Finite Group Databasebeta

← #16957997

Subgroups — #16957997

Order 4352.

1862 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11762680C211yesmaximal, characteristic
2C2×C4×#63227C211yesmaximal, characteristic
3C2×#95×D17C211yesmaximal, characteristic
4#14527052C211yesmaximal, characteristic, complemented
5#14527050C211yesmaximal, characteristic, complemented
6#14527045C211yesmaximal, characteristic, complemented
7#14527045C211yesmaximal, characteristic, complemented
8#14527017C211yesmaximal, characteristic, complemented
9#14527008C211yesmaximal, characteristic, complemented
10#14527008C211yesmaximal, characteristic, complemented
11#14527005C211yesmaximal, characteristic
12#14527005C211yesmaximal, characteristic
13#14527005C211yesmaximal, characteristic
14#14527005C211yesmaximal, characteristic
15C17×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D17C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63227C2211yescharacteristic
21C22×#63227C2211yescharacteristic
22C22×#63227C2211yescharacteristic
23C22×#63227C2211yescharacteristic
24C22×C4×Dic17C2211yescharacteristic
25#11762680C418yescomplemented
26C4×#63227—24no—
27C2×#10587502C2211yescharacteristic
28C2×#10587502C2211yescharacteristic
29C2×#10587502C2211yescharacteristic
30C2×#10587502C2211yescharacteristic
31C2×#10587502C2211yescharacteristic
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
46#95×D17—24no—
47C22×C4⋊C4×C17C2211yescharacteristic
48C22×C42×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—22no—
72C22×C4×D17—22no—
73C22×C4×D17—22no—
74C22×C4×D17—22no—
75C22×C4×D17—22no—
76C22×C4×D17—22no—
77C22×C4×D17—22no—
78C22×C4×D17—22no—
79C22×C4×D17—22no—
80C22×C4×D17—41no—
81C22×C4×D17—41no—
82C22×C4×D17—41no—
83C22×C4×D17—41no—
84C22×C4×D17—41no—
85C22×C4×D17—41no—
86C22×C4×D17—41no—
87C22×C4×D17—41no—
88C22×C4×D17C2×C414yes—
89C22×C4×D17D414yes—
90C2×C4⋊C4×C17—41no—
91C2×C4⋊C4×C17—41no—
92C2×C4⋊C4×C17C2×C414yescomplemented
93C2×C42×C17—22no—
94C2×C42×C17—41no—
95C2×C42×C17—41no—
96C2×#63227—22no—
97C2×#63227—22no—
98C2×#63227—22no—
99C2×#63227—22no—
100C2×#63227—22no—
101C2×#63227—22no—
102C2×#63227—22no—
103C2×#63227—22no—
104C2×#63227—22no—
105C2×#63227C2×C414yes—
106C2×#63227C2×C414yes—
107C2×#63227Q814yes—
108C2×#63225—41no—
109C2×#63225—41no—
110C2×#63225C2×C414yescomplemented
111C2×C4×Dic17—22no—
112C2×C4×Dic17—22no—
113C2×C4×Dic17—22no—
114C17×#95—22no—
115C17×#95—22no—
116C17×#95—22no—
117C17×#95—41no—
118C17×#95—41no—
119#10587502—22no—
120#10587502—22no—
121#10587502—22no—
122#10587502—22no—
123#10587502—22no—
124#10587502—22no—
125#10587502—22no—
126#10587502—22no—
127#10587502—22no—
128#10587502—41no—
129#10587502—41no—
130#10587502—41no—
131#10587502—41no—
132#10587502—41no—
133#10587502—41no—
134#10587502—41no—
135#10587502—41no—
136#10587502C2×C414yescomplemented
137#10587502C2×C414yescomplemented
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×D17C22×C412yes—
148C23×D17C2×D412yes—
149C23×D17C2×Q812yes—
150C23×D17#4112yes—
151C23×D17#4112yes—
152C23×D17#4112yes—
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×Dic17—21no—
243C22×Dic17—21no—
244C22×Dic17—21no—
245C22×Dic17—21no—
246C22×Dic17C22×C412yes—
247C22×Dic17C22×C412yes—
248C22×Dic17C22×C412yes—
249C22×Dic17C2×D412yes—
