Finite Group Databasebeta

← C2×#22574699 #31763543

Subgroups — C2×#22574699 #31763543

Order 17152.

6446 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574699C2132yesmaximal, direct product factor
2C2×#16864149C214yesmaximal, complemented
3C2×Q8×Dic134C211yesmaximal, characteristic, complemented
4C2×#16864124C211yesmaximal, characteristic, complemented
5C2×#16864123C212yesmaximal, complemented
6C2×#16864116C212yesmaximal, complemented
7C2×#16864116C211yesmaximal, characteristic, complemented
8C2×#16864115C212yesmaximal, complemented
9C2×#16864103C211yesmaximal, characteristic, complemented
10C2×#16864086C212yesmaximal, complemented
11C2×#16864024C212yesmaximal, complemented
12C2×#16864013C212yesmaximal
13C2×#16864008C212yesmaximal, complemented
14C2×#16864006C212yesmaximal, complemented
15C2×#16864003C214yesmaximal, complemented
16C2×#16863953C211yesmaximal, characteristic, complemented
17C2×#16863953C211yesmaximal, characteristic, complemented
18C2×#529×C67C211yesmaximal, characteristic
19#16864149C22164yescomplemented
20Q8×Dic134C22116yescomplemented
21#16864124C22116yescomplemented
22#16864123C22132yescomplemented
23#16864116C22132yescomplemented
24#16864116C22116yescomplemented
25#16864115C22132yescomplemented
26#16864103C22116yescomplemented
27#16864086C22132yescomplemented
28#16864024C22132yescomplemented
29#16864013C22132yes—
30#16864008C22132yescomplemented
31#16864006C22132yescomplemented
32#16864003C22164yescomplemented
33#16863953C22116yescomplemented
34#16863953C22116yescomplemented
35C2×#14524043C2211yescharacteristic
36C2×#14524043C2211yescharacteristic
37C2×#14524043C2212yes—
38C2×#14524043C2211yescharacteristic
39C2×#14524043C2211yescharacteristic
40C2×#14524042C2214yes—
41C2×#14524042C2214yes—
42C2×#14524042C2212yes—
43C2×#14524041C2212yes—
44C2×#14524036C2214yes—
45C2×#14524036C2214yes—
46C2×#14524036C2214yes—
47C2×#14524036C2214yes—
48C2×#14524036C2214yes—
49C2×#14524036C2214yes—
50C2×#14524035C2212yes—
51C2×#14524035C2212yes—
52C2×#14524035C2212yes—
53C2×#14524034C2214yes—
54C2×#14524034C2212yes—
55C2×#14524033C2214yes—
56C2×#14524033C2214yes—
57C2×#14524033C2214yes—
58C2×#14524033C2214yes—
59C2×#14524030C2214yes—
60C2×#14524030C2212yes—
61C2×#14524024C2214yes—
62C2×#14524022C2212yes—
63C2×#14524022C2212yes—
64C2×#14524022C2212yes—
65C2×#14524022C2212yes—
66C2×#14524022C2212yes—
67C2×#14524022C2211yescharacteristic
68C2×#14524022C2211yescharacteristic
69C2×#14524020C2214yes—
70C2×#14524020C2214yes—
