Finite Group Databasebeta

← C2×#22572739 #31734458

Subgroups — C2×#22572739 #31734458

Order 17152.

1834 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864116C211yesmaximal, characteristic
2#22572739C2116yesmaximal, direct product factor
3C2×#16863806C211yesmaximal, characteristic, complemented
4C2×#16863731C211yesmaximal, characteristic, complemented
5C2×#16863737C211yesmaximal, characteristic, complemented
6C2×#16863734C211yesmaximal, characteristic, complemented
7C2×#16863734C211yesmaximal, characteristic, complemented
8C2×#16863700C211yesmaximal, characteristic, complemented
9C2×#16863691C211yesmaximal, characteristic, complemented
10C2×#16863652C211yesmaximal, characteristic, complemented
11C2×#16863635C211yesmaximal, characteristic, complemented
12C2×#16863501C211yesmaximal, characteristic, complemented
13C2×#16863468C211yesmaximal, characteristic
14C2×#16863436C211yesmaximal, characteristic, complemented
15C2×#16863432C211yesmaximal, characteristic, complemented
16C2×#552×C67C211yesmaximal, characteristic
17C22×#11761618C2211yescharacteristic
18C22×#11761612C2211yescharacteristic
19C23×C67⋊C8C2211yescharacteristic
20#16864116—24no—
21#16864116C2218yes—
22C2×#14524043C2211yescharacteristic
23C2×#14524036—21no—
24C2×#14524036—21no—
25C2×#14524030—21no—
26C2×#14524022C2211yescharacteristic
27C2×#14524022C2211yescharacteristic
28C2×C4×Dic134C2211yescharacteristic
29C2×#14524008—21no—
30C2×#14524002C2211yescharacteristic
31C2×#14524002C2211yescharacteristic
32#16863806C2218yescomplemented
33#16863737C2218yescomplemented
34#16863734C2218yescomplemented
35#16863734C2218yescomplemented
36#16863731C2218yescomplemented
37#16863700C2218yescomplemented
38#16863691C2218yescomplemented
39#16863652C2218yescomplemented
40#16863635C2218yescomplemented
41#16863501C2218yescomplemented
42#16863468C2218yes—
43#16863436C2218yescomplemented
44#16863432C2218yescomplemented
45C2×#14523976C2211yescharacteristic
46C2×#14523976C2211yescharacteristic
47C2×#14523976C2211yescharacteristic
48C2×#14523976C2211yescharacteristic
49C2×#14523976C2211yescharacteristic
50C2×#14523974C2211yescharacteristic
51C2×#14523974C2211yescharacteristic
52C2×#14523974C2211yescharacteristic
53C2×#14523974C2211yescharacteristic
54C2×C4⋊(C67⋊C8)C2211yescharacteristic
55C2×#14523967C2211yescharacteristic
56C2×#14523967C2211yescharacteristic
57C2×#14523967C2211yescharacteristic
58C2×#14523966C2211yescharacteristic
59C2×#14523966C2211yescharacteristic
60C2×#14523966C2211yescharacteristic
61C2×C22⋊(C67⋊C8)C2211yescharacteristic
62C2×C22⋊(C67⋊C8)C2211yescharacteristic
63C2×#14523954C2211yescharacteristic
64#552×C67—24no—
65#552×C67C2218yes—
66C2×#126×C67—21no—
67C2×#125×C67—21no—
68C2×#125×C67C2211yescharacteristic
69C2×#123×C67—21no—
