Finite Group Databasebeta

← C2×#22574681 #31763455

Subgroups — C2×#22574681 #31763455

Order 17152.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574681C2132yesmaximal, direct product factor
2C2×#16864142C214yesmaximal, complemented
3C2×#16864131C211yesmaximal, characteristic, complemented
4C2×#16864129C212yesmaximal, complemented
5C2×#16864121C211yesmaximal, characteristic, complemented
6C2×#16864107C212yesmaximal, complemented
7C2×#16864067C211yesmaximal, characteristic, complemented
8C2×#16864057C212yesmaximal, complemented
9C2×#16864048C212yesmaximal, complemented
10C2×#16864020C212yesmaximal, complemented
11C2×#16864019C212yesmaximal, complemented
12C2×#16863997C212yesmaximal, complemented
13C2×#16863992C214yesmaximal, complemented
14C2×#16863970C212yesmaximal, complemented
15C2×#16863950C211yesmaximal, characteristic, complemented
16C2×#16863947C211yesmaximal, characteristic, complemented
17C2×#16863928C211yesmaximal, characteristic, complemented
18C2×D4×Q8×C67C211yesmaximal, characteristic, complemented
19C22×#11761629C2212yes—
20C22×#11761628C2212yes—
21#16864142C22164yescomplemented
22#16864131C22116yescomplemented
23#16864129C22132yescomplemented
24#16864121C22116yescomplemented
25#16864107C22132yescomplemented
26#16864067C22116yescomplemented
27#16864057C22132yescomplemented
28#16864048C22132yescomplemented
29#16864020C22132yescomplemented
30#16864019C22132yescomplemented
31#16863997C22132yescomplemented
32#16863992C22164yescomplemented
33#16863970C22132yescomplemented
34#16863950C22116yescomplemented
35#16863947C22116yescomplemented
36C2×#14524042C2211yescharacteristic
37C2×#14524041C2212yes—
38C2×#14524041C2211yescharacteristic
39C2×#14524040C2211yescharacteristic
40C2×#14524039C2212yes—
41#16863928C22116yescomplemented
42C2×#14524038C2214yes—
43C2×#14524036C2212yes—
44C2×#14524034C2211yescharacteristic
45C2×#14524034C2212yes—
46C2×#14524033C2212yes—
47C2×#14524033C2214yes—
48C2×#14524032C2212yes—
49C2×#14524032C2214yes—
50C2×#14524032C2212yes—
51C2×#14524031C2212yes—
52C2×#14524030C2211yescharacteristic
53C2×#14524029C2214yes—
54C2×#14524028C2214yes—
55C2×#14524028C2214yes—
56C2×#14524026C2214yes—
57C2×#14524026C2214yes—
58C2×#14524025C2214yes—
59C2×#14524025C2214yes—
60C2×#14524025C2212yes—
61C2×#14524023C2214yes—
62C2×#14524023C2211yescharacteristic
63C2×#14524023C2211yescharacteristic
64C2×#14524021C2212yes—
65C2×#14524019C2214yes—
66C2×#14524019C2211yescharacteristic
67C2×#14524019C2214yes—
68C2×#14524019C2214yes—
69C2×#14524018C2212yes—
70C2×#14524018C2212yes—
71C2×#14524017C2212yes—
72C2×#14524017C2214yes—
73C2×#14524016C2214yes—
