Finite Group Databasebeta

← C2×#22564494 #31025646

Subgroups — C2×#22564494 #31025646

Order 17152.

2918 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524000C211yesmaximal, characteristic
2C22×C4⋊C4×D67C211yesmaximal, characteristic
3#22564494C2116yesmaximal, direct product factor
4C2×#16863338C211yesmaximal, characteristic, complemented
5C2×#16863337C211yesmaximal, characteristic, complemented
6C2×#16863330C211yesmaximal, characteristic, complemented
7C2×#16863329C211yesmaximal, characteristic, complemented
8C2×#16863281C211yesmaximal, characteristic, complemented
9C2×#16863280C211yesmaximal, characteristic, complemented
10C2×#16863277C211yesmaximal, characteristic, complemented
11C2×#16863270C211yesmaximal, characteristic
12C2×#16863267C211yesmaximal, characteristic
13C2×#16863258C211yesmaximal, characteristic
14C2×#16863258C211yesmaximal, characteristic
15C2×#16863258C211yesmaximal, characteristic
16C2×#387×C67C211yesmaximal, characteristic, complemented
17C23×C4×D67C2211yescharacteristic
18C23×C4×D67C2211yescharacteristic
19C23×C4×D67C2211yescharacteristic
20C2×#14524000—28no—
21C2×#14524000C2218yes—
22C22×C4⋊Dic67C2211yescharacteristic
23C22×C4⋊Dic67C2211yescharacteristic
24C22×Dic67⋊C4C2211yescharacteristic
25C22×Dic67⋊C4C2211yescharacteristic
26C22×Dic67⋊C4C2211yescharacteristic
27C22×Dic67⋊C4C2211yescharacteristic
28C22×Dic67⋊C4C2211yescharacteristic
29C22×Dic67⋊C4C2211yescharacteristic
30C2×C4⋊C4×D67—28no—
31C2×C4⋊C4×D67C2218yes—
32C22×(C2×D67)⋊C4C2211yescharacteristic
33C22×(C2×D67)⋊C4C2211yescharacteristic
34C22×(C2×D67)⋊C4C2211yescharacteristic
35C22×(C2×D67)⋊C4C2211yescharacteristic
36C22×C4×Dic67C2211yescharacteristic
37#16863338C2218yescomplemented
38#16863337C2218yescomplemented
39#16863330C2218yescomplemented
40#16863329C2218yescomplemented
41#16863281C2218yescomplemented
42#16863280C2218yescomplemented
43#16863277C2218yescomplemented
44#16863270C2218yes—
45#16863267C2218yes—
46#16863258C2218yes—
47#16863258C2218yes—
48#16863258C2218yes—
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
60C2×C67⋊#95C2211yescharacteristic
61C22×C4⋊C4×C67C2211yescharacteristic
62C22×C4⋊C4×C67C2211yescharacteristic
63C22×C42×C67C2211yescharacteristic
64#387×C67C2218yescomplemented
65C2×#95×C67C2211yescharacteristic
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—24no—
84C22×C4×D67—24no—
85C22×C4×D67D418yes—
86C22×C4×D67C2314yes—
87C22×C4×D67C2314yes—
88C22×C4×D67C2314yes—
89#14524000—232no—
90C2×C4⋊Dic67—24no—
91C2×C4⋊Dic67—24no—
92C2×C4⋊Dic67C2314yes—
93C2×C4⋊Dic67C2314yes—
