Finite Group Databasebeta

← C2×#22574549 #31763513

Subgroups — C2×#22574549 #31763513

Order 17152.

7086 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574549C2132yesmaximal, direct product factor
2C2×#16864148C214yesmaximal, complemented
3C2×Q8×Dic134C211yesmaximal, characteristic, complemented
4C2×#16864111C211yesmaximal, characteristic, complemented
5C2×#16864106C211yesmaximal, characteristic, complemented
6C2×#16864103C211yesmaximal, characteristic, complemented
7C2×#16864088C212yesmaximal, complemented
8C2×#16864086C212yesmaximal, complemented
9C2×#16864050C212yesmaximal, complemented
10C2×#16864046C212yesmaximal, complemented
11C2×#16864026C212yesmaximal, complemented
12C2×#16864024C212yesmaximal, complemented
13C2×#16864017C212yesmaximal, complemented
14C2×#16864015C212yesmaximal, complemented
15C2×#16863968C214yesmaximal, complemented
16C22×#14524043C211yesmaximal, characteristic, complemented
17C2×#16863930C211yesmaximal, characteristic, complemented
18C2×#529×C67C211yesmaximal, characteristic, complemented
19C22×#11761627C2214yes—
20C23×Dic134C2212yes—
21#16864148C22164yescomplemented
22Q8×Dic134C22116yescomplemented
23#16864111C22116yescomplemented
24#16864106C22116yescomplemented
25#16864103C22116yescomplemented
26#16864088C22132yescomplemented
27#16864086C22132yescomplemented
28#16864050C22132yescomplemented
29#16864046C22132yescomplemented
30#16864026C22132yescomplemented
31#16864024C22132yescomplemented
32#16864017C22132yescomplemented
33#16864015C22132yescomplemented
34#16863968C22164yescomplemented
35C2×#14524043C2212yes—
36C2×#14524043C2212yes—
37C2×#14524043C2212yes—
38C2×#14524043C2212yes—
39C2×#14524043C2211yescharacteristic
40C2×#14524043C2211yescharacteristic
41C2×#14524043C22116yescomplemented
42C2×#14524042C2214yes—
43C2×#14524042C2214yes—
44C2×#14524042C2212yes—
45#16863930C22116yescomplemented
46C2×#14524038C2214yes—
47C2×#14524037C2212yes—
48C2×#14524036C2214yes—
49C2×#14524035C2211yescharacteristic
50C2×#14524035C2212yes—
51C2×#14524034C2214yes—
52C2×#14524034C2212yes—
53C2×#14524033C2214yes—
54C2×#14524031C2211yescharacteristic
55C2×#14524029C2214yes—
56C2×#14524029C2214yes—
57C2×#14524027C2214yes—
58C2×#14524027C2214yes—
59C2×#14524026C2212yes—
60C2×#14524025C2214yes—
61C2×#14524024C2214yes—
62C2×#14524023C2214yes—
63C2×#14524022C2212yes—
64C2×#14524022C2211yescharacteristic
65C2×#14524021C2214yes—
66C2×#14524021C2214yes—
67C2×#14524020C2214yes—
68C2×#14524020C2214yes—
69C2×#14524020C2214yes—
70C2×#14524019C2212yes—
71C2×#14524017C2212yes—
72C2×#14524017C2211yescharacteristic