74C2×#14524016C2214yes—
75C2×#14524014C2211yescharacteristic
76C2×Q8×Dic67C2212yes—
77C2×C4×Dic134C2211yescharacteristic
78C2×C4×Dic134C2211yescharacteristic
79C2×C4×Dic134C2212yes—
80C2×#14524008C2212yes—
81C2×C4×D268C2212yes—
82C2×#14524005C2212yes—
83C2×#14524005C2212yes—
84C2×#14524005C2212yes—
85C2×#14524005C2212yes—
86C2×C4×C22⋊D67C2212yes—
87C2×C4×C22⋊D67C2214yes—
88C2×#14524002C2212yes—
89C2×#14524000C2212yes—
90C2×C4⋊C4×D67C2214yes—
91C2×C42×D67C2211yescharacteristic
92C23×Q8×C67C2212yes—
93D4×Q8×C67C22116yescomplemented
94C2×C4⋊Q8×C67C2212yes—
95C2×C4⋊Q8×C67C2211yescharacteristic
96C2×C22⋊Q8×C67C2212yes—
97C2×C22⋊Q8×C67C2214yes—
98C2×C4×Q8×C67C2211yescharacteristic
99C2×C4×D4×C67C2211yescharacteristic
100C2×C4×D4×C67C2212yes—
101C2×#11761629—48no—
102C2×#11761629C23116yes—
103C2×#11761628—48no—
104C2×#11761628C23116yes—
105C22×Dic134C2311yescharacteristic
106C22×Dic134C2311yescharacteristic
107C22×Dic134C2312yes—
108C22×D268C2312yes—
109C22×D268C2312yes—
110C22×D268C2312yes—
111C22×D268C2314yes—
112C22×C22⋊D67C2312yes—
113C22×C22⋊D67C2314yes—
114C22×C22⋊D67C2314yes—
115C22×C4×D67C2311yescharacteristic
116C22×C4×D67C2311yescharacteristic
117C22×C4×D67C2311yescharacteristic
118C22×C4×D67C2314yes—
119C22×C4×D67C2314yes—
120C22×C4×D67C2314yes—
121#14524042C2318yes—
122#14524041C23116yes—
123#14524041C2318yes—
124#14524040C2318yes—
125#14524039C23116yes—
126#14524038C23132yes—
127#14524036C23116yes—
128#14524034C2318yes—
129#14524034C23116yes—
130#14524033C23132yes—
131#14524033C23116yes—
132#14524032C23116yes—
133#14524032C23132yes—
134#14524032C23116yes—
135#14524031C23116yes—
136#14524030C2318yes—
137#14524029C23132yes—
138#14524028C23132yes—
139#14524028C23132yes—
140#14524026C23132yes—
141#14524026C23132yes—
142#14524025C23132yes—
143#14524025C23132yes—
144#14524025C23116yes—
145#14524023C23132yes—
146#14524023C2318yes—
147#14524023C2318yes—
148#14524021C23116yes—
149#14524019C23132yes—
150#14524019C2318yes—
151#14524019C23132yes—
152#14524019C23132yes—
153#14524018C23116yes—
154#14524018C23116yes—
155#14524017C23116yes—
156#14524017C23132yes—
157#14524016C23132yes—
158#14524016C23132yes—
159#14524014C2318yes—
160Q8×Dic67C23116yes—
161C4×Dic134C2318yes—
162C4×Dic134C23116yes—
163C4×Dic134C2318yes—
164#14524008C23116yes—
165C4×D268C23116yes—
166#14524005C23116yes—
167#14524005C23116yes—
168#14524005C23116yes—
169#14524005C23116yes—
170C4×C22⋊D67C23116yes—
171C4×C22⋊D67C23132yes—
172#14524002C23116yes—
173#14524000C23116yes—
174C2×C4⋊Dic67C2312yes—
175C2×C4⋊Dic67C2312yes—
176C2×C4⋊Dic67C2312yes—
177C2×C4⋊Dic67C2311yescharacteristic
178C2×C4⋊Dic67C2311yescharacteristic
