631C211yesmaximal, characteristic, complemented
15#14531627C211yesmaximal, characteristic, complemented
16#14531627C211yesmaximal, characteristic, complemented
17#14531420C211yesmaximal, characteristic, complemented
18#14531416C211yesmaximal, characteristic, complemented
19#14531416C211yesmaximal, characteristic, complemented
20#14531415C211yesmaximal, characteristic, complemented
21#14531395C211yesmaximal, characteristic, complemented
22#14531361C211yesmaximal, characteristic
23#14531228C211yesmaximal, characteristic, complemented
24#14531225C211yesmaximal, characteristic, complemented
25#14531222C211yesmaximal, characteristic, complemented
26#14531222C211yesmaximal, characteristic, complemented
27C2×#11762687C211yesmaximal, characteristic
28D17×#385C211yesmaximal, characteristic, complemented
29#14531136C211yesmaximal, characteristic, complemented
30C4×C22⋊C4×D17C211yesmaximal, characteristic, complemented
31C17×#2343C211yesmaximal, characteristic, complemented
32C23×D68C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34#11763283C4116yescomplemented
35C2×C4×D68C2211yescharacteristic
36C2×C4×D68C2211yescharacteristic
37C2×C4×D68C2211yescharacteristic
38C2×C4×D68C2211yescharacteristic
39C2×#10587579C2211yescharacteristic
40C2×#10587579C2211yescharacteristic
41C2×#10587579C2211yescharacteristic
42C2×#10587579C2211yescharacteristic
43C2×#10587612C2211yescharacteristic
44C2×#10587578C2211yescharacteristic, complemented
45C2×#10587578C2211yescharacteristic, complemented
46C2×#10587558C2211yescharacteristic, complemented
47C2×#10587558C2211yescharacteristic, complemented
48C2×C4⋊C4×D17C2211yescharacteristic, complemented
49C2×C4⋊C4×D17C2211yescharacteristic, complemented
50C22×#63227C2211yescharacteristic
51C22×#63227C2211yescharacteristic
52C22×#63227C2211yescharacteristic
53C2×C22⋊C4×D17C2211yescharacteristic
54C2×C22⋊C4×D17C2211yescharacteristic
55C2×C22⋊C4×D17C2211yescharacteristic
56C2×C22⋊C4×D17C2211yescharacteristic
57C2×C22⋊C4×D17C2211yescharacteristic
58C2×C22⋊C4×D17C2211yescharacteristic
59C2×C42×D17C2211yescharacteristic, complemented
60C2×C42×D17C2211yescharacteristic, complemented
61#11762701C2211yescharacteristic, complemented
62#11762701C2211yescharacteristic, 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#11762699C2211yescharacteristic, complemented
72#11762699C2211yescharacteristic, complemented
73#11762698C2211yescharacteristic, complemented
74#11762698C2211yescharacteristic, complemented
75#11762698C2211yescharacteristic, complemented
76#11762698C2211yescharacteristic, complemented
77#11762695C2211yescharacteristic, complemented
78#11762695C2211yescharacteristic, complemented
79#11762695C2211yescharacteristic, complemented
80#11762695C2211yescharacteristic, complemented
81#11762694C2211yescharacteristic, complemented
82#11762694C2211yescharacteristic, complemented
83#11762694C2211yescharacteristic, complemented
84#11762694C2211yescharacteristic, complemented
85#11762692C2211yescharacteristic, complemented
86#11762692C2211yescharacteristic, complemented
87#11762692C2211yescharacteristic, complemented
88#11762692C2211yescharacteristic, complemented
89#11762687C2211yescharacteristic
90#11762687C2211yescharacteristic
91#11762687C2211yescharacteristic
92#11762687C2211yescharacteristic
93#11762687C2211yescharacteristic
94#11762687C2211yescharacteristic
95#11762687C2211yescharacteristic
96#11762687C2211yescharacteristic
97#11762687C2211yescharacteristic
98#11762687C2211yescharacteristic
99#11762687C2211yescharacteristic
100#11762687C2211yescharacteristic
101#11762687C2211yescharacteristic
102#11762687C2211yescharacteristic
103#11762687C2211yescharacteristic
104#11762687C2211yescharacteristic
105#11762684C2211yescharacteristic
106#11762684C2211yescharacteristic
107#11762683C2211yescharacteristic, complemented
