Finite Group Databasebeta

← C67×#18866 #30698117

Subgroups — C67×#18866 #30698117

Order 17152.

1020 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C67×#3519C211yesmaximal, characteristic, complemented
2C67×#3212C211yesmaximal, characteristic, complemented
3C67×#3207C211yesmaximal, characteristic, complemented
4C67×#3100C211yesmaximal, characteristic, complemented
5C67×#1646C211yesmaximal, characteristic, complemented
6C67×#1644C211yesmaximal, characteristic, complemented
7C67×#1641C211yesmaximal, characteristic, complemented
8C67×#1639C211yesmaximal, characteristic, complemented
9C67×#1624C211yesmaximal, characteristic, complemented
10C67×#1622C211yesmaximal, characteristic, complemented
11C67×#1621C211yesmaximal, characteristic, complemented
12C67×#1619C211yesmaximal, characteristic, complemented
13C67×#1543C211yesmaximal, characteristic, complemented
14C67×#1482C211yesmaximal, characteristic, complemented
15C67×#1478C211yesmaximal, characteristic, complemented
16#555×C67C2211yescharacteristic
17#554×C67C2211yescharacteristic
18#553×C67—21no—
19#553×C67—21no—
20#550×C67C2211yescharacteristic
21#546×C67—22no—
22#546×C67—21no—
23D42×C67—21no—
24D42×C67C2211yescharacteristic
25#540×C67—21no—
26#538×C67—22no—
27#532×C67C2211yescharacteristic
28#532×C67C2211yescharacteristic, complemented
29#529×C67C2211yescharacteristic
30#525×C67—21no—
31C2×#121×C67—21no—
32#518×C67—21no—
33C2×C4×D4×C67C2211yescharacteristic
34#495×C67—21no—
35#493×C67C2211yescharacteristic, complemented
36#492×C67C2211yescharacteristic, complemented
37#488×C67—21no—
38#487×C67C2211yescharacteristic, complemented
39#486×C67C2211yescharacteristic, complemented
40#480×C67—21no—
41#474×C67C2211yescharacteristic
42#474×C67C2211yescharacteristic, complemented
43#463×C67—22no—
44#462×C67C2211yescharacteristic, complemented
45#461×C67C2211yescharacteristic, complemented
46#460×C67C2211yescharacteristic, complemented
47#459×C67C2211yescharacteristic
48#459×C67C2211yescharacteristic, complemented
49#459×C67C2211yescharacteristic, complemented
50#452×C67—21no—
51#449×C67—22no—
52#449×C67—21no—
53#447×C67—21no—
54C4×D8×C67—21no—
55C4×D8×C67—21no—
56#431×C67C2211yescharacteristic, complemented
57#431×C67C2211yescharacteristic, complemented
58#431×C67C2211yescharacteristic, complemented
59#333×C67C2211yescharacteristic, complemented
60#333×C67C2211yescharacteristic, complemented
61#331×C67C2211yescharacteristic, complemented
62#331×C67C2211yescharacteristic, complemented
63Q8⋊C8×C67C2211yescharacteristic, complemented
64Q8⋊C8×C67C2211yescharacteristic, complemented
65D4⋊C8×C67C2211yescharacteristic
66D4⋊C8×C67C2211yescharacteristic
67D4⋊C8×C67C2211yescharacteristic, complemented
68D4⋊C8×C67C2211yescharacteristic, complemented
69D4⋊C8×C67C2211yescharacteristic, complemented
70D4⋊C8×C67C2211yescharacteristic, complemented
71C2×#41×C67—21no—
72C2×#41×C67—21no—
73C2×#41×C67D412yes—
74C22×D4×C67—22no—
75C22×D4×C67—21no—
76C22×D4×C67—21no—
77C22×D4×C67D411yescharacteristic
78C23×C4×C67—21no—
79C2×Q16×C67—21no—
80C2×SD16×C67—22no—
81C2×SD16×C67—21no—
82C2×SD16×C67—21no—
83C2×D8×C67—21no—
84C2×D8×C67—21no—
85C2×D8×C67—21no—
86C2×D8×C67—22no—
87C4⋊Q8×C67C2311yescharacteristic
