Finite Group Databasebeta

← #16957270

Subgroups — #16957270

Order 4352.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762701C211yesmaximal, characteristic
2C2×#11762683C211yesmaximal, characteristic
3C2×#11762671C211yesmaximal, characteristic
4C2×#11762660C211yesmaximal, characteristic, complemented
5C2×C4×#63227C211yesmaximal, characteristic
6#14527051C211yesmaximal, characteristic, complemented
7#14527039C211yesmaximal, characteristic, complemented
8#14527032C211yesmaximal, characteristic
9#14527028C211yesmaximal, characteristic
10#14527020C211yesmaximal, characteristic
11#14527018C211yesmaximal, characteristic, complemented
12#14527018C211yesmaximal, characteristic, complemented
13#14527018C211yesmaximal, characteristic, complemented
14#14527017C211yesmaximal, characteristic, complemented
15C17×#1434C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×C4×Dic17C2211yescharacteristic
28C22×C4×Dic17C2211yescharacteristic
29C22×C4×Dic17C2211yescharacteristic
30#11762701—24no—
31#11762683C418yescomplemented
32#11762671—24no—
33#11762660—24no—
34C4×#63227—24no—
35C2×#10587502C2211yescharacteristic
36C2×#10587502C2211yescharacteristic
37C2×#10587502C2211yescharacteristic
38C2×#10587502C2211yescharacteristic
39C2×#10587502C2211yescharacteristic
40C2×#10587502C2211yescharacteristic
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C22×C42×C17C2211yescharacteristic
50C2×C17×#95C2211yescharacteristic
51C2×C17×#95C2211yescharacteristic
52C2×C17×#95C2211yescharacteristic
53C2×C17×#95C2211yescharacteristic
54C2×C17×#95C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C24×D17C2311yescharacteristic
57C23×C4×C17C2311yescharacteristic
58C23×C4×C17C2311yescharacteristic
59C23×C4×C17C2311yescharacteristic
60C23×C4×C17C2311yescharacteristic
61C23×C4×C17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×Dic17C2311yescharacteristic
65C23×Dic17C2311yescharacteristic
66C23×Dic17C2311yescharacteristic
67C23×Dic17C2311yescharacteristic
68C23×Dic17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C22×C4×D17—22no—
72C22×C4×D17—22no—
73C22×C4×D17—22no—
74C22×C4×D17—22no—
75C22×C4×D17—41no—
76C22×C4×D17—41no—
77C22×C4×D17C2×C414yes—
78C2×C42×C17—22no—
79C2×C42×C17—22no—
80C2×C42×C17—41no—
81C2×#63227—22no—
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—22no—
94C2×#63227—41no—
95C2×#63227—41no—
96C2×#63227C2×C414yes—
97C2×#63227C2×C414yes—
98C2×#63227D414yes—
99C2×C4⋊Dic17—22no—
100C2×C4⋊Dic17—22no—
101C2×C4⋊Dic17—22no—
102C2×C4⋊Dic17—41no—
103C2×C4⋊Dic17—41no—
104C2×C4⋊Dic17C2×C414yes—
105C2×#63225—22no—
106C2×#63225—22no—
107C2×#63225—22no—
108C2×#63225—22no—
109C2×#63225—22no—
110C2×#63225C2×C414yes—
111C2×C4×Dic17—22no—
112C2×C4×Dic17—22no—
113C2×C4×Dic17—22no—
114C2×C4×Dic17—22no—
115C2×C4×Dic17—22no—
116C2×C4×Dic17—22no—
117C2×C4×Dic17—22no—
118C2×C4×Dic17—41no—
119C2×C4×Dic17—41no—
120C17×#95—22no—
121C17×#95—22no—
122C17×#95—22no—
123C17×#95—41no—
124C17×#95C2×C414yes—
125C17×#95D414yes—
126#10587502—22no—
127#10587502—22no—
128#10587502—22no—
129#10587502—22no—
130#10587502—22no—
131#10587502—22no—
132#10587502—22no—
