Finite Group Databasebeta

← C2×#22565293 #31025924

Subgroups — C2×#22565293 #31025924

Order 17152.

2726 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524035C211yesmaximal, characteristic, complemented
2C22×#14524022C211yesmaximal, characteristic
3#22565293C2116yesmaximal, direct product factor
4C2×#16863332C211yesmaximal, characteristic
5C2×#16863328C211yesmaximal, characteristic, complemented
6C2×#16863319C211yesmaximal, characteristic
7C2×#16863317C211yesmaximal, characteristic, complemented
8C2×#16863300C211yesmaximal, characteristic, complemented
9C2×#16863294C211yesmaximal, characteristic, complemented
10C2×#16863293C211yesmaximal, characteristic, complemented
11C2×#16863289C211yesmaximal, characteristic
12C2×#16863289C211yesmaximal, characteristic
13C2×#16863280C211yesmaximal, characteristic, complemented
14C2×#16863269C211yesmaximal, characteristic
15C2×C4×Dic67⋊C4C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C67C211yesmaximal, characteristic
17C23×Dic134C2211yescharacteristic
18C2×#14524035—28no—
19C2×#14524035C2218yescomplemented
20C2×#14524022—28no—
21C2×#14524022C2218yes—
22C22×C4⋊Dic67C2211yescharacteristic
23C22×C4⋊Dic67C2211yescharacteristic
24C22×C4⋊Dic67C2211yescharacteristic
25C22×C4⋊Dic67C2211yescharacteristic
26C22×C4⋊Dic67C2211yescharacteristic
27C22×Dic67⋊C4C2211yescharacteristic
28C22×Dic67⋊C4C2211yescharacteristic
29C22×Dic67⋊C4C2211yescharacteristic
30C22×Dic67⋊C4C2211yescharacteristic
31C22×Dic67⋊C4C2211yescharacteristic
32C22×Dic67⋊C4C2211yescharacteristic
33C22×Dic67⋊C4C2211yescharacteristic
34C22×Dic67⋊C4C2211yescharacteristic
35C22×C22⋊Dic67C2211yescharacteristic
36C22×C22⋊Dic67C2211yescharacteristic
37C22×C22⋊Dic67C2211yescharacteristic
38C22×C22⋊Dic67C2211yescharacteristic
39C22×C4×Dic67C2211yescharacteristic
40C22×C4×Dic67C2211yescharacteristic
41#16863332C2218yes—
42#16863328C2218yescomplemented
43#16863319C2218yes—
44#16863317C2218yescomplemented
45#16863300C2218yescomplemented
46#16863294C2218yescomplemented
47#16863293C2218yescomplemented
48#16863289C2218yes—
49#16863289C2218yes—
50#16863280C2218yescomplemented
51#16863269C2218yes—
52C4×Dic67⋊C4C2218yescomplemented
53C2×C67⋊#95C2211yescharacteristic
54C2×C67⋊#95C2211yescharacteristic
55C2×C67⋊#95C2211yescharacteristic
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2211yescharacteristic
59C2×C67⋊#95C2211yescharacteristic
60C2×C67⋊#95C2211yescharacteristic
61C24×C4×C67C2211yescharacteristic
62C22×C22⋊C4×C67C2211yescharacteristic
63C22×C22⋊C4×C67C2211yescharacteristic
64C22×C42×C67C2211yescharacteristic
65C22×C42×C67C2211yescharacteristic
