Finite Group Databasebeta

← C2×#22563926 #31023911

Subgroups — C2×#22563926 #31023911

Order 17152.

2942 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524033C211yesmaximal, characteristic, complemented
2C22×C4⋊C4×D67C211yesmaximal, characteristic
3#22563926C2116yesmaximal, direct product factor
4C2×#16863338C211yesmaximal, characteristic, complemented
5C2×#16863329C211yesmaximal, characteristic, complemented
6C2×#16863328C211yesmaximal, characteristic, complemented
7C2×#16863293C211yesmaximal, characteristic, complemented
8C2×#16863293C211yesmaximal, characteristic, complemented
9C2×#16863270C211yesmaximal, characteristic
10C2×#16863270C211yesmaximal, characteristic
11C2×#16863260C211yesmaximal, characteristic, complemented
12C2×#16863255C211yesmaximal, characteristic
13C2×#16863255C211yesmaximal, characteristic
14C2×#16863253C211yesmaximal, characteristic
15C2×#16863243C211yesmaximal, characteristic
16C2×#400×C67C211yesmaximal, characteristic, complemented
17C23×C4×D67C2211yescharacteristic
18C23×C4×D67C2211yescharacteristic
19C23×C4×D67C2211yescharacteristic
20C2×#14524033—28no—
21C2×#14524033C2218yescomplemented
22C22×C4⋊Dic67C2211yescharacteristic
23C22×C4⋊Dic67C2211yescharacteristic
24C22×C4⋊Dic67C2211yescharacteristic
25C22×C4⋊Dic67C2211yescharacteristic
26C22×Dic67⋊C4C2211yescharacteristic
27C22×Dic67⋊C4C2211yescharacteristic
28C22×Dic67⋊C4C2211yescharacteristic
29C22×Dic67⋊C4C2211yescharacteristic
30C22×Dic67⋊C4C2211yescharacteristic
31C22×Dic67⋊C4C2211yescharacteristic
32C22×Dic67⋊C4C2211yescharacteristic
33C22×Dic67⋊C4C2211yescharacteristic
34C2×C4⋊C4×D67—28no—
35C2×C4⋊C4×D67C2218yes—
36C22×(C2×D67)⋊C4C2211yescharacteristic
37C22×(C2×D67)⋊C4C2211yescharacteristic
38C22×(C2×D67)⋊C4C2211yescharacteristic
39C22×(C2×D67)⋊C4C2211yescharacteristic
40C22×C4×Dic67C2211yescharacteristic
41C22×C4×Dic67C2211yescharacteristic
42#16863338C2218yescomplemented
43#16863329C2218yescomplemented
44#16863328C2218yescomplemented
45#16863293C2218yescomplemented
46#16863293C2218yescomplemented
47#16863270C2218yes—
48#16863270C2218yes—
49#16863260C2218yescomplemented
50#16863255C2218yes—
51#16863255C2218yes—
52#16863253C2218yes—
53#16863243C2218yes—
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
63#400×C67C2218yescomplemented
64C2×#95×C67C2211yescharacteristic
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—42no—
84C22×C4×D67—42no—
85C22×C4×D67Q818yes—
86C22×C4×D67C2314yes—
87C22×C4×D67C2314yes—
88C22×C4×D67C2314yes—
89#14524033—232no—
90C2×C4⋊Dic67—24no—
91C2×C4⋊Dic67—24no—
92C2×C4⋊Dic67—42no—
93C2×C4⋊Dic67—42no—
94C2×C4⋊Dic67C2314yes—
95C2×C4⋊Dic67C2314yes—
96C2×C4⋊Dic67C2314yes—
97C2×C4⋊Dic67C2314yes—
98C2×Dic67⋊C4—24no—
99C2×Dic67⋊C4—24no—
100C2×Dic67⋊C4—24no—