70C2×C22⋊Q8×C67C2211yescharacteristic
71C2×C22⋊Q8×C67C2211yescharacteristic
72C2×C4×Q8×C67C2211yescharacteristic
73C2×C4×D4×C67C2211yescharacteristic
74C2×#117×C67—21no—
75C2×#117×C67C2211yescharacteristic
76C22×C4⋊C4×C67C2211yescharacteristic
77C22×Dic134—21no—
78C22×Dic134C2311yescharacteristic
79C2×#11761618—24no—
80C2×#11761618C2314yes—
81C2×#11761612—24no—
82C2×#11761612C2314yes—
83C22×C67⋊C8—24no—
84C22×C67⋊C8C2311yescharacteristic
85C22×C67⋊C8C2311yescharacteristic
86C22×C67⋊C8C2311yescharacteristic
87C22×C67⋊C8C2314yes—
88C22×C67⋊C8C2311yescharacteristic
89#14524043—22no—
90#14524043C2314yes—
91#14524036—28no—
92#14524036—28no—
93#14524030—28no—
94#14524022—22no—
95#14524022—22no—
96#14524022C2314yes—
97#14524022C2314yes—
98C4×Dic134—22no—
99C4×Dic134C2314yes—
100#14524008—28no—
101#14524002—22no—
102#14524002—22no—
103#14524002C2314yes—
104#14524002C2314yes—
105C2×C4⋊Dic67—21no—
106C2×C4⋊Dic67C2311yescharacteristic
107C2×C4⋊Dic67C2311yescharacteristic
108C2×C4⋊Dic67C2311yescharacteristic
109C2×Dic67⋊C4—21no—
110C2×Dic67⋊C4—21no—
111C2×Dic67⋊C4—21no—
112C2×C22⋊Dic67—21no—
113C2×C22⋊Dic67—21no—
114C2×C22⋊Dic67—21no—
115C2×C22⋊Dic67—21no—
116C2×C4×Dic67—21no—
117C2×C4×Dic67—21no—
118C2×C4×Dic67—21no—
119#14523976C2314yes—
120#14523976C2314yes—
121#14523976C2314yes—
122#14523976C2314yes—
123#14523976C2314yes—
124#14523974C2314yes—
125#14523974C2314yes—
126#14523974C2314yes—
127#14523974C2314yes—
128C4⋊(C67⋊C8)C2314yes—
129#14523967C2314yes—
130#14523967C2314yes—
131#14523967C2314yes—
132#14523966C2314yes—
133#14523966C2314yes—
134#14523966C2314yes—
135C22⋊(C67⋊C8)C2314yes—
136C22⋊(C67⋊C8)C2314yes—
137#14523954C2314yes—
138C22×Q8×C67C2311yescharacteristic
139C22×D4×C67D411yescharacteristic
140C23×C4×C67—21no—
141C23×C4×C67C2311yescharacteristic
142C23×C4×C67C2311yescharacteristic
143#126×C67—28no—
144#125×C67—28no—
145#125×C67—22no—
146#125×C67C2314yes—
147#123×C67—28no—
148C22⋊Q8×C67—22no—
149C22⋊Q8×C67—22no—
150C22⋊Q8×C67C2314yes—
151C22⋊Q8×C67C2314yes—
152C4×Q8×C67—22no—
153C4×Q8×C67C2314yes—
154C4×D4×C67D414yes—
155C4×D4×C67C2314yes—
156#117×C67—22no—
157#117×C67—28no—
158#117×C67C2314yes—
159C2×C4⋊C4×C67—21no—
160C2×C4⋊C4×C67—22no—
161C2×C4⋊C4×C67—21no—
162C2×C4⋊C4×C67—21no—
163C2×C4⋊C4×C67—21no—
164C2×C4⋊C4×C67—21no—
165C2×C4⋊C4×C67—21no—
166C2×C4⋊C4×C67D411yescharacteristic
167C2×C4⋊C4×C67C2311yescharacteristic
168C2×C4⋊C4×C67C2311yescharacteristic
169C2×C4⋊C4×C67C2314yes—
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C22⋊C4×C67—21no—
172C2×C22⋊C4×C67—21no—
173C2×C22⋊C4×C67—21no—
174C2×C22⋊C4×C67D411yescharacteristic
175C2×C22⋊C4×C67D411yescharacteristic
176C2×C42×C67—21no—
177C2×C42×C67—21no—
178C2×C42×C67C2311yescharacteristic
179C2×Dic134—22no—
180C2×Dic134—22no—
181C2×Dic134—24no—