108#11762683C2211yescharacteristic, complemented
109#11762683C2211yescharacteristic, complemented
110#11762683C2211yescharacteristic, complemented
111#11762682C2211yescharacteristic
112#11762682C2211yescharacteristic
113#11762681C2211yescharacteristic
114#11762681C2211yescharacteristic
115#11762680C2211yescharacteristic, complemented
116#11762680C2211yescharacteristic, complemented
117#11762680C2211yescharacteristic, complemented
118#11762680C2211yescharacteristic, complemented
119#11762677C2211yescharacteristic, complemented
120#11762676C2211yescharacteristic, complemented
121#11762676C2211yescharacteristic, complemented
122#11762675C2211yescharacteristic, complemented
123#11762673C2211yescharacteristic, complemented
124#11762673C2211yescharacteristic, complemented
125#11762672C2211yescharacteristic
126#11762671C2211yescharacteristic, complemented
127#11762671C2211yescharacteristic, complemented
128#11762671C2211yescharacteristic, complemented
129#11762671C2211yescharacteristic, complemented
130#11762668C2211yescharacteristic, complemented
131#11762668C2211yescharacteristic, complemented
132#11762668C2211yescharacteristic, complemented
133#11762668C2211yescharacteristic, complemented
134#11762666C2211yescharacteristic, complemented
135#11762666C2211yescharacteristic, complemented
136#11762666C2211yescharacteristic, complemented
137#11762666C2211yescharacteristic, complemented
138#11762664C2211yescharacteristic
139#11762664C2211yescharacteristic
140C4×C4⋊Dic17C2211yescharacteristic, complemented
141#11762660C2211yescharacteristic, complemented
142#11762660C2211yescharacteristic, complemented
143C22⋊C4×Dic17C2211yescharacteristic
144C22⋊C4×Dic17C2211yescharacteristic
145C22⋊C4×Dic17C2211yescharacteristic
146C22⋊C4×Dic17C2211yescharacteristic
147C4×#63227C2211yescharacteristic, complemented
148C4×#63227C2211yescharacteristic, complemented
149C4×#63227C2211yescharacteristic, complemented
150C4×#63227C2211yescharacteristic, complemented
151C4×#63227C2211yescharacteristic, complemented
152C4×#63227C2211yescharacteristic, complemented
153C4×#63227C2211yescharacteristic, complemented
154C4×#63227C2211yescharacteristic, complemented
155C4×C22⋊Dic17C2211yescharacteristic
156C4×C22⋊Dic17C2211yescharacteristic
157#11762656C2211yescharacteristic, complemented
158#11762656C2211yescharacteristic, complemented
159#11762656C2211yescharacteristic, complemented
160#11762656C2211yescharacteristic, complemented
161#11762656C2211yescharacteristic, complemented
162#11762656C2211yescharacteristic, complemented
163#11762656C2211yescharacteristic, complemented
164#11762656C2211yescharacteristic, complemented
165#11762655C2211yescharacteristic, complemented
166#11762654C2211yescharacteristic, complemented
167#11762654C2211yescharacteristic, complemented
168C2×#10587502C2211yescharacteristic
169#95×D17C2211yescharacteristic, complemented
170#95×D17C2211yescharacteristic, complemented
171#95×D17C2211yescharacteristic, complemented
172#95×D17C2211yescharacteristic, complemented
173C2×C17×#117C2211yescharacteristic
174C17×#387C2211yescharacteristic, complemented
175C17×#387C2211yescharacteristic, complemented
176C17×#387C2211yescharacteristic, complemented
177C17×#387C2211yescharacteristic, complemented
178C17×#385C2211yescharacteristic
179C17×#385C2211yescharacteristic
180C17×#383C2211yescharacteristic, complemented
181C17×#382C2211yescharacteristic, complemented
182C17×#381C2211yescharacteristic
183C4×C4⋊C4×C17C2211yescharacteristic, complemented
184C4×C22⋊C4×C17C2211yescharacteristic
185C4×C22⋊C4×C17C2211yescharacteristic
186C17×#376C2211yescharacteristic, complemented
187C2×C17×#95C2211yescharacteristic
188C24×D17C2311yescharacteristic
189C24×D17C2311yescharacteristic
190C23×C4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×Dic17C2311yescharacteristic