133#10587502—22no—
134#10587502—22no—
135#10587502—22no—
136#10587502—22no—
137#10587502—41no—
138#10587502—41no—
139#10587502C2×C414yes—
140C24×C17C2411yescharacteristic
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×D17—21no—
152C23×D17—21no—
153C23×D17C22×C412yes—
154C23×D17C2×D412yes—
155C23×D17#4112yes—
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×C17—21no—
196C22×C4×C17C22×C412yes—
197C22×C4×C17C22×C412yes—
198C22×C4×C17C22×C412yes—
199C22×C4×C17C2×D412yes—
200C22×C4×C17C2×D412yes—
201C22×C4×C17C2×D412yes—
202C22×C4×C17C2×D412yes—
203C22×C4×C17#4112yes—
204C22×C4×C17#4112yes—
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×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17—21no—
245C22×Dic17C22×C412yes—
246C22×Dic17C22×C412yes—
247C22×Dic17C22×C412yes—
248C22×Dic17C2×D412yes—
249C22×Dic17#4112yes—
250C22×Dic17#4112yes—
251C22×Dic17#4112yes—
252C22×Dic17#4112yes—
253C22×Dic17#4112yes—
254C2×C4×D17—28no—
255C2×C4×D17—28no—
256C2×C4×D17—44no—
257C2×C4×D17—44no—
258C2×C4×D17—44no—
259C2×C4×D17—44no—
260C2×C4×D17—44no—
261C42×C17—44no—
262#63227—28no—
263#63227—28no—
264#63227—28no—
265#63227—28no—
266#63227—44no—
267#63227—44no—
268C4⋊Dic17—44no—
269C4⋊Dic17—44no—
270#63225—28no—
271#63225—28no—
272C4×Dic17—28no—
273C4×Dic17—44no—
274C4×Dic17—44no—
275#13983—171nomaximal, Sylow
276C23×C17C23×C411yescharacteristic
277C23×C17C22×D411yescharacteristic
278C23×C17C22×D411yescharacteristic
279C23×C17C2×#4111yescharacteristic
280C23×C17C2×#4111yescharacteristic
281C23×C17C2×#4111yescharacteristic
282C23×C17C2×#4111yescharacteristic
283C23×C17C2×#4111yescharacteristic
284C23×C17C2×#4111yescharacteristic
285C23×C17C2×#4111yescharacteristic
286C23×C17C2×#4111yescharacteristic
287C23×C17H(5,𝔽2)11yescharacteristic
288C23×C17H(5,𝔽2)11yescharacteristic
289C23×C172−1+411yescharacteristic
290C23×C172−1+411yescharacteristic
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—22no—
308C22×D17—22no—
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×D17—41no—
324C22×D17—41no—
325C22×D17C4×D414yes—
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—22no—
346C2×C4×C17—22no—
347C2×C4×C17—22no—
348C2×C4×C17—22no—
349C2×C4×C17—22no—
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—41no—
373C2×C4×C17—41no—
374C2×C4×C17C4×D414yes—
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—41no—
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×Dic17—41no—
421C2×Dic17—41no—
422C2×Dic17#11714yes—
423C2×Dic17#12314yes—
424C4×D17—416no—
425C2×#388—171no—
426C2×#385—171no—
427C2×#381—171no—
428C2×C4×C4⋊C4—171no—
429C2×C4×C22⋊C4—171no—
430#1445—171no—
431#1442—171no—
432#1440—171no—
433#1439—171no—
434#1437—171no—
435#1436—171no—
436#1436—171no—
437#1436—171no—
438#1436—171no—
439#1434D1711yescharacteristic, complemented
440C22×C17C2×#11711yescharacteristic
441C22×C17C2×C4×D411yescharacteristic
442C22×C17C2×C4×D411yescharacteristic
443C22×C17C4×#4111yescharacteristic
444C22×C17C4×#4111yescharacteristic
445C22×C17#51811yescharacteristic
446C22×C17#51911yescharacteristic
447C22×C17C2×#12311yescharacteristic
448C22×C17#52511yescharacteristic
