Finite Group Databasebeta

← C2×#22574117 #31764203

Subgroups — C2×#22574117 #31764203

Order 17152.

7758 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574117C2132yesmaximal, direct product factor
2C2×#16864117C212yesmaximal, complemented
3C2×#16864112C211yesmaximal, characteristic, complemented
4C2×#16864111C211yesmaximal, characteristic, complemented
5C2×#16864106C211yesmaximal, characteristic, complemented
6C2×#16864099C212yesmaximal, complemented
7C2×#16864096C212yesmaximal, complemented
8C2×#16864056C214yesmaximal, complemented
9C2×#16864047C212yesmaximal, complemented
10C2×#16864016C214yesmaximal, complemented
11C2×#16863976C212yesmaximal, complemented
12C2×#16863952C212yesmaximal, complemented
13C2×#16863943C212yesmaximal, complemented
14C2×#16863943C211yesmaximal, characteristic, complemented
15C2×C4⋊Q8×D67C211yesmaximal, characteristic, complemented
16C2×#16863877C212yesmaximal, complemented
17C2×C4×#11761629C211yesmaximal, characteristic, complemented
18C2×#554×C67C211yesmaximal, characteristic, complemented
19C22×#11761629C2211yescharacteristic
20C22×#11761628C2212yes—
21C22×#11761628C2214yes—
22C22×Q8×D67C2212yes—
23#16864117C22132yescomplemented
24#16864112C22116yescomplemented
25#16864111C22116yescomplemented
26#16864106C22116yescomplemented
27#16864099C22132yescomplemented
28#16864096C22132yescomplemented
29#16864056C22164yescomplemented
30#16864047C22132yescomplemented
31#16864016C22164yescomplemented
32#16863976C22132yescomplemented
33#16863952C22132yescomplemented
34#16863943C22132yescomplemented
35#16863943C22116yescomplemented
36C2×#14524043C2211yescharacteristic
37C2×#14524042C2212yes—
38C2×#14524042C2212yes—
39C2×#14524042C2211yescharacteristic
40C2×#14524041C2212yes—
41C4⋊Q8×D67C22116yescomplemented
42C2×#14524039C2211yescharacteristic
43C2×#14524038C2214yes—
44C2×#14524036C2214yes—
45C2×#14524035C2212yes—
46C2×#14524032C2214yes—
47C2×#14524029C2212yes—
48C2×#14524029C2214yes—
49C2×#14524029C2214yes—
50C2×#14524028C2214yes—
51C2×#14524026C2214yes—
52C2×#14524021C2214yes—
53C2×#14524021C2214yes—
54C2×#14524021C2214yes—
55C2×#14524019C2212yes—
56C2×#14524018C2212yes—
57C2×#14524018C2214yes—
58C2×#14524018C2211yescharacteristic
59C2×#14524018C2212yes—
60C2×#14524017C2212yes—
61C2×#14524016C2214yes—
62C2×#14524016C2212yes—
63C2×#14524016C2214yes—
64C2×#14524014C2211yescharacteristic
65C2×#14524014C2212yes—
66#16863877C22132yescomplemented
67C4×#11761629C22116yescomplemented
68C2×Q8×Dic67C2211yescharacteristic
69C2×#14524008C2214yes—
70C2×#14524008C2214yes—
71C2×C4×D268C2212yes—
72C2×C4×D268C2211yescharacteristic
73C2×C4×D268C2212yes—
74C2×C4×D268C2211yescharacteristic
75C2×#14524005C2211yescharacteristic