71C2×#14524020C2214yes—
72C2×Q8×Dic67C2212yes—
73C2×C4×Dic134C2212yes—
74C2×C4×Dic134C2212yes—
75C2×C4×Dic134C2212yes—
76C2×C4×Dic134C2211yescharacteristic
77C2×C4×Dic134C2212yes—
78C2×C4×Dic134C2212yes—
79C2×C4×Dic134C2211yescharacteristic
80C2×#14524008C2214yes—
81C2×#14524008C2212yes—
82C2×#14524008C2212yes—
83C2×D4×Dic67C2212yes—
84C2×#14524002C2212yes—
85C2×#14524002C2212yes—
86C2×#14524002C2212yes—
87C2×#14523999C2214yes—
88C22×C4⋊Dic67C2212yes—
89#529×C67C22116yes—
90C2×#126×C67C2212yes—
91C2×#125×C67C2211yescharacteristic
92C2×#124×C67C2211yescharacteristic
93C2×#123×C67C2212yes—
94C2×C22⋊Q8×C67C2211yescharacteristic
95C2×#121×C67C2211yescharacteristic
96C2×C4×Q8×C67C2211yescharacteristic
97C2×C4×D4×C67C2212yes—
98C2×C4×D4×C67C2211yescharacteristic
99C2×#117×C67C2212yes—
100C22×C42×C67C2211yescharacteristic
101C22×Dic134C2312yes—
102C22×Dic134C2311yescharacteristic
103C22×Dic134C2311yescharacteristic
104C22×Dic134C2314yes—
105C22×Dic134C2312yes—
106C22×Dic134C2312yes—
107C23×Dic67C2314yes—
108#14524043C2318yes—
109#14524043C2318yes—
110#14524043C23116yes—
111#14524043C2318yes—
112#14524043C2318yes—
113#14524042C23132yes—
114#14524042C23116yes—
115#14524042C23132yes—
116#14524041C23116yes—
117#14524036C23132yes—
118#14524036C23132yes—
119#14524036C23132yes—
120#14524036C23132yes—
121#14524036C23132yes—
122#14524036C23132yes—
123#14524035C23116yes—
124#14524035C23116yes—
125#14524035C23116yes—
126#14524034C23132yes—
127#14524034C23116yes—
128#14524033C23132yes—
129#14524033C23132yes—
130#14524033C23132yes—
131#14524033C23132yes—
132#14524030C23116yes—
133#14524030C23132yes—
134#14524024C23132yes—
135#14524022C23116yes—
136#14524022C23116yes—
137#14524022C23116yes—
138#14524022C2318yes—
139#14524022C2318yes—
140#14524022C23116yes—
141#14524022C23116yes—
142#14524020C23132yes—
143#14524020C23132yes—
144#14524020C23132yes—
145Q8×Dic67C23116yes—
146C4×Dic134C23116yes—
147C4×Dic134C23116yes—
148C4×Dic134C23116yes—
149C4×Dic134C2318yes—
150C4×Dic134C23116yes—
151C4×Dic134C23116yes—
152C4×Dic134C2318yes—
153#14524008C23132yes—
154#14524008C23116yes—
155#14524008C23116yes—
156D4×Dic67C23116yes—
157#14524002C23116yes—
158#14524002C23116yes—
159#14524002C23116yes—
160#14523999C23132yes—
161C2×C4⋊Dic67C23116yes—
162C2×C4⋊Dic67C2311yescharacteristic
163C2×C4⋊Dic67C2312yes—
164C2×C4⋊Dic67C2314yes—
165C2×C4⋊Dic67C2312yes—
166C2×C4⋊Dic67C2311yescharacteristic
167C2×C4⋊Dic67C2312yes—
168C2×C4⋊Dic67C2312yes—
169C2×C4⋊Dic67C2312yes—
170C2×C4⋊Dic67C2312yes—
