Finite Group Databasebeta

← C2×#22574088 #31764267

Subgroups — C2×#22574088 #31764267

Order 17152.

7022 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574088C2132yesmaximal, direct product factor
2C2×#16864123C212yesmaximal, complemented
3C2×#16864122C212yesmaximal, complemented
4C2×#16864117C212yesmaximal, complemented
5C2×#16864114C212yesmaximal, complemented
6C2×#16864087C212yesmaximal, complemented
7C2×#16864085C212yesmaximal, complemented
8C2×#16864084C212yesmaximal, complemented
9C2×#16864080C212yesmaximal, complemented
10C2×#16864006C212yesmaximal, complemented
11C2×#16864004C212yesmaximal, complemented
12C2×#16863969C212yesmaximal
13C2×#16863953C211yesmaximal, characteristic, complemented
14C2×#16863951C211yesmaximal, characteristic, complemented
15C2×#16863951C211yesmaximal, characteristic, complemented
16C2×#16863951C211yesmaximal, characteristic, complemented
17C2×C4⋊Q8×D67C211yesmaximal, characteristic, complemented
18C2×#16863872C212yesmaximal, complemented
19C2×C4×#11761628C211yesmaximal, characteristic
20C2×#533×C67C211yesmaximal, characteristic, complemented
21C22×#11761628C2211yescharacteristic
22C22×Q8×D67C2212yes—
23#16864123C22132yescomplemented
24#16864122C22132yescomplemented
25#16864117C22132yescomplemented
26#16864114C22132yescomplemented
27#16864087C22132yescomplemented
28#16864085C22132yescomplemented
29#16864084C22132yescomplemented
30#16864080C22132yescomplemented
31#16864006C22132yescomplemented
32#16864004C22132yescomplemented
33#16863969C22132yes—
34#16863953C22116yescomplemented
35#16863951C22116yescomplemented
36#16863951C22116yescomplemented
37#16863951C22116yescomplemented
38C2×#14524043C2211yescharacteristic
39C2×#14524043C2211yescharacteristic
40C2×#14524042C2212yes—
41C2×#14524042C2212yes—
42C2×#14524042C2214yes—
43C2×#14524041C2212yes—
44C4⋊Q8×D67C22116yescomplemented
45C2×#14524038C2214yes—
46C2×#14524037C2214yes—
47C2×#14524036C2214yes—
48C2×#14524036C2214yes—
49C2×#14524035C2214yes—
50C2×#14524035C2212yes—
51C2×#14524034C2212yes—
52C2×#14524034C2214yes—
53C2×#14524034C2212yes—
54C2×#14524034C2212yes—
55C2×#14524033C2214yes—
56C2×#14524033C2214yes—
57C2×#14524029C2214yes—
58C2×#14524028C2214yes—
59C2×#14524025C2214yes—
60C2×#14524023C2212yes—
61C2×#14524023C2212yes—
62C2×#14524023C2212yes—
63C2×#14524022C2212yes—
64C2×#14524022C2212yes—
65C2×#14524019C2212yes—
66C2×#14524019C2212yes—
67C2×#14524019C2212yes—
68#16863872C22132yescomplemented
69C4×#11761628C22116yes—
70C2×Q8×Dic67C2212yes—
71C2×Q8×Dic67C2212yes—
72C2×Q8×Dic67C2212yes—
73C2×C4×Dic134C2212yes—
74C2×C4×Dic134C2211yescharacteristic
75C2×C4×Dic134C2211yescharacteristic
76C2×C4×Dic134C2214yes—
77C2×C4×Dic134C2212yes—
78C2×#14524008C2212yes—
79C2×#14524008C2214yes—
80C2×#14524008C2212yes—
81C2×#14524008C2212yes—
82C2×C4×D268C2211yescharacteristic
83C2×C4×D268C2211yescharacteristic
