Finite Group Databasebeta

← C2×#22574650 #31763438

Subgroups — C2×#22574650 #31763438

Order 17152.

7086 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574650C2132yesmaximal, direct product factor
2C2×#16864145C214yesmaximal, complemented
3C2×#16864121C211yesmaximal, characteristic, complemented
4C2×#16864120C211yesmaximal, characteristic, complemented
5C2×#16864101C212yesmaximal, complemented
6C2×#16864094C212yesmaximal, complemented
7C2×#16864061C211yesmaximal, characteristic, complemented
8C2×Q8×C22⋊D67C212yesmaximal, complemented
9C2×#16864057C212yesmaximal, complemented
10C2×#16864049C211yesmaximal, characteristic, complemented
11C2×#16864023C212yesmaximal, complemented
12C2×#16864020C212yesmaximal, complemented
13C2×#16864007C212yesmaximal, complemented
14C2×#16863993C214yesmaximal, complemented
15C2×#16863971C212yesmaximal, complemented
16C2×#16863930C211yesmaximal, characteristic, complemented
17C2×#16863930C211yesmaximal, characteristic, complemented
18C22×C4⋊Q8×C67C211yesmaximal, characteristic, complemented
19C22×#11761629C2212yes—
20C22×Q8×D67C2212yes—
21#16864145C22164yescomplemented
22#16864121C22116yescomplemented
23#16864120C22116yescomplemented
24#16864101C22132yescomplemented
25#16864094C22132yescomplemented
26#16864061C22116yescomplemented
27Q8×C22⋊D67C22132yescomplemented
28#16864057C22132yescomplemented
29#16864049C22116yescomplemented
30#16864023C22132yescomplemented
31#16864020C22132yescomplemented
32#16864007C22132yescomplemented
33#16863993C22164yescomplemented
34#16863971C22132yescomplemented
35C2×#14524042C2212yes—
36C2×#14524041C2214yes—
37C2×#14524041C2212yes—
38#16863930C22116yescomplemented
39#16863930C22116yescomplemented
40C2×#14524038C2214yes—
41C2×#14524038C2214yes—
42C2×#14524038C2214yes—
43C2×#14524037C2212yes—
44C2×#14524037C2212yes—
45C2×#14524035C2211yescharacteristic
46C2×#14524035C2211yescharacteristic
47C2×#14524034C2212yes—
48C2×#14524033C2214yes—
49C2×#14524033C2214yes—
50C2×#14524033C2214yes—
51C2×#14524032C2214yes—
52C2×#14524032C2212yes—
53C2×#14524031C2211yescharacteristic
54C2×#14524031C2211yescharacteristic
55C2×#14524028C2214yes—
56C2×#14524028C2214yes—
57C2×#14524028C2214yes—
58C2×#14524026C2212yes—
59C2×#14524026C2212yes—
60C2×#14524023C2212yes—
61C2×#14524022C2211yescharacteristic
62C2×#14524022C2214yes—
63C2×#14524022C2211yescharacteristic
64C2×#14524021C2214yes—
65C2×#14524021C2214yes—
66C2×#14524021C2214yes—
67C2×#14524019C2214yes—
68C2×#14524019C2214yes—
69C2×#14524019C2212yes—
70C2×#14524019C2212yes—
71C2×#14524018C2212yes—
72C2×#14524017C2211yescharacteristic
73C2×#14524017C2214yes—
