Finite Group Databasebeta

← C2×#22574128 #31764335

Subgroups — C2×#22574128 #31764335

Order 17152.

7238 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574128C2132yesmaximal, direct product factor
2C2×#16864093C214yesmaximal, complemented
3C2×#16864091C214yesmaximal, complemented
4C2×#16864089C214yesmaximal, complemented
5C2×#16864083C214yesmaximal, complemented
6C2×#16864009C211yesmaximal, characteristic, complemented
7C2×#16864008C211yesmaximal, characteristic, complemented
8C2×#16864000C211yesmaximal, characteristic, complemented
9C2×#16863975C212yesmaximal, complemented
10C2×#16863944C211yesmaximal, characteristic, complemented
11C2×#16863928C212yesmaximal, complemented
12C2×#16863927C212yesmaximal, complemented
13C2×#125×D67C211yesmaximal, characteristic, complemented
14C2×#16863875C212yesmaximal, complemented
15C2×#16863864C211yesmaximal, characteristic, complemented
16C2×#540×C67C211yesmaximal, characteristic, complemented
17C22×#11761628C2211yescharacteristic
18C22×#11761627C2212yes—
19#16864093C22164yescomplemented
20#16864091C22164yescomplemented
21#16864089C22164yescomplemented
22#16864083C22164yescomplemented
23#16864009C22116yescomplemented
24#16864008C22116yescomplemented
25#16864000C22116yescomplemented
26#16863975C22132yescomplemented
27#16863944C22116yescomplemented
28C2×#14524043C2211yescharacteristic
29#16863928C22132yescomplemented
30#16863927C22132yescomplemented
31C2×#14524038C2214yes—
32C2×#14524036C2214yes—
33C2×#14524036C2214yes—
34C2×#14524036C2214yes—
35C2×#14524035C2211yescharacteristic
36C2×#14524034C2214yes—
37C2×#14524034C2212yes—
38C2×#14524033C2214yes—
39C2×#14524033C2214yes—
40#125×D67C22116yescomplemented
41C2×#14524030C2212yes—
42C2×#14524025C2214yes—
43C2×#14524024C2214yes—
44C2×#14524024C2214yes—
45C2×#14524023C2212yes—
46C2×#14524022C2212yes—
47C2×#14524020C2214yes—
48C2×#14524016C2214yes—
49C2×#14524015C2214yes—
50C2×#14524015C2214yes—
51C2×#14524014C2212yes—
52C2×#14524014C2214yes—
53C2×#14524014C2214yes—
54#16863875C22132yescomplemented
55#16863864C22116yescomplemented
56C2×C4×Dic134C2212yes—
57C2×#14524008C2212yes—
58C2×#14524008C2212yes—
59C2×D4×Dic67C2212yes—
60C2×D4×Dic67C2214yes—
61C2×D4×Dic67C2214yes—
62C2×#14524005C2212yes—
63C2×C4×C22⋊D67C2214yes—
64C2×C4×C22⋊D67C2214yes—
65C2×(C22⋊D67)⋊C4C2212yes—
66C2×(C22⋊D67)⋊C4C2212yes—
67C2×(C22⋊D67)⋊C4C2214yes—
68C2×#14524002C2214yes—
69C2×#14524000C2211yescharacteristic
70C2×#14524000C2211yescharacteristic
71C2×#14523999C2214yes—
72C2×#14523999C2214yes—
73C22×Dic67⋊C4C2214yes—
74C2×C4⋊C4×D67C2212yes—
75C2×C4⋊C4×D67C2214yes—