171C2×C4⋊Dic67C2312yes—
172C2×C4⋊Dic67C2314yes—
173C2×Dic67⋊C4C2312yes—
174C2×Dic67⋊C4C2314yes—
175C2×Dic67⋊C4C2312yes—
176C2×Dic67⋊C4C2314yes—
177C2×Dic67⋊C4C2314yes—
178C2×Dic67⋊C4C2314yes—
179C2×Dic67⋊C4C2312yes—
180C2×Dic67⋊C4C2314yes—
181C2×Dic67⋊C4C2314yes—
182C2×Dic67⋊C4C2312yes—
183C2×Dic67⋊C4C2314yes—
184C2×Dic67⋊C4C2314yes—
185C2×C22⋊Dic67C2314yes—
186C2×C22⋊Dic67C2314yes—
187C2×C22⋊Dic67C2312yes—
188C2×C22⋊Dic67C2314yes—
189C2×C22⋊Dic67C2312yes—
190C2×C22⋊Dic67C2314yes—
191C2×C4×Dic67C2314yes—
192C2×C4×Dic67C2314yes—
193C2×C4×Dic67C2312yes—
194C2×C4×Dic67C2314yes—
195C2×C4×Dic67C2312yes—
196C2×C4×Dic67C2314yes—
197C22×Q8×C67C2311yescharacteristic
198C22×D4×C67C2311yescharacteristic
199C22×D4×C67C2312yes—
200C23×C4×C67C2311yescharacteristic
201C23×C4×C67C2311yescharacteristic
202C23×C4×C67C2312yes—
203C23×C4×C67C2311yescharacteristic
204#126×C67C23116yes—
205#125×C67C2318yes—
206#124×C67C2318yes—
207#123×C67C23116yes—
208C22⋊Q8×C67C2318yes—
209#121×C67C2318yes—
210C4×Q8×C67C2318yes—
211C4×D4×C67C23116yes—
212C4×D4×C67C2318yes—
213#117×C67C23116yes—
214C2×C4⋊C4×C67C2312yes—
215C2×C4⋊C4×C67C2312yes—
216C2×C4⋊C4×C67C2311yescharacteristic
217C2×C4⋊C4×C67C2312yes—
218C2×C4⋊C4×C67C2311yescharacteristic
219C2×C4⋊C4×C67C2312yes—
220C2×C22⋊C4×C67C2312yes—
221C2×C22⋊C4×C67C2312yes—
222C2×C22⋊C4×C67C2312yes—
223C2×C22⋊C4×C67C2312yes—
224C2×C22⋊C4×C67C2312yes—
225C2×C42×C67C2311yescharacteristic
226C2×C42×C67C2311yescharacteristic
227C2×C42×C67C2311yescharacteristic
228C2×C42×C67C2311yescharacteristic
229C2×C42×C67C2318yes—
230C2×C42×C67C2312yes—
231C2×Dic134—24no—
232C2×Dic134—24no—
233C2×Dic134—28no—
234C2×Dic134—44no—
235C2×Dic134—44no—
236C2×Dic134—48no—
237C2×Dic134C2418yes—
238C2×Dic134C2414yes—
239C2×Dic134C2414yes—
240C2×Dic134C24116yes—
241C2×Dic134C2418yes—
242C2×Dic134C2418yes—
243C22×Dic67—48no—
244C22×Dic67C2414yes—
245C22×Dic67C2412yes—
246C22×Dic67C2412yes—
247C22×Dic67C2412yes—
248C22×Dic67C2414yes—
249C22×Dic67C2412yes—
250C22×Dic67C24116yes—
251C4⋊Dic67C2414yes—
252C4⋊Dic67C2418yes—
253C4⋊Dic67C24116yes—
254C4⋊Dic67C2418yes—
255C4⋊Dic67C2414yes—
256C4⋊Dic67C2418yes—
257C4⋊Dic67C2418yes—
258C4⋊Dic67C2418yes—
259C4⋊Dic67C2418yes—
260C4⋊Dic67C2418yes—
261C4⋊Dic67C24116yes—
262Dic67⋊C4C2418yes—
263Dic67⋊C4C24116yes—
264Dic67⋊C4C2418yes—
265Dic67⋊C4C24116yes—
266Dic67⋊C4C24116yes—
267Dic67⋊C4C24116yes—
268Dic67⋊C4C2418yes—
269Dic67⋊C4C24116yes—
270Dic67⋊C4C24116yes—
271Dic67⋊C4C2418yes—
272Dic67⋊C4C24116yes—