73C2×#14524014C2212yes—
74C2×Q8×Dic67C2212yes—
75C2×C4×Dic134C2212yes—
76C2×C4×Dic134C2211yescharacteristic
77C2×C4×D268C2212yes—
78C2×C4×D268C2211yescharacteristic
79C2×D4×Dic67C2212yes—
80C2×C4×C22⋊D67C2212yes—
81C2×#14524002C2212yes—
82C2×#14524001C2212yes—
83C2×#14524000C2212yes—
84C2×#14523999C2214yes—
85C22×C4⋊Dic67C2212yes—
86C22×C4⋊Dic67C2212yes—
87C22×C4⋊Dic67C2212yes—
88C2×C4⋊C4×D67C2212yes—
89#529×C67C22116yescomplemented
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
101C2×#11761627—416no—
102C2×#11761627C23132yes—
103C22×Dic134—48no—
104C22×Dic134C2311yescharacteristic
105C22×Dic134C2312yes—
106C22×Dic134C2314yes—
107C22×Dic134C2314yes—
108C22×Dic134C2312yes—
109C22×Dic134C23116yes—
110C22×D268C2311yescharacteristic
111C22×C22⋊D67C2312yes—
112C22×C22⋊D67C2314yes—
113C23×Dic67C2314yes—
114C23×Dic67C2314yes—
115C22×C4×D67C2312yes—
116C22×C4×D67C2314yes—
117#14524043C23116yes—
118#14524043C23116yes—
119#14524043C23116yes—
120#14524043C2318yes—
121#14524043C2318yes—
122#14524043C23116yes—
123#14524042C23132yes—
124#14524042C23116yes—
125#14524042C23132yes—
126#14524038C23132yes—
127#14524037C23116yes—
128#14524036C23132yes—
129#14524035C2318yes—
130#14524035C23116yes—
131#14524034C23132yes—
132#14524034C23116yes—
133#14524033C23132yes—
134#14524031C2318yes—
135#14524029C23132yes—
136#14524029C23132yes—
137#14524027C23132yes—
138#14524027C23132yes—
139#14524026C23116yes—
140#14524025C23132yes—
141#14524024C23132yes—
142#14524023C23132yes—
143#14524022C23116yes—
144#14524022C2318yes—
145#14524021C23132yes—
146#14524021C23132yes—
147#14524020C23132yes—
148#14524020C23132yes—
149#14524020C23132yes—
150#14524019C23116yes—
151#14524017C23116yes—
152#14524017C2318yes—
153#14524014C23116yes—
154Q8×Dic67C23116yes—
155C4×Dic134C23116yes—
156C4×Dic134C2318yes—
157C4×D268C23116yes—
158C4×D268C2318yes—
159D4×Dic67C23116yes—
160C4×C22⋊D67C23116yes—
161#14524002C23116yes—
162#14524001C23116yes—
163#14524000C23116yes—
164#14523999C23132yes—
165C2×C4⋊Dic67C23116yes—
166C2×C4⋊Dic67C23116yes—
167C2×C4⋊Dic67C23116yes—
168C2×C4⋊Dic67C2312yes—
169C2×C4⋊Dic67C2312yes—
170C2×C4⋊Dic67C2311yescharacteristic
171C2×C4⋊Dic67C2312yes—
172C2×C4⋊Dic67C2312yes—
173C2×C4⋊Dic67C2314yes—
174C2×C4⋊Dic67C2314yes—
175C2×C4⋊Dic67C2314yes—
176C2×C4⋊Dic67C2311yescharacteristic
177C2×C4⋊Dic67C2314yes—
178C2×Dic67⋊C4C2314yes—
179C2×Dic67⋊C4C2314yes—
180C2×Dic67⋊C4C2314yes—
181C2×Dic67⋊C4C2312yes—
182C2×Dic67⋊C4C2312yes—
183C2×Dic67⋊C4C2312yes—
184C2×Dic67⋊C4C2312yes—
185C2×Dic67⋊C4C2314yes—
186C4⋊C4×D67C23116yes—
187C2×C22⋊Dic67C2312yes—
188C2×C22⋊Dic67C2314yes—
