Finite Group Databasebeta

← #16957191

Subgroups — #16957191

Order 4352.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D68C211yesmaximal, characteristic
2C2×#11762687C211yesmaximal, characteristic
3C2×#11762687C211yesmaximal, characteristic
4C2×#11762680C211yesmaximal, characteristic, complemented
5C2×#11762680C211yesmaximal, characteristic, complemented
6C2×#11762668C211yesmaximal, characteristic, complemented
7C2×#95×D17C211yesmaximal, characteristic, complemented
8#14527048C211yesmaximal, characteristic, complemented
9#14527041C211yesmaximal, characteristic, complemented
10#14527028C211yesmaximal, characteristic, complemented
11#14527028C211yesmaximal, characteristic, complemented
12#14527017C211yesmaximal, characteristic, complemented
13#14527005C211yesmaximal, characteristic, complemented
14#14527005C211yesmaximal, characteristic, complemented
15C17×#1436C211yesmaximal, characteristic, complemented
16C23×D68C2211yescharacteristic
17C23×C4×D17C2211yescharacteristic
18C23×C4×D17C2211yescharacteristic
19C23×C4×D17C2211yescharacteristic
20C23×C4×D17C2211yescharacteristic
21C2×C4×D68—24no—
22C2×C4×D68—24no—
23C2×C4×D68—24no—
24C22×C4⋊Dic17C2211yescharacteristic
25C22×#63225C2211yescharacteristic
26C22×#63225C2211yescharacteristic
27C22×#63225C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31C22×#63227C2211yescharacteristic
32C22×#63227C2211yescharacteristic
33C22×#63227C2211yescharacteristic
34C22×#63227C2211yescharacteristic
35C22×#63227C2211yescharacteristic
36#11762687—24no—
37#11762687C418yescomplemented
38#11762680—24no—
39#11762680—24no—
40#11762668—24no—
41C2×#10587502C2211yescharacteristic
42C2×#10587502C2211yescharacteristic
43C2×#10587502C2211yescharacteristic
44C2×#10587502C2211yescharacteristic
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52#95×D17—24no—
53C22×C4⋊C4×C17C2211yescharacteristic
54C22×C42×C17C2211yescharacteristic
55C2×C17×#95C2211yescharacteristic
56C2×C17×#95C2211yescharacteristic
57C2×C17×#95C2211yescharacteristic
58C2×C17×#95C2211yescharacteristic
59C2×C17×#95C2211yescharacteristic
60C24×D17C2311yescharacteristic
61C24×D17C2311yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C23×C4×C17C2311yescharacteristic
64C23×C4×C17C2311yescharacteristic
65C23×C4×C17C2311yescharacteristic
66C23×C4×C17C2311yescharacteristic
67C23×C4×C17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C23×Dic17C2311yescharacteristic
70C23×Dic17C2311yescharacteristic
71C23×Dic17C2311yescharacteristic
72C23×Dic17C2311yescharacteristic
73C23×Dic17C2311yescharacteristic
74C23×Dic17C2311yescharacteristic
75C22×D68—22no—
76C22×D68—22no—
77C22×D68—22no—
78C22×D68—22no—
79C22×D68C2×C414yes—
80C22×D68D414yes—
81C22×D68Q814yes—
82C22×C4×D17—22no—
83C22×C4×D17—22no—
84C22×C4×D17—22no—
85C22×C4×D17—22no—
86C22×C4×D17—22no—
87C22×C4×D17—22no—
88C22×C4×D17—22no—
89C22×C4×D17—22no—
90C22×C4×D17—22no—
91C22×C4×D17—22no—
92C22×C4×D17—22no—
93C22×C4×D17—22no—
94C22×C4×D17—22no—
95C22×C4×D17—22no—
96C22×C4×D17—22no—
97C22×C4×D17—22no—
98C22×C4×D17—22no—
99C22×C4×D17—22no—
100C22×C4×D17—41no—
101C22×C4×D17—41no—
102C22×C4×D17—41no—
103C22×C4×D17—41no—
104C22×C4×D17—41no—
105C22×C4×D17—41no—
106C22×C4×D17—41no—