182C2×Dic134—21no—
183C2×Dic134—44no—
184C2×Dic134C2412yes—
185C22×Dic67—21no—
186C22×Dic67—21no—
187C22×Dic67—21no—
188C22×Dic67—21no—
189#11761618—28no—
190#11761612—28no—
191C2×C67⋊C8—22no—
192C2×C67⋊C8—22no—
193C2×C67⋊C8—22no—
194C2×C67⋊C8—28no—
195C2×C67⋊C8#4114yes—
196C2×C67⋊C8C2412yes—
197C2×C67⋊C8C2412yes—
198C2×C67⋊C8C2412yes—
199C2×C67⋊C8C2412yes—
200C4⋊Dic67—24no—
201C4⋊Dic67—21no—
202C4⋊Dic67—21no—
203C4⋊Dic67—21no—
204C4⋊Dic67C2412yes—
205C4⋊Dic67C2412yes—
206C4⋊Dic67C2412yes—
207Dic67⋊C4—24no—
208Dic67⋊C4—24no—
209Dic67⋊C4—24no—
210C22⋊Dic67—24no—
211C22⋊Dic67—24no—
212C22⋊Dic67—24no—
213C22⋊Dic67—24no—
214C4×Dic67—24no—
215C4×Dic67—24no—
216C4×Dic67—24no—
217C24×C67C2×D411yescharacteristic
218C24×C67C2×D411yescharacteristic
219C2×Q8×C67—21no—
220C2×Q8×C67—22no—
221C2×Q8×C67—22no—
222C2×Q8×C67C2412yes—
223C2×D4×C67—42no—
224C2×D4×C67C2×D414yes—
225C22×C4×C67—22no—
226C22×C4×C67—22no—
227C22×C4×C67—22no—
228C22×C4×C67—22no—
229C22×C4×C67—21no—
230C22×C4×C67—21no—
231C22×C4×C67—21no—
232C22×C4×C67—21no—
233C22×C4×C67—24no—
234C22×C4×C67—44no—
235C22×C4×C67C2×D411yescharacteristic
236C22×C4×C67C2×D411yescharacteristic
237C22×C4×C67C2×D411yescharacteristic
238C22×C4×C67C2×D411yescharacteristic
239C22×C4×C67C2×D412yes—
240C22×C4×C67C2×D412yes—
241C22×C4×C67C2412yes—
242C22×C4×C67C2412yes—
243C22×C4×C67C2411yescharacteristic
244C4⋊C4×C67—21no—
245C4⋊C4×C67—21no—
246C4⋊C4×C67—24no—
247C4⋊C4×C67—24no—
248C4⋊C4×C67—24no—
249C4⋊C4×C67—24no—
250C4⋊C4×C67—24no—
251C4⋊C4×C67—24no—
252C4⋊C4×C67—21no—
253C4⋊C4×C67C2×D414yes—
254C4⋊C4×C67C2412yes—
255C4⋊C4×C67C2412yes—
256C4⋊C4×C67C2412yes—
257C22⋊C4×C67—24no—
258C22⋊C4×C67—24no—
259C22⋊C4×C67—24no—
260C22⋊C4×C67C2×D414yes—
261C22⋊C4×C67C2×D414yes—
262C42×C67—24no—
263C42×C67—24no—
264C42×C67C2×D412yes—
265C42×C67C2412yes—
266C23×C67—22no—
267C23×C67—22no—
268C23×C67—22no—
269C23×C67—22no—
270C23×C67—22no—
271C23×C67—22no—
272C23×C67C22×D412yes—
273C23×C67C22×D412yes—
274C23×C67C22×D411yescharacteristic
275Q8×C67—22no—
276Q8×C67—22no—
277Q8×C67—42no—
278D4×C67—44no—
279C2×C4×C67—22no—
280C2×C4×C67—22no—
281C2×C4×C67—22no—
282C2×C4×C67—22no—
283C2×C4×C67—24no—
284C2×C4×C67—24no—
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—22no—
293C2×C4×C67—48no—
294C2×C4×C67—42no—
295C2×C4×C67—42no—
296C2×C4×C67—42no—
297C2×C4×C67—42no—
298C2×C4×C67C22×D412yes—
299C2×C4×C67C22×D412yes—
300C2×C4×C67C22×D412yes—
301C2×C4×C67C22×D412yes—
302C2×C4×C67C22×D411yescharacteristic
303C2×C4×C67C2×#4112yes—
304C2×C4×C672−1+412yes—
305C2×C4×C67C2511yescharacteristic
306C2×Dic67—22no—
307C2×Dic67—22no—
308C2×Dic67—22no—
309C2×Dic67—22no—
310C2×Dic67—42no—
311C2×Dic67—42no—
312C2×Dic67—42no—
313C2×Dic67—42no—
314Dic134—22no—
315Dic134—22no—
316Dic134—48no—
317Dic134—42no—