250C22×Dic17C2×Q812yes—
251C22×Dic17#4112yes—
252C2×C4×D17—28no—
253C2×C4×D17—28no—
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—
261C2×C4×D17—44no—
262C2×C4×D17—44no—
263C2×C4×D17—44no—
264C2×C4×D17—44no—
265C2×C4×D17—44no—
266C2×C4×D17—44no—
267C2×C4×D17—44no—
268C2×C4×D17—44no—
269C2×C4×D17—44no—
270C2×C4×D17—44no—
271C2×C4×D17—44no—
272C2×C4×D17—44no—
273C4⋊C4×C17—44no—
274C42×C17—44no—
275#63227—28no—
276#63227—28no—
277#63227—28no—
278#63227—44no—
279#63225—44no—
280C4×Dic17—44no—
281#14040—171nomaximal, Sylow
282C23×C17C23×C411yescharacteristic
283C23×C17C22×D411yescharacteristic
284C23×C17C22×Q811yescharacteristic
285C23×C17C2×#4111yescharacteristic
286C23×C17C2×#4111yescharacteristic
287C23×C17C2×#4111yescharacteristic
288C23×C17C2×#4111yescharacteristic
289C23×C17C2×#4111yescharacteristic
290C23×C17C2×#4111yescharacteristic
291C23×C17C2×#4111yescharacteristic
292C23×C17C2×#4111yescharacteristic
293C23×C17H(5,𝔽2)11yescharacteristic
294C23×C17H(5,𝔽2)11yescharacteristic
295C23×C17H(5,𝔽2)11yescharacteristic
296C23×C17H(5,𝔽2)11yescharacteristic
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—22no—
310C22×D17—22no—
311C22×D17—22no—
312C22×D17—22no—
313C22×D17—22no—
314C22×D17—22no—
315C22×D17—22no—
316C22×D17—22no—
317C22×D17—22no—
318C22×D17—22no—
319C22×D17—22no—
320C22×D17—22no—
321C22×D17—22no—
322C22×D17—22no—
323C22×D17—22no—
324C22×D17—22no—
325C22×D17#11714yes—
326C22×D17C4×D414yes—
327C22×D17C4×Q814yes—
328C22×D17C22⋊Q814yes—
329C22×D17#12314yes—
330C22×D17#12514yes—
331C22×D17#12614yes—
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—22no—
351C2×C4×C17—22no—
352C2×C4×C17—22no—
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×C17—41no—
375C2×C4×C17—41no—
376C2×C4×C17—41no—
377C2×C4×C17—41no—
378C2×C4×C17—41no—
379C2×C4×C17—41no—
380C2×C4×C17#12314yes—
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—22no—
398C2×Dic17—22no—
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—41no—
423C2×Dic17—41no—
424C2×Dic17—41no—
425C2×Dic17—41no—
426C2×Dic17—41no—
427C2×Dic17—41no—
428C2×Dic17—41no—
429C2×Dic17—41no—
430C4×D17—416no—
431C4×D17—416no—
432C4×D17—416no—
433C2×#385—171no—
434C2×C4×C22⋊C4—171no—
435C22×#95—171no—
436#1445—171no—
437#1445—171no—
438#1443—171no—
439#1443—171no—
440#1436—171no—
441#1436D1711yescharacteristic, complemented
442#1434—171no—
443#1434—171no—
444C22⋊#95—171no—
445C22⋊#95—171no—
446C22⋊#95—171no—
447C22⋊#95—171no—
448C22×C17C2×#11711yescharacteristic
449C22×C17C2×C4×D411yescharacteristic
450C22×C17C2×C4×Q811yescharacteristic
451C22×C17C4×#4111yescharacteristic
452C22×C17C4×#4111yescharacteristic
453C22×C17#51811yescharacteristic
454C22×C17#51811yescharacteristic
455C22×C17C2×C22⋊Q811yescharacteristic
456C22×C17C2×#12311yescharacteristic
457C22×C17C2×#12311yescharacteristic
458C22×C17#52511yescharacteristic
459C22×C17C2×#12511yescharacteristic
460C22×C17C2×#12611yescharacteristic
461C22×C17#52911yescharacteristic
462C22×C17#52911yescharacteristic
463C22×C17#53411yescharacteristic
464C22×C17#53511yescharacteristic
465C22×C17#53811yescharacteristic
466C22×C17#53811yescharacteristic
467C22×C17#55111yescharacteristic
468C22×C17#55111yescharacteristic
469C22×C17#55111yescharacteristic
470C22×C17#55111yescharacteristic
