Finite Group Databasebeta

← C2×#22573912 #31763767

Subgroups — C2×#22573912 #31763767

Order 17152.

7910 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22573912C2132yesmaximal, direct product factor
2C2×#16864106C212yesmaximal, complemented
3C2×#16864101C212yesmaximal, complemented
4C2×#16864096C212yesmaximal, complemented
5C2×#16864090C212yesmaximal, complemented
6C2×#16864087C212yesmaximal, complemented
7C2×#16864085C212yesmaximal, complemented
8C2×#16864051C212yesmaximal, complemented
9C2×#16864047C212yesmaximal, complemented
10C2×#16864024C211yesmaximal, characteristic, complemented
11C2×#16863988C214yesmaximal, complemented
12C2×#16863974C211yesmaximal, characteristic, complemented
13C2×#16863908C211yesmaximal, characteristic, complemented
14C2×#16863905C214yesmaximal, complemented
15C2×#16863903C211yesmaximal, characteristic, complemented
16C2×#16863877C211yesmaximal, characteristic, complemented
17C22×C4⋊C4×D67C211yesmaximal, characteristic, complemented
18C2×#520×C67C211yesmaximal, characteristic, complemented
19C22×#11761628C2211yescharacteristic
20C22×#11761628C2214yes—
21C23×C4×D67C2211yescharacteristic
22C23×C4×D67C2212yes—
23#16864106C22132yescomplemented
24#16864101C22132yescomplemented
25#16864096C22132yescomplemented
26#16864090C22132yescomplemented
27#16864087C22132yescomplemented
28#16864085C22132yescomplemented
29#16864051C22132yescomplemented
30#16864047C22132yescomplemented
31#16864024C22116yescomplemented
32#16863988C22164yescomplemented
33#16863974C22116yescomplemented
34C2×#14524043C2212yescomplemented
35C2×#14524042C2212yescomplemented
36C2×#14524037C2214yescomplemented
37C2×#14524036C2214yescomplemented
38C2×#14524035C2212yescomplemented
39C2×#14524035C2214yescomplemented
40C2×#14524034C2212yescomplemented
41C2×#14524033C2214yescomplemented
42#16863908C22116yescomplemented
43#16863905C22164yescomplemented
44#16863903C22116yescomplemented
45C2×#14524028C2214yes—
46C2×#14524027C2212yes—
47C2×#14524026C2214yescomplemented
48C2×#14524025C2214yes—
49C2×#14524025C2214yescomplemented
50C2×#14524024C2212yes—
51C2×#14524023C2211yescharacteristic
52C2×#14524023C2211yescharacteristic
53C2×#14524022C2214yescomplemented
54C2×#14524022C2212yescomplemented
55C2×#14524021C2214yes—
56C2×#14524021C2214yescomplemented
57C2×#14524020C2214yes—
58C2×#14524019C2211yescharacteristic
59C2×#14524019C2211yescharacteristic
60C2×#14524019C2212yescomplemented
61C2×#14524018C2211yescharacteristic
62C2×#14524018C2211yescharacteristic
63C2×#14524017C2212yescomplemented
64C2×#14524016C2214yes—
65C2×#14524015C2214yes—
66C2×#14524014C2211yescharacteristic
67C2×#14524014C2211yescharacteristic
68C2×#14524014C2212yescomplemented
69C2×#14524013C2212yes—
70C2×#14524011C2212yes—
71#16863877C22116yescomplemented
72C2×#14524008C2212yescomplemented
73C2×C4×D268C2212yes—
74C2×C4×D268C2214yes—
75C2×C4×D268C2212yes—
76C2×#14524005C2212yescomplemented
77C2×C4×C22⋊D67C2214yes—
78C2×C4×C22⋊D67C2212yes—
79C2×C4×C22⋊D67C2212yes—
80C2×C4×C22⋊D67C2214yes—
81C2×#14524002C2211yescharacteristic
82C2×#14524001C2212yescomplemented