94C2×Dic67⋊C4—24no—
95C2×Dic67⋊C4—24no—
96C2×Dic67⋊C4—24no—
97C2×Dic67⋊C4—24no—
98C2×Dic67⋊C4—24no—
99C2×Dic67⋊C4—24no—
100C2×Dic67⋊C4C2314yes—
101C2×Dic67⋊C4C2314yes—
102C2×Dic67⋊C4C2314yes—
103C2×Dic67⋊C4C2314yes—
104C2×Dic67⋊C4C2314yes—
105C2×Dic67⋊C4C2314yes—
106C4⋊C4×D67—232no—
107C2×(C2×D67)⋊C4—24no—
108C2×(C2×D67)⋊C4—24no—
109C2×(C2×D67)⋊C4—24no—
110C2×(C2×D67)⋊C4—24no—
111C2×(C2×D67)⋊C4C2314yes—
112C2×(C2×D67)⋊C4C2314yes—
113C2×(C2×D67)⋊C4C2314yes—
114C2×(C2×D67)⋊C4C2314yes—
115C2×C4×Dic67—24no—
116C2×C4×Dic67C2314yes—
117C67⋊#95C2314yes—
118C67⋊#95C2314yes—
119C67⋊#95C2314yes—
120C67⋊#95C2314yes—
121C67⋊#95C2314yes—
122C67⋊#95C2314yes—
123C67⋊#95C2314yes—
124C67⋊#95C2314yes—
125C67⋊#95C2314yes—
126C67⋊#95C2314yes—
127C67⋊#95C2314yes—
128C67⋊#95C2314yes—
129C23×C4×C67C2311yescharacteristic
130C23×C4×C67C2311yescharacteristic
131C23×C4×C67C2311yescharacteristic
132C23×C4×C67C2311yescharacteristic
133C23×C4×C67C2311yescharacteristic
134C23×C4×C67C2311yescharacteristic
135C23×C4×C67C2311yescharacteristic
136C2×C4⋊C4×C67—24no—
137C2×C4⋊C4×C67—24no—
138C2×C4⋊C4×C67C2314yes—
139C2×C4⋊C4×C67C2314yes—
140C2×C42×C67—24no—
141C2×C42×C67C2314yes—
142#95×C67C2314yes—
143#95×C67C2314yes—
144#95×C67C2314yes—
145#95×C67C2314yes—
146C23×D67—22no—
147C23×D67—22no—
148C23×D67—22no—
149C23×D67—22no—
150C23×D67C2×D414yes—
151C23×D67#4114yes—
152C23×D67#4114yes—
153C23×D67C2412yes—
154C22×Dic67—22no—
155C22×Dic67—22no—
156C22×Dic67—22no—
157C22×Dic67—22no—
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×Dic67C2×D414yes—
174C22×Dic67#4114yes—
175C22×Dic67C2412yes—
176C22×Dic67C2412yes—
177C22×Dic67C2412yes—
178C22×Dic67C2412yes—
179C22×Dic67C2412yes—
180C22×Dic67C2412yes—
181C22×Dic67C2412yes—
182C2×C4×D67—232no—
183C2×C4×D67—232no—
184C2×C4×D67—28no—
185C2×C4×D67—28no—
186C2×C4×D67—28no—
187C2×C4×D67—28no—
188C2×C4×D67—28no—
189C2×C4×D67—28no—
190C2×C4×D67—28no—
191C2×C4×D67—28no—
192C2×C4×D67—416no—
193C2×C4×D67C2×D4116yes—
194C4⋊Dic67—28no—
195C4⋊Dic67—28no—
196Dic67⋊C4—28no—
197Dic67⋊C4—28no—
198Dic67⋊C4—28no—
199Dic67⋊C4—28no—
200Dic67⋊C4—28no—
201Dic67⋊C4—28no—
202(C2×D67)⋊C4—28no—
203(C2×D67)⋊C4—28no—
204(C2×D67)⋊C4—28no—
205(C2×D67)⋊C4—28no—
206C4×Dic67—28no—
207C24×C67C2411yescharacteristic
208C22×C4×C67—22no—
209C22×C4×C67—22no—
210C22×C4×C67—22no—
211C22×C4×C67—22no—
212C22×C4×C67—22no—
213C22×C4×C67—22no—
214C22×C4×C67—22no—
215C22×C4×C67—22no—
216C22×C4×C67—22no—
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×C67C2×D414yes—
228C22×C4×C67#4114yes—
229C22×C4×C67C2412yes—
