Finite Group Databasebeta

← C67×#18962 #30698213

Subgroups — C67×#18962 #30698213

Order 17152.

964 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C67×#3546C211yesmaximal, characteristic, complemented
2C67×#3253C211yesmaximal, characteristic, complemented
3C67×#3247C211yesmaximal, characteristic, complemented
4C67×#3207C211yesmaximal, characteristic, complemented
5C67×#1638C211yesmaximal, characteristic, complemented
6C67×#1635C211yesmaximal, characteristic, complemented
7C67×#1631C211yesmaximal, characteristic, complemented
8C67×#1629C211yesmaximal, characteristic, complemented
9C67×#1628C211yesmaximal, characteristic, complemented
10C67×#1625C211yesmaximal, characteristic, complemented
11C67×#1621C211yesmaximal, characteristic, complemented
12C67×#1619C211yesmaximal, characteristic, complemented
13C67×#1547C211yesmaximal, characteristic, complemented
14C67×#1495C211yesmaximal, characteristic, complemented
15C67×#1480C211yesmaximal, characteristic, complemented
16#560×C67—22no—
17#556×C67C2211yescharacteristic
18#553×C67—21no—
19#550×C67—21no—
20#550×C67C2211yescharacteristic
21#547×C67C2211yescharacteristic
22#546×C67—21no—
23#546×C67—21no—
24D42×C67C2211yescharacteristic
25#542×C67—21no—
26#538×C67—22no—
27#537×C67—21no—
28#535×C67—21no—
29#535×C67—21no—
30#532×C67C2211yescharacteristic
31#532×C67C2211yescharacteristic
32#532×C67C2211yescharacteristic, complemented
33#529×C67C2211yescharacteristic
34#493×C67C2211yescharacteristic
35#492×C67C2211yescharacteristic
36#487×C67C2211yescharacteristic, complemented
37#486×C67C2211yescharacteristic, complemented
38#478×C67—21no—
39#477×C67C2211yescharacteristic, complemented
40#476×C67—21no—
41#476×C67C2211yescharacteristic
42#476×C67C2211yescharacteristic
43#476×C67C2211yescharacteristic, complemented
44#469×C67—21no—
45#469×C67—21no—
46#466×C67—21no—
47#465×C67—21no—
48#463×C67—21no—
49#463×C67—22no—
50#460×C67C2211yescharacteristic, complemented
51#459×C67—21no—
52#459×C67C2211yescharacteristic
53#459×C67C2211yescharacteristic
54#459×C67C2211yescharacteristic, complemented
55#449×C67—22no—
56#431×C67C2211yescharacteristic, complemented
57#423×C67C2211yescharacteristic, complemented
58C2×C4⋊C8×C67C2211yescharacteristic, complemented
59#332×C67C2211yescharacteristic, complemented
60#332×C67C2211yescharacteristic, complemented
61#331×C67C2211yescharacteristic
62#331×C67C2211yescharacteristic
63Q8⋊C8×C67C2211yescharacteristic, complemented
64Q8⋊C8×C67C2211yescharacteristic, complemented
65D4⋊C8×C67C2211yescharacteristic
66D4⋊C8×C67C2211yescharacteristic
67D4⋊C8×C67C2211yescharacteristic
68D4⋊C8×C67C2211yescharacteristic
69D4⋊C8×C67C2211yescharacteristic, complemented
70D4⋊C8×C67C2211yescharacteristic, complemented
71C2×#41×C67—21no—
72C2×#41×C67—21no—
73C2×#41×C67—21no—
74C2×#41×C67—21no—
75C2×#41×C67—21no—
76C22×D4×C67—21no—
77C22×D4×C67—21no—
78C2×SD16×C67—21no—
79C2×SD16×C67—22no—
80C2×D8×C67—22no—
81C2×D8×C67—21no—
82C2×D8×C67—21no—
83C2×D8×C67—21no—
84C2×M16×C67—21no—
85C22×C8×C67—21no—
86C4⋊Q8×C67D411yescharacteristic
87C4⋊Q8×C67C2311yescharacteristic
88C4⋊Q8×C67C2311yescharacteristic
89#127×C67—22no—