273Dic67⋊C4C24116yes—
274C22⋊Dic67C24116yes—
275C22⋊Dic67C24116yes—
276C22⋊Dic67C2418yes—
277C22⋊Dic67C24116yes—
278C22⋊Dic67C2418yes—
279C22⋊Dic67C24116yes—
280C4×Dic67C24116yes—
281C4×Dic67C24116yes—
282C4×Dic67C2418yes—
283C4×Dic67C24116yes—
284C4×Dic67C2418yes—
285C4×Dic67C24116yes—
286C24×C67C2412yes—
287C24×C67C2411yescharacteristic
288C2×Q8×C67—24no—
289C2×Q8×C67C2414yes—
290C2×D4×C67—24no—
291C2×D4×C67—44no—
292C2×D4×C67C2414yes—
293C2×D4×C67C2418yes—
294C22×C4×C67—24no—
295C22×C4×C67—28no—
296C22×C4×C67—24no—
297C22×C4×C67—42no—
298C22×C4×C67C2411yescharacteristic
299C22×C4×C67C2411yescharacteristic
300C22×C4×C67C2411yescharacteristic
301C22×C4×C67C2411yescharacteristic
302C22×C4×C67C2414yes—
303C22×C4×C67C2414yes—
304C22×C4×C67C2412yes—
305C22×C4×C67C2412yes—
306C22×C4×C67C2412yes—
307C22×C4×C67C2418yes—
308C22×C4×C67C2414yes—
309C22×C4×C67C2411yescharacteristic
310C22×C4×C67C2411yescharacteristic
311C4⋊C4×C67C2418yes—
312C4⋊C4×C67C2418yes—
313C4⋊C4×C67C2414yes—
314C4⋊C4×C67C2418yes—
315C4⋊C4×C67C2414yes—
316C4⋊C4×C67C2418yes—
317C22⋊C4×C67C2418yes—
318C22⋊C4×C67C2418yes—
319C22⋊C4×C67C2418yes—
320C22⋊C4×C67C2418yes—
321C22⋊C4×C67C2418yes—
322C42×C67C2414yes—
323C42×C67C2414yes—
324C42×C67C2414yes—
325C42×C67C2414yes—
326C42×C67C2418yes—
327C23×C67—24no—
328C23×C67—22no—
329C23×C67—22no—
330C23×C67—24no—
331C23×C67—22no—
332C23×C67—24no—
333C23×C67C2514yes—
334C23×C67C2512yes—
335C23×C67C2511yescharacteristic
336Q8×C67—28no—
337D4×C67—28no—
338D4×C67—48no—
339C2×C4×C67—22no—
340C2×C4×C67—22no—
341C2×C4×C67—24no—
342C2×C4×C67—24no—
343C2×C4×C67—22no—
344C2×C4×C67—22no—
345C2×C4×C67—24no—
346C2×C4×C67—28no—
347C2×C4×C67—216no—
348C2×C4×C67—28no—
349C2×C4×C67—44no—
350C2×C4×C672−1+414yes—
351C2×C4×C672−1+414yes—
352C2×C4×C67C2512yes—
353C2×C4×C67C2512yes—
354C2×C4×C67C2512yes—
355C2×C4×C67C2512yes—
356C2×C4×C67C2514yes—
357C2×C4×C67C2514yes—
358C2×C4×C67C2514yes—
359C2×C4×C67C2512yes—
360C2×C4×C67C2512yes—
361C2×Dic67—24no—
362C2×Dic67—24no—
363C2×Dic67—28no—
364C2×Dic67—24no—
365C2×Dic67—28no—
366C2×Dic67—24no—
367C2×Dic67—416no—
368C2×Dic67C2518yes—
369C2×Dic67C2514yes—
370C2×Dic67C2514yes—
371C2×Dic67C2514yes—
372C2×Dic67C2518yes—
373C2×Dic67C2514yes—
374Dic134—28no—
375Dic134—28no—
376Dic134—216no—
377Dic134—416no—
378Dic134—48no—
379Dic134—48no—
380C22×C67—24no—
381C22×C67—22no—
382C22×C67—22no—
383C22×C67—24no—
384C22×C67—24no—
385C22×C67—22no—
386C22×C67—44no—
387C22×C67—48no—
388C22×C67C2×2−1+412yes—
389C22×C67C2×2−1+412yes—