74C2×#14524017C2211yescharacteristic
75C2×Q8×Dic67C2212yes—
76C2×Q8×Dic67C2212yes—
77C2×C4×Dic134C2211yescharacteristic
78C2×C4×Dic134C2211yescharacteristic
79C2×#14524008C2212yes—
80C2×C4×D268C2211yescharacteristic
81C2×C4×D268C2211yescharacteristic
82C2×#14524005C2212yes—
83C2×C4×C22⋊D67C2212yes—
84C2×C4×C22⋊D67C2214yes—
85C2×C4×C22⋊D67C2214yes—
86C2×C4×C22⋊D67C2212yes—
87C2×#14524001C2212yes—
88C2×#14524000C2212yes—
89C2×#14524000C2212yes—
90C2×C4⋊C4×D67C2212yes—
91C23×Q8×C67C2212yes—
92C2×C4⋊Q8×C67C2212yes—
93C2×C4⋊Q8×C67C2212yes—
94C2×C4⋊Q8×C67C2212yes—
95C2×C4⋊Q8×C67C2211yescharacteristic
96C2×C4⋊Q8×C67C2211yescharacteristic
97C2×C4⋊Q8×C67C22116yescomplemented
98C22×C4⋊C4×C67C2212yes—
99C22×C4⋊C4×C67C2212yes—
100C22×C42×C67C2211yescharacteristic
101C2×#11761629—48no—
102C2×#11761629C23116yes—
103C22×Dic134C2311yescharacteristic
104C22×Dic134C2311yescharacteristic
105C22×Dic134C2314yes—
106C2×Q8×D67—48no—
107C2×Q8×D67C23116yes—
108C22×D268C2311yescharacteristic
109C22×D268C2311yescharacteristic
110C22×D268C2314yes—
111C22×C22⋊D67C2312yes—
112C22×C22⋊D67C2312yes—
113C22×C4×D67C2312yes—
114C22×C4×D67C2312yes—
115C22×C4×D67C2314yes—
116C22×C4×D67C2314yes—
117#14524042C23116yes—
118#14524041C23132yes—
119#14524041C23116yes—
120#14524038C23132yes—
121#14524038C23132yes—
122#14524038C23132yes—
123#14524037C23116yes—
124#14524037C23116yes—
125#14524035C2318yes—
126#14524035C2318yes—
127#14524034C23116yes—
128#14524033C23132yes—
129#14524033C23132yes—
130#14524033C23132yes—
131#14524032C23132yes—
132#14524032C23116yes—
133#14524031C2318yes—
134#14524031C2318yes—
135#14524028C23132yes—
136#14524028C23132yes—
137#14524028C23132yes—
138#14524026C23116yes—
139#14524026C23116yes—
140#14524023C23116yes—
141#14524022C2318yes—
142#14524022C23132yes—
143#14524022C2318yes—
144#14524021C23132yes—
145#14524021C23132yes—
146#14524021C23132yes—
147#14524019C23116yes—
148#14524019C23116yes—
149#14524019C23132yes—
150#14524019C23132yes—
151#14524018C23116yes—
152#14524017C2318yes—
153#14524017C23132yes—
154#14524017C2318yes—
155Q8×Dic67C23116yes—
156Q8×Dic67C23116yes—
157C4×Dic134C2318yes—
158C4×Dic134C2318yes—
159#14524008C23116yes—
160C4×D268C2318yes—
161C4×D268C2318yes—
162#14524005C23116yes—
163C4×C22⋊D67C23116yes—
164C4×C22⋊D67C23132yes—
165C4×C22⋊D67C23132yes—
166C4×C22⋊D67C23116yes—
167#14524001C23116yes—
168#14524000C23116yes—
169#14524000C23116yes—
170C2×C4⋊Dic67C2311yescharacteristic
171C2×C4⋊Dic67C2311yescharacteristic
172C2×C4⋊Dic67C2311yescharacteristic
173C2×C4⋊Dic67C2311yescharacteristic
174C2×C4⋊Dic67C2314yes—
175C2×C4⋊Dic67C2314yes—
176C2×Dic67⋊C4C2314yes—