76C2×#14524005C2212yes—
77C2×#14524005C2214yes—
78C2×C4×C22⋊D67C2214yes—
79C2×C4×C22⋊D67C2214yes—
80C2×C4×C22⋊D67C2212yes—
81C2×#14524002C2212yes—
82C2×#14524001C2212yes—
83C2×#14524001C2211yescharacteristic
84C2×#14524001C2212yes—
85C2×#14524001C2212yes—
86C2×#14524001C2212yes—
87C2×C4⋊C4×D67C2212yes—
88C2×C4⋊C4×D67C2212yes—
89C2×C4⋊C4×D67C2212yes—
90C2×C42×D67C2211yescharacteristic
91C2×C42×D67C2212yes—
92#554×C67C22116yescomplemented
93C2×C4⋊Q8×C67C2211yescharacteristic
94C2×#125×C67C2212yes—
95C2×C22⋊Q8×C67C2214yes—
96C2×C22⋊Q8×C67C2212yes—
97C2×C4×Q8×C67C2211yescharacteristic
98C2×C4×D4×C67C2212yes—
99C2×C4×D4×C67C2211yescharacteristic
100C22×C4⋊C4×C67C2212yes—
101C2×#11761629—28no—
102C2×#11761629C2318yes—
103C2×#11761628—216no—
104C2×#11761628—416no—
105C2×#11761628C23116yes—
106C2×#11761628C23132yes—
107C22×Dic134C2312yes—
108C22×Dic134C2314yes—
109C22×Dic134C2312yes—
110C2×Q8×D67—48no—
111C2×Q8×D67C23116yes—
112C22×D268C2312yes—
113C22×D268C2312yes—
114C22×D268C2311yescharacteristic
115C22×D268C2311yescharacteristic
116C22×D268C2314yes—
117C22×C22⋊D67C2312yes—
118C22×C22⋊D67C2312yes—
119C22×C22⋊D67C2312yes—
120C22×C22⋊D67C2314yes—
121C22×C4×D67C2311yescharacteristic
122C22×C4×D67C2312yes—
123C22×C4×D67C2312yes—
124C22×C4×D67C2311yescharacteristic
125C22×C4×D67C2312yes—
126C22×C4×D67C2312yes—
127C22×C4×D67C2314yes—
128C22×C4×D67C2314yes—
129C22×C4×D67C2311yescharacteristic
130#14524043C2318yes—
131#14524042C23116yes—
132#14524042C23116yes—
133#14524042C2318yes—
134#14524041C23116yes—
135#14524039C2318yes—
136#14524038C23132yes—
137#14524036C23132yes—
138#14524035C23116yes—
139#14524032C23132yes—
140#14524029C23116yes—
141#14524029C23132yes—
142#14524029C23132yes—
143#14524028C23132yes—
144#14524026C23132yes—
145#14524021C23132yes—
146#14524021C23132yes—
147#14524021C23132yes—
148#14524019C23116yes—
149#14524018C23116yes—
150#14524018C23132yes—
151#14524018C2318yes—
152#14524018C23116yes—
153#14524017C23116yes—
154#14524016C23132yes—
155#14524016C23116yes—
156#14524016C23132yes—
157#14524014C2318yes—
158#14524014C23116yes—
159Q8×Dic67C2318yes—
160#14524008C23132yes—
161#14524008C23132yes—
162C4×D268C23116yes—
163C4×D268C23116yes—
164C4×D268C2318yes—
165C4×D268C2318yes—
166#14524005C2318yes—
167#14524005C23116yes—
168#14524005C23132yes—
169C4×C22⋊D67C23132yes—
170C4×C22⋊D67C23116yes—
171C4×C22⋊D67C23132yes—
172#14524002C23116yes—
173#14524001C23116yes—
174#14524001C23116yes—
175#14524001C23116yes—
176#14524001C23116yes—
177#14524001C2318yes—
178C2×C4⋊Dic67C2312yes—
179C2×C4⋊Dic67C2312yes—
180C2×C4⋊Dic67C2311yescharacteristic
181C2×C4⋊Dic67C2311yescharacteristic
182C2×C4⋊Dic67C2312yes—
183C2×Dic67⋊C4C2314yes—
184C2×Dic67⋊C4C2314yes—
