Finite Group Databasebeta

← C2×#22574024 #31764161

Subgroups — C2×#22574024 #31764161

Order 17152.

7478 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574024C2132yesmaximal, direct product factor
2C2×#16864126C212yesmaximal, complemented
3C2×#16864123C212yesmaximal, complemented
4C2×#16864102C212yesmaximal, complemented
5C2×#16864100C214yesmaximal, complemented
6C2×#16864061C212yesmaximal, complemented
7C2×#16864059C214yesmaximal, complemented
8C2×#16864026C212yesmaximal, complemented
9C2×#16864024C211yesmaximal, characteristic, complemented
10C2×#16864023C212yesmaximal, complemented
11C2×#16863952C212yesmaximal, complemented
12C2×#16863949C211yesmaximal, characteristic, complemented
13C22×#14524042C211yesmaximal, characteristic, complemented
14C2×C4⋊Q8×D67C212yesmaximal, complemented
15C2×#16863877C211yesmaximal, characteristic
16C2×#16863876C211yesmaximal, characteristic
17C2×#16863864C211yesmaximal, characteristic
18C2×#544×C67C211yesmaximal, characteristic, complemented
19C22×#11761628C2211yescharacteristic
20C23×Dic134C2212yes—
21C22×Q8×D67C2214yes—
22#16864126C22132yescomplemented
23#16864123C22132yescomplemented
24#16864102C22132yescomplemented
25#16864100C22164yescomplemented
26#16864061C22132yescomplemented
27#16864059C22164yescomplemented
28#16864026C22132yescomplemented
29#16864024C22116yescomplemented
30#16864023C22132yescomplemented
31#16863952C22132yescomplemented
32#16863949C22116yescomplemented
33C2×#14524043C2212yes—
34C2×#14524042C2212yes—
35C2×#14524042C2212yes—
36C2×#14524042C2214yes—
37C2×#14524042C2214yes—
38C2×#14524042C2212yes—
39C2×#14524042C2211yescharacteristic
40C2×#14524042C2212yes—
41C2×#14524042C2212yes—
42C2×#14524042C2211yescharacteristic
43C2×#14524042C22116yescomplemented
44C2×#14524041C2214yes—
45C2×#14524041C2214yes—
46C4⋊Q8×D67C22132yescomplemented
47C2×#14524035C2212yes—
48C2×#14524034C2211yescharacteristic
49C2×#14524034C2212yes—
50C2×#14524034C2211yescharacteristic
51C2×#14524033C2214yes—
52C2×#14524033C2214yes—
53C2×#14524023C2214yes—
54C2×#14524021C2214yes—
55C2×#14524021C2214yes—
56C2×#14524021C2214yes—
57C2×#14524021C2214yes—
58C2×#14524020C2214yes—
59C2×#14524020C2212yes—
60C2×#14524020C2212yes—
61C2×#14524019C2214yes—
62#16863877C22116yes—
63#16863876C22116yes—
64#16863864C22116yes—
65C2×C4×Dic134C2212yes—
66C2×C4×Dic134C2212yes—
67C2×C4×Dic134C2212yes—
68C2×#14524008C2211yescharacteristic
69C2×#14524008C2211yescharacteristic
70C2×#14524008C2212yes—
71C2×#14524008C2214yes—
72C2×#14524008C2214yes—
73C2×C4×D268C2212yes—
74C2×#14524005C2211yescharacteristic
75C2×#14524005C2211yescharacteristic
76C2×#14524005C2212yes—