83C2×#14524000C2214yes—
84C22×C4⋊Dic67C2211yescharacteristic
85C22×Dic67⋊C4C2212yes—
86C2×C4⋊C4×D67C2212yes—
87C2×C4⋊C4×D67C2212yes—
88C2×C4⋊C4×D67C2212yes—
89C2×C4⋊C4×D67C2212yes—
90C2×C4⋊C4×D67C22116yescomplemented
91C2×C4⋊C4×D67C2212yescomplemented
92C22×#41×C67C2211yescharacteristic
93#520×C67C22116yescomplemented
94C2×C4×Q8×C67C2212yescomplemented
95C2×C4×D4×C67C2214yes—
96C2×C4×D4×C67C2212yescomplemented
97C2×#117×C67C2211yescharacteristic
98C2×#117×C67C2212yescomplemented
99C22×C4⋊C4×C67C2211yescharacteristic
100C22×C4⋊C4×C67C2212yescomplemented
101C24×D67C2311yescharacteristic
102C2×#11761628—28no—
103C2×#11761628—416no—
104C2×#11761628C2318yes—
105C2×#11761628C23132yes—
106C22×Dic134C2311yescharacteristic
107C22×Dic134C2314yes—
108C22×D268C2311yescharacteristic
109C22×D268C2312yes—
110C22×D268C2312yes—
111C22×C22⋊D67C2312yes—
112C22×C22⋊D67C2312yes—
113C22×C22⋊D67C2312yes—
114C22×C22⋊D67C2314yes—
115C23×Dic67C2311yescharacteristic
116C23×Dic67C2312yes—
117C22×C4×D67—28no—
118C22×C4×D67—48no—
119C22×C4×D67C2314yes—
120C22×C4×D67C2311yescharacteristic
121C22×C4×D67C2311yescharacteristic
122C22×C4×D67C2311yescharacteristic
123C22×C4×D67C2311yescharacteristic
124C22×C4×D67C2318yes—
125C22×C4×D67C2312yes—
126C22×C4×D67C2314yes—
127C22×C4×D67C23116yes—
128C22×C4×D67C2314yes—
129#14524043C23116yescomplemented
130#14524042C23116yescomplemented
131#14524037C23132yescomplemented
132#14524036C23132yescomplemented
133#14524035C23116yescomplemented
134#14524035C23132yescomplemented
135#14524034C23116yescomplemented
136#14524033C23132yescomplemented
137#14524028C23132yes—
138#14524027C23116yes—
139#14524026C23132yescomplemented
140#14524025C23132yes—
141#14524025C23132yescomplemented
142#14524024C23116yes—
143#14524023C2318yes—
144#14524023C2318yes—
145#14524022C23132yescomplemented
146#14524022C23116yescomplemented
147#14524021C23132yes—
148#14524021C23132yescomplemented
149#14524020C23132yes—
150#14524019C2318yes—
151#14524019C2318yes—
152#14524019C23116yescomplemented
153#14524018C2318yes—
154#14524018C2318yes—
155#14524017C23116yescomplemented
156#14524016C23132yes—
157#14524015C23132yes—
158#14524014C2318yes—
159#14524014C2318yes—
160#14524014C23116yescomplemented
161#14524013C23116yes—
162#14524011C23116yes—
163#14524008C23116yescomplemented
164C4×D268C23116yes—
165C4×D268C23132yes—
166C4×D268C23116yes—
167#14524005C23116yescomplemented
168C4×C22⋊D67C23116yes—
169C4×C22⋊D67C23116yes—
170C4×C22⋊D67C23132yes—
171C4×C22⋊D67C23132yes—
172#14524002C2318yes—
173#14524001C23116yescomplemented
174#14524000C23132yes—
175C2×C4⋊Dic67C2318yes—
176C2×C4⋊Dic67C2312yes—
177C2×C4⋊Dic67C2312yes—
178C2×C4⋊Dic67C2311yescharacteristic
179C2×C4⋊Dic67C2311yescharacteristic
180C2×C4⋊Dic67C2314yes—
181C2×C4⋊Dic67C2312yes—
182C2×C4⋊Dic67C2312yes—
183C2×Dic67⋊C4C2314yes—
184C2×Dic67⋊C4C2314yes—
185C2×Dic67⋊C4C23116yes—
186C2×Dic67⋊C4C2314yes—
187C2×Dic67⋊C4C2314yes—
188C2×Dic67⋊C4C2314yes—
189C2×Dic67⋊C4C2312yes—
190C2×Dic67⋊C4C2312yes—
191C2×Dic67⋊C4C2314yes—
192C4⋊C4×D67C23116yes—
193C4⋊C4×D67C23116yes—
194C4⋊C4×D67C23116yes—