230C22×C4×C67C2412yes—
231C22×C4×C67C2412yes—
232C22×C4×C67C2412yes—
233C22×C4×C67C2412yes—
234C22×C4×C67C2412yes—
235C22×C4×C67C2412yes—
236C4⋊C4×C67—28no—
237C4⋊C4×C67—28no—
238C42×C67—28no—
239C23×C67C22×D412yes—
240C23×C67C2×#4112yes—
241C23×C67C2×#4112yes—
242C23×C67C2×#4112yes—
243C23×C67C2×#4112yes—
244C23×C672−1+412yes—
245C23×C672−1+412yes—
246C23×C67C2511yescharacteristic
247C22×D67—28no—
248C22×D67—28no—
249C22×D67—28no—
250C22×D67—28no—
251C22×D67—28no—
252C22×D67—28no—
253C22×D67—22no—
254C22×D67—22no—
255C22×D67—22no—
256C22×D67—22no—
257C22×D67#123116yes—
258C22×D67C22×D414yes—
259C22×D67C2×#4114yes—
260C22×D67C2×#4114yes—
261C2×C4×C67—28no—
262C2×C4×C67—28no—
263C2×C4×C67—22no—
264C2×C4×C67—22no—
265C2×C4×C67—22no—
266C2×C4×C67—22no—
267C2×C4×C67—22no—
268C2×C4×C67—22no—
269C2×C4×C67—22no—
270C2×C4×C67—22no—
271C2×C4×C67—22no—
272C2×C4×C67—22no—
273C2×C4×C67—22no—
274C2×C4×C67—22no—
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—44no—
283C2×C4×C67—44no—
284C2×C4×C67—44no—
285C2×C4×C67—44no—
286C2×C4×C67—44no—
287C2×C4×C67C22×D414yes—
288C2×C4×C67C2×#4114yes—
289C2×Dic67—28no—
290C2×Dic67—28no—
291C2×Dic67—22no—
292C2×Dic67—22no—
293C2×Dic67—22no—
294C2×Dic67—22no—
295C2×Dic67—22no—
296C2×Dic67—22no—
297C2×Dic67—22no—
298C2×Dic67—22no—
299C2×Dic67—22no—
300C2×Dic67—22no—
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—44no—
311C2×Dic67—44no—
312C2×Dic67—44no—
313C2×Dic67—44no—
314C2×Dic67—44no—
315C2×Dic67C22×D414yes—
316C2×Dic67C2×#4114yes—
317C4×D67—232no—
318C4×D67—232no—
319C4×D67—416no—
320C22×C67C2×#12314yes—
321C22×C67#52514yes—
322C22×C67#53614yes—
323C22×C67#55214yes—
324C22×C67#55214yes—
325C22×C67#55214yes—
326C22×C67#55214yes—
327C22×C67C23×D411yescharacteristic
328C22×C67C22×#4111yescharacteristic
329C22×C67C22×#4111yescharacteristic
330C22×C67C22×#4111yescharacteristic
331C22×C67C22×#4111yescharacteristic
332C22×C67C2×2−1+411yescharacteristic
333C22×C67C2×2−1+411yescharacteristic
334C2×D67—24no—
335C2×D67—24no—
336C2×D67—24no—
337C2×D67—24no—
338C2×D67—24no—
339C2×D67—24no—
340C2×D67—232no—
341C2×D67C2×#12318yes—
342C4×C67—24no—
343C4×C67—24no—
344C4×C67—42no—
345C4×C67—42no—
346C4×C67—42no—
347C4×C67—42no—
348C4×C67—42no—
349Dic67—24no—
350Dic67—24no—
351Dic67—42no—
352Dic67—42no—
353Dic67—42no—
354Dic67—42no—
355Dic67—42no—
356C2×#2484—671nomaximal, Sylow
357C2×C67#248418yescomplemented
358C2×C67C22×#12311yescharacteristic
359C2×C67C2×#52511yescharacteristic
360C2×C67C2×#53611yescharacteristic
361C2×C67C2×#55211yescharacteristic
