Finite Group Databasebeta

← C67×#18810 #30698061

Subgroups — C67×#18810 #30698061

Order 17152.

1042 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C67×#3519C211yesmaximal, characteristic, complemented
2C67×#3251C211yesmaximal, characteristic, complemented
3C67×#3207C211yesmaximal, characteristic, complemented
4C67×#3036C211yesmaximal, characteristic, complemented
5C67×#1646C211yesmaximal, characteristic, complemented
6C67×#1643C211yesmaximal, characteristic, complemented
7C67×#1642C211yesmaximal, characteristic, complemented
8C67×#1639C211yesmaximal, characteristic, complemented
9C67×#1624C211yesmaximal, characteristic, complemented
10C67×#1622C211yesmaximal, characteristic, complemented
11C67×#1621C211yesmaximal, characteristic, complemented
12C67×#1619C211yesmaximal, characteristic, complemented
13C67×#1560C211yesmaximal, characteristic, complemented
14C67×#1495C211yesmaximal, characteristic, complemented
15C67×#1486C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C67—21no—
17#555×C67C2211yescharacteristic
18#554×C67C2211yescharacteristic
19#553×C67—21no—
20#553×C67—21no—
21#550×C67C2211yescharacteristic
22#546×C67—22no—
23#546×C67—21no—
24D42×C67—21no—
25D42×C67C2211yescharacteristic
26#540×C67—21no—
27#538×C67—22no—
28#532×C67C2211yescharacteristic
29#532×C67C2211yescharacteristic, complemented
30#529×C67C2211yescharacteristic
31#525×C67—21no—
32C2×#121×C67—21no—
33#518×C67—21no—
34C2×C4×D4×C67C2211yescharacteristic
35#493×C67C2211yescharacteristic, complemented
36#492×C67C2211yescharacteristic, complemented
37#487×C67C2211yescharacteristic, complemented
38#486×C67C2211yescharacteristic, complemented
39#478×C67—21no—
40#475×C67C2211yescharacteristic, complemented
41#474×C67C2211yescharacteristic, complemented
42#469×C67—21no—
43#468×C67—21no—
44#463×C67—22no—
45#463×C67—21no—
46#463×C67—21no—
47#463×C67—21no—
48#461×C67C2211yescharacteristic
49#461×C67C2211yescharacteristic, complemented
50#460×C67C2211yescharacteristic, complemented
51#459×C67C2211yescharacteristic
52#459×C67C2211yescharacteristic, complemented
53#459×C67C2211yescharacteristic, complemented
54#449×C67—22no—
55#431×C67C2211yescharacteristic, complemented
56#423×C67C2211yescharacteristic, complemented
57#423×C67C2211yescharacteristic, complemented
58#417×C67—21no—
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—
79AGL(1,ℤ/8)×C67—44no—
80C2×SD16×C67—21no—
81C2×SD16×C67—21no—
82C2×SD16×C67—22no—
83C2×SD16×C67—21no—
84C2×D8×C67—21no—
85C2×D8×C67—21no—
86C2×D8×C67—22no—
87C2×D8×C67—21no—
88C2×M16×C67—21no—
89C2×M16×C67—21no—
90C4⋊Q8×C67C2311yescharacteristic
91C4⋊Q8×C67C2311yescharacteristic
92#127×C67—21no—
93#127×C67C2311yescharacteristic
94#127×C67C2311yescharacteristic
95#126×C67—22no—
96#126×C67—21no—
97#125×C67—21no—
98#125×C67D411yescharacteristic
99#124×C67—22no—
100#124×C67—21no—
101#124×C67D411yescharacteristic
102#124×C67D412yes—
103#123×C67—22no—
104#123×C67—22no—
105#123×C67—22no—
106#123×C67—21no—
107C22⋊Q8×C67—21no—