195C4⋊C4×D67C23116yes—
196C4⋊C4×D67C23116yescomplemented
197C2×C22⋊Dic67C2312yes—
198C2×C22⋊Dic67C2312yes—
199C2×C22⋊Dic67C2312yes—
200C2×C22⋊Dic67C2314yes—
201C2×(C2×D67)⋊C4C2312yes—
202C2×(C2×D67)⋊C4C2312yes—
203C2×(C2×D67)⋊C4C2314yes—
204C2×(C2×D67)⋊C4C2312yes—
205C2×(C2×D67)⋊C4C2312yes—
206C2×(C2×D67)⋊C4C2314yes—
207C2×(C2×D67)⋊C4C2312yes—
208C2×(C2×D67)⋊C4C2312yes—
209C2×C4×Dic67C2314yes—
210C2×C4×Dic67C2312yes—
211C2×#41×C67—28no—
212C2×#41×C67C2318yes—
213C22×Q8×C67C2311yescharacteristic
214C22×D4×C67C2312yes—
215C22×D4×C67C2311yescharacteristic
216C23×C4×C67C2312yes—
217C23×C4×C67C2312yes—
218C23×C4×C67C2314yes—
219C23×C4×C67C2311yescharacteristic
220C4×Q8×C67C23116yescomplemented
221C4×D4×C67C23132yes—
222C4×D4×C67C23116yescomplemented
223#117×C67C2318yes—
224#117×C67C23116yescomplemented
225C2×C4⋊C4×C67C2312yes—
226C2×C4⋊C4×C67C2312yes—
227C2×C4⋊C4×C67C2318yes—
228C2×C4⋊C4×C67C2311yescharacteristic
229C2×C4⋊C4×C67C2314yes—
230C2×C4⋊C4×C67C2311yescharacteristic
231C2×C4⋊C4×C67C23116yescomplemented
232C2×C22⋊C4×C67C2312yes—
233C2×C22⋊C4×C67C2314yes—
234C2×C42×C67C2312yes—
235C2×C42×C67C2314yes—
236C23×D67—24no—
237C23×D67—24no—
238C23×D67—24no—
239C23×D67C2412yes—
240C23×D67C2414yes—
241C23×D67C2411yescharacteristic
242C23×D67C2411yescharacteristic
243#11761628—232no—
244#11761628—464no—
245C2×Dic134—24no—
246C2×Dic134—48no—
247C2×Dic134C2414yes—
248C2×Dic134C24116yes—
249C2×D268—28no—
250C2×D268—28no—
251C2×D268—24no—
252C2×D268C2414yes—
253C2×D268C2418yes—
254C2×D268C2418yes—
255C2×C22⋊D67—28no—
256C2×C22⋊D67—28no—
257C2×C22⋊D67—28no—
258C2×C22⋊D67—48no—
259C2×C22⋊D67C2418yes—
260C2×C22⋊D67C2418yes—
261C2×C22⋊D67C2418yes—
262C2×C22⋊D67C24116yes—
263C22×Dic67—24no—
264C22×Dic67—44no—
265C22×Dic67C2412yes—
266C22×Dic67C2412yes—
267C22×Dic67C2412yes—
268C22×Dic67C2411yescharacteristic
269C22×Dic67C2411yescharacteristic
270C22×Dic67C2414yes—
271C22×Dic67C2414yes—
272C22×Dic67C2418yes—
273C2×C4×D67—216no—
274C2×C4×D67—24no—
275C2×C4×D67—24no—
276C2×C4×D67—24no—
277C2×C4×D67—24no—
278C2×C4×D67—28no—
279C2×C4×D67—232no—
280C2×C4×D67—432no—
281C2×C4×D67—48no—
282C2×C4×D67—48no—
283C2×C4×D67C24116yes—
284C2×C4×D67C2414yes—
285C2×C4×D67C2414yes—
286C2×C4×D67C2414yes—
287C2×C4×D67C2414yes—
288C2×C4×D67C2418yes—
289C2×C4×D67C24116yes—
290C2×C4×D67C24116yes—
291C4⋊Dic67C2418yes—
292C4⋊Dic67C2418yes—
293C4⋊Dic67C2414yes—
294C4⋊Dic67C2414yes—
295C4⋊Dic67C24116yes—
296C4⋊Dic67C2418yes—
297C4⋊Dic67C2418yes—
298Dic67⋊C4C24116yes—
299Dic67⋊C4C24116yes—
300Dic67⋊C4C24116yes—
301Dic67⋊C4C24116yes—
302Dic67⋊C4C24116yes—
303Dic67⋊C4C2418yes—
304Dic67⋊C4C2418yes—
305Dic67⋊C4C24116yes—
306C22⋊Dic67C2418yes—
307C22⋊Dic67C2418yes—
308C22⋊Dic67C2418yes—
309C22⋊Dic67C24116yes—
310(C2×D67)⋊C4C2418yes—
311(C2×D67)⋊C4C2418yes—
312(C2×D67)⋊C4C24116yes—
313(C2×D67)⋊C4C2418yes—
314(C2×D67)⋊C4C2418yes—
315(C2×D67)⋊C4C24116yes—
316(C2×D67)⋊C4C2418yes—
317(C2×D67)⋊C4C2418yes—
318C4×Dic67C24116yes—
319C4×Dic67C2418yes—
320C24×C67C2412yes—
321C24×C67C2411yescharacteristic
322#41×C67—232no—
323C2×Q8×C67—24no—
324C2×Q8×C67C2414yes—