76C22×C4×Dic67C2211yescharacteristic
77C2×C42×D67C2211yescharacteristic
78C2×C42×D67C2211yescharacteristic
79#540×C67C22116yescomplemented
80C2×#127×C67C2211yescharacteristic
81C2×#125×C67C2211yescharacteristic
82C2×#123×C67C2214yes—
83C2×#121×C67C2214yes—
84C2×#121×C67C2212yes—
85C2×C4×D4×C67C2212yes—
86C2×#117×C67C2211yescharacteristic
87C2×#11761628—28no—
88C2×#11761628C2318yes—
89C2×#11761627—216no—
90C2×#11761627C23116yes—
91C22×Dic134C2311yescharacteristic
92C22×Dic134C2312yes—
93C22×D268C2311yescharacteristic
94C22×C22⋊D67C2311yescharacteristic
95C22×C22⋊D67C2311yescharacteristic
96C22×C22⋊D67C2314yes—
97C22×C22⋊D67C2314yes—
98C23×Dic67C2314yes—
99C23×Dic67C2312yes—
100C23×Dic67C2314yes—
101C22×C4×D67C2311yescharacteristic
102C22×C4×D67C2312yes—
103C22×C4×D67C2312yes—
104C22×C4×D67C2314yes—
105C22×C4×D67C2311yescharacteristic
106#14524043C2318yes—
107#14524038C23132yes—
108#14524036C23132yes—
109#14524036C23132yes—
110#14524036C23132yes—
111#14524035C2318yes—
112#14524034C23132yes—
113#14524034C23116yes—
114#14524033C23132yes—
115#14524033C23132yes—
116#14524030C23116yes—
117#14524025C23132yes—
118#14524024C23132yes—
119#14524024C23132yes—
120#14524023C23116yes—
121#14524022C23116yes—
122#14524020C23132yes—
123#14524016C23132yes—
124#14524015C23132yes—
125#14524015C23132yes—
126#14524014C23116yes—
127#14524014C23132yes—
128#14524014C23132yes—
129C4×Dic134C23116yes—
130#14524008C23116yes—
131#14524008C23116yes—
132D4×Dic67C23116yes—
133D4×Dic67C23132yes—
134D4×Dic67C23132yes—
135#14524005C23116yes—
136C4×C22⋊D67C23132yes—
137C4×C22⋊D67C23132yes—
138(C22⋊D67)⋊C4C23116yes—
139(C22⋊D67)⋊C4C23132yes—
140(C22⋊D67)⋊C4C23116yes—
141#14524002C23132yes—
142#14524000C2318yes—
143#14524000C2318yes—
144#14523999C23132yes—
145#14523999C23132yes—
146C2×C4⋊Dic67C2314yes—
147C2×C4⋊Dic67C2312yes—
148C2×C4⋊Dic67C2314yes—
149C2×C4⋊Dic67C2314yes—
150C2×Dic67⋊C4C23132yes—
151C2×Dic67⋊C4C2314yes—
152C2×Dic67⋊C4C2314yes—
153C2×Dic67⋊C4C2314yes—
154C2×Dic67⋊C4C2312yes—
155C2×Dic67⋊C4C2314yes—
156C2×Dic67⋊C4C2314yes—
157C2×Dic67⋊C4C2314yes—
158C2×Dic67⋊C4C2312yes—
159C4⋊C4×D67C23132yes—
160C4⋊C4×D67C23116yes—
161C2×C22⋊Dic67C2314yes—
162C2×C22⋊Dic67C2314yes—
163C2×C22⋊Dic67C2314yes—
164C2×C22⋊Dic67C2314yes—
165C2×C22⋊Dic67C2314yes—
166C2×(C2×D67)⋊C4C2312yes—
167C2×(C2×D67)⋊C4C2312yes—
168C2×(C2×D67)⋊C4C2314yes—
169C2×C4×Dic67C2311yescharacteristic
170C2×C4×Dic67C2312yes—
171C2×C4×Dic67C2312yes—
172C2×C4×Dic67C2312yes—
173C2×C4×Dic67C2311yescharacteristic
174C2×C4×Dic67C2318yes—
175C2×C4×Dic67C2314yes—
176C2×C4×Dic67C2314yes—
177C42×D67C2318yes—