88C4⋊Q8×C67C2311yescharacteristic
89#127×C67—21no—
90#127×C67C2311yescharacteristic
91#127×C67C2311yescharacteristic
92#126×C67—22no—
93#126×C67—21no—
94#125×C67—21no—
95#125×C67D411yescharacteristic
96#124×C67—22no—
97#124×C67—21no—
98#124×C67D412yes—
99#124×C67D411yescharacteristic
100#123×C67—22no—
101#123×C67—22no—
102#123×C67—22no—
103#123×C67—21no—
104C22⋊Q8×C67—21no—
105C22⋊Q8×C67—22no—
106C22⋊Q8×C67D411yescharacteristic
107#121×C67—22no—
108#121×C67—22no—
109#121×C67—22no—
110#121×C67—22no—
111#121×C67—21no—
112#121×C67—22no—
113#121×C67—21no—
114#121×C67—21no—
115#121×C67—21no—
116#121×C67—21no—
117#121×C67—21no—
118#121×C67—21no—
119#121×C67—21no—
120#121×C67—21no—
121#121×C67D411yescharacteristic
122#120×C67—22no—
123#120×C67—22no—
124#120×C67—22no—
125C4×Q8×C67C2311yescharacteristic
126C4×D4×C67—22no—
127C4×D4×C67—22no—
128C4×D4×C67—22no—
129C4×D4×C67—21no—
130C4×D4×C67—21no—
131C4×D4×C67—21no—
132C4×D4×C67—21no—
133C4×D4×C67—21no—
134C4×D4×C67—21no—
135C4×D4×C67—21no—
136C4×D4×C67—21no—
137C4×D4×C67—21no—
138C4×D4×C67D411yescharacteristic
139C4×D4×C67D411yescharacteristic
140C4×D4×C67C2311yescharacteristic
141C4×D4×C67C2311yescharacteristic
142C4×D4×C67C2311yescharacteristic
143#117×C67—21no—
144#117×C67—21no—
145#117×C67—21no—
146C2×C4⋊C4×C67—21no—
147C2×C4⋊C4×C67D411yescharacteristic
148C2×C22⋊C4×C67—22no—
149C2×C22⋊C4×C67—22no—
150C2×C22⋊C4×C67—21no—
151C2×C42×C67C2311yescharacteristic
152#107×C67—21no—
153#107×C67—21no—
154C4⋊C8×C67—21no—
155C4⋊C8×C67C2311yescharacteristic
156C4⋊C8×C67C2311yescharacteristic
157C4⋊C8×C67C2311yescharacteristic
158C4⋊C8×C67C2311yescharacteristic
159#103×C67—22no—
160#103×C67—21no—
161#103×C67—21no—
162#102×C67—22no—
163#102×C67—21no—
164#102×C67—21no—
165#102×C67—21no—
166#102×C67—21no—
167#102×C67—21no—
168#102×C67—21no—
169C22⋊C8×C67—21no—
170C22⋊C8×C67—21no—
171C22⋊C8×C67—21no—
172C4×C8×C67—21no—
173C4×C8×C67—21no—
174C4×C8×C67C2311yescharacteristic
175C4×C8×C67C2311yescharacteristic
176C24×C67—22no—
177C24×C67—21no—
178#41×C67—81no—
179#41×C67—81no—
180#41×C67—81no—
181#41×C67—81no—
182#41×C67—82no—
183C2×Q8×C67—21no—
184C2×Q8×C67C2×D411yescharacteristic
185C2×Q8×C67C2×D412yes—
186C2×D4×C67—22no—
187C2×D4×C67—22no—
188C2×D4×C67—22no—
189C2×D4×C67—21no—
190C2×D4×C67—22no—
191C2×D4×C67—22no—
192C2×D4×C67—22no—
193C2×D4×C67—22no—
194C2×D4×C67—21no—
195C2×D4×C67—21no—
196C2×D4×C67—21no—
197C2×D4×C67—21no—
198C2×D4×C67—21no—
199C2×D4×C67—21no—
200C2×D4×C67—41no—
201C2×D4×C67—42no—
202C2×D4×C67—42no—
203C2×D4×C67—41no—
204C2×D4×C67—81no—
205C2×D4×C67—81no—
206C2×D4×C67—84no—
207C2×D4×C67C2×D411yescharacteristic
208C2×D4×C67C2×D411yescharacteristic
209C2×D4×C67C2×D411yescharacteristic
210C2×D4×C67C2×D412yes—
211C22×C4×C67—22no—
212C22×C4×C67—22no—
213C22×C4×C67—21no—
214C22×C4×C67—21no—
215C22×C4×C67—21no—
216C22×C4×C67—21no—
217C22×C4×C67—21no—
218C22×C4×C67—22no—
219C22×C4×C67—21no—
220C22×C4×C67—41no—
221C22×C4×C67—81no—
222C22×C4×C67—81no—
223C22×C4×C67C2×D411yescharacteristic
224C22×C4×C67C2×D411yescharacteristic
225C22×C4×C67C2×D411yescharacteristic
226Q16×C67—81no—
227SD16×C67—81no—
228SD16×C67—81no—
229SD16×C67—82no—
230D8×C67—42no—
231D8×C67—42no—
232D8×C67—81no—
233D8×C67—82no—
234C2×C8×C67—21no—