90#127×C67—21no—
91#127×C67D411yescharacteristic
92#127×C67C2311yescharacteristic
93#127×C67C2311yescharacteristic
94#126×C67—22no—
95#126×C67—22no—
96#126×C67—21no—
97#125×C67D411yescharacteristic
98#124×C67—22no—
99#124×C67—21no—
100#124×C67—21no—
101#124×C67—21no—
102#124×C67—21no—
103#124×C67D411yescharacteristic
104#123×C67—22no—
105#123×C67—22no—
106#123×C67—21no—
107#123×C67—22no—
108C22⋊Q8×C67—22no—
109C22⋊Q8×C67—21no—
110C22⋊Q8×C67—21no—
111C22⋊Q8×C67D411yescharacteristic
112#121×C67—22no—
113#121×C67—22no—
114#121×C67—22no—
115#121×C67—22no—
116#121×C67—22no—
117#121×C67—21no—
118#121×C67—22no—
119#121×C67—21no—
120#121×C67—21no—
121#121×C67—21no—
122#121×C67—21no—
123#121×C67—21no—
124#121×C67—21no—
125#121×C67—21no—
126#121×C67D412yes—
127#121×C67D411yescharacteristic
128#121×C67D411yescharacteristic
129#121×C67D411yescharacteristic
130#120×C67—22no—
131#120×C67—22no—
132#120×C67—22no—
133#120×C67—22no—
134C4×Q8×C67—21no—
135C4×Q8×C67C2311yescharacteristic
136C4×D4×C67—22no—
137C4×D4×C67—21no—
138C4×D4×C67—21no—
139C4×D4×C67—21no—
140C4×D4×C67—21no—
141C4×D4×C67—21no—
142C4×D4×C67—21no—
143C4×D4×C67D412yes—
144C4×D4×C67C2311yescharacteristic
145C4×D4×C67C2311yescharacteristic
146C4×D4×C67C2311yescharacteristic
147#117×C67—21no—
148#117×C67—21no—
149C2×C4⋊C4×C67—21no—
150C2×C22⋊C4×C67—22no—
151C2×C42×C67C2311yescharacteristic
152#107×C67—21no—
153#106×C67—21no—
154#106×C67—21no—
155#106×C67—21no—
156C4⋊C8×C67—21no—
157C4⋊C8×C67—21no—
158C4⋊C8×C67—21no—
159C4⋊C8×C67C2311yescharacteristic
160C4⋊C8×C67C2311yescharacteristic
161C4⋊C8×C67C2311yescharacteristic
162C4⋊C8×C67C2311yescharacteristic
163#103×C67—21no—
164#103×C67—22no—
165#102×C67—21no—
166#102×C67—21no—
167#102×C67—21no—
168#102×C67—22no—
169#102×C67—21no—
170#102×C67—21no—
171#102×C67—21no—
172#102×C67—21no—
173C22⋊C8×C67—21no—
174C4×C8×C67C2311yescharacteristic
175C4×C8×C67C2311yescharacteristic
176C24×C67—22no—
177#41×C67—81no—
178#41×C67—81no—
179#41×C67—81no—
180#41×C67—81no—
181#41×C67—81no—
182#41×C67—81no—
183#41×C67—81no—
184#41×C67—81no—
185#41×C67—82no—
186C2×Q8×C67—21no—
187C2×Q8×C67—21no—
188C2×Q8×C67—21no—
189C2×Q8×C67C2×D411yescharacteristic
190C2×D4×C67—22no—
191C2×D4×C67—22no—
192C2×D4×C67—22no—
193C2×D4×C67—22no—
194C2×D4×C67—22no—
195C2×D4×C67—21no—
196C2×D4×C67—21no—
197C2×D4×C67—22no—
198C2×D4×C67—21no—
199C2×D4×C67—21no—
200C2×D4×C67—21no—
201C2×D4×C67—21no—
202C2×D4×C67—21no—
203C2×D4×C67—21no—
204C2×D4×C67—21no—
205C2×D4×C67—21no—
206C2×D4×C67—41no—
207C2×D4×C67—81no—
208C2×D4×C67—81no—
209C2×D4×C67—81no—
210C2×D4×C67—81no—
211C2×D4×C67C2×D411yescharacteristic
212C2×D4×C67C2×D411yescharacteristic
213C2×D4×C67C2×D411yescharacteristic
214C2×D4×C67C2×D412yes—
215C22×C4×C67—22no—
216C22×C4×C67—22no—
217C22×C4×C67—21no—
218C22×C4×C67—21no—
219C22×C4×C67—21no—
220C22×C4×C67—22no—
221C22×C4×C67—41no—
222C22×C4×C67C2×D411yescharacteristic
223C22×C4×C67C2×D411yescharacteristic
224C22×C4×C67C2×D411yescharacteristic
225SD16×C67—81no—
226SD16×C67—82no—
227D8×C67—81no—
228D8×C67—81no—
229D8×C67—81no—
230D8×C67—82no—
231M16×C67—81no—
232C2×C8×C67—21no—
233C2×C8×C67—21no—
234C2×C8×C67—21no—
