Finite Group Databasebeta

← #16958463

Subgroups — #16958463

Order 4352.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762690C211yesmaximal, characteristic, complemented
2C2×#11762680C211yesmaximal, characteristic
3C2×#11762656C211yesmaximal, characteristic
4#14527045C211yesmaximal, characteristic, complemented
5#14527030C211yesmaximal, characteristic
6#14527026C211yesmaximal, characteristic
7#14527020C211yesmaximal, characteristic
8#14527020C211yesmaximal, characteristic
9#14527018C211yesmaximal, characteristic, complemented
10#14527015C211yesmaximal, characteristic, complemented
11#14527013C211yesmaximal, characteristic, complemented
12#14527008C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic
14#95×Dic17C211yesmaximal, characteristic, complemented
15C17×#1441C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×#63225C2211yescharacteristic
19C22×#63227C2211yescharacteristic
20C22×#63227C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×C4×Dic17C2211yescharacteristic
26C22×C4×Dic17C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29#11762690—24no—
30#11762680C418yescomplemented
31#11762656—24no—
32C2×#10587502C2211yescharacteristic
33C2×#10587502C2211yescharacteristic
34C2×#10587502C2211yescharacteristic
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C22×C4⋊C4×C17C2211yescharacteristic
48C22×C4⋊C4×C17C2211yescharacteristic
49C2×C17×#95C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C24×D17C2311yescharacteristic
55C23×C4×C17C2311yescharacteristic
56C23×C4×C17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×Dic17C2311yescharacteristic
63C23×Dic17C2311yescharacteristic
64C23×Dic17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C22×C4×D17—22no—
70C22×C4×D17—22no—
71C22×C4×D17—41no—
72C22×C4×D17—41no—
73C22×C4×D17—41no—
74C22×C4×D17—41no—
75C22×C4×D17C2×C414yes—
76C2×C4⋊C4×C17—22no—
77C2×C4⋊C4×C17—41no—
78C2×C4⋊C4×C17—41no—
79C2×C4⋊C4×C17—41no—
80C2×C4⋊C4×C17—41no—
81C2×C4⋊C4×C17C2×C414yes—
82C2×#63227—22no—
83C2×#63227—22no—
84C2×#63227—22no—
85C2×#63227—22no—
86C2×#63227—22no—
87C2×#63227—22no—
88C2×#63227—22no—
89C2×#63227—22no—
90C2×#63227—22no—
91C2×#63227—22no—
92C2×#63227—22no—
93C2×#63227—41no—
94C2×#63227—41no—
95C2×#63227—41no—
96C2×#63227—41no—
97C2×#63227C2×C414yes—
98C2×#63227C2×C414yes—
99C2×#63227Q814yes—
100C2×C4⋊Dic17—22no—
101C2×C4⋊Dic17—22no—
102C2×C4⋊Dic17—41no—
103C2×#63225—22no—
104C2×#63225—22no—
105C2×#63225C2×C414yes—
106C2×C4×Dic17—22no—
107C2×C4×Dic17—22no—
108C2×C4×Dic17—22no—
109C2×C4×Dic17—22no—
110C2×C4×Dic17—22no—
111C2×C4×Dic17—41no—
112C2×C4×Dic17—41no—
113C2×C4×Dic17—41no—
114C2×C4×Dic17—41no—
115C2×C4×Dic17—41no—
116C2×C4×Dic17—41no—
117C2×C4×Dic17D414yes—
118C17×#95—22no—
119C17×#95—22no—
120C17×#95—22no—
121C17×#95—41no—
122C17×#95—41no—
123#10587502—22no—
124#10587502—22no—
125#10587502—22no—
126#10587502—22no—
127#10587502—22no—