101C2×Dic67⋊C4—24no—
102C2×Dic67⋊C4—24no—
103C2×Dic67⋊C4—42no—
104C2×Dic67⋊C4—42no—
105C2×Dic67⋊C4D418yes—
106C2×Dic67⋊C4C2314yes—
107C2×Dic67⋊C4C2314yes—
108C2×Dic67⋊C4C2314yes—
109C2×Dic67⋊C4C2314yes—
110C2×Dic67⋊C4C2314yes—
111C2×Dic67⋊C4C2314yes—
112C2×Dic67⋊C4C2314yes—
113C2×Dic67⋊C4C2314yes—
114C4⋊C4×D67—232no—
115C2×(C2×D67)⋊C4—24no—
116C2×(C2×D67)⋊C4—24no—
117C2×(C2×D67)⋊C4—24no—
118C2×(C2×D67)⋊C4—24no—
119C2×(C2×D67)⋊C4C2314yes—
120C2×(C2×D67)⋊C4C2314yes—
121C2×(C2×D67)⋊C4C2314yes—
122C2×(C2×D67)⋊C4C2314yes—
123C2×C4×Dic67—24no—
124C2×C4×Dic67—24no—
125C2×C4×Dic67C2314yes—
126C2×C4×Dic67C2314yes—
127C67⋊#95C2314yes—
128C67⋊#95C2314yes—
129C67⋊#95C2314yes—
130C67⋊#95C2314yes—
131C67⋊#95C2314yes—
132C67⋊#95C2314yes—
133C67⋊#95C2314yes—
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×C67C2314yes—
144C2×C4⋊C4×C67C2314yes—
145#95×C67C2314yes—
146#95×C67C2314yes—
147#95×C67C2314yes—
148#95×C67C2314yes—
149#95×C67C2314yes—
150C23×D67—22no—
151C23×D67—22no—
152C23×D67—22no—
153C23×D67—22no—
154C23×D67C2×Q814yes—
155C23×D67#4114yes—
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×Dic67C2×D414yes—
176C22×Dic67C2×D414yes—
177C22×Dic67C2×Q814yes—
178C22×Dic67#4114yes—
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×Q8116yes—
198C4⋊Dic67—28no—
199C4⋊Dic67—28no—
200C4⋊Dic67—44no—
201C4⋊Dic67—44no—
202Dic67⋊C4—28no—
203Dic67⋊C4—28no—
204Dic67⋊C4—28no—
205Dic67⋊C4—28no—
206Dic67⋊C4—28no—
207Dic67⋊C4—44no—
208Dic67⋊C4—44no—
209Dic67⋊C4C2×D4116yes—
210(C2×D67)⋊C4—28no—
211(C2×D67)⋊C4—28no—
212(C2×D67)⋊C4—28no—
213(C2×D67)⋊C4—28no—
214C4×Dic67—28no—
215C4×Dic67—28no—
216C24×C67C2411yescharacteristic
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×C67—22no—
235C22×C4×C67—22no—
236C22×C4×C67C2×D414yes—
237C22×C4×C67C2×Q814yes—
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—
247C23×C67C22×D412yes—
248C23×C67C22×Q812yes—
249C23×C67C2×#4112yes—
250C23×C67C2×#4112yes—
251C23×C67C2×#4112yes—
252C23×C67H(5,𝔽2)12yes—
253C23×C672−1+412yes—
254C23×C67C2511yescharacteristic
255C22×D67—28no—
256C22×D67—28no—
257C22×D67—28no—
258C22×D67—28no—
259C22×D67—28no—
260C22×D67—28no—
261C22×D67—22no—
262C22×D67—22no—
263C22×D67—22no—
264C22×D67—22no—
265C22×D67#125116yescomplemented
266C22×D67C22×Q814yes—
267C22×D67C2×#4114yes—
268C22×D67C2×#4114yes—
269C2×C4×C67—28no—
270C2×C4×C67—28no—
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—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—44no—
291C2×C4×C67—44no—
292C2×C4×C67—44no—
293C2×C4×C67—44no—
294C2×C4×C67—44no—
295C2×C4×C67C22×D414yes—
296C2×C4×C67C22×Q814yes—
297C2×Dic67—28no—
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—22no—
311C2×Dic67—22no—
312C2×Dic67—22no—
313C2×Dic67—22no—
314C2×Dic67—22no—