77C2×C4×C22⋊D67C2214yes—
78C2×(C22⋊D67)⋊C4C2212yes—
79C2×(C22⋊D67)⋊C4C2212yes—
80C2×(C22⋊D67)⋊C4C2214yes—
81C2×#14524002C2211yescharacteristic
82C2×#14524001C2212yes—
83C2×#14524001C2212yes—
84C2×#14524000C2212yes—
85C22×C4⋊Dic67C2211yescharacteristic
86C22×Dic67⋊C4C2212yes—
87C2×C4⋊C4×D67C2212yes—
88C2×C4⋊C4×D67C2212yes—
89C2×C4⋊C4×D67C2214yes—
90C22×C4×Dic67C2211yescharacteristic
91C2×C42×D67C2212yes—
92#544×C67C22116yescomplemented
93C2×C4⋊Q8×C67C2212yes—
94C2×C4⋊Q8×C67C2212yes—
95C2×#125×C67C2212yes—
96C2×#125×C67C2212yes—
97C2×C22⋊Q8×C67C2214yes—
98C2×#117×C67C2211yescharacteristic
99C2×#117×C67C2211yescharacteristic
100C22×C4⋊C4×C67C2211yescharacteristic
101C2×#11761628Q8116yescomplemented
102C2×#11761628C2318yes—
103C22×Dic134—48no—
104C22×Dic134C2312yes—
105C22×Dic134C2314yes—
106C22×Dic134C2312yes—
107C22×Dic134C23116yes—
108C22×Dic134C2314yes—
109C22×Dic134C2314yes—
110C22×Dic134C2311yescharacteristic
111C2×Q8×D67—416no—
112C2×Q8×D67C23132yes—
113C22×D268C2311yescharacteristic
114C22×C22⋊D67C2312yes—
115C23×Dic67C2311yescharacteristic
116C23×Dic67C2311yescharacteristic
117C23×Dic67C2312yes—
118C22×C4×D67C2312yes—
119C22×C4×D67C2312yes—
120C22×C4×D67C2314yes—
121C22×C4×D67C2314yes—
122C22×C4×D67C2312yes—
123#14524043C23116yes—
124#14524042C23116yes—
125#14524042C23116yes—
126#14524042C23132yes—
127#14524042C23132yes—
128#14524042C23116yes—
129#14524042C23116yes—
130#14524042C2318yes—
131#14524042C23116yes—
132#14524042C2318yes—
133#14524041C23132yes—
134#14524041C23132yes—
135#14524035C23116yes—
136#14524034C2318yes—
137#14524034C23116yes—
138#14524034C2318yes—
139#14524033C23132yes—
140#14524033C23132yes—
141#14524023C23132yes—
142#14524021C23132yes—
143#14524021C23132yes—
144#14524021C23132yes—
145#14524021C23132yes—
146#14524020C23132yes—
147#14524020C23116yes—
148#14524020C23116yes—
149#14524019C23132yes—
150C4×Dic134C23116yes—
151C4×Dic134C23116yes—
152C4×Dic134C23116yes—
153#14524008C23132yes—
154#14524008C23132yes—
155#14524008C2318yes—
156#14524008C2318yes—
157#14524008C23116yes—
158C4×D268C23116yes—
159#14524005C2318yes—
160#14524005C23116yes—
161#14524005C2318yes—
162C4×C22⋊D67C23132yes—
163(C22⋊D67)⋊C4C23116yes—
164(C22⋊D67)⋊C4C23132yes—
165(C22⋊D67)⋊C4C23116yes—
166#14524002C2318yes—
167#14524001C23116yes—
168#14524001C23116yes—
169#14524000C23116yes—
170C2×C4⋊Dic67C2318yes—
171C2×C4⋊Dic67C2311yescharacteristic
172C2×C4⋊Dic67C2312yes—
173C2×C4⋊Dic67C2314yes—
174C2×C4⋊Dic67C2312yes—
175C2×C4⋊Dic67C2311yescharacteristic
176C2×C4⋊Dic67C2312yes—
177C2×C4⋊Dic67C2312yes—
178C2×Dic67⋊C4C23116yes—
179C2×Dic67⋊C4C2312yes—
180C2×Dic67⋊C4C2314yes—
181C2×Dic67⋊C4C2314yes—