128#10587502—22no—
129#10587502—22no—
130#10587502—22no—
131#10587502—22no—
132#10587502—22no—
133#10587502—41no—
134#10587502—41no—
135#10587502—41no—
136#10587502C2×C414yes—
137#10587502C2×C414yes—
138C24×C17C2411yescharacteristic
139C23×D17—21no—
140C23×D17—21no—
141C23×D17—21no—
142C23×D17—21no—
143C23×D17—21no—
144C23×D17—21no—
145C23×D17—21no—
146C23×D17—21no—
147C23×D17—21no—
148C23×D17—21no—
149C23×D17—21no—
150C23×D17—21no—
151C23×D17C22×C412yes—
152C23×D17C2×Q812yes—
153C23×D17#4112yes—
154C22×C4×C17—21no—
155C22×C4×C17—21no—
156C22×C4×C17—21no—
157C22×C4×C17—21no—
158C22×C4×C17—21no—
159C22×C4×C17—21no—
160C22×C4×C17—21no—
161C22×C4×C17—21no—
162C22×C4×C17—21no—
163C22×C4×C17—21no—
164C22×C4×C17—21no—
165C22×C4×C17—21no—
166C22×C4×C17—21no—
167C22×C4×C17—21no—
168C22×C4×C17—21no—
169C22×C4×C17—21no—
170C22×C4×C17—21no—
171C22×C4×C17—21no—
172C22×C4×C17—21no—
173C22×C4×C17—21no—
174C22×C4×C17—21no—
175C22×C4×C17—21no—
176C22×C4×C17—21no—
177C22×C4×C17—21no—
178C22×C4×C17—21no—
179C22×C4×C17—21no—
180C22×C4×C17—21no—
181C22×C4×C17—21no—
182C22×C4×C17—21no—
183C22×C4×C17—21no—
184C22×C4×C17—21no—
185C22×C4×C17—21no—
186C22×C4×C17—21no—
187C22×C4×C17—21no—
188C22×C4×C17—21no—
189C22×C4×C17—21no—
190C22×C4×C17—21no—
191C22×C4×C17—21no—
192C22×C4×C17—21no—
193C22×C4×C17—21no—
194C22×C4×C17—21no—
195C22×C4×C17C22×C412yes—
196C22×C4×C17C22×C412yes—
197C22×C4×C17C22×C412yes—
198C22×C4×C17C2×D412yes—
199C22×C4×C17C2×Q812yes—
200C22×C4×C17#4112yes—
201C22×C4×C17#4112yes—
202C22×C4×C17#4112yes—
203C22×Dic17—21no—
204C22×Dic17—21no—
205C22×Dic17—21no—
206C22×Dic17—21no—
207C22×Dic17—21no—
208C22×Dic17—21no—
209C22×Dic17—21no—
210C22×Dic17—21no—
211C22×Dic17—21no—
212C22×Dic17—21no—
213C22×Dic17—21no—
214C22×Dic17—21no—
215C22×Dic17—21no—
216C22×Dic17—21no—
217C22×Dic17—21no—
218C22×Dic17—21no—
219C22×Dic17—21no—
220C22×Dic17—21no—
221C22×Dic17—21no—
222C22×Dic17—21no—
223C22×Dic17—21no—
224C22×Dic17—21no—
225C22×Dic17—21no—
226C22×Dic17—21no—
227C22×Dic17—21no—
228C22×Dic17—21no—
229C22×Dic17—21no—
230C22×Dic17—21no—
231C22×Dic17—21no—
232C22×Dic17—21no—
233C22×Dic17—21no—
234C22×Dic17—21no—
235C22×Dic17—21no—
236C22×Dic17—21no—
237C22×Dic17—21no—
238C22×Dic17—21no—
239C22×Dic17—21no—
240C22×Dic17—21no—
241C22×Dic17—21no—
242C22×Dic17C22×C412yes—
243C22×Dic17C22×C412yes—
244C22×Dic17C22×C412yes—
245C22×Dic17C2×D412yes—
246C22×Dic17C2×D412yes—
247C22×Dic17C2×Q812yes—
248C22×Dic17#4112yes—
249C22×Dic17#4112yes—
250C22×Dic17#4112yes—
251C22×Dic17#4112yes—
252C2×C4×D17—28no—
253C2×C4×D17—44no—
254C2×C4×D17—44no—
255C2×C4×D17—44no—
256C2×C4×D17—44no—
257C2×C4×D17—44no—
258C2×C4×D17—44no—
259C4⋊C4×C17—44no—
260C4⋊C4×C17—44no—
261#63227—28no—
262#63227—28no—
263#63227—28no—
264#63227—44no—
265#63227—44no—
266#63227—44no—
267C4⋊Dic17—44no—
268#63225—28no—
269C4×Dic17—44no—
270C4×Dic17—44no—
271C4×Dic17—44no—
