Finite Group Databasebeta

← C2×#22574118 #31764204

Subgroups — C2×#22574118 #31764204

Order 17152.

7758 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574118C2132yesmaximal, direct product factor
2C2×#16864117C212yesmaximal, complemented
3C2×#16864110C212yesmaximal, complemented
4C2×#16864104C212yesmaximal, complemented
5C2×#16864089C214yesmaximal, complemented
6C2×#16864052C214yesmaximal, complemented
7C2×#16864046C212yesmaximal, complemented
8C2×#16864019C212yesmaximal, complemented
9C2×#16864013C212yesmaximal, complemented
10C2×#16863974C211yesmaximal, characteristic, complemented
11C2×#16863948C212yesmaximal, complemented
12C2×#16863942C211yesmaximal, characteristic, complemented
13C2×#16863941C212yesmaximal, complemented
14C22×#14524042C211yesmaximal, characteristic, complemented
15C2×#16863879C211yesmaximal, characteristic, complemented
16C2×#16863877C211yesmaximal, characteristic, complemented
17C2×#41×Dic67C211yesmaximal, characteristic, complemented
18C2×#537×C67C211yesmaximal, characteristic, complemented
19C22×#11761628C2211yescharacteristic
20C22×#11761627C2214yes—
21C23×Dic134C2212yes—
22#16864117C22132yescomplemented
23#16864110C22132yescomplemented
24#16864104C22132yescomplemented
25#16864089C22164yescomplemented
26#16864052C22164yescomplemented
27#16864046C22132yescomplemented
28#16864019C22132yescomplemented
29#16864013C22132yescomplemented
30#16863974C22116yescomplemented
31#16863948C22132yescomplemented
32#16863942C22116yescomplemented
33#16863941C22132yescomplemented
34C2×#14524042C2212yes—
35C2×#14524042C2212yes—
36C2×#14524042C2212yes—
37C2×#14524042C2212yes—
38C2×#14524042C22116yescomplemented
39C2×#14524041C2211yescharacteristic
40C2×#14524039C2211yescharacteristic
41C2×#14524038C2214yes—
42C2×#14524036C2214yes—
43C2×#14524033C2214yes—
44C2×#14524032C2211yescharacteristic
45C2×#14524030C2211yescharacteristic
46C2×#14524030C2214yes—
47C2×#14524029C2214yes—
48C2×#14524029C2214yes—
49C2×#14524025C2214yes—
50C2×#14524024C2214yes—
51C2×#14524023C2214yes—
52C2×#14524022C2212yes—
53C2×#14524020C2214yes—
54C2×#14524020C2214yes—
55C2×#14524019C2212yes—
56C2×#14524017C2212yes—
57C2×#14524015C2212yes—
58C2×#14524015C2214yes—
59C2×#14524015C2212yes—
60C2×#14524015C2214yes—
61C2×#14524014C2212yes—
62#16863879C22116yescomplemented
63#16863877C22116yescomplemented
64#41×Dic67C22116yescomplemented
65C2×Q8×Dic67C2212yes—
66C2×Q8×Dic67C2211yescharacteristic
67C2×Q8×Dic67C2211yescharacteristic
68C2×#14524008C2212yes—
69C2×#14524008C2214yes—
70C2×D4×Dic67C2212yes—
71C2×D4×Dic67C2211yescharacteristic
72C2×D4×Dic67C2212yes—
73C2×D4×Dic67C2212yes—
74C2×D4×Dic67C2211yescharacteristic
75C2×D4×Dic67C2214yes—
76C2×#14524005C2212yes—
77C2×C4×C22⋊D67C2214yes—