471C22×C17#55111yescharacteristic
472C22×C17#55111yescharacteristic
473C22×C17#55111yescharacteristic
474C22×C17#55111yescharacteristic
475C22×C17#55311yescharacteristic
476C22×C17#55311yescharacteristic
477C22×C17#55311yescharacteristic
478C22×C17#55311yescharacteristic
479C22×C17#55411yescharacteristic
480C22×C17#55411yescharacteristic
481C22×C17#55411yescharacteristic
482C22×C17#55411yescharacteristic
483C2×D17—24no—
484C2×D17—24no—
485C2×D17—24no—
486C2×D17—24no—
487C2×D17—24no—
488C2×D17—24no—
489C2×D17—24no—
490C2×D17—24no—
491C2×D17—24no—
492C2×D17—24no—
493C2×D17—24no—
494C2×D17—24no—
495C2×D17—24no—
496C2×D17—24no—
497C2×D17#38718yes—
498C4×C17—24no—
499C4×C17—42no—
500C4×C17—42no—
501C4×C17—42no—
502C4×C17—42no—
503C4×C17—42no—
504C4×C17—81no—
505Dic17—42no—
506Dic17—42no—
507Dic17—42no—
508Dic17—42no—
509Dic17—42no—
510Dic17—42no—
511Dic17—81no—
512C24×C4—171no—
513C24×C4—171no—
514C24×C4—171no—
515C22×C4⋊C4—171no—
516C22×C4⋊C4C2×D1711yescharacteristic
517C22×C22⋊C4—171no—
518C22×C22⋊C4—171no—
519C22×C22⋊C4—171no—
520C22×C22⋊C4—171no—
521C22×C42—171no—
522C22×C42C2×D1711yescharacteristic
523#385—178no—
524C4×C22⋊C4—344no—
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×#95—171no—
539C2×#95—171no—
540C2×#95—171no—
541C2×#95—171no—
542C2×#95—171no—
543C2×#95—171no—
544C2×#95—344no—
545C2×#95C2×D1711yescharacteristic
546C2×#95C2×D1711yescharacteristic
547C2×#95C2×D1711yescharacteristic
548C2×#95C2×D1711yescharacteristic
549C2×#95C2×D1711yescharacteristic
550C2×C17C2×#38711yescharacteristic
551C2×C17C4×#12311yescharacteristic
552C2×C17#232111yescharacteristic
553C2×C17#235311yescharacteristic
554C2×C17#235311yescharacteristic
555C2×C17#236811yescharacteristic
556C2×C17#236811yescharacteristic
557C2×C17#248211yescharacteristic
558C2×C17#248311yescharacteristic
559C2×C17#248711yescharacteristic
560C2×C17#250511yescharacteristic
561C2×C17#250511yescharacteristic
562C2×C17#251011yescharacteristic
563C2×C17#251011yescharacteristic
564C2×C17#257911yescharacteristic
565D17—28no—
566C25—171no—
567C23×C4—171no—
568C23×C4—171no—
569C23×C4—171no—
570C23×C4—171no—
571C23×C4—171no—
572C23×C4—171no—
573C23×C4—174no—
574C23×C4—174no—
575C23×C4—171no—
576C23×C4—342no—
577C23×C4—342no—
578C23×C4—342no—
579C23×C4—342no—
580C23×C4—342no—
581C23×C4—342no—
582C23×C4—342no—
583C23×C4—342no—
584C23×C4—342no—
585C23×C4—342no—
586C23×C4—342no—
587C23×C4—681no—
588C23×C4—681no—
589C23×C4—681no—
590C23×C4—681no—
591C23×C4—681no—
592C23×C4—681no—
593C23×C4—681no—
594C23×C4—681no—
595C23×C4C22×D1711yescharacteristic
596C23×C4C22×D1711yescharacteristic
597C23×C4C22×D1711yescharacteristic
598C23×C4C22×D1711yescharacteristic
599C23×C4C22×D1711yescharacteristic
600C23×C4C22×D1711yescharacteristic
601C23×C4C22×D1711yescharacteristic
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—174no—
605C2×C4⋊C4—681no—
606C2×C4⋊C4—681no—
607C2×C4⋊C4C4×D1714yescomplemented
608C2×C22⋊C4—174no—
609C2×C22⋊C4—174no—
610C2×C22⋊C4—174no—
611C2×C22⋊C4—342no—
612C2×C22⋊C4—342no—
613C2×C22⋊C4—342no—
614C2×C22⋊C4—342no—
615C2×C22⋊C4—342no—
616C2×C22⋊C4—342no—
617C2×C22⋊C4—342no—
618C2×C22⋊C4—342no—
619C2×C22⋊C4—342no—
620C2×C42—22no—
621C2×C42—41no—
622C2×C42—41no—
623C2×C42—342no—
624C2×C42—342no—