318C67⋊C8—22no—
319C67⋊C8—22no—
320C67⋊C8—22no—
321C67⋊C8C2×#4114yes—
322C22×C67—22no—
323C22×C67—22no—
324C22×C67—22no—
325C22×C67—22no—
326C22×C67—22no—
327C22×C67—22no—
328C22×C67—44no—
329C22×C67—44no—
330C22×C67#54712yes—
331C22×C67#57512yes—
332C22×C67#57812yes—
333C22×C67C23×D411yescharacteristic
334C4×C67—22no—
335C4×C67—22no—
336C4×C67—22no—
337C4×C67—22no—
338C4×C67—42no—
339C4×C67—42no—
340C4×C67—42no—
341C4×C67—42no—
342C4×C67#54712yes—
343C4×C67C22×#4111yescharacteristic
344C4×C67C2×2−1+411yescharacteristic
345Dic67—42no—
346Dic67—42no—
347Dic67—42no—
348Dic67—42no—
349C2×#3349—671nomaximal, Sylow
350C2×C67—42no—
351C2×C67—42no—
352C2×C67#334914yescomplemented
353C2×C67C2×#54711yescharacteristic
354C2×C67C2×#57511yescharacteristic
355C2×C67C2×#57811yescharacteristic
356C2×#556—671no—
357C2×#552D6711yescharacteristic
358#3349—6716no—
359C2×#501—671no—
360C2×#484—671no—
361C2×#485—671no—
362C2×#485—671no—
363C2×#485—671no—
364C2×#479—671no—
365C2×#477—671no—
366C2×#470—671no—
367C2×#467—671no—
368C2×#441—671no—
369C2×#435—671no—
370C2×#428—671no—
371C2×#427—671no—
372C67C2×#334911yescharacteristic, complemented, Sylow
373C22×Q16—671no—
374C22×M16—671no—
375C23×C8—671no—
376#556—678no—
377#556—1344no—
378#552—24no—
379#552C2×D6718yes—
380C2×C4⋊Q8—671no—
381C2×#126—21no—
382C2×#126—1341no—
383C2×#126—1341no—
384C2×#125—21no—
385C2×#125C2×D6711yescharacteristic
386C2×#124—1341no—
387C2×#123—21no—
388C2×C22⋊Q8—671no—
389C2×C22⋊Q8—671no—
390C2×C22⋊Q8C2×D6711yescharacteristic
391C2×C22⋊Q8C2×D6711yescharacteristic
392C2×C4×Q8—671no—
393C2×C4×Q8—1341no—
394C2×C4×Q8C2×D6711yescharacteristic
395C2×C4×D4C2×D6711yescharacteristic
396C2×#117—21no—
397C2×#117—671no—
398C2×#117—671no—
399C2×#117C2×D6711yescharacteristic
400C22×C4⋊C4C2×D6711yescharacteristic
401#501—678no—
402#485—678no—
403#485—678no—
404#485—678no—
405#484—678no—
406#479—678no—
407#477—678no—
408#470—678no—
409#467—678no—
410#441—678no—
411#435—678no—
412#428—678no—
413#427—678no—
414C2×#107—671no—
415C2×#107—671no—
416C2×#107—671no—
417C2×#107—671no—
418C2×#107—671no—
419C2×#106—671no—
420C2×#106—671no—
421C2×#106—671no—
422C2×#106—671no—
423C2×C4⋊C8—671no—
424C2×#103—671no—
425C2×#103—671no—
426C2×#103—671no—
427C2×#103—671no—
428C2×#103—671no—
429C2×#103—671no—
430C2×C22⋊C8—671no—
431C2×C22⋊C8—671no—
432C2×#97—671no—
433C22×Q8—671no—
434C22×Q8—1341no—
435C22×Q8C22×D6711yescharacteristic
436C22×D4C22⋊D6711yescharacteristic
437C23×C4—21no—
438C23×C4C22×D6711yescharacteristic
439C23×C4C22×D6711yescharacteristic
440C2×Q16—674no—
441C2×Q16—1344no—
442C2×M16—674no—
443C2×M16—1344no—
444C22×C8—671no—
445C22×C8—671no—
446C22×C8—674no—
447C22×C8—671no—
448C22×C8—671no—
449C22×C8—1344no—
450C4⋊Q8—674no—
451C4⋊Q8—1342no—
452#126—28no—
453#126—1348no—