177C2×Dic67⋊C4C2312yes—
178C2×Dic67⋊C4C2312yes—
179C2×Dic67⋊C4C2312yes—
180C2×Dic67⋊C4C2312yes—
181C2×Dic67⋊C4C2314yes—
182C2×Dic67⋊C4C2312yes—
183C2×Dic67⋊C4C2314yes—
184C2×Dic67⋊C4C2312yes—
185C2×Dic67⋊C4C2314yes—
186C2×Dic67⋊C4C2312yes—
187C2×Dic67⋊C4C2312yes—
188C4⋊C4×D67C23116yes—
189C2×C22⋊Dic67C2312yes—
190C2×C22⋊Dic67C2312yes—
191C2×(C2×D67)⋊C4C2312yes—
192C2×(C2×D67)⋊C4C2312yes—
193C2×(C2×D67)⋊C4C2312yes—
194C2×(C2×D67)⋊C4C2312yes—
195C2×(C2×D67)⋊C4C2314yes—
196C2×(C2×D67)⋊C4C2314yes—
197C2×(C2×D67)⋊C4C2312yes—
198C2×(C2×D67)⋊C4C2312yes—
199C2×(C2×D67)⋊C4C2314yes—
200C2×(C2×D67)⋊C4C2314yes—
201C2×(C2×D67)⋊C4C2312yes—
202C2×(C2×D67)⋊C4C2312yes—
203C2×C4×Dic67C2312yes—
204C2×C4×Dic67C2312yes—
205C2×C4×Dic67C2314yes—
206C2×C4×Dic67C2314yes—
207C22×Q8×C67—48no—
208C22×Q8×C67C2312yes—
209C22×Q8×C67C2312yes—
210C22×Q8×C67C23116yes—
211C22×Q8×C67C2314yes—
212C23×C4×C67C2311yescharacteristic
213C23×C4×C67C2311yescharacteristic
214C23×C4×C67C2311yescharacteristic
215C23×C4×C67C2314yes—
216C4⋊Q8×C67C23116yes—
217C4⋊Q8×C67C23116yes—
218C4⋊Q8×C67C2318yes—
219C4⋊Q8×C67C2318yes—
220C4⋊Q8×C67C23116yes—
221C2×C4⋊C4×C67C2312yes—
222C2×C4⋊C4×C67C2312yes—
223C2×C4⋊C4×C67C2312yes—
224C2×C4⋊C4×C67C2314yes—
225C2×C4⋊C4×C67C2314yes—
226C2×C4⋊C4×C67C2312yes—
227C2×C4⋊C4×C67C23116yes—
228C2×C4⋊C4×C67C23116yes—
229C2×C42×C67C2311yescharacteristic
230C2×C42×C67C2311yescharacteristic
231C2×C42×C67C2311yescharacteristic
232C2×C42×C67C2311yescharacteristic
233C2×C42×C67C2318yes—
234C23×D67C2412yes—
235C23×D67C2412yes—
236#11761629—432no—
237C2×Dic134—24no—
238C2×Dic134—24no—
239C2×Dic134—48no—
240C2×Dic134C2414yes—
241C2×Dic134C2414yes—
242C2×Dic134C24116yes—
243Q8×D67—432no—
244C2×D268—24no—
245C2×D268—24no—
246C2×D268—48no—
247C2×D268C2414yes—
248C2×D268C2414yes—
249C2×D268C24116yes—
250C2×C22⋊D67—28no—
251C2×C22⋊D67—28no—
252C2×C22⋊D67C2418yes—
253C2×C22⋊D67C2418yes—
254C22×Dic67C2412yes—
255C22×Dic67C2412yes—
256C22×Dic67C2412yes—
257C22×Dic67C2412yes—
258C22×Dic67C2412yes—
259C22×Dic67C2412yes—
260C2×C4×D67—28no—
261C2×C4×D67—28no—
262C2×C4×D67—48no—
263C2×C4×D67—48no—
264C2×C4×D67C2418yes—
265C2×C4×D67C2418yes—
266C2×C4×D67C24116yes—
267C2×C4×D67C24116yes—
268C4⋊Dic67C2414yes—
269C4⋊Dic67C2414yes—
270C4⋊Dic67C2414yes—
271C4⋊Dic67C2414yes—
272C4⋊Dic67C24116yes—
273C4⋊Dic67C24116yes—
274Dic67⋊C4C24116yes—
275Dic67⋊C4C2418yes—
276Dic67⋊C4C2418yes—
277Dic67⋊C4C2418yes—
278Dic67⋊C4C2418yes—
279Dic67⋊C4C24116yes—
280Dic67⋊C4C2418yes—
281Dic67⋊C4C24116yes—
282Dic67⋊C4C2418yes—
283Dic67⋊C4C24116yes—
284Dic67⋊C4C2418yes—
285Dic67⋊C4C2418yes—
286C22⋊Dic67C2418yes—
287C22⋊Dic67C2418yes—