185C2×Dic67⋊C4C2314yes—
186C2×Dic67⋊C4C2312yes—
187C2×Dic67⋊C4C2314yes—
188C4⋊C4×D67C23116yes—
189C4⋊C4×D67C23116yes—
190C4⋊C4×D67C23116yes—
191C2×C22⋊Dic67C2314yes—
192C2×C22⋊Dic67C2312yes—
193C2×(C2×D67)⋊C4C2312yes—
194C2×(C2×D67)⋊C4C2314yes—
195C2×(C2×D67)⋊C4C2312yes—
196C2×(C2×D67)⋊C4C2312yes—
197C2×(C2×D67)⋊C4C2314yes—
198C2×(C2×D67)⋊C4C2314yes—
199C2×(C2×D67)⋊C4C2312yes—
200C2×(C2×D67)⋊C4C2314yes—
201C2×(C2×D67)⋊C4C2312yes—
202C2×C4×Dic67C2311yescharacteristic
203C2×C4×Dic67C2312yes—
204C2×C4×Dic67C2311yescharacteristic
205C2×C4×Dic67C2311yescharacteristic
206C2×C4×Dic67C2312yes—
207C2×C4×Dic67C2314yes—
208C2×C4×Dic67C2314yes—
209C42×D67C2318yes—
210C42×D67C23116yes—
211C22×Q8×C67C2311yescharacteristic
212C22×Q8×C67C2312yes—
213C22×D4×C67C2311yescharacteristic
214C23×C4×C67C2312yes—
215C23×C4×C67C2314yes—
216C4⋊Q8×C67C2318yes—
217#125×C67C23116yes—
218C22⋊Q8×C67C23132yes—
219C22⋊Q8×C67C23116yes—
220C4×Q8×C67C2318yes—
221C4×D4×C67C23116yes—
222C4×D4×C67C2318yes—
223C2×C4⋊C4×C67C23116yes—
224C2×C4⋊C4×C67C2311yescharacteristic
225C2×C4⋊C4×C67C2314yes—
226C2×C4⋊C4×C67C2312yes—
227C2×C4⋊C4×C67C2311yescharacteristic
228C2×C4⋊C4×C67C2312yes—
229C2×C4⋊C4×C67C2312yes—
230C2×C4⋊C4×C67C2314yes—
231C2×C22⋊C4×C67C2314yes—
232C2×C22⋊C4×C67C2312yes—
233C2×C42×C67C2312yes—
234C2×C42×C67C2311yescharacteristic
235C23×D67C2412yes—
236C23×D67C2412yes—
237C23×D67C2411yescharacteristic
238#11761629—232no—
239#11761628—264no—
240#11761628—464no—
241C2×Dic134—28no—
242C2×Dic134—216no—
243C2×Dic134—44no—
244C2×Dic134C2418yes—
245C2×Dic134C24116yes—
246C2×Dic134C2418yes—
247Q8×D67—432no—
248C2×D268—28no—
249C2×D268—28no—
250C2×D268—24no—
251C2×D268—24no—
252C2×D268—48no—
253C2×D268C2418yes—
254C2×D268C2418yes—
255C2×D268C2414yes—
256C2×D268C2414yes—
257C2×D268C24116yes—
258C2×C22⋊D67—28no—
259C2×C22⋊D67—28no—
260C2×C22⋊D67—28no—
261C2×C22⋊D67—48no—
262C2×C22⋊D67C2418yes—
263C2×C22⋊D67C2418yes—
264C2×C22⋊D67C2418yes—
265C2×C22⋊D67C24116yes—
266C22×Dic67C2412yes—
267C22×Dic67C2411yescharacteristic
268C22×Dic67C2412yes—
269C22×Dic67C2414yes—
270C22×Dic67C2411yescharacteristic
271C22×Dic67C2411yescharacteristic
272C2×C4×D67—28no—
273C2×C4×D67—24no—
274C2×C4×D67—28no—
275C2×C4×D67—28no—
276C2×C4×D67—24no—
277C2×C4×D67—28no—
278C2×C4×D67—48no—
279C2×C4×D67—48no—
280C2×C4×D67#4118yescomplemented
281C2×C4×D67C2414yes—
282C2×C4×D67C2418yes—
283C2×C4×D67C2418yes—
284C2×C4×D67C2414yes—
285C2×C4×D67C2418yes—
286C2×C4×D67C2418yes—
287C2×C4×D67C24116yes—
288C2×C4×D67C24116yes—
289C2×C4×D67C2414yes—
290C4⋊Dic67C2418yes—
291C4⋊Dic67C2418yes—
292C4⋊Dic67C2414yes—
293C4⋊Dic67C2414yes—
294C4⋊Dic67C2418yes—
295Dic67⋊C4C24116yes—
296Dic67⋊C4C24116yes—
297Dic67⋊C4C24116yes—