189C2×C22⋊Dic67C2314yes—
190C2×(C2×D67)⋊C4C2312yes—
191C2×(C2×D67)⋊C4C2312yes—
192C2×(C2×D67)⋊C4C2314yes—
193C2×(C2×D67)⋊C4C2312yes—
194C2×(C2×D67)⋊C4C2314yes—
195C2×(C2×D67)⋊C4C2312yes—
196C2×C4×Dic67C2314yes—
197C2×C4×Dic67C2314yes—
198C2×C4×Dic67C2312yes—
199C22×Q8×C67C2311yescharacteristic
200C22×D4×C67C2312yes—
201C22×D4×C67C2311yescharacteristic
202C23×C4×C67C2311yescharacteristic
203C23×C4×C67C2311yescharacteristic
204C23×C4×C67C2311yescharacteristic
205C23×C4×C67C2312yes—
206#126×C67C23116yes—
207#125×C67C2318yes—
208#124×C67C2318yes—
209#123×C67C23116yes—
210C22⋊Q8×C67C2318yes—
211#121×C67C2318yes—
212C4×Q8×C67C2318yes—
213C4×D4×C67C23116yes—
214C4×D4×C67C2318yes—
215#117×C67C23116yes—
216C2×C4⋊C4×C67C2312yes—
217C2×C4⋊C4×C67C2312yes—
218C2×C4⋊C4×C67C2311yescharacteristic
219C2×C4⋊C4×C67C2312yes—
220C2×C4⋊C4×C67C2311yescharacteristic
221C2×C4⋊C4×C67C2312yes—
222C2×C22⋊C4×C67C2312yes—
223C2×C22⋊C4×C67C2312yes—
224C2×C22⋊C4×C67C2312yes—
225C2×C22⋊C4×C67C2312yes—
226C2×C22⋊C4×C67C2312yes—
227C2×C42×C67C2311yescharacteristic
228C2×C42×C67C2311yescharacteristic
229C2×C42×C67C2311yescharacteristic
230C2×C42×C67C2311yescharacteristic
231C2×C42×C67C2318yes—
232C2×C42×C67C2312yes—
233C23×D67C2412yes—
234#11761627—464no—
235C2×Dic134—24no—
236C2×Dic134—44no—
237C2×Dic134—48no—
238C2×Dic134—44no—
239C2×Dic134—432no—
240C2×Dic134—48no—
241C2×Dic134C2414yes—
242C2×Dic134C2418yes—
243C2×Dic134C24116yes—
244C2×Dic134C24116yes—
245C2×Dic134C2418yes—
246C2×D268—24no—
247C2×D268C2414yes—
248C2×C22⋊D67—28no—
249C2×C22⋊D67—48no—
250C2×C22⋊D67C2418yes—
251C2×C22⋊D67C24116yes—
252C22×Dic67—216no—
253C22×Dic67—48no—
254C22×Dic67C2412yes—
255C22×Dic67C2412yes—
256C22×Dic67C2414yes—
257C22×Dic67C2412yes—
258C22×Dic67C2414yes—
259C22×Dic67C24116yes—
260C22×Dic67C24116yes—
261C2×C4×D67—28no—
262C2×C4×D67—48no—
263C2×C4×D67C2418yes—
264C2×C4×D67C24116yes—
265C4⋊Dic67C2418yes—
266C4⋊Dic67C2418yes—
267C4⋊Dic67C2414yes—
268C4⋊Dic67C2418yes—
269C4⋊Dic67C2418yes—
270C4⋊Dic67C24116yes—
271C4⋊Dic67C24116yes—
272C4⋊Dic67C24116yes—
273C4⋊Dic67C2414yes—
274C4⋊Dic67C24116yes—
275Dic67⋊C4C24116yes—
276Dic67⋊C4C24116yes—
277Dic67⋊C4C24116yes—
278Dic67⋊C4C2418yes—
279Dic67⋊C4C2418yes—
280Dic67⋊C4C2418yes—
281Dic67⋊C4C2418yes—
282Dic67⋊C4C24116yes—
283C22⋊Dic67C2418yes—
284C22⋊Dic67C24116yes—
285C22⋊Dic67C24116yes—
286(C2×D67)⋊C4C2418yes—
287(C2×D67)⋊C4C2418yes—
288(C2×D67)⋊C4C24116yes—
289(C2×D67)⋊C4C2418yes—
290(C2×D67)⋊C4C24116yes—
291(C2×D67)⋊C4C2418yes—
292C4×Dic67C24116yes—
293C4×Dic67C24116yes—
294C4×Dic67C2418yes—
295C24×C67C2412yes—