235C2×C8×C67—21no—
236C2×C8×C67—21no—
237C2×C8×C67—21no—
238C2×C8×C67—81no—
239C4⋊C4×C67—22no—
240C4⋊C4×C67—22no—
241C4⋊C4×C67—21no—
242C4⋊C4×C67—21no—
243C4⋊C4×C67—21no—
244C4⋊C4×C67—21no—
245C4⋊C4×C67—21no—
246C4⋊C4×C67—21no—
247C4⋊C4×C67—21no—
248C4⋊C4×C67—21no—
249C4⋊C4×C67C2×D412yes—
250C4⋊C4×C67C2×D411yescharacteristic
251C4⋊C4×C67C2×D411yescharacteristic
252C4⋊C4×C67C2×D411yescharacteristic
253C4⋊C4×C67C2×D411yescharacteristic
254C22⋊C4×C67—22no—
255C22⋊C4×C67—22no—
256C22⋊C4×C67—22no—
257C22⋊C4×C67—22no—
258C22⋊C4×C67—22no—
259C22⋊C4×C67—21no—
260C22⋊C4×C67—21no—
261C22⋊C4×C67—21no—
262C22⋊C4×C67—21no—
263C22⋊C4×C67—21no—
264C22⋊C4×C67—21no—
265C22⋊C4×C67—22no—
266C22⋊C4×C67—22no—
267C22⋊C4×C67—21no—
268C22⋊C4×C67—21no—
269C22⋊C4×C67—21no—
270C22⋊C4×C67—41no—
271C22⋊C4×C67—41no—
272C42×C67—22no—
273C42×C67—21no—
274C42×C67C2×D411yescharacteristic
275C42×C67C2×D411yescharacteristic
276C42×C67C2×D411yescharacteristic
277C42×C67C2411yescharacteristic
278C23×C67—21no—
279C23×C67—21no—
280C23×C67—22no—
281C23×C67—21no—
282C23×C67—41no—
283C23×C67—82no—
284C23×C67—82no—
285C23×C67—82no—
286C23×C67#12011yescharacteristic
287Q8×C67—21no—
288Q8×C67—21no—
289Q8×C67—42no—
290Q8×C67—41no—
291Q8×C67—41no—
292Q8×C67—81no—
293D4×C67—21no—
294D4×C67—21no—
295D4×C67—21no—
296D4×C67—21no—
297D4×C67—21no—
298D4×C67—21no—
299D4×C67—42no—
300D4×C67—42no—
301D4×C67—41no—
302D4×C67—41no—
303D4×C67—41no—
304D4×C67—41no—
305D4×C67—41no—
306D4×C67—41no—
307D4×C67—41no—
308D4×C67—41no—
309D4×C67—81no—
310D4×C67—81no—
311D4×C67—81no—
312D4×C67—81no—
313D4×C67—81no—
314D4×C67—82no—
315D4×C67—82no—
316D4×C67—82no—
317D4×C67—82no—
318D4×C67—82no—
319D4×C67—82no—
320D4×C67—82no—
321C2×C4×C67—21no—
322C2×C4×C67—21no—
323C2×C4×C67—21no—
324C2×C4×C67—21no—
325C2×C4×C67—21no—
326C2×C4×C67—21no—
327C2×C4×C67—21no—
328C2×C4×C67—22no—
329C2×C4×C67—21no—
330C2×C4×C67—21no—
331C2×C4×C67—41no—
332C2×C4×C67—41no—
333C2×C4×C67—41no—
334C2×C4×C67—41no—
335C2×C4×C67—41no—
336C2×C4×C67—41no—
337C2×C4×C67—41no—
338C2×C4×C67—41no—
339C2×C4×C67—82no—
340C2×C4×C67—82no—
341C2×C4×C67—82no—
342C2×C4×C67—82no—
343C2×C4×C67#12011yescharacteristic
344C2×C4×C67#12011yescharacteristic
345C2×C4×C67#12011yescharacteristic
346C2×C4×C67C22×D411yescharacteristic
347C2×C4×C67C22×D411yescharacteristic
348C2×C4×C67C22×D411yescharacteristic
349C8×C67—41no—
350C8×C67—41no—
351C8×C67—41no—
352C8×C67—41no—
353C8×C67—41no—
354C8×C67—41no—
355C22×C67—21no—
356C22×C67—21no—
357C22×C67—21no—
358C22×C67—41no—
359C22×C67—41no—
360C22×C67—41no—
361C22×C67—41no—
362C22×C67—42no—
363C22×C67—42no—
364C22×C67—41no—
365C22×C67—41no—
366C22×C67—42no—
367C22×C67—41no—
368C22×C67—41no—
369C22×C67—41no—
370C22×C67—81no—
371C22×C67—81no—
372C22×C67—81no—
373C22×C67—164no—
374C22×C67C2×#12011yescharacteristic
375C4×C67—21no—
376C4×C67—21no—
377C4×C67—21no—
378C4×C67—21no—
379C4×C67—41no—
380C4×C67—41no—
381C4×C67—41no—
382C4×C67—41no—
383C4×C67—42no—
384C4×C67—41no—
385C4×C67—81no—
386C4×C67#57611yescharacteristic
387C4×C67#57611yescharacteristic
388C4×C67#57711yescharacteristic
389C4×C67#57711yescharacteristic
390#18962C6711yesmaximal, characteristic, direct product factor, Sylow