78C2×C4×C22⋊D67C2212yes—
79C2×C4×C22⋊D67C2212yes—
80C2×(C22⋊D67)⋊C4C2214yes—
81C2×#14524002C2212yes—
82C2×#14524002C2211yescharacteristic
83C2×#14524002C2212yes—
84C2×#14524001C2212yes—
85C2×#14523999C2214yes—
86C22×C4⋊Dic67C2212yes—
87C22×C4⋊Dic67C2211yescharacteristic
88C22×Dic67⋊C4C2212yes—
89C2×C4⋊C4×D67C2212yes—
90C22×C4×Dic67C2211yescharacteristic
91C22×C4×Dic67C2212yes—
92C22×#41×C67C2211yescharacteristic
93C22×#41×C67C2211yescharacteristic
94#537×C67C22116yescomplemented
95C2×C22⋊Q8×C67C2212yes—
96C2×C22⋊Q8×C67C2212yes—
97C2×#121×C67C2212yes—
98C2×#121×C67C2212yes—
99C2×#121×C67C2214yes—
100C22×C4⋊C4×C67C2211yescharacteristic
101C2×#11761628—28no—
102C2×#11761628C2318yes—
103C2×#11761627—416no—
104C2×#11761627C23132yes—
105C22×Dic134—48no—
106C22×Dic134C2311yescharacteristic
107C22×Dic134C2314yes—
108C22×Dic134C23116yes—
109C22×Dic134C2314yes—
110C22×D268C2311yescharacteristic
111C22×C22⋊D67C2312yes—
112C22×C22⋊D67C2312yes—
113C22×C22⋊D67C2312yes—
114C22×C22⋊D67C2314yes—
115C23×Dic67C2311yescharacteristic
116C23×Dic67C2312yes—
117C23×Dic67C2311yescharacteristic
118C23×Dic67C2312yes—
119C23×Dic67C2312yes—
120C23×Dic67C2314yes—
121C22×C4×D67C2312yes—
122C22×C4×D67C2314yes—
123#14524042C23116yes—
124#14524042C23116yes—
125#14524042C23116yes—
126#14524042C23116yes—
127#14524041C2318yes—
128#14524039C2318yes—
129#14524038C23132yes—
130#14524036C23132yes—
131#14524033C23132yes—
132#14524032C2318yes—
133#14524030C2318yes—
134#14524030C23132yes—
135#14524029C23132yes—
136#14524029C23132yes—
137#14524025C23132yes—
138#14524024C23132yes—
139#14524023C23132yes—
140#14524022C23116yes—
141#14524020C23132yes—
142#14524020C23132yes—
143#14524019C23116yes—
144#14524017C23116yes—
145#14524015C23116yes—
146#14524015C23132yes—
147#14524015C23116yes—
148#14524015C23132yes—
149#14524014C23116yes—
150Q8×Dic67C23116yes—
151Q8×Dic67C2318yes—
152Q8×Dic67C2318yes—
153#14524008C23116yes—
154#14524008C23132yes—
155D4×Dic67C23116yes—
156D4×Dic67C2318yes—
157D4×Dic67C23116yes—
158D4×Dic67C23132yes—
159D4×Dic67C23116yes—
160D4×Dic67C2318yes—
161#14524005C23116yes—
162C4×C22⋊D67C23116yes—
163C4×C22⋊D67C23132yes—
164C4×C22⋊D67C23116yes—
165(C22⋊D67)⋊C4C23132yes—
166#14524002C23116yes—
167#14524002C23116yes—
168#14524002C2318yes—
169#14524001C23116yes—
170#14523999C23132yes—
171C2×C4⋊Dic67C23116yes—
172C2×C4⋊Dic67C2311yescharacteristic
173C2×C4⋊Dic67C2312yes—
174C2×C4⋊Dic67C2312yes—
175C2×C4⋊Dic67C2314yes—
176C2×C4⋊Dic67C2318yes—
177C2×C4⋊Dic67C2311yescharacteristic
178C2×C4⋊Dic67C2312yes—
179C2×C4⋊Dic67C2312yes—
180C2×Dic67⋊C4C23116yes—
181C2×Dic67⋊C4C2314yes—
182C2×Dic67⋊C4C2314yes—
183C2×Dic67⋊C4C2314yes—
184C2×Dic67⋊C4C2312yes—
185C2×Dic67⋊C4C2312yes—
186C2×Dic67⋊C4C2314yes—
187C4⋊C4×D67C23116yes—