272C4×Dic17—44no—
273#14075—171nomaximal, Sylow
274C23×C17C23×C411yescharacteristic
275C23×C17C22×D411yescharacteristic
276C23×C17C22×Q811yescharacteristic
277C23×C17C2×#4111yescharacteristic
278C23×C17C2×#4111yescharacteristic
279C23×C17C2×#4111yescharacteristic
280C23×C17C2×#4111yescharacteristic
281C23×C17C2×#4111yescharacteristic
282C23×C17C2×#4111yescharacteristic
283C23×C17C2×#4111yescharacteristic
284C23×C17C2×#4111yescharacteristic
285C23×C17H(5,𝔽2)11yescharacteristic
286C23×C17H(5,𝔽2)11yescharacteristic
287C23×C17H(5,𝔽2)11yescharacteristic
288C23×C17H(5,𝔽2)11yescharacteristic
289C22×D17—22no—
290C22×D17—22no—
291C22×D17—22no—
292C22×D17—22no—
293C22×D17—22no—
294C22×D17—22no—
295C22×D17—22no—
296C22×D17—22no—
297C22×D17—22no—
298C22×D17—22no—
299C22×D17—22no—
300C22×D17—22no—
301C22×D17—22no—
302C22×D17—22no—
303C22×D17—22no—
304C22×D17—22no—
305C22×D17—22no—
306C22×D17—22no—
307C22×D17—41no—
308C22×D17—41no—
309C22×D17—41no—
310C22×D17—41no—
311C22×D17—41no—
312C22×D17—41no—
313C22×D17—41no—
314C22×D17—41no—
315C22×D17—41no—
316C22×D17—41no—
317C22×D17—41no—
318C22×D17—41no—
319C22×D17—41no—
320C22×D17—41no—
321C22×D17—41no—
322C22×D17—41no—
323C22×D17C4×Q814yes—
324C2×C4×C17—22no—
325C2×C4×C17—22no—
326C2×C4×C17—22no—
327C2×C4×C17—22no—
328C2×C4×C17—22no—
329C2×C4×C17—22no—
330C2×C4×C17—22no—
331C2×C4×C17—22no—
332C2×C4×C17—22no—
333C2×C4×C17—22no—
334C2×C4×C17—22no—
335C2×C4×C17—22no—
336C2×C4×C17—22no—
337C2×C4×C17—22no—
338C2×C4×C17—22no—
339C2×C4×C17—22no—
340C2×C4×C17—22no—
341C2×C4×C17—22no—
342C2×C4×C17—22no—
343C2×C4×C17—22no—
344C2×C4×C17—22no—
345C2×C4×C17—41no—
346C2×C4×C17—41no—
347C2×C4×C17—41no—
348C2×C4×C17—41no—
349C2×C4×C17—41no—
350C2×C4×C17—41no—
351C2×C4×C17—41no—
352C2×C4×C17—41no—
353C2×C4×C17—41no—
354C2×C4×C17—41no—
355C2×C4×C17—41no—
356C2×C4×C17—41no—
357C2×C4×C17—41no—
358C2×C4×C17—41no—
359C2×C4×C17—41no—
360C2×C4×C17—41no—
361C2×C4×C17—41no—
362C2×C4×C17—41no—
363C2×C4×C17—41no—
364C2×C4×C17—41no—
365C2×C4×C17—41no—
366C2×C4×C17—41no—
367C2×C4×C17—41no—
368C2×C4×C17—41no—
369C2×C4×C17—41no—
370C2×C4×C17—41no—
371C2×C4×C17—41no—
372C2×C4×C17#11714yes—
373C2×Dic17—22no—
374C2×Dic17—22no—
375C2×Dic17—22no—
376C2×Dic17—22no—
377C2×Dic17—22no—
378C2×Dic17—22no—
379C2×Dic17—22no—
380C2×Dic17—22no—
381C2×Dic17—22no—
382C2×Dic17—22no—
383C2×Dic17—22no—
384C2×Dic17—22no—
385C2×Dic17—22no—
386C2×Dic17—22no—
387C2×Dic17—22no—
388C2×Dic17—22no—
389C2×Dic17—22no—
390C2×Dic17—22no—
391C2×Dic17—22no—
392C2×Dic17—22no—
393C2×Dic17—22no—
394C2×Dic17—22no—
395C2×Dic17—22no—
396C2×Dic17—22no—
397C2×Dic17—41no—
398C2×Dic17—41no—
399C2×Dic17—41no—
400C2×Dic17—41no—
401C2×Dic17—41no—
402C2×Dic17—41no—
403C2×Dic17—41no—
404C2×Dic17—41no—
405C2×Dic17—41no—
406C2×Dic17—41no—
407C2×Dic17—41no—
408C2×Dic17—41no—
409C2×Dic17—41no—
410C2×Dic17—41no—
411C2×Dic17—41no—
412C2×Dic17—41no—
413C2×Dic17—41no—