625C2×C42—342no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—41no—
630#95—41no—
631#95—174no—
632#95—174no—
633#95—342no—
634#95—342no—
635#95—342no—
636#95—342no—
637#95—342no—
638#95—342no—
639#95—342no—
640#95—342no—
641#95—342no—
642#95—681no—
643#95—681no—
644#95—681no—
645#95—681no—
646#95—681no—
647#95—681no—
648#95—681no—
649#95—681no—
650C17#1404011yescharacteristic, complemented, Sylow
651C24—172no—
652C24—172no—
653C24—172no—
654C24—172no—
655C24—172no—
656C24—172no—
657C24—172no—
658C24—341no—
659C24—341no—
660C24—341no—
661C24—341no—
662C24—341no—
663C24—341no—
664C24—341no—
665C24—341no—
666C24C23×D1711yescharacteristic
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—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—172no—
709C22×C4—172no—
710C22×C4—172no—
711C22×C4—172no—
712C22×C4—172no—
713C22×C4—172no—
714C22×C4—348no—
715C22×C4—348no—
716C22×C4—348no—
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—341no—
749C22×C4—341no—
750C22×C4—341no—
751C22×C4—341no—
752C22×C4—341no—
753C22×C4—348no—
754C22×C4—341no—
755C22×C4—341no—
756C22×C4—341no—
757C22×C4—341no—
758C22×C4—341no—
759C22×C4—341no—
760C22×C4—341no—
761C22×C4—684no—
762C22×C4—684no—
763C22×C4—684no—
764C22×C4—684no—
765C22×C4—684no—
766C22×C4—684no—
767C22×C4—684no—
768C22×C4—684no—
769C22×C4—684no—
770C22×C4—684no—
771C22×C4—684no—
772C22×C4—684no—
773C22×C4—684no—
774C22×C4—684no—
775C22×C4—684no—
776C22×C4—684no—
777C22×C4—684no—
778C22×C4C2×C4×D1712yes—
779C22×C4C2×C4×D1712yes—
780C22×C4C2×C4×D1712yes—
781C22×C4#6325212yes—
782C22×C4#6325212yes—
783C22×C4D4×D1712yes—
784C22×C4Q8×D1712yes—
785C22×C4#6325612yes—
786C4⋊C4—44no—
787C4⋊C4—684no—
788C22⋊C4—348no—
789C22⋊C4—348no—
790C22⋊C4—348no—
791C22⋊C4—684no—
792C42—44no—
793C42—684no—
794C23—174no—
795C23—174no—
796C23—174no—
797C23—174no—
798C23—174no—
799C23—174no—
800C23—174no—
801C23—342no—
802C23—342no—
803C23—342no—
804C23—342no—
805C23—342no—
806C23—342no—
807C23—342no—
808C23—342no—
809C23—342no—
810C23—342no—
811C23—342no—
812C23—342no—
813C23—342no—
814C23—342no—
815C23—342no—
816C23—342no—
817C23—342no—
818C23—342no—
819C23—342no—
820C23—342no—
821C23—342no—
822C23—342no—
823C23—342no—
824C23—342no—
825C23—342no—
826C23—342no—
827C23—342no—
828C23—342no—
829C23C22×C4×D1711yescharacteristic
830C23C2×#6325211yescharacteristic
831C23C2×#6325211yescharacteristic
832C23C2×D4×D1711yescharacteristic
833C23#1058769111yescharacteristic
834C23#1058769111yescharacteristic
835C23#1058769111yescharacteristic
836C23C2×Q8×D1711yescharacteristic
837C23C2×#6325611yescharacteristic
838C23#41×D1711yescharacteristic
839C23#41×D1711yescharacteristic
840C23#41×D1711yescharacteristic
841C23#41×D1711yescharacteristic
842C23#41×D1711yescharacteristic
843C23#1058769611yescharacteristic
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—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
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—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
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—342no—
902C2×C4—342no—
903C2×C4—342no—
904C2×C4—342no—
905C2×C4—342no—
906C2×C4—342no—
907C2×C4—342no—
908C2×C4—342no—
909C2×C4—342no—
910C2×C4—6816no—
911C2×C4—6816no—
912C2×C4—6816no—
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×C4—681no—