194C23×Dic17C2311yescharacteristic
195C22×D68—24no—
196C22×D68—24no—
197C22×D68C2×C418yes—
198C22×D68C2311yescharacteristic
199C22×D68C2311yescharacteristic
200C22×D68C2311yescharacteristic
201C22×D68C2311yescharacteristic
202C22×C4×D17—24no—
203C22×C4×D17—42no—
204C22×C4×D17—42no—
205C22×C4×D17C2311yescharacteristic
206C22×C4×D17C2311yescharacteristic
207C22×C4×D17C2311yescharacteristic
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
221C17×#117C2×C418yescomplemented
222C2×C4⋊C4×C17C2311yescharacteristic
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×C42×C17C2311yescharacteristic
233C2×C42×C17C2311yescharacteristic
234C2×C42×C17C2311yescharacteristic
235C2×C42×C17C2311yescharacteristic
236C2×C42×C17C2311yescharacteristic
237C2×C42×C17C2311yescharacteristic
238C2×C22⋊Dic17C2311yescharacteristic
239C2×C22⋊Dic17C2311yescharacteristic
240C2×C22⋊Dic17C2311yescharacteristic
241C2×C22⋊Dic17C2311yescharacteristic
242C2×#63227—24no—
243C2×#63227—42no—
244C2×#63227—42no—
245C2×#63227C2311yescharacteristic
246C2×#63227C2311yescharacteristic
247C2×#63227C2311yescharacteristic
248C2×#63227C2311yescharacteristic
249C2×#63227C2311yescharacteristic
250C2×#63227C2311yescharacteristic
251C2×#63227C2311yescharacteristic
252C2×#63227C2311yescharacteristic
253C2×#63227C2311yescharacteristic
254C2×#63227C2311yescharacteristic
255C2×#63227C2311yescharacteristic
256C2×#63227C2311yescharacteristic
257C2×#63227C2311yescharacteristic
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
277#10587612C2×C418yescomplemented
278C2×C4⋊Dic17C2311yescharacteristic
279C2×C4⋊Dic17C2311yescharacteristic
280C2×C4⋊Dic17C2311yescharacteristic
281C2×C4⋊Dic17C2311yescharacteristic
282C2×C4⋊Dic17C2311yescharacteristic
283C2×C4⋊Dic17C2311yescharacteristic
284C2×#63225C2311yescharacteristic
285C2×#63225C2311yescharacteristic
286C2×#63225C2311yescharacteristic
287C2×#63225C2311yescharacteristic
288C2×#63225C2311yescharacteristic
289C2×#63225C2311yescharacteristic
290C2×#63225C2311yescharacteristic
291C2×#63225C2311yescharacteristic
292C2×C4×Dic17C2311yescharacteristic
293C2×C4×Dic17C2311yescharacteristic
294C2×C4×Dic17C2311yescharacteristic
295C2×C4×Dic17C2311yescharacteristic
296C2×C4×Dic17C2311yescharacteristic
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
306#10587579C2×C418yescomplemented
307#10587579C2×C418yescomplemented
308#10587579C2×C418yescomplemented
309#10587579C2×C418yescomplemented
310#10587578—42no—
311#10587578—42no—
312C4⋊C4×D17—42no—
313C4⋊C4×D17—42no—
314C22⋊C4×D17—24no—
315C22⋊C4×D17—24no—
316C22⋊C4×D17C2×C418yes—
317C22⋊C4×D17C2×C418yes—
318C22⋊C4×D17C2×C418yescomplemented
319C22⋊C4×D17C2×C418yescomplemented
320C4×D68C2×C418yescomplemented
321C4×D68C2×C418yescomplemented
322C4×D68C2×C418yescomplemented
323C4×D68C2×C418yescomplemented
324#10587558—42no—
325#10587558—42no—
326C42×D17—42no—
327C42×D17—42no—
328C17×#95C2311yescharacteristic
329C17×#95C2311yescharacteristic
330C17×#95C2311yescharacteristic
331C17×#95C2311yescharacteristic
332C17×#95C2311yescharacteristic
333C17×#95C2311yescharacteristic
334C17×#95C2311yescharacteristic
335C17×#95C2311yescharacteristic
336C17×#95C2311yescharacteristic
337C17×#95C2311yescharacteristic
338C17×#95C2311yescharacteristic
339C17×#95C2311yescharacteristic
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342C17×#95C2311yescharacteristic
343C17×#95C2311yescharacteristic
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
377C23×D17—22no—
378C23×D17—22no—
379C23×D17—41no—
380C23×D17—41no—
381C23×D17—41no—
382C23×D17—41no—
383C23×D17—41no—
384C23×D17—41no—
385C23×D17—41no—
386C23×D17—41no—
387C23×D17C22×C414yes—
388C23×D17C22×C414yes—
389C23×D17#4114yes—
390C23×D17#4114yes—
391C23×D17C2411yescharacteristic
392C23×D17C2411yescharacteristic
393C23×D17C2411yescharacteristic
394C23×D17C2411yescharacteristic