414C2×Dic17—41no—
415C2×Dic17—41no—
416C2×Dic17—41no—
417C2×Dic17—41no—
418C2×Dic17—41no—
419C2×Dic17—41no—
420C2×Dic17C4×D414yes—
421C2×Dic17C22⋊Q814yes—
422C4×D17—416no—
423C2×#387—171no—
424C2×#385—171no—
425C2×C4×C22⋊C4—171no—
426#1443—171no—
427#1441D1711yescharacteristic, complemented
428#1439—171no—
429#1439—171no—
430#1437—171no—
431#1437—171no—
432#1436—171no—
433#1436—171no—
434C4⋊#95—171no—
435#1434—171no—
436C22⋊#95—171no—
437C4×#95—171no—
438C22×C17C2×#11711yescharacteristic
439C22×C17C2×C4×D411yescharacteristic
440C22×C17C2×C4×Q811yescharacteristic
441C22×C17C4×#4111yescharacteristic
442C22×C17C4×#4111yescharacteristic
443C22×C17#51811yescharacteristic
444C22×C17#51811yescharacteristic
445C22×C17C2×C22⋊Q811yescharacteristic
446C22×C17#52511yescharacteristic
447C22×C17#52911yescharacteristic
448C22×C17#52911yescharacteristic
449C22×C17#52911yescharacteristic
450C22×C17#53211yescharacteristic
451C22×C17#53211yescharacteristic
452C22×C17#53311yescharacteristic
453C22×C17#53411yescharacteristic
454C22×C17#53511yescharacteristic
455C22×C17#53811yescharacteristic
456C22×C17#53811yescharacteristic
457C22×C17#55111yescharacteristic
458C22×C17#55111yescharacteristic
459C22×C17#55111yescharacteristic
460C22×C17#55111yescharacteristic
461C22×C17#55111yescharacteristic
462C22×C17#55311yescharacteristic
463C22×C17#55311yescharacteristic
464C22×C17#55311yescharacteristic
465C22×C17#55311yescharacteristic
466C22×C17#55311yescharacteristic
467C22×C17#55311yescharacteristic
468C22×C17#55411yescharacteristic
469C22×C17#55411yescharacteristic
470C22×C17#55411yescharacteristic
471C22×C17#55411yescharacteristic
472C22×C17#55911yescharacteristic
473C2×D17—24no—
474C2×D17—24no—
475C2×D17—24no—
476C2×D17—42no—
477C2×D17—42no—
478C2×D17—42no—
479C2×D17—42no—
480C2×D17—42no—
481C2×D17—42no—
482C2×D17—42no—
483C2×D17—42no—
484C2×D17—42no—
485C2×D17—42no—
486C2×D17—42no—
487C2×D17—42no—
488C4×C17—24no—
489C4×C17—42no—
490C4×C17—42no—
491C4×C17—42no—
492C4×C17—42no—
493C4×C17—42no—
494C4×C17—81no—
495Dic17—24no—
496Dic17—24no—
497Dic17—42no—
498Dic17—42no—
499Dic17—42no—
500Dic17—42no—
501Dic17—81no—
502C24×C4—171no—
503C22×C4⋊C4—171no—
504C22×C4⋊C4—171no—
505C22×C4⋊C4C2×D1711yescharacteristic
506C22×C4⋊C4C2×D1711yescharacteristic
507C22×C22⋊C4—171no—
508C22×C22⋊C4—171no—
509C22×C22⋊C4—171no—
510C22×C22⋊C4—171no—
511C22×C22⋊C4—171no—
512C22×C22⋊C4—171no—
513C22×C42—171no—
514C22×C42—171no—
515C22×C42—171no—
516C22×C42—171no—
517#387—344no—
518#385—178no—
519C4×C22⋊C4—344no—
520C2×#95—171no—
521C2×#95—171no—
522C2×#95—171no—
523C2×#95—171no—
524C2×#95—171no—
525C2×#95—171no—
526C2×#95—171no—
527C2×#95—171no—
528C2×#95—171no—
529C2×#95—171no—
530C2×#95—171no—
531C2×#95—171no—
532C2×#95—171no—
533C2×#95—171no—
534C2×#95—171no—
535C2×#95C2×D1711yescharacteristic
536C2×#95C2×D1711yescharacteristic
537C2×#95C2×D1711yescharacteristic