188C2×C22⋊Dic67C2314yes—
189C2×C22⋊Dic67C2312yes—
190C2×C22⋊Dic67C2314yes—
191C2×C22⋊Dic67C2312yes—
192C2×C22⋊Dic67C2312yes—
193C2×C22⋊Dic67C2312yes—
194C2×C22⋊Dic67C2312yes—
195C2×(C2×D67)⋊C4C2314yes—
196C2×(C2×D67)⋊C4C2314yes—
197C2×(C2×D67)⋊C4C2312yes—
198C2×(C2×D67)⋊C4C2312yes—
199C2×C4×Dic67C2311yescharacteristic
200C2×C4×Dic67C2312yes—
201C2×C4×Dic67C2311yescharacteristic
202C2×C4×Dic67C2312yes—
203C2×C4×Dic67C2311yescharacteristic
204C2×C4×Dic67C2311yescharacteristic
205C2×C4×Dic67C2312yes—
206C2×C4×Dic67C2318yes—
207C2×C4×Dic67C23116yes—
208C2×C4×Dic67C2314yes—
209C2×C4×Dic67C2314yes—
210C2×#41×C67—28no—
211C2×#41×C67—28no—
212C2×#41×C67C2318yes—
213C2×#41×C67C2318yes—
214C22×Q8×C67C2311yescharacteristic
215C22×Q8×C67C2311yescharacteristic
216C22×D4×C67C2311yescharacteristic
217C22×D4×C67C2312yes—
218C22×D4×C67C2312yes—
219C22×D4×C67C2311yescharacteristic
220C22×D4×C67C2314yes—
221C23×C4×C67C2312yes—
222C23×C4×C67C2312yes—
223C23×C4×C67C2312yes—
224C23×C4×C67C2311yescharacteristic
225C22⋊Q8×C67C23116yes—
226C22⋊Q8×C67C23116yes—
227#121×C67C23116yes—
228#121×C67C23116yes—
229#121×C67C23132yes—
230C2×C4⋊C4×C67C2312yes—
231C2×C4⋊C4×C67C2312yes—
232C2×C4⋊C4×C67C2318yes—
233C2×C4⋊C4×C67C2314yes—
234C2×C22⋊C4×C67C2314yes—
235C2×C22⋊C4×C67C2314yes—
236C23×D67C2412yes—
237#11761628—232no—
238#11761627—464no—
239C2×Dic134—24no—
240C2×Dic134—216no—
241C2×Dic134—432no—
242C2×Dic134—48no—
243C2×Dic134C2414yes—
244C2×Dic134C24116yes—
245C2×Dic134C24116yes—
246C2×D268—24no—
247C2×D268C2414yes—
248C2×C22⋊D67—28no—
249C2×C22⋊D67—28no—
250C2×C22⋊D67—28no—
251C2×C22⋊D67—48no—
252C2×C22⋊D67C2418yes—
253C2×C22⋊D67C2418yes—
254C2×C22⋊D67C2418yes—
255C2×C22⋊D67C24116yes—
256C22×Dic67—24no—
257C22×Dic67—28no—
258C22×Dic67—24no—
259C22×Dic67—28no—
260C22×Dic67—44no—
261C22×Dic67—48no—
262C22×Dic67C2412yes—
263C22×Dic67C2411yescharacteristic
264C22×Dic67C2411yescharacteristic
265C22×Dic67C2412yes—
266C22×Dic67C2412yes—
267C22×Dic67C2414yes—
268C22×Dic67C2418yes—
269C22×Dic67C2414yes—
270C22×Dic67C2418yes—
271C22×Dic67C2414yes—
272C22×Dic67C2418yes—
273C22×Dic67C24116yes—
274C22×Dic67C2411yescharacteristic
275C22×Dic67C2411yescharacteristic
276C2×C4×D67—28no—
277C2×C4×D67—48no—
278C2×C4×D67C2418yes—
279C2×C4×D67C24116yes—
280C4⋊Dic67C2414yes—
281C4⋊Dic67C2418yes—
282C4⋊Dic67C2418yes—
283C4⋊Dic67C24116yes—
284C4⋊Dic67C2414yes—
285C4⋊Dic67C2418yes—
286C4⋊Dic67C2418yes—
287Dic67⋊C4C24116yes—
288Dic67⋊C4C24116yes—
289Dic67⋊C4C24116yes—
290Dic67⋊C4C2418yes—
291Dic67⋊C4C2418yes—
292Dic67⋊C4C24116yes—
293C22⋊Dic67C24116yes—
294C22⋊Dic67C2418yes—
295C22⋊Dic67C24116yes—
296C22⋊Dic67C2418yes—
297C22⋊Dic67C2418yes—
298C22⋊Dic67C2418yes—
299C22⋊Dic67C2418yes—
300(C2×D67)⋊C4C24116yes—