362C2×C67C2×#55211yescharacteristic
363C2×C67C2×#55211yescharacteristic
364C2×C67C2×#55211yescharacteristic
365D67—28no—
366C22×#117—671no—
367C23×C4⋊C4—671no—
368#2484—6716no—
369C2×#400—671no—
370C2×#400—671no—
371C2×#398—671no—
372C2×#398—671no—
373C2×#387—671no—
374C2×#387—671no—
375C2×#387—671no—
376C2×#387D6711yescharacteristic, complemented
377C2×#385—671no—
378C2×#385—671no—
379C2×#381—671no—
380C2×#381—671no—
381C2×#381—671no—
382C67C2×#248411yescharacteristic, complemented, Sylow
383C24×C4—671no—
384C24×C4—671no—
385C24×C4—671no—
386C2×#117—678no—
387C2×#117—1348no—
388C22×C4⋊C4—671no—
389C22×C4⋊C4—671no—
390C22×C4⋊C4—671no—
391C22×C4⋊C4—671no—
392C22×C4⋊C4—671no—
393C22×C4⋊C4—671no—
394C22×C4⋊C4—671no—
395C22×C4⋊C4—671no—
396C22×C4⋊C4—678no—
397C22×C4⋊C4—1348no—
398C22×C4⋊C4C2×D6711yescharacteristic
399C22×C4⋊C4C2×D6711yescharacteristic
400C22×C22⋊C4—671no—
401C22×C22⋊C4—671no—
402C22×C22⋊C4—671no—
403C22×C22⋊C4—671no—
404C22×C42—671no—
405C22×C42C2×D6711yescharacteristic
406#400—678no—
407#400—678no—
408#398—678no—
409#398—678no—
410#387—678no—
411#387—678no—
412#387—678no—
413#387C2×D6718yescomplemented
414#385—678no—
415#385—678no—
416#381—678no—
417#381—678no—
418#381—678no—
419C2×#95—671no—
420C2×#95—671no—
421C2×#95—671no—
422C2×#95—671no—
423C2×#95—671no—
424C2×#95—671no—
425C2×#95—671no—
426C2×#95—671no—
427C2×#95—671no—
428C2×#95—671no—
429C2×#95—671no—
430C2×#95—671no—
431C2×#95C2×D6711yescharacteristic
432C2×#95C2×D6711yescharacteristic
433C2×#95C2×D6711yescharacteristic
434C2×#95C2×D6711yescharacteristic
435C25—671no—
436C23×C4—671no—
437C23×C4—671no—
438C23×C4—678no—
439C23×C4—674no—
440C23×C4—671no—
441C23×C4—671no—
442C23×C4—671no—
443C23×C4—671no—
444C23×C4—671no—
445C23×C4—674no—
446C23×C4—674no—
447C23×C4—1344no—
448C23×C4—1344no—
449C23×C4—1344no—
450C23×C4—1344no—
451C23×C4—1344no—
452C23×C4—1344no—
453C23×C4—1344no—
454C23×C4—1344no—
455C23×C4C22×D6711yescharacteristic
456C23×C4C22×D6711yescharacteristic
457C23×C4C22×D6711yescharacteristic
458C23×C4C22×D6711yescharacteristic
459C23×C4C22×D6711yescharacteristic
460C23×C4C22×D6711yescharacteristic
461C23×C4C22×D6711yescharacteristic
462#117—13432no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—674no—
466C2×C4⋊C4—674no—
467C2×C4⋊C4—674no—
468C2×C4⋊C4—674no—
469C2×C4⋊C4—674no—
470C2×C4⋊C4—674no—
471C2×C4⋊C4—674no—
472C2×C4⋊C4—674no—
473C2×C4⋊C4—13432no—
474C2×C4⋊C4—1344no—
475C2×C4⋊C4—1344no—
476C2×C4⋊C4—1344no—
477C2×C4⋊C4—1344no—
478C2×C4⋊C4—1344no—
479C2×C4⋊C4—1344no—
480C2×C4⋊C4—1344no—