296C24×C67C2411yescharacteristic
297C2×Q8×C67—24no—
298C2×Q8×C67C2414yes—
299C2×D4×C67—28no—
300C2×D4×C67—24no—
301C2×D4×C67C2418yes—
302C2×D4×C67C2414yes—
303C22×C4×C67—24no—
304C22×C4×C67—24no—
305C22×C4×C67—28no—
306C22×C4×C67—24no—
307C22×C4×C67C2411yescharacteristic
308C22×C4×C67C2411yescharacteristic
309C22×C4×C67C2411yescharacteristic
310C22×C4×C67C2411yescharacteristic
311C22×C4×C67C2414yes—
312C22×C4×C67C2414yes—
313C22×C4×C67C2414yes—
314C22×C4×C67C2412yes—
315C22×C4×C67C2412yes—
316C22×C4×C67C2412yes—
317C22×C4×C67C2418yes—
318C22×C4×C67C2411yescharacteristic
319C22×C4×C67C2411yescharacteristic
320C4⋊C4×C67C2418yes—
321C4⋊C4×C67C2418yes—
322C4⋊C4×C67C2414yes—
323C4⋊C4×C67C2418yes—
324C4⋊C4×C67C2414yes—
325C4⋊C4×C67C2418yes—
326C22⋊C4×C67C2418yes—
327C22⋊C4×C67C2418yes—
328C22⋊C4×C67C2418yes—
329C22⋊C4×C67C2418yes—
330C22⋊C4×C67C2418yes—
331C42×C67C2414yes—
332C42×C67C2414yes—
333C42×C67C2414yes—
334C42×C67C2414yes—
335C42×C67C2418yes—
336C23×C67—22no—
337C23×C67—22no—
338C23×C67—24no—
339C23×C67—24no—
340C23×C67—24no—
341C23×C67H(5,𝔽2)14yes—
342C23×C67C2514yes—
343C23×C67C2512yes—
344C23×C67C2511yescharacteristic
345C22×D67—24no—
346C22×D67—24no—
347C22×D67—24no—
348C22×D67C2514yes—
349Q8×C67—28no—
350D4×C67—216no—
351D4×C67—28no—
352C2×C4×C67—28no—
353C2×C4×C67—22no—
354C2×C4×C67—22no—
355C2×C4×C67—24no—
356C2×C4×C67—22no—
357C2×C4×C67—22no—
358C2×C4×C67—24no—
359C2×C4×C67—24no—
360C2×C4×C67—28no—
361C2×C4×C67—216no—
362C2×C4×C67—28no—
363C2×C4×C672−1+414yes—
364C2×C4×C672−1+414yes—
365C2×C4×C67C2512yes—
366C2×C4×C67C2512yes—
367C2×C4×C67C2512yes—
368C2×C4×C67C2512yes—
369C2×C4×C67C2514yes—
370C2×C4×C67C2514yes—
371C2×C4×C67C2514yes—
372C2×C4×C67C2512yes—
373C2×C4×C67C2512yes—
374C22⋊D67—216no—
375C22⋊D67—416no—
376C2×Dic67—28no—
377C2×Dic67—28no—
378C2×Dic67—232no—
379C2×Dic67—24no—
380C2×Dic67—24no—
381C2×Dic67—24no—
382C2×Dic67—416no—
383C2×Dic67C2514yes—
384C2×Dic67C2514yes—
385C2×Dic67C2518yes—
386C2×Dic67C2514yes—
387C2×Dic67C2518yes—
388D268—28no—
389C4×D67—216no—
390C4×D67—416no—
391Dic134—28no—
392Dic134—48no—
393Dic134—416no—
394Dic134—48no—
395Dic134—416no—
396C22×C67—22no—
397C22×C67—22no—
398C22×C67—28no—
399C22×C67—24no—
400C22×C67—24no—
401C22×C67—24no—
402C22×C67—48no—
403C22×C67C2×H(5,𝔽2)14yes—
404C22×C67C2×H(5,𝔽2)12yes—
405C22×C67C2×2−1+412yes—
406C22×C67C2×2−1+412yes—
407C22×C67C2611yescharacteristic
408C2×D67—24no—
409C2×D67—24no—
410C2×D67—24no—
411C2×D67—48no—
412C4×C67—22no—
413C4×C67—22no—
414C4×C67—24no—
415C4×C67—22no—
416C4×C67—22no—
417C4×C67—24no—
418C4×C67—24no—
419C4×C67C2×2−1+414yes—
420C4×C67C2×2−1+414yes—