301(C2×D67)⋊C4C24116yes—
302(C2×D67)⋊C4C2418yes—
303(C2×D67)⋊C4C2418yes—
304C4×Dic67C2414yes—
305C4×Dic67C2418yes—
306C4×Dic67C2414yes—
307C4×Dic67C2418yes—
308C4×Dic67C2414yes—
309C4×Dic67C2414yes—
310C4×Dic67C2418yes—
311C4×Dic67C24116yes—
312C4×Dic67C24116yes—
313C24×C67C2412yes—
314C24×C67C2412yes—
315C24×C67C2411yescharacteristic
316#41×C67—232no—
317#41×C67—232no—
318C2×Q8×C67—24no—
319C2×Q8×C67—24no—
320C2×Q8×C67C2414yes—
321C2×Q8×C67C2414yes—
322C2×D4×C67—28no—
323C2×D4×C67—28no—
324C2×D4×C67—24no—
325C2×D4×C67—24no—
326C2×D4×C67—48no—
327C2×D4×C67C2414yes—
328C2×D4×C67C2418yes—
329C2×D4×C67C2418yes—
330C2×D4×C67C2414yes—
331C2×D4×C67C24116yes—
332C22×C4×C67—28no—
333C22×C4×C67—28no—
334C22×C4×C67—44no—
335C22×C4×C67#4118yescomplemented
336C22×C4×C67C2414yes—
337C22×C4×C67C2412yes—
338C22×C4×C67C2412yes—
339C22×C4×C67C2418yes—
340C22×C4×C67C2418yes—
341C22×C4×C67C2418yes—
342C22×C4×C67C2411yescharacteristic
343C22×C4×C67C2411yescharacteristic
344C22×C4×C67C2414yes—
345C4⋊C4×C67C2418yes—
346C4⋊C4×C67C2418yes—
347C4⋊C4×C67C24116yes—
348C22⋊C4×C67C24116yes—
349C22⋊C4×C67C24116yes—
350C23×C67—22no—
351C23×C67—22no—
352C23×C67—24no—
353C23×C67—24no—
354C23×C67—24no—
355C23×C67—24no—
356C23×C67—24no—
357C23×C67—24no—
358C23×C67C2×#4114yes—
359C23×C67C2514yes—
360C23×C67C2514yes—
361C23×C67C2512yes—
362C23×C67C2511yescharacteristic
363C22×D67—24no—
364C22×D67—24no—
365C22×D67—24no—
366C22×D67C2514yes—
367Q8×C67—28no—
368Q8×C67—28no—
369D4×C67—216no—
370D4×C67—216no—
371D4×C67—28no—
372D4×C67—28no—
373D4×C67—416no—
374C2×C4×C67—24no—
375C2×C4×C67—24no—
376C2×C4×C67—28no—
377C2×C4×C67—216no—
378C2×C4×C67—216no—
379C2×C4×C67—48no—
380C2×C4×C67C2×#4114yes—
381C2×C4×C67C2×#4114yes—
382C2×C4×C67C2×#41116yescomplemented
383C2×C4×C67C2518yes—
384C2×C4×C67C2514yes—
385C2×C4×C67C2514yes—
386C2×C4×C67C2512yes—
387C2×C4×C67C2512yes—
388C22⋊D67—216no—
389C22⋊D67—216no—
390C22⋊D67—216no—
391C22⋊D67—416no—
392C2×Dic67—24no—
393C2×Dic67—24no—
394C2×Dic67—22no—
395C2×Dic67—28no—
396C2×Dic67—24no—
397C2×Dic67—22no—
398C2×Dic67—28no—
399C2×Dic67—216no—
400C2×Dic67—28no—
401C2×Dic67—216no—
402C2×Dic67—48no—
403C2×Dic67—416no—
404C2×Dic67H(5,𝔽2)14yes—
405C2×Dic672−1+414yes—
406C2×Dic67C2514yes—
407C2×Dic67C2512yes—
408C2×Dic67C2512yes—
409C2×Dic67C2514yes—
410C2×Dic67C2514yes—
411C2×Dic67C2518yes—
412C2×Dic67C2512yes—
413C2×Dic67C2512yes—
414D268—28no—
415C4×D67—216no—
416C4×D67—416no—
417Dic134—28no—
418Dic134—232no—
419Dic134—416no—
420C22×C67—22no—
421C22×C67—22no—
422C22×C67—28no—
423C22×C67—24no—
424C22×C67—24no—
425C22×C67—24no—
426C22×C67—24no—
427C22×C67—24no—
428C22×C67—24no—
429C22×C67—48no—
430C22×C67—48no—
431C22×C67C22×#4114yes—
432C22×C67C22×#4112yes—
433C22×C67C2×H(5,𝔽2)12yes—