179C2×C4⋊Dic67C2314yes—
180C2×Dic67⋊C4C2312yes—
181C2×Dic67⋊C4C2314yes—
182C2×Dic67⋊C4C2312yes—
183C2×Dic67⋊C4C2312yes—
184C2×Dic67⋊C4C2312yes—
185C2×Dic67⋊C4C2314yes—
186C2×Dic67⋊C4C2312yes—
187C2×Dic67⋊C4C2312yes—
188C2×Dic67⋊C4C2312yes—
189C4⋊C4×D67C23132yes—
190C2×C22⋊Dic67C2312yes—
191C2×C22⋊Dic67C2312yes—
192C2×C22⋊Dic67C2312yes—
193C2×(C2×D67)⋊C4C2312yes—
194C2×(C2×D67)⋊C4C2312yes—
195C2×(C2×D67)⋊C4C2314yes—
196C2×(C2×D67)⋊C4C2312yes—
197C2×(C2×D67)⋊C4C2314yes—
198C2×(C2×D67)⋊C4C2314yes—
199C2×(C2×D67)⋊C4C2314yes—
200C2×(C2×D67)⋊C4C2314yes—
201C2×(C2×D67)⋊C4C2314yes—
202C2×C4×Dic67C2311yescharacteristic
203C2×C4×Dic67C2311yescharacteristic
204C2×C4×Dic67C2311yescharacteristic
205C2×C4×Dic67C2312yes—
206C2×C4×Dic67C2312yes—
207C2×C4×Dic67C2314yes—
208C42×D67C2318yes—
209C22×Q8×C67—48no—
210C22×Q8×C67C2311yescharacteristic
211C22×Q8×C67C2312yes—
212C22×Q8×C67C23116yes—
213C22×Q8×C67C2314yes—
214C22×D4×C67C2311yescharacteristic
215C23×C4×C67C2312yes—
216C23×C4×C67C2314yes—
217C4⋊Q8×C67C23116yes—
218C4⋊Q8×C67C2318yes—
219C22⋊Q8×C67C23116yes—
220C22⋊Q8×C67C23132yes—
221C4×Q8×C67C2318yes—
222C4×D4×C67C2318yes—
223C4×D4×C67C23116yes—
224C2×C4⋊C4×C67C2311yescharacteristic
225C2×C4⋊C4×C67C2312yes—
226C2×C4⋊C4×C67C2311yescharacteristic
227C2×C4⋊C4×C67C2312yes—
228C2×C4⋊C4×C67C2314yes—
229C2×C4⋊C4×C67C2312yes—
230C2×C22⋊C4×C67C2312yes—
231C2×C22⋊C4×C67C2314yes—
232C2×C42×C67C2311yescharacteristic
233C2×C42×C67C2312yes—
234C23×D67C2411yescharacteristic
235C23×D67C2414yes—
236#11761629—432no—
237#11761628—432no—
238C2×Dic134—24no—
239C2×Dic134—24no—
240C2×Dic134—44no—
241C2×Dic134C2414yes—
242C2×Dic134C2414yes—
243C2×Dic134C2418yes—
244C2×D268—28no—
245C2×D268—28no—
246C2×D268—44no—
247C2×D268—48no—
248C2×D268C2418yes—
249C2×D268C2418yes—
250C2×D268C2418yes—
251C2×D268C24116yes—
252C2×C22⋊D67—44no—
253C2×C22⋊D67—48no—
254C2×C22⋊D67—48no—
255C2×C22⋊D67C2418yes—
256C2×C22⋊D67C24116yes—
257C2×C22⋊D67C24116yes—
258C22×Dic67C2412yes—
259C22×Dic67C2412yes—
260C22×Dic67C2411yescharacteristic
261C22×Dic67C2411yescharacteristic
262C22×Dic67C2411yescharacteristic
263C22×Dic67C2412yes—
264C22×Dic67C2412yes—
265C2×C4×D67—24no—
266C2×C4×D67—24no—
267C2×C4×D67—48no—
268C2×C4×D67—42no—
269C2×C4×D67—48no—
270C2×C4×D67—48no—
271C2×C4×D67C2414yes—
272C2×C4×D67C2414yes—
273C2×C4×D67C2414yes—
274C2×C4×D67C24116yes—
275C2×C4×D67C24116yes—
276C2×C4×D67C24116yes—
277C4⋊Dic67C2418yes—
278C4⋊Dic67C2418yes—
279C4⋊Dic67C2418yes—
280C4⋊Dic67C2414yes—
281C4⋊Dic67C2414yes—
282C4⋊Dic67C24116yes—
283Dic67⋊C4C2418yes—
284Dic67⋊C4C24116yes—
285Dic67⋊C4C2418yes—
286Dic67⋊C4C2418yes—