421Dic67—28no—
422Dic67—28no—
423Dic67—24no—
424Dic67—24no—
425Dic67—24no—
426C2×#3544—671nomaximal, Sylow
427C2×C67—24no—
428C2×C67—44no—
429C2×C67#354414yescomplemented
430C2×C67C22×H(5,𝔽2)11yescharacteristic
431C2×C67C22×2−1+411yescharacteristic
432C2×C67C22×2−1+411yescharacteristic
433D67—44no—
434#3544—6732no—
435C2×#563—674no—
436C2×Q82—671no—
437C2×#555—671no—
438C2×#554—671no—
439C2×#554—671no—
440C2×#552—672no—
441C2×#552—672no—
442C2×#547—672no—
443C2×#547—672no—
444C2×#544—672no—
445C2×#544—672no—
446C2×#542—672no—
447C2×#542—672no—
448C2×#536—674no—
449C22×C4⋊Q8—671no—
450C2×#529—671no—
451C2×#529D6711yescharacteristic, complemented
452C67C2×#354411yescharacteristic, complemented, Sylow
453C22×#41—674no—
454C23×Q8—672no—
455#563—6764no—
456Q82—6716no—
457#555—6716no—
458#554—6716no—
459#554—6716no—
460#552—6732no—
461#552—6732no—
462#547—6732no—
463#547—6732no—
464#544—6732no—
465#544—6732no—
466#542—6732no—
467#542—6732no—
468#536—6764no—
469C2×C4⋊Q8—674no—
470C2×C4⋊Q8—674no—
471C2×C4⋊Q8—672no—
472C2×C4⋊Q8—672no—
473C2×C4⋊Q8—672no—
474C2×C4⋊Q8—671no—
475C2×C4⋊Q8—671no—
476C2×C4⋊Q8—672no—
477C2×C4⋊Q8—6716no—
478C2×C4⋊Q8—672no—
479#529—6716no—
480#529C2×D67116yescomplemented
481C2×#126—674no—
482C2×#126—674no—
483C2×#126—672no—
484C2×#126C2×D6712yes—
485C2×#125—672no—
486C2×#125—674no—
487C2×#125—674no—
488C2×#125—671no—
489C2×#125—672no—
490C2×#125C2×D6711yescharacteristic
491C2×#124—674no—
492C2×#124—674no—
493C2×#124—671no—
494C2×#124C2×D6711yescharacteristic
495C2×#123—674no—
496C2×#123—672no—
497C2×#123—674no—
498C2×#123—674no—
499C2×#123—674no—
500C2×#123C2×D6712yes—
501C2×C22⋊Q8—672no—
502C2×C22⋊Q8—671no—
503C2×C22⋊Q8—672no—
504C2×C22⋊Q8—674no—
505C2×C22⋊Q8—674no—
506C2×C22⋊Q8—674no—
507C2×C22⋊Q8—674no—
508C2×C22⋊Q8—674no—
509C2×C22⋊Q8—674no—
510C2×C22⋊Q8C2×D6711yescharacteristic
511C2×#121—672no—
512C2×#121—671no—
513C2×#121—672no—
514C2×#121C2×D6711yescharacteristic
515C2×C4×Q8—672no—
516C2×C4×Q8—671no—
517C2×C4×Q8—672no—
518C2×C4×Q8C2×D6711yescharacteristic
519C2×C4×D4—672no—
520C2×C4×D4—672no—
521C2×C4×D4—671no—
522C2×C4×D4—672no—
523C2×C4×D4C2×D6712yes—
524C2×C4×D4C2×D6711yescharacteristic
525C2×#117—672no—
526C2×#117—672no—
527C2×#117—674no—
528C2×#117—672no—
529C2×#117C2×D6712yes—
530C22×C4⋊C4—672no—
531C22×C4⋊C4—672no—
532C22×C4⋊C4—672no—
533C22×C4⋊C4—672no—
534C22×C42C2×D6711yescharacteristic
535C2×#41—26816no—
536C2×#41—6732no—
537C22×Q8—2688no—
538C22×Q8—672no—
539C22×Q8—674no—
540C22×Q8—674no—
541C22×Q8—672no—
542C22×Q8—6716no—
543C22×Q8—671no—
544C22×Q8C22×D6711yescharacteristic