182C2×Dic67⋊C4C2314yes—
183C2×Dic67⋊C4C2314yes—
184C2×Dic67⋊C4C2312yes—
185C2×Dic67⋊C4C2312yes—
186C2×Dic67⋊C4C2312yes—
187C2×Dic67⋊C4C2314yes—
188C2×Dic67⋊C4C2314yes—
189C2×Dic67⋊C4C2312yes—
190C2×Dic67⋊C4C2312yes—
191C4⋊C4×D67C23116yes—
192C4⋊C4×D67C23116yes—
193C4⋊C4×D67C23132yes—
194C2×C22⋊Dic67C2312yes—
195C2×(C2×D67)⋊C4C2312yes—
196C2×(C2×D67)⋊C4C2312yes—
197C2×(C2×D67)⋊C4C2314yes—
198C2×(C2×D67)⋊C4C2314yes—
199C2×C4×Dic67C2311yescharacteristic
200C2×C4×Dic67C2312yes—
201C2×C4×Dic67C2312yes—
202C2×C4×Dic67C2311yescharacteristic
203C2×C4×Dic67C2311yescharacteristic
204C2×C4×Dic67C2311yescharacteristic
205C2×C4×Dic67C2318yes—
206C2×C4×Dic67C2314yes—
207C2×C4×Dic67C2314yes—
208C2×C4×Dic67C2312yes—
209C42×D67C23116yes—
210C22×Q8×C67C2314yes—
211C23×C4×C67C2312yes—
212C23×C4×C67C2311yescharacteristic
213C4⋊Q8×C67C23116yes—
214C4⋊Q8×C67C23116yes—
215#125×C67C23116yes—
216#125×C67C23116yes—
217C22⋊Q8×C67C23132yes—
218#117×C67C2318yes—
219#117×C67C2318yes—
220C2×C4⋊C4×C67C2312yes—
221C2×C4⋊C4×C67C2312yes—
222C2×C4⋊C4×C67C2318yes—
223C2×C4⋊C4×C67C2311yescharacteristic
224C2×C4⋊C4×C67C2311yescharacteristic
225C2×C4⋊C4×C67C2311yescharacteristic
226C2×C4⋊C4×C67C2311yescharacteristic
227C2×C4⋊C4×C67C2314yes—
228C2×C4⋊C4×C67C2314yes—
229C2×C4⋊C4×C67C2314yes—
230C2×C22⋊C4×C67C2312yes—
231C2×C22⋊C4×C67C2312yes—
232C2×C42×C67C2312yes—
233C2×C42×C67C2312yes—
234C23×D67C2412yes—
235#11761628C2×Q8164yescomplemented
236C2×Dic134—28no—
237C2×Dic134—216no—
238C2×Dic134—28no—
239C2×Dic134—432no—
240C2×Dic134—48no—
241C2×Dic134—48no—
242C2×Dic134C2×Q818yescomplemented
243C2×Dic134C2418yes—
244C2×Dic134C24116yes—
245C2×Dic134C2418yes—
246C2×Dic134C24116yes—
247C2×Dic134C24116yes—
248C2×Dic134C2414yes—
249Q8×D67—464no—
250C2×D268C2×Q818yescomplemented
251C2×D268C2414yes—
252C2×C22⋊D67C2×Q8116yescomplemented
253C2×C22⋊D67C2418yes—
254C22×Dic67—24no—
255C22×Dic67—24no—
256C22×Dic67—44no—
257C22×Dic67C2412yes—
258C22×Dic67C2411yescharacteristic
259C22×Dic67C2411yescharacteristic
260C22×Dic67C2414yes—
261C22×Dic67C2414yes—
262C22×Dic67C2414yes—
263C22×Dic67C2412yes—
264C22×Dic67C2418yes—
265C22×Dic67C2412yes—
266C22×Dic67C2411yescharacteristic
267C22×Dic67C2411yescharacteristic
268C2×C4×D67—28no—
269C2×C4×D67—28no—
270C2×C4×D67—48no—
271C2×C4×D67—48no—
272C2×C4×D67C2×Q8116yescomplemented
273C2×C4×D67C2418yes—
274C2×C4×D67C2418yes—
275C2×C4×D67C24116yes—
276C2×C4×D67C24116yes—
277C2×C4×D67C2418yes—
278C4⋊Dic67C2414yes—
279C4⋊Dic67C2418yes—
280C4⋊Dic67C24116yes—
281C4⋊Dic67C2418yes—
282C4⋊Dic67C2414yes—
283C4⋊Dic67C2418yes—
284C4⋊Dic67C2418yes—
285Dic67⋊C4C2418yes—
286Dic67⋊C4C24116yes—
287Dic67⋊C4C24116yes—