287Dic67⋊C4C2418yes—
288Dic67⋊C4C24116yes—
289Dic67⋊C4C2418yes—
290Dic67⋊C4C2418yes—
291Dic67⋊C4C2418yes—
292C22⋊Dic67C2418yes—
293C22⋊Dic67C2418yes—
294C22⋊Dic67C2418yes—
295(C2×D67)⋊C4C2418yes—
296(C2×D67)⋊C4C2418yes—
297(C2×D67)⋊C4C24116yes—
298(C2×D67)⋊C4C2418yes—
299(C2×D67)⋊C4C24116yes—
300(C2×D67)⋊C4C24116yes—
301(C2×D67)⋊C4C24116yes—
302(C2×D67)⋊C4C24116yes—
303(C2×D67)⋊C4C24116yes—
304C4×Dic67C2414yes—
305C4×Dic67C2414yes—
306C4×Dic67C2414yes—
307C4×Dic67C2418yes—
308C4×Dic67C2418yes—
309C4×Dic67C24116yes—
310C24×C67C2412yes—
311C2×Q8×C67—24no—
312C2×Q8×C67—28no—
313C2×Q8×C67—48no—
314C2×Q8×C67—432no—
315C2×Q8×C67C2414yes—
316C2×Q8×C67C2418yes—
317C2×Q8×C67C24116yes—
318C2×D4×C67—24no—
319C2×D4×C67C2414yes—
320C22×C4×C67—28no—
321C22×C4×C67—48no—
322C22×C4×C67C2411yescharacteristic
323C22×C4×C67C2412yes—
324C22×C4×C67C2412yes—
325C22×C4×C67C2414yes—
326C22×C4×C67C2412yes—
327C22×C4×C67C2418yes—
328C22×C4×C67C24116yes—
329C22×C4×C67C2411yescharacteristic
330C22×C4×C67C2411yescharacteristic
331C4⋊C4×C67C2414yes—
332C4⋊C4×C67C2418yes—
333C4⋊C4×C67C2414yes—
334C4⋊C4×C67C2418yes—
335C4⋊C4×C67C24116yes—
336C4⋊C4×C67C2418yes—
337C22⋊C4×C67C2418yes—
338C22⋊C4×C67C24116yes—
339C42×C67C2414yes—
340C42×C67C2418yes—
341C23×C67—24no—
342C23×C67—24no—
343C23×C67—24no—
344C23×C67C2514yes—
345C23×C67C2511yescharacteristic
346C22×D67—22no—
347C22×D67—28no—
348C22×D67—22no—
349C22×D67—28no—
350C22×D67—22no—
351C22×D67—28no—
352C22×D67C2512yes—
353C22×D67C2518yes—
354Q8×C67—28no—
355Q8×C67—216no—
356Q8×C67—416no—
357D4×C67—28no—
358C2×C4×C67—24no—
359C2×C4×C67—24no—
360C2×C4×C67—28no—
361C2×C4×C67—24no—
362C2×C4×C67—22no—
363C2×C4×C67—216no—
364C2×C4×C67—416no—
365C2×C4×C67H(5,𝔽2)14yes—
366C2×C4×C672−1+414yes—
367C2×C4×C67C2512yes—
368C2×C4×C67C2514yes—
369C2×C4×C67C2514yes—
370C2×C4×C67C2518yes—
371C2×C4×C67C2514yes—
372C2×C4×C67C2512yes—
373C2×C4×C67C2512yes—
374C22⋊D67—416no—
375C22⋊D67—48no—
376C22⋊D67—416no—
377C2×Dic67—22no—
378C2×Dic67—24no—
379C2×Dic67—22no—
380C2×Dic67—24no—
381C2×Dic67—24no—
382C2×Dic67—22no—
383C2×Dic67—24no—
384C2×Dic67C2514yes—
385C2×Dic67C2514yes—
386C2×Dic67C2512yes—
387C2×Dic67C2512yes—
388C2×Dic67C2512yes—
389C2×Dic67C2514yes—
390C2×Dic67C2514yes—
391D268—216no—
392D268—216no—
393D268—48no—
394D268—416no—
395C4×D67—28no—
396C4×D67—28no—
397C4×D67—44no—
398C4×D67—416no—
399C4×D67—416no—
400C4×D67—416no—
401Dic134—28no—
402Dic134—28no—
403Dic134—48no—
404C22×C67—24no—
405C22×C67—24no—
406C22×C67—24no—
407C22×C67—48no—
408C22×C67C2×H(5,𝔽2)12yes—
409C22×C67C2×2−1+412yes—
410C22×C67#58512yes—
411C22×C67C2611yescharacteristic
412C2×D67—22no—
