Finite Group Databasebeta

← C67×#18931 #30698182

Subgroups — C67×#18931 #30698182

Order 17152.

986 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C67×#3543C211yesmaximal, characteristic
2C67×#3252C211yesmaximal, characteristic, complemented
3C67×#3233C211yesmaximal, characteristic, complemented
4C67×#3208C211yesmaximal, characteristic, complemented
5C67×#1642C211yesmaximal, characteristic, complemented
6C67×#1641C211yesmaximal, characteristic, complemented
7C67×#1640C211yesmaximal, characteristic, complemented
8C67×#1639C211yesmaximal, characteristic, complemented
9C67×#1631C211yesmaximal, characteristic, complemented
10C67×#1631C211yesmaximal, characteristic, complemented
11C67×#1630C211yesmaximal, characteristic, complemented
12C67×#1629C211yesmaximal, characteristic, complemented
13C67×#1545C211yesmaximal, characteristic, complemented
14C67×#1495C211yesmaximal, characteristic, complemented
15C67×#1482C211yesmaximal, characteristic, complemented
16#560×C67—22no—
17#559×C67C2211yescharacteristic
18#550×C67C2211yescharacteristic
19#550×C67C2211yescharacteristic
20#546×C67—21no—
21#546×C67—21no—
22D42×C67—21no—
23D42×C67—21no—
24D42×C67C2211yescharacteristic
25#540×C67—21no—
26#540×C67—21no—
27#535×C67—21no—
28#535×C67—21no—
29#534×C67—22no—
30#533×C67C2211yescharacteristic, complemented
31C2×#127×C67C2211yescharacteristic
32#529×C67C2211yescharacteristic
33#529×C67C2211yescharacteristic
34#499×C67—21no—
35#492×C67C2211yescharacteristic
36#492×C67C2211yescharacteristic, complemented
37#488×C67—21no—
38#486×C67C2211yescharacteristic
39#486×C67C2211yescharacteristic, complemented
40#485×C67—21no—
41#482×C67—21no—
42#479×C67—21no—
43#477×C67C2211yescharacteristic, complemented
44#477×C67C2211yescharacteristic, complemented
45#476×C67C2211yescharacteristic, complemented
46#476×C67C2211yescharacteristic, complemented
47#475×C67C2211yescharacteristic, complemented
48#474×C67C2211yescharacteristic, complemented
49#470×C67—21no—
50#468×C67—21no—
51#464×C67—21no—
52#462×C67C2211yescharacteristic, complemented
53#461×C67C2211yescharacteristic, complemented
54#460×C67—22no—
55#450×C67—22no—
56#431×C67C2211yescharacteristic, complemented
57#431×C67C2211yescharacteristic, complemented
58#423×C67C2211yescharacteristic, complemented
59#331×C67C2211yescharacteristic
60#331×C67C2211yescharacteristic
61#331×C67C2211yescharacteristic, complemented
62#331×C67C2211yescharacteristic, complemented
63Q8⋊C8×C67C2211yescharacteristic, complemented
64Q8⋊C8×C67C2211yescharacteristic, complemented
65Q8⋊C8×C67C2211yescharacteristic, complemented
66Q8⋊C8×C67C2211yescharacteristic, complemented
67D4⋊C8×C67C2211yescharacteristic, complemented
68D4⋊C8×C67C2211yescharacteristic, complemented
69D4⋊C8×C67C2211yescharacteristic, complemented
70D4⋊C8×C67C2211yescharacteristic, complemented
71C2×#41×C67—21no—
72C2×#41×C67—21no—
73C22×D4×C67—22no—
74C22×D4×C67—21no—
75C22×D4×C67—21no—
76C22×D4×C67—21no—
77C22×D4×C67—21no—
78C22×D4×C67D412yes—
79C2×Q16×C67—21no—
80C2×SD16×C67—22no—
81C2×SD16×C67—22no—
82C2×SD16×C67—21no—
83C2×M16×C67—21no—
84C4⋊Q8×C67C2311yescharacteristic
85C4⋊Q8×C67C2311yescharacteristic
86#127×C67—21no—
87#127×C67—21no—