545C22×D4—674no—
546C22×D4—672no—
547C22×D4—671no—
548C22×D4C22×D6711yescharacteristic
549C22×D4C22×D6712yes—
550C23×C4—674no—
551C23×C4—674no—
552C23×C4—674no—
553C23×C4—672no—
554C23×C4C22×D6711yescharacteristic
555C23×C4C22×D6711yescharacteristic
556C23×C4C22×D6712yes—
557C23×C4C22×D6711yescharacteristic
558C4⋊Q8—6732no—
559C4⋊Q8—6732no—
560C4⋊Q8—6716no—
561C4⋊Q8—6716no—
562C4⋊Q8—6716no—
563C4⋊Q8—678no—
564C4⋊Q8—678no—
565C4⋊Q8—6716no—
566C4⋊Q8—6716no—
567#126—6732no—
568#126—6732no—
569#126—6716no—
570#126C22×D67116yes—
571#125—6716no—
572#125—6732no—
573#125—6732no—
574#125—678no—
575#125—6716no—
576#125C22×D6718yes—
577#124—6732no—
578#124—6732no—
579#124—678no—
580#124C22×D6718yes—
581#123—6732no—
582#123—6716no—
583#123—6732no—
584#123—6732no—
585#123—6732no—
586#123C22×D67116yes—
587C22⋊Q8—6716no—
588C22⋊Q8—678no—
589C22⋊Q8—6716no—
590C22⋊Q8—6732no—
591C22⋊Q8—6732no—
592C22⋊Q8—6732no—
593C22⋊Q8—6732no—
594C22⋊Q8—6732no—
595C22⋊Q8—6732no—
596C22⋊Q8C22×D6718yes—
597#121—6716no—
598#121—678no—
599#121—6716no—
600#121C22×D6718yes—
601C4×Q8—6716no—
602C4×Q8—678no—
603C4×Q8—6716no—
604C4×Q8C22×D6718yes—
605C4×D4—6716no—
606C4×D4—6716no—
607C4×D4—678no—
608C4×D4—6716no—
609C4×D4C22×D67116yes—
610C4×D4C22×D6718yes—
611#117—6716no—
612#117—6716no—
613#117—6732no—
614#117—6716no—
615#117C22×D67116yes—
616C2×C4⋊C4—672no—
617C2×C4⋊C4—672no—
618C2×C4⋊C4—671no—
619C2×C4⋊C4—672no—
620C2×C4⋊C4—672no—
621C2×C4⋊C4—674no—
622C2×C4⋊C4—674no—
623C2×C4⋊C4—674no—
624C2×C4⋊C4—674no—
625C2×C4⋊C4—6716no—
626C2×C4⋊C4—6716no—
627C2×C4⋊C4—6716no—
628C2×C4⋊C4—671no—
629C2×C4⋊C4—674no—
630C2×C4⋊C4—674no—
631C2×C4⋊C4—672no—
632C2×C4⋊C4—672no—
633C2×C4⋊C4—672no—
634C2×C4⋊C4—672no—
635C2×C4⋊C4—674no—
636C2×C4⋊C4—674no—
637C2×C4⋊C4—6716no—
638C2×C4⋊C4C22×D6711yescharacteristic
639C2×C4⋊C4C22×D6711yescharacteristic
640C2×C4⋊C4C22×D6712yes—
641C2×C4⋊C4C22×D6712yes—
642C2×C4⋊C4C22×D6712yes—
643C2×C4⋊C4C22×D6712yes—
644C2×C22⋊C4—672no—
645C2×C22⋊C4—674no—
646C2×C22⋊C4—674no—
647C2×C22⋊C4—672no—
648C2×C22⋊C4—674no—
649C2×C22⋊C4—672no—
650C2×C22⋊C4—674no—
651C2×C22⋊C4—672no—
652C2×C22⋊C4—672no—
653C2×C22⋊C4C22×D6712yes—
654C2×C22⋊C4C22×D6712yes—
655C2×C22⋊C4C22×D6712yes—
656C2×C22⋊C4C22×D6712yes—
657C2×C22⋊C4C22×D6712yes—
658C2×C42—674no—
659C2×C42—672no—
660C2×C42—674no—
661C2×C42C22×D6711yescharacteristic
662C2×C42C22×D6711yescharacteristic
663C2×C42C22×D6712yes—
664C2×C42C22×D6711yescharacteristic
665C2×C42C22×D6711yescharacteristic
666C2×C42C22×D6718yes—
667C24—672no—
668C24C23×D6712yes—
669C24C23×D6711yescharacteristic
670#41—26864no—
671C2×Q8—24no—