395C22×C4×C17—22no—
396C22×C4×C17—22no—
397C22×C4×C17—22no—
398C22×C4×C17—22no—
399C22×C4×C17—22no—
400C22×C4×C17—41no—
401C22×C4×C17—41no—
402C22×C4×C17—41no—
403C22×C4×C17C22×C414yes—
404C22×C4×C17C2411yescharacteristic
405C22×C4×C17C2411yescharacteristic
406C22×C4×C17C2411yescharacteristic
407C22×C4×C17C2411yescharacteristic
408C22×C4×C17C2411yescharacteristic
409C22×C4×C17C2411yescharacteristic
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×Dic17—22no—
419C22×Dic17—22no—
420C22×Dic17—22no—
421C22×Dic17—41no—
422C22×Dic17—41no—
423C22×Dic17—41no—
424C22×Dic17C2411yescharacteristic
425C22×Dic17C2411yescharacteristic
426C22×Dic17C2411yescharacteristic
427C22×Dic17C2411yescharacteristic
428C22×Dic17C2411yescharacteristic
429C22×Dic17C2411yescharacteristic
430C22×Dic17C2411yescharacteristic
431C22×Dic17C2411yescharacteristic
432C22×Dic17C2411yescharacteristic
433C22×Dic17C2411yescharacteristic
434C22×Dic17C2411yescharacteristic
435C22×Dic17C2411yescharacteristic
436C2×D68—232no—
437C2×D68—22no—
438C2×D68—22no—
439C2×D68—22no—
440C2×D68—22no—
441C2×D68—22no—
442C2×D68—22no—
443C2×D68—22no—
444C2×D68—22no—
445C2×D68C22×C414yes—
446C2×D68C22×C414yes—
447C2×D68C22×C414yes—
448C2×D68C22×C414yes—
449C2×C4×D17—22no—
450C2×C4×D17—22no—
451C2×C4×D17—22no—
452C2×C4×D17—22no—
453C2×C4×D17—22no—
454C2×C4×D17—22no—
455C2×C4×D17—22no—
456C2×C4×D17—22no—
457C2×C4×D17—22no—
458C2×C4×D17—22no—
459C2×C4×D17—22no—
460C2×C4×D17—22no—
461C2×C4×D17—416no—
462C2×C4×D17—41no—
463C2×C4×D17—41no—
464C2×C4×D17—41no—
465C2×C4×D17—41no—
466C2×C4×D17—41no—
467C2×C4×D17—41no—
468C2×C4×D17—41no—
469C2×C4×D17—41no—
470C2×C4×D17—41no—
471C2×C4×D17—41no—
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—41no—
485C2×C4×D17—41no—
486C2×C4×D17—41no—
487C2×C4×D17—41no—
488C2×C4×D17—41no—
489C2×C4×D17—41no—
490C2×C4×D17C22×C414yes—
491C2×C4×D17C22×C414yes—
492C2×C4×D17C22×C414yes—
493C2×C4×D17C22×C414yes—
494C2×C4×D17C22×C414yescomplemented
495C2×C4×D17C22×C414yescomplemented
496C2×C4×D17C22×C414yescomplemented
497C2×C4×D17C22×C414yescomplemented
498C4⋊C4×C17—22no—
499C4⋊C4×C17—41no—
500C4⋊C4×C17—41no—
501C4⋊C4×C17—41no—
502C4⋊C4×C17C22×C414yescomplemented
503C4⋊C4×C17C22×C414yescomplemented
504C22⋊C4×C17—22no—
505C22⋊C4×C17—22no—
506C22⋊C4×C17C22×C414yes—
507C22⋊C4×C17C22×C414yes—
508C42×C17—22no—
509C42×C17—41no—
510C42×C17—41no—
511C42×C17—41no—
512C42×C17C22×C414yescomplemented
513C42×C17C22×C414yescomplemented
514C22⋊Dic17—22no—
515C22⋊Dic17—22no—
516C22⋊Dic17C22×C414yes—
517C22⋊Dic17C22×C414yes—
518#63227—22no—
519#63227—22no—
520#63227—22no—
521#63227—22no—
522#63227—22no—
523#63227—22no—
524#63227—22no—
525#63227—22no—
526#63227—22no—
527#63227—22no—
528#63227—22no—
529#63227—22no—
530#63227—41no—
531#63227—41no—
532#63227—41no—
533#63227—41no—
534#63227—41no—
535#63227—41no—
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×C414yescomplemented
547#63227C22×C414yescomplemented
548#63227C22×C414yescomplemented
549#63227C22×C414yescomplemented
550C4⋊Dic17—22no—
551C4⋊Dic17—41no—
552C4⋊Dic17—41no—
553C4⋊Dic17—41no—
554C4⋊Dic17C22×C414yescomplemented
555C4⋊Dic17C22×C414yescomplemented
556#63225—22no—
557#63225—22no—
558#63225—41no—
559#63225—41no—
560#63225—41no—
561#63225—41no—
562#63225—41no—
563#63225—41no—
564C4×Dic17—22no—
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×Dic17—41no—
576C4×Dic17C22×C414yescomplemented
577C4×Dic17C22×C414yescomplemented
578#34251—171nomaximal, Sylow
579C23×C17—21no—
580C23×C17—21no—
581C23×C17—21no—
582C23×C17—21no—
583C23×C17C23×C412yes—
584C23×C17C2×#4112yes—
585C23×C17C2×#4112yes—
586C23×C17C2511yescharacteristic
587C22×D17—21no—
588C22×D17—21no—
589C22×D17—21no—
590C22×D17—21no—
591C22×D17—21no—
592C22×D17—21no—
593C22×D17—21no—
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—28no—