391C2×C67—41no—
392C2×C67—81no—
393C2×C67—82no—
394C2×C67—81no—
395C2×C67—81no—
396C2×C67—161no—
397C2×C67#301211yescharacteristic
398C2×C67#301211yescharacteristic
399C2×C67#302111yescharacteristic
400#3546C2×C6711yescharacteristic, complemented
401#3253C2×C6711yescharacteristic, complemented
402#3247C2×C6711yescharacteristic, complemented
403#3207C2×C6711yescharacteristic, complemented
404#1638C2×C6711yescharacteristic, complemented
405#1635C2×C6711yescharacteristic, complemented
406#1631C2×C6711yescharacteristic, complemented
407#1629C2×C6711yescharacteristic, complemented
408#1628C2×C6711yescharacteristic, complemented
409#1625C2×C6711yescharacteristic, complemented
410#1621C2×C6711yescharacteristic, complemented
411#1619C2×C6711yescharacteristic, complemented
412#1547C2×C6711yescharacteristic, complemented
413#1495C2×C6711yescharacteristic, complemented
414#1480C2×C6711yescharacteristic, complemented
415C67#1896211yescharacteristic, direct product factor, Sylow
416#560—22no—
417#556C22×C6711yescharacteristic
418#553—21no—
419#550—21no—
420#550C22×C6711yescharacteristic
421#547C22×C6711yescharacteristic
422#546—21no—
423#546—21no—
424D42C22×C6711yescharacteristic
425#542—21no—
426#538—22no—
427#537—21no—
428#535—21no—
429#535—21no—
430#532C22×C6711yescharacteristic
431#532C22×C6711yescharacteristic
432#532C22×C6711yescharacteristic, complemented
433#529C22×C6711yescharacteristic
434#493C22×C6711yescharacteristic
435#492C22×C6711yescharacteristic
436#487C22×C6711yescharacteristic, complemented
437#486C22×C6711yescharacteristic, complemented
438#478—21no—
439#477C22×C6711yescharacteristic, complemented
440#476—21no—
441#476C22×C6711yescharacteristic
442#476C22×C6711yescharacteristic
443#476C22×C6711yescharacteristic, complemented
444#469—21no—
445#469—21no—
446#466—21no—
447#465—21no—
448#463—21no—
449#463—22no—
450#460C22×C6711yescharacteristic, complemented
451#459—21no—
452#459C22×C6711yescharacteristic
453#459C22×C6711yescharacteristic
454#459C22×C6711yescharacteristic, complemented
455#449—22no—
456#431C22×C6711yescharacteristic, complemented
457#423C22×C6711yescharacteristic, complemented
458C2×C4⋊C8C22×C6711yescharacteristic, complemented
459#332C22×C6711yescharacteristic, complemented
460#332C22×C6711yescharacteristic, complemented
461#331C22×C6711yescharacteristic
462#331C22×C6711yescharacteristic
463Q8⋊C8C22×C6711yescharacteristic, complemented
464Q8⋊C8C22×C6711yescharacteristic, complemented
465D4⋊C8C22×C6711yescharacteristic
466D4⋊C8C22×C6711yescharacteristic
467D4⋊C8C22×C6711yescharacteristic
468D4⋊C8C22×C6711yescharacteristic
469D4⋊C8C22×C6711yescharacteristic, complemented
470D4⋊C8C22×C6711yescharacteristic, complemented
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C22×D4—21no—
477C22×D4—21no—
478C2×SD16—21no—
479C2×SD16—22no—
480C2×D8—22no—
481C2×D8—21no—
482C2×D8—21no—
483C2×D8—21no—
484C2×M16—21no—
485C22×C8—21no—
486C4⋊Q8D4×C6711yescharacteristic
487C4⋊Q8C23×C6711yescharacteristic
488C4⋊Q8C23×C6711yescharacteristic
489#127—22no—
490#127—21no—
491#127D4×C6711yescharacteristic
492#127C23×C6711yescharacteristic