538C2×#95C2×D1711yescharacteristic
539C2×#95C2×D1711yescharacteristic
540C2×C17#229311yescharacteristic
541C2×C17C4×C22⋊Q811yescharacteristic
542C2×C17#232111yescharacteristic
543C2×C17#234511yescharacteristic
544C2×C17#235311yescharacteristic
545C2×C17#236811yescharacteristic
546C2×C17#237411yescharacteristic
547C2×C17#256411yescharacteristic
548C2×C17#256611yescharacteristic
549C2×C17#257611yescharacteristic
550C2×C17#257811yescharacteristic
551C2×C17#258711yescharacteristic
552C2×C17#258911yescharacteristic
553C2×C17#260211yescharacteristic
554C2×C17#260311yescharacteristic
555D17—44no—
556C25—171no—
557C23×C4—171no—
558C23×C4—171no—
559C23×C4—171no—
560C23×C4—171no—
561C23×C4—171no—
562C23×C4—171no—
563C23×C4—174no—
564C23×C4—171no—
565C23×C4—342no—
566C23×C4—342no—
567C23×C4—681no—
568C23×C4—681no—
569C23×C4—681no—
570C23×C4—681no—
571C23×C4C22×D1711yescharacteristic
572C23×C4C22×D1711yescharacteristic
573C23×C4C22×D1711yescharacteristic
574C23×C4C22×D1711yescharacteristic
575C23×C4C22×D1711yescharacteristic
576C23×C4C22×D1711yescharacteristic
577C23×C4C22×D1711yescharacteristic
578C2×C4⋊C4—22no—
579C2×C4⋊C4—41no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4—41no—
583C2×C4⋊C4—174no—
584C2×C4⋊C4—342no—
585C2×C4⋊C4—342no—
586C2×C4⋊C4—342no—
587C2×C4⋊C4—342no—
588C2×C4⋊C4—681no—
589C2×C4⋊C4C4×D1714yes—
590C2×C22⋊C4—174no—
591C2×C22⋊C4—174no—
592C2×C22⋊C4—174no—
593C2×C22⋊C4—342no—
594C2×C22⋊C4—342no—
595C2×C22⋊C4—342no—
596C2×C22⋊C4—342no—
597C2×C22⋊C4—342no—
598C2×C22⋊C4—342no—
599C2×C22⋊C4—342no—
600C2×C22⋊C4—342no—
601C2×C22⋊C4—342no—
602C2×C22⋊C4—342no—
603C2×C22⋊C4—342no—
604C2×C22⋊C4—681no—
605C2×C22⋊C4—681no—
606C2×C22⋊C4—681no—
607C2×C22⋊C4—681no—
608C2×C42—174no—
609C2×C42—342no—
610C2×C42—342no—
611C2×C42—342no—
612C2×C42—342no—
613C2×C42—342no—
614C2×C42—681no—
615C2×C42—681no—
616C2×C42—681no—
617C2×C42—681no—
618C2×C42—681no—
619C2×C42—681no—
620#95—22no—
621#95—22no—
622#95—22no—
623#95—41no—
624#95—41no—
625#95—174no—
626#95—174no—
627#95—342no—
628#95—342no—
629#95—342no—
630#95—342no—
631#95—342no—
632#95—342no—
633#95—342no—
634#95—342no—
635#95—342no—
636#95—342no—
637#95—681no—
638#95—681no—
639#95—681no—
640C17#1407511yescharacteristic, complemented, Sylow
641C24—172no—
642C24—172no—
643C24—172no—
644C24—341no—
645C24—341no—
646C24—341no—
647C24—341no—
648C24—341no—
649C24—341no—
650C24—341no—
651C24—341no—
652C24—341no—
653C24—341no—
654C24—341no—
655C24—341no—
656C24C23×D1711yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—172no—
699C22×C4—172no—
700C22×C4—172no—
701C22×C4—172no—
702C22×C4—172no—
703C22×C4—172no—
704C22×C4—172no—
705C22×C4—172no—
706C22×C4—172no—
707C22×C4—172no—
708C22×C4—348no—
709C22×C4—341no—
710C22×C4—341no—
711C22×C4—341no—
712C22×C4—341no—
713C22×C4—341no—
714C22×C4—341no—
715C22×C4—341no—
716C22×C4—341no—
717C22×C4—341no—
718C22×C4—341no—