178C42×D67C2318yes—
179C22×D4×C67C2312yes—
180C22×D4×C67C2314yes—
181C22×D4×C67C2314yes—
182C23×C4×C67C2311yescharacteristic
183C23×C4×C67C2314yes—
184#127×C67C2318yes—
185#125×C67C2318yes—
186#123×C67C23132yes—
187#121×C67C23132yes—
188#121×C67C23116yes—
189C4×D4×C67C23116yes—
190#117×C67C2318yes—
191C2×C4⋊C4×C67C2312yes—
192C2×C4⋊C4×C67C2312yes—
193C2×C4⋊C4×C67C2314yes—
194C2×C22⋊C4×C67C2312yes—
195C2×C22⋊C4×C67C2314yes—
196C2×C22⋊C4×C67C2314yes—
197C2×C42×C67C2311yescharacteristic
198C2×C42×C67C2311yescharacteristic
199C23×D67C2411yescharacteristic
200C23×D67C2411yescharacteristic
201#11761628—232no—
202#11761627—264no—
203C2×Dic134—28no—
204C2×Dic134—24no—
205C2×Dic134C2414yes—
206C2×Dic134C2418yes—
207C2×D268—24no—
208C2×D268C2414yes—
209C2×C22⋊D67—216no—
210C2×C22⋊D67—24no—
211C2×C22⋊D67—24no—
212C2×C22⋊D67—48no—
213C2×C22⋊D67C2414yes—
214C2×C22⋊D67C2414yes—
215C2×C22⋊D67C24116yes—
216C2×C22⋊D67C24116yes—
217C22×Dic67—216no—
218C22×Dic67—44no—
219C22×Dic67—48no—
220C22×Dic67C2412yes—
221C22×Dic67C2412yes—
222C22×Dic67C2414yes—
223C22×Dic67C2411yescharacteristic
224C22×Dic67C2414yes—
225C22×Dic67C24116yes—
226C22×Dic67C2418yes—
227C22×Dic67C24116yes—
228C22×Dic67C2411yescharacteristic
229C2×C4×D67—24no—
230C2×C4×D67—44no—
231C2×C4×D67—44no—
232C2×C4×D67—48no—
233C2×C4×D67#4118yes—
234C2×C4×D67C2414yes—
235C2×C4×D67C2418yes—
236C2×C4×D67C2418yes—
237C2×C4×D67C24116yes—
238C2×C4×D67C2414yes—
239C4⋊Dic67C24116yes—
240C4⋊Dic67C2418yes—
241C4⋊Dic67C24116yes—
242C4⋊Dic67C24116yes—
243Dic67⋊C4C24116yes—
244Dic67⋊C4C24116yes—
245Dic67⋊C4C24116yes—
246Dic67⋊C4C2418yes—
247Dic67⋊C4C24116yes—
248Dic67⋊C4C24116yes—
249Dic67⋊C4C24116yes—
250Dic67⋊C4C2418yes—
251C22⋊Dic67C24116yes—
252C22⋊Dic67C24116yes—
253C22⋊Dic67C24116yes—
254C22⋊Dic67C24116yes—
255C22⋊Dic67C24116yes—
256(C2×D67)⋊C4C2418yes—
257(C2×D67)⋊C4C2418yes—
258(C2×D67)⋊C4C24116yes—
259C4×Dic67C2414yes—
260C4×Dic67C2418yes—
261C4×Dic67C2418yes—
262C4×Dic67C2418yes—
263C4×Dic67C2414yes—
264C4×Dic67C24116yes—
265C4×Dic67C24116yes—
266C24×C67C2411yescharacteristic
267C24×C67C2414yes—
268C2×D4×C67—28no—
269C2×D4×C67—48no—
270C2×D4×C67—48no—
271C2×D4×C67C2418yes—
272C2×D4×C67C24116yes—
273C2×D4×C67C24116yes—
274C22×C4×C67—24no—
275C22×C4×C67—48no—
276C22×C4×C67C2412yes—
277C22×C4×C67C2412yes—
278C22×C4×C67C2411yescharacteristic
279C22×C4×C67C2414yes—
280C22×C4×C67C2414yes—
281C22×C4×C67C24116yes—
282C22×C4×C67C2411yescharacteristic
283C4⋊C4×C67C2418yes—
284C4⋊C4×C67C2418yes—
285C4⋊C4×C67C24116yes—
286C22⋊C4×C67C2418yes—
287C22⋊C4×C67C24116yes—
288C22⋊C4×C67C24116yes—