413C2×D67—28no—
414C2×D67—22no—
415C2×D67—28no—
416C2×D67—28no—
417C2×D67—22no—
418C2×D67—44no—
419C2×D67—416no—
420C4×C67—24no—
421C4×C67—28no—
422C4×C67—24no—
423C4×C67—24no—
424C4×C67—22no—
425C4×C67C2×H(5,𝔽2)14yes—
426C4×C67C2×2−1+414yes—
427Dic67—24no—
428Dic67—22no—
429Dic67—24no—
430Dic67—22no—
431Dic67—22no—
432Dic67—24no—
433Dic67—24no—
434C2×#3554—671nomaximal, Sylow
435C2×C67—44no—
436C2×C67#355414yescomplemented
437C2×C67C22×H(5,𝔽2)11yescharacteristic
438C2×C67C22×2−1+411yescharacteristic
439C2×C67C2×#58511yescharacteristic
440D67—42no—
441D67—48no—
442#3554—6732no—
443C2×#562—674no—
444C2×#559—671no—
445C2×#559—672no—
446C2×#557—671no—
447C2×#554—672no—
448C2×#550—671no—
449C2×D4×Q8D6711yescharacteristic, complemented
450C2×#548—672no—
451C2×#547—672no—
452C2×#542—672no—
453C2×#542—672no—
454C2×#540—672no—
455C2×#539—674no—
456C2×#536—672no—
457C2×#533—671no—
458C2×#532—671no—
459C2×#529—671no—
460C67C2×#355411yescharacteristic, complemented, Sylow
461C22×#41—672no—
462C22×#41—672no—
463C23×Q8C2×D6712yes—
464#562—6764no—
465#559—6716no—
466#559—6732no—
467#557—6716no—
468#554—6732no—
469#550—6716no—
470D4×Q8C2×D67116yescomplemented
471#548—6732no—
472#547—6732no—
473#542—6732no—
474#542—6732no—
475#540—6732no—
476#539—6764no—
477#536—6732no—
478#533—6716no—
479#532—6716no—
480C2×C4⋊Q8—671no—
481C2×C4⋊Q8—672no—
482C2×C4⋊Q8—671no—
483C2×C4⋊Q8C2×D6711yescharacteristic
484C2×C4⋊Q8C2×D6712yes—
485C2×#127—672no—
486C2×#127—671no—
487#529—6716no—
488C2×#126—674no—
489C2×#126—672no—
490C2×#125—671no—
491C2×#125—672no—
492C2×#125—674no—
493C2×#125—672no—
494C2×#124—672no—
495C2×#124—672no—
496C2×#124—674no—
497C2×#124—671no—
498C2×#124—674no—
499C2×#124—672no—
500C2×#123—674no—
501C2×#123—674no—
502C2×#123—674no—
503C2×#123—674no—
504C2×#123—672no—
505C2×#123—674no—
506C2×#123—674no—
507C2×C22⋊Q8—671no—
508C2×C22⋊Q8—674no—
509C2×C22⋊Q8—674no—
510C2×C22⋊Q8—674no—
511C2×C22⋊Q8—671no—
512C2×C22⋊Q8—671no—
513C2×C22⋊Q8—672no—
514C2×C22⋊Q8—674no—
515C2×C22⋊Q8C2×D6714yes—
516C2×C22⋊Q8C2×D6712yes—
517C2×#121—671no—
518C2×#121—674no—
519C2×#121—672no—
520C2×#121—672no—
521C2×#121—672no—
522C2×#121—674no—
523C2×#121—674no—
524C2×C4×Q8—672no—
525C2×C4×Q8—672no—
526C2×C4×Q8—671no—
527C2×C4×Q8—671no—
528C2×C4×Q8—672no—
529C2×C4×Q8C2×D6711yescharacteristic
530C2×C4×D4—672no—
531C2×C4×D4—674no—
532C2×C4×D4—672no—
533C2×C4×D4—672no—
534C2×C4×D4—672no—
535C2×C4×D4—672no—
536C2×C4×D4—672no—
537C2×C4×D4C2×D6711yescharacteristic
538C2×C4×D4C2×D6712yes—
539C2×#117—672no—
540C2×#117—672no—
541C22×C4⋊C4—674no—
542C22×C42—671no—
543C2×#41—2688no—
544C2×#41—2688no—
545C2×#41—6716no—