434C22×C67C2×2−1+412yes—
435C22×C67C2611yescharacteristic
436C2×D67—24no—
437C2×D67—24no—
438C2×D67—24no—
439C2×D67—48no—
440C4×C67—24no—
441C4×C67—24no—
442C4×C67—28no—
443C4×C67C22×#4114yes—
444C4×C67C22×#4114yes—
445Dic67—24no—
446Dic67—28no—
447Dic67—22no—
448Dic67—24no—
449Dic67—24no—
450Dic67—22no—
451Dic67C2×H(5,𝔽2)14yes—
452Dic67C2×2−1+414yes—
453C2×#3511—671nomaximal, Sylow
454C2×C67—24no—
455C2×C67—44no—
456C2×C67—44no—
457C2×C67#351114yescomplemented
458C2×C67C23×#4111yescharacteristic
459C2×C67C22×H(5,𝔽2)11yescharacteristic
460C2×C67C22×2−1+411yescharacteristic
461D67—44no—
462#3511—6732no—
463C2×#556—672no—
464C2×#555—672no—
465C2×#554—672no—
466C2×#553—674no—
467C2×#548—674no—
468C2×#547—672no—
469C2×#542—672no—
470C2×#542—672no—
471C2×#537—671no—
472C2×#537D6711yescharacteristic, complemented
473C2×#533—672no—
474C2×#532—671no—
475C2×#532—672no—
476C22×C4⋊Q8—671no—
477C2×#520—671no—
478C2×#520—671no—
479C2×C4×#41—671no—
480C67C2×#351111yescharacteristic, complemented, Sylow
481C22×#41—674no—
482C22×#41—671no—
483C22×#41C2×D6711yescharacteristic
484C22×#41C2×D6711yescharacteristic
485C23×Q8—672no—
486#556—6732no—
487#555—6732no—
488#554—6732no—
489#553—6764no—
490#548—6764no—
491#547—6732no—
492#542—6732no—
493#542—6732no—
494#537—6716no—
495#537C2×D67116yescomplemented
496#533—6732no—
497#532—6716no—
498#532—6732no—
499C2×C4⋊Q8—671no—
500C2×C4⋊Q8—672no—
501C2×C4⋊Q8—672no—
502C2×C4⋊Q8—672no—
503C2×C4⋊Q8—672no—
504C2×C4⋊Q8—6716no—
505C2×#127—671no—
506C2×#126—674no—
507C2×#126—674no—
508C2×#125—674no—
509C2×#124—671no—
510C2×#124—671no—
511C2×#124—674no—
512C2×#124—674no—
513C2×#124—674no—
514C2×#123—674no—
515C2×#123—674no—
516C2×C22⋊Q8—672no—
517C2×C22⋊Q8—672no—
518C2×C22⋊Q8—674no—
519C2×C22⋊Q8—674no—
520C2×C22⋊Q8—674no—
521C2×C22⋊Q8C2×D6712yes—
522C2×C22⋊Q8C2×D6712yes—
523C2×#121—672no—
524C2×#121—672no—
525C2×#121—674no—
526C2×#121—672no—
527C2×#121—674no—
528C2×#121—672no—
529C2×#121C2×D6712yes—
530C2×#121C2×D6712yes—
531C2×#121C2×D6714yes—
532#520—6716no—
533#520—6716no—
534C4×#41—6716no—
535C2×C4×Q8—671no—
536C2×C4×Q8—671no—
537C2×C4×Q8—672no—
538C2×C4×Q8—672no—
539C2×C4×Q8—674no—
540C2×C4×D4—671no—
541C2×C4×D4—672no—
542C2×C4×D4—672no—
543C2×C4×D4—671no—
544C2×C4×D4—672no—
545C2×C4×D4—674no—
546C2×C4×D4—674no—
547C2×C4×D4—672no—
548C2×C4×D4—672no—
549C2×C4×D4—672no—
550C2×C4×D4—674no—
551C2×#117—671no—
552C2×#117—672no—
553C2×#117—672no—
554C2×#117—672no—
555C2×#117—674no—
556C22×C4⋊C4—671no—
557C22×C4⋊C4—672no—
558C22×C4⋊C4—672no—
559C22×C4⋊C4—672no—
560C22×C4⋊C4C2×D6711yescharacteristic
561C22×C42—671no—
562C22×C42—672no—
563C2×#41—28no—
564C2×#41—28no—
565C2×#41—26816no—
566C2×#41—6732no—
567C2×#41—678no—
568C2×#41—1348no—
569C2×#41C22×D6718yes—
