Finite Group Databasebeta

← C2×#22574188 #31763939

Subgroups — C2×#22574188 #31763939

Order 17152.

7142 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574188C2132yesmaximal, direct product factor
2C2×#16864125C211yesmaximal, characteristic, complemented
3C2×#16864107C211yesmaximal, characteristic, complemented
4C2×#16864094C212yesmaximal, complemented
5C2×#16864088C212yesmaximal, complemented
6C2×#16864088C214yesmaximal, complemented
7C2×#16864084C212yesmaximal, complemented
8C2×#16864050C211yesmaximal, characteristic, complemented
9C2×#16864050C212yesmaximal, complemented
10C2×#16864009C212yesmaximal, complemented
11C2×#16863995C214yesmaximal, complemented
12C2×#16863951C211yesmaximal, characteristic, complemented
13C2×#16863933C211yesmaximal, characteristic, complemented
14C2×#16863932C212yesmaximal, complemented
15C22×#14524034C212yesmaximal, complemented
16C2×#16863875C212yesmaximal, complemented
17C2×C4×#11761627C211yesmaximal, characteristic, complemented
18C2×#554×C67C211yesmaximal, characteristic, complemented
19C22×#11761627C2211yescharacteristic
20C22×#11761627C2212yes—
21#16864125C22116yescomplemented
22#16864107C22116yescomplemented
23#16864094C22132yescomplemented
24#16864088C22132yescomplemented
25#16864088C22164yescomplemented
26#16864084C22132yescomplemented
27#16864050C22116yescomplemented
28#16864050C22132yescomplemented
29#16864009C22132yescomplemented
30#16863995C22164yescomplemented
31#16863951C22116yescomplemented
32C2×#14524043C2212yes—
33C2×#14524043C2211yescharacteristic
34#16863933C22116yescomplemented
35#16863932C22132yescomplemented
36C2×#14524038C2214yes—
37C2×#14524038C2214yes—
38C2×#14524038C2214yes—
39C2×#14524038C2212yes—
40C2×#14524034C2214yes—
41C2×#14524034C2214yes—
42C2×#14524034C2211yescharacteristic
43C2×#14524034C2214yes—
44C2×#14524034C2212yes—
45C2×#14524034C2212yes—
46C2×#14524034C2212yes—
47C2×#14524034C2214yes—
48C2×#14524034C22132yescomplemented
49C2×#14524032C2211yescharacteristic
50C2×#14524028C2214yes—
51C2×#14524028C2212yes—
52C2×#14524027C2214yes—
53C2×#14524027C2214yes—
54C2×#14524027C2214yes—
55C2×#14524023C2212yes—
56C2×#14524023C2212yes—
57C2×#14524023C2212yes—
58C2×#14524019C2211yescharacteristic
59C2×#14524019C2214yes—
60C2×#14524019C2212yes—
61C2×#14524018C2211yescharacteristic
62C2×#14524017C2212yes—
63C2×#14524017C2214yes—
64#16863875C22132yescomplemented
65C4×#11761627C22116yescomplemented
66C2×Q8×Dic67C2212yes—
67C2×Q8×Dic67C2212yes—
68C2×C4×Dic134C2211yescharacteristic
69C2×C4×Dic134C2212yes—
70C2×#14524008C2211yescharacteristic
71C2×#14524008C2212yes—