288Dic67⋊C4C24116yes—
289Dic67⋊C4C24116yes—
290Dic67⋊C4C2418yes—
291Dic67⋊C4C2418yes—
292Dic67⋊C4C2418yes—
293Dic67⋊C4C24116yes—
294Dic67⋊C4C24116yes—
295Dic67⋊C4C2418yes—
296Dic67⋊C4C2418yes—
297C22⋊Dic67C2418yes—
298(C2×D67)⋊C4C2418yes—
299(C2×D67)⋊C4C2418yes—
300(C2×D67)⋊C4C24116yes—
301(C2×D67)⋊C4C24116yes—
302C4×Dic67C2414yes—
303C4×Dic67C2418yes—
304C4×Dic67C2418yes—
305C4×Dic67C2414yes—
306C4×Dic67C2414yes—
307C4×Dic67C2414yes—
308C4×Dic67C24116yes—
309C4×Dic67C24116yes—
310C4×Dic67C2418yes—
311C24×C67C2411yescharacteristic
312C2×Q8×C67—48no—
313C2×Q8×C67C24116yes—
314C22×C4×C67—44no—
315C22×C4×C67C2×Q818yescomplemented
316C22×C4×C67C2412yes—
317C22×C4×C67C2412yes—
318C22×C4×C67C2412yes—
319C22×C4×C67C2412yes—
320C22×C4×C67C2414yes—
321C22×C4×C67C2418yes—
322C22×C4×C67C2411yescharacteristic
323C22×C4×C67C2411yescharacteristic
324C22×C4×C67C2414yes—
325C4⋊C4×C67C2418yes—
326C4⋊C4×C67C2418yes—
327C4⋊C4×C67C2414yes—
328C4⋊C4×C67C2414yes—
329C4⋊C4×C67C2414yes—
330C4⋊C4×C67C2414yes—
331C4⋊C4×C67C24116yes—
332C4⋊C4×C67C24116yes—
333C4⋊C4×C67C24116yes—
334C22⋊C4×C67C2418yes—
335C22⋊C4×C67C2418yes—
336C42×C67C2418yes—
337C42×C67C2418yes—
338C23×C67—22no—
339C23×C67—22no—
340C23×C67C22×Q814yes—
341C23×C67C2512yes—
342C23×C67C2511yescharacteristic
343C22×D67—24no—
344C22×D67—24no—
345C22×D67C22×Q818yes—
346C22×D67C2514yes—
347Q8×C67—416no—
348C2×C4×C67—28no—
349C2×C4×C67—24no—
350C2×C4×C67—24no—
351C2×C4×C67—24no—
352C2×C4×C67—24no—
353C2×C4×C67—48no—
354C2×C4×C67C22×Q814yes—
355C2×C4×C67C22×Q814yes—
356C2×C4×C67C22×Q8116yescomplemented
357C2×C4×C67C2514yes—
358C2×C4×C67C2514yes—
359C2×C4×C67C2514yes—
360C2×C4×C67C2514yes—
361C2×C4×C67C2518yes—
362C2×C4×C67C2512yes—
363C2×C4×C67C2512yes—
364C22⋊D67C22×Q8132yescomplemented
365C2×Dic67—24no—
366C2×Dic67—28no—
367C2×Dic67—22no—
368C2×Dic67—22no—
369C2×Dic67—24no—
370C2×Dic67—28no—
371C2×Dic67—28no—
372C2×Dic67—48no—
373C2×Dic67C22×Q818yes—
374C2×Dic67H(5,𝔽2)14yes—
375C2×Dic672−1+414yes—
376C2×Dic67C2514yes—
377C2×Dic67C2512yes—
378C2×Dic67C2512yes—
379C2×Dic67C2518yes—
380C2×Dic67C2514yes—
381C2×Dic67C2514yes—
382C2×Dic67C2512yes—
383C2×Dic67C2512yes—
384D268C22×Q8116yescomplemented
385C4×D67—216no—
386C4×D67—216no—
387C4×D67—416no—
388C4×D67—416no—
389C4×D67C22×Q8132yescomplemented
390Dic134—216no—
391Dic134—232no—
392Dic134—216no—
393Dic134—416no—
394Dic134—416no—
395Dic134C22×Q8116yescomplemented
396C22×C67—22no—
397C22×C67—22no—
398C22×C67—28no—
399C22×C67C23×Q814yes—
400C22×C67C23×Q812yes—
401C22×C67C2×H(5,𝔽2)12yes—
402C22×C67C2×2−1+412yes—
403C22×C67C2611yescharacteristic
404C2×D67—24no—
405C2×D67—24no—
406C2×D67—216no—
