Finite Group Databasebeta

← C2×#22574132 #31764333

Subgroups — C2×#22574132 #31764333

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#22574132C2132yesmaximal, direct product factor
2C2×#16864099C214yesmaximal, complemented
3C2×#16864097C214yesmaximal, complemented
4C2×#16864097C214yesmaximal, complemented
5C2×#16864078C214yesmaximal, complemented
6C2×#16864007C211yesmaximal, characteristic, complemented
7C2×#16864002C211yesmaximal, characteristic, complemented
8C2×#16864001C211yesmaximal, characteristic, complemented
9C2×#16863976C212yesmaximal, complemented
10C2×#16863947C211yesmaximal, characteristic, complemented
11C2×#16863933C212yesmaximal, complemented
12C2×#16863932C212yesmaximal, complemented
13C2×#125×D67C211yesmaximal, characteristic, complemented
14C2×#16863878C212yesmaximal, complemented
15C2×#16863864C211yesmaximal, characteristic, complemented
16C2×#541×C67C211yesmaximal, characteristic, complemented
17C22×#11761629C2212yes—
18C22×#11761628C2211yescharacteristic
19#16864099C22164yescomplemented
20#16864097C22164yescomplemented
21#16864097C22164yescomplemented
22#16864078C22164yescomplemented
23#16864007C22116yescomplemented
24#16864002C22116yescomplemented
25#16864001C22116yescomplemented
26#16863976C22132yescomplemented
27#16863947C22116yescomplemented
28C2×#14524040C2211yescharacteristic
29#16863933C22132yescomplemented
30#16863932C22132yescomplemented
31C2×#14524038C2214yes—
32C2×#14524038C2214yes—
33C2×#14524038C2214yes—
34C2×#14524035C2211yescharacteristic
35C2×#14524034C2212yes—
36C2×#14524033C2214yes—
37C2×#14524033C2214yes—
38#125×D67C22116yescomplemented
39C2×#14524032C2212yes—
40C2×#14524028C2214yes—
41C2×#14524028C2214yes—
42C2×#14524028C2214yes—
43C2×#14524027C2214yes—
44C2×#14524021C2214yes—
45C2×#14524019C2212yes—
46C2×#14524018C2214yes—
47C2×#14524018C2212yes—
48C2×#14524018C2214yes—
49C2×#14524018C2214yes—
50C2×#14524017C2212yes—
51C2×#14524016C2214yes—
52C2×#14524016C2214yes—
53C2×#14524016C2214yes—
54#16863878C22132yescomplemented
55#16863864C22116yescomplemented
56C2×Q8×Dic67C2212yes—
57C2×#14524008C2212yes—
58C2×C4×D268C2212yes—
59C2×C4×D268C2214yes—
60C2×C4×D268C2214yes—
61C2×#14524005C2212yes—
62C2×#14524005C2212yes—
63C2×#14524005C2214yes—
64C2×#14524005C2214yes—
65C2×(C22⋊D67)⋊C4C2212yes—
66C2×(C22⋊D67)⋊C4C2212yes—
67C2×(C22⋊D67)⋊C4C2214yes—
68C2×#14524001C2214yes—
69C2×#14524000C2211yescharacteristic
70C2×#14524000C2211yescharacteristic
71C2×#14524000C2214yes—
72C2×#14524000C2214yes—