298Dic67⋊C4C2418yes—
299Dic67⋊C4C24116yes—
300C22⋊Dic67C24116yes—
301C22⋊Dic67C2418yes—
302(C2×D67)⋊C4C2418yes—
303(C2×D67)⋊C4C24116yes—
304(C2×D67)⋊C4C2418yes—
305(C2×D67)⋊C4C2418yes—
306(C2×D67)⋊C4C24116yes—
307(C2×D67)⋊C4C24116yes—
308(C2×D67)⋊C4C2418yes—
309(C2×D67)⋊C4C24116yes—
310(C2×D67)⋊C4C2418yes—
311C4×Dic67C2414yes—
312C4×Dic67C2418yes—
313C4×Dic67C2414yes—
314C4×Dic67C2414yes—
315C4×Dic67C2418yes—
316C4×Dic67C24116yes—
317C4×Dic67C24116yes—
318C24×C67C2412yes—
319C2×Q8×C67—24no—
320C2×Q8×C67—44no—
321C2×Q8×C67C2414yes—
322C2×Q8×C67C2418yes—
323C2×D4×C67—24no—
324C2×D4×C67C2414yes—
325C22×C4×C67—28no—
326C22×C4×C67—48no—
327C22×C4×C67C2412yes—
328C22×C4×C67C2411yescharacteristic
329C22×C4×C67C2412yes—
330C22×C4×C67C2412yes—
331C22×C4×C67C2414yes—
332C22×C4×C67C2418yes—
333C22×C4×C67C24116yes—
334C22×C4×C67C2411yescharacteristic
335C22×C4×C67C2411yescharacteristic
336C4⋊C4×C67C2414yes—
337C4⋊C4×C67C24116yes—
338C4⋊C4×C67C2418yes—
339C4⋊C4×C67C2414yes—
340C4⋊C4×C67C2418yes—
341C4⋊C4×C67C2418yes—
342C4⋊C4×C67C24116yes—
343C22⋊C4×C67C24116yes—
344C22⋊C4×C67C2418yes—
345C42×C67C2418yes—
346C42×C67C2414yes—
347C23×C67—24no—
348C23×C67—24no—
349C23×C67—24no—
350C23×C67C2514yes—
351C23×C67C2511yescharacteristic
352C22×D67—22no—
353C22×D67—22no—
354C22×D67—24no—
355C22×D67—24no—
356C22×D67—24no—
357C22×D67—24no—
358C22×D67—24no—
359C22×D67—24no—
360C22×D67C2×#4114yes—
361C22×D67C2514yes—
362C22×D67C2514yes—
363C22×D67C2512yes—
364Q8×C67—28no—
365Q8×C67—48no—
366D4×C67—28no—
367C2×C4×C67—24no—
368C2×C4×C67—24no—
369C2×C4×C67—24no—
370C2×C4×C67—28no—
371C2×C4×C67—22no—
372C2×C4×C67—216no—
373C2×C4×C67—416no—
374C2×C4×C67C2×#4114yes—
375C2×C4×C672−1+414yes—
376C2×C4×C67C2514yes—
377C2×C4×C67C2512yes—
378C2×C4×C67C2514yes—
379C2×C4×C67C2514yes—
380C2×C4×C67C2518yes—
381C2×C4×C67C2512yes—
382C2×C4×C67C2512yes—
383C22⋊D67—216no—
384C22⋊D67—216no—
385C22⋊D67—216no—
386C22⋊D67—416no—
387C2×Dic67—24no—
388C2×Dic67—28no—
389C2×Dic67—24no—
390C2×Dic67—22no—
391C2×Dic67C2×#4114yes—
392C2×Dic67H(5,𝔽2)14yes—
393C2×Dic67C2514yes—
394C2×Dic67C2512yes—
395C2×Dic67C2514yes—
396C2×Dic67C2518yes—
397C2×Dic67C2512yes—
398C2×Dic67C2512yes—
399D268—216no—
400D268—216no—
401D268—28no—
402D268—28no—
403D268—416no—
404C4×D67—216no—
405C4×D67—28no—
406C4×D67—216no—
407C4×D67—216no—
408C4×D67—28no—
409C4×D67—216no—
410C4×D67—416no—
411C4×D67—416no—
412C4×D67C2×#41116yescomplemented
413Dic134—216no—
414Dic134—232no—
415Dic134—48no—
416C22×C67—24no—
417C22×C67—24no—
418C22×C67—24no—
419C22×C67—48no—
420C22×C67C22×#4112yes—
421C22×C67C2×H(5,𝔽2)12yes—
422C22×C67C2×2−1+412yes—
423C22×C67C2611yescharacteristic
424C2×D67—22no—
425C2×D67—22no—
426C2×D67—28no—
427C2×D67—24no—