407C2×D67C23×Q818yes—
408C4×C67—28no—
409C4×C67—24no—
410C4×C67—24no—
411C4×C67—24no—
412C4×C67—24no—
413C4×C67C23×Q814yes—
414C4×C67C23×Q814yes—
415Dic67—24no—
416Dic67—28no—
417Dic67—22no—
418Dic67—24no—
419Dic67—22no—
420Dic67C23×Q818yes—
421Dic67C2×H(5,𝔽2)14yes—
422Dic67C2×2−1+414yes—
423C2×#3503—671nomaximal, Sylow
424C2×C67—24no—
425C2×C67#350314yescomplemented
426C2×C67C24×Q811yescharacteristic
427C2×C67C22×H(5,𝔽2)11yescharacteristic
428C2×C67C22×2−1+411yescharacteristic
429D67—28no—
430#3503—6732no—
431C2×Q82—672no—
432C2×#557—672no—
433C2×#554—672no—
434C2×#554—674no—
435C2×D4×Q8—672no—
436C2×D4×Q8—674no—
437C2×#544—672no—
438C2×#544—672no—
439C2×#544—671no—
440C2×#544D6711yescharacteristic, complemented
441C2×#533—672no—
442C2×#533—671no—
443C22×C4⋊Q8—672no—
444C22×C4⋊Q8—671no—
445C2×#520—671no—
446C2×#520—671no—
447C2×C4×#41—671no—
448C67C2×#350311yescharacteristic, complemented, Sylow
449C22×#41—671no—
450C23×Q8—674no—
451C23×Q8—672no—
452Q82—6732no—
453#557—6732no—
454#554—6732no—
455#554—6764no—
456D4×Q8—6732no—
457D4×Q8—6764no—
458#544—6732no—
459#544—6732no—
460#544—6716no—
461#544C2×D67116yescomplemented
462#533—6732no—
463#533—6716no—
464C2×C4⋊Q8—674no—
465C2×C4⋊Q8—674no—
466C2×C4⋊Q8—6732no—
467C2×C4⋊Q8—671no—
468C2×C4⋊Q8—672no—
469C2×C4⋊Q8—672no—
470C2×C4⋊Q8—674no—
471C2×C4⋊Q8—672no—
472C2×C4⋊Q8—672no—
473C2×C4⋊Q8—6716no—
474C2×C4⋊Q8—671no—
475C2×C4⋊Q8—674no—
476C2×C4⋊Q8—672no—
477C2×C4⋊Q8—672no—
478C2×C4⋊Q8C2×D6712yes—
479C2×C4⋊Q8C2×D6712yes—
480C2×#125—671no—
481C2×#125—671no—
482C2×#125—674no—
483C2×#125—674no—
484C2×#125—672no—
485C2×#125—672no—
486C2×#125C2×D6712yes—
487C2×#125C2×D6712yes—
488C2×C22⋊Q8—674no—
489C2×C22⋊Q8—674no—
490C2×C22⋊Q8—674no—
491C2×C22⋊Q8—674no—
492C2×C22⋊Q8—674no—
493C2×C22⋊Q8—674no—
494C2×C22⋊Q8—672no—
495C2×C22⋊Q8—672no—
496C2×C22⋊Q8—674no—
497C2×C22⋊Q8C2×D6714yes—
498#520—6716no—
499#520—6716no—
500C4×#41—6716no—
501C2×C4×Q8—671no—
502C2×C4×Q8—671no—
503C2×C4×Q8—672no—
504C2×C4×Q8—674no—
505C2×C4×Q8—674no—
506C2×C4×Q8—672no—
507C2×C4×Q8—672no—
508C2×C4×Q8—672no—
509C2×C4×D4—674no—
510C2×C4×D4—671no—
511C2×C4×D4—671no—
512C2×C4×D4—672no—
513C2×C4×D4—672no—
514C2×C4×D4—672no—
515C2×C4×D4—674no—
516C2×C4×D4—672no—
517C2×#117—671no—
518C2×#117—672no—
519C2×#117—672no—
520C2×#117—672no—
521C2×#117C2×D6711yescharacteristic
522C2×#117C2×D6711yescharacteristic
523C22×C4⋊C4—671no—
524C22×C4⋊C4—672no—
525C22×C4⋊C4—672no—
526C22×C4⋊C4—672no—
527C22×C4⋊C4—674no—
528C22×C4⋊C4C2×D6711yescharacteristic
529C22×C42—671no—
530C22×C42—672no—
531C2×#41—6716no—
532C2×#41—678no—
533C22×Q8—2688no—
534C22×Q8—26816no—
535C22×Q8—6732no—
536C22×Q8—674no—
