Finite Group Databasebeta

← C2×#22563878 #31024470

Subgroups — C2×#22563878 #31024470

Order 17152.

3006 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524019C211yesmaximal, characteristic
2C22×#14524001C211yesmaximal, characteristic
3#22563878C2116yesmaximal, direct product factor
4C2×#16863338C211yesmaximal, characteristic, complemented
5C2×#16863329C211yesmaximal, characteristic, complemented
6C2×#16863328C211yesmaximal, characteristic, complemented
7C2×#16863303C211yesmaximal, characteristic, complemented
8C2×#16863291C211yesmaximal, characteristic, complemented
9C2×#16863282C211yesmaximal, characteristic, complemented
10C2×#16863281C211yesmaximal, characteristic, complemented
11C2×#16863270C211yesmaximal, characteristic
12C2×#16863267C211yesmaximal, characteristic
13C2×#16863258C211yesmaximal, characteristic
14C2×#16863253C211yesmaximal, characteristic
15C2×#95×D67C211yesmaximal, characteristic
16C2×#395×C67C211yesmaximal, characteristic, complemented
17C23×C4×D67C2211yescharacteristic
18C23×C4×D67C2211yescharacteristic
19C23×C4×D67C2211yescharacteristic
20C2×#14524019—28no—
21C2×#14524019C2218yes—
22C2×#14524001—28no—
23C2×#14524001C2218yes—
24C22×C4⋊Dic67C2211yescharacteristic
25C22×C4⋊Dic67C2211yescharacteristic
26C22×C4⋊Dic67C2211yescharacteristic
27C22×C4⋊Dic67C2211yescharacteristic
28C22×Dic67⋊C4C2211yescharacteristic
29C22×Dic67⋊C4C2211yescharacteristic
30C22×Dic67⋊C4C2211yescharacteristic
31C22×Dic67⋊C4C2211yescharacteristic
32C22×(C2×D67)⋊C4C2211yescharacteristic
33C22×(C2×D67)⋊C4C2211yescharacteristic
34C22×(C2×D67)⋊C4C2211yescharacteristic
35C22×(C2×D67)⋊C4C2211yescharacteristic
36C22×C4×Dic67C2211yescharacteristic
37C22×C4×Dic67C2211yescharacteristic
38#16863338C2218yescomplemented
39#16863329C2218yescomplemented
40#16863328C2218yescomplemented
41#16863303C2218yescomplemented
42#16863291C2218yescomplemented
43#16863282C2218yescomplemented
44#16863281C2218yescomplemented
45#16863270C2218yes—
46#16863267C2218yes—
47#16863258C2218yes—
48#16863253C2218yes—
49C2×C67⋊#95C2211yescharacteristic
50C2×C67⋊#95C2211yescharacteristic
51C2×C67⋊#95C2211yescharacteristic
52C2×C67⋊#95C2211yescharacteristic
53C2×C67⋊#95C2211yescharacteristic
54C2×C67⋊#95C2211yescharacteristic
55C2×C67⋊#95C2211yescharacteristic
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2211yescharacteristic
59C2×C67⋊#95C2211yescharacteristic
60#95×D67C2218yes—
61C23×Q8×C67C2211yescharacteristic
62C22×C4⋊C4×C67C2211yescharacteristic