107C22×C4×D17—41no—
108C22×C4×D17C2×C414yescomplemented
109C22×C4×D17D414yes—
110C2×C4⋊C4×C17—22no—
111C2×C4⋊C4×C17—22no—
112C2×C4⋊C4×C17—22no—
113C2×C42×C17—22no—
114C2×C42×C17—22no—
115C2×C42×C17—22no—
116C2×#63227—22no—
117C2×#63227—22no—
118C2×#63227—22no—
119C2×#63227—22no—
120C2×#63227—22no—
121C2×#63227—22no—
122C2×#63227—22no—
123C2×#63227—22no—
124C2×#63227—22no—
125C2×#63227—22no—
126C2×#63227—22no—
127C2×#63227—22no—
128C2×#63227—22no—
129C2×#63227—22no—
130C2×#63227—22no—
131C2×#63227—22no—
132C2×#63227—41no—
133C2×#63227—41no—
134C2×#63227—41no—
135C2×#63227—41no—
136C2×#63227C2×C414yescomplemented
137C2×#63227C2×C414yescomplemented
138C2×#63227C2×C414yescomplemented
139C2×#63227D414yes—
140C2×C4⋊Dic17—22no—
141C2×C4⋊Dic17—22no—
142C2×C4⋊Dic17—22no—
143C2×#63225—22no—
144C2×#63225—22no—
145C2×#63225—22no—
146C2×#63225—22no—
147C2×#63225—22no—
148C2×#63225—41no—
149C2×#63225—41no—
150C2×#63225—41no—
151C2×#63225—41no—
152C4×D68—232no—
153C17×#95—22no—
154C17×#95—22no—
155C17×#95—22no—
156C17×#95—22no—
157C17×#95C2×C414yescomplemented
158#10587502—22no—
159#10587502—22no—
160#10587502—22no—
161#10587502—22no—
162#10587502—22no—
163#10587502—22no—
164#10587502—22no—
165#10587502—41no—
166#10587502—41no—
167#10587502C2×C414yescomplemented
168#10587502D414yescomplemented
169C24×C17C2411yescharacteristic
170C23×D17—21no—
171C23×D17—21no—
172C23×D17—21no—
173C23×D17—21no—
174C23×D17—21no—
175C23×D17—21no—
176C23×D17—21no—
177C23×D17—21no—
178C23×D17—21no—
179C23×D17—21no—
180C23×D17—21no—
181C23×D17—21no—
182C23×D17—21no—
183C23×D17—21no—
184C23×D17—21no—
185C23×D17—21no—
186C23×D17—21no—
187C23×D17—21no—
188C23×D17—21no—
189C23×D17—21no—
190C23×D17C22×C412yes—
191C23×D17C22×C412yes—
192C23×D17C2×D412yes—
193C23×D17C2×D412yes—
194C23×D17C2×D412yes—
195C23×D17C2×D412yes—
196C23×D17C2×Q812yes—
197C23×D17C2×Q812yes—
198C23×D17#4112yes—
199C23×D17#4112yes—
200C22×C4×C17—21no—
201C22×C4×C17—21no—
202C22×C4×C17—21no—
203C22×C4×C17—21no—
204C22×C4×C17—21no—
205C22×C4×C17—21no—
206C22×C4×C17—21no—
207C22×C4×C17—21no—
208C22×C4×C17—21no—
209C22×C4×C17—21no—
210C22×C4×C17—21no—
211C22×C4×C17—21no—
212C22×C4×C17—21no—
213C22×C4×C17—21no—
214C22×C4×C17—21no—
215C22×C4×C17—21no—
216C22×C4×C17—21no—
217C22×C4×C17—21no—
218C22×C4×C17—21no—
219C22×C4×C17—21no—
220C22×C4×C17—21no—
221C22×C4×C17—21no—
222C22×C4×C17—21no—
223C22×C4×C17—21no—
224C22×C4×C17—21no—
225C22×C4×C17—21no—
226C22×C4×C17—21no—
227C22×C4×C17—21no—
228C22×C4×C17—21no—
229C22×C4×C17—21no—
230C22×C4×C17—21no—
231C22×C4×C17—21no—
232C22×C4×C17—21no—
233C22×C4×C17—21no—
234C22×C4×C17—21no—
235C22×C4×C17—21no—
236C22×C4×C17—21no—
237C22×C4×C17—21no—
238C22×C4×C17—21no—
239C22×C4×C17C22×C412yes—
240C22×C4×C17C22×C412yes—
241C22×C4×C17C22×C412yes—
242C22×C4×C17C2×D412yes—
243C22×C4×C17C2×D412yes—
244C22×C4×C17C2×D412yes—
245C22×C4×C17C2×D412yes—
246C22×C4×C17C2×Q812yes—
247C22×C4×C17#4112yes—
248C22×C4×C17#4112yes—
249C22×Dic17—21no—
250C22×Dic17—21no—
251C22×Dic17—21no—
252C22×Dic17—21no—
253C22×Dic17—21no—
254C22×Dic17—21no—
255C22×Dic17—21no—
256C22×Dic17—21no—
257C22×Dic17—21no—
258C22×Dic17—21no—
259C22×Dic17—21no—
260C22×Dic17—21no—
261C22×Dic17—21no—