88#127×C67—21no—
89#127×C67—21no—
90#127×C67D412yes—
91#127×C67C2311yescharacteristic
92#127×C67C2311yescharacteristic
93#126×C67—21no—
94#126×C67—21no—
95#125×C67—21no—
96#125×C67D411yescharacteristic
97#125×C67D411yescharacteristic
98#124×C67—21no—
99#124×C67—21no—
100#124×C67D411yescharacteristic
101#124×C67D411yescharacteristic
102#123×C67—22no—
103#123×C67—22no—
104#123×C67—22no—
105#123×C67—22no—
106#123×C67—21no—
107#123×C67—21no—
108C22⋊Q8×C67—21no—
109C22⋊Q8×C67—21no—
110C22⋊Q8×C67D411yescharacteristic
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—22no—
118#121×C67—22no—
119#121×C67—22no—
120#121×C67—21no—
121#121×C67—21no—
122#121×C67—21no—
123#121×C67—21no—
124#121×C67D411yescharacteristic
125#121×C67D411yescharacteristic
126#120×C67—22no—
127#120×C67—22no—
128#120×C67—22no—
129#120×C67—22no—
130#120×C67—22no—
131#120×C67—22no—
132C4×Q8×C67—21no—
133C4×Q8×C67—21no—
134C4×Q8×C67C2311yescharacteristic
135C4×Q8×C67C2311yescharacteristic
136C4×D4×C67—21no—
137C4×D4×C67—21no—
138C4×D4×C67—21no—
139C4×D4×C67—21no—
140C4×D4×C67—21no—
141C4×D4×C67—21no—
142C4×D4×C67C2311yescharacteristic
143C4×D4×C67C2311yescharacteristic
144#117×C67—21no—
145#117×C67—21no—
146#117×C67—21no—
147C2×C22⋊C4×C67—22no—
148C2×C42×C67C2311yescharacteristic
149#107×C67—21no—
150#107×C67—21no—
151#107×C67—21no—
152#106×C67—21no—
153#106×C67—21no—
154#106×C67—21no—
155C4⋊C8×C67—21no—
156C4⋊C8×C67—21no—
157C4⋊C8×C67C2311yescharacteristic
158C4⋊C8×C67C2311yescharacteristic
159C4⋊C8×C67C2311yescharacteristic
160C4⋊C8×C67C2311yescharacteristic
161#103×C67—21no—
162#103×C67—21no—
163#103×C67—21no—
164#103×C67—21no—
165#103×C67—21no—
166#102×C67—22no—
167#102×C67—22no—
168#102×C67—21no—
169#102×C67—21no—
170#102×C67—21no—
171C22⋊C8×C67—21no—
172C22⋊C8×C67—21no—
173C4×C8×C67—21no—
174C4×C8×C67C2311yescharacteristic
175C4×C8×C67C2311yescharacteristic
176C24×C67—22no—
177C24×C67—22no—
178#41×C67—81no—
179#41×C67—81no—
180#41×C67—81no—
181#41×C67—81no—
182C2×Q8×C67—21no—
183C2×Q8×C67—21no—
184C2×Q8×C67C2×D411yescharacteristic
185C2×Q8×C67C2×D411yescharacteristic
186C2×D4×C67—21no—
187C2×D4×C67—21no—
188C2×D4×C67—22no—
189C2×D4×C67—22no—
190C2×D4×C67—22no—
191C2×D4×C67—22no—
192C2×D4×C67—22no—
193C2×D4×C67—22no—
194C2×D4×C67—22no—
195C2×D4×C67—22no—
196C2×D4×C67—22no—
197C2×D4×C67—21no—
198C2×D4×C67—21no—
199C2×D4×C67—21no—
200C2×D4×C67—21no—
201C2×D4×C67—81no—
202C2×D4×C67—81no—
203C2×D4×C67—81no—
204C2×D4×C67—81no—
205C2×D4×C67—81no—
206C2×D4×C67—81no—
207C2×D4×C67—81no—
208C2×D4×C67—81no—
209C2×D4×C67—82no—
210C2×D4×C67—84no—
211C2×D4×C67C2×D411yescharacteristic
212C2×D4×C67C2×D411yescharacteristic
213C2×D4×C67C2×D412yes—
214C2×D4×C67C2×D412yes—
215C22×C4×C67—22no—
216C22×C4×C67—22no—
217C22×C4×C67—22no—
218C22×C4×C67—21no—
219C22×C4×C67—21no—
220C22×C4×C67C2×D411yescharacteristic
221C22×C4×C67C2×D411yescharacteristic
222C22×C4×C67C2×D411yescharacteristic
223Q16×C67—81no—
224SD16×C67—81no—
225SD16×C67—82no—
226SD16×C67—82no—
227M16×C67—81no—
228C2×C8×C67—21no—
229C2×C8×C67—21no—
230C2×C8×C67—21no—
231C2×C8×C67—21no—
232C2×C8×C67—21no—
233C2×C8×C67—21no—
234C4⋊C4×C67—21no—
235C4⋊C4×C67—21no—
236C4⋊C4×C67—21no—