390C22×C67#58512yes—
391C22×C67C2611yescharacteristic
392C4×C67—22no—
393C4×C67—22no—
394C4×C67—24no—
395C4×C67—24no—
396C4×C67—22no—
397C4×C67—22no—
398C4×C67—24no—
399C4×C67C2×2−1+414yes—
400C4×C67C2×2−1+414yes—
401Dic67—24no—
402Dic67—24no—
403Dic67—28no—
404Dic67—24no—
405Dic67—28no—
406Dic67—24no—
407C2×#3555—671nomaximal, Sylow
408C2×C67—42no—
409C2×C67—44no—
410C2×C67#355514yescomplemented
411C2×C67C22×2−1+411yescharacteristic
412C2×C67C22×2−1+411yescharacteristic
413C2×C67C2×#58511yescharacteristic
414#3555—6732no—
415C2×#563—674no—
416C2×Q82—671no—
417C2×#557—672no—
418C2×#557—671no—
419C2×#556—672no—
420C2×#556—672no—
421C2×#556—671no—
422C2×#554—671no—
423C2×#552—672no—
424C2×#544—672no—
425C2×#542—672no—
426C2×#541—674no—
427C2×#541—672no—
428C2×#541—672no—
429C2×#533—671no—
430C2×#533—671no—
431C2×#529D6711yescharacteristic
432C67C2×#355511yescharacteristic, complemented, Sylow
433#563—6764no—
434Q82—6716no—
435#557—6732no—
436#557—6716no—
437#556—6732no—
438#556—6732no—
439#556—6716no—
440#554—6716no—
441#552—6732no—
442#544—6732no—
443#542—6732no—
444#541—6764no—
445#541—6732no—
446#541—6732no—
447#533—6716no—
448#533—6716no—
449C2×C4⋊Q8—672no—
450C2×C4⋊Q8—674no—
451C2×C4⋊Q8—672no—
452C2×C4⋊Q8—674no—
453C2×C4⋊Q8—671no—
454C2×C4⋊Q8—671no—
455C2×C4⋊Q8—671no—
456C2×C4⋊Q8—671no—
457C2×C4⋊Q8—672no—
458#529C2×D67116yes—
459C2×#126—674no—
460C2×#126—674no—
461C2×#126—674no—
462C2×#126—674no—
463C2×#126—674no—
464C2×#126—674no—
465C2×#126C2×D6712yes—
466C2×#125—674no—
467C2×#125—674no—
468C2×#125—674no—
469C2×#125—672no—
470C2×#125—674no—
471C2×#125—674no—
472C2×#125—672no—
473C2×#125—672no—
474C2×#125—672no—
475C2×#125C2×D6711yescharacteristic
476C2×#124—672no—
477C2×#124—674no—
478C2×#124C2×D6711yescharacteristic
479C2×#123—674no—
480C2×#123C2×D6712yes—
481C2×C22⋊Q8—672no—
482C2×C22⋊Q8—671no—
483C2×C22⋊Q8—671no—
484C2×C22⋊Q8—672no—
485C2×C22⋊Q8—672no—
486C2×C22⋊Q8—672no—
487C2×C22⋊Q8—672no—
488C2×C22⋊Q8—674no—
489C2×C22⋊Q8—674no—
490C2×C22⋊Q8—674no—
491C2×C22⋊Q8C2×D6711yescharacteristic
492C2×#121C2×D6711yescharacteristic
493C2×C4×Q8—672no—
494C2×C4×Q8—674no—
495C2×C4×Q8—672no—
496C2×C4×Q8—672no—
497C2×C4×Q8—672no—
498C2×C4×Q8—671no—
499C2×C4×Q8—672no—
500C2×C4×Q8—672no—
501C2×C4×Q8—671no—
502C2×C4×Q8—672no—
503C2×C4×Q8—672no—
504C2×C4×Q8C2×D6711yescharacteristic
505C2×C4×D4—672no—
506C2×C4×D4C2×D6712yes—
507C2×C4×D4C2×D6711yescharacteristic
508C2×#117—672no—
509C2×#117—672no—
510C2×#117—672no—
511C2×#117—674no—
512C2×#117C2×D6712yes—