66C4×C22⋊C4×C67C2218yes—
67C2×#95×C67C2211yescharacteristic
68C2×#95×C67C2211yescharacteristic
69C22×Dic134—24no—
70C22×Dic134—24no—
71C22×Dic134—42no—
72C22×Dic134C2314yes—
73C23×Dic67C2311yescharacteristic
74C23×Dic67C2311yescharacteristic
75C23×Dic67C2311yescharacteristic
76C23×Dic67C2311yescharacteristic
77C23×Dic67C2311yescharacteristic
78C23×Dic67C2311yescharacteristic
79C23×Dic67C2311yescharacteristic
80C23×Dic67C2311yescharacteristic
81#14524035—232no—
82#14524022—232no—
83C2×C4⋊Dic67—24no—
84C2×C4⋊Dic67—24no—
85C2×C4⋊Dic67—24no—
86C2×C4⋊Dic67—24no—
87C2×C4⋊Dic67—42no—
88C2×C4⋊Dic67C2314yes—
89C2×C4⋊Dic67C2314yes—
90C2×C4⋊Dic67C2314yes—
91C2×C4⋊Dic67C2314yes—
92C2×C4⋊Dic67C2314yes—
93C2×Dic67⋊C4—24no—
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⋊C4D418yes—
101C2×Dic67⋊C4C2314yes—
102C2×Dic67⋊C4C2314yes—
103C2×Dic67⋊C4C2314yes—
104C2×Dic67⋊C4C2314yes—
105C2×Dic67⋊C4C2314yes—
106C2×Dic67⋊C4C2314yes—
107C2×Dic67⋊C4C2314yes—
108C2×Dic67⋊C4C2314yes—
109C2×C22⋊Dic67—24no—
110C2×C22⋊Dic67—24no—
111C2×C22⋊Dic67—24no—
112C2×C22⋊Dic67—42no—
113C2×C22⋊Dic67C2314yes—
114C2×C22⋊Dic67C2314yes—
115C2×C22⋊Dic67C2314yes—
116C2×C22⋊Dic67C2314yes—
117C2×C4×Dic67—24no—
118C2×C4×Dic67—42no—
119C2×C4×Dic67C2314yes—
120C2×C4×Dic67C2314yes—
121C67⋊#95C2314yes—
122C67⋊#95C2314yes—
123C67⋊#95C2314yes—
124C67⋊#95C2314yes—
125C67⋊#95C2314yes—
126C67⋊#95C2314yes—
127C67⋊#95C2314yes—
128C67⋊#95C2314yes—
129C25×C67C2311yescharacteristic
130C23×C4×C67—24no—
131C23×C4×C67—24no—
132C23×C4×C67—42no—
133C23×C4×C67C2311yescharacteristic
134C23×C4×C67C2314yes—
135C23×C4×C67C2311yescharacteristic
136C23×C4×C67C2311yescharacteristic
137C23×C4×C67C2311yescharacteristic
138C23×C4×C67C2311yescharacteristic
139C23×C4×C67C2311yescharacteristic
140C2×C22⋊C4×C67—24no—
141C2×C22⋊C4×C67Q818yescomplemented
142C2×C22⋊C4×C67C2314yes—
143C2×C22⋊C4×C67C2314yes—
144C2×C42×C67—24no—
145C2×C42×C67—42no—
146C2×C42×C67C2314yes—
147C2×C42×C67C2314yes—
148#95×C67C2314yes—
149#95×C67C2314yes—
150C2×Dic134—28no—
151C2×Dic134—28no—
152C2×Dic134—44no—
153C2×Dic134—416no—
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×Dic67—22no—
174C22×Dic67—22no—
175C22×Dic67C2×D414yes—
176C22×Dic67C2×D414yes—
177C22×Dic67#4114yes—
178C22×Dic67C2412yes—
179C22×Dic67C2412yes—
180C22×Dic67C2412yes—
181C22×Dic67C2412yes—
182C22×Dic67C2412yes—
183C22×Dic67C2412yes—
184C22×Dic67C2412yes—
185C22×Dic67C2412yes—
186C4⋊Dic67—28no—
187C4⋊Dic67—28no—
188C4⋊Dic67—28no—
189C4⋊Dic67—28no—
190C4⋊Dic67—44no—
191Dic67⋊C4—28no—
192Dic67⋊C4—28no—
193Dic67⋊C4—28no—
194Dic67⋊C4—28no—