672C2×Q8—2684no—
673C2×Q8—2688no—
674C2×Q8—2684no—
675C2×Q8—26832no—
676C2×Q8—2688no—
677C2×Q8—678no—
678C2×Q8—6716no—
679C2×Q8—6716no—
680C2×Q8—678no—
681C2×Q8—674no—
682C2×Q8—1344no—
683C2×Q8C23×D6714yes—
684C2×D4—28no—
685C2×D4—24no—
686C2×D4—2688no—
687C2×D4—6716no—
688C2×D4—678no—
689C2×D4—674no—
690C2×D4—1348no—
691C2×D4—1344no—
692C2×D4C23×D6714yes—
693C2×D4C23×D6718yes—
694C22×C4—24no—
695C22×C4—24no—
696C22×C4—28no—
697C22×C4—24no—
698C22×C4—2688no—
699C22×C4—2688no—
700C22×C4—6716no—
701C22×C4—6716no—
702C22×C4—6716no—
703C22×C4—672no—
704C22×C4—672no—
705C22×C4—674no—
706C22×C4—672no—
707C22×C4—674no—
708C22×C4—678no—
709C22×C4—13416no—
710C22×C4—1348no—
711C22×C4C23×D6714yes—
712C22×C4C23×D6714yes—
713C22×C4C23×D6714yes—
714C22×C4C23×D6718yes—
715C22×C4C23×D6712yes—
716C22×C4C23×D6712yes—
717C22×C4C23×D6711yescharacteristic
718C22×C4C23×D6711yescharacteristic
719C22×C4C23×D6711yescharacteristic
720C22×C4C23×D6711yescharacteristic
721C22×C4C23×D6712yes—
722C22×C4C23×D6711yescharacteristic
723C22×C4C23×D6711yescharacteristic
724C4⋊C4—678no—
725C4⋊C4—678no—
726C4⋊C4—674no—
727C4⋊C4—678no—
728C4⋊C4—678no—
729C4⋊C4—6716no—
730C4⋊C4—6716no—
731C4⋊C4—6716no—
732C4⋊C4—6716no—
733C4⋊C4—674no—
734C4⋊C4—6716no—
735C4⋊C4—6716no—
736C4⋊C4—678no—
737C4⋊C4—678no—
738C4⋊C4—678no—
739C4⋊C4—678no—
740C4⋊C4—6716no—
741C4⋊C4—6716no—
742C4⋊C4C23×D6714yes—
743C4⋊C4C23×D6714yes—
744C4⋊C4C23×D6718yes—
745C4⋊C4C23×D6718yes—
746C4⋊C4C23×D6718yes—
747C4⋊C4C23×D6718yes—
748C22⋊C4—678no—
749C22⋊C4—6716no—
750C22⋊C4—6716no—
751C22⋊C4—678no—
752C22⋊C4—6716no—
753C22⋊C4—678no—
754C22⋊C4—6716no—
755C22⋊C4—678no—
756C22⋊C4—678no—
757C22⋊C4C23×D6718yes—
758C22⋊C4C23×D6718yes—
759C22⋊C4C23×D6718yes—
760C22⋊C4C23×D6718yes—
761C22⋊C4C23×D6718yes—
762C42—6716no—
763C42—678no—
764C42—6716no—
765C42C23×D6714yes—
766C42C23×D6714yes—
767C42C23×D6714yes—
768C42C23×D6714yes—
769C42C23×D6718yes—
770C23—22no—
771C23—22no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—674no—
776C23—1344no—
777C23—1344no—
778C23—1344no—
779C23#1452408914yes—
780C23C24×D6714yes—
781C23C24×D6712yes—
782C23C24×D6711yescharacteristic
783Q8—28no—
784Q8—2688no—
785Q8—26816no—
786Q8—2688no—
787Q8—26816no—
788Q8—1348no—
789D4—216no—
790D4—28no—
791D4—26816no—
792D4—13416no—
793D4—1348no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—28no—
803C2×C4—216no—
804C2×C4—28no—
805C2×C4—26816no—
806C2×C4—26816no—
807C2×C4—674no—
808C2×C4—674no—
809C2×C4—678no—
810C2×C4—674no—
811C2×C4—678no—
812C2×C4—1348no—
813C2×C4—1344no—
814C2×C4—1348no—
815C2×C4—13432no—
816C2×C4—1344no—
817C2×C4—1344no—