73C2×C4⋊C4×D67C2214yes—
74C2×C4⋊C4×D67C2212yes—
75C2×C4⋊C4×D67C2214yes—
76C22×C4×Dic67C2211yescharacteristic
77C2×C42×D67C2211yescharacteristic
78C2×C42×D67C2211yescharacteristic
79#541×C67C22116yescomplemented
80C2×C4⋊Q8×C67C2211yescharacteristic
81C2×#126×C67C2214yes—
82C2×#125×C67C2211yescharacteristic
83C2×#125×C67C2214yes—
84C2×C22⋊Q8×C67C2212yes—
85C2×C4×Q8×C67C2212yes—
86C2×#117×C67C2211yescharacteristic
87C2×#11761629—216no—
88C2×#11761629C23116yes—
89C2×#11761628—28no—
90C2×#11761628C2318yes—
91C22×Dic134C2311yescharacteristic
92C22×D268C2311yescharacteristic
93C22×D268C2314yes—
94C22×D268C2312yes—
95C22×D268C2314yes—
96C22×D268C2314yes—
97C22×C22⋊D67C2311yescharacteristic
98C22×C22⋊D67C2311yescharacteristic
99C22×C22⋊D67C2314yes—
100C23×Dic67C2312yes—
101C22×C4×D67C2311yescharacteristic
102C22×C4×D67C2314yes—
103C22×C4×D67C2312yes—
104C22×C4×D67C2312yes—
105C22×C4×D67C2314yes—
106C22×C4×D67C2314yes—
107C22×C4×D67C2314yes—
108C22×C4×D67C2311yescharacteristic
109#14524040C2318yes—
110#14524038C23132yes—
111#14524038C23132yes—
112#14524038C23132yes—
113#14524035C2318yes—
114#14524034C23116yes—
115#14524033C23132yes—
116#14524033C23132yes—
117#14524032C23116yes—
118#14524028C23132yes—
119#14524028C23132yes—
120#14524028C23132yes—
121#14524027C23132yes—
122#14524021C23132yes—
123#14524019C23116yes—
124#14524018C23132yes—
125#14524018C23116yes—
126#14524018C23132yes—
127#14524018C23132yes—
128#14524017C23116yes—
129#14524016C23132yes—
130#14524016C23132yes—
131#14524016C23132yes—
132Q8×Dic67C23116yes—
133#14524008C23116yes—
134C4×D268C23116yes—
135C4×D268C23132yes—
136C4×D268C23132yes—
137#14524005C23116yes—
138#14524005C23132yes—
139#14524005C23132yes—
140#14524005C23116yes—
141(C22⋊D67)⋊C4C23116yes—
142(C22⋊D67)⋊C4C23116yes—
143(C22⋊D67)⋊C4C23132yes—
144#14524001C23132yes—
145#14524000C2318yes—
146#14524000C23132yes—
147#14524000C23132yes—
148#14524000C2318yes—
149C2×C4⋊Dic67C2314yes—
150C2×C4⋊Dic67C2312yes—
151C2×C4⋊Dic67C2314yes—
152C2×Dic67⋊C4C2312yes—
153C2×Dic67⋊C4C2314yes—
154C2×Dic67⋊C4C2314yes—
155C2×Dic67⋊C4C2314yes—
156C2×Dic67⋊C4C2312yes—
157C2×Dic67⋊C4C2314yes—
158C4⋊C4×D67C23132yes—
159C4⋊C4×D67C23132yes—
160C4⋊C4×D67C23116yes—
161C2×(C2×D67)⋊C4C2314yes—
162C2×(C2×D67)⋊C4C2312yes—
163C2×(C2×D67)⋊C4C2312yes—
164C2×(C2×D67)⋊C4C2314yes—
165C2×(C2×D67)⋊C4C2314yes—
166C2×(C2×D67)⋊C4C2314yes—
167C2×(C2×D67)⋊C4C2314yes—
168C2×(C2×D67)⋊C4C2314yes—
169C2×(C2×D67)⋊C4C2314yes—
170C2×C4×Dic67C2311yescharacteristic
171C2×C4×Dic67C2312yes—