195Dic67⋊C4—28no—
196Dic67⋊C4—28no—
197Dic67⋊C4—28no—
198Dic67⋊C4C2×D4116yes—
199C22⋊Dic67—28no—
200C22⋊Dic67—28no—
201C22⋊Dic67—28no—
202C22⋊Dic67—44no—
203C4×Dic67—28no—
204C4×Dic67—44no—
205C24×C67—22no—
206C24×C67—22no—
207C24×C67—22no—
208C24×C67—22no—
209C24×C67—22no—
210C24×C67—22no—
211C24×C67C2×Q814yes—
212C24×C67C2412yes—
213C24×C67C2411yescharacteristic
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×C67—28no—
228C22×C4×C67—28no—
229C22×C4×C67—44no—
230C22×C4×C67—416no—
231C22×C4×C67C2×D414yes—
232C22×C4×C67C2×Q814yes—
233C22×C4×C67C2×Q814yes—
234C22×C4×C67#4114yes—
235C22×C4×C67#4114yes—
236C22×C4×C67C2412yes—
237C22×C4×C67C2412yes—
238C22×C4×C67C2412yes—
239C22×C4×C67C2412yes—
240C22×C4×C67C2412yes—
241C22×C4×C67C2412yes—
242C22⋊C4×C67—28no—
243C22⋊C4×C67C2×Q8116yescomplemented
244C42×C67—28no—
245C42×C67—44no—
246C23×C67—28no—
247C23×C67—28no—
248C23×C67—28no—
249C23×C67—22no—
250C23×C67—22no—
251C23×C67—22no—
252C23×C67—22no—
253C23×C67—22no—
254C23×C67—22no—
255C23×C67—44no—
256C23×C67—44no—
257C23×C67—44no—
258C23×C67—44no—
259C23×C67C22×D412yes—
260C23×C67C22×Q814yes—
261C23×C67C22×Q812yes—
262C23×C67C2×#4112yes—
263C23×C67C2×#4112yes—
264C23×C67C2×#4112yes—
265C23×C67H(5,𝔽2)12yes—
266C23×C672−1+412yes—
267C23×C67C2511yescharacteristic
268C2×C4×C67—28no—
269C2×C4×C67—28no—
270C2×C4×C67—28no—
271C2×C4×C67—28no—
272C2×C4×C67—28no—
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—416no—
287C2×C4×C67—44no—
288C2×C4×C67C22×D414yes—
289C2×C4×C67C22×Q814yes—
290C2×C4×C67C22×Q814yes—
291C2×C4×C67C2×#4114yes—
292C2×C4×C67C2×#4114yes—
293C2×Dic67—28no—
294C2×Dic67—28no—
295C2×Dic67—28no—
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—22no—
311C2×Dic67—22no—
312C2×Dic67—22no—
313C2×Dic67—22no—
314C2×Dic67—22no—
315C2×Dic67—22no—
316C2×Dic67—22no—
317C2×Dic67—44no—
318C2×Dic67—44no—
319C2×Dic67—44no—
320C2×Dic67—44no—
321C2×Dic67—44no—
322C2×Dic67C22×D414yes—
323C2×Dic67C22×D414yes—
324C2×Dic67C2×#4114yes—
325Dic134—416no—
326C22×C67—24no—
327C22×C67—24no—
328C22×C67—24no—
329C22×C67—42no—
330C22×C67—42no—
331C22×C67—42no—
332C22×C67—42no—
333C22×C67—416no—
334C22×C67#53214yes—
335C22×C67#53314yes—
336C22×C67#53914yes—
337C22×C67#54614yes—
338C22×C67D4×Q814yes—
339C22×C67#55214yes—
340C22×C67#55414yes—
341C22×C67C23×D411yescharacteristic
342C22×C67C23×Q811yescharacteristic
343C22×C67C22×#4111yescharacteristic
344C22×C67C22×#4111yescharacteristic
345C22×C67C22×#4111yescharacteristic
346C22×C67C2×H(5,𝔽2)11yescharacteristic
347C22×C67C2×2−1+411yescharacteristic
348C4×C67—24no—
349C4×C67—24no—
350C4×C67—24no—