288(C2×D67)⋊C4C2418yes—
289(C2×D67)⋊C4C2418yes—
290(C2×D67)⋊C4C2418yes—
291(C2×D67)⋊C4C2418yes—
292(C2×D67)⋊C4C24116yes—
293(C2×D67)⋊C4C24116yes—
294(C2×D67)⋊C4C2418yes—
295(C2×D67)⋊C4C2418yes—
296(C2×D67)⋊C4C24116yes—
297(C2×D67)⋊C4C24116yes—
298(C2×D67)⋊C4C2418yes—
299(C2×D67)⋊C4C2418yes—
300C4×Dic67C2418yes—
301C4×Dic67C2418yes—
302C4×Dic67C24116yes—
303C4×Dic67C24116yes—
304C24×C67C2411yescharacteristic
305C2×Q8×C67—28no—
306C2×Q8×C67—28no—
307C2×Q8×C67—48no—
308C2×Q8×C67—432no—
309C2×Q8×C67C2418yes—
310C2×Q8×C67C2418yes—
311C2×Q8×C67C24116yes—
312C22×C4×C67—24no—
313C22×C4×C67—24no—
314C22×C4×C67—24no—
315C22×C4×C67—48no—
316C22×C4×C67C2411yescharacteristic
317C22×C4×C67C2411yescharacteristic
318C22×C4×C67C2411yescharacteristic
319C22×C4×C67C2414yes—
320C22×C4×C67C2414yes—
321C22×C4×C67C2411yescharacteristic
322C22×C4×C67C2414yes—
323C22×C4×C67C2414yes—
324C22×C4×C67C2414yes—
325C22×C4×C67C24116yes—
326C22×C4×C67C2411yescharacteristic
327C22×C4×C67C2411yescharacteristic
328C4⋊C4×C67C2418yes—
329C4⋊C4×C67C2418yes—
330C4⋊C4×C67C2418yes—
331C4⋊C4×C67C24116yes—
332C4⋊C4×C67C24116yes—
333C4⋊C4×C67C2418yes—
334C42×C67C2414yes—
335C42×C67C2414yes—
336C42×C67C2414yes—
337C42×C67C2414yes—
338C23×C67—22no—
339C23×C67—22no—
340C23×C672−1+414yes—
341C23×C67C2512yes—
342C23×C67C2511yescharacteristic
343C22×D67—24no—
344C22×D67—24no—
345C22×D67—24no—
346C22×D67—24no—
347C22×D67—24no—
348C22×D67—24no—
349C22×D67C2514yes—
350C22×D67C2514yes—
351Q8×C67—216no—
352Q8×C67—216no—
353Q8×C67—416no—
354C2×C4×C67—22no—
355C2×C4×C67—28no—
356C2×C4×C67—28no—
357C2×C4×C67—28no—
358C2×C4×C67—22no—
359C2×C4×C67—22no—
360C2×C4×C67—22no—
361C2×C4×C67—28no—
362C2×C4×C67—28no—
363C2×C4×C67—416no—
364C2×C4×C67H(5,𝔽2)14yes—
365C2×C4×C672−1+414yes—
366C2×C4×C67C2512yes—
367C2×C4×C67C2512yes—
368C2×C4×C67C2512yes—
369C2×C4×C67C2512yes—
370C2×C4×C67C2518yes—
371C2×C4×C67C2518yes—
372C2×C4×C67C2512yes—
373C2×C4×C67C2512yes—
374C22⋊D67—216no—
375C22⋊D67—216no—
376C2×Dic67—24no—
377C2×Dic67—24no—
378C2×Dic67—24no—
379C2×Dic67—24no—
380C2×Dic67—24no—
381C2×Dic67—24no—
382C2×Dic67C2514yes—
383C2×Dic67C2514yes—
384C2×Dic67C2514yes—
385C2×Dic67C2514yes—
386C2×Dic67C2514yes—
387C2×Dic67C2514yes—
388D268—28no—
389D268—28no—
390D268—416no—
391C4×D67—216no—
392C4×D67—216no—
393C4×D67—416no—
394C4×D67—416no—
395Dic134—28no—
396Dic134—28no—
397Dic134—416no—
398C22×C67—22no—
399C22×C67—22no—
400C22×C67—28no—
401C22×C67C2×H(5,𝔽2)12yes—
402C22×C67C2×2−1+414yes—
403C22×C67C2×2−1+412yes—
404C22×C67C2×2−1+412yes—
405C22×C67C2611yescharacteristic
406C2×D67—24no—
407C2×D67—24no—
408C2×D67—24no—