108C22⋊Q8×C67—22no—
109C22⋊Q8×C67D411yescharacteristic
110#121×C67—22no—
111#121×C67—22no—
112#121×C67—22no—
113#121×C67—22no—
114#121×C67—21no—
115#121×C67—22no—
116#121×C67—21no—
117#121×C67—21no—
118#121×C67—21no—
119#121×C67—21no—
120#121×C67—21no—
121#121×C67—21no—
122#121×C67—21no—
123#121×C67—21no—
124#121×C67D411yescharacteristic
125#120×C67—22no—
126#120×C67—22no—
127#120×C67—22no—
128C4×Q8×C67C2311yescharacteristic
129C4×D4×C67—22no—
130C4×D4×C67—22no—
131C4×D4×C67—22no—
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×C67—21no—
139C4×D4×C67—21no—
140C4×D4×C67—21no—
141C4×D4×C67D411yescharacteristic
142C4×D4×C67D411yescharacteristic
143C4×D4×C67C2311yescharacteristic
144C4×D4×C67C2311yescharacteristic
145C4×D4×C67C2311yescharacteristic
146#117×C67—21no—
147#117×C67—21no—
148#117×C67—21no—
149C2×C4⋊C4×C67—21no—
150C2×C4⋊C4×C67D411yescharacteristic
151C2×C22⋊C4×C67—22no—
152C2×C22⋊C4×C67—22no—
153C2×C22⋊C4×C67—21no—
154C2×C42×C67C2311yescharacteristic
155#107×C67—21no—
156#106×C67—21no—
157C4⋊C8×C67—21no—
158C4⋊C8×C67—21no—
159C4⋊C8×C67—21no—
160C4⋊C8×C67C2311yescharacteristic
161C4⋊C8×C67C2311yescharacteristic
162C4⋊C8×C67C2311yescharacteristic
163C4⋊C8×C67C2311yescharacteristic
164#103×C67—22no—
165#103×C67—21no—
166#103×C67—21no—
167#103×C67—21no—
168#102×C67—22no—
169#102×C67—21no—
170#102×C67—21no—
171#102×C67—21no—
172#102×C67—21no—
173#102×C67—21no—
174C22⋊C8×C67—21no—
175C4×C8×C67C2311yescharacteristic
176C4×C8×C67C2311yescharacteristic
177C24×C67—22no—
178C24×C67—21no—
179#41×C67—42no—
180#41×C67—42no—
181#41×C67—81no—
182#41×C67—81no—
183#41×C67—82no—
184C2×Q8×C67—21no—
185C2×Q8×C67C2×D411yescharacteristic
186C2×Q8×C67C2×D412yes—
187C2×D4×C67—22no—
188C2×D4×C67—22no—
189C2×D4×C67—22no—
190C2×D4×C67—21no—
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—21no—
198C2×D4×C67—21no—
199C2×D4×C67—21no—
200C2×D4×C67—21no—
201C2×D4×C67—41no—
202C2×D4×C67—42no—
203C2×D4×C67—42no—
204C2×D4×C67—41no—
205C2×D4×C67—81no—
206C2×D4×C67—81no—
207C2×D4×C67—84no—
208C2×D4×C67C2×D411yescharacteristic
209C2×D4×C67C2×D411yescharacteristic
210C2×D4×C67C2×D411yescharacteristic
211C2×D4×C67C2×D412yes—
212C22×C4×C67—22no—
213C22×C4×C67—22no—
214C22×C4×C67—21no—
215C22×C4×C67—21no—
216C22×C4×C67—21no—
217C22×C4×C67—21no—
218C22×C4×C67—21no—
219C22×C4×C67—22no—
220C22×C4×C67—21no—
221C22×C4×C67—41no—
222C22×C4×C67—81no—
223C22×C4×C67—81no—
224C22×C4×C67C2×D411yescharacteristic
225C22×C4×C67C2×D411yescharacteristic
226C22×C4×C67C2×D411yescharacteristic
227SD16×C67—42no—
228SD16×C67—42no—
229SD16×C67—81no—
230SD16×C67—82no—
231D8×C67—42no—
232D8×C67—42no—
233D8×C67—81no—
234D8×C67—82no—
235M16×C67—42no—
236M16×C67—81no—
237C2×C8×C67—21no—
238C2×C8×C67—21no—
239C2×C8×C67—21no—
240C2×C8×C67—21no—
241C2×C8×C67—21no—
242C2×C8×C67—21no—
243C4⋊C4×C67—22no—
244C4⋊C4×C67—22no—
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×C67—21no—
252C4⋊C4×C67—21no—
253C4⋊C4×C67—21no—
254C4⋊C4×C67C2×D411yescharacteristic