513C22×C4⋊C4—672no—
514C22×C42C2×D6711yescharacteristic
515C22×Q8—672no—
516C22×Q8—672no—
517C22×Q8—674no—
518C22×Q8—671no—
519C22×Q8—671no—
520C22×Q8—672no—
521C22×Q8C22×D6711yescharacteristic
522C22×D4C22×D6711yescharacteristic
523C22×D4C22×D6712yes—
524C23×C4—674no—
525C23×C4C22×D6712yes—
526C23×C4C22×D6711yescharacteristic
527C23×C4C22×D6711yescharacteristic
528C23×C4C22×D6711yescharacteristic
529C4⋊Q8—6716no—
530C4⋊Q8—6732no—
531C4⋊Q8—6716no—
532C4⋊Q8—6732no—
533C4⋊Q8—678no—
534C4⋊Q8—678no—
535C4⋊Q8—678no—
536C4⋊Q8—678no—
537C4⋊Q8—6716no—
538#126—6732no—
539#126—6732no—
540#126—6732no—
541#126—6732no—
542#126—6732no—
543#126—6732no—
544#126C22×D67116yes—
545#125—6732no—
546#125—6732no—
547#125—6732no—
548#125—6716no—
549#125—6732no—
550#125—6732no—
551#125—6716no—
552#125—6716no—
553#125—6716no—
554#125C22×D6718yes—
555#124—6716no—
556#124—6732no—
557#124C22×D6718yes—
558#123—6732no—
559#123C22×D67116yes—
560C22⋊Q8—6716no—
561C22⋊Q8—678no—
562C22⋊Q8—678no—
563C22⋊Q8—6716no—
564C22⋊Q8—6716no—
565C22⋊Q8—6716no—
566C22⋊Q8—6716no—
567C22⋊Q8—6732no—
568C22⋊Q8—6732no—
569C22⋊Q8—6732no—
570C22⋊Q8C22×D6718yes—
571#121C22×D6718yes—
572C4×Q8—6716no—
573C4×Q8—6732no—
574C4×Q8—6716no—
575C4×Q8—6716no—
576C4×Q8—6716no—
577C4×Q8—678no—
578C4×Q8—6716no—
579C4×Q8—6716no—
580C4×Q8—678no—
581C4×Q8—6716no—
582C4×Q8—6716no—
583C4×Q8C22×D6718yes—
584C4×D4—6716no—
585C4×D4C22×D67116yes—
586C4×D4C22×D6718yes—
587#117—6716no—
588#117—6716no—
589#117—6716no—
590#117—6732no—
591#117C22×D67116yes—
592C2×C4⋊C4—671no—
593C2×C4⋊C4—672no—
594C2×C4⋊C4—674no—
595C2×C4⋊C4—6716no—
596C2×C4⋊C4—672no—
597C2×C4⋊C4—672no—
598C2×C4⋊C4—671no—
599C2×C4⋊C4—672no—
600C2×C4⋊C4—674no—
601C2×C4⋊C4—672no—
602C2×C4⋊C4—672no—
603C2×C4⋊C4—672no—
604C2×C4⋊C4—672no—
605C2×C4⋊C4—674no—
606C2×C4⋊C4—674no—
607C2×C4⋊C4—674no—
608C2×C4⋊C4—674no—
609C2×C4⋊C4—674no—
610C2×C4⋊C4—672no—
611C2×C4⋊C4—672no—
612C2×C4⋊C4—672no—
613C2×C4⋊C4—674no—
614C2×C4⋊C4—674no—
615C2×C4⋊C4—674no—
616C2×C4⋊C4C22×D6712yes—
617C2×C4⋊C4C22×D6712yes—
618C2×C4⋊C4C22×D6711yescharacteristic
619C2×C4⋊C4C22×D6712yes—
620C2×C4⋊C4C22×D6711yescharacteristic
621C2×C4⋊C4C22×D6712yes—
622C2×C22⋊C4—672no—
623C2×C22⋊C4—674no—
624C2×C22⋊C4—672no—
625C2×C22⋊C4—674no—
626C2×C22⋊C4—674no—
627C2×C22⋊C4—674no—
628C2×C22⋊C4C22×D6712yes—
629C2×C22⋊C4C22×D6712yes—
630C2×C22⋊C4C22×D6712yes—
631C2×C22⋊C4C22×D6712yes—
632C2×C22⋊C4C22×D6712yes—
633C2×C42—674no—
634C2×C42—672no—
635C2×C42—672no—
636C2×C42—674no—
637C2×C42—674no—