493#127C23×C6711yescharacteristic
494#126—22no—
495#126—22no—
496#126—21no—
497#125D4×C6711yescharacteristic
498#124—22no—
499#124—21no—
500#124—21no—
501#124—21no—
502#124—21no—
503#124D4×C6711yescharacteristic
504#123—22no—
505#123—22no—
506#123—21no—
507#123—22no—
508C22⋊Q8—22no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8D4×C6711yescharacteristic
512#121—22no—
513#121—22no—
514#121—22no—
515#121—22no—
516#121—22no—
517#121—21no—
518#121—22no—
519#121—21no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121D4×C6711yescharacteristic
527#121D4×C6711yescharacteristic
528#121D4×C6711yescharacteristic
529#121D4×C6712yes—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534C4×Q8—21no—
535C4×Q8C23×C6711yescharacteristic
536C4×D4—22no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4D4×C6712yes—
544C4×D4C23×C6711yescharacteristic
545C4×D4C23×C6711yescharacteristic
546C4×D4C23×C6711yescharacteristic
547#117—21no—
548#117—21no—
549C2×C4⋊C4—21no—
550C2×C22⋊C4—22no—
551C2×C42C23×C6711yescharacteristic
552#107—21no—
553#106—21no—
554#106—21no—
555#106—21no—
556C4⋊C8—21no—
557C4⋊C8—21no—
558C4⋊C8—21no—
559C4⋊C8C23×C6711yescharacteristic
560C4⋊C8C23×C6711yescharacteristic
561C4⋊C8C23×C6711yescharacteristic
562C4⋊C8C23×C6711yescharacteristic
563#103—21no—
564#103—22no—
565#102—21no—
566#102—21no—
567#102—21no—
568#102—22no—
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573C22⋊C8—21no—
574C4×C8C23×C6711yescharacteristic
575C4×C8C23×C6711yescharacteristic
576C24—22no—
577#41—81no—
578#41—81no—
579#41—81no—
580#41—81no—
581#41—81no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—82no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8C2×D4×C6711yescharacteristic
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—41no—
607C2×D4—81no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4C2×D4×C6711yescharacteristic
612C2×D4C2×D4×C6711yescharacteristic
613C2×D4C2×D4×C6711yescharacteristic
614C2×D4C2×D4×C6712yes—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—41no—
622C22×C4C2×D4×C6711yescharacteristic
623C22×C4C2×D4×C6711yescharacteristic
624C22×C4C2×D4×C6711yescharacteristic
625SD16—81no—
626SD16—82no—
627D8—81no—
628D8—81no—
629D8—81no—
630D8—82no—
631M16—81no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—81no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4C2×D4×C6712yes—
650C4⋊C4C2×D4×C6711yescharacteristic
651C4⋊C4C2×D4×C6711yescharacteristic
652C4⋊C4C2×D4×C6711yescharacteristic
653C4⋊C4C2×D4×C6711yescharacteristic
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C42—22no—
673C42—21no—
674C42C2×D4×C6711yescharacteristic
675C42C2×D4×C6711yescharacteristic
676C42C2×D4×C6711yescharacteristic
677C42C24×C6711yescharacteristic
678C23—21no—
679C23—21no—
680C23—22no—
681C23—21no—
682C23—41no—
683C23—82no—
684C23—82no—
685C23—82no—
686C23#120×C6711yescharacteristic
687Q8—21no—
688Q8—21no—
689Q8—42no—
690Q8—41no—
691Q8—41no—
692Q8—81no—
693D4—21no—
694D4—21no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—42no—
700D4—42no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—81no—
710D4—81no—
711D4—81no—
712D4—81no—
713D4—82no—