63C22×C4⋊C4×C67C2211yescharacteristic
64C22×C4⋊C4×C67C2211yescharacteristic
65#395×C67C2218yescomplemented
66C2×#95×C67C2211yescharacteristic
67C2×#95×C67C2211yescharacteristic
68C2×#95×C67C2211yescharacteristic
69C24×D67C2311yescharacteristic
70C23×Dic67C2311yescharacteristic
71C23×Dic67C2311yescharacteristic
72C23×Dic67C2311yescharacteristic
73C23×Dic67C2311yescharacteristic
74C23×Dic67C2311yescharacteristic
75C23×Dic67C2311yescharacteristic
76C23×Dic67C2311yescharacteristic
77C22×C4×D67—24no—
78C22×C4×D67—24no—
79C22×C4×D67—24no—
80C22×C4×D67—24no—
81C22×C4×D67—24no—
82C22×C4×D67—24no—
83C22×C4×D67—42no—
84C22×C4×D67—42no—
85C22×C4×D67Q818yescomplemented
86C22×C4×D67C2314yes—
87C22×C4×D67C2314yes—
88C22×C4×D67C2314yes—
89#14524019—232no—
90#14524001—232no—
91C2×C4⋊Dic67—24no—
92C2×C4⋊Dic67—24no—
93C2×C4⋊Dic67—24no—
94C2×C4⋊Dic67—42no—
95C2×C4⋊Dic67C2314yes—
96C2×C4⋊Dic67C2314yes—
97C2×C4⋊Dic67C2314yes—
98C2×C4⋊Dic67C2314yes—
99C2×Dic67⋊C4—24no—
100C2×Dic67⋊C4—24no—
101C2×Dic67⋊C4—24no—
102C2×Dic67⋊C4—42no—
103C2×Dic67⋊C4C2314yes—
104C2×Dic67⋊C4C2314yes—
105C2×Dic67⋊C4C2314yes—
106C2×Dic67⋊C4C2314yes—
107C2×(C2×D67)⋊C4—24no—
108C2×(C2×D67)⋊C4—24no—
109C2×(C2×D67)⋊C4—24no—
110C2×(C2×D67)⋊C4D418yes—
111C2×(C2×D67)⋊C4C2314yes—
112C2×(C2×D67)⋊C4C2314yes—
113C2×(C2×D67)⋊C4C2314yes—
114C2×(C2×D67)⋊C4C2314yes—
115C2×C4×Dic67—24no—
116C2×C4×Dic67—24no—
117C2×C4×Dic67C2314yes—
118C2×C4×Dic67C2314yes—
119C67⋊#95C2314yes—
120C67⋊#95C2314yes—
121C67⋊#95C2314yes—
122C67⋊#95C2314yes—
123C67⋊#95C2314yes—
124C67⋊#95C2314yes—
125C67⋊#95C2314yes—
126C67⋊#95C2314yes—
127C67⋊#95C2314yes—
128C67⋊#95C2314yes—
129C67⋊#95C2314yes—
130C22×Q8×C67—24no—
131C22×Q8×C67—24no—
132C22×Q8×C67—42no—
133C22×Q8×C67C2314yes—
134C23×C4×C67C2311yescharacteristic
135C23×C4×C67C2311yescharacteristic
136C23×C4×C67C2311yescharacteristic
137C23×C4×C67C2311yescharacteristic
138C23×C4×C67C2311yescharacteristic
139C23×C4×C67C2311yescharacteristic
140C23×C4×C67C2311yescharacteristic
141C2×C4⋊C4×C67—24no—
142C2×C4⋊C4×C67—24no—
143C2×C4⋊C4×C67—42no—
144C2×C4⋊C4×C67C2314yes—
145C2×C4⋊C4×C67C2314yes—
146C2×C4⋊C4×C67C2314yes—
147#95×C67C2314yes—
148#95×C67C2314yes—
149#95×C67C2314yes—
150C23×D67—22no—
151C23×D67—22no—
152C23×D67—22no—
153C23×D67—22no—
154C23×D67C2×D414yes—
155C23×D67C2×Q814yes—
156C23×D67#4114yes—
157C23×D67C2412yes—
158C22×Dic67—22no—
159C22×Dic67—22no—
160C22×Dic67—22no—
161C22×Dic67—22no—
162C22×Dic67—22no—
163C22×Dic67—22no—