172C2×C4×Dic67C2312yes—
173C2×C4×Dic67C2311yescharacteristic
174C2×C4×Dic67C2312yes—
175C2×C4×Dic67C2318yes—
176C2×C4×Dic67C2314yes—
177C42×D67C2318yes—
178C42×D67C2318yes—
179C22×Q8×C67C2312yes—
180C23×C4×C67C2311yescharacteristic
181C4⋊Q8×C67C2318yes—
182#126×C67C23132yes—
183#125×C67C2318yes—
184#125×C67C23132yes—
185C22⋊Q8×C67C23116yes—
186C4×Q8×C67C23116yes—
187#117×C67C2318yes—
188C2×C4⋊C4×C67C2312yes—
189C2×C4⋊C4×C67C2312yes—
190C2×C4⋊C4×C67C2314yes—
191C2×C4⋊C4×C67C2314yes—
192C2×C4⋊C4×C67C2314yes—
193C2×C4⋊C4×C67C2314yes—
194C2×C22⋊C4×C67C2312yes—
195C2×C22⋊C4×C67C2314yes—
196C2×C42×C67C2311yescharacteristic
197C2×C42×C67C2311yescharacteristic
198C2×C42×C67C2314yes—
199C23×D67C2411yescharacteristic
200C23×D67C2414yes—
201C23×D67C2411yescharacteristic
202#11761629—264no—
203#11761628—232no—
204C2×Dic134—24no—
205C2×Dic134C2414yes—
206C2×D268—24no—
207C2×D268—216no—
208C2×D268—28no—
209C2×D268—48no—
210C2×D268—48no—
211C2×D268C2414yes—
212C2×D268C24116yes—
213C2×D268C2418yes—
214C2×D268C24116yes—
215C2×D268C24116yes—
216C2×C22⋊D67—24no—
217C2×C22⋊D67—24no—
218C2×C22⋊D67—48no—
219C2×C22⋊D67C2414yes—
220C2×C22⋊D67C2414yes—
221C2×C22⋊D67C24116yes—
222C22×Dic67—44no—
223C22×Dic67C2412yes—
224C22×Dic67C2412yes—
225C22×Dic67C2411yescharacteristic
226C22×Dic67C2414yes—
227C22×Dic67C2418yes—
228C22×Dic67C2411yescharacteristic
229C2×C4×D67—24no—
230C2×C4×D67—216no—
231C2×C4×D67—44no—
232C2×C4×D67—48no—
233C2×C4×D67—44no—
234C2×C4×D67—48no—
235C2×C4×D67—48no—
236C2×C4×D67#4118yes—
237C2×C4×D67C2414yes—
238C2×C4×D67C24116yes—
239C2×C4×D67C2418yes—
240C2×C4×D67C2418yes—
241C2×C4×D67C24116yes—
242C2×C4×D67C24116yes—
243C2×C4×D67C24116yes—
244C2×C4×D67C2414yes—
245C4⋊Dic67C24116yes—
246C4⋊Dic67C2418yes—
247C4⋊Dic67C24116yes—
248Dic67⋊C4C2418yes—
249Dic67⋊C4C24116yes—
250Dic67⋊C4C24116yes—
251Dic67⋊C4C24116yes—
252Dic67⋊C4C2418yes—
253Dic67⋊C4C24116yes—
254(C2×D67)⋊C4C24116yes—
255(C2×D67)⋊C4C2418yes—
256(C2×D67)⋊C4C2418yes—
257(C2×D67)⋊C4C24116yes—
258(C2×D67)⋊C4C24116yes—
259(C2×D67)⋊C4C24116yes—
260(C2×D67)⋊C4C24116yes—
261(C2×D67)⋊C4C24116yes—
262(C2×D67)⋊C4C24116yes—
263C4×Dic67C2414yes—
264C4×Dic67C2418yes—
265C4×Dic67C2418yes—
266C4×Dic67C2414yes—
267C4×Dic67C2418yes—
268C4×Dic67C24116yes—
269C24×C67C2411yescharacteristic
270C2×Q8×C67—28no—
271C2×Q8×C67C2418yes—
272C22×C4×C67—24no—
273C22×C4×C67C2412yes—
274C22×C4×C67C2412yes—
275C22×C4×C67C2414yes—
276C22×C4×C67C2414yes—
277C22×C4×C67C2411yescharacteristic
278C22×C4×C67C2414yes—