428C2×D67—24no—
429C2×D67—24no—
430C2×D67—24no—
431C2×D67—24no—
432C2×D67—24no—
433C2×D67—48no—
434C2×D67—48no—
435C2×D67C22×#4114yes—
436C4×C67—24no—
437C4×C67—24no—
438C4×C67—28no—
439C4×C67—22no—
440C4×C67—24no—
441C4×C67C22×#4114yes—
442C4×C67C2×2−1+414yes—
443Dic67—24no—
444Dic67—28no—
445Dic67—24no—
446Dic67—22no—
447Dic67C22×#4114yes—
448Dic67C2×H(5,𝔽2)14yes—
449C2×#3511—671nomaximal, Sylow
450C2×C67—44no—
451C2×C67#351114yescomplemented
452C2×C67C23×#4111yescharacteristic
453C2×C67C22×H(5,𝔽2)11yescharacteristic
454C2×C67C22×2−1+411yescharacteristic
455D67—24no—
456D67—44no—
457D67—44no—
458#3511—6732no—
459C2×#556—672no—
460C2×#555—671no—
461C2×#555—671no—
462C2×#554—671no—
463C2×#554D6711yescharacteristic, complemented
464C2×#553—672no—
465C2×#553—672no—
466C2×#548—674no—
467C2×#547—672no—
468C2×#542—674no—
469C2×#537—672no—
470C2×#533—672no—
471C2×#532—672no—
472C2×#532—671no—
473C22×C4⋊Q8—671no—
474C2×#520—672no—
475C2×C4×#41—671no—
476C67C2×#351111yescharacteristic, complemented, Sylow
477C22×#41—671no—
478C22×#41—674no—
479C22×#41—672no—
480C23×Q8—672no—
481#556—6732no—
482#555—6716no—
483#555—6716no—
484#554—6716no—
485#554C2×D67116yescomplemented
486#553—6732no—
487#553—6732no—
488#548—6764no—
489#547—6732no—
490#542—6764no—
491#537—6732no—
492#533—6732no—
493#532—6716no—
494#532—6732no—
495C2×C4⋊Q8—672no—
496C2×C4⋊Q8—6716no—
497C2×C4⋊Q8—672no—
498C2×C4⋊Q8—672no—
499C2×C4⋊Q8—671no—
500C2×C4⋊Q8—671no—
501C2×C4⋊Q8C2×D6711yescharacteristic
502C2×#127—671no—
503C2×#126—674no—
504C2×#126—674no—
505C2×#125—672no—
506C2×#125C2×D6712yes—
507C2×#124—674no—
508C2×#124—672no—
509C2×#124—674no—
510C2×#124—674no—
511C2×#123—674no—
512C2×#123—674no—
513C2×C22⋊Q8—672no—
514C2×C22⋊Q8—674no—
515C2×C22⋊Q8—674no—
516C2×C22⋊Q8—674no—
517C2×C22⋊Q8C2×D6712yes—
518C2×C22⋊Q8C2×D6714yes—
519C2×#121—671no—
520C2×#121—672no—
521C2×#121—672no—
522C2×#121—671no—
523C2×#121—672no—
524C2×#121—672no—
525C2×#121—674no—
526C2×#121—674no—
527C2×#121—672no—
528C2×#121—674no—
529#520—6732no—
530C4×#41—6716no—
531C2×C4×Q8—671no—
532C2×C4×Q8—674no—
533C2×C4×Q8—674no—
534C2×C4×Q8C2×D6711yescharacteristic
535C2×C4×D4—674no—
536C2×C4×D4—674no—
537C2×C4×D4—672no—
538C2×C4×D4—671no—
539C2×C4×D4—672no—
540C2×C4×D4—674no—
541C2×C4×D4—672no—
542C2×C4×D4—671no—
543C2×C4×D4—672no—
544C2×C4×D4—671no—
545C2×C4×D4C2×D6712yes—
546C2×C4×D4C2×D6711yescharacteristic
547C2×#117—672no—
548C2×#117—671no—
549C2×#117—672no—
550C2×#117—672no—
551C2×#117—672no—
552C2×#117—672no—
553C22×C4⋊C4—672no—
554C22×C4⋊C4—672no—
555C22×C4⋊C4—672no—
556C22×C4⋊C4C2×D6712yes—
557C22×C42—671no—
558C22×C42—672no—
559C2×#41—26816no—
560C2×#41—678no—
561C2×#41—6732no—
562C2×#41—6716no—