237C4⋊C4×C67—21no—
238C4⋊C4×C67—21no—
239C4⋊C4×C67—21no—
240C4⋊C4×C67—21no—
241C4⋊C4×C67—21no—
242C4⋊C4×C67—21no—
243C4⋊C4×C67—21no—
244C4⋊C4×C67—21no—
245C4⋊C4×C67—21no—
246C4⋊C4×C67—41no—
247C4⋊C4×C67—41no—
248C4⋊C4×C67C2×D411yescharacteristic
249C4⋊C4×C67C2×D411yescharacteristic
250C4⋊C4×C67C2×D411yescharacteristic
251C4⋊C4×C67C2×D411yescharacteristic
252C22⋊C4×C67—22no—
253C22⋊C4×C67—22no—
254C22⋊C4×C67—22no—
255C22⋊C4×C67—22no—
256C22⋊C4×C67—22no—
257C22⋊C4×C67—22no—
258C22⋊C4×C67—21no—
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—21no—
266C22⋊C4×C67—21no—
267C22⋊C4×C67—21no—
268C22⋊C4×C67—41no—
269C42×C67—21no—
270C42×C67—21no—
271C42×C67—41no—
272C42×C67C2×D411yescharacteristic
273C42×C67C2×D411yescharacteristic
274C42×C67C2×D411yescharacteristic
275C42×C67C2411yescharacteristic
276C23×C67—21no—
277C23×C67—21no—
278C23×C67—22no—
279C23×C67—22no—
280C23×C67—44no—
281C23×C67—82no—
282C23×C67—82no—
283C23×C67—82no—
284C23×C67—82no—
285C23×C67—82no—
286C23×C67#12011yescharacteristic
287Q8×C67—21no—
288Q8×C67—21no—
289Q8×C67—21no—
290Q8×C67—21no—
291Q8×C67—42no—
292Q8×C67—41no—
293Q8×C67—41no—
294D4×C67—21no—
295D4×C67—21no—
296D4×C67—21no—
297D4×C67—21no—
298D4×C67—42no—
299D4×C67—42no—
300D4×C67—42no—
301D4×C67—42no—
302D4×C67—41no—
303D4×C67—41no—
304D4×C67—41no—
305D4×C67—41no—
306D4×C67—41no—
307D4×C67—41no—
308D4×C67—41no—
309D4×C67—41no—
310D4×C67—82no—
311D4×C67—82no—
312D4×C67—82no—
313D4×C67—82no—
314D4×C67—82no—
315D4×C67—82no—
316D4×C67—82no—
317D4×C67—82no—
318D4×C67—82no—
319C2×C4×C67—21no—
320C2×C4×C67—21no—
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—21no—
329C2×C4×C67—41no—
330C2×C4×C67—41no—
331C2×C4×C67—41no—
332C2×C4×C67—41no—
333C2×C4×C67—41no—
334C2×C4×C67—41no—
335C2×C4×C67—41no—
336C2×C4×C67—82no—
337C2×C4×C67—82no—
338C2×C4×C67—82no—
339C2×C4×C67#12011yescharacteristic
340C2×C4×C67#12011yescharacteristic
341C2×C4×C67#12011yescharacteristic
342C2×C4×C67C22×D411yescharacteristic
343C2×C4×C67C22×D411yescharacteristic
344C2×C4×C67C22×D411yescharacteristic
345C8×C67—41no—
346C8×C67—41no—
347C8×C67—41no—
348C8×C67—41no—
349C8×C67—41no—
350C8×C67—41no—
351C22×C67—21no—
352C22×C67—21no—
353C22×C67—21no—
354C22×C67—41no—
355C22×C67—42no—
356C22×C67—41no—
357C22×C67—42no—
358C22×C67—41no—
359C22×C67—42no—
360C22×C67—41no—
361C22×C67—42no—
362C22×C67—42no—
363C22×C67—41no—
364C22×C67—41no—
365C22×C67—42no—
366C22×C67—164no—
367C22×C67—164no—
368C22×C67C2×#12011yescharacteristic
369C4×C67—21no—
370C4×C67—21no—
371C4×C67—21no—
372C4×C67—21no—
373C4×C67—41no—
374C4×C67—41no—
375C4×C67—41no—
376C4×C67—41no—
377C4×C67—41no—
378C4×C67—41no—
379C4×C67—81no—
380C4×C67—81no—
381C4×C67#57611yescharacteristic
382C4×C67#57711yescharacteristic
383C4×C67#57711yescharacteristic
384C4×C67#57711yescharacteristic
385#18931C6711yesmaximal, characteristic, direct product factor, Sylow
386C2×C67—41no—
387C2×C67—82no—
388C2×C67—81no—
389C2×C67—81no—
390C2×C67—82no—
391C2×C67#300911yescharacteristic
392C2×C67#301211yescharacteristic
393C2×C67#301911yescharacteristic
394#3543C2×C6711yescharacteristic
395#3252C2×C6711yescharacteristic, complemented
396#3233C2×C6711yescharacteristic, complemented