325C2×D4×C67—28no—
326C2×D4×C67—24no—
327C2×D4×C67C2418yes—
328C2×D4×C67C2414yes—
329C22×C4×C67—28no—
330C22×C4×C67—44no—
331C22×C4×C67—48no—
332C22×C4×C67#4118yescomplemented
333C22×C4×C67C2412yes—
334C22×C4×C67C2412yes—
335C22×C4×C67C2414yes—
336C22×C4×C67C2412yes—
337C22×C4×C67C2418yes—
338C22×C4×C67C2418yes—
339C22×C4×C67C24116yes—
340C22×C4×C67C2411yescharacteristic
341C22×C4×C67C2411yescharacteristic
342C22×C4×C67C2414yes—
343C4⋊C4×C67C2418yes—
344C4⋊C4×C67C2418yes—
345C4⋊C4×C67C2414yes—
346C4⋊C4×C67C24116yes—
347C4⋊C4×C67C2414yes—
348C22⋊C4×C67C2418yes—
349C22⋊C4×C67C24116yes—
350C42×C67C2418yes—
351C42×C67C24116yes—
352C23×C67—22no—
353C23×C67—22no—
354C23×C67—24no—
355C23×C67—24no—
356C23×C67—24no—
357C23×C67C2×#4114yes—
358C23×C67C2514yes—
359C23×C67C2512yes—
360C23×C67C2511yescharacteristic
361C22×D67—232no—
362C22×D67—28no—
363C22×D67—22no—
364C22×D67—22no—
365C22×D67—22no—
366C22×D67—22no—
367C22×D67—28no—
368C22×D67—28no—
369C22×D67—24no—
370C22×D67—24no—
371C22×D67—24no—
372C22×D67H(5,𝔽2)14yes—
373C22×D672−1+414yes—
374C22×D67C2514yes—
375C22×D67C2512yes—
376C22×D67C2512yes—
377Q8×C67—28no—
378D4×C67—216no—
379D4×C67—28no—
380C2×C4×C67—24no—
381C2×C4×C67—28no—
382C2×C4×C67—24no—
383C2×C4×C67—24no—
384C2×C4×C67—216no—
385C2×C4×C67—48no—
386C2×C4×C67—416no—
387C2×C4×C67C2×#4114yes—
388C2×C4×C67C2×#4114yes—
389C2×C4×C67C2×#41116yescomplemented
390C2×C4×C67C2514yes—
391C2×C4×C67C2514yes—
392C2×C4×C67C2518yes—
393C2×C4×C67C2514yes—
394C2×C4×C67C2512yes—
395C2×C4×C67C2512yes—
396C22⋊D67—216no—
397C22⋊D67—216no—
398C22⋊D67—216no—
399C22⋊D67—416no—
400C2×Dic67—28no—
401C2×Dic67—22no—
402C2×Dic67—22no—
403C2×Dic67—24no—
404C2×Dic67—28no—
405C2×Dic67—24no—
406C2×Dic67—24no—
407C2×Dic67—48no—
408C2×Dic67C2514yes—
409C2×Dic67C2514yes—
410C2×Dic67C2514yes—
411C2×Dic67C2512yes—
412C2×Dic67C2512yes—
413C2×Dic67C2518yes—
414D268—216no—
415D268—216no—
416D268—28no—
417C4×D67—232no—
418C4×D67—28no—
419C4×D67—28no—
420C4×D67—28no—
421C4×D67—28no—
422C4×D67—216no—
423C4×D67—416no—
424C4×D67—416no—
425Dic134—28no—
426Dic134—416no—
427C22×C67—22no—
428C22×C67—22no—
429C22×C67—28no—
430C22×C67—24no—
431C22×C67—24no—
432C22×C67—24no—
433C22×C67—48no—
434C22×C67C22×#4114yes—
435C22×C67C22×#4112yes—
436C22×C67C2×H(5,𝔽2)12yes—
437C22×C67C2×2−1+412yes—
438C22×C67C2611yescharacteristic
439C2×D67—232no—
440C2×D67—22no—
441C2×D67—22no—
442C2×D67—22no—
443C2×D67—22no—
444C2×D67—28no—
445C2×D67—28no—
446C2×D67—24no—
447C2×D67—24no—
448C2×D67—24no—
449C2×D67—48no—
450C2×D67C2×H(5,𝔽2)14yes—
451C2×D67C2×2−1+414yes—
452C4×C67—24no—
453C4×C67—24no—
454C4×C67—28no—
455C4×C67—24no—
456C4×C67C22×#4114yes—
457C4×C67C22×#4114yes—
458Dic67—24no—
459Dic67—22no—
460Dic67—22no—
461Dic67—24no—
462Dic67—28no—
463Dic67—24no—
464C2×#3492—671nomaximal, Sylow
465C2×C67—24no—
466C2×C67—44no—
467C2×C67#349214yescomplemented
468C2×C67C23×#4111yescharacteristic
469C2×C67C22×H(5,𝔽2)11yescharacteristic
470C2×C67C22×2−1+411yescharacteristic
471D67—24no—
472D67—24no—
473D67—44no—
474#3492—6732no—
475C2×#554—672no—
476C2×#554—672no—