409C2×D67—24no—
410C2×D67—24no—
411C2×D67—24no—
412C2×D67—48no—
413C2×D67—48no—
414C4×C67—28no—
415C4×C67—28no—
416C4×C67—22no—
417C4×C67—22no—
418C4×C67—22no—
419C4×C67—22no—
420C4×C67C2×H(5,𝔽2)14yes—
421C4×C67C2×2−1+414yes—
422Dic67—24no—
423Dic67—24no—
424Dic67—24no—
425Dic67—24no—
426Dic67—24no—
427Dic67—24no—
428C2×#3552—671nomaximal, Sylow
429C2×C67—24no—
430C2×C67#355214yescomplemented
431C2×C67C22×H(5,𝔽2)11yescharacteristic
432C2×C67C22×2−1+411yescharacteristic
433C2×C67C22×2−1+411yescharacteristic
434D67—44no—
435D67—44no—
436#3552—6732no—
437C2×#563—674no—
438C2×#557—671no—
439C2×#556—671no—
440C2×#554—672no—
441C2×#553—672no—
442C2×D4×Q8—672no—
443C2×D4×Q8—671no—
444C2×#548—672no—
445C2×#547—671no—
446C2×#544—672no—
447C2×#542—672no—
448C2×#541—672no—
449C2×#539—674no—
450C2×#536—672no—
451C22×C4⋊Q8D6711yescharacteristic, complemented
452C2×#529—671no—
453C2×#529—671no—
454C67C2×#355211yescharacteristic, complemented, Sylow
455C22×#41—672no—
456C23×Q8—672no—
457C23×Q8C2×D6712yes—
458#563—6764no—
459#557—6716no—
460#556—6716no—
461#554—6732no—
462#553—6732no—
463D4×Q8—6732no—
464D4×Q8—6716no—
465#548—6732no—
466#547—6716no—
467#544—6732no—
468#542—6732no—
469#541—6732no—
470#539—6764no—
471#536—6732no—
472C2×C4⋊Q8—672no—
473C2×C4⋊Q8—674no—
474C2×C4⋊Q8—672no—
475C2×C4⋊Q8C2×D6712yes—
476C2×C4⋊Q8C2×D6712yes—
477C2×C4⋊Q8C2×D6711yescharacteristic
478C2×C4⋊Q8C2×D6711yescharacteristic
479C2×C4⋊Q8C2×D6712yes—
480C2×C4⋊Q8C2×D67116yescomplemented
481#529—6716no—
482#529—6716no—
483C2×#126—674no—
484C2×#126—674no—
485C2×#126—674no—
486C2×#126—672no—
487C2×#126—672no—
488C2×#125—674no—
489C2×#125—674no—
490C2×#125—674no—
491C2×#125—672no—
492C2×#125—671no—
493C2×#125—671no—
494C2×#124—672no—
495C2×#124—674no—
496C2×#124—671no—
497C2×#124—671no—
498C2×#123—672no—
499C2×#123—672no—
500C2×#123—674no—
501C2×#123—674no—
502C2×#123—674no—
503C2×C22⋊Q8—672no—
504C2×C22⋊Q8—672no—
505C2×C22⋊Q8—674no—
506C2×C22⋊Q8—674no—
507C2×C22⋊Q8—671no—
508C2×C22⋊Q8—671no—
509C2×C22⋊Q8—674no—
510C2×C22⋊Q8—674no—
511C2×C22⋊Q8—674no—
512C2×C22⋊Q8—674no—
513C2×C22⋊Q8—672no—
514C2×#121—671no—
515C2×#121—671no—
516C2×#121—674no—
517C2×#121—672no—
518C2×C4×Q8—672no—
519C2×C4×Q8—672no—
520C2×C4×Q8—672no—
521C2×C4×Q8—671no—
522C2×C4×Q8—671no—
523C2×C4×D4—672no—
524C2×C4×D4—672no—
525C2×C4×D4—674no—
526C2×C4×D4—674no—
527C2×C4×D4—672no—
528C2×C4×D4—671no—
529C2×C4×D4—671no—
530C2×#117—672no—
531C2×#117—672no—
532C2×#117—672no—
533C22×C4⋊C4—672no—
534C22×C4⋊C4C2×D6712yes—
535C22×C4⋊C4C2×D6712yes—
536C22×C42C2×D6711yescharacteristic
537C2×#41—2688no—
538C2×#41—6716no—
539C22×Q8—48no—
540C22×Q8—2688no—