449C22×C17#52511yescharacteristic
450C22×C17#52511yescharacteristic
451C22×C17#52911yescharacteristic
452C22×C17#52911yescharacteristic
453C22×C17#52911yescharacteristic
454C22×C17#52911yescharacteristic
455C22×C17#53911yescharacteristic
456C22×C17#53911yescharacteristic
457C22×C17#54211yescharacteristic
458C22×C17#54211yescharacteristic
459C22×C17D4211yescharacteristic
460C22×C17#54611yescharacteristic
461C22×C17#54611yescharacteristic
462C22×C17#54711yescharacteristic
463C22×C17#54711yescharacteristic
464C22×C17#54711yescharacteristic
465C22×C17#54811yescharacteristic
466C22×C17#55111yescharacteristic
467C22×C17#55211yescharacteristic
468C22×C17#55211yescharacteristic
469C22×C17#55211yescharacteristic
470C22×C17#55311yescharacteristic
471C22×C17#55311yescharacteristic
472C22×C17#55611yescharacteristic
473C22×C17#55911yescharacteristic
474C22×C17#55911yescharacteristic
475C2×D17—24no—
476C2×D17—24no—
477C2×D17—24no—
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—
488C2×D17—42no—
489C2×D17—42no—
490C4×C17—24no—
491C4×C17—42no—
492C4×C17—42no—
493C4×C17—42no—
494C4×C17—42no—
495C4×C17—42no—
496C4×C17—42no—
497Dic17—24no—
498Dic17—24no—
499Dic17—42no—
500Dic17—42no—
501Dic17—42no—
502Dic17—81no—
503Dic17—81no—
504C24×C4—171no—
505C22×C4⋊C4—171no—
506C22×C4⋊C4—171no—
507C22×C4⋊C4—171no—
508C22×C4⋊C4—171no—
509C22×C22⋊C4—171no—
510C22×C22⋊C4—171no—
511C22×C22⋊C4—171no—
512C22×C22⋊C4—171no—
513C22×C22⋊C4—171no—
514C22×C22⋊C4—171no—
515C22×C42—171no—
516C22×C42—171no—
517C22×C42—171no—
518C22×C42C2×D1711yescharacteristic
519#388—344no—
520#385—178no—
521#381—344no—
522C4×C4⋊C4—344no—
523C4×C22⋊C4—344no—
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×#95—171no—
536C2×#95—171no—
537C2×#95—171no—
538C2×#95C2×D1711yescharacteristic
539C2×#95C2×D1711yescharacteristic
540C2×#95C2×D1711yescharacteristic
541C2×#95C2×D1711yescharacteristic
542C2×#95C2×D1711yescharacteristic
543C2×#95C2×D1711yescharacteristic
544C2×C17#229011yescharacteristic
545C2×C17C4×#12311yescharacteristic
546C2×C17#233211yescharacteristic
547C2×C17#234411yescharacteristic
548C2×C17#235711yescharacteristic
549C2×C17#235811yescharacteristic
550C2×C17#236211yescharacteristic
551C2×C17#244311yescharacteristic
552C2×C17#244711yescharacteristic
553C2×C17#245511yescharacteristic
554C2×C17#245811yescharacteristic
555C2×C17#246811yescharacteristic
556C2×C17#247011yescharacteristic
557C2×C17#257311yescharacteristic
558C2×C17#257511yescharacteristic
559D17—44no—
560C25—171no—
561C23×C4—171no—
562C23×C4—171no—
563C23×C4—171no—
564C23×C4—171no—
565C23×C4—171no—
566C23×C4—174no—
567C23×C4—171no—
568C23×C4—171no—
569C23×C4—342no—
570C23×C4—342no—
571C23×C4—342no—
572C23×C4—342no—
573C23×C4—681no—
574C23×C4—681no—
575C23×C4C22×D1711yescharacteristic
576C23×C4C22×D1711yescharacteristic
577C23×C4C22×D1711yescharacteristic
578C23×C4C22×D1711yescharacteristic
579C23×C4C22×D1711yescharacteristic
580C23×C4C22×D1711yescharacteristic
581C23×C4C22×D1711yescharacteristic
582C2×C4⋊C4—174no—
583C2×C4⋊C4—174no—
584C2×C4⋊C4—342no—
585C2×C4⋊C4—342no—
586C2×C4⋊C4—342no—
587C2×C4⋊C4—342no—