477C2×#553—672no—
478C2×#553—672no—
479C2×#552—672no—
480C2×#552—672no—
481C2×#547—672no—
482C2×#547—672no—
483C2×#544—671no—
484C2×#539—674no—
485C2×#537—671no—
486C2×#525—671no—
487C2×#525—674no—
488C2×#525—671no—
489C2×#520—671no—
490C2×#520D6711yescharacteristic, complemented
491C23×C4⋊C4—671no—
492C67C2×#349211yescharacteristic, complemented, Sylow
493C22×#41—674no—
494C22×#41—671no—
495C22×#41C2×D6711yescharacteristic
496C24×C4—672no—
497C24×C4—671no—
498#554—6732no—
499#554—6732no—
500#553—6732no—
501#553—6732no—
502#552—6732no—
503#552—6732no—
504#547—6732no—
505#547—6732no—
506#544—6716no—
507#539—6764no—
508#537—6716no—
509C2×C4⋊Q8—672no—
510C2×C4⋊Q8—672no—
511C2×#126—674no—
512C2×#126—674no—
513C2×#125—674no—
514C2×#125—672no—
515C2×#125—674no—
516C2×#125—672no—
517#525—6716no—
518#525—6764no—
519#525—6716no—
520C2×#123—672no—
521C2×#123—674no—
522C2×#123—674no—
523C2×#123—672no—
524C2×#123—674no—
525C2×#123—674no—
526C2×C22⋊Q8—671no—
527C2×C22⋊Q8—671no—
528C2×C22⋊Q8—672no—
529C2×C22⋊Q8—672no—
530C2×C22⋊Q8—674no—
531C2×C22⋊Q8—671no—
532C2×C22⋊Q8—674no—
533C2×C22⋊Q8—671no—
534C2×C22⋊Q8—674no—
535C2×C22⋊Q8—674no—
536C2×#121—674no—
537C2×#121—671no—
538C2×#121—671no—
539C2×#121—672no—
540C2×#121—672no—
541C2×#121—671no—
542C2×#121—671no—
543C2×#121—674no—
544C2×#120—672no—
545C2×#120—672no—
546#520—6716no—
547#520C2×D67116yescomplemented
548C2×C4×Q8—672no—
549C2×C4×Q8C2×D6712yescomplemented
550C2×C4×D4—674no—
551C2×C4×D4—672no—
552C2×C4×D4—674no—
553C2×C4×D4—672no—
554C2×C4×D4—672no—
555C2×C4×D4—672no—
556C2×C4×D4—674no—
557C2×C4×D4—672no—
558C2×C4×D4C2×D6714yes—
559C2×C4×D4C2×D6712yescomplemented
560C2×#117—671no—
561C2×#117—672no—
562C2×#117—674no—
563C2×#117C2×D6711yescharacteristic
564C2×#117C2×D6712yescomplemented
565C22×C4⋊C4—672no—
566C22×C4⋊C4—671no—
567C22×C4⋊C4—672no—
568C22×C4⋊C4—672no—
569C22×C4⋊C4—672no—
570C22×C4⋊C4—672no—
571C22×C4⋊C4—6716no—
572C22×C4⋊C4—672no—
573C22×C4⋊C4C2×D6711yescharacteristic
574C22×C4⋊C4C2×D6712yescomplemented
575C25—671no—
576C2×#41—28no—
577C2×#41—26816no—
578C2×#41—6732no—
579C2×#41—678no—
580C2×#41—1348no—
581C2×#41C22×D6718yes—
582C22×Q8—674no—
583C22×Q8—671no—
584C22×Q8C22×D6711yescharacteristic
585C22×D4—674no—
586C22×D4—672no—
587C22×D4—672no—
588C22×D4—672no—
589C22×D4—672no—
590C22×D4—671no—
591C22×D4—672no—
592C22×D4C22×D6712yes—
593C22×D4C22×D6711yescharacteristic
594C23×C4—2688no—
595C23×C4—672no—
596C23×C4—674no—
597C23×C4—6716no—
598C23×C4—674no—
599C23×C4—671no—
600C23×C4—674no—
601C23×C4—671no—
602C23×C4—671no—
603C23×C4—671no—
604C23×C4—671no—
605C23×C4—678no—
606C23×C4—672no—
607C23×C4—1348no—
608C23×C4C22×D6712yes—
609C23×C4C22×D6712yes—
610C23×C4C22×D6714yes—
611C23×C4C22×D6711yescharacteristic
612C4⋊Q8—6716no—
613C4⋊Q8—6716no—
614#126—6732no—
615#126—6732no—
616#125—6732no—
617#125—6716no—
618#125—6732no—
619#125—6716no—
620#123—6716no—
621#123—6732no—
622#123—6732no—
623#123—6716no—
624#123—6732no—
625#123—6732no—
626C22⋊Q8—678no—
627C22⋊Q8—678no—
628C22⋊Q8—6716no—
629C22⋊Q8—6716no—
630C22⋊Q8—6732no—
631C22⋊Q8—678no—
632C22⋊Q8—6732no—