929C2×C4—681no—
930C2×C4—681no—
931C2×C4—681no—
932C2×C4—681no—
933C2×C4—681no—
934C2×C4—681no—
935C2×C4—681no—
936C2×C4—681no—
937C2×C4—681no—
938C2×C4—681no—
939C2×C4—681no—
940C2×C4—681no—
941C2×C4—681no—
942C2×C4—681no—
943C2×C4—681no—
944C2×C4#1058758014yes—
945C22—178no—
946C22—344no—
947C22—344no—
948C22—344no—
949C22—344no—
950C22—344no—
951C22—344no—
952C22—344no—
953C22—344no—
954C22—344no—
955C22—344no—
956C22—344no—
957C22—344no—
958C22—344no—
959C22—344no—
960C22#117×D1711yescharacteristic
961C22C4×D4×D1711yescharacteristic
962C22C4×Q8×D1711yescharacteristic
963C22C4×#6325211yescharacteristic
964C22C4×#6325611yescharacteristic
965C22#1176328111yescharacteristic
966C22#1176328211yescharacteristic
967C22C22⋊Q8×D1711yescharacteristic
968C22#123×D1711yescharacteristic
969C22C2×#1058758011yescharacteristic
970C22#1176331811yescharacteristic
971C22#125×D1711yescharacteristic
972C22#126×D1711yescharacteristic
973C22#1176333711yescharacteristic
974C22#1176334611yescharacteristic
975C22#1176336911yescharacteristic
976C22#1176337511yescharacteristic
977C22#1176339111yescharacteristic
978C22#1176339511yescharacteristic
979C22#1176348311yescharacteristic
980C22#1176348411yescharacteristic
981C22#1176348611yescharacteristic
982C22#1176348611yescharacteristic
983C22#1176348811yescharacteristic
984C22#1176348811yescharacteristic
985C22#1176348811yescharacteristic
986C22#1176348911yescharacteristic
987C22#1176350411yescharacteristic
988C22#1176350911yescharacteristic
989C22#1176350911yescharacteristic
990C22#1176351211yescharacteristic
991C22#1176351311yescharacteristic
992C22#1176351411yescharacteristic
993C22#1176351911yescharacteristic
994C22#1176352011yescharacteristic
995C4—24no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—81no—
1002C4—682no—
1003C4—682no—
1004C4—682no—
1005C4—682no—
1006C4—682no—
1007C4—682no—
1008C4—1361no—
1009C2—348no—
1010C2D17×#38711yescharacteristic
1011C2C4×#1058758011yescharacteristic
1012C2#1453144011yescharacteristic
1013C2#1453172311yescharacteristic
1014C2#1453172711yescharacteristic
1015C2#1453186311yescharacteristic
1016C2#1453186811yescharacteristic
1017C2#1453305611yescharacteristic
1018C2#1453306411yescharacteristic
1019C2#1453309911yescharacteristic
1020C2#1453329011yescharacteristic
1021C2#1453329211yescharacteristic
1022C2#1453334111yescharacteristic
1023C2#1453334311yescharacteristic
1024C2#1453412911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1436C2
socle, cosocleC24×C17C24
prime radicalC24×D17C23
hypercenter#1436D17
hypocenterC17#14040
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. #14527052C2semidirect
5. #14527050C2semidirect
6. #14527045C2semidirect
7. #14527045C2semidirect
8. #14527017C2semidirect
9. #14527008C2semidirect
10. #14527008C2semidirect
15. C17×#1436C2semidirect
25. #11762680C4semidirect
92. C2×C4⋊C4×C17C2×C4semidirect
110. C2×#63225C2×C4semidirect
136. #10587502C2×C4semidirect
137. #10587502C2×C4semidirect
441. #1436D17semidirect
607. C2×C4⋊C4C4×D17semidirect
650. C17#14040semidirect

Maximal subgroups

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

subgroupindex
C2×#117626802
C2×C4×#632272
C2×#95×D172
#145270522
#145270502
#145270452
#145270172
#145270082
#145270052
C17×#14362
#1404017