563C2×#41—13416no—
564C2×#41—1348no—
565C22×Q8—2688no—
566C22×Q8—6716no—
567C22×Q8—672no—
568C22×Q8—672no—
569C22×Q8—674no—
570C22×Q8C22×D6711yescharacteristic
571C22×Q8C22×D6712yes—
572C22×D4—674no—
573C22×D4—672no—
574C22×D4—672no—
575C22×D4—672no—
576C22×D4—674no—
577C22×D4—671no—
578C22×D4—672no—
579C22×D4—672no—
580C22×D4—671no—
581C22×D4C22×D6711yescharacteristic
582C23×C4—674no—
583C23×C4—674no—
584C23×C4—671no—
585C23×C4—671no—
586C23×C4—672no—
587C23×C4—672no—
588C23×C4—672no—
589C23×C4—671no—
590C23×C4—672no—
591C23×C4C22×D6712yes—
592C23×C4C22×D6714yes—
593C4⋊Q8—6716no—
594C4⋊Q8—6716no—
595C4⋊Q8—6716no—
596C4⋊Q8—678no—
597C4⋊Q8—678no—
598C4⋊Q8C22×D6718yes—
599#127—678no—
600#126—6732no—
601#126—6732no—
602#125—6716no—
603#125C22×D67116yes—
604#124—6732no—
605#124—6716no—
606#124—6732no—
607#124—6732no—
608#123—6732no—
609#123—6732no—
610C22⋊Q8—6716no—
611C22⋊Q8—6732no—
612C22⋊Q8—6732no—
613C22⋊Q8—6732no—
614C22⋊Q8C22×D67116yes—
615C22⋊Q8C22×D67132yes—
616#121—678no—
617#121—6716no—
618#121—6716no—
619#121—678no—
620#121—6716no—
621#121—6716no—
622#121—6732no—
623#121—6732no—
624#121—6716no—
625#121—6732no—
626C4×Q8—678no—
627C4×Q8—6732no—
628C4×Q8—6732no—
629C4×Q8C22×D6718yes—
630C4×D4—6732no—
631C4×D4—6732no—
632C4×D4—6716no—
633C4×D4—678no—
634C4×D4—6716no—
635C4×D4—6732no—
636C4×D4—6716no—
637C4×D4—678no—
638C4×D4—6716no—
639C4×D4—678no—
640C4×D4C22×D67116yes—
641C4×D4C22×D6718yes—
642#117—6716no—
643#117—678no—
644#117—6716no—
645#117—6716no—
646#117—6716no—
647#117—6716no—
648C2×C4⋊C4—672no—
649C2×C4⋊C4—672no—
650C2×C4⋊C4—674no—
651C2×C4⋊C4—674no—
652C2×C4⋊C4—674no—
653C2×C4⋊C4—671no—
654C2×C4⋊C4—671no—
655C2×C4⋊C4—672no—
656C2×C4⋊C4—672no—
657C2×C4⋊C4—674no—
658C2×C4⋊C4—6716no—
659C2×C4⋊C4—6716no—
660C2×C4⋊C4—6716no—
661C2×C4⋊C4C22×D6711yescharacteristic
662C2×C4⋊C4C22×D6712yes—
663C2×C4⋊C4C22×D6712yes—
664C2×C4⋊C4C22×D6714yes—
665C2×C4⋊C4C22×D67116yes—
666C2×C4⋊C4C22×D6711yescharacteristic
667C2×C4⋊C4C22×D6712yes—
668C2×C4⋊C4C22×D6714yes—
669C2×C22⋊C4—674no—
670C2×C22⋊C4—672no—
671C2×C22⋊C4—672no—
672C2×C22⋊C4—674no—
673C2×C22⋊C4—672no—
674C2×C22⋊C4—672no—
675C2×C22⋊C4—674no—
676C2×C22⋊C4—674no—
677C2×C22⋊C4—674no—
678C2×C22⋊C4—672no—
679C2×C22⋊C4—672no—
680C2×C22⋊C4C22×D6714yes—
681C2×C22⋊C4C22×D6712yes—
682C2×C42—672no—
683C2×C42—674no—
684C2×C42—674no—
685C2×C42—671no—
686C2×C42—671no—
687C2×C42—672no—
688C2×C42—671no—
689C2×C42—678no—
690C2×C42—6716no—
691C2×C42C22×D6712yes—
692C2×C42C22×D6711yescharacteristic
693C24—671no—
694C24—672no—
695C24—672no—
696C24C23×D6712yes—
697#41—26864no—
698#41—13464no—
699#41—13432no—
700C2×Q8—24no—
701C2×Q8—44no—
702C2×Q8—2684no—
703C2×Q8—26832no—
704C2×Q8—678no—
705C2×Q8—678no—