608C22×D17—44no—
609C22×D17—44no—
610C22×D17—44no—
611C22×D17—44no—
612C22×D17—44no—
613C22×D17—44no—
614C22×D17—44no—
615C22×D17—44no—
616C22×D17—82no—
617C22×D17—82no—
618C22×D17—82no—
619C22×D17—82no—
620C22×D17#117116yescomplemented
621C22×D17C23×C412yes—
622C22×D17C23×C412yes—
623C22×D17C23×C412yes—
624C22×D17C23×C412yes—
625C22×D17C2×#4112yes—
626C22×D17C2×#4112yes—
627C22×D17C2×#4112yes—
628C22×D17C2×#4112yes—
629C2×C4×C17—28no—
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—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—21no—
664C2×C4×C17—21no—
665C2×C4×C17—44no—
666C2×C4×C17—82no—
667C2×C4×C17C23×C412yes—
668C2×C4×C17C23×C412yes—
669C2×C4×C17C23×C412yes—
670C2×C4×C17C23×C412yes—
671C2×C4×C17C23×C412yes—
672C2×C4×C17C23×C412yes—
673C2×C4×C17H(5,𝔽2)12yes—
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—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—44no—
706C2×Dic17—82no—
707C2×Dic17C23×C412yes—
708C2×Dic17C23×C412yes—
709C2×Dic17C23×C412yes—
710C2×Dic17C23×C412yes—
711C2×Dic17H(5,𝔽2)12yes—
712D68—28no—
713D68—28no—
714D68—28no—
715D68—28no—
716C4×D17—28no—
717C4×D17—44no—
718C4×D17—44no—
719C4×D17—44no—
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—44no—
729C4×D17—44no—
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#2343D1711yescharacteristic, complemented
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#2290—171no—
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×C17C2×#11714yes—
770C22×C17C24×C411yescharacteristic
771C22×C17C22×#4111yescharacteristic
772C22×C17C22×#4111yescharacteristic
773C22×C17C2×H(5,𝔽2)11yescharacteristic
774C22×C17C2×H(5,𝔽2)11yescharacteristic
775C22×C17#58511yescharacteristic
776C22×C17#58511yescharacteristic
777C2×D17—22no—
778C2×D17—22no—
779C2×D17—22no—
780C2×D17—22no—
781C2×D17—22no—
782C2×D17—22no—
783C2×D17—22no—
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—416no—
796C2×D17—41no—
797C2×D17—41no—
798C2×D17—41no—
799C2×D17—41no—
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—
820C4×C17—41no—
821Dic17—22no—
822Dic17—22no—
823Dic17—22no—
824Dic17—22no—
825Dic17—22no—
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×D4—171no—
844C2×#117—171no—
845C2×#117—171no—
846C2×#117—171no—
847C2×#117—171no—
848C2×#117—171no—
849C2×#117C2×D1711yescharacteristic
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×C42—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#388—171no—
877#388—171no—
878#388—171no—
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#387C2×D1711yescharacteristic, complemented
892#387C2×D1711yescharacteristic, complemented
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#386—171no—
910#386—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#385—171no—
921#385—171no—
922#385—171no—
923#385—171no—
924#385—171no—
925#385C2×D1711yescharacteristic
926#385C2×D1711yescharacteristic
927#383—171no—
928#383—171no—
929#383—171no—
930#383C2×D1711yescharacteristic, complemented
931#382—171no—
932#382—171no—
933#382—171no—
934#382C2×D1711yescharacteristic, complemented
935#381—171no—
936#381—171no—
937#381—171no—
938#381—171no—
939#381—171no—
940#381C2×D1711yescharacteristic
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
978C4×C22⋊C4C2×D1711yescharacteristic
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×#95C2×D1711yescharacteristic
989C2×C17—24no—
990C2×C17C22×#11711yescharacteristic
991C2×C17C4×H(5,𝔽2)11yescharacteristic
992C2×C17C4×H(5,𝔽2)11yescharacteristic
993C2×C17#349011yescharacteristic
994C2×C17#349111yescharacteristic
995C2×C17#350511yescharacteristic
996C2×C17#350511yescharacteristic
997D17—24no—
998D17—24no—
999D17—42no—
1000D17—42no—
1001C25—171no—
1002C25—171no—
1003C22×D4—178no—
1004C22×D4—171no—
1005C22×D4—171no—
1006C22×D4—171no—
1007C22×D4—171no—
1008C22×D4—344no—
1009C22×D4—344no—