315C2×Dic67—44no—
316C2×Dic67—44no—
317C2×Dic67—44no—
318C2×Dic67—44no—
319C2×Dic67—44no—
320C2×Dic67C22⋊Q8116yes—
321C2×Dic67C22×D414yes—
322C2×Dic67C22×D414yes—
323C2×Dic67C22×Q814yes—
324C2×Dic67C2×#4114yes—
325C4×D67—232no—
326C4×D67—416no—
327C4×D67—416no—
328C22×C67C2×C22⋊Q814yes—
329C22×C67C2×#12514yes—
330C22×C67#54414yes—
331C22×C67#54614yes—
332C22×C67#54814yes—
333C22×C67#55214yes—
334C22×C67#55314yes—
335C22×C67C23×D411yescharacteristic
336C22×C67C23×Q811yescharacteristic
337C22×C67C22×#4111yescharacteristic
338C22×C67C22×#4111yescharacteristic
339C22×C67C22×#4111yescharacteristic
340C22×C67C2×H(5,𝔽2)11yescharacteristic
341C22×C67C2×2−1+411yescharacteristic
342C2×D67—24no—
343C2×D67—24no—
344C2×D67—24no—
345C2×D67—24no—
346C2×D67—232no—
347C2×D67—24no—
348C2×D67—24no—
349C2×D67C2×#12518yescomplemented
350C4×C67—24no—
351C4×C67—24no—
352C4×C67—42no—
353C4×C67—42no—
354C4×C67—42no—
355C4×C67—42no—
356C4×C67—42no—
357Dic67—24no—
358Dic67—42no—
359Dic67—42no—
360Dic67—42no—
361Dic67—42no—
362Dic67—42no—
363Dic67C2×C22⋊Q818yes—
364C2×#2442—671nomaximal, Sylow
365C2×C67#244218yescomplemented
366C2×C67C22×C22⋊Q811yescharacteristic
367C2×C67C22×#12511yescharacteristic
368C2×C67C2×#54411yescharacteristic
369C2×C67C2×#54611yescharacteristic
370C2×C67C2×#54811yescharacteristic
371C2×C67C2×#55211yescharacteristic
372C2×C67C2×#55311yescharacteristic
373D67—28no—
374C22×#125—671no—
375C23×C4⋊C4—671no—
376#2442—6716no—
377C2×#400—671no—
378C2×#400D6711yescharacteristic, complemented
379C2×#398—671no—
380C2×#398—671no—
381C2×#389—671no—
382C2×#389—671no—
383C2×#385—671no—
384C2×#385—671no—
385C2×#382—671no—
386C2×#380—671no—
387C2×#380—671no—
388C2×#380—671no—
389C2×C4×C22⋊C4—671no—
390C67C2×#244211yescharacteristic, complemented, Sylow
391C24×C4—671no—
392C24×C4—671no—
393C24×C4—671no—
394C2×#125—678no—
395C2×#125—1348no—
396C22×C4⋊C4—671no—
397C22×C4⋊C4—671no—
398C22×C4⋊C4—671no—
399C22×C4⋊C4—671no—
400C22×C4⋊C4—671no—
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—678no—
409C22×C4⋊C4—1348no—
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#400C2×D6718yescomplemented
420#398—678no—
421#398—678no—
422#389—678no—
423#389—678no—
424#385—678no—
425#385—678no—
426#382—678no—
427#380—678no—
428#380—678no—
429#380—678no—
430C4×C22⋊C4—678no—
431C2×#95—671no—
432C2×#95—671no—
433C2×#95—671no—
434C2×#95—671no—
435C2×#95—671no—
436C2×#95—671no—
437C2×#95—671no—
438C2×#95C2×D6711yescharacteristic
439C2×#95C2×D6711yescharacteristic
440C2×#95C2×D6711yescharacteristic
441C2×#95C2×D6711yescharacteristic
442C2×#95C2×D6711yescharacteristic
443C25—671no—
444C23×C4—2682no—
445C23×C4—2682no—
446C23×C4—674no—
447C23×C4—674no—
448C23×C4—671no—
449C23×C4—671no—
450C23×C4—678no—
451C23×C4—674no—