633C22⋊Q8—678no—
634C22⋊Q8—6732no—
635C22⋊Q8—6732no—
636#121—6732no—
637#121—678no—
638#121—678no—
639#121—6716no—
640#121—6716no—
641#121—678no—
642#121—678no—
643#121—6732no—
644#120—6716no—
645#120—6716no—
646C4×Q8—6716no—
647C4×Q8C22×D67116yescomplemented
648C4×D4—6732no—
649C4×D4—6716no—
650C4×D4—6732no—
651C4×D4—6716no—
652C4×D4—6716no—
653C4×D4—6716no—
654C4×D4—6732no—
655C4×D4—6716no—
656C4×D4C22×D67132yes—
657C4×D4C22×D67116yescomplemented
658#117—678no—
659#117—6716no—
660#117—6732no—
661#117C22×D6718yes—
662#117C22×D67116yescomplemented
663C2×C4⋊C4—672no—
664C2×C4⋊C4—672no—
665C2×C4⋊C4—674no—
666C2×C4⋊C4—674no—
667C2×C4⋊C4—678no—
668C2×C4⋊C4—6716no—
669C2×C4⋊C4—671no—
670C2×C4⋊C4—674no—
671C2×C4⋊C4—671no—
672C2×C4⋊C4—674no—
673C2×C4⋊C4—674no—
674C2×C4⋊C4—672no—
675C2×C4⋊C4—672no—
676C2×C4⋊C4—674no—
677C2×C4⋊C4—674no—
678C2×C4⋊C4—672no—
679C2×C4⋊C4—672no—
680C2×C4⋊C4—6716no—
681C2×C4⋊C4—6716no—
682C2×C4⋊C4—6716no—
683C2×C4⋊C4—6716no—
684C2×C4⋊C4—6716no—
685C2×C4⋊C4C22×D6712yes—
686C2×C4⋊C4C22×D6712yes—
687C2×C4⋊C4C22×D6718yes—
688C2×C4⋊C4C22×D6711yescharacteristic
689C2×C4⋊C4C22×D6714yes—
690C2×C4⋊C4C22×D6711yescharacteristic
691C2×C4⋊C4C22×D67116yescomplemented
692C2×C22⋊C4—672no—
693C2×C22⋊C4—674no—
694C2×C22⋊C4—672no—
695C2×C22⋊C4—672no—
696C2×C22⋊C4—672no—
697C2×C22⋊C4—672no—
698C2×C22⋊C4—674no—
699C2×C22⋊C4—672no—
700C2×C22⋊C4—672no—
701C2×C22⋊C4—674no—
702C2×C22⋊C4—672no—
703C2×C22⋊C4—672no—
704C2×C22⋊C4C22×D6712yes—
705C2×C22⋊C4C22×D6714yes—
706C2×C42—674no—
707C2×C42—672no—
708C2×C42C22×D6714yes—
709C2×C42C22×D6712yes—
710C24—671no—
711C24—671no—
712C24—674no—
713C24—672no—
714C24—1344no—
715C24—1344no—
716C24—1344no—
717C24C23×D6712yes—
718C24C23×D6711yescharacteristic
719#41—232no—
720#41—26864no—
721#41—13432no—
722C2×Q8—24no—
723C2×Q8—2688no—
724C2×Q8—6716no—
725C2×Q8—674no—
726C2×Q8—1344no—
727C2×Q8C23×D6714yes—
728C2×D4—28no—
729C2×D4—24no—
730C2×D4—2688no—
731C2×D4—6716no—
732C2×D4—678no—
733C2×D4—678no—
734C2×D4—678no—
735C2×D4—678no—
736C2×D4—674no—
737C2×D4—678no—
738C2×D4—1348no—
739C2×D4—1348no—
740C2×D4—1348no—
741C2×D4—1348no—
742C2×D4—1348no—
743C2×D4—1344no—
744C2×D4C23×D6718yes—
745C2×D4C23×D6714yes—
746C22×C4—28no—
747C22×C4—44no—
748C22×C4—48no—
749C22×C4—2688no—
750C22×C4—2688no—
751C22×C4—26832no—
752C22×C4—2684no—
753C22×C4—678no—
754C22×C4—6716no—
755C22×C4—6716no—
756C22×C4—674no—
757C22×C4—672no—
758C22×C4—672no—
759C22×C4—672no—
760C22×C4—671no—
761C22×C4—671no—
762C22×C4—674no—
763C22×C4—6716no—
764C22×C4—674no—
765C22×C4—674no—
766C22×C4—674no—
767C22×C4—674no—
768C22×C4—678no—
769C22×C4—13416no—
770C22×C4—1344no—
771C22×C4—1344no—
772C22×C4—1344no—
773C22×C4—1344no—
774C22×C4—1344no—
775C22×C4—1348no—
776C22×C4—13432no—
777C22×C4#1176162818yescomplemented
778C22×C4C23×D6718yes—
779C22×C4C23×D6714yes—
780C22×C4C23×D6712yes—
781C22×C4C23×D6712yes—
782C22×C4C23×D6712yes—
783C22×C4C23×D6718yes—
784C22×C4C23×D67116yes—
785C22×C4C23×D6711yescharacteristic
786C22×C4C23×D6711yescharacteristic
787C22×C4C23×D6714yes—
788C4⋊C4—678no—
789C4⋊C4—678no—
790C4⋊C4—6716no—