537C22×Q8—674no—
538C22×Q8—6716no—
539C22×Q8—671no—
540C22×Q8—672no—
541C22×Q8—674no—
542C22×Q8—672no—
543C22×Q8C22×D6714yes—
544C22×D4—672no—
545C22×D4—671no—
546C23×C4—672no—
547C23×C4—674no—
548C23×C4—674no—
549C23×C4—672no—
550C23×C4—671no—
551C23×C4—671no—
552C23×C4—672no—
553C23×C4—672no—
554C23×C4C22×D6712yes—
555C23×C4C22×D6711yescharacteristic
556C4⋊Q8—6732no—
557C4⋊Q8—6732no—
558C4⋊Q8—678no—
559C4⋊Q8—6716no—
560C4⋊Q8—6716no—
561C4⋊Q8—6732no—
562C4⋊Q8—6716no—
563C4⋊Q8—6716no—
564C4⋊Q8—678no—
565C4⋊Q8—6732no—
566C4⋊Q8—6716no—
567C4⋊Q8—6716no—
568C4⋊Q8C22×D67116yes—
569C4⋊Q8C22×D67116yes—
570#125—678no—
571#125—678no—
572#125—6732no—
573#125—6732no—
574#125—6716no—
575#125—6716no—
576#125C22×D67116yes—
577#125C22×D67116yes—
578C22⋊Q8—6732no—
579C22⋊Q8—6732no—
580C22⋊Q8—6732no—
581C22⋊Q8—6732no—
582C22⋊Q8—6732no—
583C22⋊Q8—6732no—
584C22⋊Q8—6716no—
585C22⋊Q8—6716no—
586C22⋊Q8—6732no—
587C22⋊Q8C22×D67132yes—
588C4×Q8—678no—
589C4×Q8—678no—
590C4×Q8—6716no—
591C4×Q8—6732no—
592C4×Q8—6732no—
593C4×Q8—6716no—
594C4×Q8—6716no—
595C4×Q8—6716no—
596C4×D4—6732no—
597C4×D4—678no—
598C4×D4—678no—
599C4×D4—6716no—
600C4×D4—6716no—
601C4×D4—6716no—
602C4×D4—6732no—
603C4×D4—6716no—
604#117—678no—
605#117—6716no—
606#117—6716no—
607#117—6716no—
608#117C22×D6718yes—
609#117C22×D6718yes—
610C2×C4⋊C4—672no—
611C2×C4⋊C4—671no—
612C2×C4⋊C4—674no—
613C2×C4⋊C4—672no—
614C2×C4⋊C4—674no—
615C2×C4⋊C4—674no—
616C2×C4⋊C4—672no—
617C2×C4⋊C4—678no—
618C2×C4⋊C4—674no—
619C2×C4⋊C4—674no—
620C2×C4⋊C4—6716no—
621C2×C4⋊C4—671no—
622C2×C4⋊C4—672no—
623C2×C4⋊C4—672no—
624C2×C4⋊C4—672no—
625C2×C4⋊C4—674no—
626C2×C4⋊C4—672no—
627C2×C4⋊C4—672no—
628C2×C4⋊C4—672no—
629C2×C4⋊C4—674no—
630C2×C4⋊C4—672no—
631C2×C4⋊C4—6716no—
632C2×C4⋊C4—6716no—
633C2×C4⋊C4—6732no—
634C2×C4⋊C4C22×D6711yescharacteristic
635C2×C4⋊C4C22×D6712yes—
636C2×C4⋊C4C22×D6714yes—
637C2×C4⋊C4C22×D6712yes—
638C2×C4⋊C4C22×D6718yes—
639C2×C4⋊C4C22×D6711yescharacteristic
640C2×C4⋊C4C22×D6711yescharacteristic
641C2×C4⋊C4C22×D6711yescharacteristic
642C2×C4⋊C4C22×D6714yes—
643C2×C4⋊C4C22×D6714yes—
644C2×C22⋊C4—672no—
645C2×C22⋊C4—674no—
646C2×C22⋊C4—672no—
647C2×C22⋊C4—672no—
648C2×C22⋊C4—674no—
649C2×C22⋊C4C22×D6712yes—
650C2×C22⋊C4C22×D6712yes—
651C2×C42—671no—
652C2×C42—674no—
653C2×C42—674no—
654C2×C42—672no—
655C2×C42—672no—
656C2×C42—672no—
657C2×C42—671no—
658C2×C42—671no—
659C2×C42—678no—
660C2×C42—671no—
661C2×C42—6716no—
662C2×C42C22×D6712yes—
663C2×C42C22×D6712yes—
664C24—672no—
665C24C23×D6711yescharacteristic
666#41—6764no—
667C2×Q8—48no—
668C2×Q8—2688no—
669C2×Q8—2688no—
670C2×Q8—26832no—
671C2×Q8—26864no—
672C2×Q8—678no—
673C2×Q8—6716no—