289C42×C67C2414yes—
290C42×C67C2414yes—
291C23×C67—22no—
292C23×C67—28no—
293C23×C67—28no—
294C23×C67—24no—
295C23×C67—28no—
296C23×C67C2518yes—
297C23×C67C2512yes—
298C23×C67C2511yescharacteristic
299C22×D67—24no—
300C22×D67—22no—
301C22×D67—24no—
302C22×D67C2×#4114yes—
303C22×D67C2512yes—
304C22×D67C2512yes—
305D4×C67—216no—
306D4×C67—416no—
307D4×C67—416no—
308C2×C4×C67—22no—
309C2×C4×C67—24no—
310C2×C4×C67—28no—
311C2×C4×C67—24no—
312C2×C4×C67—28no—
313C2×C4×C67—416no—
314C2×C4×C67C2×#4114yes—
315C2×C4×C67C2514yes—
316C2×C4×C67C2514yes—
317C2×C4×C67C2512yes—
318C2×C4×C67C2518yes—
319C2×C4×C67C2512yes—
320C22⋊D67—232no—
321C22⋊D67—28no—
322C22⋊D67—28no—
323C22⋊D67—416no—
324C2×Dic67—22no—
325C2×Dic67—28no—
326C2×Dic67—24no—
327C2×Dic67—28no—
328C2×Dic67—24no—
329C2×Dic67—232no—
330C2×Dic67—48no—
331C2×Dic67—416no—
332C2×Dic67C2×#4114yes—
333C2×Dic67C2514yes—
334C2×Dic67C2514yes—
335C2×Dic67C2518yes—
336C2×Dic67C2512yes—
337C2×Dic67C2518yes—
338C2×Dic67C2512yes—
339D268—28no—
340C4×D67—28no—
341C4×D67—48no—
342C4×D67—48no—
343C4×D67—416no—
344C4×D67C2×#41116yes—
345Dic134—216no—
346Dic134—28no—
347C22×C67—28no—
348C22×C67—22no—
349C22×C67—28no—
350C22×C67—24no—
351C22×C67—28no—
352C22×C67—44no—
353C22×C67—416no—
354C22×C67C22×#4112yes—
355C22×C67#58514yes—
356C22×C67C2611yescharacteristic
357C2×D67—24no—
358C2×D67—28no—
359C2×D67—22no—
360C2×D67—24no—
361C2×D67—44no—
362C2×D67C22×#4114yes—
363C4×C67—22no—
364C4×C67—24no—
365C4×C67—28no—
366C4×C67—24no—
367C4×C67C22×#4114yes—
368Dic67—22no—
369Dic67—28no—
370Dic67—24no—
371Dic67—28no—
372Dic67—24no—
373Dic67C22×#4114yes—
374C2×#3512—671nomaximal, Sylow
375C2×C67—48no—
376C2×C67—42no—
377C2×C67#351214yescomplemented
378C2×C67C23×#4111yescharacteristic
379C2×C67C2×#58512yes—
380D67—24no—
381D67—42no—
382#3512—6732no—
383C2×#553—674no—
384C2×#553—674no—
385C2×#553—674no—
386C2×#552—674no—
387C2×#541—671no—
388C2×#541—671no—
389C2×#540—671no—
390C2×#540D6711yescharacteristic, complemented
391C2×#537—672no—
392C2×#532—671no—
393C2×#529—672no—
394C2×#529—672no—
395C22×#125—671no—
396C2×#520—672no—
397C2×C4×#41—671no—
398C67C2×#351211yescharacteristic, complemented, Sylow
399C22×#41—672no—
400C22×#41—671no—
401#553—6764no—
402#553—6764no—
403#553—6764no—
404#552—6764no—
405#541—6716no—
406#541—6716no—
407#540—6716no—
408#540C2×D67116yescomplemented
409#537—6732no—
410#532—6716no—
411C2×C4⋊Q8—671no—
412C2×#127C2×D6711yescharacteristic
413#529—6732no—
414#529—6732no—
415C2×#126—674no—
416C2×#126—674no—
417C2×#126—674no—
418C2×#126—674no—
419C2×#125—6716no—
420C2×#125—672no—
421C2×#125—674no—