719C22×C4—341no—
720C22×C4—341no—
721C22×C4—341no—
722C22×C4—341no—
723C22×C4—341no—
724C22×C4—341no—
725C22×C4—341no—
726C22×C4—341no—
727C22×C4—341no—
728C22×C4—341no—
729C22×C4—341no—
730C22×C4—341no—
731C22×C4—341no—
732C22×C4—341no—
733C22×C4—341no—
734C22×C4—341no—
735C22×C4—341no—
736C22×C4—341no—
737C22×C4—341no—
738C22×C4—341no—
739C22×C4—341no—
740C22×C4—341no—
741C22×C4—341no—
742C22×C4—341no—
743C22×C4—341no—
744C22×C4—341no—
745C22×C4—341no—
746C22×C4—341no—
747C22×C4—341no—
748C22×C4—684no—
749C22×C4—684no—
750C22×C4—684no—
751C22×C4—684no—
752C22×C4—684no—
753C22×C4—684no—
754C22×C4C2×C4×D1712yes—
755C22×C4C2×C4×D1712yes—
756C22×C4C2×C4×D1712yes—
757C22×C4D4×D1712yes—
758C22×C4#6325412yes—
759C22×C4Q8×D1712yes—
760C22×C4#6325612yes—
761C22×C4#6325612yes—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—348no—
765C4⋊C4—684no—
766C22⋊C4—348no—
767C22⋊C4—348no—
768C22⋊C4—348no—
769C22⋊C4—684no—
770C22⋊C4—684no—
771C22⋊C4—684no—
772C42—684no—
773C42—684no—
774C42—684no—
775C42—684no—
776C23—174no—
777C23—342no—
778C23—342no—
779C23—342no—
780C23—342no—
781C23—342no—
782C23—342no—
783C23—342no—
784C23—342no—
785C23—342no—
786C23—342no—
787C23—342no—
788C23—342no—
789C23—342no—
790C23—342no—
791C23—342no—
792C23—342no—
793C23—342no—
794C23—342no—
795C23—681no—
796C23—681no—
797C23—681no—
798C23—681no—
799C23—681no—
800C23—681no—
801C23—681no—
802C23—681no—
803C23—681no—
804C23—681no—
805C23—681no—
806C23—681no—
807C23—681no—
808C23—681no—
809C23—681no—
810C23—681no—
811C23C22×C4×D1711yescharacteristic
812C23C2×D4×D1711yescharacteristic
813C23C2×#6325411yescharacteristic
814C23#1058769111yescharacteristic
815C23#1058769111yescharacteristic
816C23#1058769111yescharacteristic
817C23C2×Q8×D1711yescharacteristic
818C23C2×#6325611yescharacteristic
819C23C2×#6325611yescharacteristic
820C23#41×D1711yescharacteristic
821C23#41×D1711yescharacteristic
822C23#41×D1711yescharacteristic
823C23#41×D1711yescharacteristic
824C23#41×D1711yescharacteristic
825C23#1058769611yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—174no—
875C2×C4—174no—
876C2×C4—342no—
877C2×C4—342no—
878C2×C4—342no—
879C2×C4—342no—
880C2×C4—342no—
881C2×C4—342no—
882C2×C4—342no—
883C2×C4—342no—
884C2×C4—342no—
885C2×C4—342no—
886C2×C4—342no—
887C2×C4—342no—
888C2×C4—342no—
889C2×C4—342no—
890C2×C4—342no—
891C2×C4—342no—
892C2×C4—342no—
893C2×C4—342no—
894C2×C4—342no—
895C2×C4—342no—
896C2×C4—342no—
897C2×C4—342no—
898C2×C4—342no—
899C2×C4—342no—
900C2×C4—6816no—
901C2×C4—681no—
902C2×C4—681no—
903C2×C4—681no—
904C2×C4—681no—
905C2×C4—681no—
906C2×C4—681no—
907C2×C4—681no—
908C2×C4—681no—
909C2×C4—681no—
910C2×C4—681no—
911C2×C4—681no—
912C2×C4—681no—
913C2×C4—681no—
914C2×C4—681no—
915C2×C4—681no—
916C2×C4—681no—
917C2×C4—681no—
918C2×C4—681no—
919C2×C4—681no—
920C2×C4—681no—
921C2×C4—681no—
922C2×C4—681no—
923C2×C4—681no—
924C2×C4#1058757814yes—