235C2×C8×C67—21no—
236C2×C8×C67—21no—
237C2×C8×C67—21no—
238C2×C8×C67—21no—
239C2×C8×C67—21no—
240C4⋊C4×C67—22no—
241C4⋊C4×C67—22no—
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×C67—21no—
250C4⋊C4×C67—21no—
251C4⋊C4×C67C2×D411yescharacteristic
252C4⋊C4×C67C2×D411yescharacteristic
253C4⋊C4×C67C2×D411yescharacteristic
254C4⋊C4×C67C2×D411yescharacteristic
255C22⋊C4×C67—22no—
256C22⋊C4×C67—22no—
257C22⋊C4×C67—22no—
258C22⋊C4×C67—22no—
259C22⋊C4×C67—22no—
260C22⋊C4×C67—21no—
261C22⋊C4×C67—21no—
262C22⋊C4×C67—21no—
263C22⋊C4×C67—21no—
264C22⋊C4×C67—22no—
265C22⋊C4×C67—21no—
266C22⋊C4×C67—21no—
267C22⋊C4×C67—22no—
268C22⋊C4×C67—21no—
269C22⋊C4×C67—21no—
270C22⋊C4×C67—21no—
271C22⋊C4×C67—41no—
272C22⋊C4×C67—41no—
273C42×C67—22no—
274C42×C67—21no—
275C42×C67C2×D411yescharacteristic
276C42×C67C2×D411yescharacteristic
277C42×C67C2×D411yescharacteristic
278C42×C67C2411yescharacteristic
279C23×C67—21no—
280C23×C67—21no—
281C23×C67—21no—
282C23×C67—22no—
283C23×C67—42no—
284C23×C67—42no—
285C23×C67—44no—
286C23×C67—41no—
287C23×C67—81no—
288C23×C67—82no—
289C23×C67—82no—
290C23×C67#12011yescharacteristic
291Q8×C67—21no—
292Q8×C67—21no—
293Q8×C67—42no—
294Q8×C67—41no—
295Q8×C67—41no—
296D4×C67—21no—
297D4×C67—21no—
298D4×C67—21no—
299D4×C67—21no—
300D4×C67—21no—
301D4×C67—42no—
302D4×C67—42no—
303D4×C67—42no—
304D4×C67—44no—
305D4×C67—42no—
306D4×C67—44no—
307D4×C67—41no—
308D4×C67—41no—
309D4×C67—41no—
310D4×C67—41no—
311D4×C67—41no—
312D4×C67—41no—
313D4×C67—41no—
314D4×C67—41no—
315D4×C67—82no—
316D4×C67—82no—
317D4×C67—82no—
318D4×C67—82no—
319D4×C67—82no—
320D4×C67#13512yes—
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—81no—
340C2×C4×C67—81no—
341C2×C4×C67—82no—
342C2×C4×C67—82no—
343C2×C4×C67—81no—
344C2×C4×C67—82no—
345C2×C4×C67—82no—
346C2×C4×C67#12011yescharacteristic
347C2×C4×C67#12011yescharacteristic
348C2×C4×C67#12011yescharacteristic
349C2×C4×C67C22×D411yescharacteristic
350C2×C4×C67C22×D411yescharacteristic
351C2×C4×C67C22×D411yescharacteristic
352C8×C67—41no—
353C8×C67—41no—
354C8×C67—41no—
355C8×C67—41no—
356C8×C67—41no—
357C8×C67—41no—
358C22×C67—21no—
359C22×C67—22no—
360C22×C67—21no—
361C22×C67—21no—
362C22×C67—41no—
363C22×C67—41no—
364C22×C67—41no—
365C22×C67—41no—
366C22×C67—42no—
367C22×C67—41no—
368C22×C67—42no—
369C22×C67—41no—
370C22×C67—42no—
371C22×C67—41no—
372C22×C67—41no—
373C22×C67—84no—
374C22×C67—81no—
375C22×C67—81no—
376C22×C67—81no—
377C22×C67—164no—
378C22×C67C2×#12011yescharacteristic
379C4×C67—21no—
380C4×C67—21no—
381C4×C67—21no—
382C4×C67—21no—
383C4×C67—41no—
384C4×C67—41no—
385C4×C67—41no—
386C4×C67—41no—
387C4×C67—41no—
388C4×C67—42no—
389C4×C67—81no—
390C4×C67C2×#13511yescharacteristic
391C4×C67#57511yescharacteristic
392C4×C67#57611yescharacteristic
393C4×C67#57611yescharacteristic
394#18866C6711yesmaximal, characteristic, direct product factor, Sylow
395C2×C67—41no—
396C2×C67—42no—
397C2×C67—81no—
398C2×C67—82no—
399C2×C67—81no—
400C2×C67—161no—
401C2×C67#300211yescharacteristic
402C2×C67#300811yescharacteristic
403C2×C67#301911yescharacteristic
404#3519C2×C6711yescharacteristic, complemented
405#3212C2×C6711yescharacteristic, complemented
406#3207C2×C6711yescharacteristic, complemented