72C2×C4×D268C2212yes—
73C2×C4×D268C2211yescharacteristic
74C2×D4×Dic67C2211yescharacteristic
75C2×#14524005C2212yes—
76C2×C4×C22⋊D67C2212yes—
77C2×C4×C22⋊D67C2214yes—
78C2×(C22⋊D67)⋊C4C2212yes—
79C2×(C22⋊D67)⋊C4C2214yes—
80C2×#14524001C2211yescharacteristic
81C2×#14524001C2214yes—
82C2×#14524001C2212yes—
83C2×#14524000C2212yes—
84C2×#14523999C2212yes—
85C2×#14523999C2214yes—
86C22×C4⋊Dic67C2212yes—
87C22×C4⋊Dic67C2214yes—
88C22×Dic67⋊C4C2214yes—
89C2×C4⋊C4×D67C2212yes—
90C22×C4×Dic67C2212yes—
91C2×C42×D67C2211yescharacteristic
92#554×C67C22116yescomplemented
93C2×C4⋊Q8×C67C2211yescharacteristic
94C2×#125×C67C2212yes—
95C2×C22⋊Q8×C67C2212yes—
96C2×C22⋊Q8×C67C2214yes—
97C2×C4×Q8×C67C2211yescharacteristic
98C2×C4×D4×C67C2211yescharacteristic
99C2×C4×D4×C67C2212yes—
100C22×C4⋊C4×C67C2212yes—
101C2×#11761627—28no—
102C2×#11761627—216no—
103C2×#11761627C2318yes—
104C2×#11761627C23116yes—
105C22×Dic134C2311yescharacteristic
106C22×Dic134C2312yes—
107C22×D268C2311yescharacteristic
108C22×D268C2312yes—
109C22×C22⋊D67C2312yes—
110C22×C22⋊D67C2314yes—
111C23×Dic67C2312yes—
112C23×Dic67C2314yes—
113C23×Dic67C2312yes—
114C22×C4×D67C2311yescharacteristic
115C22×C4×D67C2311yescharacteristic
116C22×C4×D67C2312yes—
117C22×C4×D67C2311yescharacteristic
118C22×C4×D67C2314yes—
119#14524043C23116yes—
120#14524043C2318yes—
121#14524038C23132yes—
122#14524038C23132yes—
123#14524038C23132yes—
124#14524038C23116yes—
125#14524034C23132yes—
126#14524034C23132yes—
127#14524034C23132yes—
128#14524034C23116yes—
129#14524034C23132yes—
130#14524034C23116yes—
131#14524034C2318yes—
132#14524034C23116yes—
133#14524032C2318yes—
134#14524028C23132yes—
135#14524028C23116yes—
136#14524027C23132yes—
137#14524027C23132yes—
138#14524027C23132yes—
139#14524023C23116yes—
140#14524023C23116yes—
141#14524023C23116yes—
142#14524019C2318yes—
143#14524019C23132yes—
144#14524019C23116yes—
145#14524018C2318yes—
146#14524017C23116yes—
147#14524017C23132yes—
148Q8×Dic67C23116yes—
149Q8×Dic67C23116yes—
150C4×Dic134C23116yes—
151C4×Dic134C2318yes—
152#14524008C2318yes—
153#14524008C23116yes—
154C4×D268C23116yes—
155C4×D268C2318yes—
156D4×Dic67C2318yes—
157#14524005C23116yes—
158C4×C22⋊D67C23116yes—
159C4×C22⋊D67C23132yes—
160(C22⋊D67)⋊C4C23116yes—
161(C22⋊D67)⋊C4C23132yes—
162#14524001C2318yes—
163#14524001C23132yes—
164#14524001C23116yes—
165#14524000C23116yes—
166#14523999C23116yes—
167#14523999C23132yes—
168C2×C4⋊Dic67C23116yes—
169C2×C4⋊Dic67C23132yes—
170C2×C4⋊Dic67C2311yescharacteristic
171C2×C4⋊Dic67C2311yescharacteristic
172C2×C4⋊Dic67C2312yes—
173C2×C4⋊Dic67C2312yes—
174C2×C4⋊Dic67C2314yes—