84C2×C4×C22⋊D67C2211yescharacteristic
85C2×C4×C22⋊D67C2211yescharacteristic
86C2×C4×C22⋊D67C2211yescharacteristic
87C2×C4×C22⋊D67C2211yescharacteristic
88C2×#14524002C2211yescharacteristic
89C2×#14524002C2212yes—
90C2×#14524001C2214yes—
91C2×#14524001C2212yes—
92C2×#14524001C2212yes—
93C2×#14524001C2212yes—
94C2×#14524000C2211yescharacteristic
95C2×#14524000C2211yescharacteristic
96C2×#14524000C2214yes—
97C2×C4⋊C4×D67C2212yes—
98C2×C4⋊C4×D67C2212yes—
99C2×C42×D67C2211yescharacteristic
100C2×C42×D67C2211yescharacteristic
101#533×C67C22116yescomplemented
102C2×C4⋊Q8×C67C2211yescharacteristic
103C2×C4⋊Q8×C67C2211yescharacteristic
104C2×#125×C67C2212yes—
105C2×C22⋊Q8×C67C2212yes—
106C2×C22⋊Q8×C67C2212yes—
107C2×C4×Q8×C67C2212yes—
108C2×C4×Q8×C67C2212yes—
109C2×#117×C67C2212yes—
110C22×C42×C67C2211yescharacteristic
111C2×#11761628—28no—
112C2×#11761628C2318yes—
113C22×Dic134C2312yes—
114C22×Dic134C2312yes—
115C22×Dic134C2314yes—
116C22×Dic134C2311yescharacteristic
117C2×Q8×D67—216no—
118C2×Q8×D67C23116yes—
119C22×D268C2311yescharacteristic
120C22×C22⋊D67C2311yescharacteristic
121C22×C22⋊D67C2311yescharacteristic
122C22×C4×D67C2311yescharacteristic
123C22×C4×D67C2311yescharacteristic
124C22×C4×D67C2311yescharacteristic
125C22×C4×D67C2311yescharacteristic
126C22×C4×D67C2311yescharacteristic
127C22×C4×D67C2314yes—
128C22×C4×D67C2311yescharacteristic
129#14524043C2318yes—
130#14524043C2318yes—
131#14524042C23116yes—
132#14524042C23116yes—
133#14524042C23132yes—
134#14524041C23116yes—
135#14524038C23132yes—
136#14524037C23132yes—
137#14524036C23132yes—
138#14524036C23132yes—
139#14524035C23132yes—
140#14524035C23116yes—
141#14524034C23116yes—
142#14524034C23132yes—
143#14524034C23116yes—
144#14524034C23116yes—
145#14524033C23132yes—
146#14524033C23132yes—
147#14524029C23132yes—
148#14524028C23132yes—
149#14524025C23132yes—
150#14524023C23116yes—
151#14524023C23116yes—
152#14524023C23116yes—
153#14524022C23116yes—
154#14524022C23116yes—
155#14524019C23116yes—
156#14524019C23116yes—
157#14524019C23116yes—
158Q8×Dic67C23116yes—
159Q8×Dic67C23116yes—
160Q8×Dic67C23116yes—
161C4×Dic134C23116yes—
162C4×Dic134C23116yes—
163C4×Dic134C23132yes—
164C4×Dic134C2318yes—
165C4×Dic134C2318yes—
166#14524008C23116yes—
167#14524008C23116yes—
168#14524008C23116yes—
169#14524008C23132yes—
170C4×D268C2318yes—
171C4×D268C2318yes—
172C4×C22⋊D67C2318yes—
173C4×C22⋊D67C2318yes—
174C4×C22⋊D67C2318yes—
175C4×C22⋊D67C2318yes—
176#14524002C2318yes—
177#14524002C23116yes—
178#14524001C23132yes—
179#14524001C23116yes—
180#14524001C23116yes—
181#14524001C23116yes—
182#14524000C2318yes—
183#14524000C23132yes—
184#14524000C2318yes—
185C2×C4⋊Dic67C2312yes—
186C2×C4⋊Dic67C2312yes—
187C2×C4⋊Dic67C2312yes—
188C2×C4⋊Dic67C2312yes—
189C2×C4⋊Dic67C2314yes—
190C2×C4⋊Dic67C2311yescharacteristic