541C22×Q8—6716no—
542C22×Q8—674no—
543C22×Q8—671no—
544C22×Q8—671no—
545C22×Q8C22×D6712yes—
546C22×Q8C22×D6712yes—
547C22×Q8C22×D6714yes—
548C22×Q8C22×D67116yes—
549C22×D4—672no—
550C22×D4—672no—
551C22×D4—674no—
552C22×D4—671no—
553C22×D4—671no—
554C23×C4—674no—
555C23×C4—674no—
556C23×C4—672no—
557C23×C4—672no—
558C23×C4C22×D6711yescharacteristic
559C23×C4C22×D6711yescharacteristic
560C23×C4C22×D6711yescharacteristic
561C23×C4C22×D6714yes—
562C4⋊Q8—6716no—
563C4⋊Q8—6732no—
564C4⋊Q8—6716no—
565C4⋊Q8C22×D67116yes—
566C4⋊Q8C22×D67116yes—
567C4⋊Q8C22×D6718yes—
568C4⋊Q8C22×D6718yes—
569C4⋊Q8C22×D67116yes—
570#126—6732no—
571#126—6732no—
572#126—6732no—
573#126—6716no—
574#126—6716no—
575#125—6732no—
576#125—6732no—
577#125—6732no—
578#125—6716no—
579#125—678no—
580#125—678no—
581#124—6716no—
582#124—6732no—
583#124—678no—
584#124—678no—
585#123—6716no—
586#123—6716no—
587#123—6732no—
588#123—6732no—
589#123—6732no—
590C22⋊Q8—6716no—
591C22⋊Q8—6716no—
592C22⋊Q8—6732no—
593C22⋊Q8—6732no—
594C22⋊Q8—678no—
595C22⋊Q8—678no—
596C22⋊Q8—6732no—
597C22⋊Q8—6732no—
598C22⋊Q8—6732no—
599C22⋊Q8—6732no—
600C22⋊Q8—6716no—
601#121—678no—
602#121—678no—
603#121—6732no—
604#121—6716no—
605C4×Q8—6716no—
606C4×Q8—6716no—
607C4×Q8—6716no—
608C4×Q8—678no—
609C4×Q8—678no—
610C4×D4—6716no—
611C4×D4—6716no—
612C4×D4—6732no—
613C4×D4—6732no—
614C4×D4—6716no—
615C4×D4—678no—
616C4×D4—678no—
617#117—6716no—
618#117—6716no—
619#117—6716no—
620C2×C4⋊C4—671no—
621C2×C4⋊C4—674no—
622C2×C4⋊C4—671no—
623C2×C4⋊C4—672no—
624C2×C4⋊C4—672no—
625C2×C4⋊C4—672no—
626C2×C4⋊C4—672no—
627C2×C4⋊C4—671no—
628C2×C4⋊C4—674no—
629C2×C4⋊C4—672no—
630C2×C4⋊C4—674no—
631C2×C4⋊C4—672no—
632C2×C4⋊C4—671no—
633C2×C4⋊C4—674no—
634C2×C4⋊C4—674no—
635C2×C4⋊C4—674no—
636C2×C4⋊C4—672no—
637C2×C4⋊C4—672no—
638C2×C4⋊C4—6716no—
639C2×C4⋊C4C22×D6712yes—
640C2×C4⋊C4C22×D6712yes—
641C2×C4⋊C4C22×D6712yes—
642C2×C4⋊C4C22×D6714yes—
643C2×C4⋊C4C22×D6714yes—
644C2×C4⋊C4C22×D6712yes—
645C2×C4⋊C4C22×D67116yes—
646C2×C4⋊C4C22×D67116yes—
647C2×C22⋊C4—672no—
648C2×C22⋊C4—672no—
649C2×C22⋊C4—674no—
650C2×C22⋊C4—672no—
651C2×C22⋊C4—672no—
652C2×C22⋊C4—672no—
653C2×C22⋊C4—672no—
654C2×C22⋊C4—674no—
655C2×C22⋊C4—674no—
656C2×C22⋊C4—672no—
657C2×C22⋊C4—672no—
658C2×C22⋊C4—674no—
659C2×C22⋊C4—672no—
660C2×C22⋊C4—672no—
661C2×C42—672no—
662C2×C42—672no—
663C2×C42—674no—
664C2×C42—674no—
665C2×C42C22×D6711yescharacteristic
666C2×C42C22×D6711yescharacteristic
667C2×C42C22×D6711yescharacteristic
668C2×C42C22×D6711yescharacteristic
669C2×C42C22×D6718yes—
670C24—672no—
671C24—672no—
672C24C23×D6711yescharacteristic
673#41—26832no—