175C2×C4⋊Dic67C2314yes—
176C2×C4⋊Dic67C2314yes—
177C2×C4⋊Dic67C2314yes—
178C2×C4⋊Dic67C2312yes—
179C2×C4⋊Dic67C2314yes—
180C2×Dic67⋊C4C2314yes—
181C2×Dic67⋊C4C2312yes—
182C2×Dic67⋊C4C2314yes—
183C2×Dic67⋊C4C2314yes—
184C2×Dic67⋊C4C23132yes—
185C2×Dic67⋊C4C2312yes—
186C2×Dic67⋊C4C2312yes—
187C2×Dic67⋊C4C2312yes—
188C4⋊C4×D67C23116yes—
189C2×C22⋊Dic67C2312yes—
190C2×(C2×D67)⋊C4C2312yes—
191C2×(C2×D67)⋊C4C2312yes—
192C2×(C2×D67)⋊C4C2312yes—
193C2×(C2×D67)⋊C4C2312yes—
194C2×(C2×D67)⋊C4C2314yes—
195C2×(C2×D67)⋊C4C2314yes—
196C2×(C2×D67)⋊C4C2314yes—
197C2×(C2×D67)⋊C4C2312yes—
198C2×(C2×D67)⋊C4C2312yes—
199C2×C4×Dic67C2311yescharacteristic
200C2×C4×Dic67C2311yescharacteristic
201C2×C4×Dic67C2311yescharacteristic
202C2×C4×Dic67C2312yes—
203C2×C4×Dic67C2312yes—
204C2×C4×Dic67C2312yes—
205C2×C4×Dic67C23116yes—
206C2×C4×Dic67C2314yes—
207C2×C4×Dic67C2314yes—
208C42×D67C2318yes—
209C22×Q8×C67C2311yescharacteristic
210C22×Q8×C67C2312yes—
211C22×D4×C67C2311yescharacteristic
212C23×C4×C67C2312yes—
213C23×C4×C67C2314yes—
214C4⋊Q8×C67C2318yes—
215#125×C67C23116yes—
216C22⋊Q8×C67C23116yes—
217C22⋊Q8×C67C23132yes—
218C4×Q8×C67C2318yes—
219C4×D4×C67C2318yes—
220C4×D4×C67C23116yes—
221C2×C4⋊C4×C67C2311yescharacteristic
222C2×C4⋊C4×C67C2314yes—
223C2×C4⋊C4×C67C2312yes—
224C2×C4⋊C4×C67C23116yes—
225C2×C4⋊C4×C67C2311yescharacteristic
226C2×C4⋊C4×C67C2312yes—
227C2×C4⋊C4×C67C2312yes—
228C2×C4⋊C4×C67C2314yes—
229C2×C22⋊C4×C67C2314yes—
230C2×C22⋊C4×C67C2312yes—
231C2×C42×C67C2312yes—
232C2×C42×C67C2311yescharacteristic
233C23×D67C2411yescharacteristic
234C23×D67C2412yes—
235#11761627—232no—
236#11761627—264no—
237C2×Dic134—24no—
238C2×Dic134—28no—
239C2×Dic134C2414yes—
240C2×Dic134C2418yes—
241C2×D268—24no—
242C2×D268—44no—
243C2×D268C2414yes—
244C2×D268C2418yes—
245C2×C22⋊D67—28no—
246C2×C22⋊D67—216no—
247C2×C22⋊D67C2418yes—
248C2×C22⋊D67C24116yes—
249C22×Dic67—28no—
250C22×Dic67—216no—
251C22×Dic67—44no—
252C22×Dic67C2411yescharacteristic
253C22×Dic67C2411yescharacteristic
254C22×Dic67C2411yescharacteristic
255C22×Dic67C2412yes—
256C22×Dic67C2412yes—
257C22×Dic67C2414yes—
258C22×Dic67C2418yes—
259C22×Dic67C2412yes—
260C22×Dic67C24116yes—
261C22×Dic67C2418yes—
262C2×C4×D67—24no—
263C2×C4×D67—28no—
264C2×C4×D67—24no—
265C2×C4×D67—48no—
266C2×C4×D67—42no—
267C2×C4×D67C2414yes—
268C2×C4×D67C2414yes—
269C2×C4×D67C2418yes—
270C2×C4×D67C2414yes—
271C2×C4×D67C24116yes—
272C4⋊Dic67C2414yes—
273C4⋊Dic67C2414yes—
274C4⋊Dic67C2418yes—
275C4⋊Dic67C2418yes—
276C4⋊Dic67C24116yes—
277C4⋊Dic67C24116yes—
278C4⋊Dic67C24116yes—
279C4⋊Dic67C24116yes—
280C4⋊Dic67C2418yes—