164C22×Dic67—22no—
165C22×Dic67—22no—
166C22×Dic67—22no—
167C22×Dic67—22no—
168C22×Dic67—22no—
169C22×Dic67—22no—
170C22×Dic67—22no—
171C22×Dic67—22no—
172C22×Dic67—22no—
173C22×Dic67—22no—
174C22×Dic67—22no—
175C22×Dic67—22no—
176C22×Dic67—22no—
177C22×Dic67C2×D414yes—
178C22×Dic67C2×Q814yes—
179C22×Dic67C2412yes—
180C22×Dic67C2412yes—
181C22×Dic67C2412yes—
182C22×Dic67C2412yes—
183C22×Dic67C2412yes—
184C22×Dic67C2412yes—
185C22×Dic67C2412yes—
186C2×C4×D67—232no—
187C2×C4×D67—28no—
188C2×C4×D67—28no—
189C2×C4×D67—28no—
190C2×C4×D67—28no—
191C2×C4×D67—28no—
192C2×C4×D67—28no—
193C2×C4×D67—44no—
194C2×C4×D67—44no—
195C2×C4×D67—416no—
196C2×C4×D67—416no—
197C2×C4×D67C2×Q8116yescomplemented
198C4⋊Dic67—28no—
199C4⋊Dic67—28no—
200C4⋊Dic67—28no—
201C4⋊Dic67—44no—
202Dic67⋊C4—28no—
203Dic67⋊C4—28no—
204Dic67⋊C4—28no—
205Dic67⋊C4—44no—
206(C2×D67)⋊C4—28no—
207(C2×D67)⋊C4—28no—
208(C2×D67)⋊C4—28no—
209(C2×D67)⋊C4C2×D4116yes—
210C4×Dic67—28no—
211C4×Dic67—28no—
212C24×C67C2411yescharacteristic
213C2×Q8×C67—28no—
214C2×Q8×C67—28no—
215C2×Q8×C67—44no—
216C2×Q8×C67—416no—
217C22×C4×C67—22no—
218C22×C4×C67—22no—
219C22×C4×C67—22no—
220C22×C4×C67—22no—
221C22×C4×C67—22no—
222C22×C4×C67—22no—
223C22×C4×C67—22no—
224C22×C4×C67—22no—
225C22×C4×C67—22no—
226C22×C4×C67—22no—
227C22×C4×C67—22no—
228C22×C4×C67—22no—
229C22×C4×C67—22no—
230C22×C4×C67—22no—
231C22×C4×C67—22no—
232C22×C4×C67—22no—
233C22×C4×C67—22no—
234C22×C4×C67C2×D414yes—
235C22×C4×C67C2×Q814yes—
236C22×C4×C67#4114yes—
237C22×C4×C67#4114yes—
238C22×C4×C67C2412yes—
239C22×C4×C67C2412yes—
240C22×C4×C67C2412yes—
241C22×C4×C67C2412yes—
242C22×C4×C67C2412yes—
243C22×C4×C67C2412yes—
244C22×C4×C67C2412yes—
245C4⋊C4×C67—28no—
246C4⋊C4×C67—28no—
247C4⋊C4×C67—44no—
248C23×C67C22×D412yes—
249C23×C67C22×Q812yes—
250C23×C67C2×#4112yes—
251C23×C67C2×#4112yes—
252C23×C67C2×#4112yes—
253C23×C67H(5,𝔽2)12yes—
254C23×C672−1+412yes—
255C23×C67C2511yescharacteristic
256C22×D67—28no—
257C22×D67—28no—
258C22×D67—28no—
259C22×D67—28no—
260C22×D67—28no—
261C22×D67—28no—
262C22×D67—22no—
263C22×D67—22no—
264C22×D67—22no—
265C22×D67—22no—
266C22×D67C22⋊Q8116yes—
267C22×D67C22×D414yes—
268C22×D67C22×Q814yes—
269C22×D67C2×#4114yes—
270Q8×C67—416no—
271C2×C4×C67—28no—
272C2×C4×C67—28no—
273C2×C4×C67—28no—
274C2×C4×C67—28no—
275C2×C4×C67—22no—
276C2×C4×C67—22no—
277C2×C4×C67—22no—
278C2×C4×C67—22no—
279C2×C4×C67—22no—
280C2×C4×C67—22no—
281C2×C4×C67—22no—
282C2×C4×C67—22no—
283C2×C4×C67—22no—