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—171no—
1028C23×C4—344no—
1029C23×C4—682no—
1030C23×C4—682no—
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×D4—178no—
1042#117—178no—
1043#117—682no—
1044#117—682no—
1045#117—682no—
1046#117—682no—
1047#117C4×D1718yescomplemented
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—682no—
1063C2×C4⋊C4—682no—
1064C2×C4⋊C4C22×D1711yescharacteristic
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—171no—
1073C2×C22⋊C4—171no—
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—178no—
1081C2×C22⋊C4—178no—
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—171no—
1107C2×C22⋊C4—171no—
1108C2×C22⋊C4—171no—
1109C2×C22⋊C4—171no—
1110C2×C22⋊C4—344no—
1111C2×C22⋊C4—344no—
1112C2×C22⋊C4—344no—
1113C2×C22⋊C4—682no—
1114C2×C22⋊C4—682no—
1115C2×C22⋊C4C22×D1711yescharacteristic
1116C2×C22⋊C4C22×D1711yescharacteristic
1117C2×C22⋊C4C22×D1711yescharacteristic
1118C2×C22⋊C4C22×D1711yescharacteristic
1119C2×C42—171no—
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×C42—682no—
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#95C22×D1711yescharacteristic
1174#95C22×D1711yescharacteristic
1175#95C22×D1711yescharacteristic
1176#95C22×D1711yescharacteristic
1177#95C22×D1711yescharacteristic
1178#95C22×D1711yescharacteristic
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—171no—
1197C24—174no—
1198C24—342no—
1199C24—342no—
1200C24—681no—
1201C24—681no—
1202C24—681no—
1203C24—681no—
1204C24—681no—
1205C24—681no—
1206C24—681no—
1207C24—681no—
1208C24C23×D1711yescharacteristic
1209C2×D4—174no—
1210C2×D4—174no—
1211C2×D4—174no—
1212C2×D4—174no—
1213C2×D4—3432no—
1214C2×D4—342no—
1215C2×D4—342no—
1216C2×D4—342no—
1217C2×D4—342no—
1218C2×D4—342no—
1219C2×D4—342no—
1220C2×D4—342no—
1221C2×D4—342no—
1222C22×C4—22no—
1223C22×C4—22no—
1224C22×C4—22no—
1225C22×C4—22no—
1226C22×C4—22no—
1227C22×C4—41no—
1228C22×C4—41no—
1229C22×C4—41no—
1230C22×C4—171no—
1231C22×C4—171no—
1232C22×C4—171no—
1233C22×C4—171no—
1234C22×C4—171no—
1235C22×C4—174no—
1236C22×C4—174no—
1237C22×C4—174no—
1238C22×C4—174no—
1239C22×C4—174no—
1240C22×C4—174no—
1241C22×C4—174no—
1242C22×C4—174no—
1243C22×C4—171no—
1244C22×C4—171no—
1245C22×C4—171no—
1246C22×C4—171no—
1247C22×C4—171no—
1248C22×C4—171no—
1249C22×C4—171no—
1250C22×C4—342no—
1251C22×C4—342no—
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—681no—
1266C22×C4—681no—
1267C22×C4—681no—
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—681no—
1289C22×C4—681no—
1290C22×C4—681no—
1291C22×C4—681no—
1292C22×C4—681no—
1293C22×C4—6816no—
1294C22×C4—681no—
1295C22×C4—681no—
1296C22×C4—681no—
1297C22×C4C2×C4×D1714yes—
1298C22×C4C23×D1711yescharacteristic
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—41no—
1314C4⋊C4—41no—
1315C4⋊C4—41no—
1316C4⋊C4—174no—
1317C4⋊C4—174no—
1318C4⋊C4—342no—
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⋊C4C2×C4×D1714yescomplemented
1331C4⋊C4C2×C4×D1714yescomplemented
1332C22⋊C4—22no—
1333C22⋊C4—22no—
1334C22⋊C4—174no—
1335C22⋊C4—174no—
1336C22⋊C4—174no—
1337C22⋊C4—174no—
1338C22⋊C4—174no—
1339C22⋊C4—174no—
1340C22⋊C4—174no—
1341C22⋊C4—174no—
1342C22⋊C4—174no—
1343C22⋊C4—174no—
1344C22⋊C4—342no—
1345C22⋊C4—342no—
1346C22⋊C4—342no—
1347C22⋊C4—342no—
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—681no—
1359C22⋊C4—681no—
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×D1714yes—
1372C42—22no—
1373C42—41no—
1374C42—41no—
1375C42—41no—
1376C42—174no—
1377C42—174no—
1378C42—342no—
1379C42—342no—
1380C42—342no—
1381C42—681no—
1382C42—681no—
1383C42—681no—
1384C42—681no—
1385C42—681no—
1386C42—681no—
1387C42—681no—
1388C42—681no—
1389C42—681no—
1390C42C2×C4×D1714yescomplemented
1391C42C2×C4×D1714yescomplemented
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—172no—
1397C23—172no—
1398C23—172no—