279C22×C4×C67C2411yescharacteristic
280C4⋊C4×C67C2418yes—
281C4⋊C4×C67C2418yes—
282C4⋊C4×C67C24116yes—
283C4⋊C4×C67C24116yes—
284C4⋊C4×C67C24116yes—
285C4⋊C4×C67C24116yes—
286C22⋊C4×C67C2418yes—
287C22⋊C4×C67C24116yes—
288C42×C67C2414yes—
289C42×C67C2414yes—
290C42×C67C24116yes—
291C23×C67—22no—
292C23×C67—24no—
293C23×C67C2512yes—
294C23×C67C2511yescharacteristic
295C22×D67—24no—
296C22×D67—22no—
297C22×D67—28no—
298C22×D67—28no—
299C22×D67—24no—
300C22×D67—28no—
301C22×D67C2×#4114yes—
302C22×D67C2518yes—
303C22×D67C2512yes—
304C22×D67C2512yes—
305Q8×C67—216no—
306C2×C4×C67—22no—
307C2×C4×C67—28no—
308C2×C4×C67—24no—
309C2×C4×C67—28no—
310C2×C4×C67—24no—
311C2×C4×C67—28no—
312C2×C4×C67C2×#4114yes—
313C2×C4×C67C2514yes—
314C2×C4×C67C2514yes—
315C2×C4×C67C2518yes—
316C2×C4×C67C2518yes—
317C2×C4×C67C2512yes—
318C2×C4×C67C2512yes—
319C22⋊D67—28no—
320C22⋊D67—28no—
321C22⋊D67—416no—
322C2×Dic67—22no—
323C2×Dic67—24no—
324C2×Dic67—24no—
325C2×Dic67—28no—
326C2×Dic67—48no—
327C2×Dic67C2×#4114yes—
328C2×Dic67C2514yes—
329C2×Dic67C2514yes—
330C2×Dic67C2512yes—
331C2×Dic67C2518yes—
332C2×Dic67C2512yes—
333D268—28no—
334D268—232no—
335D268—216no—
336D268—416no—
337D268—416no—
338C4×D67—28no—
339C4×D67—232no—
340C4×D67—48no—
341C4×D67—416no—
342C4×D67—48no—
343C4×D67—416no—
344C4×D67—416no—
345C4×D67C2×#41116yes—
346Dic134—28no—
347C22×C67—22no—
348C22×C67—24no—
349C22×C67—44no—
350C22×C67C22×#4112yes—
351C22×C67#58514yes—
352C22×C67C2611yescharacteristic
353C2×D67—24no—
354C2×D67—28no—
355C2×D67—28no—
356C2×D67—22no—
357C2×D67—28no—
358C2×D67—24no—
359C2×D67—28no—
360C2×D67—44no—
361C2×D67—416no—
362C2×D67C22×#4114yes—
363C4×C67—22no—
364C4×C67—28no—
365C4×C67—24no—
366C4×C67—28no—
367C4×C67—24no—
368C4×C67C22×#4114yes—
369Dic67—22no—
370Dic67—24no—
371Dic67—24no—
372Dic67—28no—
373Dic67C22×#4114yes—
374C2×#3512—671nomaximal, Sylow
375C2×C67—42no—
376C2×C67#351214yescomplemented
377C2×C67C23×#4111yescharacteristic
378C2×C67C2×#58512yes—
379D67—24no—
380D67—48no—
381D67—42no—
382#3512—6732no—
383C2×#553—674no—
384C2×#553—674no—
385C2×#553—674no—
386C2×#552—674no—
387C2×#541—671no—
388C2×#541D6711yescharacteristic, complemented
389C2×#540—671no—
390C2×#540—671no—
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#541C2×D67116yescomplemented
407#540—6716no—
408#540—6716no—
409#537—6732no—
410#532—6716no—
411C2×C4⋊Q8C2×D6711yescharacteristic
412C2×#127—671no—
413#529—6732no—
414#529—6732no—
415C2×#126—674no—
416C2×#126—674no—
417C2×#126—674no—