262C22×Dic17—21no—
263C22×Dic17—21no—
264C22×Dic17—21no—
265C22×Dic17—21no—
266C22×Dic17—21no—
267C22×Dic17—21no—
268C22×Dic17—21no—
269C22×Dic17—21no—
270C22×Dic17—21no—
271C22×Dic17—21no—
272C22×Dic17—21no—
273C22×Dic17—21no—
274C22×Dic17—21no—
275C22×Dic17—21no—
276C22×Dic17—21no—
277C22×Dic17—21no—
278C22×Dic17—21no—
279C22×Dic17—21no—
280C22×Dic17—21no—
281C22×Dic17—21no—
282C22×Dic17—21no—
283C22×Dic17—21no—
284C22×Dic17C22×C412yes—
285C22×Dic17C22×C412yes—
286C22×Dic17C2×D412yes—
287C22×Dic17C2×D412yes—
288C22×Dic17C2×D412yes—
289C22×Dic17C2×D412yes—
290C22×Dic17#4112yes—
291C2×D68—28no—
292C2×D68—28no—
293C2×D68—28no—
294C2×D68—28no—
295C2×D68—28no—
296C2×D68—28no—
297C2×D68C4⋊C4116yescomplemented
298C2×C4×D17—28no—
299C2×C4×D17—28no—
300C2×C4×D17—28no—
301C2×C4×D17—28no—
302C2×C4×D17—28no—
303C2×C4×D17—28no—
304C2×C4×D17—44no—
305C2×C4×D17—44no—
306C2×C4×D17—44no—
307C2×C4×D17—44no—
308C2×C4×D17—44no—
309C2×C4×D17—44no—
310C2×C4×D17—44no—
311C2×C4×D17—44no—
312C2×C4×D17—44no—
313C2×C4×D17—44no—
314C2×C4×D17—44no—
315C2×C4×D17—44no—
316C2×C4×D17—44no—
317C2×C4×D17—44no—
318C2×C4×D17—44no—
319C2×C4×D17—44no—
320C2×C4×D17—44no—
321C2×C4×D17—44no—
322C2×C4×D17—44no—
323C2×C4×D17—44no—
324C2×C4×D17—44no—
325C2×C4×D17—44no—
326C4⋊C4×C17—44no—
327C42×C17—28no—
328#63227—28no—
329#63227—28no—
330#63227—28no—
331#63227—28no—
332#63227—44no—
333#63227—44no—
334#63227—44no—
335#63227—44no—
336C4⋊Dic17—28no—
337#63225—44no—
338#63225—44no—
339#63225—44no—
340#13975—171nomaximal, Sylow
341C23×C17C23×C411yescharacteristic
342C23×C17C22×D411yescharacteristic
343C23×C17C22×D411yescharacteristic
344C23×C17C22×D411yescharacteristic
345C23×C17C22×D411yescharacteristic
346C23×C17C22×Q811yescharacteristic
347C23×C17C2×#4111yescharacteristic
348C23×C17C2×#4111yescharacteristic
349C23×C17C2×#4111yescharacteristic
350C23×C17C2×#4111yescharacteristic
351C23×C17C2×#4111yescharacteristic
352C23×C17H(5,𝔽2)11yescharacteristic
353C23×C17H(5,𝔽2)11yescharacteristic
354C23×C17H(5,𝔽2)11yescharacteristic
355C23×C172−1+411yescharacteristic
356C22×D17—22no—
357C22×D17—22no—
358C22×D17—22no—
359C22×D17—22no—
360C22×D17—22no—
361C22×D17—22no—
362C22×D17—22no—
363C22×D17—22no—
364C22×D17—22no—
365C22×D17—22no—
366C22×D17—22no—
367C22×D17—22no—
368C22×D17—22no—
369C22×D17—22no—
370C22×D17—22no—
371C22×D17—22no—
372C22×D17—22no—
373C22×D17—22no—
374C22×D17—22no—
375C22×D17—22no—
376C22×D17—22no—
377C22×D17—22no—
378C22×D17—22no—
379C22×D17—22no—
380C22×D17—22no—
381C22×D17—22no—
382C22×D17—22no—
383C22×D17—22no—
384C22×D17—22no—
385C22×D17—22no—
386C22×D17—22no—
387C22×D17—22no—
388C22×D17—22no—
389C22×D17—22no—
390C22×D17—22no—
391C22×D17—22no—
392C22×D17—22no—
393C22×D17—22no—
394C22×D17—22no—
395C22×D17—22no—
396C22×D17—22no—
397C22×D17—22no—
398C22×D17—22no—
399C22×D17—22no—
400C22×D17—22no—
401C22×D17—22no—
402C22×D17—41no—
403C22×D17—41no—
404C22×D17—41no—
405C22×D17—41no—
406C22×D17—41no—
407C22×D17—41no—
408C22×D17—41no—
409C22×D17—41no—
410C22×D17—41no—
411C22×D17—41no—
412C22×D17—41no—
413C22×D17—41no—
414C22×D17—41no—
415C22×D17—41no—
416C22×D17—41no—
417C22×D17—41no—
418C22×D17C2×C4⋊C414yes—
419C22×D17C2×C4⋊C414yes—
420C22×D17C4×D414yes—