1399C23—172no—
1400C23—172no—
1401C23—172no—
1402C23—1716no—
1403C23—172no—
1404C23—172no—
1405C23—341no—
1406C23—341no—
1407C23—341no—
1408C23—341no—
1409C23—341no—
1410C23—341no—
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—348no—
1426C23—684no—
1427C23—684no—
1428C23—684no—
1429C23—684no—
1430C23—684no—
1431C23—684no—
1432C23—684no—
1433C23—684no—
1434C23—1362no—
1435C23—1362no—
1436C23—1362no—
1437C23—1362no—
1438C23C22×C4×D1712yes—
1439C23#41×D1712yes—
1440C23#41×D1712yes—
1441C23C24×D1711yescharacteristic
1442D4—348no—
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—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—44no—
1483C2×C4—82no—
1484C2×C4—172no—
1485C2×C4—172no—
1486C2×C4—172no—
1487C2×C4—172no—
1488C2×C4—172no—
1489C2×C4—348no—
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—684no—
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—684no—
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×C4C22×C4×D1712yes—
1544C2×C4#1058769612yes—
1545C22—22no—
1546C22—22no—
1547C22—22no—
1548C22—22no—
1549C22—22no—
1550C22—22no—
1551C22—174no—
1552C22—174no—
1553C22—342no—
1554C22—342no—
1555C22—342no—
1556C22—342no—
1557C22—342no—
1558C22—342no—
1559C22—342no—
1560C22—342no—
1561C22—342no—
1562C22—342no—
1563C22—342no—
1564C22—342no—
1565C22—342no—
1566C22—342no—
1567C22—342no—
1568C22—342no—
1569C22—342no—
1570C22—342no—
1571C22—6816no—
1572C22—681no—
1573C22—681no—
1574C22—681no—
1575C22—681no—
1576C22—681no—
1577C22—681no—
1578C22—681no—
1579C22—681no—
1580C22—1368no—
1581C22#117×D1714yes—
1582C22C23×C4×D1711yescharacteristic
1583C22C2×#41×D1711yescharacteristic
1584C22C2×#41×D1711yescharacteristic
1585C22H(5,𝔽2)×D1711yescharacteristic
1586C22C2×#1058769611yescharacteristic
1587C22#1176364511yescharacteristic
1588C22#1176364611yescharacteristic
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—41no—
1603C4—342no—
1604C4—342no—
1605C4—342no—
1606C4—342no—
1607C4—342no—
1608C4—681no—
1609C4—681no—
1610C4—681no—
1611C4—681no—
1612C4—681no—
1613C4—681no—
1614C4—681no—
1615C2—24no—
1616C2—344no—
1617C2—344no—
1618C2—682no—
1619C2—682no—
1620C2C2×#117×D1711yescharacteristic
1621C2#1454199011yescharacteristic
1622C2C4×#1058769611yescharacteristic
1623C2#1454246811yescharacteristic
1624C2#1454247911yescharacteristic
1625C2#1454261511yescharacteristic
1626C2#1454262411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2343C2
socle, cosocleC23×C17C25
prime radicalC23×D68C22
hypercenter#2343D17
hypocenterC17#34251
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2343

Complements

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

NH ≅ G/Ntype
2. #14531725C2semidirect
3. #14531723C2semidirect
4. #14531723C2semidirect
5. #14531717C2semidirect
6. #14531716C2semidirect
7. #14531710C2semidirect
8. #14531708C2semidirect
9. #14531708C2semidirect
10. #14531646C2semidirect
11. #14531644C2semidirect
12. #14531640C2semidirect
13. #14531631C2semidirect
14. #14531631C2semidirect
15. #14531627C2semidirect
16. #14531627C2semidirect
17. #14531420C2semidirect
18. #14531416C2semidirect
19. #14531416C2semidirect
20. #14531415C2semidirect
21. #14531395C2semidirect
23. #14531228C2semidirect
24. #14531225C2semidirect
25. #14531222C2semidirect
26. #14531222C2semidirect
28. D17×#385C2semidirect
29. #14531136C2semidirect
30. C4×C22⋊C4×D17C2semidirect
31. C17×#2343C2semidirect
34. #11763283C4semidirect
44. C2×#10587578C22semidirect
45. C2×#10587578C22semidirect
46. C2×#10587558C22semidirect
47. C2×#10587558C22semidirect
48. C2×C4⋊C4×D17C22semidirect
49. C2×C4⋊C4×D17C22semidirect
59. C2×C42×D17C22semidirect
60. C2×C42×D17C22semidirect
61. #11762701C22semidirect
62. #11762701C22semidirect
63. #11762701C22semidirect
64. #11762701C22semidirect
65. #11762700C22semidirect
66. #11762700C22semidirect
67. #11762700C22semidirect