284C2×C4×C67—22no—
285C2×C4×C67—22no—
286C2×C4×C67—22no—
287C2×C4×C67—22no—
288C2×C4×C67—22no—
289C2×C4×C67—22no—
290C2×C4×C67—22no—
291C2×C4×C67—22no—
292C2×C4×C67—44no—
293C2×C4×C67—44no—
294C2×C4×C67—44no—
295C2×C4×C67C22×D414yes—
296C2×C4×C67C22×Q814yes—
297C2×C4×C67C2×#4114yes—
298C2×C4×C67C2×#4114yes—
299C2×Dic67—28no—
300C2×Dic67—28no—
301C2×Dic67—22no—
302C2×Dic67—22no—
303C2×Dic67—22no—
304C2×Dic67—22no—
305C2×Dic67—22no—
306C2×Dic67—22no—
307C2×Dic67—22no—
308C2×Dic67—22no—
309C2×Dic67—22no—
310C2×Dic67—22no—
311C2×Dic67—22no—
312C2×Dic67—22no—
313C2×Dic67—22no—
314C2×Dic67—22no—
315C2×Dic67—22no—
316C2×Dic67—22no—
317C2×Dic67—22no—
318C2×Dic67—22no—
319C2×Dic67—22no—
320C2×Dic67—44no—
321C2×Dic67—44no—
322C2×Dic67—44no—
323C2×Dic67—44no—
324C2×Dic67—44no—
325C2×Dic67C22×D414yes—
326C2×Dic67C22×Q814yes—
327C4×D67—232no—
328C4×D67—416no—
329C4×D67—416no—
330C22×C67C2×C22⋊Q814yes—
331C22×C67#53314yes—
332C22×C67#54414yes—
333C22×C67#54614yes—
334C22×C67#54714yes—
335C22×C67#55114yes—
336C22×C67#55214yes—
337C22×C67C23×D411yescharacteristic
338C22×C67C23×Q811yescharacteristic
339C22×C67C22×#4111yescharacteristic
340C22×C67C22×#4111yescharacteristic
341C22×C67C22×#4111yescharacteristic
342C22×C67C2×H(5,𝔽2)11yescharacteristic
343C22×C67C2×2−1+411yescharacteristic
344C2×D67—24no—
345C2×D67—24no—
346C2×D67—232no—
347C2×D67—24no—
348C2×D67—24no—
349C2×D67—24no—
350C2×D67—24no—
351C2×D67C2×C22⋊Q818yes—
352C4×C67—24no—
353C4×C67—24no—
354C4×C67—24no—
355C4×C67—24no—
356C4×C67—42no—
357C4×C67—42no—
358C4×C67—42no—
359Dic67—24no—
360Dic67—24no—
361Dic67—42no—
362Dic67—42no—
363Dic67—42no—
364Dic67—42no—
365Dic67—42no—
366C2×#2438—671nomaximal, Sylow
367C2×C67#243818yescomplemented
368C2×C67C22×C22⋊Q811yescharacteristic
369C2×C67C2×#53311yescharacteristic
370C2×C67C2×#54411yescharacteristic
371C2×C67C2×#54611yescharacteristic
372C2×C67C2×#54711yescharacteristic
373C2×C67C2×#55111yescharacteristic
374C2×C67C2×#55211yescharacteristic
375D67—28no—
376C22×C22⋊Q8—671no—
377C22×#117—671no—
378#2438—6716no—
379C2×#400—671no—
380C2×#398—671no—
381C2×#398—671no—
382C2×#395D6711yescharacteristic, complemented
383C2×#391—671no—
384C2×#389—671no—
385C2×#387—671no—
386C2×#387—671no—
387C2×#385—671no—
388C2×#385—671no—
389C2×#381—671no—
390C2×#380—671no—
391C22×#95—671no—
392C67C2×#243811yescharacteristic, complemented, Sylow
393C23×Q8C2×D6711yescharacteristic
394C24×C4—671no—
395C24×C4—671no—
396C24×C4—671no—
397C2×C22⋊Q8—678no—