791C4⋊C4—6716no—
792C4⋊C4—674no—
793C4⋊C4—6716no—
794C4⋊C4—674no—
795C4⋊C4—6716no—
796C4⋊C4—6716no—
797C4⋊C4—678no—
798C4⋊C4—678no—
799C4⋊C4—6716no—
800C4⋊C4—6716no—
801C4⋊C4—678no—
802C4⋊C4—678no—
803C4⋊C4C23×D6718yes—
804C4⋊C4C23×D6718yes—
805C4⋊C4C23×D6714yes—
806C4⋊C4C23×D67116yes—
807C4⋊C4C23×D6714yes—
808C22⋊C4—678no—
809C22⋊C4—6716no—
810C22⋊C4—678no—
811C22⋊C4—678no—
812C22⋊C4—678no—
813C22⋊C4—678no—
814C22⋊C4—6716no—
815C22⋊C4—678no—
816C22⋊C4—678no—
817C22⋊C4—6716no—
818C22⋊C4—678no—
819C22⋊C4—678no—
820C22⋊C4C23×D6718yes—
821C22⋊C4C23×D67116yes—
822C42—6716no—
823C42—678no—
824C42C23×D67116yes—
825C42C23×D6718yes—
826C23—22no—
827C23—22no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—674no—
832C23—674no—
833C23—672no—
834C23—672no—
835C23—674no—
836C23—1348no—
837C23—1348no—
838C23—13432no—
839C23—1344no—
840C23—1344no—
841C23—1344no—
842C23—1348no—
843C23—1342no—
844C23—1342no—
845C23—1342no—
846C23—1342no—
847C23C2×#1176162814yes—
848C23C24×D6714yes—
849C23C24×D6712yes—
850C23C24×D6711yescharacteristic
851Q8—28no—
852Q8—26816no—
853Q8—1348no—
854D4—216no—
855D4—28no—
856D4—26816no—
857D4—13416no—
858D4—13416no—
859D4—13416no—
860D4—13416no—
861D4—13416no—
862D4—1348no—
863C2×C4—24no—
864C2×C4—28no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—216no—
868C2×C4—48no—
869C2×C4—416no—
870C2×C4—26816no—
871C2×C4—26816no—
872C2×C4—2688no—
873C2×C4—674no—
874C2×C4—674no—
875C2×C4—674no—
876C2×C4—672no—
877C2×C4—672no—
878C2×C4—678no—
879C2×C4—13432no—
880C2×C4—1348no—
881C2×C4—1342no—
882C2×C4—1342no—
883C2×C4—1344no—
884C2×C4—1348no—
885C2×C4—1344no—
886C2×C4—1344no—
887C2×C4—1348no—
888C2×C4—1348no—
889C2×C4—1348no—
890C2×C4—1348no—
891C2×C4—13416no—
892C2×C4C2×#1176162814yes—
893C2×C4C2×#1176162814yes—
894C2×C4C2×#11761628116yescomplemented
895C2×C4C24×D6718yes—
896C2×C4C24×D6714yes—
897C2×C4C24×D6714yes—
898C2×C4C24×D6714yes—
899C2×C4C24×D6712yes—
900C2×C4C24×D6712yes—
901C22—28no—
902C22—22no—
903C22—22no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—48no—
908C22—2688no—
909C22—674no—
910C22—674no—
911C22—13432no—
912C22—1344no—
913C22—1344no—
914C22—1344no—
915C22—1348no—
916C22—1348no—
917C22—1342no—
918C22—1342no—
919C22—1342no—
920C22—1342no—
921C22C22×#1176162814yes—
922C22C22×#1176162812yes—
923C22H(5,𝔽2)×D6712yes—
924C222−1+4×D6712yes—
925C22C25×D6711yescharacteristic
926C4—24no—
927C4—28no—
928C4—24no—
929C4—24no—
930C4—1342no—
931C4—1342no—
932C4—1344no—
933C4—1348no—
934C4—1344no—
935C4—1344no—
936C4C22×#1176162814yes—
937C4C22×#1176162814yes—
938C2—24no—
939C2—44no—
940C2—2684no—
941C2—1344no—
942C2—1344no—
943C2#2257391214yesdirect product factor
944C2C23×#1176162811yescharacteristic
945C2C2×H(5,𝔽2)×D6711yescharacteristic
946C2C2×2−1+4×D6711yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#520×C67C2
socleC23×C67C25
hypercenterC2×#520D67
hypocenterC67C2×#3492
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #22573912C2direct (N × H)
2. C2×#16864106C2semidirect
3. C2×#16864101C2semidirect
4. C2×#16864096C2semidirect
5. C2×#16864090C2semidirect
6. C2×#16864087C2semidirect