255C4⋊C4×C67C2×D411yescharacteristic
256C4⋊C4×C67C2×D411yescharacteristic
257C4⋊C4×C67C2×D411yescharacteristic
258C22⋊C4×C67—22no—
259C22⋊C4×C67—22no—
260C22⋊C4×C67—22no—
261C22⋊C4×C67—22no—
262C22⋊C4×C67—22no—
263C22⋊C4×C67—21no—
264C22⋊C4×C67—21no—
265C22⋊C4×C67—21no—
266C22⋊C4×C67—21no—
267C22⋊C4×C67—22no—
268C22⋊C4×C67—21no—
269C22⋊C4×C67—21no—
270C22⋊C4×C67—22no—
271C22⋊C4×C67—21no—
272C22⋊C4×C67—21no—
273C22⋊C4×C67—21no—
274C22⋊C4×C67—41no—
275C22⋊C4×C67—41no—
276C42×C67—22no—
277C42×C67—21no—
278C42×C67C2×D411yescharacteristic
279C42×C67C2×D411yescharacteristic
280C42×C67C2×D411yescharacteristic
281C42×C67C2411yescharacteristic
282C23×C67—21no—
283C23×C67—21no—
284C23×C67—21no—
285C23×C67—22no—
286C23×C67—42no—
287C23×C67—42no—
288C23×C67—44no—
289C23×C67—41no—
290C23×C67—81no—
291C23×C67—82no—
292C23×C67—82no—
293C23×C67#12011yescharacteristic
294Q8×C67—21no—
295Q8×C67—21no—
296Q8×C67—42no—
297Q8×C67—41no—
298Q8×C67—41no—
299D4×C67—21no—
300D4×C67—21no—
301D4×C67—21no—
302D4×C67—21no—
303D4×C67—21no—
304D4×C67—42no—
305D4×C67—42no—
306D4×C67—42no—
307D4×C67—44no—
308D4×C67—42no—
309D4×C67—44no—
310D4×C67—41no—
311D4×C67—41no—
312D4×C67—41no—
313D4×C67—41no—
314D4×C67—41no—
315D4×C67—41no—
316D4×C67—41no—
317D4×C67—41no—
318D4×C67—82no—
319D4×C67—82no—
320D4×C67—82no—
321D4×C67—82no—
322D4×C67—82no—
323D4×C67AGL(1,ℤ/8)12yes—
324C2×C4×C67—21no—
325C2×C4×C67—21no—
326C2×C4×C67—21no—
327C2×C4×C67—21no—
328C2×C4×C67—21no—
329C2×C4×C67—21no—
330C2×C4×C67—21no—
331C2×C4×C67—22no—
332C2×C4×C67—21no—
333C2×C4×C67—21no—
334C2×C4×C67—41no—
335C2×C4×C67—41no—
336C2×C4×C67—41no—
337C2×C4×C67—41no—
338C2×C4×C67—41no—
339C2×C4×C67—41no—
340C2×C4×C67—41no—
341C2×C4×C67—41no—
342C2×C4×C67—81no—
343C2×C4×C67—81no—
344C2×C4×C67—82no—
345C2×C4×C67—82no—
346C2×C4×C67—81no—
347C2×C4×C67—82no—
348C2×C4×C67—82no—
349C2×C4×C67#12011yescharacteristic
350C2×C4×C67#12011yescharacteristic
351C2×C4×C67#12011yescharacteristic
352C2×C4×C67C22×D411yescharacteristic
353C2×C4×C67C22×D411yescharacteristic
354C2×C4×C67C22×D411yescharacteristic
355C8×C67—41no—
356C8×C67—41no—
357C8×C67—41no—
358C8×C67—41no—
359C8×C67—41no—
360C8×C67—41no—
361C22×C67—21no—
362C22×C67—22no—
363C22×C67—21no—
364C22×C67—21no—
365C22×C67—41no—
366C22×C67—41no—
367C22×C67—41no—
368C22×C67—41no—
369C22×C67—42no—
370C22×C67—41no—
371C22×C67—42no—
372C22×C67—41no—
373C22×C67—42no—
374C22×C67—41no—
375C22×C67—41no—
376C22×C67—84no—
377C22×C67—81no—
378C22×C67—81no—
379C22×C67—81no—
380C22×C67—164no—
381C22×C67C2×#12011yescharacteristic
382C4×C67—21no—
383C4×C67—21no—
384C4×C67—21no—
385C4×C67—21no—
386C4×C67—41no—
387C4×C67—41no—
388C4×C67—41no—
389C4×C67—41no—
390C4×C67—41no—
391C4×C67—42no—
392C4×C67—81no—
393C4×C67C2×AGL(1,ℤ/8)11yescharacteristic
394C4×C67#57511yescharacteristic
395C4×C67#57611yescharacteristic
396C4×C67#57711yescharacteristic
397#18810C6711yesmaximal, characteristic, direct product factor, Sylow
398C2×C67—41no—
399C2×C67—42no—
400C2×C67—81no—