818C2×C4—13416no—
819C2×C4#1452409014yes—
820C2×C4#1452409014yes—
821C2×C4C24×D6714yes—
822C2×C4C24×D6714yes—
823C2×C4C24×D6712yes—
824C2×C4C24×D6712yes—
825C2×C4C24×D6712yes—
826C2×C4C24×D6712yes—
827C2×C4C24×D6714yes—
828C2×C4C24×D6712yes—
829C2×C4C24×D6712yes—
830C22—22no—
831C22—22no—
832C22—28no—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—48no—
837C22—2688no—
838C22—1344no—
839C22—1344no—
840C22—1344no—
841C22C2×#1452408914yes—
842C22C2×#1452408912yes—
843C22C2×#1452409012yes—
844C22C2×#1452409012yes—
845C22C25×D6711yescharacteristic
846C4—22no—
847C4—22no—
848C4—24no—
849C4—24no—
850C4—22no—
851C4—22no—
852C4—24no—
853C4—1348no—
854C4—1344no—
855C4—1348no—
856C4—1344no—
857C4—1344no—
858C4C2×#1452409014yes—
859C4C2×#1452409014yes—
860C2—24no—
861C2—44no—
862C2—2684no—
863C2#2257454914yesdirect product factor
864C2C22×#1452408911yescharacteristic
865C2C22×#1452409011yescharacteristic
866C2C22×#1452409011yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#529×C67C2
socleC23×C67C25
hypercenterC2×#529D67
hypocenterC67C2×#3544
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #22574549C2direct (N × H)
2. C2×#16864148C2semidirect
3. C2×Q8×Dic134C2semidirect
4. C2×#16864111C2semidirect
5. C2×#16864106C2semidirect
6. C2×#16864103C2semidirect
7. C2×#16864088C2semidirect
8. C2×#16864086C2semidirect
9. C2×#16864050C2semidirect
10. C2×#16864046C2semidirect
11. C2×#16864026C2semidirect
12. C2×#16864024C2semidirect
13. C2×#16864017C2semidirect
14. C2×#16864015C2semidirect
15. C2×#16863968C2semidirect
16. C22×#14524043C2semidirect
17. C2×#16863930C2semidirect
18. C2×#529×C67C2semidirect
21. #16864148C22semidirect
22. Q8×Dic134C22semidirect
23. #16864111C22semidirect
24. #16864106C22semidirect
25. #16864103C22semidirect
26. #16864088C22semidirect
27. #16864086C22semidirect
28. #16864050C22semidirect
29. #16864046C22semidirect
30. #16864026C22semidirect
31. #16864024C22semidirect
32. #16864017C22semidirect
33. #16864015C22semidirect
34. #16863968C22semidirect
41. C2×#14524043C22semidirect
45. #16863930C22semidirect
89. #529×C67C22semidirect
429. C2×C67#3544semidirect
451. C2×#529D67semidirect
452. C67C2×#3544semidirect
480. #529C2×D67semidirect
863. C2#22574549direct (N × H)

Maximal subgroups

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

subgroupindex
#225745492
C2×#168641482
C2×Q8×Dic1342
C2×#168641112
C2×#168641062
C2×#168641032
C2×#168640882
C2×#168640862
C2×#168640502
C2×#168640462
C2×#168640262
C2×#168640242
C2×#168640172
C2×#168640152
C2×#168639682
C22×#145240432
C2×#168639302
C2×#529×C672
C2×#354467