351C4×C67—24no—
352C4×C67—24no—
353C4×C67—42no—
354Dic67—24no—
355Dic67—24no—
356Dic67—24no—
357Dic67—42no—
358Dic67—42no—
359Dic67—42no—
360Dic67—42no—
361Dic67—42no—
362C2×#2556—671nomaximal, Sylow
363C2×C67—44no—
364C2×C67#255618yescomplemented
365C2×C67C2×#53211yescharacteristic
366C2×C67C2×#53311yescharacteristic
367C2×C67C2×#53911yescharacteristic
368C2×C67C2×#54611yescharacteristic
369C2×C67C2×D4×Q811yescharacteristic
370C2×C67C2×#55211yescharacteristic
371C2×C67C2×#55411yescharacteristic
372C22×#125—671no—
373C22×C22⋊Q8—671no—
374#2556—6716no—
375C2×#399—671no—
376C2×#398—671no—
377C2×#396—671no—
378C2×#395—671no—
379C2×#391—671no—
380C2×#389—671no—
381C2×#389—671no—
382C2×#388—671no—
383C2×#388—671no—
384C2×#387—671no—
385C2×#385—671no—
386C2×C4×C4⋊C4—671no—
387C2×C4×C22⋊C4D6711yescharacteristic
388C67C2×#255611yescharacteristic, complemented, Sylow
389C23×Q8—671no—
390C24×C4C2×D6711yescharacteristic
391C2×#125—678no—
392C2×#125—1348no—
393C2×C22⋊Q8—678no—
394C2×C22⋊Q8—1348no—
395C22×C4⋊C4—671no—
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×C22⋊C4—671no—
409C22×C22⋊C4—671no—
410C22×C22⋊C4—671no—
411C22×C22⋊C4—671no—
412C22×C22⋊C4C2×D6711yescharacteristic
413C22×C22⋊C4C2×D6711yescharacteristic
414C22×C42—671no—
415C22×C42—671no—
416C22×C42C2×D6711yescharacteristic
417C22×C42C2×D6711yescharacteristic
418#399—678no—
419#398—678no—
420#396—678no—
421#395—678no—
422#391—678no—
423#389—678no—
424#389—678no—
425#388—678no—
426#388—678no—
427#387—678no—
428#385—678no—
429C4×C4⋊C4—678no—
430C4×C22⋊C4C2×D6718yes—
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×#95C2×D6711yescharacteristic
440C2×#95C2×D6711yescharacteristic
441C25C22×D6711yescharacteristic
442C22×Q8—2682no—
443C22×Q8—674no—
444C22×Q8—1344no—
445C22×Q8—1344no—
446C23×C4—24no—
447C23×C4—24no—
448C23×C4—42no—
449C23×C4—671no—
450C23×C4—671no—
451C23×C4—671no—
452C23×C4—671no—
453C23×C4—671no—
454C23×C4—671no—
455C23×C4—671no—
456C23×C4—671no—
457C23×C4C22×D6711yescharacteristic
458C23×C4C22×D6714yes—
459C23×C4C22×D6711yescharacteristic
460C23×C4C22×D6711yescharacteristic
461C23×C4C22×D6711yescharacteristic
462C23×C4C22×D6711yescharacteristic
463C23×C4C22×D6711yescharacteristic
464#125—13432no—
465C22⋊Q8—13432no—
466C2×C4⋊C4—2682no—
467C2×C4⋊C4—674no—
468C2×C4⋊C4—678no—
469C2×C4⋊C4—674no—
470C2×C4⋊C4—674no—
471C2×C4⋊C4—674no—
472C2×C4⋊C4—674no—
473C2×C4⋊C4—674no—
474C2×C4⋊C4—674no—
475C2×C4⋊C4—674no—
476C2×C4⋊C4—674no—
477C2×C4⋊C4—674no—
478C2×C4⋊C4—674no—
479C2×C4⋊C4—674no—
480C2×C4⋊C4—674no—
481C2×C4⋊C4—1344no—
482C2×C4⋊C4—1344no—
483C2×C4⋊C4—1344no—