418C2×#126C2×D6714yes—
419C2×#125—6716no—
420C2×#125—672no—
421C2×#125—674no—
422C2×#125—674no—
423C2×#125—671no—
424C2×#125C2×D6711yescharacteristic
425C2×#125C2×D6714yes—
426C2×#124—672no—
427C2×#123—674no—
428C2×#123—674no—
429C2×#123—674no—
430C2×#123—674no—
431C2×C22⋊Q8—672no—
432C2×C22⋊Q8—674no—
433C2×C22⋊Q8C2×D6712yes—
434C2×#121—672no—
435C2×#121—672no—
436C2×#121—674no—
437C2×#121—674no—
438C2×#121—674no—
439C2×#121—674no—
440C2×#121—674no—
441C2×#121—674no—
442#520—6732no—
443C4×#41—6716no—
444C2×C4×Q8—672no—
445C2×C4×Q8—672no—
446C2×C4×Q8C2×D6712yes—
447C2×C4×D4—672no—
448C2×C4×D4—672no—
449C2×C4×D4—674no—
450C2×C4×D4—674no—
451C2×C4×D4—672no—
452C2×C4×D4—672no—
453C2×C4×D4—674no—
454C2×C4×D4—672no—
455C2×C4×D4—674no—
456C2×C4×D4—674no—
457C2×#117—674no—
458C2×#117—671no—
459C2×#117—671no—
460C2×#117—674no—
461C2×#117—674no—
462C2×#117C2×D6711yescharacteristic
463C22×C4⋊C4—672no—
464C22×C4⋊C4—674no—
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×Q8C22×D6712yes—
475C22×D4—674no—
476C22×D4—671no—
477C22×D4—671no—
478C22×D4—674no—
479C22×D4—674no—
480C22×D4—671no—
481C22×D4—674no—
482C22×D4—672no—
483C23×C4—672no—
484C23×C4—674no—
485C23×C4—672no—
486C23×C4—674no—
487C23×C4—674no—
488C23×C4—672no—
489C23×C4—671no—
490C23×C4—674no—
491C23×C4—671no—
492C23×C4C22×D6711yescharacteristic
493C4⋊Q8C22×D6718yes—
494#127—678no—
495#126—6732no—
496#126—6732no—
497#126—6732no—
498#126C22×D67132yes—
499#125—6716no—
500#125—6732no—
501#125—6732no—
502#125—678no—
503#125C22×D6718yes—
504#125C22×D67132yes—
505#124—6716no—
506#123—6732no—
507#123—6732no—
508#123—6732no—
509#123—6732no—
510C22⋊Q8—6716no—
511C22⋊Q8—6732no—
512C22⋊Q8C22×D67116yes—
513#121—6716no—
514#121—6716no—
515#121—6732no—
516#121—6732no—
517#121—6732no—
518#121—6732no—
519#121—6732no—
520#121—6732no—
521C4×Q8—6716no—
522C4×Q8—6716no—
523C4×Q8C22×D67116yes—
524C4×D4—6716no—
525C4×D4—6716no—
526C4×D4—6732no—
527C4×D4—6732no—
528C4×D4—6716no—
529C4×D4—6716no—
530C4×D4—6732no—
531C4×D4—6716no—
532C4×D4—6732no—
533C4×D4—6732no—
534#117—6732no—
535#117—678no—
536#117—678no—
537#117—6732no—
538#117—6732no—
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—672no—
548C2×C4⋊C4—674no—
549C2×C4⋊C4—6716no—
550C2×C4⋊C4—6732no—
551C2×C4⋊C4—6732no—
552C2×C4⋊C4C22×D6712yes—
553C2×C4⋊C4C22×D6714yes—
554C2×C4⋊C4C22×D6714yes—
555C2×C4⋊C4C22×D6714yes—
556C2×C4⋊C4C22×D6712yes—
557C2×C4⋊C4C22×D6714yes—
558C2×C22⋊C4—674no—
559C2×C22⋊C4—672no—
560C2×C22⋊C4—672no—
561C2×C22⋊C4—674no—