281C4⋊Dic67C24116yes—
282Dic67⋊C4C24116yes—
283Dic67⋊C4C2418yes—
284Dic67⋊C4C24116yes—
285Dic67⋊C4C24116yes—
286Dic67⋊C4C2418yes—
287Dic67⋊C4C2418yes—
288Dic67⋊C4C2418yes—
289C22⋊Dic67C2418yes—
290(C2×D67)⋊C4C2418yes—
291(C2×D67)⋊C4C2418yes—
292(C2×D67)⋊C4C2418yes—
293(C2×D67)⋊C4C2418yes—
294(C2×D67)⋊C4C24116yes—
295(C2×D67)⋊C4C24116yes—
296(C2×D67)⋊C4C24116yes—
297(C2×D67)⋊C4C2418yes—
298(C2×D67)⋊C4C2418yes—
299C4×Dic67C2414yes—
300C4×Dic67C2414yes—
301C4×Dic67C2414yes—
302C4×Dic67C2418yes—
303C4×Dic67C2418yes—
304C4×Dic67C2418yes—
305C4×Dic67C24116yes—
306C4×Dic67C24116yes—
307C24×C67C2412yes—
308C2×Q8×C67—24no—
309C2×Q8×C67—44no—
310C2×Q8×C67C2414yes—
311C2×Q8×C67C2418yes—
312C2×D4×C67#4118yes—
313C2×D4×C67C2414yes—
314C22×C4×C67—28no—
315C22×C4×C67—48no—
316C22×C4×C67C2412yes—
317C22×C4×C67C2411yescharacteristic
318C22×C4×C67C2412yes—
319C22×C4×C67C2412yes—
320C22×C4×C67C2414yes—
321C22×C4×C67C2418yes—
322C22×C4×C67C24116yes—
323C22×C4×C67C2411yescharacteristic
324C22×C4×C67C2411yescharacteristic
325C4⋊C4×C67C2414yes—
326C4⋊C4×C67C24116yes—
327C4⋊C4×C67C2418yes—
328C4⋊C4×C67C2414yes—
329C4⋊C4×C67C2418yes—
330C4⋊C4×C67C2418yes—
331C4⋊C4×C67C24116yes—
332C22⋊C4×C67C24116yes—
333C22⋊C4×C67C2418yes—
334C42×C67C2418yes—
335C42×C67C2414yes—
336C23×C67—24no—
337C23×C67—24no—
338C23×C67C2×#4118yes—
339C23×C67C2514yes—
340C23×C67C2511yescharacteristic
341C22×D67—22no—
342C22×D67—24no—
343C22×D67—22no—
344C22×D67—24no—
345C22×D67—24no—
346C22×D67—22no—
347C22×D67C2512yes—
348C22×D67C2514yes—
349Q8×C67—28no—
350Q8×C67—48no—
351D4×C67C2×#41116yes—
352C2×C4×C67—24no—
353C2×C4×C67—24no—
354C2×C4×C67—24no—
355C2×C4×C67—28no—
356C2×C4×C67—22no—
357C2×C4×C67—216no—
358C2×C4×C67—416no—
359C2×C4×C67C2×#4114yes—
360C2×C4×C672−1+414yes—
361C2×C4×C67C2514yes—
362C2×C4×C67C2512yes—
363C2×C4×C67C2514yes—
364C2×C4×C67C2514yes—
365C2×C4×C67C2518yes—
366C2×C4×C67C2512yes—
367C2×C4×C67C2512yes—
368C22⋊D67—216no—
369C22⋊D67—232no—
370C2×Dic67—22no—
371C2×Dic67—24no—
372C2×Dic67—24no—
373C2×Dic67—28no—
374C2×Dic67—216no—
375C2×Dic67—232no—
376C2×Dic67—22no—
377C2×Dic67—24no—
378C2×Dic67—22no—
379C2×Dic67—48no—
380C2×Dic67C2512yes—
381C2×Dic67C2512yes—
382C2×Dic67C2512yes—
383C2×Dic67C2514yes—
384C2×Dic67C2514yes—
385C2×Dic67C2518yes—
386C2×Dic67C2514yes—
387D268—28no—
388D268—48no—
389C4×D67—28no—
390C4×D67—216no—
391C4×D67—28no—
392C4×D67—416no—
393C4×D67—44no—
394Dic134—28no—
395Dic134—216no—
396C22×C67—24no—
397C22×C67—24no—
398C22×C67—216no—
399C22×C67C22×#4118yes—
400C22×C67C22×#4112yes—
401C22×C67C2×2−1+412yes—
402C22×C67#58512yes—