706C2×Q8—6716no—
707C2×Q8—13416no—
708C2×Q8—1348no—
709C2×Q8C23×D6714yes—
710C2×Q8C23×D6718yes—
711C2×D4—24no—
712C2×D4—2688no—
713C2×D4—2688no—
714C2×D4—6716no—
715C2×D4—678no—
716C2×D4—678no—
717C2×D4—678no—
718C2×D4—6716no—
719C2×D4—674no—
720C2×D4—678no—
721C2×D4—678no—
722C2×D4—674no—
723C2×D4—1348no—
724C2×D4—1348no—
725C2×D4—1348no—
726C2×D4—1348no—
727C2×D4—1348no—
728C2×D4—1344no—
729C2×D4—1344no—
730C2×D4C23×D6714yes—
731C22×C4—28no—
732C22×C4—48no—
733C22×C4—2688no—
734C22×C4—2688no—
735C22×C4—6716no—
736C22×C4—6716no—
737C22×C4—671no—
738C22×C4—671no—
739C22×C4—678no—
740C22×C4—674no—
741C22×C4—672no—
742C22×C4—671no—
743C22×C4—672no—
744C22×C4—674no—
745C22×C4—674no—
746C22×C4—678no—
747C22×C4—678no—
748C22×C4—674no—
749C22×C4—678no—
750C22×C4—678no—
751C22×C4—1344no—
752C22×C4—1348no—
753C22×C4—1348no—
754C22×C4—1348no—
755C22×C4—1348no—
756C22×C4—1344no—
757C22×C4C23×D6718yes—
758C22×C4C23×D6712yes—
759C22×C4C23×D6711yescharacteristic
760C22×C4C23×D6712yes—
761C22×C4C23×D6712yes—
762C22×C4C23×D6714yes—
763C22×C4C23×D67116yes—
764C22×C4C23×D6711yescharacteristic
765C22×C4C23×D6711yescharacteristic
766C4⋊C4—678no—
767C4⋊C4—678no—
768C4⋊C4—6716no—
769C4⋊C4—6716no—
770C4⋊C4—6716no—
771C4⋊C4—674no—
772C4⋊C4—674no—
773C4⋊C4—678no—
774C4⋊C4—678no—
775C4⋊C4—6716no—
776C4⋊C4C23×D6714yes—
777C4⋊C4C23×D6718yes—
778C4⋊C4C23×D6718yes—
779C4⋊C4C23×D67116yes—
780C4⋊C4C23×D6714yes—
781C4⋊C4C23×D6718yes—
782C4⋊C4C23×D67116yes—
783C22⋊C4—6716no—
784C22⋊C4—678no—
785C22⋊C4—678no—
786C22⋊C4—6716no—
787C22⋊C4—678no—
788C22⋊C4—678no—
789C22⋊C4—6716no—
790C22⋊C4—6716no—
791C22⋊C4—6716no—
792C22⋊C4—678no—
793C22⋊C4—678no—
794C22⋊C4C23×D67116yes—
795C22⋊C4C23×D6718yes—
796C42—674no—
797C42—678no—
798C42—674no—
799C42—674no—
800C42—678no—
801C42—6716no—
802C42—6716no—
803C42C23×D6718yes—
804C42C23×D6714yes—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—674no—
809C23—672no—
810C23—674no—
811C23—674no—
812C23—1344no—
813C23—1344no—
814C23—1344no—
815C23—1344no—
816C23—1344no—
817C23—1344no—
818C23—1342no—
819C23—1342no—
820C23C24×D6714yes—
821C23C24×D6711yescharacteristic
822Q8—28no—
823Q8—48no—
824Q8—2688no—
825Q8—13432no—
826Q8—13416no—
827D4—28no—
828D4—26816no—
829D4—26816no—
830D4—13416no—
831D4—13416no—
832D4—13416no—
833D4—13416no—
834D4—13416no—
835D4—1348no—
836D4—1348no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—28no—
841C2×C4—22no—
842C2×C4—216no—
843C2×C4—416no—
844C2×C4—26816no—
845C2×C4—26816no—
846C2×C4—674no—
847C2×C4—674no—
848C2×C4—672no—
849C2×C4—672no—
850C2×C4—6716no—
851C2×C4—674no—
852C2×C4—672no—
853C2×C4—674no—
854C2×C4—678no—
855C2×C4—1348no—
856C2×C4—13416no—
857C2×C4—13416no—
858C2×C4—1344no—
859C2×C4—1348no—