421C22×D17C4×D414yes—
422C22×D17#12014yes—
423C22×D17C22⋊Q814yes—
424C22×D17C22⋊Q814yes—
425C22×D17#12314yes—
426C2×C4×C17—22no—
427C2×C4×C17—22no—
428C2×C4×C17—22no—
429C2×C4×C17—22no—
430C2×C4×C17—22no—
431C2×C4×C17—22no—
432C2×C4×C17—22no—
433C2×C4×C17—22no—
434C2×C4×C17—22no—
435C2×C4×C17—22no—
436C2×C4×C17—22no—
437C2×C4×C17—22no—
438C2×C4×C17—22no—
439C2×C4×C17—22no—
440C2×C4×C17—22no—
441C2×C4×C17—22no—
442C2×C4×C17—22no—
443C2×C4×C17—22no—
444C2×C4×C17—22no—
445C2×C4×C17—22no—
446C2×C4×C17—22no—
447C2×C4×C17—22no—
448C2×C4×C17—22no—
449C2×C4×C17—22no—
450C2×C4×C17—41no—
451C2×C4×C17—41no—
452C2×C4×C17—41no—
453C2×C4×C17—41no—
454C2×C4×C17—41no—
455C2×C4×C17—41no—
456C2×C4×C17—41no—
457C2×C4×C17—41no—
458C2×C4×C17—41no—
459C2×C4×C17—41no—
460C2×C4×C17—41no—
461C2×C4×C17—41no—
462C2×C4×C17—41no—
463C2×C4×C17—41no—
464C2×C4×C17—41no—
465C2×C4×C17—41no—
466C2×C4×C17—41no—
467C2×C4×C17—41no—
468C2×C4×C17—41no—
469C2×C4×C17—41no—
470C2×C4×C17—41no—
471C2×C4×C17—41no—
472C2×C4×C17—41no—
473C2×C4×C17C2×C4⋊C414yes—
474C2×C4×C17#12114yes—
475C2×Dic17—22no—
476C2×Dic17—22no—
477C2×Dic17—22no—
478C2×Dic17—22no—
479C2×Dic17—22no—
480C2×Dic17—22no—
481C2×Dic17—22no—
482C2×Dic17—22no—
483C2×Dic17—22no—
484C2×Dic17—22no—
485C2×Dic17—22no—
486C2×Dic17—22no—
487C2×Dic17—22no—
488C2×Dic17—22no—
489C2×Dic17—22no—
490C2×Dic17—22no—
491C2×Dic17—22no—
492C2×Dic17—22no—
493C2×Dic17—41no—
494C2×Dic17—41no—
495C2×Dic17—41no—
496C2×Dic17—41no—
497C2×Dic17—41no—
498C2×Dic17—41no—
499C2×Dic17—41no—
500C2×Dic17—41no—
501C2×Dic17—41no—
502C2×Dic17—41no—
503C2×Dic17—41no—
504C2×Dic17—41no—
505C2×Dic17—41no—
506C2×Dic17—41no—
507C2×Dic17—41no—
508C2×Dic17—41no—
509C2×Dic17—41no—
510C2×Dic17—41no—
511C2×Dic17—41no—
512C2×Dic17—41no—
513C2×Dic17—41no—
514C2×Dic17—41no—
515C2×Dic17—41no—
516C2×Dic17C4×D414yescomplemented
517D68—232no—
518C4×D17—416no—
519C4×D17—416no—
520C4×D17—416no—
521C4×D17—416no—
522C22×C4×D4—171no—
523C2×#386—171no—
524C2×#386—171no—
525C2×#385—171no—
526C2×#385—171no—
527C2×#380—171no—
528C22×#95—171no—
529#1444—171no—
530#1442—171no—
531#1439—171no—
532#1439—171no—
533#1436—171no—
534#1436D1711yescharacteristic, complemented
535C22⋊#95—171no—
536C22⋊#95—171no—
537C22×C17C22×C4⋊C411yescharacteristic
538C22×C17C2×C4×D411yescharacteristic
539C22×C17C2×C4×D411yescharacteristic
540C22×C17C2×C4×D411yescharacteristic
541C22×C17C4×#4111yescharacteristic
542C22×C17#51811yescharacteristic
543C22×C17#52011yescharacteristic
544C22×C17C2×#12011yescharacteristic
545C22×C17C2×#12111yescharacteristic
546C22×C17C2×C22⋊Q811yescharacteristic
547C22×C17C2×C22⋊Q811yescharacteristic
548C22×C17C2×#12311yescharacteristic
549C22×C17#52511yescharacteristic
550C22×C17#52911yescharacteristic
551C22×C17#53211yescharacteristic
552C22×C17#53411yescharacteristic
553C22×C17#53711yescharacteristic
554C22×C17#53811yescharacteristic
555C22×C17#53911yescharacteristic
556C22×C17D4211yescharacteristic
557C22×C17D4211yescharacteristic
558C22×C17#54611yescharacteristic
559C22×C17#54611yescharacteristic
560C22×C17#54611yescharacteristic
561C22×C17#54611yescharacteristic
562C22×C17#54611yescharacteristic
563C22×C17#54711yescharacteristic
564C22×C17#54711yescharacteristic