422C2×#125—674no—
423C2×#125—674no—
424C2×#125—671no—
425C2×#125C2×D6711yescharacteristic
426C2×#124—672no—
427C2×#123—674no—
428C2×#123—674no—
429C2×#123—674no—
430C2×#123C2×D6714yes—
431C2×C22⋊Q8—672no—
432C2×C22⋊Q8—672no—
433C2×C22⋊Q8—674no—
434C2×#121—672no—
435C2×#121—674no—
436C2×#121—674no—
437C2×#121—674no—
438C2×#121—674no—
439C2×#121—674no—
440C2×#121C2×D6712yes—
441C2×#121C2×D6714yes—
442#520—6732no—
443C4×#41—6716no—
444C2×C4×Q8—672no—
445C2×C4×Q8—672no—
446C2×C4×Q8—672no—
447C2×C4×D4—672no—
448C2×C4×D4—674no—
449C2×C4×D4—674no—
450C2×C4×D4—674no—
451C2×C4×D4—674no—
452C2×C4×D4—672no—
453C2×C4×D4—672no—
454C2×C4×D4—672no—
455C2×C4×D4—674no—
456C2×C4×D4C2×D6712yes—
457C2×#117—674no—
458C2×#117—674no—
459C2×#117—674no—
460C2×#117—671no—
461C2×#117—671no—
462C2×#117C2×D6711yescharacteristic
463C22×C4⋊C4—674no—
464C22×C4⋊C4—672no—
465C22×C4⋊C4—674no—
466C22×C42—671no—
467C22×C42—671no—
468C22×C42—671no—
469C2×#41—6716no—
470C2×#41—678no—
471C2×#41—1348no—
472C2×#41—13416no—
473C22×Q8—671no—
474C22×Q8—672no—
475C22×D4—674no—
476C22×D4—671no—
477C22×D4—674no—
478C22×D4—671no—
479C22×D4—671no—
480C22×D4C22×D6712yes—
481C22×D4C22×D6714yes—
482C22×D4C22×D6714yes—
483C23×C4—674no—
484C23×C4—672no—
485C23×C4—674no—
486C23×C4—672no—
487C23×C4—672no—
488C23×C4—671no—
489C23×C4—674no—
490C23×C4—671no—
491C23×C4C22×D6711yescharacteristic
492C23×C4C22×D6714yes—
493C4⋊Q8—678no—
494#127C22×D6718yes—
495#126—6732no—
496#126—6732no—
497#126—6732no—
498#126—6732no—
499#125—6716no—
500#125—6732no—
501#125—6732no—
502#125—6732no—
503#125—678no—
504#125C22×D6718yes—
505#124—6716no—
506#123—6732no—
507#123—6732no—
508#123—6732no—
509#123C22×D67132yes—
510C22⋊Q8—6716no—
511C22⋊Q8—6716no—
512C22⋊Q8—6732no—
513#121—6716no—
514#121—6732no—
515#121—6732no—
516#121—6732no—
517#121—6732no—
518#121—6732no—
519#121C22×D67116yes—
520#121C22×D67132yes—
521C4×Q8—6716no—
522C4×Q8—6716no—
523C4×Q8—6716no—
524C4×D4—6716no—
525C4×D4—6732no—
526C4×D4—6732no—
527C4×D4—6732no—
528C4×D4—6732no—
529C4×D4—6716no—
530C4×D4—6716no—
531C4×D4—6716no—
532C4×D4—6732no—
533C4×D4C22×D67116yes—
534#117—6732no—
535#117—6732no—
536#117—6732no—
537#117—678no—
538#117—678no—
539#117C22×D6718yes—
540C2×C4⋊C4—672no—
541C2×C4⋊C4—674no—
542C2×C4⋊C4—674no—
543C2×C4⋊C4—674no—
544C2×C4⋊C4—672no—
545C2×C4⋊C4—674no—
546C2×C4⋊C4—674no—
547C2×C4⋊C4—6732no—
548C2×C4⋊C4—674no—
549C2×C4⋊C4—672no—
550C2×C4⋊C4—674no—
551C2×C4⋊C4—674no—
552C2×C4⋊C4—674no—
553C2×C4⋊C4—6716no—
554C2×C4⋊C4—6732no—
555C2×C4⋊C4C22×D6712yes—
556C2×C4⋊C4C22×D6714yes—
557C2×C4⋊C4C22×D6712yes—
558C2×C22⋊C4—674no—