454#126—1348no—
455#125—28no—
456#125—22no—
457#125C22×D6714yes—
458#124—1348no—
459#123—28no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—674no—
463C22⋊Q8—674no—
464C22⋊Q8—1342no—
465C22⋊Q8—1342no—
466C22⋊Q8C22×D6714yes—
467C22⋊Q8C22×D6714yes—
468C4×Q8—22no—
469C4×Q8—674no—
470C4×Q8—1348no—
471C4×Q8—1342no—
472C4×Q8C22×D6714yes—
473C4×D4C22⋊D6714yes—
474C4×D4C22×D6714yes—
475#117—22no—
476#117—28no—
477#117—674no—
478#117—674no—
479#117—1342no—
480#117—1342no—
481#117C22×D6714yes—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—671no—
490C2×C4⋊C4—671no—
491C2×C4⋊C4—671no—
492C2×C4⋊C4—1341no—
493C2×C4⋊C4—1341no—
494C2×C4⋊C4—1341no—
495C2×C4⋊C4—1341no—
496C2×C4⋊C4C22⋊D6711yescharacteristic
497C2×C4⋊C4C22×D6711yescharacteristic
498C2×C4⋊C4C22×D6711yescharacteristic
499C2×C4⋊C4C22×D6714yes—
500C2×C4⋊C4C22×D6711yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—1341no—
505C2×C22⋊C4—1341no—
506C2×C22⋊C4—1341no—
507C2×C22⋊C4—1341no—
508C2×C22⋊C4C22⋊D6711yescharacteristic
509C2×C22⋊C4C22⋊D6711yescharacteristic
510C2×C42—21no—
511C2×C42—21no—
512C2×C42—1341no—
513C2×C42—1341no—
514C2×C42—1341no—
515C2×C42C22×D6711yescharacteristic
516#107—674no—
517#107—674no—
518#107—674no—
519#107—674no—
520#107—674no—
521#106—674no—
522#106—674no—
523#106—674no—
524#106—674no—
525C4⋊C8—674no—
526#103—674no—
527#103—674no—
528#103—674no—
529#103—674no—
530#103—674no—
531#103—674no—
532C22⋊C8—674no—
533C22⋊C8—674no—
534#97—674no—
535C24C2×C22⋊D6711yescharacteristic
536C24C2×C22⋊D6711yescharacteristic
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—2684no—
541C2×Q8—672no—
542C2×Q8—1342no—
543C2×Q8—1342no—
544C2×Q8—1341no—
545C2×Q8—1344no—
546C2×Q8C23×D6712yes—
547C2×D4—42no—
548C2×D4C2×C22⋊D6714yes—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—44no—
559C22×C4—1341no—
560C22×C4—1341no—
561C22×C4—1341no—
562C22×C4—1341no—
563C22×C4C2×C22⋊D6712yes—
564C22×C4C2×C22⋊D6712yes—
565C22×C4C2×C22⋊D6711yescharacteristic
566C22×C4C2×C22⋊D6711yescharacteristic
567C22×C4C2×C22⋊D6711yescharacteristic
568C22×C4C2×C22⋊D6711yescharacteristic
569C22×C4C23×D6712yes—
570C22×C4C23×D6712yes—
571C22×C4C23×D6711yescharacteristic
572Q16—1348no—
573M16—1348no—
574C2×C8—674no—
575C2×C8—672no—
576C2×C8—672no—
577C2×C8—672no—
578C2×C8—672no—
579C2×C8—1348no—
580C2×C8—1342no—
581C2×C8—1342no—
582C2×C8—1342no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—21no—
592C4⋊C4—672no—
593C4⋊C4—672no—
594C4⋊C4—672no—
595C4⋊C4—1341no—
596C4⋊C4—1341no—
597C4⋊C4—1341no—
598C4⋊C4—1344no—
599C4⋊C4—1344no—
600C4⋊C4—1344no—
601C4⋊C4—1344no—
602C4⋊C4C2×C22⋊D6714yes—
603C4⋊C4C23×D6712yes—
604C4⋊C4C23×D6712yes—
605C4⋊C4C23×D6712yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—1344no—
610C22⋊C4—1344no—
611C22⋊C4—1344no—