674C2×Q8—6716no—
675C2×Q8—674no—
676C2×Q8—678no—
677C2×Q8—6716no—
678C2×Q8—678no—
679C2×Q8—13416no—
680C2×Q8—1348no—
681C2×Q8—1348no—
682C2×Q8C23×D67116yes—
683C2×D4—6716no—
684C2×D4—678no—
685C2×D4—678no—
686C2×D4—674no—
687C22×C4—44no—
688C22×C4—2688no—
689C22×C4—2688no—
690C22×C4—2684no—
691C22×C4—678no—
692C22×C4—6716no—
693C22×C4—6716no—
694C22×C4—672no—
695C22×C4—671no—
696C22×C4—671no—
697C22×C4—6716no—
698C22×C4—678no—
699C22×C4—674no—
700C22×C4—674no—
701C22×C4—672no—
702C22×C4—671no—
703C22×C4—671no—
704C22×C4—672no—
705C22×C4—674no—
706C22×C4—678no—
707C22×C4—678no—
708C22×C4—1348no—
709C22×C4—1348no—
710C22×C4—1344no—
711C22×C4—1344no—
712C22×C4Q8×D6718yescomplemented
713C22×C4C23×D6712yes—
714C22×C4C23×D6712yes—
715C22×C4C23×D6712yes—
716C22×C4C23×D6714yes—
717C22×C4C23×D6712yes—
718C22×C4C23×D6718yes—
719C22×C4C23×D6711yescharacteristic
720C22×C4C23×D6711yescharacteristic
721C22×C4C23×D6714yes—
722C4⋊C4—678no—
723C4⋊C4—674no—
724C4⋊C4—6716no—
725C4⋊C4—678no—
726C4⋊C4—6716no—
727C4⋊C4—6716no—
728C4⋊C4—678no—
729C4⋊C4—6716no—
730C4⋊C4—6716no—
731C4⋊C4—674no—
732C4⋊C4—678no—
733C4⋊C4—678no—
734C4⋊C4—678no—
735C4⋊C4—6716no—
736C4⋊C4—678no—
737C4⋊C4—678no—
738C4⋊C4—678no—
739C4⋊C4—6716no—
740C4⋊C4—678no—
741C4⋊C4C23×D6714yes—
742C4⋊C4C23×D6718yes—
743C4⋊C4C23×D67116yes—
744C4⋊C4C23×D6718yes—
745C4⋊C4C23×D6714yes—
746C4⋊C4C23×D6714yes—
747C4⋊C4C23×D6714yes—
748C4⋊C4C23×D67116yes—
749C4⋊C4C23×D67116yes—
750C22⋊C4—678no—
751C22⋊C4—6716no—
752C22⋊C4—678no—
753C22⋊C4—678no—
754C22⋊C4—6716no—
755C22⋊C4C23×D6718yes—
756C22⋊C4C23×D6718yes—
757C42—674no—
758C42—674no—
759C42—678no—
760C42—678no—
761C42—674no—
762C42—674no—
763C42—6716no—
764C42—6716no—
765C42—678no—
766C42C23×D6718yes—
767C42C23×D6718yes—
768C23—22no—
769C23—22no—
770C23—678no—
771C23—674no—
772C23—1344no—
773C23—1344no—
774C23C2×Q8×D6714yes—
775C23C24×D6712yes—
776C23C24×D6711yescharacteristic
777Q8—416no—
778Q8—26816no—
779Q8—26816no—
780Q8—6716no—
781Q8—13432no—
782Q8—13416no—
783Q8—13416no—
784D4—6732no—
785D4—6716no—
786C2×C4—28no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—48no—
792C2×C4—26816no—
793C2×C4—26816no—
794C2×C4—2688no—
795C2×C4—678no—
796C2×C4—674no—
797C2×C4—674no—
798C2×C4—674no—
799C2×C4—672no—
800C2×C4—672no—
801C2×C4—6732no—
802C2×C4—674no—
803C2×C4—672no—
804C2×C4—672no—
805C2×C4—674no—
806C2×C4—678no—
807C2×C4—13416no—
808C2×C4—13416no—
809C2×C4—1348no—
810C2×C4—1348no—
811C2×C4—1344no—
812C2×C4—1348no—
813C2×C4—1342no—
814C2×C4—1342no—
815C2×C4—1344no—
816C2×C4C2×Q8×D6714yes—
817C2×C4C2×Q8×D6714yes—
818C2×C4C2×Q8×D67116yescomplemented
819C2×C4C24×D6714yes—
820C2×C4C24×D6714yes—