191C2×C4⋊Dic67C2311yescharacteristic
192C2×C4⋊Dic67C2314yes—
193C2×C4⋊Dic67C2314yes—
194C2×Dic67⋊C4C2314yes—
195C2×Dic67⋊C4C2314yes—
196C2×Dic67⋊C4C2311yescharacteristic
197C2×Dic67⋊C4C2311yescharacteristic
198C2×Dic67⋊C4C2311yescharacteristic
199C2×Dic67⋊C4C2311yescharacteristic
200C2×Dic67⋊C4C2314yes—
201C2×Dic67⋊C4C2314yes—
202C2×Dic67⋊C4C2314yes—
203C2×Dic67⋊C4C2314yes—
204C2×Dic67⋊C4C2314yes—
205C4⋊C4×D67C23116yes—
206C4⋊C4×D67C23116yes—
207C2×C22⋊Dic67C2311yescharacteristic
208C2×C22⋊Dic67C2311yescharacteristic
209C2×C22⋊Dic67C2314yes—
210C2×(C2×D67)⋊C4C2311yescharacteristic
211C2×(C2×D67)⋊C4C2311yescharacteristic
212C2×(C2×D67)⋊C4C2314yes—
213C2×(C2×D67)⋊C4C2311yescharacteristic
214C2×(C2×D67)⋊C4C2311yescharacteristic
215C2×(C2×D67)⋊C4C2314yes—
216C2×(C2×D67)⋊C4C2314yes—
217C2×C4×Dic67C2311yescharacteristic
218C2×C4×Dic67C2311yescharacteristic
219C2×C4×Dic67C2311yescharacteristic
220C2×C4×Dic67C2311yescharacteristic
221C2×C4×Dic67C2311yescharacteristic
222C2×C4×Dic67C2311yescharacteristic
223C2×C4×Dic67C2314yes—
224C2×C4×Dic67C2314yes—
225C2×C4×Dic67C2314yes—
226C2×C4×Dic67C2314yes—
227C42×D67C2318yes—
228C42×D67C2318yes—
229C22×Q8×C67C2312yes—
230C22×Q8×C67C2312yes—
231C23×C4×C67C2311yescharacteristic
232C23×C4×C67C2311yescharacteristic
233C23×C4×C67C2311yescharacteristic
234C4⋊Q8×C67C2318yes—
235C4⋊Q8×C67C2318yes—
236#125×C67C23116yes—
237C22⋊Q8×C67C23116yes—
238C22⋊Q8×C67C23116yes—
239C4×Q8×C67C23116yes—
240C4×Q8×C67C23116yes—
241#117×C67C23116yes—
242C2×C4⋊C4×C67C2312yes—
243C2×C4⋊C4×C67C2312yes—
244C2×C4⋊C4×C67C2314yes—
245C2×C4⋊C4×C67C2314yes—
246C2×C4⋊C4×C67C2312yes—
247C2×C4⋊C4×C67C2312yes—
248C2×C22⋊C4×C67C2314yes—
249C2×C42×C67C2311yescharacteristic
250C2×C42×C67C2311yescharacteristic
251C2×C42×C67C2311yescharacteristic
252C2×C42×C67C2311yescharacteristic
253C2×C42×C67C2318yes—
254C2×C42×C67C2314yes—
255C23×D67C2411yescharacteristic
256C23×D67C2411yescharacteristic
257#11761628—232no—
258C2×Dic134—28no—
259C2×Dic134—28no—
260C2×Dic134—216no—
261C2×Dic134—24no—
262C2×Dic134C2418yes—
263C2×Dic134C2418yes—
264C2×Dic134C24116yes—
265C2×Dic134C2414yes—
266Q8×D67—264no—
267C2×D268—24no—
268C2×D268C2414yes—
269C2×C22⋊D67—24no—
270C2×C22⋊D67—24no—
271C2×C22⋊D67C2414yes—
272C2×C22⋊D67C2414yes—
273C22×Dic67C2411yescharacteristic
274C22×Dic67C2411yescharacteristic
275C22×Dic67C2414yes—
276C22×Dic67C2411yescharacteristic
277C22×Dic67C2411yescharacteristic
278C22×Dic67C2414yes—
279C22×Dic67C2411yescharacteristic
280C22×Dic67C2411yescharacteristic
281C2×C4×D67—216no—
282C2×C4×D67—24no—
283C2×C4×D67—24no—
284C2×C4×D67—24no—
285C2×C4×D67—24no—
286C2×C4×D67—24no—
287C2×C4×D67#4118yes—
288C2×C4×D67C2414yes—
289C2×C4×D67C2414yes—
290C2×C4×D67C2414yes—
291C2×C4×D67C2414yes—
292C2×C4×D67C2414yes—
293C2×C4×D67C24116yes—
294C2×C4×D67C2414yes—
295C4⋊Dic67C2418yes—
296C4⋊Dic67C2418yes—