860C2×C4—1344no—
861C2×C4—1342no—
862C2×C4—13416no—
863C2×C4—13416no—
864C2×C4—1348no—
865C2×C4#41×D6714yes—
866C2×C4#1452409114yes—
867C2×C4C24×D6714yes—
868C2×C4C24×D6712yes—
869C2×C4C24×D6714yes—
870C2×C4C24×D6714yes—
871C2×C4C24×D6718yes—
872C2×C4C24×D6712yes—
873C2×C4C24×D6712yes—
874C22—24no—
875C22—24no—
876C22—24no—
877C22—48no—
878C22—2688no—
879C22—2688no—
880C22—674no—
881C22—1344no—
882C22—1344no—
883C22—1344no—
884C22—1344no—
885C22—1344no—
886C22—1344no—
887C22—1348no—
888C22—1342no—
889C22—1342no—
890C22C2×#41×D6712yes—
891C22H(5,𝔽2)×D6712yes—
892C22C2×#1452409112yes—
893C22C25×D6711yescharacteristic
894C4—24no—
895C4—24no—
896C4—24no—
897C4—28no—
898C4—22no—
899C4—674no—
900C4—674no—
901C4—1344no—
902C4—1348no—
903C4—1344no—
904C4—1342no—
905C4C2×#41×D6714yes—
906C4C2×#1452409114yes—
907C2—44no—
908C2—2684no—
909C2—2684no—
910C2—1344no—
911C2#2257411714yesdirect product factor
912C2C22×#41×D6711yescharacteristic
913C2C2×H(5,𝔽2)×D6711yescharacteristic
914C2C22×#1452409111yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#554×C67C2
socleC23×C67C25
hypercenterC2×#554D67
hypocenterC67C2×#3511
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #22574117C2direct (N × H)
2. C2×#16864117C2semidirect
3. C2×#16864112C2semidirect
4. C2×#16864111C2semidirect
5. C2×#16864106C2semidirect
6. C2×#16864099C2semidirect
7. C2×#16864096C2semidirect
8. C2×#16864056C2semidirect
9. C2×#16864047C2semidirect
10. C2×#16864016C2semidirect
11. C2×#16863976C2semidirect
12. C2×#16863952C2semidirect
13. C2×#16863943C2semidirect
14. C2×#16863943C2semidirect
15. C2×C4⋊Q8×D67C2semidirect
16. C2×#16863877C2semidirect
17. C2×C4×#11761629C2semidirect
18. C2×#554×C67C2semidirect
23. #16864117C22semidirect
24. #16864112C22semidirect
25. #16864111C22semidirect
26. #16864106C22semidirect
27. #16864099C22semidirect
28. #16864096C22semidirect
29. #16864056C22semidirect
30. #16864047C22semidirect
31. #16864016C22semidirect
32. #16863976C22semidirect
33. #16863952C22semidirect
34. #16863943C22semidirect
35. #16863943C22semidirect
41. C4⋊Q8×D67C22semidirect
66. #16863877C22semidirect
67. C4×#11761629C22semidirect
92. #554×C67C22semidirect
280. C2×C4×D67#41semidirect
412. C4×D67C2×#41semidirect
451. C2×C67#3511semidirect
463. C2×#554D67semidirect
476. C67C2×#3511semidirect
485. #554C2×D67semidirect
911. C2#22574117direct (N × H)

Maximal subgroups

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

subgroupindex
#225741172
C2×#168641172
C2×#168641122
C2×#168641112
C2×#168641062
C2×#168640992
C2×#168640962
C2×#168640562
C2×#168640472
C2×#168640162
C2×#168639762
C2×#168639522
C2×#168639432
C2×C4⋊Q8×D672
C2×#168638772
C2×C4×#117616292
C2×#554×C672
C2×#351167