407#3100C2×C6711yescharacteristic, complemented
408#1646C2×C6711yescharacteristic, complemented
409#1644C2×C6711yescharacteristic, complemented
410#1641C2×C6711yescharacteristic, complemented
411#1639C2×C6711yescharacteristic, complemented
412#1624C2×C6711yescharacteristic, complemented
413#1622C2×C6711yescharacteristic, complemented
414#1621C2×C6711yescharacteristic, complemented
415#1619C2×C6711yescharacteristic, complemented
416#1543C2×C6711yescharacteristic, complemented
417#1482C2×C6711yescharacteristic, complemented
418#1478C2×C6711yescharacteristic, complemented
419C67#1886611yescharacteristic, direct product factor, Sylow
420#555C22×C6711yescharacteristic
421#554C22×C6711yescharacteristic
422#553—21no—
423#553—21no—
424#550C22×C6711yescharacteristic
425#546—22no—
426#546—21no—
427D42—21no—
428D42C22×C6711yescharacteristic
429#540—21no—
430#538—22no—
431#532C22×C6711yescharacteristic
432#532C22×C6711yescharacteristic, complemented
433#529C22×C6711yescharacteristic
434#525—21no—
435C2×#121—21no—
436#518—21no—
437C2×C4×D4C22×C6711yescharacteristic
438#495—21no—
439#493C22×C6711yescharacteristic, complemented
440#492C22×C6711yescharacteristic, complemented
441#488—21no—
442#487C22×C6711yescharacteristic, complemented
443#486C22×C6711yescharacteristic, complemented
444#480—21no—
445#474C22×C6711yescharacteristic
446#474C22×C6711yescharacteristic, complemented
447#463—22no—
448#462C22×C6711yescharacteristic, complemented
449#461C22×C6711yescharacteristic, complemented
450#460C22×C6711yescharacteristic, complemented
451#459C22×C6711yescharacteristic
452#459C22×C6711yescharacteristic, complemented
453#459C22×C6711yescharacteristic, complemented
454#452—21no—
455#449—22no—
456#449—21no—
457#447—21no—
458C4×D8—21no—
459C4×D8—21no—
460#431C22×C6711yescharacteristic, complemented
461#431C22×C6711yescharacteristic, complemented
462#431C22×C6711yescharacteristic, complemented
463#333C22×C6711yescharacteristic, complemented
464#333C22×C6711yescharacteristic, complemented
465#331C22×C6711yescharacteristic, complemented
466#331C22×C6711yescharacteristic, complemented
467Q8⋊C8C22×C6711yescharacteristic, complemented
468Q8⋊C8C22×C6711yescharacteristic, complemented
469D4⋊C8C22×C6711yescharacteristic
470D4⋊C8C22×C6711yescharacteristic
471D4⋊C8C22×C6711yescharacteristic, complemented
472D4⋊C8C22×C6711yescharacteristic, complemented
473D4⋊C8C22×C6711yescharacteristic, complemented
474D4⋊C8C22×C6711yescharacteristic, complemented
475C2×#41—21no—
476C2×#41—21no—
477C2×#41D4×C6712yes—
478C22×D4—22no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4D4×C6711yescharacteristic
482C23×C4—21no—
483C2×Q16—21no—
484C2×SD16—22no—
485C2×SD16—21no—
486C2×SD16—21no—
487C2×D8—21no—
488C2×D8—21no—
489C2×D8—21no—
490C2×D8—22no—
491C4⋊Q8C23×C6711yescharacteristic
492C4⋊Q8C23×C6711yescharacteristic
493#127—21no—
494#127C23×C6711yescharacteristic
495#127C23×C6711yescharacteristic
496#126—22no—
497#126—21no—
498#125—21no—
499#125D4×C6711yescharacteristic
500#124—22no—
501#124—21no—
502#124D4×C6711yescharacteristic
503#124D4×C6712yes—
504#123—22no—
505#123—22no—
506#123—22no—
507#123—21no—
508C22⋊Q8—21no—
509C22⋊Q8—22no—
510C22⋊Q8D4×C6711yescharacteristic
511#121—22no—