565C22×C17D4×Q811yescharacteristic
566C22×C17#55111yescharacteristic
567C22×C17#55111yescharacteristic
568C22×C17#55211yescharacteristic
569C22×C17#55411yescharacteristic
570C22×C17#55411yescharacteristic
571C22×C17#55411yescharacteristic
572C2×D17—24no—
573C2×D17—24no—
574C2×D17—24no—
575C2×D17—24no—
576C2×D17—24no—
577C2×D17—24no—
578C2×D17—24no—
579C2×D17—24no—
580C2×D17—24no—
581C2×D17—24no—
582C2×D17—24no—
583C2×D17—24no—
584C2×D17—24no—
585C2×D17—24no—
586C2×D17—24no—
587C2×D17—24no—
588C2×D17—24no—
589C2×D17—42no—
590C2×D17—42no—
591C2×D17—42no—
592C2×D17—42no—
593C2×D17—42no—
594C2×D17—42no—
595C2×D17—42no—
596C2×D17—42no—
597C2×D17—42no—
598C2×D17—42no—
599C2×D17—42no—
600C2×D17—42no—
601C2×D17#38518yescomplemented
602C4×C17—24no—
603C4×C17—24no—
604C4×C17—42no—
605C4×C17—42no—
606C4×C17—42no—
607C4×C17—42no—
608C4×C17—81no—
609Dic17—24no—
610Dic17—42no—
611Dic17—42no—
612Dic17—42no—
613Dic17—42no—
614Dic17—81no—
615C23×D4—171no—
616C24×C4—171no—
617C24×C4—171no—
618C24×C4—171no—
619C24×C4—171no—
620C2×C4×D4—344no—
621C2×C4×D4—344no—
622C2×C4×D4—344no—
623C22×C4⋊C4—171no—
624C22×C4⋊C4—171no—
625C22×C4⋊C4—171no—
626C22×C4⋊C4—171no—
627C22×C4⋊C4C2×D1711yescharacteristic
628C22×C22⋊C4—171no—
629C22×C22⋊C4—171no—
630C22×C22⋊C4—171no—
631C22×C22⋊C4—171no—
632C22×C22⋊C4—171no—
633C22×C22⋊C4—171no—
634C22×C22⋊C4—171no—
635C22×C22⋊C4—171no—
636C22×C42C2×D1711yescharacteristic
637#386—178no—
638#386—344no—
639#385—344no—
640#385—344no—
641#380—344no—
642C2×#95—171no—
643C2×#95—171no—
644C2×#95—171no—
645C2×#95—171no—
646C2×#95—171no—
647C2×#95—171no—
648C2×#95—171no—
649C2×#95—171no—
650C2×#95—171no—
651C2×#95—171no—
652C2×#95—171no—
653C2×#95—344no—
654C2×#95C2×D1711yescharacteristic
655C2×#95C2×D1711yescharacteristic
656C2×#95C2×D1711yescharacteristic
657C2×#95C2×D1711yescharacteristic
658C2×#95C2×D1711yescharacteristic
659C2×C17C2×#38511yescharacteristic
660C2×C17C4×#12111yescharacteristic
661C2×C17#232511yescharacteristic
662C2×C17D4×C4⋊C411yescharacteristic
663C2×C17#234911yescharacteristic
664C2×C17#235811yescharacteristic
665C2×C17#235911yescharacteristic
666C2×C17#241011yescharacteristic
667C2×C17#241711yescharacteristic
668C2×C17#241811yescharacteristic
669C2×C17#241911yescharacteristic
670C2×C17#243011yescharacteristic
671C2×C17#244911yescharacteristic
672C2×C17#245011yescharacteristic
673C2×C17#256411yescharacteristic
674D17—28no—
675D17—44no—
676C25—171no—
677C25—171no—
678C22×D4—174no—
679C22×D4—174no—
680C22×D4—174no—
681C22×D4—342no—
682C22×D4—342no—
683C22×D4—342no—
684C22×D4—342no—
685C23×C4—171no—
686C23×C4—171no—
687C23×C4—171no—
688C23×C4—171no—
689C23×C4—171no—
690C23×C4—174no—
691C23×C4—174no—
692C23×C4—171no—
693C23×C4—342no—
694C23×C4—342no—
695C23×C4—342no—
696C23×C4—342no—
697C23×C4—342no—
698C23×C4—342no—
699C23×C4—342no—
700C23×C4—342no—
701C23×C4—342no—
702C23×C4—342no—
703C23×C4—342no—
704C23×C4—342no—
705C23×C4—342no—
706C23×C4—342no—
707C23×C4—342no—
708C23×C4—342no—
709C23×C4—342no—
710C23×C4—342no—
711C23×C4—681no—
712C23×C4—681no—
713C23×C4—681no—
714C23×C4—681no—
715C23×C4—681no—
716C23×C4—681no—
717C23×C4—681no—
718C23×C4—681no—
719C23×C4C22×D1711yescharacteristic
720C23×C4C22×D1711yescharacteristic