925C22—344no—
926C22—344no—
927C22—344no—
928C22—682no—
929C22—682no—
930C22—682no—
931C22—682no—
932C22—682no—
933C22—682no—
934C22—682no—
935C22—682no—
936C22—682no—
937C22—682no—
938C22—682no—
939C22—682no—
940C22C2×#1058757811yescharacteristic
941C22C4×D4×D1711yescharacteristic
942C22C4×Q8×D1711yescharacteristic
943C22#1176327711yescharacteristic
944C22C4×#6325611yescharacteristic
945C22#1176328111yescharacteristic
946C22#1176328211yescharacteristic
947C22C22⋊Q8×D1711yescharacteristic
948C22#1176331711yescharacteristic
949C22#1176334211yescharacteristic
950C22#1176334411yescharacteristic
951C22#1176334511yescharacteristic
952C22#1176335411yescharacteristic
953C22#1176336011yescharacteristic
954C22#1176336511yescharacteristic
955C22#1176336911yescharacteristic
956C22#1176337511yescharacteristic
957C22#1176339111yescharacteristic
958C22#1176339511yescharacteristic
959C22#1176348611yescharacteristic
960C22#1176348611yescharacteristic
961C22#1176348611yescharacteristic
962C22#1176348611yescharacteristic
963C22#1176348911yescharacteristic
964C22#1176350211yescharacteristic
965C22#1176350211yescharacteristic
966C22#1176350611yescharacteristic
967C22#1176351011yescharacteristic
968C22#1176351211yescharacteristic
969C22#1176351211yescharacteristic
970C22#1176351311yescharacteristic
971C22#1176351711yescharacteristic
972C22#1176352011yescharacteristic
973C22#1176352011yescharacteristic
974C22#1176354311yescharacteristic
975C4—24no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—81no—
982C4—344no—
983C4—344no—
984C4—682no—
985C4—682no—
986C4—682no—
987C4—682no—
988C4—1361no—
989C2—684no—
990C2#1453124211yescharacteristic
991C2#1453131811yescharacteristic
992C2#1453144011yescharacteristic
993C2#1453166011yescharacteristic
994C2#1453172611yescharacteristic
995C2#1453186311yescharacteristic
996C2#1453191611yescharacteristic
997C2#1453396511yescharacteristic
998C2#1453397911yescharacteristic
999C2#1453408111yescharacteristic
1000C2#1453411311yescharacteristic
1001C2#1453420611yescharacteristic
1002C2#1453423811yescharacteristic
1003C2#1453439911yescharacteristic
1004C2#1453441211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1441C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenter#1441D17
hypocenterC17#14075
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
1. C2×#11762690C2semidirect
4. #14527045C2semidirect
9. #14527018C2semidirect
10. #14527015C2semidirect
11. #14527013C2semidirect
12. #14527008C2semidirect
14. #95×Dic17C2semidirect
15. C17×#1441C2semidirect
30. #11762680C4semidirect
427. #1441D17semidirect
640. C17#14075semidirect

Maximal subgroups

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

subgroupindex
C2×#117626902
C2×#117626802
C2×#117626562
#145270452
#145270302
#145270262
#145270202
#145270182
#145270152
#145270132
#145270082
#145270052
#95×Dic172
C17×#14412
#1407517