7. C2×#16864085C2semidirect
8. C2×#16864051C2semidirect
9. C2×#16864047C2semidirect
10. C2×#16864024C2semidirect
11. C2×#16863988C2semidirect
12. C2×#16863974C2semidirect
13. C2×#16863908C2semidirect
14. C2×#16863905C2semidirect
15. C2×#16863903C2semidirect
16. C2×#16863877C2semidirect
17. C22×C4⋊C4×D67C2semidirect
18. C2×#520×C67C2semidirect
23. #16864106C22semidirect
24. #16864101C22semidirect
25. #16864096C22semidirect
26. #16864090C22semidirect
27. #16864087C22semidirect
28. #16864085C22semidirect
29. #16864051C22semidirect
30. #16864047C22semidirect
31. #16864024C22semidirect
32. #16863988C22semidirect
33. #16863974C22semidirect
34. C2×#14524043C22semidirect
35. C2×#14524042C22semidirect
36. C2×#14524037C22semidirect
37. C2×#14524036C22semidirect
38. C2×#14524035C22semidirect
39. C2×#14524035C22semidirect
40. C2×#14524034C22semidirect
41. C2×#14524033C22semidirect
42. #16863908C22semidirect
43. #16863905C22semidirect
44. #16863903C22semidirect
47. C2×#14524026C22semidirect
49. C2×#14524025C22semidirect
53. C2×#14524022C22semidirect
54. C2×#14524022C22semidirect
56. C2×#14524021C22semidirect
60. C2×#14524019C22semidirect
63. C2×#14524017C22semidirect
68. C2×#14524014C22semidirect
71. #16863877C22semidirect
72. C2×#14524008C22semidirect
76. C2×#14524005C22semidirect
82. C2×#14524001C22semidirect
90. C2×C4⋊C4×D67C22semidirect
91. C2×C4⋊C4×D67C22semidirect
93. #520×C67C22semidirect
94. C2×C4×Q8×C67C22semidirect
96. C2×C4×D4×C67C22semidirect
98. C2×#117×C67C22semidirect
100. C22×C4⋊C4×C67C22semidirect
129. #14524043C23semidirect
130. #14524042C23semidirect
131. #14524037C23semidirect
132. #14524036C23semidirect
133. #14524035C23semidirect
134. #14524035C23semidirect
135. #14524034C23semidirect
136. #14524033C23semidirect
139. #14524026C23semidirect
141. #14524025C23semidirect
145. #14524022C23semidirect
146. #14524022C23semidirect
148. #14524021C23semidirect
152. #14524019C23semidirect
155. #14524017C23semidirect
160. #14524014C23semidirect
163. #14524008C23semidirect
167. #14524005C23semidirect
173. #14524001C23semidirect
196. C4⋊C4×D67C23semidirect
220. C4×Q8×C67C23semidirect
222. C4×D4×C67C23semidirect
224. #117×C67C23semidirect
231. C2×C4⋊C4×C67C23semidirect
332. C22×C4×C67#41semidirect
389. C2×C4×C67C2×#41semidirect
467. C2×C67#3492semidirect
490. C2×#520D67semidirect
492. C67C2×#3492semidirect
547. #520C2×D67semidirect
549. C2×C4×Q8C2×D67semidirect
559. C2×C4×D4C2×D67semidirect
564. C2×#117C2×D67semidirect
574. C22×C4⋊C4C2×D67semidirect
647. C4×Q8C22×D67semidirect
657. C4×D4C22×D67semidirect
662. #117C22×D67semidirect
691. C2×C4⋊C4C22×D67semidirect
777. C22×C4#11761628semidirect
894. C2×C4C2×#11761628semidirect
943. C2#22573912direct (N × H)

Maximal subgroups

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

subgroupindex
#225739122
C2×#168641062
C2×#168641012
C2×#168640962
C2×#168640902
C2×#168640872
C2×#168640852
C2×#168640512
C2×#168640472
C2×#168640242
C2×#168639882
C2×#168639742
C2×#168639082
C2×#168639052
C2×#168639032
C2×#168638772
C22×C4⋊C4×D672
C2×#520×C672
C2×#349267