403C22×C67C2611yescharacteristic
404C2×D67—22no—
405C2×D67—24no—
406C2×D67—22no—
407C2×D67—24no—
408C2×D67—24no—
409C2×D67—22no—
410C2×D67—44no—
411C2×D67—48no—
412C4×C67—24no—
413C4×C67—24no—
414C4×C67—28no—
415C4×C67—22no—
416C4×C67—24no—
417C4×C67C22×#4114yes—
418C4×C67C2×2−1+414yes—
419Dic67—24no—
420Dic67—28no—
421Dic67—22no—
422Dic67—24no—
423Dic67—22no—
424Dic67—24no—
425Dic67—22no—
426C2×#3515—671nomaximal, Sylow
427C2×C67—28no—
428C2×C67#351514yescomplemented
429C2×C67C23×#4111yescharacteristic
430C2×C67C22×2−1+411yescharacteristic
431C2×C67C2×#58511yescharacteristic
432D67—42no—
433D67—44no—
434#3515—6732no—
435C2×#557—671no—
436C2×#554—671no—
437C2×#554D6711yescharacteristic, complemented
438C2×#553—672no—
439C2×#552—672no—
440C2×#552—674no—
441C2×#552—672no—
442C2×#547—672no—
443C2×#547—671no—
444C2×#541—672no—
445C2×#539—674no—
446C2×#533—671no—
447C2×#529—672no—
448C2×#529—671no—
449C22×#125—672no—
450C2×#520—672no—
451C2×C4×#41—671no—
452C67C2×#351511yescharacteristic, complemented, Sylow
453C22×#41—671no—
454C22×#41—672no—
455#557—6716no—
456#554—6716no—
457#554C2×D67116yescomplemented
458#553—6732no—
459#552—6732no—
460#552—6764no—
461#552—6732no—
462#547—6732no—
463#547—6716no—
464#541—6732no—
465#539—6764no—
466#533—6716no—
467C2×C4⋊Q8—671no—
468C2×C4⋊Q8—672no—
469C2×C4⋊Q8C2×D6711yescharacteristic
470#529—6732no—
471#529—6716no—
472C2×#126—674no—
473C2×#126—672no—
474C2×#126—674no—
475C2×#126—674no—
476C2×#125—671no—
477C2×#125—672no—
478C2×#125—674no—
479C2×#125—674no—
480C2×#125—672no—
481C2×#125—672no—
482C2×#125—6732no—
483C2×#125—674no—
484C2×#125—674no—
485C2×#125C2×D6712yes—
486C2×#124—671no—
487C2×#123—672no—
488C2×#123—674no—
489C2×#123—674no—
490C2×#123—674no—
491C2×#123—674no—
492C2×C22⋊Q8—671no—
493C2×C22⋊Q8—672no—
494C2×C22⋊Q8—674no—
495C2×C22⋊Q8—672no—
496C2×C22⋊Q8—672no—
497C2×C22⋊Q8—672no—
498C2×C22⋊Q8C2×D6712yes—
499C2×C22⋊Q8C2×D6714yes—
500C2×#121—672no—
501C2×#121—674no—
502C2×#121—671no—
503#520—6732no—
504C4×#41—6716no—
505C2×C4×Q8—672no—
506C2×C4×Q8—672no—
507C2×C4×Q8—671no—
508C2×C4×Q8—672no—
509C2×C4×Q8—671no—
510C2×C4×Q8—672no—
511C2×C4×Q8C2×D6711yescharacteristic
512C2×C4×D4—671no—
513C2×C4×D4—672no—
514C2×C4×D4—674no—
515C2×C4×D4—672no—
516C2×C4×D4—672no—
517C2×C4×D4—674no—
518C2×C4×D4—672no—
519C2×C4×D4—671no—
520C2×C4×D4C2×D6711yescharacteristic
521C2×C4×D4C2×D6712yes—
522C2×#117—671no—
523C2×#117—674no—
524C2×#117—672no—
525C2×#117—672no—
526C2×#117—674no—
527C2×#117—672no—
528C22×C4⋊C4—674no—
529C22×C4⋊C4—672no—
530C22×C4⋊C4—674no—
531C22×C4⋊C4—672no—
532C22×C4⋊C4C2×D6712yes—
533C22×C42—672no—