297C4⋊Dic67C2418yes—
298C4⋊Dic67C2418yes—
299C4⋊Dic67C24116yes—
300C4⋊Dic67C2414yes—
301C4⋊Dic67C2414yes—
302C4⋊Dic67C24116yes—
303C4⋊Dic67C24116yes—
304Dic67⋊C4C24116yes—
305Dic67⋊C4C24116yes—
306Dic67⋊C4C2414yes—
307Dic67⋊C4C2414yes—
308Dic67⋊C4C2414yes—
309Dic67⋊C4C2414yes—
310Dic67⋊C4C24116yes—
311Dic67⋊C4C24116yes—
312Dic67⋊C4C24116yes—
313Dic67⋊C4C24116yes—
314Dic67⋊C4C24116yes—
315C22⋊Dic67C2414yes—
316C22⋊Dic67C2414yes—
317C22⋊Dic67C24116yes—
318(C2×D67)⋊C4C2414yes—
319(C2×D67)⋊C4C2414yes—
320(C2×D67)⋊C4C24116yes—
321(C2×D67)⋊C4C2414yes—
322(C2×D67)⋊C4C2414yes—
323(C2×D67)⋊C4C24116yes—
324(C2×D67)⋊C4C24116yes—
325C4×Dic67C2414yes—
326C4×Dic67C2414yes—
327C4×Dic67C2414yes—
328C4×Dic67C2414yes—
329C4×Dic67C2414yes—
330C4×Dic67C2414yes—
331C4×Dic67C24116yes—
332C4×Dic67C24116yes—
333C4×Dic67C24116yes—
334C4×Dic67C24116yes—
335C24×C67C2411yescharacteristic
336C2×Q8×C67—28no—
337C2×Q8×C67—28no—
338C2×Q8×C67C2418yes—
339C2×Q8×C67C2418yes—
340C22×C4×C67—24no—
341C22×C4×C67—24no—
342C22×C4×C67—24no—
343C22×C4×C67C2411yescharacteristic
344C22×C4×C67C2411yescharacteristic
345C22×C4×C67C2411yescharacteristic
346C22×C4×C67C2414yes—
347C22×C4×C67C2414yes—
348C22×C4×C67C2414yes—
349C22×C4×C67C2414yes—
350C22×C4×C67C2414yes—
351C22×C4×C67C2411yescharacteristic
352C22×C4×C67C2411yescharacteristic
353C22×C4×C67C2411yescharacteristic
354C4⋊C4×C67C2418yes—
355C4⋊C4×C67C2418yes—
356C4⋊C4×C67C24116yes—
357C4⋊C4×C67C24116yes—
358C4⋊C4×C67C2418yes—
359C4⋊C4×C67C2418yes—
360C22⋊C4×C67C24116yes—
361C42×C67C2414yes—
362C42×C67C2414yes—
363C42×C67C2414yes—
364C42×C67C2414yes—
365C42×C67C24116yes—
366C23×C67—22no—
367C23×C67—22no—
368C23×C67—22no—
369C23×C67C2512yes—
370C23×C67C2511yescharacteristic
371C22×D67—22no—
372C22×D67—22no—
373C22×D67—22no—
374C22×D67—22no—
375C22×D67—22no—
376C22×D67C2×#4114yes—
377C22×D67C2512yes—
378C22×D67C2512yes—
379Q8×C67—216no—
380Q8×C67—216no—
381C2×C4×C67—22no—
382C2×C4×C67—28no—
383C2×C4×C67—22no—
384C2×C4×C67—22no—
385C2×C4×C67—28no—
386C2×C4×C67—28no—
387C2×C4×C67—28no—
388C2×C4×C67—28no—
389C2×C4×C67C2×#4114yes—
390C2×C4×C672−1+414yes—
391C2×C4×C672−1+414yes—
392C2×C4×C67C2512yes—
393C2×C4×C67C2512yes—
394C2×C4×C67C2512yes—
395C2×C4×C67C2518yes—
396C2×C4×C67C2518yes—
397C2×C4×C67C2512yes—
398C2×C4×C67C2512yes—
399C2×C4×C67C2512yes—
400C22⋊D67—28no—
401C22⋊D67—28no—
402C2×Dic67—22no—
403C2×Dic67—28no—
404C2×Dic67—22no—
405C2×Dic67—22no—
406C2×Dic67—22no—
407C2×Dic67—22no—
408C2×Dic67—28no—
409C2×Dic67C2×#4114yes—
410C2×Dic67C2512yes—
411C2×Dic67C2512yes—
412C2×Dic67C2518yes—
413C2×Dic67C2512yes—
414C2×Dic67C2512yes—
415C2×Dic67C2518yes—
416C2×Dic67C2512yes—
417C2×Dic67C2512yes—
418D268—28no—
419C4×D67—232no—
420C4×D67—28no—
421C4×D67—28no—
422C4×D67—28no—
423C4×D67—28no—
424C4×D67—28no—
425C4×D67C2×#41116yes—
426Dic134—216no—
427Dic134—216no—
428Dic134—232no—