397#3208C2×C6711yescharacteristic, complemented
398#1642C2×C6711yescharacteristic, complemented
399#1641C2×C6711yescharacteristic, complemented
400#1640C2×C6711yescharacteristic, complemented
401#1639C2×C6711yescharacteristic, complemented
402#1631C2×C6711yescharacteristic, complemented
403#1631C2×C6711yescharacteristic, complemented
404#1630C2×C6711yescharacteristic, complemented
405#1629C2×C6711yescharacteristic, complemented
406#1545C2×C6711yescharacteristic, complemented
407#1495C2×C6711yescharacteristic, complemented
408#1482C2×C6711yescharacteristic, complemented
409C67#1893111yescharacteristic, direct product factor, Sylow
410#560—22no—
411#559C22×C6711yescharacteristic
412#550C22×C6711yescharacteristic
413#550C22×C6711yescharacteristic
414#546—21no—
415#546—21no—
416D42—21no—
417D42—21no—
418D42C22×C6711yescharacteristic
419#540—21no—
420#540—21no—
421#535—21no—
422#535—21no—
423#534—22no—
424#533C22×C6711yescharacteristic, complemented
425C2×#127C22×C6711yescharacteristic
426#529C22×C6711yescharacteristic
427#529C22×C6711yescharacteristic
428#499—21no—
429#492C22×C6711yescharacteristic
430#492C22×C6711yescharacteristic, complemented
431#488—21no—
432#486C22×C6711yescharacteristic
433#486C22×C6711yescharacteristic, complemented
434#485—21no—
435#482—21no—
436#479—21no—
437#477C22×C6711yescharacteristic, complemented
438#477C22×C6711yescharacteristic, complemented
439#476C22×C6711yescharacteristic, complemented
440#476C22×C6711yescharacteristic, complemented
441#475C22×C6711yescharacteristic, complemented
442#474C22×C6711yescharacteristic, complemented
443#470—21no—
444#468—21no—
445#464—21no—
446#462C22×C6711yescharacteristic, complemented
447#461C22×C6711yescharacteristic, complemented
448#460—22no—
449#450—22no—
450#431C22×C6711yescharacteristic, complemented
451#431C22×C6711yescharacteristic, complemented
452#423C22×C6711yescharacteristic, complemented
453#331C22×C6711yescharacteristic
454#331C22×C6711yescharacteristic
455#331C22×C6711yescharacteristic, complemented
456#331C22×C6711yescharacteristic, complemented
457Q8⋊C8C22×C6711yescharacteristic, complemented
458Q8⋊C8C22×C6711yescharacteristic, complemented
459Q8⋊C8C22×C6711yescharacteristic, complemented
460Q8⋊C8C22×C6711yescharacteristic, complemented
461D4⋊C8C22×C6711yescharacteristic, complemented
462D4⋊C8C22×C6711yescharacteristic, complemented
463D4⋊C8C22×C6711yescharacteristic, complemented
464D4⋊C8C22×C6711yescharacteristic, complemented
465C2×#41—21no—
466C2×#41—21no—
467C22×D4—22no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4D4×C6712yes—
473C2×Q16—21no—
474C2×SD16—22no—
475C2×SD16—22no—
476C2×SD16—21no—
477C2×M16—21no—
478C4⋊Q8C23×C6711yescharacteristic
479C4⋊Q8C23×C6711yescharacteristic
480#127—21no—
481#127—21no—
482#127—21no—
483#127—21no—
484#127D4×C6712yes—
485#127C23×C6711yescharacteristic
486#127C23×C6711yescharacteristic
487#126—21no—
488#126—21no—
489#125—21no—
490#125D4×C6711yescharacteristic
491#125D4×C6711yescharacteristic
492#124—21no—
493#124—21no—
494#124D4×C6711yescharacteristic
495#124D4×C6711yescharacteristic
496#123—22no—
497#123—22no—
498#123—22no—
499#123—22no—
500#123—21no—
501#123—21no—
502C22⋊Q8—21no—