612C22⋊C4—1344no—
613C22⋊C4C2×C22⋊D6714yes—
614C22⋊C4C2×C22⋊D6714yes—
615C42—24no—
616C42—24no—
617C42—1344no—
618C42—1344no—
619C42—1344no—
620C42C2×C22⋊D6712yes—
621C42C23×D6712yes—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23C22×C22⋊D6712yes—
629C23C22×C22⋊D6712yes—
630C23C22×C22⋊D6711yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—42no—
634Q8—2688no—
635Q8—2682no—
636Q8—1342no—
637Q8—1342no—
638D4—44no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—24no—
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—48no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—2682no—
659C2×C4—2682no—
660C2×C4—2682no—
661C2×C4—2682no—
662C2×C4—1342no—
663C2×C4—1342no—
664C2×C4—1342no—
665C2×C4—1342no—
666C2×C4C22×C22⋊D6712yes—
667C2×C4C22×C22⋊D6712yes—
668C2×C4C22×C22⋊D6712yes—
669C2×C4C22×C22⋊D6712yes—
670C2×C4C22×C22⋊D6711yescharacteristic
671C2×C4#41×D6712yes—
672C2×C4#1452409012yes—
673C2×C4C24×D6711yescharacteristic
674C8—674no—
675C8—1342no—
676C8—1342no—
677C8—1342no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—44no—
685C22—44no—
686C22#1686404512yes—
687C22#1686419412yes—
688C22#1686421112yes—
689C22C23×C22⋊D6711yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—2682no—
699C4—2682no—
700C4—2682no—
701C4—2682no—
702C4#1686404512yes—
703C4C2×#41×D6711yescharacteristic
704C4C2×#1452409011yescharacteristic
705C2—42no—
706C2—42no—
707C2#2257273914yesdirect product factor
708C2C2×#1686404511yescharacteristic
709C2C2×#1686419411yescharacteristic
710C2C2×#1686421111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#552×C67C2
socleC23×C67C22×D4
prime radicalC22×D4×C67D4
hypercenterC2×#552D67
hypocenterC67C2×#3349
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #22572739C2direct (N × H)
3. C2×#16863806C2semidirect
4. C2×#16863731C2semidirect
5. C2×#16863737C2semidirect
6. C2×#16863734C2semidirect
7. C2×#16863734C2semidirect
8. C2×#16863700C2semidirect
9. C2×#16863691C2semidirect
10. C2×#16863652C2semidirect
11. C2×#16863635C2semidirect
12. C2×#16863501C2semidirect
14. C2×#16863436C2semidirect
15. C2×#16863432C2semidirect
32. #16863806C22semidirect
33. #16863737C22semidirect
34. #16863734C22semidirect
35. #16863734C22semidirect
36. #16863731C22semidirect
37. #16863700C22semidirect
38. #16863691C22semidirect
39. #16863652C22semidirect
40. #16863635C22semidirect
41. #16863501C22semidirect
43. #16863436C22semidirect
44. #16863432C22semidirect
352. C2×C67#3349semidirect
372. C67C2×#3349semidirect
707. C2#22572739direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168641162
#225727392
C2×#168638062
C2×#168637312
C2×#168637372
C2×#168637342
C2×#168637002
C2×#168636912
C2×#168636522
C2×#168636352
C2×#168635012
C2×#168634682
C2×#168634362
C2×#168634322
C2×#552×C672
C2×#334967