429Dic134—28no—
430C22×C67—22no—
431C22×C67—22no—
432C22×C67—22no—
433C22×C67—44no—
434C22×C67C22×#4112yes—
435C22×C67C2×2−1+412yes—
436C22×C67C2×2−1+412yes—
437C22×C67C2611yescharacteristic
438C2×D67—22no—
439C2×D67—22no—
440C2×D67—28no—
441C2×D67—22no—
442C2×D67—22no—
443C2×D67—22no—
444C2×D67—44no—
445C2×D67C22×#4114yes—
446C4×C67—28no—
447C4×C67—22no—
448C4×C67—22no—
449C4×C67—22no—
450C4×C67—28no—
451C4×C67C22×#4114yes—
452C4×C67C2×2−1+414yes—
453C4×C67C2×2−1+414yes—
454Dic67—28no—
455Dic67—22no—
456Dic67—28no—
457Dic67—22no—
458Dic67—22no—
459Dic67—22no—
460Dic67—22no—
461Dic67C22×#4114yes—
462C2×#3509—671nomaximal, Sylow
463C2×C67—42no—
464C2×C67#350914yescomplemented
465C2×C67C23×#4111yescharacteristic
466C2×C67C22×2−1+411yescharacteristic
467C2×C67C22×2−1+411yescharacteristic
468D67—24no—
469D67—42no—
470#3509—6732no—
471C2×#557—672no—
472C2×#557—672no—
473C2×#556—672no—
474C2×#556—672no—
475C2×#552—672no—
476C2×#552—672no—
477C2×#552—672no—
478C2×#552—672no—
479C2×#541—672no—
480C2×#541—672no—
481C2×#536—672no—
482C2×#533—671no—
483C2×#533—671no—
484C2×#533—671no—
485C2×#533—671no—
486C2×#533D6711yescharacteristic, complemented
487C22×C4⋊Q8—671no—
488C2×#519—672no—
489C2×C4×#41—671no—
490C67C2×#350911yescharacteristic, complemented, Sylow
491C22×#41—671no—
492C23×Q8—672no—
493#557—6732no—
494#557—6732no—
495#556—6732no—
496#556—6732no—
497#552—6732no—
498#552—6732no—
499#552—6732no—
500#552—6732no—
501#541—6732no—
502#541—6732no—
503#536—6732no—
504#533—6716no—
505#533—6716no—
506#533—6716no—
507#533—6716no—
508#533C2×D67116yescomplemented
509C2×C4⋊Q8—672no—
510C2×C4⋊Q8—6716no—
511C2×C4⋊Q8—672no—
512C2×C4⋊Q8—672no—
513C2×C4⋊Q8—674no—
514C2×C4⋊Q8—671no—
515C2×C4⋊Q8—671no—
516C2×C4⋊Q8C2×D6711yescharacteristic
517C2×C4⋊Q8C2×D6711yescharacteristic
518C2×#126—674no—
519C2×#126—674no—
520C2×#126—674no—
521C2×#126—674no—
522C2×#125—672no—
523C2×#125—672no—
524C2×#125—672no—
525C2×#125—674no—
526C2×#125—674no—
527C2×#125—674no—
528C2×#125—672no—
529C2×#125—674no—
530C2×#125C2×D6712yes—
531C2×#124—674no—
532C2×#123—674no—
533C2×#123—674no—
534C2×C22⋊Q8—672no—
535C2×C22⋊Q8—672no—
536C2×C22⋊Q8—672no—
537C2×C22⋊Q8—672no—
538C2×C22⋊Q8—672no—
539C2×C22⋊Q8—672no—
540C2×C22⋊Q8—672no—
541C2×C22⋊Q8—672no—
542C2×C22⋊Q8C2×D6712yes—
543C2×C22⋊Q8C2×D6712yes—
544#519—6732no—
545C4×#41—6716no—
546C2×C4×Q8—672no—
547C2×C4×Q8—672no—
548C2×C4×Q8—672no—
549C2×C4×Q8—672no—
550C2×C4×Q8—674no—
551C2×C4×Q8—672no—
552C2×C4×Q8—672no—
553C2×C4×Q8—671no—
554C2×C4×Q8—671no—
555C2×C4×Q8—672no—
556C2×C4×Q8—674no—
557C2×C4×Q8—672no—
558C2×C4×Q8C2×D6712yes—
559C2×C4×Q8C2×D6712yes—
560C2×C4×D4—671no—
561C2×C4×D4—671no—
562C2×C4×D4—671no—
563C2×C4×D4—671no—
564C2×C4×D4—671no—
565C2×C4×D4—671no—
566C2×#117—671no—
567C2×#117—672no—
568C2×#117—672no—
569C2×#117—674no—
570C2×#117—672no—
571C2×#117—672no—