546C2×#41—6716no—
547C22×Q8—48no—
548C22×Q8—672no—
549C22×Q8—671no—
550C22×Q8—671no—
551C22×Q8C22×D6712yes—
552C22×Q8C22×D6711yescharacteristic
553C22×Q8C22×D6714yes—
554C22×Q8C22×D67116yes—
555C22×D4—672no—
556C22×D4—674no—
557C22×D4—674no—
558C22×D4—672no—
559C22×D4—674no—
560C22×D4—672no—
561C22×D4—672no—
562C22×D4C22×D6711yescharacteristic
563C23×C4—674no—
564C23×C4—674no—
565C23×C4—674no—
566C23×C4—671no—
567C23×C4—671no—
568C23×C4—671no—
569C23×C4C22×D6712yes—
570C23×C4C22×D6714yes—
571C4⋊Q8—678no—
572C4⋊Q8—6716no—
573C4⋊Q8—678no—
574C4⋊Q8C22×D6718yes—
575C4⋊Q8C22×D67116yes—
576#127—6716no—
577#127—678no—
578#126—6732no—
579#126—6716no—
580#125—678no—
581#125—6716no—
582#125—6732no—
583#125—6716no—
584#124—6716no—
585#124—6716no—
586#124—6732no—
587#124—678no—
588#124—6732no—
589#124—6716no—
590#123—6732no—
591#123—6732no—
592#123—6732no—
593#123—6732no—
594#123—6716no—
595#123—6732no—
596#123—6732no—
597C22⋊Q8—678no—
598C22⋊Q8—6732no—
599C22⋊Q8—6732no—
600C22⋊Q8—6732no—
601C22⋊Q8—678no—
602C22⋊Q8—678no—
603C22⋊Q8—6716no—
604C22⋊Q8—6732no—
605C22⋊Q8C22×D67132yes—
606C22⋊Q8C22×D67116yes—
607#121—678no—
608#121—6732no—
609#121—6716no—
610#121—6716no—
611#121—6716no—
612#121—6732no—
613#121—6732no—
614C4×Q8—6716no—
615C4×Q8—6716no—
616C4×Q8—678no—
617C4×Q8—678no—
618C4×Q8—6716no—
619C4×Q8C22×D6718yes—
620C4×D4—6716no—
621C4×D4—6732no—
622C4×D4—6716no—
623C4×D4—6716no—
624C4×D4—6716no—
625C4×D4—6716no—
626C4×D4—6716no—
627C4×D4C22×D6718yes—
628C4×D4C22×D67116yes—
629#117—6716no—
630#117—6716no—
631C2×C4⋊C4—672no—
632C2×C4⋊C4—672no—
633C2×C4⋊C4—674no—
634C2×C4⋊C4—672no—
635C2×C4⋊C4—672no—
636C2×C4⋊C4—672no—
637C2×C4⋊C4—672no—
638C2×C4⋊C4—671no—
639C2×C4⋊C4—672no—
640C2×C4⋊C4—671no—
641C2×C4⋊C4—672no—
642C2×C4⋊C4—674no—
643C2×C4⋊C4—672no—
644C2×C4⋊C4—674no—
645C2×C4⋊C4—672no—
646C2×C4⋊C4—6732no—
647C2×C4⋊C4C22×D6714yes—
648C2×C4⋊C4C22×D6711yescharacteristic
649C2×C4⋊C4C22×D6711yescharacteristic
650C2×C4⋊C4C22×D6712yes—
651C2×C4⋊C4C22×D6712yes—
652C2×C4⋊C4C22×D6712yes—
653C2×C22⋊C4—672no—
654C2×C22⋊C4—672no—
655C2×C22⋊C4—672no—
656C2×C22⋊C4—672no—
657C2×C22⋊C4—672no—
658C2×C22⋊C4—674no—
659C2×C22⋊C4—674no—
660C2×C22⋊C4—674no—
661C2×C22⋊C4—674no—
662C2×C22⋊C4—672no—
663C2×C22⋊C4—674no—
664C2×C22⋊C4—674no—
665C2×C22⋊C4C22×D6712yes—
666C2×C22⋊C4C22×D6714yes—
667C2×C42—671no—
668C2×C42—672no—
669C2×C42—672no—
670C2×C42—671no—
671C2×C42—671no—
672C2×C42—674no—
673C2×C42—678no—
674C2×C42C22×D6712yes—
675C2×C42C22×D6711yescharacteristic
676C24—674no—
677C24—671no—
678C24C23×D6712yes—
679#41—26832no—
680#41—26832no—
681C2×Q8—24no—
682C2×Q8—28no—
683C2×Q8—48no—