481C2×C4⋊C4—1344no—
482C2×C4⋊C4C22×D6714yes—
483C2×C4⋊C4C22×D6714yes—
484C2×C22⋊C4—674no—
485C2×C22⋊C4—674no—
486C2×C22⋊C4—674no—
487C2×C22⋊C4—674no—
488C2×C22⋊C4—1344no—
489C2×C22⋊C4—1344no—
490C2×C22⋊C4—1344no—
491C2×C22⋊C4—1344no—
492C2×C42—24no—
493C2×C42—674no—
494C2×C42—1344no—
495C2×C42C22×D6714yes—
496#95—674no—
497#95—674no—
498#95—674no—
499#95—674no—
500#95—674no—
501#95—674no—
502#95—674no—
503#95—674no—
504#95—674no—
505#95—674no—
506#95—674no—
507#95—674no—
508#95C22×D6714yes—
509#95C22×D6714yes—
510#95C22×D6714yes—
511#95C22×D6714yes—
512C24—674no—
513C24—674no—
514C24—674no—
515C24—672no—
516C24—1342no—
517C24—1342no—
518C24—1342no—
519C24—1342no—
520C24C23×D6711yescharacteristic
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—26816no—
541C22×C4—674no—
542C22×C4—674no—
543C22×C4—672no—
544C22×C4—672no—
545C22×C4—6716no—
546C22×C4—672no—
547C22×C4—672no—
548C22×C4—672no—
549C22×C4—672no—
550C22×C4—672no—
551C22×C4—1348no—
552C22×C4—1348no—
553C22×C4—1348no—
554C22×C4—1348no—
555C22×C4—1348no—
556C22×C4—13432no—
557C22×C4—1348no—
558C22×C4—1348no—
559C22×C4—13432no—
560C22×C4—1342no—
561C22×C4—1342no—
562C22×C4—1342no—
563C22×C4—1342no—
564C22×C4—1342no—
565C22×C4—1342no—
566C22×C4—1342no—
567C22×C4—1342no—
568C22×C4—1342no—
569C22×C4—1342no—
570C22×C4—1342no—
571C22×C4—1342no—
572C22×C4—1342no—
573C22×C4—1342no—
574C22×C4—1342no—
575C22×C4—1342no—
576C22×C4—1342no—
577C22×C4—1342no—
578C22×C4—1342no—
579C22×C4—1348no—
580C22×C4D4×D6714yes—
581C22×C4#1176162814yes—
582C22×C4C23×D6712yes—
583C22×C4C23×D6712yes—
584C22×C4C23×D6712yes—
585C22×C4C23×D6712yes—
586C22×C4C23×D6712yes—
587C22×C4C23×D6712yes—
588C22×C4C23×D6712yes—
589C4⋊C4—28no—
590C4⋊C4—28no—
591C4⋊C4—1348no—
592C4⋊C4—1348no—
593C4⋊C4—1348no—
594C4⋊C4—1348no—
595C4⋊C4—1348no—
596C4⋊C4—1348no—
597C4⋊C4—1348no—
598C4⋊C4—1348no—
599C22⋊C4—1348no—
600C22⋊C4—1348no—
601C22⋊C4—1348no—
602C22⋊C4—1348no—
603C42—28no—
604C42—1348no—
605C23—6716no—
606C23—674no—
607C23—674no—
608C23—674no—
609C23—1348no—
610C23—1348no—
611C23—1348no—
612C23—1348no—
613C23—1348no—
614C23—1342no—
615C23—1342no—
616C23—1348no—
617C23—1342no—
618C23—1342no—
619C23C2×D4×D6712yes—
620C23#41×D6712yes—
621C23#41×D6712yes—
622C23#41×D6712yes—
623C23C2×#1176162812yes—
624C23#1452409012yes—
625C23#1452409112yes—
626C23C24×D6711yescharacteristic
627C2×C4—28no—
628C2×C4—28no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—44no—
652C2×C4—44no—
653C2×C4—26816no—
654C2×C4—2684no—
655C2×C4—2684no—
656C2×C4—2684no—
657C2×C4—2684no—
658C2×C4—2684no—