572C2×#117—671no—
573C2×#117—671no—
574C2×#117—674no—
575C2×#117C2×D6712yes—
576C22×C4⋊C4—672no—
577C22×C4⋊C4—672no—
578C22×C42—671no—
579C22×C42—671no—
580C22×C42C2×D6711yescharacteristic
581C2×#41—678no—
582C2×#41—1348no—
583C22×Q8—6716no—
584C22×Q8—672no—
585C22×Q8—672no—
586C22×Q8—674no—
587C22×Q8—671no—
588C22×Q8—13416no—
589C22×Q8C22×D6712yes—
590C22×Q8C22×D6712yes—
591C22×D4—671no—
592C22×D4—671no—
593C22×D4—671no—
594C23×C4—671no—
595C23×C4—674no—
596C23×C4—671no—
597C23×C4—671no—
598C23×C4—671no—
599C23×C4—671no—
600C23×C4—671no—
601C23×C4C22×D6711yescharacteristic
602C23×C4C22×D6711yescharacteristic
603C23×C4C22×D6711yescharacteristic
604C4⋊Q8—6716no—
605C4⋊Q8—6716no—
606C4⋊Q8—6716no—
607C4⋊Q8—6732no—
608C4⋊Q8—678no—
609C4⋊Q8—678no—
610C4⋊Q8C22×D6718yes—
611C4⋊Q8C22×D6718yes—
612#126—6732no—
613#126—6732no—
614#126—6732no—
615#126—6732no—
616#125—6716no—
617#125—6716no—
618#125—6716no—
619#125—6732no—
620#125—6732no—
621#125—6732no—
622#125—6716no—
623#125—6732no—
624#125C22×D67116yes—
625#124—6732no—
626#123—6732no—
627#123—6732no—
628C22⋊Q8—6716no—
629C22⋊Q8—6716no—
630C22⋊Q8—6716no—
631C22⋊Q8—6716no—
632C22⋊Q8—6716no—
633C22⋊Q8—6716no—
634C22⋊Q8—6716no—
635C22⋊Q8—6716no—
636C22⋊Q8C22×D67116yes—
637C22⋊Q8C22×D67116yes—
638C4×Q8—6716no—
639C4×Q8—6716no—
640C4×Q8—6716no—
641C4×Q8—6716no—
642C4×Q8—6732no—
643C4×Q8—6716no—
644C4×Q8—6716no—
645C4×Q8—678no—
646C4×Q8—678no—
647C4×Q8—6716no—
648C4×Q8—6732no—
649C4×Q8—6716no—
650C4×Q8C22×D67116yes—
651C4×Q8C22×D67116yes—
652C4×D4—678no—
653C4×D4—678no—
654C4×D4—678no—
655C4×D4—678no—
656C4×D4—678no—
657C4×D4—678no—
658#117—678no—
659#117—6716no—
660#117—6716no—
661#117—6732no—
662#117—6716no—
663#117—6716no—
664#117—678no—
665#117—678no—
666#117—6732no—
667#117C22×D67116yes—
668C2×C4⋊C4—672no—
669C2×C4⋊C4—672no—
670C2×C4⋊C4—674no—
671C2×C4⋊C4—674no—
672C2×C4⋊C4—672no—
673C2×C4⋊C4—671no—
674C2×C4⋊C4—671no—
675C2×C4⋊C4—671no—
676C2×C4⋊C4—671no—
677C2×C4⋊C4—671no—
678C2×C4⋊C4—671no—
679C2×C4⋊C4—672no—
680C2×C4⋊C4—674no—
681C2×C4⋊C4—674no—
682C2×C4⋊C4—674no—
683C2×C4⋊C4—674no—
684C2×C4⋊C4—674no—
685C2×C4⋊C4—674no—
686C2×C4⋊C4—674no—
687C2×C4⋊C4—674no—
688C2×C4⋊C4—6716no—
689C2×C4⋊C4—6716no—
690C2×C4⋊C4C22×D6712yes—
691C2×C4⋊C4C22×D6712yes—
692C2×C4⋊C4C22×D6712yes—
693C2×C4⋊C4C22×D6712yes—
694C2×C4⋊C4C22×D6714yes—
695C2×C4⋊C4C22×D6714yes—
696C2×C22⋊C4—671no—
697C2×C22⋊C4—671no—
698C2×C22⋊C4—674no—
699C2×C22⋊C4—671no—
700C2×C22⋊C4—671no—
701C2×C22⋊C4—674no—
702C2×C22⋊C4—671no—
703C2×C22⋊C4—671no—
704C2×C22⋊C4—674no—
705C2×C22⋊C4—674no—
706C2×C22⋊C4C22×D6714yes—
707C2×C42—671no—
708C2×C42—674no—
709C2×C42—674no—
710C2×C42—674no—
711C2×C42—671no—
712C2×C42—674no—
713C2×C42—671no—
714C2×C42—671no—
715C2×C42—671no—
716C2×C42—671no—
717C2×C42—678no—
718C2×C42—678no—
719C2×C42C22×D6711yescharacteristic
720C2×C42C22×D6714yes—