562C2×C22⋊C4—674no—
563C2×C22⋊C4—674no—
564C2×C22⋊C4—674no—
565C2×C22⋊C4—674no—
566C2×C22⋊C4—674no—
567C2×C22⋊C4C22×D6712yes—
568C2×C22⋊C4C22×D6714yes—
569C2×C42—671no—
570C2×C42—674no—
571C2×C42—672no—
572C2×C42—672no—
573C2×C42—672no—
574C2×C42—678no—
575C2×C42—671no—
576C2×C42—678no—
577C2×C42—678no—
578C2×C42C22×D6714yes—
579C2×C42C22×D6711yescharacteristic
580C2×C42C22×D6711yescharacteristic
581C24—671no—
582C24—674no—
583C24—671no—
584C24C23×D6711yescharacteristic
585#41—13432no—
586#41—13464no—
587C2×Q8—28no—
588C2×Q8—674no—
589C2×Q8—1344no—
590C2×Q8C23×D6718yes—
591C2×D4—2688no—
592C2×D4—2688no—
593C2×D4—2688no—
594C2×D4—6716no—
595C2×D4—674no—
596C2×D4—674no—
597C2×D4—6716no—
598C2×D4—6716no—
599C2×D4—674no—
600C2×D4—6716no—
601C2×D4—678no—
602C2×D4—1344no—
603C2×D4—13416no—
604C2×D4—1344no—
605C2×D4—1344no—
606C2×D4—1348no—
607C22×C4—24no—
608C22×C4—2684no—
609C22×C4—2688no—
610C22×C4—2688no—
611C22×C4—2688no—
612C22×C4—2684no—
613C22×C4—2684no—
614C22×C4—678no—
615C22×C4—678no—
616C22×C4—678no—
617C22×C4—6716no—
618C22×C4—6716no—
619C22×C4—6716no—
620C22×C4—671no—
621C22×C4—678no—
622C22×C4—674no—
623C22×C4—672no—
624C22×C4—672no—
625C22×C4—671no—
626C22×C4—674no—
627C22×C4—674no—
628C22×C4—6716no—
629C22×C4—13416no—
630C22×C4—1344no—
631C22×C4C23×D6714yes—
632C22×C4C23×D6711yescharacteristic
633C22×C4C23×D6712yes—
634C22×C4C23×D6714yes—
635C22×C4C23×D6712yes—
636C22×C4C23×D6714yes—
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—678no—
646C4⋊C4—6716no—
647C4⋊C4C23×D6718yes—
648C4⋊C4C23×D67116yes—
649C4⋊C4C23×D67116yes—
650C4⋊C4C23×D67116yes—
651C4⋊C4C23×D6718yes—
652C4⋊C4C23×D67116yes—
653C22⋊C4—6716no—
654C22⋊C4—678no—
655C22⋊C4—678no—
656C22⋊C4—6716no—
657C22⋊C4—6716no—
658C22⋊C4—6716no—
659C22⋊C4—6716no—
660C22⋊C4—6716no—
661C22⋊C4—6716no—
662C22⋊C4C23×D6718yes—
663C22⋊C4C23×D67116yes—
664C42—674no—
665C42—674no—
666C42—678no—
667C42—678no—
668C42—678no—
669C42—6716no—
670C42C23×D6714yes—
671C42C23×D6714yes—
672C42C23×D67116yes—
673C23—22no—
674C23—24no—
675C23—674no—
676C23—672no—
677C23—678no—
678C23—672no—
679C23—1348no—
680C23—1342no—
681C23—1348no—
682C23—1344no—
683C23—1348no—
684C23—1344no—
685C23C24×D6712yes—
686C23C24×D6711yescharacteristic
687Q8—216no—
688Q8—1348no—
689D4—26816no—
690D4—26816no—
691D4—26816no—
692D4—1348no—
693D4—13432no—
694D4—1348no—
695D4—1348no—
696D4—13416no—
697C2×C4—22no—
698C2×C4—28no—
699C2×C4—24no—
700C2×C4—28no—
701C2×C4—24no—
702C2×C4—28no—
703C2×C4—2688no—
704C2×C4—26816no—