659C2×C4—674no—
660C2×C4—674no—
661C2×C4—13432no—
662C2×C4—13432no—
663C2×C4—1342no—
664C2×C4—1342no—
665C2×C4—1342no—
666C2×C4—1342no—
667C2×C4—1342no—
668C2×C4—1342no—
669C2×C4—1342no—
670C2×C4—1342no—
671C2×C4—1342no—
672C2×C4—1342no—
673C2×C4—1342no—
674C2×C4—1342no—
675C2×C4—1342no—
676C2×C4—1342no—
677C2×C4—1342no—
678C2×C4—1348no—
679C2×C4—1348no—
680C2×C4—1342no—
681C2×C4—1342no—
682C2×C4—1342no—
683C2×C4—1342no—
684C2×C4C2×D4×D6714yes—
685C2×C4C2×#1176162814yes—
686C22—678no—
687C22—1344no—
688C22—13432no—
689C22—1344no—
690C22—1344no—
691C22—1344no—
692C22—1344no—
693C22—1344no—
694C22#123×D6714yes—
695C22#1686390514yes—
696C22#1686396914yes—
697C22#1686407814yes—
698C22#1686408214yes—
699C22#1686408514yes—
700C22#1686408714yes—
701C22C22×D4×D6711yescharacteristic
702C22C2×#41×D6711yescharacteristic
703C22C2×#41×D6711yescharacteristic
704C22C2×#41×D6711yescharacteristic
705C22C22×#1176162811yescharacteristic
706C22C2×#1452409011yescharacteristic
707C22C2×#1452409111yescharacteristic
708C4—24no—
709C4—24no—
710C4—42no—
711C4—42no—
712C4—42no—
713C4—42no—
714C4—42no—
715C4—2682no—
716C4—2682no—
717C4—2682no—
718C4—2682no—
719C4—2682no—
720C4—1344no—
721C4—1344no—
722C2—1348no—
723C2#2256449418yesdirect product factor
724C2C2×#123×D6711yescharacteristic
725C2C2×#1686390511yescharacteristic
726C2C2×#1686396911yescharacteristic
727C2C2×#1686407811yescharacteristic
728C2C2×#1686408211yescharacteristic
729C2C2×#1686408511yescharacteristic
730C2C2×#1686408711yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×#387×C67C2
socleC24×C67C24
prime radicalC24×D67C23
hypercenterC2×#387D67
hypocenterC67C2×#2484
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. #22564494C2direct (N × H)
4. C2×#16863338C2semidirect
5. C2×#16863337C2semidirect
6. C2×#16863330C2semidirect
7. C2×#16863329C2semidirect
8. C2×#16863281C2semidirect
9. C2×#16863280C2semidirect
10. C2×#16863277C2semidirect
16. C2×#387×C67C2semidirect
37. #16863338C22semidirect
38. #16863337C22semidirect
39. #16863330C22semidirect
40. #16863329C22semidirect
41. #16863281C22semidirect
42. #16863280C22semidirect
43. #16863277C22semidirect
64. #387×C67C22semidirect
357. C2×C67#2484semidirect
376. C2×#387D67semidirect
382. C67C2×#2484semidirect
413. #387C2×D67semidirect
723. C2#22564494direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240002
C22×C4⋊C4×D672
#225644942
C2×#168633382
C2×#168633372
C2×#168633302
C2×#168633292
C2×#168632812
C2×#168632802
C2×#168632772
C2×#168632702
C2×#168632672
C2×#168632582
C2×#387×C672
C2×#248467