398C2×C22⋊Q8—1348no—
399C2×#117—678no—
400C2×#117—1348no—
401C22×C4⋊C4—671no—
402C22×C4⋊C4—671no—
403C22×C4⋊C4—671no—
404C22×C4⋊C4—671no—
405C22×C4⋊C4—671no—
406C22×C4⋊C4—671no—
407C22×C4⋊C4—671no—
408C22×C4⋊C4—671no—
409C22×C4⋊C4C2×D6711yescharacteristic
410C22×C4⋊C4C2×D6711yescharacteristic
411C22×C4⋊C4C2×D6711yescharacteristic
412C22×C22⋊C4—671no—
413C22×C22⋊C4—671no—
414C22×C22⋊C4—671no—
415C22×C22⋊C4—671no—
416C22×C42—671no—
417C22×C42—671no—
418#400—678no—
419#398—678no—
420#398—678no—
421#395C2×D6718yescomplemented
422#391—678no—
423#389—678no—
424#387—678no—
425#387—678no—
426#385—678no—
427#385—678no—
428#381—678no—
429#380—678no—
430C2×#95—671no—
431C2×#95—671no—
432C2×#95—671no—
433C2×#95—671no—
434C2×#95—671no—
435C2×#95—671no—
436C2×#95—671no—
437C2×#95—671no—
438C2×#95—671no—
439C2×#95—671no—
440C2×#95—671no—
441C2×#95—678no—
442C2×#95C2×D6711yescharacteristic
443C2×#95C2×D6711yescharacteristic
444C2×#95C2×D6711yescharacteristic
445C25—671no—
446C22×Q8—24no—
447C22×Q8—24no—
448C22×Q8—42no—
449C22×Q8C22×D6714yes—
450C23×C4—2682no—
451C23×C4—2682no—
452C23×C4—674no—
453C23×C4—674no—
454C23×C4—671no—
455C23×C4—671no—
456C23×C4—678no—
457C23×C4—674no—
458C23×C4—671no—
459C23×C4—671no—
460C23×C4—671no—
461C23×C4—671no—
462C23×C4—671no—
463C23×C4—1344no—
464C23×C4—1344no—
465C23×C4—1344no—
466C23×C4—1344no—
467C23×C4—1344no—
468C23×C4—1344no—
469C23×C4C22×D6711yescharacteristic
470C23×C4C22×D6711yescharacteristic
471C23×C4C22×D6711yescharacteristic
472C23×C4C22×D6711yescharacteristic
473C23×C4C22×D6711yescharacteristic
474C23×C4C22×D6711yescharacteristic
475C23×C4C22×D6711yescharacteristic
476C22⋊Q8—13432no—
477#117—13432no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—2682no—
482C2×C4⋊C4—2682no—
483C2×C4⋊C4—674no—
484C2×C4⋊C4—674no—
485C2×C4⋊C4—674no—
486C2×C4⋊C4—674no—
487C2×C4⋊C4—674no—
488C2×C4⋊C4—674no—
489C2×C4⋊C4—674no—
490C2×C4⋊C4—674no—
491C2×C4⋊C4—1344no—
492C2×C4⋊C4—1344no—
493C2×C4⋊C4—1344no—
494C2×C4⋊C4—1344no—
495C2×C4⋊C4—1344no—
496C2×C4⋊C4—1344no—
497C2×C4⋊C4C22×D6714yes—
498C2×C4⋊C4C22×D6714yes—
499C2×C4⋊C4C22×D6714yes—
500C2×C22⋊C4—678no—
501C2×C22⋊C4—674no—
502C2×C22⋊C4—674no—
503C2×C22⋊C4—674no—
504C2×C22⋊C4—674no—
505C2×C22⋊C4—1344no—
506C2×C22⋊C4—1344no—
507C2×C22⋊C4—1344no—
508C2×C42—674no—
509C2×C42—674no—
510C2×C42—1344no—
511C2×C42—1344no—
512#95—674no—
513#95—674no—
514#95—674no—
515#95—674no—
516#95—674no—
517#95—674no—
518#95—674no—
519#95—674no—
520#95—674no—