503C22⋊Q8—21no—
504C22⋊Q8D4×C6711yescharacteristic
505C22⋊Q8D4×C6711yescharacteristic
506#121—22no—
507#121—22no—
508#121—22no—
509#121—22no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121D4×C6711yescharacteristic
519#121D4×C6711yescharacteristic
520#120—22no—
521#120—22no—
522#120—22no—
523#120—22no—
524#120—22no—
525#120—22no—
526C4×Q8—21no—
527C4×Q8—21no—
528C4×Q8C23×C6711yescharacteristic
529C4×Q8C23×C6711yescharacteristic
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—21no—
533C4×D4—21no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4C23×C6711yescharacteristic
537C4×D4C23×C6711yescharacteristic
538#117—21no—
539#117—21no—
540#117—21no—
541C2×C22⋊C4—22no—
542C2×C42C23×C6711yescharacteristic
543#107—21no—
544#107—21no—
545#107—21no—
546#106—21no—
547#106—21no—
548#106—21no—
549C4⋊C8—21no—
550C4⋊C8—21no—
551C4⋊C8C23×C6711yescharacteristic
552C4⋊C8C23×C6711yescharacteristic
553C4⋊C8C23×C6711yescharacteristic
554C4⋊C8C23×C6711yescharacteristic
555#103—21no—
556#103—21no—
557#103—21no—
558#103—21no—
559#103—21no—
560#102—22no—
561#102—22no—
562#102—21no—
563#102—21no—
564#102—21no—
565C22⋊C8—21no—
566C22⋊C8—21no—
567C4×C8—21no—
568C4×C8C23×C6711yescharacteristic
569C4×C8C23×C6711yescharacteristic
570C24—22no—
571C24—22no—
572#41—81no—
573#41—81no—
574#41—81no—
575#41—81no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8C2×D4×C6711yescharacteristic
579C2×Q8C2×D4×C6711yescharacteristic
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4—81no—
598C2×D4—81no—
599C2×D4—81no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—81no—
603C2×D4—82no—
604C2×D4—84no—
605C2×D4C2×D4×C6711yescharacteristic
606C2×D4C2×D4×C6711yescharacteristic
607C2×D4C2×D4×C6712yes—
608C2×D4C2×D4×C6712yes—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4C2×D4×C6711yescharacteristic
615C22×C4C2×D4×C6711yescharacteristic
616C22×C4C2×D4×C6711yescharacteristic
617Q16—81no—
618SD16—81no—
619SD16—82no—
620SD16—82no—
621M16—81no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4C2×D4×C6711yescharacteristic
643C4⋊C4C2×D4×C6711yescharacteristic
644C4⋊C4C2×D4×C6711yescharacteristic
645C4⋊C4C2×D4×C6711yescharacteristic
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—41no—
663C42—21no—
664C42—21no—
665C42—41no—
666C42C2×D4×C6711yescharacteristic
667C42C2×D4×C6711yescharacteristic
668C42C2×D4×C6711yescharacteristic
669C42C24×C6711yescharacteristic
670C23—21no—
671C23—21no—
672C23—22no—
673C23—22no—
674C23—44no—
675C23—82no—
676C23—82no—
677C23—82no—
678C23—82no—
679C23—82no—
680C23#120×C6711yescharacteristic
681Q8—21no—
682Q8—21no—
683Q8—21no—
684Q8—21no—
685Q8—42no—
686Q8—41no—
687Q8—41no—
688D4—21no—
689D4—21no—
690D4—21no—
691D4—21no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—82no—
705D4—82no—
706D4—82no—
707D4—82no—
708D4—82no—
709D4—82no—
710D4—82no—
711D4—82no—
712D4—82no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—82no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4#120×C6711yescharacteristic
734C2×C4#120×C6711yescharacteristic
735C2×C4#120×C6711yescharacteristic
736C2×C4C22×D4×C6711yescharacteristic
737C2×C4C22×D4×C6711yescharacteristic
738C2×C4C22×D4×C6711yescharacteristic