452C23×C4—671no—
453C23×C4—671no—
454C23×C4—671no—
455C23×C4—671no—
456C23×C4—671no—
457C23×C4—1344no—
458C23×C4—1344no—
459C23×C4—1344no—
460C23×C4—1344no—
461C23×C4—1344no—
462C23×C4—1344no—
463C23×C4C22×D6711yescharacteristic
464C23×C4C22×D6711yescharacteristic
465C23×C4C22×D6711yescharacteristic
466C23×C4C22×D6711yescharacteristic
467C23×C4C22×D6711yescharacteristic
468C23×C4C22×D6711yescharacteristic
469C23×C4C22×D6711yescharacteristic
470#125—13432no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—2682no—
474C2×C4⋊C4—2682no—
475C2×C4⋊C4—2682no—
476C2×C4⋊C4—2682no—
477C2×C4⋊C4—674no—
478C2×C4⋊C4—674no—
479C2×C4⋊C4—674no—
480C2×C4⋊C4—674no—
481C2×C4⋊C4—678no—
482C2×C4⋊C4—674no—
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—13432no—
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⋊C4—1344no—
498C2×C4⋊C4C22×D6714yes—
499C2×C4⋊C4C22×D6714yes—
500C2×C22⋊C4—674no—
501C2×C22⋊C4—674no—
502C2×C22⋊C4—674no—
503C2×C22⋊C4—674no—
504C2×C22⋊C4—1344no—
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#95C22×D6714yes—
520#95C22×D6714yes—
521#95C22×D6714yes—
522#95C22×D6714yes—
523#95C22×D6714yes—
524C24—674no—
525C24—674no—
526C24—674no—
527C24—672no—
528C24—1342no—
529C24—1342no—
530C24—1342no—
531C24—1342no—
532C24C23×D6711yescharacteristic
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
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—26816no—
553C22×C4—2684no—
554C22×C4—2684no—
555C22×C4—26816no—
556C22×C4—674no—
557C22×C4—674no—
558C22×C4—674no—
559C22×C4—672no—
560C22×C4—674no—
561C22×C4—672no—
562C22×C4—6716no—
563C22×C4—672no—
564C22×C4—672no—
565C22×C4—672no—
566C22×C4—672no—
567C22×C4—672no—
568C22×C4—1348no—
569C22×C4—1348no—
570C22×C4—1348no—
571C22×C4—1348no—
572C22×C4—13432no—
573C22×C4—1348no—
574C22×C4—1342no—
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—1348no—
590C22×C4—1342no—
591C22×C4—1342no—
592C22×C4D4×D6714yes—
593C22×C4Q8×D6714yes—
594C22×C4C23×D6712yes—
595C22×C4C23×D6712yes—
596C22×C4C23×D6712yes—
597C22×C4C23×D6712yes—
598C22×C4C23×D6712yes—
599C22×C4C23×D6712yes—
600C22×C4C23×D6712yes—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—2684no—
604C4⋊C4—2684no—
605C4⋊C4—2684no—
606C4⋊C4—2684no—
607C4⋊C4—6716no—
608C4⋊C4—1348no—
609C4⋊C4—1348no—
610C4⋊C4—1348no—
611C4⋊C4—1348no—
612C4⋊C4—1348no—
613C4⋊C4—1348no—
614C4⋊C4—1348no—
615C22⋊C4—1348no—
616C22⋊C4—1348no—
617C22⋊C4—1348no—
618C22⋊C4—1348no—
619C42—1348no—
620C42—1348no—
621C23—6716no—
622C23—674no—
623C23—674no—
624C23—674no—
625C23—1348no—
626C23—1348no—
627C23—1348no—
628C23—1348no—
629C23—1348no—
630C23—1348no—
631C23—1342no—
632C23—1342no—
633C23—1342no—
634C23—1342no—
635C23C2×D4×D6712yes—
636C23C2×Q8×D6712yes—
637C23#41×D6712yes—
638C23#41×D6712yes—