684C2×Q8—432no—
685C2×Q8—2684no—
686C2×Q8—678no—
687C2×Q8—674no—
688C2×Q8—674no—
689C2×Q8—1344no—
690C2×Q8—1344no—
691C2×Q8C23×D6718yes—
692C2×Q8C23×D6714yes—
693C2×Q8C23×D67116yes—
694C2×D4—24no—
695C2×D4—2688no—
696C2×D4—2684no—
697C2×D4—2688no—
698C2×D4—2684no—
699C2×D4—2688no—
700C2×D4—678no—
701C2×D4—6716no—
702C2×D4—6716no—
703C2×D4—678no—
704C2×D4—6716no—
705C2×D4—678no—
706C2×D4—678no—
707C2×D4—1348no—
708C2×D4—1348no—
709C2×D4C23×D6714yes—
710C22×C4—28no—
711C22×C4—48no—
712C22×C4—2688no—
713C22×C4—2688no—
714C22×C4—2688no—
715C22×C4—2682no—
716C22×C4—674no—
717C22×C4—6716no—
718C22×C4—6716no—
719C22×C4—6716no—
720C22×C4—672no—
721C22×C4—672no—
722C22×C4—671no—
723C22×C4—671no—
724C22×C4—671no—
725C22×C4—672no—
726C22×C4—672no—
727C22×C4—674no—
728C22×C4—674no—
729C22×C4—1344no—
730C22×C4—1344no—
731C22×C4C23×D6718yes—
732C22×C4C23×D6711yescharacteristic
733C22×C4C23×D6714yes—
734C22×C4C23×D6712yes—
735C22×C4C23×D6712yes—
736C22×C4C23×D6712yes—
737C22×C4C23×D67116yes—
738C22×C4C23×D6711yescharacteristic
739C22×C4C23×D6711yescharacteristic
740C4⋊C4—678no—
741C4⋊C4—678no—
742C4⋊C4—6716no—
743C4⋊C4—678no—
744C4⋊C4—678no—
745C4⋊C4—678no—
746C4⋊C4—678no—
747C4⋊C4—674no—
748C4⋊C4—678no—
749C4⋊C4—674no—
750C4⋊C4—678no—
751C4⋊C4—6716no—
752C4⋊C4—678no—
753C4⋊C4—6716no—
754C4⋊C4—678no—
755C4⋊C4C23×D67116yes—
756C4⋊C4C23×D6714yes—
757C4⋊C4C23×D6714yes—
758C4⋊C4C23×D6718yes—
759C4⋊C4C23×D6718yes—
760C4⋊C4C23×D6718yes—
761C22⋊C4—678no—
762C22⋊C4—678no—
763C22⋊C4—678no—
764C22⋊C4—678no—
765C22⋊C4—678no—
766C22⋊C4—6716no—
767C22⋊C4—6716no—
768C22⋊C4—6716no—
769C22⋊C4—6716no—
770C22⋊C4—678no—
771C22⋊C4—6716no—
772C22⋊C4—6716no—
773C22⋊C4C23×D6718yes—
774C22⋊C4C23×D67116yes—
775C42—674no—
776C42—674no—
777C42—674no—
778C42—678no—
779C42—678no—
780C42—6716no—
781C42C23×D6714yes—
782C42C23×D6718yes—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—678no—
787C23—672no—
788C23—1348no—
789C23—1342no—
790C23—1342no—
791C23—1348no—
792C23—1348no—
793C23—1342no—
794C23C24×D6714yes—
795C23C24×D6711yescharacteristic
796Q8—28no—
797Q8—216no—
798Q8—416no—
799Q8—2688no—
800Q8—1348no—
801Q8—1348no—
802D4—28no—
803D4—26816no—
804D4—2688no—
805D4—26816no—
806D4—2688no—
807D4—26816no—
808D4—13416no—
809D4—13416no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—28no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—216no—
816C2×C4—416no—
817C2×C4—26816no—
818C2×C4—26816no—
819C2×C4—26816no—
820C2×C4—2684no—
821C2×C4—674no—
822C2×C4—674no—
823C2×C4—672no—
824C2×C4—672no—
825C2×C4—672no—
826C2×C4—674no—
827C2×C4—674no—
828C2×C4—1342no—
829C2×C4—1344no—
830C2×C4—1342no—