570C2×#41C22×D6718yes—
571C22×Q8—2688no—
572C22×Q8—674no—
573C22×Q8—6716no—
574C22×Q8—671no—
575C22×Q8—674no—
576C22×Q8C22×D6711yescharacteristic
577C22×Q8C22×D6711yescharacteristic
578C22×D4—674no—
579C22×D4—672no—
580C22×D4—672no—
581C22×D4—672no—
582C22×D4—671no—
583C22×D4C22×D6712yes—
584C22×D4C22×D6712yes—
585C22×D4C22×D6711yescharacteristic
586C22×D4C22×D6711yescharacteristic
587C22×D4C22×D6714yes—
588C23×C4—672no—
589C23×C4—674no—
590C23×C4—674no—
591C23×C4—671no—
592C23×C4—672no—
593C23×C4—671no—
594C23×C4—672no—
595C23×C4—672no—
596C23×C4C22×D6712yes—
597C23×C4C22×D6712yes—
598C23×C4C22×D6712yes—
599C23×C4C22×D6711yescharacteristic
600C4⋊Q8—678no—
601C4⋊Q8—6716no—
602C4⋊Q8—6716no—
603C4⋊Q8—6716no—
604C4⋊Q8—6716no—
605#127—678no—
606#126—6732no—
607#126—6732no—
608#125—6732no—
609#124—678no—
610#124—678no—
611#124—6732no—
612#124—6732no—
613#124—6732no—
614#123—6732no—
615#123—6732no—
616C22⋊Q8—6716no—
617C22⋊Q8—6716no—
618C22⋊Q8—6732no—
619C22⋊Q8—6732no—
620C22⋊Q8—6732no—
621C22⋊Q8C22×D67116yes—
622C22⋊Q8C22×D67116yes—
623#121—6716no—
624#121—6716no—
625#121—6732no—
626#121—6716no—
627#121—6732no—
628#121—6716no—
629#121C22×D67116yes—
630#121C22×D67116yes—
631#121C22×D67132yes—
632C4×Q8—678no—
633C4×Q8—678no—
634C4×Q8—6716no—
635C4×Q8—6716no—
636C4×Q8—6732no—
637C4×D4—678no—
638C4×D4—6716no—
639C4×D4—6716no—
640C4×D4—678no—
641C4×D4—6716no—
642C4×D4—6732no—
643C4×D4—6732no—
644C4×D4—6716no—
645C4×D4—6716no—
646C4×D4—6716no—
647C4×D4—6732no—
648#117—678no—
649#117—6716no—
650#117—6716no—
651#117—6716no—
652#117—6732no—
653C2×C4⋊C4—671no—
654C2×C4⋊C4—672no—
655C2×C4⋊C4—674no—
656C2×C4⋊C4—672no—
657C2×C4⋊C4—674no—
658C2×C4⋊C4—674no—
659C2×C4⋊C4—678no—
660C2×C4⋊C4—6716no—
661C2×C4⋊C4—674no—
662C2×C4⋊C4—6716no—
663C2×C4⋊C4—671no—
664C2×C4⋊C4—672no—
665C2×C4⋊C4—672no—
666C2×C4⋊C4—672no—
667C2×C4⋊C4—672no—
668C2×C4⋊C4—674no—
669C2×C4⋊C4—6716no—
670C2×C4⋊C4C22×D6712yes—
671C2×C4⋊C4C22×D6712yes—
672C2×C4⋊C4C22×D6718yes—
673C2×C4⋊C4C22×D6714yes—
674C2×C22⋊C4—672no—
675C2×C22⋊C4—674no—
676C2×C22⋊C4—672no—
677C2×C22⋊C4—672no—
678C2×C22⋊C4—674no—
679C2×C22⋊C4—672no—
680C2×C22⋊C4—672no—
681C2×C22⋊C4—674no—
682C2×C22⋊C4—674no—
683C2×C22⋊C4—672no—
684C2×C22⋊C4—672no—
685C2×C22⋊C4C22×D6714yes—
686C2×C22⋊C4C22×D6714yes—
687C2×C42—672no—
688C2×C42—674no—
689C2×C42—674no—
690C2×C42—671no—
691C2×C42—672no—
692C2×C42—671no—
693C2×C42—671no—
694C2×C42—672no—
695C2×C42—678no—
696C2×C42—6716no—
697C2×C42—671no—
698C24—672no—
699C24C23×D6712yes—
700C24C23×D6712yes—
701C24C23×D6711yescharacteristic
702#41—232no—
703#41—232no—
704#41—26864no—
705#41—13432no—
706C2×Q8—24no—
707C2×Q8—24no—
708C2×Q8—2688no—
709C2×Q8—26832no—
710C2×Q8—6716no—
711C2×Q8—674no—
712C2×Q8—6716no—
713C2×Q8—13416no—