521#95—674no—
522#95—674no—
523#95C22×D6714yes—
524#95C22×D6714yes—
525#95C22×D6714yes—
526C24—674no—
527C24—674no—
528C24—674no—
529C24—672no—
530C24—1342no—
531C24—1342no—
532C24—1342no—
533C24—1342no—
534C24C23×D6711yescharacteristic
535C2×Q8—28no—
536C2×Q8—28no—
537C2×Q8—44no—
538C2×Q8—416no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—26816no—
557C22×C4—26816no—
558C22×C4—2684no—
559C22×C4—2684no—
560C22×C4—674no—
561C22×C4—674no—
562C22×C4—672no—
563C22×C4—672no—
564C22×C4—6716no—
565C22×C4—672no—
566C22×C4—672no—
567C22×C4—672no—
568C22×C4—672no—
569C22×C4—672no—
570C22×C4—1348no—
571C22×C4—1348no—
572C22×C4—1348no—
573C22×C4—13432no—
574C22×C4—1348no—
575C22×C4—1342no—
576C22×C4—1342no—
577C22×C4—1342no—
578C22×C4—1342no—
579C22×C4—1342no—
580C22×C4—1342no—
581C22×C4—1342no—
582C22×C4—1342no—
583C22×C4—1342no—
584C22×C4—1342no—
585C22×C4—1342no—
586C22×C4—1342no—
587C22×C4—1342no—
588C22×C4—1342no—
589C22×C4—1342no—
590C22×C4—1348no—
591C22×C4—1348no—
592C22×C4—1342no—
593C22×C4—1342no—
594C22×C4—1342no—
595C22×C4—1342no—
596C22×C4D4×D6714yes—
597C22×C4Q8×D6714yes—
598C22×C4#1176162714yes—
599C22×C4#1176162914yes—
600C22×C4C23×D6712yes—
601C22×C4C23×D6712yes—
602C22×C4C23×D6712yes—
603C22×C4C23×D6712yes—
604C22×C4C23×D6712yes—
605C22×C4C23×D6712yes—
606C22×C4C23×D6712yes—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—44no—
610C4⋊C4—2684no—
611C4⋊C4—2684no—
612C4⋊C4—1348no—
613C4⋊C4—1348no—
614C4⋊C4—1348no—
615C4⋊C4—1348no—
616C4⋊C4—1348no—
617C4⋊C4—1348no—
618C22⋊C4—6716no—
619C22⋊C4—1348no—
620C22⋊C4—1348no—
621C22⋊C4—1348no—
622C42—1348no—
623C42—1348no—
624C23—6716no—
625C23—674no—
626C23—674no—
627C23—674no—
628C23—1348no—
629C23—1348no—
630C23—1348no—
631C23—1348no—
632C23—1348no—
633C23—1348no—
634C23—1342no—
635C23—1342no—
636C23—1342no—
637C23—1342no—
638C23C2×D4×D6712yes—
639C23C2×Q8×D6712yes—
640C23#41×D6712yes—
641C23C2×#1176162712yes—
642C23C2×#1176162912yes—
643C23#1452408812yes—
644C23#1452409112yes—
645C23C24×D6711yescharacteristic
646Q8—416no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—28no—
650C2×C4—28no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—26816no—
672C2×C4—26816no—
673C2×C4—2684no—
674C2×C4—2684no—
675C2×C4—2684no—
676C2×C4—2684no—
677C2×C4—2684no—
678C2×C4—674no—
679C2×C4—674no—
680C2×C4—13432no—
681C2×C4—1342no—
682C2×C4—1342no—
683C2×C4—1342no—
684C2×C4—1342no—
685C2×C4—1342no—
686C2×C4—1342no—
687C2×C4—1342no—
688C2×C4—1342no—
689C2×C4—1342no—