484C2×C4⋊C4—1344no—
485C2×C4⋊C4—1344no—
486C2×C4⋊C4—1344no—
487C2×C4⋊C4—1344no—
488C2×C4⋊C4—1344no—
489C2×C4⋊C4—1344no—
490C2×C4⋊C4—1344no—
491C2×C4⋊C4—1344no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—2682no—
494C2×C22⋊C4—674no—
495C2×C22⋊C4—674no—
496C2×C22⋊C4—674no—
497C2×C22⋊C4—674no—
498C2×C22⋊C4—1344no—
499C2×C22⋊C4—1344no—
500C2×C22⋊C4—1344no—
501C2×C22⋊C4Dic13418yescomplemented
502C2×C22⋊C4C22×D6714yes—
503C2×C22⋊C4C22×D6714yes—
504C2×C42—24no—
505C2×C42—42no—
506C2×C42—2682no—
507C2×C42—674no—
508C2×C42—674no—
509C2×C42—1344no—
510C2×C42C22×D6714yes—
511C2×C42C22×D6714yes—
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#95C22×D6714yes—
521#95C22×D6714yes—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24C2×Dic13414yes—
529C24C23×D6712yes—
530C24C23×D6711yescharacteristic
531C2×Q8—26816no—
532C2×Q8—2684no—
533C2×Q8—1348no—
534C2×Q8—1348no—
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—28no—
549C22×C4—28no—
550C22×C4—44no—
551C22×C4—416no—
552C22×C4—674no—
553C22×C4—674no—
554C22×C4—674no—
555C22×C4—672no—
556C22×C4—672no—
557C22×C4—672no—
558C22×C4—672no—
559C22×C4—672no—
560C22×C4—672no—
561C22×C4—672no—
562C22×C4—672no—
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—1342no—
580C22×C4—1342no—
581C22×C4—1342no—
582C22×C4—1342no—
583C22×C4—1342no—
584C22×C4D4×D6714yes—
585C22×C4C2×Dic13414yes—
586C22×C4C2×Dic13414yes—
587C22×C4#1176162814yes—
588C22×C4#1176162814yes—
589C22×C4C23×D6712yes—
590C22×C4C23×D6712yes—
591C22×C4C23×D6712yes—
592C22×C4C23×D6712yes—
593C22×C4C23×D6712yes—
594C22×C4C23×D6712yes—
595C4⋊C4—2684no—
596C4⋊C4—6716no—
597C4⋊C4—1348no—
598C4⋊C4—1348no—
599C4⋊C4—1348no—
600C4⋊C4—1348no—
601C4⋊C4—1348no—
602C4⋊C4—1348no—
603C4⋊C4—1348no—
604C4⋊C4—1348no—
605C4⋊C4—1348no—
606C4⋊C4—1348no—
607C4⋊C4—1348no—
608C22⋊C4—28no—
609C22⋊C4—2684no—
610C22⋊C4—1348no—
611C22⋊C4—1348no—
612C22⋊C4—1348no—
613C22⋊C4C2×Dic134116yescomplemented
614C42—28no—
615C42—44no—
616C42—2684no—
617C42—1348no—
618C23—28no—
619C23—28no—
620C23—28no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23C2×D4×D6712yes—
632C23C22×Dic13414yes—
633C23C22×Dic13412yes—
634C23#41×D6712yes—
635C23C2×#1176162812yes—
636C23C2×#1176162812yes—
637C23#1452408812yes—
638C23#1452409012yes—
639C23C24×D6711yescharacteristic
640Q8—26816no—
641C2×C4—28no—
642C2×C4—28no—
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—28no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—416no—
660C2×C4—44no—
661C2×C4—2684no—
662C2×C4—2684no—
663C2×C4—2684no—
664C2×C4—2684no—
665C2×C4—2684no—
666C2×C4—674no—
667C2×C4—674no—
668C2×C4—674no—