588C2×C4⋊C4—342no—
589C2×C4⋊C4—342no—
590C2×C4⋊C4—342no—
591C2×C4⋊C4—342no—
592C2×C4⋊C4—681no—
593C2×C4⋊C4—681no—
594C2×C22⋊C4—174no—
595C2×C22⋊C4—174no—
596C2×C22⋊C4—174no—
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—342no—
605C2×C22⋊C4—342no—
606C2×C22⋊C4—342no—
607C2×C22⋊C4—342no—
608C2×C22⋊C4—342no—
609C2×C22⋊C4—342no—
610C2×C22⋊C4—681no—
611C2×C22⋊C4—681no—
612C2×C42—22no—
613C2×C42—22no—
614C2×C42—41no—
615C2×C42—342no—
616C2×C42—342no—
617C2×C42—342no—
618C2×C42—342no—
619C2×C42—342no—
620C2×C42—342no—
621C2×C42—342no—
622C2×C42—681no—
623C2×C42—681no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—41no—
628#95—174no—
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—342no—
638#95—342no—
639#95—342no—
640#95—681no—
641#95—681no—
642#95C4×D1714yes—
643#95D6814yes—
644C17#1398311yescharacteristic, complemented, Sylow
645C24—172no—
646C24—172no—
647C24—172no—
648C24—341no—
649C24—341no—
650C24—341no—
651C24—341no—
652C24—341no—
653C24—341no—
654C24—341no—
655C24—341no—
656C24—341no—
657C24—341no—
658C24—341no—
659C24—341no—
660C24C23×D1711yescharacteristic
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—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—172no—
702C22×C4—172no—
703C22×C4—172no—
704C22×C4—172no—
705C22×C4—172no—
706C22×C4—172no—
707C22×C4—172no—
708C22×C4—172no—
709C22×C4—172no—
710C22×C4—348no—
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—348no—
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—341no—
749C22×C4—341no—
750C22×C4—341no—
751C22×C4—341no—
752C22×C4—684no—
753C22×C4—684no—
754C22×C4—684no—
755C22×C4—684no—
756C22×C4—684no—
757C22×C4C2×C4×D1712yes—
758C22×C4C2×C4×D1712yes—
759C22×C4C2×C4×D1712yes—
760C22×C4C2×D6812yes—
761C22×C4C2×D6812yes—
762C22×C4C2×D6812yes—
763C22×C4#6325212yes—
764C22×C4D4×D1712yes—
765C22×C4#6325412yes—
766C4⋊C4—348no—
767C4⋊C4—348no—
768C4⋊C4—684no—
769C4⋊C4—684no—
770C22⋊C4—348no—
771C22⋊C4—348no—
772C22⋊C4—348no—
773C22⋊C4—348no—
774C22⋊C4—684no—
775C22⋊C4—684no—
776C42—44no—
777C42—348no—
778C42—684no—
779C42—684no—
780C23—174no—
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—342no—
796C23—342no—
797C23—342no—
798C23—342no—
799C23—681no—
800C23—681no—
801C23—681no—
802C23—681no—
803C23—681no—
804C23—681no—
805C23—681no—
806C23—681no—
807C23—681no—
808C23—681no—
809C23—681no—
810C23—681no—
811C23—681no—
812C23—681no—
813C23—681no—
814C23—681no—
815C23C22×C4×D1711yescharacteristic
816C23C22×D6811yescharacteristic
817C23C2×#6325211yescharacteristic
818C23C2×D4×D1711yescharacteristic
819C23C2×#6325411yescharacteristic
820C23#1058769111yescharacteristic
821C23#1058769411yescharacteristic
822C23#41×D1711yescharacteristic
823C23#41×D1711yescharacteristic
824C23#41×D1711yescharacteristic
825C23#41×D1711yescharacteristic
826C23#41×D1711yescharacteristic
827C23#41×D1711yescharacteristic
828C23#1058769611yescharacteristic
829C23#1058769711yescharacteristic
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—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
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—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—174no—