512#121—22no—
513#121—22no—
514#121—22no—
515#121—21no—
516#121—22no—
517#121—21no—
518#121—21no—
519#121—21no—
520#121—21no—
521#121—21no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121D4×C6711yescharacteristic
526#120—22no—
527#120—22no—
528#120—22no—
529C4×Q8C23×C6711yescharacteristic
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—21no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4D4×C6711yescharacteristic
543C4×D4D4×C6711yescharacteristic
544C4×D4C23×C6711yescharacteristic
545C4×D4C23×C6711yescharacteristic
546C4×D4C23×C6711yescharacteristic
547#117—21no—
548#117—21no—
549#117—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4D4×C6711yescharacteristic
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—21no—
555C2×C42C23×C6711yescharacteristic
556#107—21no—
557#107—21no—
558C4⋊C8—21no—
559C4⋊C8C23×C6711yescharacteristic
560C4⋊C8C23×C6711yescharacteristic
561C4⋊C8C23×C6711yescharacteristic
562C4⋊C8C23×C6711yescharacteristic
563#103—22no—
564#103—21no—
565#103—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—
574C22⋊C8—21no—
575C22⋊C8—21no—
576C4×C8—21no—
577C4×C8—21no—
578C4×C8C23×C6711yescharacteristic
579C4×C8C23×C6711yescharacteristic
580C24—22no—
581C24—21no—
582#41—81no—
583#41—81no—
584#41—81no—
585#41—81no—
586#41—82no—
587C2×Q8—21no—
588C2×Q8C2×D4×C6711yescharacteristic
589C2×Q8C2×D4×C6712yes—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—21no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—41no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—41no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4—84no—
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—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—41no—
625C22×C4—81no—
626C22×C4—81no—
627C22×C4C2×D4×C6711yescharacteristic
628C22×C4C2×D4×C6711yescharacteristic
629C22×C4C2×D4×C6711yescharacteristic
630Q16—81no—
631SD16—81no—
632SD16—81no—
633SD16—82no—
634D8—42no—
635D8—42no—
636D8—81no—
637D8—82no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4C2×D4×C6711yescharacteristic
656C4⋊C4C2×D4×C6711yescharacteristic
657C4⋊C4C2×D4×C6711yescharacteristic
658C4⋊C4C2×D4×C6711yescharacteristic
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C42—22no—
678C42—21no—
679C42C2×D4×C6711yescharacteristic
680C42C2×D4×C6711yescharacteristic
681C42C2×D4×C6711yescharacteristic
682C42C24×C6711yescharacteristic
683C23—21no—
684C23—21no—
685C23—22no—
686C23—21no—
687C23—42no—
688C23—42no—
689C23—44no—
690C23—41no—
691C23—81no—
692C23—82no—
693C23—82no—
694C23#120×C6711yescharacteristic
695Q8—21no—
696Q8—21no—
697Q8—42no—
698Q8—41no—
699Q8—41no—
700D4—21no—
701D4—21no—
702D4—21no—
703D4—21no—
704D4—21no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—44no—
709D4—42no—
710D4—44no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—82no—
720D4—82no—
721D4—82no—
722D4—82no—
723D4—82no—
724D4#135×C6712yes—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—82no—
746C2×C4—82no—
747C2×C4—81no—
748C2×C4—82no—
749C2×C4—82no—
750C2×C4#120×C6711yescharacteristic
751C2×C4#120×C6711yescharacteristic
752C2×C4#120×C6711yescharacteristic
753C2×C4C22×D4×C6711yescharacteristic
754C2×C4C22×D4×C6711yescharacteristic
755C2×C4C22×D4×C6711yescharacteristic