674C2×Q8—28no—
675C2×Q8—28no—
676C2×Q8—48no—
677C2×Q8—432no—
678C2×Q8—2688no—
679C2×Q8—26832no—
680C2×Q8—6716no—
681C2×Q8—674no—
682C2×Q8—674no—
683C2×Q8—1344no—
684C2×Q8—1344no—
685C2×Q8C23×D6718yes—
686C2×Q8C23×D6718yes—
687C2×Q8C23×D67116yes—
688C2×D4—2688no—
689C2×D4—678no—
690C2×D4—678no—
691C2×D4—6716no—
692C2×D4—674no—
693C2×D4—674no—
694C2×D4—1348no—
695C2×D4—1348no—
696C2×D4—1344no—
697C2×D4—1344no—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—48no—
702C22×C4—2688no—
703C22×C4—2688no—
704C22×C4—6716no—
705C22×C4—6716no—
706C22×C4—672no—
707C22×C4—672no—
708C22×C4—672no—
709C22×C4—672no—
710C22×C4—672no—
711C22×C4—672no—
712C22×C4—678no—
713C22×C4—678no—
714C22×C4—1348no—
715C22×C4—1348no—
716C22×C4C23×D6714yes—
717C22×C4C23×D6714yes—
718C22×C4C23×D6714yes—
719C22×C4C23×D6714yes—
720C22×C4C23×D6714yes—
721C22×C4C23×D6711yescharacteristic
722C22×C4C23×D6711yescharacteristic
723C22×C4C23×D6711yescharacteristic
724C22×C4C23×D6711yescharacteristic
725C22×C4C23×D67116yes—
726C22×C4C23×D6711yescharacteristic
727C22×C4C23×D6711yescharacteristic
728C4⋊C4—674no—
729C4⋊C4—6716no—
730C4⋊C4—674no—
731C4⋊C4—678no—
732C4⋊C4—678no—
733C4⋊C4—678no—
734C4⋊C4—678no—
735C4⋊C4—674no—
736C4⋊C4—6716no—
737C4⋊C4—678no—
738C4⋊C4—6716no—
739C4⋊C4—678no—
740C4⋊C4—674no—
741C4⋊C4—6716no—
742C4⋊C4—6716no—
743C4⋊C4—6716no—
744C4⋊C4—678no—
745C4⋊C4—678no—
746C4⋊C4C23×D6718yes—
747C4⋊C4C23×D6718yes—
748C4⋊C4C23×D6718yes—
749C4⋊C4C23×D67116yes—
750C4⋊C4C23×D67116yes—
751C4⋊C4C23×D6718yes—
752C22⋊C4—678no—
753C22⋊C4—678no—
754C22⋊C4—6716no—
755C22⋊C4—678no—
756C22⋊C4—678no—
757C22⋊C4—678no—
758C22⋊C4—678no—
759C22⋊C4—6716no—
760C22⋊C4—6716no—
761C22⋊C4—678no—
762C22⋊C4—678no—
763C22⋊C4—6716no—
764C22⋊C4—678no—
765C22⋊C4—678no—
766C42—678no—
767C42—678no—
768C42—6716no—
769C42—6716no—
770C42C23×D6714yes—
771C42C23×D6714yes—
772C42C23×D6714yes—
773C42C23×D6714yes—
774C23—22no—
775C23—22no—
776C23—674no—
777C23—674no—
778C23—1344no—
779C23—1344no—
780C23—1344no—
781C23—1344no—
782C23—1344no—
783C23—1344no—
784C23#1452409114yes—
785C23C24×D6712yes—
786C23C24×D6711yescharacteristic
787Q8—216no—
788Q8—216no—
789Q8—416no—
790Q8—26816no—
791Q8—1348no—
792Q8—1348no—
793D4—26816no—
794D4—13416no—
795D4—13416no—
796D4—1348no—
797D4—1348no—
798C2×C4—22no—
799C2×C4—28no—
800C2×C4—28no—
801C2×C4—28no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—28no—
806C2×C4—28no—
807C2×C4—416no—
808C2×C4—26816no—
809C2×C4—26816no—
810C2×C4—674no—
811C2×C4—674no—
812C2×C4—674no—
813C2×C4—674no—
814C2×C4—674no—
815C2×C4—674no—
816C2×C4—1344no—
817C2×C4—1344no—
818C2×C4—1344no—
819C2×C4—1344no—