831C2×C4—1344no—
832C2×C4—1344no—
833C2×C4—1342no—
834C2×C4—1344no—
835C2×C4—1348no—
836C2×C4—1348no—
837C2×C4#1452408814yes—
838C2×C4#1452409114yes—
839C2×C4C24×D6712yes—
840C2×C4C24×D6718yes—
841C2×C4C24×D6714yes—
842C2×C4C24×D6714yes—
843C2×C4C24×D6714yes—
844C2×C4C24×D6712yes—
845C2×C4C24×D6712yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—48no—
850C22—26816no—
851C22—2684no—
852C22—1348no—
853C22—1342no—
854C22—1342no—
855C22—1348no—
856C22—1348no—
857C22—1342no—
858C22C2×#1452408812yes—
859C22C2×#1452409112yes—
860C22#1686423312yes—
861C22C25×D6711yescharacteristic
862C4—24no—
863C4—24no—
864C4—28no—
865C4—24no—
866C4—22no—
867C4—1342no—
868C4—1344no—
869C4—1342no—
870C4—1344no—
871C4—1344no—
872C4—1342no—
873C4—1344no—
874C4C2×#1452408814yes—
875C4C2×#1452409114yes—
876C2—44no—
877C2—2688no—
878C2—2682no—
879C2#2257468114yesdirect product factor
880C2C22×#1452408811yescharacteristic
881C2C22×#1452409111yescharacteristic
882C2C2×#1686423311yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×D4×Q8×C67C2
socleC23×C67C25
hypercenterC2×D4×Q8D67
hypocenterC67C2×#3554
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #22574681C2direct (N × H)
2. C2×#16864142C2semidirect
3. C2×#16864131C2semidirect
4. C2×#16864129C2semidirect
5. C2×#16864121C2semidirect
6. C2×#16864107C2semidirect
7. C2×#16864067C2semidirect
8. C2×#16864057C2semidirect
9. C2×#16864048C2semidirect
10. C2×#16864020C2semidirect
11. C2×#16864019C2semidirect
12. C2×#16863997C2semidirect
13. C2×#16863992C2semidirect
14. C2×#16863970C2semidirect
15. C2×#16863950C2semidirect
16. C2×#16863947C2semidirect
17. C2×#16863928C2semidirect
18. C2×D4×Q8×C67C2semidirect
21. #16864142C22semidirect
22. #16864131C22semidirect
23. #16864129C22semidirect
24. #16864121C22semidirect
25. #16864107C22semidirect
26. #16864067C22semidirect
27. #16864057C22semidirect
28. #16864048C22semidirect
29. #16864020C22semidirect
30. #16864019C22semidirect
31. #16863997C22semidirect
32. #16863992C22semidirect
33. #16863970C22semidirect
34. #16863950C22semidirect
35. #16863947C22semidirect
41. #16863928C22semidirect
93. D4×Q8×C67C22semidirect
436. C2×C67#3554semidirect
449. C2×D4×Q8D67semidirect
460. C67C2×#3554semidirect
470. D4×Q8C2×D67semidirect
879. C2#22574681direct (N × H)

Maximal subgroups

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

subgroupindex
#225746812
C2×#168641422
C2×#168641312
C2×#168641292
C2×#168641212
C2×#168641072
C2×#168640672
C2×#168640572
C2×#168640482
C2×#168640202
C2×#168640192
C2×#168639972
C2×#168639922
C2×#168639702
C2×#168639502
C2×#168639472
C2×#168639282
C2×D4×Q8×C672
C2×#355467