756C8—41no—
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C8—41no—
762C22—21no—
763C22—21no—
764C22—22no—
765C22—21no—
766C22—41no—
767C22—41no—
768C22—42no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—84no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—164no—
782C22C2×#120×C6711yescharacteristic
783C4—21no—
784C4—21no—
785C4—21no—
786C4—21no—
787C4—41no—
788C4—42no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—81no—
794C4C2×#135×C6711yescharacteristic
795C4#575×C6711yescharacteristic
796C4#576×C6711yescharacteristic
797C4#576×C6711yescharacteristic
798C2—41no—
799C2—42no—
800C2—81no—
801C2—81no—
802C2—82no—
803C2—161no—
804C2C67×#300211yescharacteristic
805C2C67×#300811yescharacteristic
806C2C67×#301911yescharacteristic
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×#3519C2semidirect
2. C67×#3212C2semidirect
3. C67×#3207C2semidirect
4. C67×#3100C2semidirect
5. C67×#1646C2semidirect
6. C67×#1644C2semidirect
7. C67×#1641C2semidirect
8. C67×#1639C2semidirect
9. C67×#1624C2semidirect
10. C67×#1622C2semidirect
11. C67×#1621C2semidirect
12. C67×#1619C2semidirect
13. C67×#1543C2semidirect
14. C67×#1482C2semidirect
15. C67×#1478C2semidirect
28. #532×C67C22semidirect
35. #493×C67C22semidirect
36. #492×C67C22semidirect
38. #487×C67C22semidirect
39. #486×C67C22semidirect
42. #474×C67C22semidirect
44. #462×C67C22semidirect
45. #461×C67C22semidirect
46. #460×C67C22semidirect
48. #459×C67C22semidirect
49. #459×C67C22semidirect
56. #431×C67C22semidirect
57. #431×C67C22semidirect
58. #431×C67C22semidirect
59. #333×C67C22semidirect
60. #333×C67C22semidirect
61. #331×C67C22semidirect
62. #331×C67C22semidirect
63. Q8⋊C8×C67C22semidirect
64. Q8⋊C8×C67C22semidirect
67. D4⋊C8×C67C22semidirect
68. D4⋊C8×C67C22semidirect
69. D4⋊C8×C67C22semidirect
70. D4⋊C8×C67C22semidirect
394. #18866C67direct (N × H)
404. #3519C2×C67semidirect
405. #3212C2×C67semidirect
406. #3207C2×C67semidirect
407. #3100C2×C67semidirect
408. #1646C2×C67semidirect
409. #1644C2×C67semidirect
410. #1641C2×C67semidirect
411. #1639C2×C67semidirect
412. #1624C2×C67semidirect
413. #1622C2×C67semidirect
414. #1621C2×C67semidirect
415. #1619C2×C67semidirect
416. #1543C2×C67semidirect
417. #1482C2×C67semidirect
418. #1478C2×C67semidirect
419. C67#18866direct (N × H)
432. #532C22×C67semidirect
439. #493C22×C67semidirect
440. #492C22×C67semidirect
442. #487C22×C67semidirect
443. #486C22×C67semidirect
446. #474C22×C67semidirect
448. #462C22×C67semidirect
449. #461C22×C67semidirect
450. #460C22×C67semidirect
452. #459C22×C67semidirect
453. #459C22×C67semidirect
460. #431C22×C67semidirect
461. #431C22×C67semidirect
462. #431C22×C67semidirect
463. #333C22×C67semidirect
464. #333C22×C67semidirect
465. #331C22×C67semidirect
466. #331C22×C67semidirect
467. Q8⋊C8C22×C67semidirect
468. Q8⋊C8C22×C67semidirect
471. D4⋊C8C22×C67semidirect
472. D4⋊C8C22×C67semidirect
473. D4⋊C8C22×C67semidirect
474. D4⋊C8C22×C67semidirect

Maximal subgroups

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

subgroupindex
C67×#35192
C67×#32122
C67×#32072
C67×#31002
C67×#16462
C67×#16442
C67×#16412
C67×#16392
C67×#16242
C67×#16222
C67×#16212
C67×#16192
C67×#15432
C67×#14822
C67×#14782
#1886667