714C2×Q8—1344no—
715C2×Q8C23×D6714yes—
716C2×Q8C23×D6714yes—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—24no—
720C2×D4—24no—
721C2×D4—48no—
722C2×D4—2688no—
723C2×D4—6716no—
724C2×D4—678no—
725C2×D4—678no—
726C2×D4—678no—
727C2×D4—674no—
728C2×D4—1348no—
729C2×D4—1348no—
730C2×D4—1348no—
731C2×D4—1344no—
732C2×D4C23×D6718yes—
733C2×D4C23×D6718yes—
734C2×D4C23×D6714yes—
735C2×D4C23×D6714yes—
736C2×D4C23×D67116yes—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—44no—
740C22×C4—2688no—
741C22×C4—2684no—
742C22×C4—2688no—
743C22×C4—678no—
744C22×C4—6716no—
745C22×C4—6716no—
746C22×C4—671no—
747C22×C4—671no—
748C22×C4—674no—
749C22×C4—678no—
750C22×C4—674no—
751C22×C4—678no—
752C22×C4—672no—
753C22×C4—671no—
754C22×C4—671no—
755C22×C4—672no—
756C22×C4—672no—
757C22×C4—674no—
758C22×C4—678no—
759C22×C4—1344no—
760C22×C4—1348no—
761C22×C4—1344no—
762C22×C4—1348no—
763C22×C4—1348no—
764C22×C4#1176162718yescomplemented
765C22×C4C23×D6718yes—
766C22×C4C23×D6718yes—
767C22×C4C23×D6712yes—
768C22×C4C23×D6712yes—
769C22×C4C23×D6714yes—
770C22×C4C23×D6718yes—
771C22×C4C23×D6711yescharacteristic
772C22×C4C23×D6711yescharacteristic
773C22×C4C23×D6714yes—
774C4⋊C4—674no—
775C4⋊C4—678no—
776C4⋊C4—6716no—
777C4⋊C4—678no—
778C4⋊C4—6716no—
779C4⋊C4—6716no—
780C4⋊C4—6716no—
781C4⋊C4—674no—
782C4⋊C4—678no—
783C4⋊C4—678no—
784C4⋊C4—678no—
785C4⋊C4—678no—
786C4⋊C4—6716no—
787C4⋊C4C23×D6718yes—
788C4⋊C4C23×D6718yes—
789C4⋊C4C23×D67116yes—
790C22⋊C4—678no—
791C22⋊C4—6716no—
792C22⋊C4—678no—
793C22⋊C4—678no—
794C22⋊C4—6716no—
795C22⋊C4—678no—
796C22⋊C4—678no—
797C22⋊C4—6716no—
798C22⋊C4—6716no—
799C22⋊C4—678no—
800C22⋊C4—678no—
801C22⋊C4C23×D67116yes—
802C22⋊C4C23×D67116yes—
803C42—674no—
804C42—678no—
805C42—674no—
806C42—678no—
807C42—674no—
808C42—674no—
809C42—678no—
810C42—6716no—
811C42—6716no—
812C23—22no—
813C23—22no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—674no—
821C23—1344no—
822C23—1344no—
823C23—1344no—
824C23C2×#1176162714yes—
825C23C24×D6714yes—
826C23C24×D6714yes—
827C23C24×D6712yes—
828C23C24×D6711yescharacteristic
829Q8—28no—
830Q8—28no—
831Q8—26816no—
832Q8—13432no—
833Q8—1348no—
834D4—216no—
835D4—216no—
836D4—28no—
837D4—28no—
838D4—416no—
839D4—26816no—
840D4—13416no—
841D4—13416no—
842D4—13416no—
843D4—1348no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—28no—
847C2×C4—216no—
848C2×C4—216no—
849C2×C4—48no—
850C2×C4—26816no—
851C2×C4—2688no—
852C2×C4—26816no—
853C2×C4—674no—
854C2×C4—674no—
855C2×C4—672no—
856C2×C4—672no—
857C2×C4—674no—
858C2×C4—672no—
859C2×C4—672no—
860C2×C4—674no—
861C2×C4—674no—
862C2×C4—678no—
863C2×C4—1348no—
864C2×C4—13416no—
865C2×C4—1348no—
866C2×C4—13416no—
867C2×C4—1344no—
868C2×C4—1344no—
869C2×C4—1348no—