739C8—41no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—41no—
744C8—41no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—42no—
752C22—41no—
753C22—42no—
754C22—41no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—164no—
761C22—164no—
762C22C2×#120×C6711yescharacteristic
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—81no—
774C4—81no—
775C4#576×C6711yescharacteristic
776C4#577×C6711yescharacteristic
777C4#577×C6711yescharacteristic
778C4#577×C6711yescharacteristic
779C2—41no—
780C2—81no—
781C2—81no—
782C2—82no—
783C2—82no—
784C2C67×#300911yescharacteristic
785C2C67×#301211yescharacteristic
786C2C67×#301911yescharacteristic
subgroupG/H
center, socleC22×C67C2×#120
commutator, Frattini, cosocleC42C24×C67
prime radicalC67×#3543C2
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
2. C67×#3252C2semidirect
3. C67×#3233C2semidirect
4. C67×#3208C2semidirect
5. C67×#1642C2semidirect
6. C67×#1641C2semidirect
7. C67×#1640C2semidirect
8. C67×#1639C2semidirect
9. C67×#1631C2semidirect
10. C67×#1631C2semidirect
11. C67×#1630C2semidirect
12. C67×#1629C2semidirect
13. C67×#1545C2semidirect
14. C67×#1495C2semidirect
15. C67×#1482C2semidirect
30. #533×C67C22semidirect
36. #492×C67C22semidirect
39. #486×C67C22semidirect
43. #477×C67C22semidirect
44. #477×C67C22semidirect
45. #476×C67C22semidirect
46. #476×C67C22semidirect
47. #475×C67C22semidirect
48. #474×C67C22semidirect
52. #462×C67C22semidirect
53. #461×C67C22semidirect
56. #431×C67C22semidirect
57. #431×C67C22semidirect
58. #423×C67C22semidirect
61. #331×C67C22semidirect
62. #331×C67C22semidirect
63. Q8⋊C8×C67C22semidirect
64. Q8⋊C8×C67C22semidirect
65. Q8⋊C8×C67C22semidirect
66. Q8⋊C8×C67C22semidirect
67. D4⋊C8×C67C22semidirect
68. D4⋊C8×C67C22semidirect
69. D4⋊C8×C67C22semidirect
70. D4⋊C8×C67C22semidirect
385. #18931C67direct (N × H)
395. #3252C2×C67semidirect
396. #3233C2×C67semidirect
397. #3208C2×C67semidirect
398. #1642C2×C67semidirect
399. #1641C2×C67semidirect
400. #1640C2×C67semidirect
401. #1639C2×C67semidirect
402. #1631C2×C67semidirect
403. #1631C2×C67semidirect
404. #1630C2×C67semidirect
405. #1629C2×C67semidirect
406. #1545C2×C67semidirect
407. #1495C2×C67semidirect
408. #1482C2×C67semidirect
409. C67#18931direct (N × H)
424. #533C22×C67semidirect
430. #492C22×C67semidirect
433. #486C22×C67semidirect
437. #477C22×C67semidirect
438. #477C22×C67semidirect
439. #476C22×C67semidirect
440. #476C22×C67semidirect
441. #475C22×C67semidirect
442. #474C22×C67semidirect
446. #462C22×C67semidirect
447. #461C22×C67semidirect
450. #431C22×C67semidirect
451. #431C22×C67semidirect
452. #423C22×C67semidirect
455. #331C22×C67semidirect
456. #331C22×C67semidirect
457. Q8⋊C8C22×C67semidirect
458. Q8⋊C8C22×C67semidirect
459. Q8⋊C8C22×C67semidirect
460. Q8⋊C8C22×C67semidirect
461. D4⋊C8C22×C67semidirect
462. D4⋊C8C22×C67semidirect
463. D4⋊C8C22×C67semidirect
464. D4⋊C8C22×C67semidirect

Maximal subgroups

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

subgroupindex
C67×#35432
C67×#32522
C67×#32332
C67×#32082
C67×#16422
C67×#16412
C67×#16402
C67×#16392
C67×#16312
C67×#16302
C67×#16292
C67×#15452
C67×#14952
C67×#14822
#1893167