534C22×C42—671no—
535C2×#41—678no—
536C2×#41—6716no—
537C2×#41—1348no—
538C2×#41—13416no—
539C22×Q8—671no—
540C22×Q8—672no—
541C22×Q8C22×D6711yescharacteristic
542C22×Q8C22×D6712yes—
543C22×D4—672no—
544C22×D4—674no—
545C22×D4—672no—
546C22×D4—671no—
547C22×D4C22×D6711yescharacteristic
548C23×C4—672no—
549C23×C4—674no—
550C23×C4—671no—
551C23×C4—674no—
552C23×C4—672no—
553C23×C4—672no—
554C23×C4—671no—
555C23×C4—671no—
556C23×C4C22×D6712yes—
557C23×C4C22×D6714yes—
558C4⋊Q8—678no—
559C4⋊Q8—6716no—
560C4⋊Q8C22×D6718yes—
561#126—6732no—
562#126—6716no—
563#126—6732no—
564#126—6732no—
565#125—678no—
566#125—6716no—
567#125—6732no—
568#125—6732no—
569#125—6716no—
570#125—6716no—
571#125—6732no—
572#125—6732no—
573#125C22×D67116yes—
574#124—678no—
575#123—6716no—
576#123—6732no—
577#123—6732no—
578#123—6732no—
579#123—6732no—
580C22⋊Q8—678no—
581C22⋊Q8—6716no—
582C22⋊Q8—6732no—
583C22⋊Q8—6716no—
584C22⋊Q8—6716no—
585C22⋊Q8—6716no—
586C22⋊Q8C22×D67116yes—
587C22⋊Q8C22×D67132yes—
588#121—6716no—
589#121—6732no—
590#121—678no—
591C4×Q8—6716no—
592C4×Q8—6716no—
593C4×Q8—678no—
594C4×Q8—6716no—
595C4×Q8—678no—
596C4×Q8—6716no—
597C4×Q8C22×D6718yes—
598C4×D4—678no—
599C4×D4—6716no—
600C4×D4—6732no—
601C4×D4—6716no—
602C4×D4—6716no—
603C4×D4—6732no—
604C4×D4—6716no—
605C4×D4—678no—
606C4×D4C22×D6718yes—
607C4×D4C22×D67116yes—
608#117—678no—
609#117—6732no—
610#117—6716no—
611#117—6716no—
612#117—6732no—
613#117—6716no—
614C2×C4⋊C4—671no—
615C2×C4⋊C4—674no—
616C2×C4⋊C4—672no—
617C2×C4⋊C4—671no—
618C2×C4⋊C4—672no—
619C2×C4⋊C4—672no—
620C2×C4⋊C4—674no—
621C2×C4⋊C4—674no—
622C2×C4⋊C4—674no—
623C2×C4⋊C4—6732no—
624C2×C4⋊C4—674no—
625C2×C4⋊C4—674no—
626C2×C4⋊C4—674no—
627C2×C4⋊C4—6716no—
628C2×C4⋊C4—6732no—
629C2×C4⋊C4—672no—
630C2×C4⋊C4—672no—
631C2×C4⋊C4—672no—
632C2×C4⋊C4—672no—
633C2×C4⋊C4—674no—
634C2×C4⋊C4—6716no—
635C2×C4⋊C4C22×D6712yes—
636C2×C4⋊C4C22×D6711yescharacteristic
637C2×C4⋊C4C22×D6712yes—
638C2×C4⋊C4C22×D6714yes—
639C2×C4⋊C4C22×D67116yes—
640C2×C4⋊C4C22×D6711yescharacteristic
641C2×C4⋊C4C22×D6714yes—
642C2×C4⋊C4C22×D6712yes—
643C2×C22⋊C4—672no—
644C2×C22⋊C4—672no—
645C2×C22⋊C4—672no—
646C2×C22⋊C4—672no—
647C2×C22⋊C4—672no—
648C2×C22⋊C4—674no—
649C2×C22⋊C4—674no—
650C2×C22⋊C4—674no—
651C2×C22⋊C4—672no—
652C2×C22⋊C4—672no—
653C2×C22⋊C4C22×D6714yes—
654C2×C22⋊C4C22×D6712yes—
655C2×C42—672no—
656C2×C42—671no—
657C2×C42—674no—
658C2×C42—674no—
659C2×C42—671no—
660C2×C42—672no—
661C2×C42—672no—
662C2×C42—6716no—
663C2×C42—671no—
664C2×C42—678no—
665C2×C42C22×D6712yes—
666C2×C42C22×D6711yescharacteristic
667C24—671no—
668C24—672no—
669C24C23×D6712yes—