721C23×C4C22×D1711yescharacteristic
722C23×C4C22×D1711yescharacteristic
723C23×C4C22×D1711yescharacteristic
724C23×C4C22×D1711yescharacteristic
725C23×C4C22×D1711yescharacteristic
726C4×D4—3432no—
727C2×C4⋊C4—22no—
728C2×C4⋊C4—22no—
729C2×C4⋊C4—22no—
730C2×C4⋊C4—342no—
731C2×C4⋊C4—342no—
732C2×C4⋊C4—342no—
733C2×C4⋊C4—342no—
734C2×C4⋊C4—342no—
735C2×C4⋊C4—342no—
736C2×C4⋊C4—342no—
737C2×C4⋊C4—342no—
738C2×C4⋊C4—681no—
739C2×C4⋊C4—681no—
740C2×C4⋊C4—681no—
741C2×C4⋊C4—681no—
742C2×C22⋊C4—174no—
743C2×C22⋊C4—174no—
744C2×C22⋊C4—174no—
745C2×C22⋊C4—174no—
746C2×C22⋊C4—342no—
747C2×C22⋊C4—342no—
748C2×C22⋊C4—342no—
749C2×C22⋊C4—342no—
750C2×C22⋊C4—342no—
751C2×C22⋊C4—342no—
752C2×C22⋊C4—342no—
753C2×C22⋊C4—342no—
754C2×C22⋊C4—342no—
755C2×C22⋊C4—342no—
756C2×C22⋊C4—342no—
757C2×C22⋊C4—342no—
758C2×C22⋊C4—342no—
759C2×C22⋊C4—342no—
760C2×C22⋊C4—342no—
761C2×C22⋊C4—342no—
762C2×C22⋊C4—681no—
763C2×C22⋊C4—681no—
764C2×C22⋊C4—681no—
765C2×C22⋊C4—681no—
766C2×C42—22no—
767C2×C42—22no—
768C2×C42—22no—
769#95—22no—
770#95—22no—
771#95—22no—
772#95—22no—
773#95—174no—
774#95—174no—
775#95—342no—
776#95—342no—
777#95—342no—
778#95—342no—
779#95—342no—
780#95—342no—
781#95—342no—
782#95—681no—
783#95—681no—
784#95C4×D1714yescomplemented
785C17#1397511yescharacteristic, complemented, Sylow
786C24—172no—
787C24—172no—
788C24—172no—
789C24—172no—
790C24—172no—
791C24—172no—
792C24—172no—
793C24—172no—
794C24—172no—
795C24—172no—
796C24—341no—
797C24—341no—
798C24—341no—
799C24—341no—
800C24—341no—
801C24—341no—
802C24—341no—
803C24—341no—
804C24—341no—
805C24—341no—
806C24—341no—
807C24—341no—
808C24—341no—
809C24—341no—
810C24—341no—
811C24—341no—
812C24—341no—
813C24—341no—
814C24—341no—
815C24—341no—
816C24C23×D1711yescharacteristic
817C2×D4—1716no—
818C2×D4—348no—
819C2×D4—348no—
820C2×D4—348no—
821C2×D4—348no—
822C2×D4—348no—
823C2×D4—348no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—172no—
864C22×C4—172no—
865C22×C4—172no—
866C22×C4—172no—
867C22×C4—172no—
868C22×C4—172no—
869C22×C4—172no—
870C22×C4—348no—
871C22×C4—348no—
872C22×C4—348no—
873C22×C4—348no—
874C22×C4—348no—
875C22×C4—341no—
876C22×C4—341no—
877C22×C4—341no—
878C22×C4—341no—
879C22×C4—341no—
880C22×C4—341no—
881C22×C4—341no—
882C22×C4—341no—
883C22×C4—341no—
884C22×C4—341no—
885C22×C4—341no—
886C22×C4—341no—
887C22×C4—341no—
888C22×C4—341no—
889C22×C4—341no—
890C22×C4—341no—
891C22×C4—341no—
892C22×C4—341no—
893C22×C4—341no—
894C22×C4—341no—
895C22×C4—341no—
896C22×C4—341no—
897C22×C4—341no—
898C22×C4—341no—
899C22×C4—341no—
900C22×C4—341no—
901C22×C4—341no—
902C22×C4—341no—
903C22×C4—348no—
904C22×C4—341no—
905C22×C4—341no—
906C22×C4—341no—
907C22×C4—341no—
908C22×C4—341no—
909C22×C4—341no—
910C22×C4—341no—
911C22×C4—684no—
912C22×C4—684no—
913C22×C4—684no—
914C22×C4—684no—
915C22×C4—684no—
916C22×C4—684no—
917C22×C4—684no—
918C22×C4—684no—
919C22×C4—684no—
920C22×C4—684no—
921C22×C4—684no—
922C22×C4—684no—
923C22×C4—684no—
924C22×C4—684no—
925C22×C4—684no—
926C22×C4—684no—
927C22×C4—684no—
928C22×C4—684no—
929C22×C4—684no—
930C22×C4—684no—
931C22×C4—684no—
932C22×C4—684no—
933C22×C4C2×C4×D1712yes—
934C22×C4C2×C4×D1712yes—
935C22×C4C2×C4×D1712yes—