714D4—81no—
715D4—82no—
716D4—82no—
717D4—82no—
718D4—82no—
719D4—82no—
720D4—82no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—82no—
740C2×C4—82no—
741C2×C4—82no—
742C2×C4—82no—
743C2×C4#120×C6711yescharacteristic
744C2×C4#120×C6711yescharacteristic
745C2×C4#120×C6711yescharacteristic
746C2×C4C22×D4×C6711yescharacteristic
747C2×C4C22×D4×C6711yescharacteristic
748C2×C4C22×D4×C6711yescharacteristic
749C8—41no—
750C8—41no—
751C8—41no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—164no—
774C22C2×#120×C6711yescharacteristic
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—42no—
784C4—41no—
785C4—81no—
786C4#576×C6711yescharacteristic
787C4#576×C6711yescharacteristic
788C4#577×C6711yescharacteristic
789C4#577×C6711yescharacteristic
790C2—41no—
791C2—81no—
792C2—81no—
793C2—82no—
794C2—81no—
795C2—161no—
796C2C67×#301211yescharacteristic
797C2C67×#301211yescharacteristic
798C2C67×#302111yescharacteristic
subgroupG/H
center, socleC22×C67C2×#120
commutator, Frattini, cosocleC42C24×C67
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G

Complements

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

NH ≅ G/Ntype
1. C67×#3546C2semidirect
2. C67×#3253C2semidirect
3. C67×#3247C2semidirect
4. C67×#3207C2semidirect
5. C67×#1638C2semidirect
6. C67×#1635C2semidirect
7. C67×#1631C2semidirect
8. C67×#1629C2semidirect
9. C67×#1628C2semidirect
10. C67×#1625C2semidirect
11. C67×#1621C2semidirect
12. C67×#1619C2semidirect
13. C67×#1547C2semidirect
14. C67×#1495C2semidirect
15. C67×#1480C2semidirect
32. #532×C67C22semidirect
36. #487×C67C22semidirect
37. #486×C67C22semidirect
39. #477×C67C22semidirect
43. #476×C67C22semidirect
50. #460×C67C22semidirect
54. #459×C67C22semidirect
56. #431×C67C22semidirect
57. #423×C67C22semidirect
58. C2×C4⋊C8×C67C22semidirect
59. #332×C67C22semidirect
60. #332×C67C22semidirect
63. Q8⋊C8×C67C22semidirect
64. Q8⋊C8×C67C22semidirect
69. D4⋊C8×C67C22semidirect
70. D4⋊C8×C67C22semidirect
390. #18962C67direct (N × H)
400. #3546C2×C67semidirect
401. #3253C2×C67semidirect
402. #3247C2×C67semidirect
403. #3207C2×C67semidirect
404. #1638C2×C67semidirect
405. #1635C2×C67semidirect
406. #1631C2×C67semidirect
407. #1629C2×C67semidirect
408. #1628C2×C67semidirect
409. #1625C2×C67semidirect
410. #1621C2×C67semidirect
411. #1619C2×C67semidirect
412. #1547C2×C67semidirect
413. #1495C2×C67semidirect
414. #1480C2×C67semidirect
415. C67#18962direct (N × H)
432. #532C22×C67semidirect
436. #487C22×C67semidirect
437. #486C22×C67semidirect
439. #477C22×C67semidirect
443. #476C22×C67semidirect
450. #460C22×C67semidirect
454. #459C22×C67semidirect
456. #431C22×C67semidirect
457. #423C22×C67semidirect
458. C2×C4⋊C8C22×C67semidirect
459. #332C22×C67semidirect
460. #332C22×C67semidirect
463. Q8⋊C8C22×C67semidirect
464. Q8⋊C8C22×C67semidirect
469. D4⋊C8C22×C67semidirect
470. D4⋊C8C22×C67semidirect

Maximal subgroups

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

subgroupindex
C67×#35462
C67×#32532
C67×#32472
C67×#32072
C67×#16382
C67×#16352
C67×#16312
C67×#16292
C67×#16282
C67×#16252
C67×#16212
C67×#16192
C67×#15472
C67×#14952
C67×#14802
#1896267