721C2×C42C22×D6711yescharacteristic
722C2×C42C22×D6711yescharacteristic
723C2×C42C22×D6718yes—
724C2×C42C22×D6711yescharacteristic
725C24—671no—
726C24—671no—
727C24C23×D6711yescharacteristic
728#41—13432no—
729C2×Q8—28no—
730C2×Q8—28no—
731C2×Q8—678no—
732C2×Q8—678no—
733C2×Q8—6716no—
734C2×Q8—674no—
735C2×Q8—13416no—
736C2×Q8—1344no—
737C2×Q8—13464no—
738C2×Q8—1348no—
739C2×Q8—1348no—
740C2×Q8C23×D6718yes—
741C2×Q8C23×D6718yes—
742C2×D4—674no—
743C2×D4—674no—
744C2×D4—674no—
745C2×D4—1344no—
746C2×D4—1344no—
747C2×D4—1344no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—671no—
752C22×C4—678no—
753C22×C4—674no—
754C22×C4—671no—
755C22×C4—671no—
756C22×C4—674no—
757C22×C4—671no—
758C22×C4—671no—
759C22×C4—674no—
760C22×C4—671no—
761C22×C4—674no—
762C22×C4—674no—
763C22×C4—674no—
764C22×C4—674no—
765C22×C4—674no—
766C22×C4—6716no—
767C22×C4—13416no—
768C22×C4—1344no—
769C22×C4—1344no—
770C22×C4—1344no—
771C22×C4—1344no—
772C22×C4—1344no—
773C22×C4C23×D6714yes—
774C22×C4C23×D6714yes—
775C22×C4C23×D6714yes—
776C22×C4C23×D6711yescharacteristic
777C22×C4C23×D6714yes—
778C22×C4C23×D6714yes—
779C22×C4C23×D6711yescharacteristic
780C22×C4C23×D6711yescharacteristic
781C22×C4C23×D6711yescharacteristic
782C22×C4C23×D6711yescharacteristic
783C22×C4C23×D6711yescharacteristic
784C4⋊C4—678no—
785C4⋊C4—678no—
786C4⋊C4—6716no—
787C4⋊C4—6716no—
788C4⋊C4—678no—
789C4⋊C4—674no—
790C4⋊C4—674no—
791C4⋊C4—674no—
792C4⋊C4—674no—
793C4⋊C4—674no—
794C4⋊C4—674no—
795C4⋊C4—678no—
796C4⋊C4—6716no—
797C4⋊C4—6716no—
798C4⋊C4—6716no—
799C4⋊C4—6716no—
800C4⋊C4—6716no—
801C4⋊C4—6716no—
802C4⋊C4—6716no—
803C4⋊C4—6716no—
804C4⋊C4C23×D6718yes—
805C4⋊C4C23×D6718yes—
806C4⋊C4C23×D6718yes—
807C4⋊C4C23×D6718yes—
808C4⋊C4C23×D67116yes—
809C4⋊C4C23×D67116yes—
810C22⋊C4—674no—
811C22⋊C4—674no—
812C22⋊C4—6716no—
813C22⋊C4—674no—
814C22⋊C4—674no—
815C22⋊C4—6716no—
816C22⋊C4—674no—
817C22⋊C4—674no—
818C22⋊C4—6716no—
819C22⋊C4—6716no—
820C22⋊C4C23×D67116yes—
821C42—674no—
822C42—674no—
823C42—674no—
824C42—674no—
825C42—674no—
826C42—674no—
827C42—6716no—
828C42—6716no—
829C42—6716no—
830C42—6716no—
831C42C23×D6714yes—
832C42C23×D6714yes—
833C42C23×D6714yes—
834C42C23×D6714yes—
835C42C23×D67116yes—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—674no—
840C23—672no—
841C23—672no—
842C23—1342no—
843C23—1342no—
844C23—1342no—
845C23—1342no—
846C23—1342no—
847C23C24×D6712yes—
848C23C24×D6711yescharacteristic
849Q8—216no—
850Q8—216no—
851Q8—13432no—
852Q8—1348no—
853Q8—13416no—
854Q8—13416no—
855D4—1348no—
856D4—1348no—
857D4—1348no—
858C2×C4—22no—
859C2×C4—28no—
860C2×C4—22no—
861C2×C4—28no—
862C2×C4—22no—
863C2×C4—28no—
864C2×C4—28no—
865C2×C4—28no—
866C2×C4—674no—
867C2×C4—672no—
868C2×C4—6716no—
869C2×C4—672no—
870C2×C4—672no—
871C2×C4—678no—
872C2×C4—672no—
873C2×C4—672no—
874C2×C4—678no—
875C2×C4—672no—
876C2×C4—13432no—