638C2×C42—674no—
639C2×C42C22×D6711yescharacteristic
640C2×C42C22×D6712yes—
641C2×C42C22×D6711yescharacteristic
642C2×C42C22×D6711yescharacteristic
643C2×C42C22×D6711yescharacteristic
644C2×C42C22×D6718yes—
645C24C23×D6711yescharacteristic
646C24C23×D6712yes—
647C2×Q8—24no—
648C2×Q8—2684no—
649C2×Q8—2684no—
650C2×Q8—2688no—
651C2×Q8—678no—
652C2×Q8—678no—
653C2×Q8—6716no—
654C2×Q8—674no—
655C2×Q8—674no—
656C2×Q8—678no—
657C2×Q8—1344no—
658C2×Q8—1344no—
659C2×Q8—1348no—
660C2×Q8C23×D6714yes—
661C2×D4—24no—
662C2×D4—44no—
663C2×D4C23×D6714yes—
664C2×D4C23×D6718yes—
665C22×C4—28no—
666C22×C4—24no—
667C22×C4—24no—
668C22×C4—42no—
669C22×C4—2688no—
670C22×C4—6716no—
671C22×C4—674no—
672C22×C4—672no—
673C22×C4—672no—
674C22×C4—672no—
675C22×C4—674no—
676C22×C4—672no—
677C22×C4C23×D6714yes—
678C22×C4C23×D6714yes—
679C22×C4C23×D6718yes—
680C22×C4C23×D6711yescharacteristic
681C22×C4C23×D6712yes—
682C22×C4C23×D6712yes—
683C22×C4C23×D6712yes—
684C22×C4C23×D6711yescharacteristic
685C22×C4C23×D6711yescharacteristic
686C22×C4C23×D6711yescharacteristic
687C22×C4C23×D6714yes—
688C22×C4C23×D6711yescharacteristic
689C22×C4C23×D6711yescharacteristic
690C4⋊C4—674no—
691C4⋊C4—678no—
692C4⋊C4—6716no—
693C4⋊C4—678no—
694C4⋊C4—678no—
695C4⋊C4—674no—
696C4⋊C4—678no—
697C4⋊C4—6716no—
698C4⋊C4—678no—
699C4⋊C4—678no—
700C4⋊C4—678no—
701C4⋊C4—678no—
702C4⋊C4—6716no—
703C4⋊C4—6716no—
704C4⋊C4—6716no—
705C4⋊C4—6716no—
706C4⋊C4—6716no—
707C4⋊C4—678no—
708C4⋊C4—678no—
709C4⋊C4—678no—
710C4⋊C4—6716no—
711C4⋊C4—6716no—
712C4⋊C4—6716no—
713C4⋊C4C23×D6718yes—
714C4⋊C4C23×D6718yes—
715C4⋊C4C23×D6714yes—
716C4⋊C4C23×D6718yes—
717C4⋊C4C23×D6714yes—
718C4⋊C4C23×D6718yes—
719C22⋊C4—678no—
720C22⋊C4—6716no—
721C22⋊C4—678no—
722C22⋊C4—6716no—
723C22⋊C4—6716no—
724C22⋊C4—6716no—
725C22⋊C4C23×D6718yes—
726C22⋊C4C23×D6718yes—
727C22⋊C4C23×D6718yes—
728C22⋊C4C23×D6718yes—
729C22⋊C4C23×D6718yes—
730C42—6716no—
731C42—678no—
732C42—678no—
733C42—6716no—
734C42—6716no—
735C42—6716no—
736C42C23×D6714yes—
737C42C23×D6714yes—
738C42C23×D6714yes—
739C42C23×D6714yes—
740C42C23×D6718yes—
741C23—22no—
742C23—22no—
743C23—24no—
744C23—24no—
745C23—22no—
746C23—24no—
747C23C24×D6712yes—
748C23C24×D6714yes—
749C23C24×D6711yescharacteristic
750Q8—28no—
751Q8—2688no—
752Q8—2688no—
753Q8—26816no—
754Q8—1348no—
755Q8—1348no—
756Q8—13416no—
757D4—28no—
758D4—48no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—28no—
767C2×C4—216no—
768C2×C4—28no—
769C2×C4—44no—
770C2×C4—26816no—
771C2×C4—678no—