936C22×C4#6325212yes—
937C22×C4#6325212yes—
938C22×C4D4×D1712yes—
939C22×C4D4×D1712yes—
940C22×C4D4×D1712yes—
941C22×C4D4×D1712yes—
942C22×C4Q8×D1712yes—
943C4⋊C4—44no—
944C4⋊C4—348no—
945C4⋊C4—684no—
946C4⋊C4—684no—
947C4⋊C4—684no—
948C22⋊C4—348no—
949C22⋊C4—348no—
950C22⋊C4—348no—
951C22⋊C4—348no—
952C22⋊C4—684no—
953C22⋊C4—684no—
954C22⋊C4—684no—
955C22⋊C4—684no—
956C42—28no—
957C23—174no—
958C23—174no—
959C23—174no—
960C23—174no—
961C23—174no—
962C23—174no—
963C23—174no—
964C23—174no—
965C23—342no—
966C23—342no—
967C23—342no—
968C23—342no—
969C23—342no—
970C23—342no—
971C23—342no—
972C23—342no—
973C23—342no—
974C23—342no—
975C23—342no—
976C23—342no—
977C23—342no—
978C23—342no—
979C23—342no—
980C23—342no—
981C23—342no—
982C23—342no—
983C23—342no—
984C23—342no—
985C23—342no—
986C23—342no—
987C23—342no—
988C23—342no—
989C23—342no—
990C23—342no—
991C23—342no—
992C23—342no—
993C23—342no—
994C23—342no—
995C23—342no—
996C23—342no—
997C23—342no—
998C23—342no—
999C23—342no—
1000C23—342no—
1001C23—342no—
1002C23—342no—
1003C23—342no—
1004C23—342no—
1005C23—342no—
1006C23—342no—
1007C23—342no—
1008C23—342no—
1009C23—342no—
1010C23—342no—
1011C23—681no—
1012C23—681no—
1013C23—681no—
1014C23—681no—
1015C23—681no—
1016C23—681no—
1017C23—681no—
1018C23—681no—
1019C23—681no—
1020C23—681no—
1021C23—681no—
1022C23—681no—
1023C23—681no—
1024C23—681no—
1025C23—681no—
1026C23—681no—
1027C23C22×C4×D1711yescharacteristic
1028C23C2×#6325211yescharacteristic
1029C23C2×#6325211yescharacteristic
1030C23C2×D4×D1711yescharacteristic
1031C23C2×D4×D1711yescharacteristic
1032C23C2×D4×D1711yescharacteristic
1033C23C2×D4×D1711yescharacteristic
1034C23C2×Q8×D1711yescharacteristic
1035C23#1058769411yescharacteristic
1036C23#41×D1711yescharacteristic
1037C23#41×D1711yescharacteristic
1038C23#41×D1711yescharacteristic
1039C23#1058769611yescharacteristic
1040C23#1058769611yescharacteristic
1041C23#1058769611yescharacteristic
1042D4—3432no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—174no—
1091C2×C4—342no—
1092C2×C4—342no—
1093C2×C4—342no—
1094C2×C4—342no—
1095C2×C4—342no—
1096C2×C4—342no—
1097C2×C4—342no—
1098C2×C4—342no—
1099C2×C4—342no—
1100C2×C4—342no—
1101C2×C4—342no—
1102C2×C4—342no—
1103C2×C4—342no—
1104C2×C4—342no—
1105C2×C4—342no—
1106C2×C4—342no—
1107C2×C4—342no—
1108C2×C4—342no—
1109C2×C4—6816no—
1110C2×C4—6816no—
1111C2×C4—6816no—
1112C2×C4—6816no—
1113C2×C4—681no—
1114C2×C4—681no—
1115C2×C4—681no—
1116C2×C4—681no—
1117C2×C4—681no—
1118C2×C4—681no—
1119C2×C4—681no—
1120C2×C4—681no—
1121C2×C4—681no—
1122C2×C4—681no—
1123C2×C4—681no—
1124C2×C4—681no—
1125C2×C4—681no—
1126C2×C4—681no—
1127C2×C4—681no—
1128C2×C4—681no—
1129C2×C4—681no—
1130C2×C4—681no—
1131C2×C4—681no—
1132C2×C4—681no—
1133C2×C4—681no—
1134C2×C4—681no—
1135C2×C4—681no—
1136C2×C4#1058757014yes—
1137C2×C4C4⋊C4×D1714yes—
1138C22—178no—
1139C22—344no—
1140C22—344no—
1141C22—344no—
1142C22—344no—
1143C22—344no—
1144C22—344no—
1145C22—344no—
1146C22—344no—
1147C22—344no—
1148C22—344no—
1149C22—344no—
1150C22—344no—
1151C22—344no—
1152C22—344no—
1153C22—344no—
1154C22—344no—
1155C22—344no—
1156C22—682no—
1157C22—682no—
1158C22—682no—
1159C22—682no—
1160C22—682no—