879C2×C4—174no—
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—342no—
901C2×C4—6816no—
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—681no—
925C2×C4—681no—
926C2×C4—681no—
927C2×C4—681no—
928C2×C4C4×D6814yes—
929C22—344no—
930C22—344no—
931C22—344no—
932C22—682no—
933C22—682no—
934C22—682no—
935C22—682no—
936C22—682no—
937C22—682no—
938C22—682no—
939C22—682no—
940C22—682no—
941C22—682no—
942C22—682no—
943C22—682no—
944C22#117×D1711yescharacteristic
945C22C4×D4×D1711yescharacteristic
946C22C2×C4×D6811yescharacteristic
947C22C4×#6325411yescharacteristic
948C22#1176327711yescharacteristic
949C22#1176328111yescharacteristic
950C22#1176328511yescharacteristic
951C22#123×D1711yescharacteristic
952C22#1176331911yescharacteristic
953C22#1176332111yescharacteristic
954C22#1176332111yescharacteristic
955C22#1176333711yescharacteristic
956C22#1176333711yescharacteristic
957C22#1176333811yescharacteristic
958C22#1176334211yescharacteristic
959C22#1176340011yescharacteristic
960C22#1176340711yescharacteristic
961C22#1176342711yescharacteristic
962C22#1176342911yescharacteristic
963C22D4×D6811yescharacteristic
964C22#1176344911yescharacteristic
965C22#1176345411yescharacteristic
966C22#1176345711yescharacteristic
967C22#1176346111yescharacteristic
968C22#1176346311yescharacteristic
969C22#1176347111yescharacteristic
970C22#1176348311yescharacteristic
971C22#1176349111yescharacteristic
972C22#1176349411yescharacteristic
973C22#1176349511yescharacteristic
974C22#1176350211yescharacteristic
975C22#1176351011yescharacteristic
976C22#1176352711yescharacteristic
977C22#1176354111yescharacteristic
978C22#1176354311yescharacteristic
979C4—24no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—344no—
987C4—344no—
988C4—682no—
989C4—682no—
990C4—682no—
991C4—1361no—
992C4—1361no—
993C2—684no—
994C2#1453122811yescharacteristic
995C2#1453131111yescharacteristic
996C2#1453153811yescharacteristic
997C2#1453165011yescharacteristic
998C2#1453175411yescharacteristic
999C2#1453176611yescharacteristic
1000C2#1453181311yescharacteristic
1001C2#1453252411yescharacteristic
1002C2#1453257011yescharacteristic
1003C2#1453266411yescharacteristic
1004C2#1453270411yescharacteristic
1005C2#1453285511yescharacteristic
1006C2#1453287811yescharacteristic
1007C2#1453404111yescharacteristic
1008C2#1453407111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1434C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenter#1434D17
hypocenterC17#13983
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
4. C2×#11762660C2semidirect
6. #14527051C2semidirect
7. #14527039C2semidirect
11. #14527018C2semidirect
12. #14527018C2semidirect
13. #14527018C2semidirect
14. #14527017C2semidirect
15. C17×#1434C2semidirect
31. #11762683C4semidirect
439. #1434D17semidirect
644. C17#13983semidirect

Maximal subgroups

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

subgroupindex
C2×#117627012
C2×#117626832
C2×#117626712
C2×#117626602
C2×C4×#632272
#145270512
#145270392
#145270322
#145270282
#145270202
#145270182
#145270172
C17×#14342
#1398317