68. #11762700C22semidirect
69. #11762699C22semidirect
70. #11762699C22semidirect
71. #11762699C22semidirect
72. #11762699C22semidirect
73. #11762698C22semidirect
74. #11762698C22semidirect
75. #11762698C22semidirect
76. #11762698C22semidirect
77. #11762695C22semidirect
78. #11762695C22semidirect
79. #11762695C22semidirect
80. #11762695C22semidirect
81. #11762694C22semidirect
82. #11762694C22semidirect
83. #11762694C22semidirect
84. #11762694C22semidirect
85. #11762692C22semidirect
86. #11762692C22semidirect
87. #11762692C22semidirect
88. #11762692C22semidirect
107. #11762683C22semidirect
108. #11762683C22semidirect
109. #11762683C22semidirect
110. #11762683C22semidirect
115. #11762680C22semidirect
116. #11762680C22semidirect
117. #11762680C22semidirect
118. #11762680C22semidirect
119. #11762677C22semidirect
120. #11762676C22semidirect
121. #11762676C22semidirect
122. #11762675C22semidirect
123. #11762673C22semidirect
124. #11762673C22semidirect
126. #11762671C22semidirect
127. #11762671C22semidirect
128. #11762671C22semidirect
129. #11762671C22semidirect
130. #11762668C22semidirect
131. #11762668C22semidirect
132. #11762668C22semidirect
133. #11762668C22semidirect
134. #11762666C22semidirect
135. #11762666C22semidirect
136. #11762666C22semidirect
137. #11762666C22semidirect
140. C4×C4⋊Dic17C22semidirect
141. #11762660C22semidirect
142. #11762660C22semidirect
147. C4×#63227C22semidirect
148. C4×#63227C22semidirect
149. C4×#63227C22semidirect
150. C4×#63227C22semidirect
151. C4×#63227C22semidirect
152. C4×#63227C22semidirect
153. C4×#63227C22semidirect
154. C4×#63227C22semidirect
157. #11762656C22semidirect
158. #11762656C22semidirect
159. #11762656C22semidirect
160. #11762656C22semidirect
161. #11762656C22semidirect
162. #11762656C22semidirect
163. #11762656C22semidirect
164. #11762656C22semidirect
165. #11762655C22semidirect
166. #11762654C22semidirect
167. #11762654C22semidirect
169. #95×D17C22semidirect
170. #95×D17C22semidirect
171. #95×D17C22semidirect
172. #95×D17C22semidirect
174. C17×#387C22semidirect
175. C17×#387C22semidirect
176. C17×#387C22semidirect
177. C17×#387C22semidirect
180. C17×#383C22semidirect
181. C17×#382C22semidirect
183. C4×C4⋊C4×C17C22semidirect
186. C17×#376C22semidirect
221. C17×#117C2×C4semidirect
277. #10587612C2×C4semidirect
306. #10587579C2×C4semidirect
307. #10587579C2×C4semidirect
308. #10587579C2×C4semidirect
309. #10587579C2×C4semidirect
318. C22⋊C4×D17C2×C4semidirect
319. C22⋊C4×D17C2×C4semidirect
320. C4×D68C2×C4semidirect
321. C4×D68C2×C4semidirect
322. C4×D68C2×C4semidirect
323. C4×D68C2×C4semidirect
494. C2×C4×D17C22×C4semidirect
495. C2×C4×D17C22×C4semidirect
496. C2×C4×D17C22×C4semidirect
497. C2×C4×D17C22×C4semidirect
502. C4⋊C4×C17C22×C4semidirect
503. C4⋊C4×C17C22×C4semidirect
512. C42×C17C22×C4semidirect
513. C42×C17C22×C4semidirect
546. #63227C22×C4semidirect
547. #63227C22×C4semidirect
548. #63227C22×C4semidirect
549. #63227C22×C4semidirect
554. C4⋊Dic17C22×C4semidirect
555. C4⋊Dic17C22×C4semidirect
576. C4×Dic17C22×C4semidirect
577. C4×Dic17C22×C4semidirect
620. C22×D17#117semidirect
744. #2343D17semidirect
891. #387C2×D17semidirect
892. #387C2×D17semidirect
893. #387C2×D17semidirect
894. #387C2×D17semidirect
930. #383C2×D17semidirect
934. #382C2×D17semidirect
954. C4×C4⋊C4C2×D17semidirect
982. #376C2×D17semidirect
1047. #117C4×D17semidirect
1189. C17#34251semidirect
1330. C4⋊C4C2×C4×D17semidirect
1331. C4⋊C4C2×C4×D17semidirect
1390. C42C2×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×#117632832
#145317252
#145317232
#145317172
#145317162
#145317102
#145317082
#145316462
#145316442
#145316402
#145316312
#145316272
#145314202
#145314162
#145314152
#145313952
#145313612
#145312282
#145312252
#145312222
C2×#117626872
D17×#3852
#145311362
C4×C22⋊C4×D172
C17×#23432
#3425117