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—1342no—
679C2×C4—1342no—
680C2×C4—1342no—
681C2×C4—1342no—
682C2×C4—1342no—
683C2×C4—1342no—
684C2×C4—1348no—
685C2×C4—1348no—
686C2×C4—1348no—
687C2×C4—1342no—
688C2×C4—1342no—
689C2×C4—1342no—
690C2×C4—1342no—
691C2×C4—1342no—
692C2×C4—1342no—
693C2×C4C2×D4×D6714yes—
694C2×C4C22×Dic13414yes—
695C2×C4C22×Dic13414yes—
696C2×C4C2×#1176162814yes—
697C2×C4C2×#1176162814yes—
698C22—24no—
699C22—24no—
700C22—24no—
701C22—42no—
702C22—42no—
703C22—416no—
704C22—42no—
705C22—42no—
706C22#1686394314yes—
707C22#1686395314yes—
708C22#1686398814yes—
709C22#1686403614yes—
710C22D4×Dic13414yes—
711C22#1686408514yes—
712C22#1686410514yes—
713C22C22×D4×D6711yescharacteristic
714C22C23×Dic13411yescharacteristic
715C22C2×#41×D6711yescharacteristic
716C22C22×#1176162811yescharacteristic
717C22C22×#1176162811yescharacteristic
718C22C2×#1452408811yescharacteristic
719C22C2×#1452409011yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—24no—
724C4—24no—
725C4—42no—
726C4—2682no—
727C4—2682no—
728C4—2682no—
729C4—2682no—
730C4—2682no—
731C4—1344no—
732C4—1344no—
733C4—1344no—
734C2—44no—
735C2#2256529318yesdirect product factor
736C2C2×#1686394311yescharacteristic
737C2C2×#1686395311yescharacteristic
738C2C2×#1686398811yescharacteristic
739C2C2×#1686403611yescharacteristic
740C2C2×D4×Dic13411yescharacteristic
741C2C2×#1686408511yescharacteristic
742C2C2×#1686410511yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×C4×C22⋊C4×C67C2
socleC24×C67C24
prime radicalC25×C67C23
hypercenterC2×C4×C22⋊C4D67
hypocenterC67C2×#2556
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#14524035C2semidirect
3. #22565293C2direct (N × H)
5. C2×#16863328C2semidirect
7. C2×#16863317C2semidirect
8. C2×#16863300C2semidirect
9. C2×#16863294C2semidirect
10. C2×#16863293C2semidirect
13. C2×#16863280C2semidirect
15. C2×C4×Dic67⋊C4C2semidirect
19. C2×#14524035C22semidirect
42. #16863328C22semidirect
44. #16863317C22semidirect
45. #16863300C22semidirect
46. #16863294C22semidirect
47. #16863293C22semidirect
50. #16863280C22semidirect
52. C4×Dic67⋊C4C22semidirect
141. C2×C22⋊C4×C67Q8semidirect
243. C22⋊C4×C67C2×Q8semidirect
364. C2×C67#2556semidirect
388. C67C2×#2556semidirect
501. C2×C22⋊C4Dic134semidirect
613. C22⋊C4C2×Dic134semidirect
735. C2#22565293direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240352
C22×#145240222
#225652932
C2×#168633322
C2×#168633282
C2×#168633192
C2×#168633172
C2×#168633002
C2×#168632942
C2×#168632932
C2×#168632892
C2×#168632802
C2×#168632692
C2×C4×Dic67⋊C42
C2×C4×C22⋊C4×C672
C2×#255667