670#41—13432no—
671#41—13464no—
672C2×Q8—24no—
673C2×Q8—44no—
674C2×Q8—674no—
675C2×Q8—678no—
676C2×Q8—1344no—
677C2×Q8—1348no—
678C2×Q8C23×D6714yes—
679C2×Q8C23×D6718yes—
680C2×D4—2684no—
681C2×D4—678no—
682C2×D4—6716no—
683C2×D4—678no—
684C2×D4—674no—
685C2×D4—1348no—
686C2×D4—13416no—
687C2×D4—1344no—
688C2×D4#1176162918yes—
689C2×D4C23×D6714yes—
690C22×C4—28no—
691C22×C4—48no—
692C22×C4—2688no—
693C22×C4—2682no—
694C22×C4—2684no—
695C22×C4—678no—
696C22×C4—674no—
697C22×C4—6716no—
698C22×C4—678no—
699C22×C4—6716no—
700C22×C4—671no—
701C22×C4—671no—
702C22×C4—672no—
703C22×C4—671no—
704C22×C4—674no—
705C22×C4—672no—
706C22×C4—672no—
707C22×C4—674no—
708C22×C4—674no—
709C22×C4—678no—
710C22×C4—13416no—
711C22×C4—1348no—
712C22×C4—1348no—
713C22×C4—1344no—
714C22×C4—1344no—
715C22×C4C23×D6718yes—
716C22×C4C23×D6712yes—
717C22×C4C23×D6712yes—
718C22×C4C23×D6711yescharacteristic
719C22×C4C23×D6714yes—
720C22×C4C23×D6712yes—
721C22×C4C23×D67116yes—
722C22×C4C23×D6711yescharacteristic
723C22×C4C23×D6711yescharacteristic
724C4⋊C4—674no—
725C4⋊C4—6716no—
726C4⋊C4—678no—
727C4⋊C4—674no—
728C4⋊C4—678no—
729C4⋊C4—678no—
730C4⋊C4—6716no—
731C4⋊C4—6716no—
732C4⋊C4—6716no—
733C4⋊C4—6716no—
734C4⋊C4—6716no—
735C4⋊C4—6716no—
736C4⋊C4—678no—
737C4⋊C4—678no—
738C4⋊C4—678no—
739C4⋊C4—678no—
740C4⋊C4—6716no—
741C4⋊C4C23×D6718yes—
742C4⋊C4C23×D6714yes—
743C4⋊C4C23×D6718yes—
744C4⋊C4C23×D67116yes—
745C4⋊C4C23×D6714yes—
746C4⋊C4C23×D67116yes—
747C4⋊C4C23×D6718yes—
748C22⋊C4—678no—
749C22⋊C4—678no—
750C22⋊C4—678no—
751C22⋊C4—678no—
752C22⋊C4—678no—
753C22⋊C4—6716no—
754C22⋊C4—6716no—
755C22⋊C4—6716no—
756C22⋊C4—678no—
757C22⋊C4—678no—
758C22⋊C4C23×D67116yes—
759C22⋊C4C23×D6718yes—
760C42—674no—
761C42—678no—
762C42—674no—
763C42—674no—
764C42—678no—
765C42—678no—
766C42—6716no—
767C42—6716no—
768C42C23×D6714yes—
769C42C23×D6718yes—
770C23—24no—
771C23—24no—
772C23—672no—
773C23—674no—
774C23—1342no—
775C23—1344no—
776C23—1342no—
777C23—1344no—
778C23—1344no—
779C23—1342no—
780C23C2×#1176162918yes—
781C23C24×D6714yes—
782C23C24×D6711yescharacteristic
783Q8—28no—
784Q8—48no—
785Q8—1348no—
786Q8—13416no—
787D4—2688no—
788D4—13416no—
789D4—13432no—
790D4—1348no—
791D4C2×#11761629116yes—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—216no—
798C2×C4—416no—
799C2×C4—26816no—
800C2×C4—2684no—
801C2×C4—2688no—
802C2×C4—672no—
803C2×C4—672no—
804C2×C4—672no—
805C2×C4—674no—
806C2×C4—674no—
807C2×C4—678no—
808C2×C4—674no—
809C2×C4—1342no—
810C2×C4—1344no—
811C2×C4—1348no—
812C2×C4—1344no—
813C2×C4—13416no—
814C2×C4—13432no—
815C2×C4—1342no—