877C2×C4—1342no—
878C2×C4—1348no—
879C2×C4—1342no—
880C2×C4—1342no—
881C2×C4—1342no—
882C2×C4—1342no—
883C2×C4—1348no—
884C2×C4—1348no—
885C2×C4—1348no—
886C2×C4—1348no—
887C2×C4—1348no—
888C2×C4—1348no—
889C2×C4#41×D6714yes—
890C2×C4#1452409014yes—
891C2×C4#1452409114yes—
892C2×C4C24×D6712yes—
893C2×C4C24×D6718yes—
894C2×C4C24×D6718yes—
895C2×C4C24×D6712yes—
896C2×C4C24×D6712yes—
897C2×C4C24×D6712yes—
898C2×C4C24×D6712yes—
899C2×C4C24×D6712yes—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—44no—
904C22—2684no—
905C22—674no—
906C22—1342no—
907C22—1342no—
908C22—1342no—
909C22—1348no—
910C22—1342no—
911C22—1342no—
912C22C2×#41×D6712yes—
913C22C2×#1452409012yes—
914C22C2×#1452409112yes—
915C22C25×D6711yescharacteristic
916C4—22no—
917C4—28no—
918C4—22no—
919C4—28no—
920C4—22no—
921C4—674no—
922C4—1342no—
923C4—1348no—
924C4—1342no—
925C4—1342no—
926C4—1342no—
927C4—1342no—
928C4—1348no—
929C4C2×#41×D6714yes—
930C4C2×#1452409014yes—
931C4C2×#1452409114yes—
932C2—42no—
933C2—2682no—
934C2—1344no—
935C2#2257408814yesdirect product factor
936C2C22×#41×D6711yescharacteristic
937C2C22×#1452409011yescharacteristic
938C2C22×#1452409111yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#533×C67C2
socleC23×C67C25
prime radicalC22×#11761628C22
hypercenterC2×#533D67
hypocenterC67C2×#3509
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #22574088C2direct (N × H)
2. C2×#16864123C2semidirect
3. C2×#16864122C2semidirect
4. C2×#16864117C2semidirect
5. C2×#16864114C2semidirect
6. C2×#16864087C2semidirect
7. C2×#16864085C2semidirect
8. C2×#16864084C2semidirect
9. C2×#16864080C2semidirect
10. C2×#16864006C2semidirect
11. C2×#16864004C2semidirect
13. C2×#16863953C2semidirect
14. C2×#16863951C2semidirect
15. C2×#16863951C2semidirect
16. C2×#16863951C2semidirect
17. C2×C4⋊Q8×D67C2semidirect
18. C2×#16863872C2semidirect
20. C2×#533×C67C2semidirect
23. #16864123C22semidirect
24. #16864122C22semidirect
25. #16864117C22semidirect
26. #16864114C22semidirect
27. #16864087C22semidirect
28. #16864085C22semidirect
29. #16864084C22semidirect
30. #16864080C22semidirect
31. #16864006C22semidirect
32. #16864004C22semidirect
34. #16863953C22semidirect
35. #16863951C22semidirect
36. #16863951C22semidirect
37. #16863951C22semidirect
44. C4⋊Q8×D67C22semidirect
68. #16863872C22semidirect
101. #533×C67C22semidirect
464. C2×C67#3509semidirect
486. C2×#533D67semidirect
490. C67C2×#3509semidirect
508. #533C2×D67semidirect
935. C2#22574088direct (N × H)

Maximal subgroups

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

subgroupindex
#225740882
C2×#168641232
C2×#168641222
C2×#168641172
C2×#168641142
C2×#168640872
C2×#168640852
C2×#168640842
C2×#168640802
C2×#168640062
C2×#168640042
C2×#168639692
C2×#168639532
C2×#168639512
C2×C4⋊Q8×D672
C2×#168638722
C2×C4×#117616282
C2×#533×C672
C2×#350967