821C2×C4C24×D6714yes—
822C2×C4C24×D6718yes—
823C2×C4C24×D6714yes—
824C2×C4C24×D6712yes—
825C2×C4C24×D6712yes—
826C22—22no—
827C22—22no—
828C22—28no—
829C22—678no—
830C22—1344no—
831C22—1344no—
832C22—13416no—
833C22C22×Q8×D6714yes—
834C22C22×Q8×D6712yes—
835C22H(5,𝔽2)×D6712yes—
836C222−1+4×D6712yes—
837C22C25×D6711yescharacteristic
838C4—28no—
839C4—24no—
840C4—24no—
841C4—24no—
842C4—24no—
843C4—678no—
844C4—674no—
845C4—674no—
846C4—1344no—
847C4—1348no—
848C4—1342no—
849C4—1342no—
850C4—1344no—
851C4C22×Q8×D6714yes—
852C4C22×Q8×D6714yes—
853C2—24no—
854C2—1348no—
855C2#2257402414yesdirect product factor
856C2C23×Q8×D6711yescharacteristic
857C2C2×H(5,𝔽2)×D6711yescharacteristic
858C2C2×2−1+4×D6711yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#544×C67C2
socleC23×C67C25
prime radicalC22×#11761628C22
hypercenterC2×#544D67
hypocenterC67C2×#3503
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #22574024C2direct (N × H)
2. C2×#16864126C2semidirect
3. C2×#16864123C2semidirect
4. C2×#16864102C2semidirect
5. C2×#16864100C2semidirect
6. C2×#16864061C2semidirect
7. C2×#16864059C2semidirect
8. C2×#16864026C2semidirect
9. C2×#16864024C2semidirect
10. C2×#16864023C2semidirect
11. C2×#16863952C2semidirect
12. C2×#16863949C2semidirect
13. C22×#14524042C2semidirect
14. C2×C4⋊Q8×D67C2semidirect
18. C2×#544×C67C2semidirect
22. #16864126C22semidirect
23. #16864123C22semidirect
24. #16864102C22semidirect
25. #16864100C22semidirect
26. #16864061C22semidirect
27. #16864059C22semidirect
28. #16864026C22semidirect
29. #16864024C22semidirect
30. #16864023C22semidirect
31. #16863952C22semidirect
32. #16863949C22semidirect
43. C2×#14524042C22semidirect
46. C4⋊Q8×D67C22semidirect
92. #544×C67C22semidirect
101. C2×#11761628Q8semidirect
235. #11761628C2×Q8semidirect
242. C2×Dic134C2×Q8semidirect
250. C2×D268C2×Q8semidirect
252. C2×C22⋊D67C2×Q8semidirect
272. C2×C4×D67C2×Q8semidirect
315. C22×C4×C67C2×Q8semidirect
356. C2×C4×C67C22×Q8semidirect
364. C22⋊D67C22×Q8semidirect
384. D268C22×Q8semidirect
389. C4×D67C22×Q8semidirect
395. Dic134C22×Q8semidirect
425. C2×C67#3503semidirect
440. C2×#544D67semidirect
448. C67C2×#3503semidirect
461. #544C2×D67semidirect
712. C22×C4Q8×D67semidirect
818. C2×C4C2×Q8×D67semidirect
855. C2#22574024direct (N × H)

Maximal subgroups

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

subgroupindex
#225740242
C2×#168641262
C2×#168641232
C2×#168641022
C2×#168641002
C2×#168640612
C2×#168640592
C2×#168640262
C2×#168640242
C2×#168640232
C2×#168639522
C2×#168639492
C22×#145240422
C2×C4⋊Q8×D672
C2×#168638772
C2×#168638762
C2×#168638642
C2×#544×C672
C2×#350367