816C2×C4—1344no—
817C2×C4—1342no—
818C2×C4—1348no—
819C2×C4—13416no—
820C2×C4—1348no—
821C2×C4C2×#1176162914yes—
822C2×C4#1452409014yes—
823C2×C4C24×D6714yes—
824C2×C4C24×D6714yes—
825C2×C4C24×D6712yes—
826C2×C4C24×D6718yes—
827C2×C4C24×D6714yes—
828C2×C4C24×D6712yes—
829C2×C4C24×D6712yes—
830C22—216no—
831C22—24no—
832C22—24no—
833C22—2684no—
834C22—2688no—
835C22—1342no—
836C22—1344no—
837C22—1342no—
838C22—1344no—
839C22—1344no—
840C22—1342no—
841C22C22×#1176162918yes—
842C22C22×#1176162912yes—
843C22C2×#1452409012yes—
844C22#1686423112yes—
845C22C25×D6711yescharacteristic
846C4—24no—
847C4—24no—
848C4—24no—
849C4—28no—
850C4—22no—
851C4—1342no—
852C4—1344no—
853C4—1344no—
854C4—1348no—
855C4—1342no—
856C4—1344no—
857C4—1342no—
858C4C22×#1176162914yes—
859C4C2×#1452409014yes—
860C2—28no—
861C2—2682no—
862C2—2684no—
863C2#2257418814yesdirect product factor
864C2C23×#1176162911yescharacteristic
865C2C22×#1452409011yescharacteristic
866C2C2×#1686423111yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#554×C67C2
socleC23×C67C25
hypercenterC2×#554D67
hypocenterC67C2×#3515
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #22574188C2direct (N × H)
2. C2×#16864125C2semidirect
3. C2×#16864107C2semidirect
4. C2×#16864094C2semidirect
5. C2×#16864088C2semidirect
6. C2×#16864088C2semidirect
7. C2×#16864084C2semidirect
8. C2×#16864050C2semidirect
9. C2×#16864050C2semidirect
10. C2×#16864009C2semidirect
11. C2×#16863995C2semidirect
12. C2×#16863951C2semidirect
13. C2×#16863933C2semidirect
14. C2×#16863932C2semidirect
15. C22×#14524034C2semidirect
16. C2×#16863875C2semidirect
17. C2×C4×#11761627C2semidirect
18. C2×#554×C67C2semidirect
21. #16864125C22semidirect
22. #16864107C22semidirect
23. #16864094C22semidirect
24. #16864088C22semidirect
25. #16864088C22semidirect
26. #16864084C22semidirect
27. #16864050C22semidirect
28. #16864050C22semidirect
29. #16864009C22semidirect
30. #16863995C22semidirect
31. #16863951C22semidirect
34. #16863933C22semidirect
35. #16863932C22semidirect
48. C2×#14524034C22semidirect
64. #16863875C22semidirect
65. C4×#11761627C22semidirect
92. #554×C67C22semidirect
428. C2×C67#3515semidirect
437. C2×#554D67semidirect
452. C67C2×#3515semidirect
457. #554C2×D67semidirect
863. C2#22574188direct (N × H)

Maximal subgroups

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

subgroupindex
#225741882
C2×#168641252
C2×#168641072
C2×#168640942
C2×#168640882
C2×#168640842
C2×#168640502
C2×#168640092
C2×#168639952
C2×#168639512
C2×#168639332
C2×#168639322
C22×#145240342
C2×#168638752
C2×C4×#117616272
C2×#554×C672
C2×#351567