559C2×C22⋊C4—674no—
560C2×C22⋊C4—674no—
561C2×C22⋊C4—674no—
562C2×C22⋊C4—674no—
563C2×C22⋊C4—672no—
564C2×C22⋊C4—672no—
565C2×C22⋊C4—674no—
566C2×C22⋊C4C22×D6714yes—
567C2×C22⋊C4C22×D6714yes—
568C2×C22⋊C4C22×D6712yes—
569C2×C42—671no—
570C2×C42—674no—
571C2×C42—674no—
572C2×C42—672no—
573C2×C42—672no—
574C2×C42—672no—
575C2×C42—678no—
576C2×C42—671no—
577C2×C42—678no—
578C2×C42—678no—
579C2×C42C22×D6711yescharacteristic
580C2×C42C22×D6711yescharacteristic
581C24—671no—
582C24—671no—
583C24C23×D6711yescharacteristic
584C24C23×D6714yes—
585#41—13432no—
586#41—13464no—
587C2×Q8—674no—
588C2×Q8—678no—
589C2×Q8—1344no—
590C2×Q8—1348no—
591C2×D4—28no—
592C2×D4—48no—
593C2×D4—48no—
594C2×D4—2688no—
595C2×D4—6716no—
596C2×D4—674no—
597C2×D4—6716no—
598C2×D4—674no—
599C2×D4—674no—
600C2×D4—1344no—
601C2×D4—1344no—
602C2×D4—1344no—
603C2×D4—13416no—
604C2×D4C23×D6718yes—
605C2×D4C23×D67116yes—
606C2×D4C23×D67116yes—
607C22×C4—24no—
608C22×C4—48no—
609C22×C4—2684no—
610C22×C4—2688no—
611C22×C4—2684no—
612C22×C4—2684no—
613C22×C4—2688no—
614C22×C4—678no—
615C22×C4—6716no—
616C22×C4—678no—
617C22×C4—678no—
618C22×C4—6716no—
619C22×C4—671no—
620C22×C4—678no—
621C22×C4—674no—
622C22×C4—6716no—
623C22×C4—672no—
624C22×C4—672no—
625C22×C4—674no—
626C22×C4—671no—
627C22×C4—674no—
628C22×C4—674no—
629C22×C4—13416no—
630C22×C4—1344no—
631C22×C4C23×D6714yes—
632C22×C4C23×D6712yes—
633C22×C4C23×D6711yescharacteristic
634C22×C4C23×D6712yes—
635C22×C4C23×D6714yes—
636C22×C4C23×D67116yes—
637C22×C4C23×D6711yescharacteristic
638C4⋊C4—678no—
639C4⋊C4—6716no—
640C4⋊C4—6716no—
641C4⋊C4—6716no—
642C4⋊C4—678no—
643C4⋊C4—6716no—
644C4⋊C4—6716no—
645C4⋊C4—6716no—
646C4⋊C4—678no—
647C4⋊C4—6716no—
648C4⋊C4—6716no—
649C4⋊C4—6716no—
650C4⋊C4C23×D6718yes—
651C4⋊C4C23×D67116yes—
652C4⋊C4C23×D6718yes—
653C22⋊C4—6716no—
654C22⋊C4—6716no—
655C22⋊C4—6716no—
656C22⋊C4—6716no—
657C22⋊C4—6716no—
658C22⋊C4—678no—
659C22⋊C4—678no—
660C22⋊C4—6716no—
661C22⋊C4C23×D67116yes—
662C22⋊C4C23×D67116yes—
663C22⋊C4C23×D6718yes—
664C42—674no—
665C42—674no—
666C42—678no—
667C42—678no—
668C42—678no—
669C42—6716no—
670C42—6716no—
671C42C23×D6714yes—
672C42C23×D6714yes—
673C23—22no—
674C23—28no—
675C23—28no—
676C23—24no—
677C23—28no—
678C23—674no—
679C23—672no—
680C23—672no—
681C23—1342no—
682C23—1344no—
683C23—1344no—
684C23C24×D6712yes—
685C23C24×D6718yes—
686C23C24×D6711yescharacteristic
687Q8—1348no—
688Q8—13416no—
689D4—216no—
690D4—416no—
691D4—416no—
692D4—26816no—
693D4—1348no—
694D4—1348no—
695D4—1348no—
696D4—13432no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—28no—