690C2×C4—1342no—
691C2×C4—1342no—
692C2×C4—1342no—
693C2×C4—1342no—
694C2×C4—1342no—
695C2×C4—1342no—
696C2×C4—1348no—
697C2×C4—1348no—
698C2×C4—1342no—
699C2×C4—1342no—
700C2×C4—1342no—
701C2×C4—1342no—
702C2×C4C2×D4×D6714yes—
703C2×C4C2×Q8×D6714yes—
704C2×C4C2×#1176162714yes—
705C2×C4C2×#1176162914yes—
706C22—678no—
707C22—13432no—
708C22—1344no—
709C22—1344no—
710C22—1344no—
711C22—1344no—
712C22—1344no—
713C22—1344no—
714C22C22⋊Q8×D6714yes—
715C22#1686395114yes—
716C22#1686402314yes—
717C22#1686403314yes—
718C22#1686404914yes—
719C22#1686407314yes—
720C22#1686408014yes—
721C22C22×D4×D6711yescharacteristic
722C22C22×Q8×D6711yescharacteristic
723C22C2×#41×D6711yescharacteristic
724C22C22×#1176162711yescharacteristic
725C22C22×#1176162911yescharacteristic
726C22C2×#1452408811yescharacteristic
727C22C2×#1452409111yescharacteristic
728C4—24no—
729C4—24no—
730C4—24no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—2682no—
736C4—2682no—
737C4—2682no—
738C4—2682no—
739C4—2682no—
740C4—1344no—
741C4—1344no—
742C2—1348no—
743C2#2256387818yesdirect product factor
744C2C2×C22⋊Q8×D6711yescharacteristic
745C2C2×#1686395111yescharacteristic
746C2C2×#1686402311yescharacteristic
747C2C2×#1686403311yescharacteristic
748C2C2×#1686404911yescharacteristic
749C2C2×#1686407311yescharacteristic
750C2C2×#1686408011yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×#395×C67C2
socleC24×C67C24
prime radicalC24×D67C23
hypercenterC2×#395D67
hypocenterC67C2×#2438
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
3. #22563878C2direct (N × H)
4. C2×#16863338C2semidirect
5. C2×#16863329C2semidirect
6. C2×#16863328C2semidirect
7. C2×#16863303C2semidirect
8. C2×#16863291C2semidirect
9. C2×#16863282C2semidirect
10. C2×#16863281C2semidirect
16. C2×#395×C67C2semidirect
38. #16863338C22semidirect
39. #16863329C22semidirect
40. #16863328C22semidirect
41. #16863303C22semidirect
42. #16863291C22semidirect
43. #16863282C22semidirect
44. #16863281C22semidirect
65. #395×C67C22semidirect
85. C22×C4×D67Q8semidirect
197. C2×C4×D67C2×Q8semidirect
367. C2×C67#2438semidirect
382. C2×#395D67semidirect
392. C67C2×#2438semidirect
421. #395C2×D67semidirect
743. C2#22563878direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240192
C22×#145240012
#225638782
C2×#168633382
C2×#168633292
C2×#168633282
C2×#168633032
C2×#168632912
C2×#168632822
C2×#168632812
C2×#168632702
C2×#168632672
C2×#168632582
C2×#168632532
C2×#95×D672
C2×#395×C672
C2×#243867