870C2×C4—1342no—
871C2×C4—1344no—
872C2×C4—1342no—
873C2×C4—13416no—
874C2×C4C2×#1176162714yes—
875C2×C4C2×#1176162714yes—
876C2×C4C2×#11761627116yescomplemented
877C2×C4C24×D6714yes—
878C2×C4C24×D6714yes—
879C2×C4C24×D6718yes—
880C2×C4C24×D6712yes—
881C2×C4C24×D6712yes—
882C22—28no—
883C22—22no—
884C22—22no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—48no—
892C22—48no—
893C22—2688no—
894C22—1344no—
895C22—1344no—
896C22—1344no—
897C22C22×#1176162714yes—
898C22C22×#1176162712yes—
899C22H(5,𝔽2)×D6712yes—
900C222−1+4×D6712yes—
901C22C25×D6711yescharacteristic
902C4—24no—
903C4—24no—
904C4—28no—
905C4—674no—
906C4—674no—
907C4—1344no—
908C4—1344no—
909C4—1348no—
910C4—1342no—
911C4—1344no—
912C4—1342no—
913C4C22×#1176162714yes—
914C4C22×#1176162714yes—
915C2—24no—
916C2—44no—
917C2—44no—
918C2—2684no—
919C2#2257411814yesdirect product factor
920C2C23×#1176162711yescharacteristic
921C2C2×H(5,𝔽2)×D6711yescharacteristic
922C2C2×2−1+4×D6711yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#537×C67C2
socleC23×C67C25
hypercenterC2×#537D67
hypocenterC67C2×#3511
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. #22574118C2direct (N × H)
2. C2×#16864117C2semidirect
3. C2×#16864110C2semidirect
4. C2×#16864104C2semidirect
5. C2×#16864089C2semidirect
6. C2×#16864052C2semidirect
7. C2×#16864046C2semidirect
8. C2×#16864019C2semidirect
9. C2×#16864013C2semidirect
10. C2×#16863974C2semidirect
11. C2×#16863948C2semidirect
12. C2×#16863942C2semidirect
13. C2×#16863941C2semidirect
14. C22×#14524042C2semidirect
15. C2×#16863879C2semidirect
16. C2×#16863877C2semidirect
17. C2×#41×Dic67C2semidirect
18. C2×#537×C67C2semidirect
22. #16864117C22semidirect
23. #16864110C22semidirect
24. #16864104C22semidirect
25. #16864089C22semidirect
26. #16864052C22semidirect
27. #16864046C22semidirect
28. #16864019C22semidirect
29. #16864013C22semidirect
30. #16863974C22semidirect
31. #16863948C22semidirect
32. #16863942C22semidirect
33. #16863941C22semidirect
38. C2×#14524042C22semidirect
62. #16863879C22semidirect
63. #16863877C22semidirect
64. #41×Dic67C22semidirect
94. #537×C67C22semidirect
335. C22×C4×C67#41semidirect
382. C2×C4×C67C2×#41semidirect
457. C2×C67#3511semidirect
472. C2×#537D67semidirect
480. C67C2×#3511semidirect
495. #537C2×D67semidirect
764. C22×C4#11761627semidirect
876. C2×C4C2×#11761627semidirect
919. C2#22574118direct (N × H)

Maximal subgroups

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

subgroupindex
#225741182
C2×#168641172
C2×#168641102
C2×#168641042
C2×#168640892
C2×#168640522
C2×#168640462
C2×#168640192
C2×#168640132
C2×#168639742
C2×#168639482
C2×#168639422
C2×#168639412
C22×#145240422
C2×#168638792
C2×#168638772
C2×#41×Dic672
C2×#537×C672
C2×#351167