1161C22—682no—
1162C22—682no—
1163C22—682no—
1164C22—682no—
1165C22—682no—
1166C22—682no—
1167C22—682no—
1168C22C2×C4⋊C4×D1711yescharacteristic
1169C22C4×D4×D1711yescharacteristic
1170C22C4×D4×D1711yescharacteristic
1171C22C4×D4×D1711yescharacteristic
1172C22C4×#6325211yescharacteristic
1173C22#1176328311yescharacteristic
1174C22#1176329111yescharacteristic
1175C22#120×D1711yescharacteristic
1176C22C2×#1058757011yescharacteristic
1177C22C22⋊Q8×D1711yescharacteristic
1178C22C22⋊Q8×D1711yescharacteristic
1179C22#123×D1711yescharacteristic
1180C22#1176331811yescharacteristic
1181C22#1176333711yescharacteristic
1182C22#1176335611yescharacteristic
1183C22#1176337011yescharacteristic
1184C22#1176338911yescharacteristic
1185C22#1176339811yescharacteristic
1186C22#1176340711yescharacteristic
1187C22#1176344311yescharacteristic
1188C22#1176344311yescharacteristic
1189C22#1176345111yescharacteristic
1190C22#1176345211yescharacteristic
1191C22#1176345511yescharacteristic
1192C22#1176345511yescharacteristic
1193C22#1176345511yescharacteristic
1194C22#1176346011yescharacteristic
1195C22#1176346111yescharacteristic
1196C22#1176347411yescharacteristic
1197C22#1176348311yescharacteristic
1198C22#1176348411yescharacteristic
1199C22#1176350011yescharacteristic
1200C22#1176351511yescharacteristic
1201C22#1176351911yescharacteristic
1202C22#1176351911yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—42no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—81no—
1210C4—344no—
1211C4—682no—
1212C4—682no—
1213C4—682no—
1214C4—682no—
1215C4—1361no—
1216C2—348no—
1217C2—684no—
1218C2D17×#38511yescharacteristic
1219C2C4×#1058757011yescharacteristic
1220C2#1453148311yescharacteristic
1221C2#1453168511yescharacteristic
1222C2#1453169511yescharacteristic
1223C2#1453176211yescharacteristic
1224C2#1453178111yescharacteristic
1225C2#1453216111yescharacteristic
1226C2#1453223811yescharacteristic
1227C2#1453225311yescharacteristic
1228C2#1453226611yescharacteristic
1229C2#1453239311yescharacteristic
1230C2#1453260011yescharacteristic
1231C2#1453260711yescharacteristic
1232C2#1453396311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC17×#1436C2
socle, cosocleC24×C17C24
prime radicalC23×D68C22
hypercenter#1436D17
hypocenterC17#13975
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. C2×#11762680C2semidirect
5. C2×#11762680C2semidirect
6. C2×#11762668C2semidirect
7. C2×#95×D17C2semidirect
8. #14527048C2semidirect
9. #14527041C2semidirect
10. #14527028C2semidirect
11. #14527028C2semidirect
12. #14527017C2semidirect
13. #14527005C2semidirect
14. #14527005C2semidirect
15. C17×#1436C2semidirect
37. #11762687C4semidirect
108. C22×C4×D17C2×C4semidirect
136. C2×#63227C2×C4semidirect
137. C2×#63227C2×C4semidirect
138. C2×#63227C2×C4semidirect
157. C17×#95C2×C4semidirect
167. #10587502C2×C4semidirect
168. #10587502D4semidirect
297. C2×D68C4⋊C4semidirect
516. C2×Dic17C4×D4semidirect
534. #1436D17semidirect
601. C2×D17#385semidirect
784. #95C4×D17semidirect
785. C17#13975semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D682
C2×#117626872
C2×#117626802
C2×#117626682
C2×#95×D172
#145270482
#145270412
#145270282
#145270172
#145270052
C17×#14362
#1397517