639C23#41×D6712yes—
640C23#1452408912yes—
641C23#1452409012yes—
642C23C24×D6711yescharacteristic
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
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—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—26816no—
670C2×C4—26816no—
671C2×C4—2684no—
672C2×C4—2684no—
673C2×C4—2684no—
674C2×C4—2684no—
675C2×C4—2684no—
676C2×C4—6716no—
677C2×C4—674no—
678C2×C4—674no—
679C2×C4—674no—
680C2×C4—674no—
681C2×C4—13432no—
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—1342no—
697C2×C4—1348no—
698C2×C4—1342no—
699C2×C4—1342no—
700C2×C4C2×D4×D6714yes—
701C2×C4C2×Q8×D6714yes—
702C22—678no—
703C22—1344no—
704C22—13432no—
705C22—1344no—
706C22—1344no—
707C22—1344no—
708C22—1344no—
709C22—1344no—
710C22C22⋊Q8×D6714yes—
711C22#125×D6714yes—
712C22#1686402614yes—
713C22#1686403814yes—
714C22#1686405414yes—
715C22#1686408214yes—
716C22#1686409714yes—
717C22C22×D4×D6711yescharacteristic
718C22C22×Q8×D6711yescharacteristic
719C22C2×#41×D6711yescharacteristic
720C22C2×#41×D6711yescharacteristic
721C22C2×#41×D6711yescharacteristic
722C22C2×#1452408911yescharacteristic
723C22C2×#1452409011yescharacteristic
724C4—24no—
725C4—24no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—2682no—
732C4—2682no—
733C4—2682no—
734C4—2682no—
735C4—2682no—
736C4—678no—
737C4—1344no—
738C2—1348no—
739C2#2256392618yesdirect product factor
740C2C2×C22⋊Q8×D6711yescharacteristic
741C2C2×#125×D6711yescharacteristic
742C2C2×#1686402611yescharacteristic
743C2C2×#1686403811yescharacteristic
744C2C2×#1686405411yescharacteristic
745C2C2×#1686408211yescharacteristic
746C2C2×#1686409711yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×#400×C67C2
socleC24×C67C24
prime radicalC24×D67C23
hypercenterC2×#400D67
hypocenterC67C2×#2442
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. C22×#14524033C2semidirect
3. #22563926C2direct (N × H)
4. C2×#16863338C2semidirect
5. C2×#16863329C2semidirect
6. C2×#16863328C2semidirect
7. C2×#16863293C2semidirect
8. C2×#16863293C2semidirect
11. C2×#16863260C2semidirect
16. C2×#400×C67C2semidirect
21. C2×#14524033C22semidirect
42. #16863338C22semidirect
43. #16863329C22semidirect
44. #16863328C22semidirect
45. #16863293C22semidirect
46. #16863293C22semidirect
49. #16863260C22semidirect
63. #400×C67C22semidirect
265. C22×D67#125semidirect
349. C2×D67C2×#125semidirect
365. C2×C67#2442semidirect
378. C2×#400D67semidirect
390. C67C2×#2442semidirect
419. #400C2×D67semidirect
739. C2#22563926direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240332
C22×C4⋊C4×D672
#225639262
C2×#168633382
C2×#168633292
C2×#168633282
C2×#168632932
C2×#168632702
C2×#168632602
C2×#168632552
C2×#168632532
C2×#168632432
C2×#400×C672
C2×#244267