772C2×C4—674no—
773C2×C4—674no—
774C2×C4—674no—
775C2×C4—678no—
776C2×C4—674no—
777C2×C4—1344no—
778C2×C4—1344no—
779C2×C4—1348no—
780C2×C4—1344no—
781C2×C4—1348no—
782C2×C4—1344no—
783C2×C4#1452409014yes—
784C2×C4#1452409014yes—
785C2×C4C24×D6712yes—
786C2×C4C24×D6714yes—
787C2×C4C24×D6714yes—
788C2×C4C24×D6714yes—
789C2×C4C24×D6712yes—
790C2×C4C24×D6712yes—
791C2×C4C24×D6712yes—
792C2×C4C24×D6712yes—
793C2×C4C24×D6712yes—
794C22—22no—
795C22—22no—
796C22—24no—
797C22—24no—
798C22—22no—
799C22—24no—
800C22—44no—
801C22—48no—
802C22C2×#1452409012yes—
803C22C2×#1452409012yes—
804C22#1686423212yes—
805C22C25×D6711yescharacteristic
806C4—22no—
807C4—24no—
808C4—22no—
809C4—24no—
810C4—22no—
811C4—22no—
812C4—24no—
813C4—1344no—
814C4—1344no—
815C4—1348no—
816C4—1344no—
817C4—1348no—
818C4—1344no—
819C4C2×#1452409014yes—
820C4C2×#1452409014yes—
821C2—42no—
822C2—44no—
823C2#2257469914yesdirect product factor
824C2C22×#1452409011yescharacteristic
825C2C22×#1452409011yescharacteristic
826C2C2×#1686423211yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#529×C67C2
socleC23×C67C25
prime radicalC2×#121×C67C22
hypercenterC2×#529D67
hypocenterC67C2×#3555
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #22574699C2direct (N × H)
2. C2×#16864149C2semidirect
3. C2×Q8×Dic134C2semidirect
4. C2×#16864124C2semidirect
5. C2×#16864123C2semidirect
6. C2×#16864116C2semidirect
7. C2×#16864116C2semidirect
8. C2×#16864115C2semidirect
9. C2×#16864103C2semidirect
10. C2×#16864086C2semidirect
11. C2×#16864024C2semidirect
13. C2×#16864008C2semidirect
14. C2×#16864006C2semidirect
15. C2×#16864003C2semidirect
16. C2×#16863953C2semidirect
17. C2×#16863953C2semidirect
19. #16864149C22semidirect
20. Q8×Dic134C22semidirect
21. #16864124C22semidirect
22. #16864123C22semidirect
23. #16864116C22semidirect
24. #16864116C22semidirect
25. #16864115C22semidirect
26. #16864103C22semidirect
27. #16864086C22semidirect
28. #16864024C22semidirect
30. #16864008C22semidirect
31. #16864006C22semidirect
32. #16864003C22semidirect
33. #16863953C22semidirect
34. #16863953C22semidirect
410. C2×C67#3555semidirect
432. C67C2×#3555semidirect
823. C2#22574699direct (N × H)

Maximal subgroups

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

subgroupindex
#225746992
C2×#168641492
C2×Q8×Dic1342
C2×#168641242
C2×#168641232
C2×#168641162
C2×#168641152
C2×#168641032
C2×#168640862
C2×#168640242
C2×#168640132
C2×#168640082
C2×#168640062
C2×#168640032
C2×#168639532
C2×#529×C672
C2×#355567