820C2×C4—1344no—
821C2×C4—1344no—
822C2×C4—13416no—
823C2×C4—13416no—
824C2×C4#1452408814yes—
825C2×C4#1452409114yes—
826C2×C4C24×D6718yes—
827C2×C4C24×D6718yes—
828C2×C4C24×D6712yes—
829C2×C4C24×D6712yes—
830C2×C4C24×D6712yes—
831C2×C4C24×D6712yes—
832C2×C4C24×D6712yes—
833C2×C4C24×D6712yes—
834C22—28no—
835C22—22no—
836C22—22no—
837C22—2688no—
838C22—2688no—
839C22—1344no—
840C22—1344no—
841C22—1344no—
842C22—1344no—
843C22—1344no—
844C22—1344no—
845C22C2×#1452408812yes—
846C22C2×#1452409114yes—
847C22C2×#1452409112yes—
848C22C2×#1452409112yes—
849C22C25×D6711yescharacteristic
850C4—22no—
851C4—28no—
852C4—28no—
853C4—22no—
854C4—22no—
855C4—22no—
856C4—1344no—
857C4—1344no—
858C4—1344no—
859C4—1344no—
860C4—1344no—
861C4—1344no—
862C4C2×#1452408814yes—
863C4C2×#1452409114yes—
864C2—24no—
865C2—2684no—
866C2—2684no—
867C2#2257465014yesdirect product factor
868C2C22×#1452408811yescharacteristic
869C2C22×#1452409111yescharacteristic
870C2C22×#1452409111yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC22×C4⋊Q8×C67C2
socleC23×C67C25
hypercenterC22×C4⋊Q8D67
hypocenterC67C2×#3552
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #22574650C2direct (N × H)
2. C2×#16864145C2semidirect
3. C2×#16864121C2semidirect
4. C2×#16864120C2semidirect
5. C2×#16864101C2semidirect
6. C2×#16864094C2semidirect
7. C2×#16864061C2semidirect
8. C2×Q8×C22⋊D67C2semidirect
9. C2×#16864057C2semidirect
10. C2×#16864049C2semidirect
11. C2×#16864023C2semidirect
12. C2×#16864020C2semidirect
13. C2×#16864007C2semidirect
14. C2×#16863993C2semidirect
15. C2×#16863971C2semidirect
16. C2×#16863930C2semidirect
17. C2×#16863930C2semidirect
18. C22×C4⋊Q8×C67C2semidirect
21. #16864145C22semidirect
22. #16864121C22semidirect
23. #16864120C22semidirect
24. #16864101C22semidirect
25. #16864094C22semidirect
26. #16864061C22semidirect
27. Q8×C22⋊D67C22semidirect
28. #16864057C22semidirect
29. #16864049C22semidirect
30. #16864023C22semidirect
31. #16864020C22semidirect
32. #16864007C22semidirect
33. #16863993C22semidirect
34. #16863971C22semidirect
38. #16863930C22semidirect
39. #16863930C22semidirect
97. C2×C4⋊Q8×C67C22semidirect
430. C2×C67#3552semidirect
451. C22×C4⋊Q8D67semidirect
454. C67C2×#3552semidirect
480. C2×C4⋊Q8C2×D67semidirect
867. C2#22574650direct (N × H)

Maximal subgroups

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

subgroupindex
#225746502
C2×#168641452
C2×#168641212
C2×#168641202
C2×#168641012
C2×#168640942
C2×#168640612
C2×Q8×C22⋊D672
C2×#168640572
C2×#168640492
C2×#168640232
C2×#168640202
C2×#168640072
C2×#168639932
C2×#168639712
C2×#168639302
C22×C4⋊Q8×C672
C2×#355267