700C2×C4—24no—
701C2×C4—28no—
702C2×C4—416no—
703C2×C4—2688no—
704C2×C4—26816no—
705C2×C4—2688no—
706C2×C4—2688no—
707C2×C4—26816no—
708C2×C4—674no—
709C2×C4—672no—
710C2×C4—6716no—
711C2×C4—674no—
712C2×C4—674no—
713C2×C4—672no—
714C2×C4—678no—
715C2×C4—678no—
716C2×C4—13432no—
717C2×C4—1348no—
718C2×C4—1342no—
719C2×C4—1344no—
720C2×C4—1344no—
721C2×C4—1348no—
722C2×C4—1348no—
723C2×C4#41×D6714yes—
724C2×C4C24×D6714yes—
725C2×C4C24×D6712yes—
726C2×C4C24×D6714yes—
727C2×C4C24×D6718yes—
728C2×C4C24×D6712yes—
729C22—22no—
730C22—28no—
731C22—28no—
732C22—24no—
733C22—28no—
734C22—44no—
735C22—416no—
736C22—2684no—
737C22—674no—
738C22—1342no—
739C22—1344no—
740C22—1348no—
741C22—1344no—
742C22C2×#41×D6712yes—
743C22#1686423114yes—
744C22C25×D6711yescharacteristic
745C4—22no—
746C4—24no—
747C4—28no—
748C4—24no—
749C4—674no—
750C4—1348no—
751C4—1342no—
752C4—1344no—
753C4—1344no—
754C4—1348no—
755C4C2×#41×D6714yes—
756C2—42no—
757C2—48no—
758C2—2682no—
759C2—1344no—
760C2#2257412814yesdirect product factor
761C2C22×#41×D6711yescharacteristic
762C2C2×#1686423112yes—
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#540×C67C2
socleC23×C67C25
hypercenterC2×#540D67
hypocenterC67C2×#3512
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #22574128C2direct (N × H)
2. C2×#16864093C2semidirect
3. C2×#16864091C2semidirect
4. C2×#16864089C2semidirect
5. C2×#16864083C2semidirect
6. C2×#16864009C2semidirect
7. C2×#16864008C2semidirect
8. C2×#16864000C2semidirect
9. C2×#16863975C2semidirect
10. C2×#16863944C2semidirect
11. C2×#16863928C2semidirect
12. C2×#16863927C2semidirect
13. C2×#125×D67C2semidirect
14. C2×#16863875C2semidirect
15. C2×#16863864C2semidirect
16. C2×#540×C67C2semidirect
19. #16864093C22semidirect
20. #16864091C22semidirect
21. #16864089C22semidirect
22. #16864083C22semidirect
23. #16864009C22semidirect
24. #16864008C22semidirect
25. #16864000C22semidirect
26. #16863975C22semidirect
27. #16863944C22semidirect
29. #16863928C22semidirect
30. #16863927C22semidirect
40. #125×D67C22semidirect
54. #16863875C22semidirect
55. #16863864C22semidirect
79. #540×C67C22semidirect
377. C2×C67#3512semidirect
390. C2×#540D67semidirect
398. C67C2×#3512semidirect
408. #540C2×D67semidirect
760. C2#22574128direct (N × H)

Maximal subgroups

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

subgroupindex
#225741282
C2×#168640932
C2×#168640912
C2×#168640892
C2×#168640832
C2×#168640092
C2×#168640082
C2×#168640002
C2×#168639752
C2×#168639442
C2×#168639282
C2×#168639272
C2×#125×D672
C2×#168638752
C2×#168638642
C2×#540×C672
C2×#351267