705C2×C4—26816no—
706C2×C4—26816no—
707C2×C4—2688no—
708C2×C4—2688no—
709C2×C4—674no—
710C2×C4—672no—
711C2×C4—6716no—
712C2×C4—674no—
713C2×C4—674no—
714C2×C4—672no—
715C2×C4—678no—
716C2×C4—13432no—
717C2×C4—1342no—
718C2×C4—1344no—
719C2×C4—1344no—
720C2×C4—1348no—
721C2×C4—1348no—
722C2×C4#41×D6714yes—
723C2×C4C24×D6712yes—
724C2×C4C24×D6714yes—
725C2×C4C24×D6718yes—
726C2×C4C24×D6714yes—
727C2×C4C24×D6718yes—
728C2×C4C24×D6712yes—
729C22—22no—
730C22—24no—
731C22—44no—
732C22—26816no—
733C22—2684no—
734C22—674no—
735C22—1348no—
736C22—1342no—
737C22—1348no—
738C22—1344no—
739C22—1348no—
740C22—1348no—
741C22—1344no—
742C22C2×#41×D6712yes—
743C22#1686423314yes—
744C22C25×D6711yescharacteristic
745C4—22no—
746C4—28no—
747C4—24no—
748C4—28no—
749C4—24no—
750C4—674no—
751C4—1342no—
752C4—1344no—
753C4—1344no—
754C4—1348no—
755C4C2×#41×D6714yes—
756C2—42no—
757C2—2688no—
758C2—2682no—
759C2—1344no—
760C2#2257413214yesdirect product factor
761C2C22×#41×D6711yescharacteristic
762C2C2×#1686423312yes—
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#541×C67C2
socleC23×C67C25
hypercenterC2×#541D67
hypocenterC67C2×#3512
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. #22574132C2direct (N × H)
2. C2×#16864099C2semidirect
3. C2×#16864097C2semidirect
4. C2×#16864097C2semidirect
5. C2×#16864078C2semidirect
6. C2×#16864007C2semidirect
7. C2×#16864002C2semidirect
8. C2×#16864001C2semidirect
9. C2×#16863976C2semidirect
10. C2×#16863947C2semidirect
11. C2×#16863933C2semidirect
12. C2×#16863932C2semidirect
13. C2×#125×D67C2semidirect
14. C2×#16863878C2semidirect
15. C2×#16863864C2semidirect
16. C2×#541×C67C2semidirect
19. #16864099C22semidirect
20. #16864097C22semidirect
21. #16864097C22semidirect
22. #16864078C22semidirect
23. #16864007C22semidirect
24. #16864002C22semidirect
25. #16864001C22semidirect
26. #16863976C22semidirect
27. #16863947C22semidirect
29. #16863933C22semidirect
30. #16863932C22semidirect
38. #125×D67C22semidirect
54. #16863878C22semidirect
55. #16863864C22semidirect
79. #541×C67C22semidirect
376. C2×C67#3512semidirect
388. C2×#541D67semidirect
398. C67C2×#3512semidirect
406. #541C2×D67semidirect
760. C2#22574132direct (N × H)

Maximal subgroups

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

subgroupindex
#225741322
C2×#168640992
C2×#168640972
C2×#168640782
C2×#168640072
C2×#168640022
C2×#168640012
C2×#168639762
C2×#168639472
C2×#168639332
C2×#168639322
C2×#125×D672
C2×#168638782
C2×#168638642
C2×#541×C672
C2×#351267