401C2×C67—82no—
402C2×C67—81no—
403C2×C67—161no—
404C2×C67#300611yescharacteristic
405C2×C67#301211yescharacteristic
406C2×C67#301911yescharacteristic
407#3519C2×C6711yescharacteristic, complemented
408#3251C2×C6711yescharacteristic, complemented
409#3207C2×C6711yescharacteristic, complemented
410#3036C2×C6711yescharacteristic, complemented
411#1646C2×C6711yescharacteristic, complemented
412#1643C2×C6711yescharacteristic, complemented
413#1642C2×C6711yescharacteristic, complemented
414#1639C2×C6711yescharacteristic, complemented
415#1624C2×C6711yescharacteristic, complemented
416#1622C2×C6711yescharacteristic, complemented
417#1621C2×C6711yescharacteristic, complemented
418#1619C2×C6711yescharacteristic, complemented
419#1560C2×C6711yescharacteristic, complemented
420#1495C2×C6711yescharacteristic, complemented
421#1486C2×C6711yescharacteristic, complemented
422C67#1881011yescharacteristic, direct product factor, Sylow
423C2×AGL(1,ℤ/8)—21no—
424#555C22×C6711yescharacteristic
425#554C22×C6711yescharacteristic
426#553—21no—
427#553—21no—
428#550C22×C6711yescharacteristic
429#546—22no—
430#546—21no—
431D42—21no—
432D42C22×C6711yescharacteristic
433#540—21no—
434#538—22no—
435#532C22×C6711yescharacteristic
436#532C22×C6711yescharacteristic, complemented
437#529C22×C6711yescharacteristic
438#525—21no—
439C2×#121—21no—
440#518—21no—
441C2×C4×D4C22×C6711yescharacteristic
442#493C22×C6711yescharacteristic, complemented
443#492C22×C6711yescharacteristic, complemented
444#487C22×C6711yescharacteristic, complemented
445#486C22×C6711yescharacteristic, complemented
446#478—21no—
447#475C22×C6711yescharacteristic, complemented
448#474C22×C6711yescharacteristic, complemented
449#469—21no—
450#468—21no—
451#463—22no—
452#463—21no—
453#463—21no—
454#463—21no—
455#461C22×C6711yescharacteristic
456#461C22×C6711yescharacteristic, complemented
457#460C22×C6711yescharacteristic, complemented
458#459C22×C6711yescharacteristic
459#459C22×C6711yescharacteristic, complemented
460#459C22×C6711yescharacteristic, complemented
461#449—22no—
462#431C22×C6711yescharacteristic, complemented
463#423C22×C6711yescharacteristic, complemented
464#423C22×C6711yescharacteristic, complemented
465#417—21no—
466#333C22×C6711yescharacteristic, complemented
467#333C22×C6711yescharacteristic, complemented
468#331C22×C6711yescharacteristic, complemented
469#331C22×C6711yescharacteristic, complemented
470Q8⋊C8C22×C6711yescharacteristic, complemented
471Q8⋊C8C22×C6711yescharacteristic, complemented
472D4⋊C8C22×C6711yescharacteristic
473D4⋊C8C22×C6711yescharacteristic
474D4⋊C8C22×C6711yescharacteristic, complemented
475D4⋊C8C22×C6711yescharacteristic, complemented
476D4⋊C8C22×C6711yescharacteristic, complemented
477D4⋊C8C22×C6711yescharacteristic, complemented
478C2×#41—21no—
479C2×#41—21no—
480C2×#41D4×C6712yes—
481C22×D4—22no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4D4×C6711yescharacteristic
485C23×C4—21no—
486AGL(1,ℤ/8)—44no—
487C2×SD16—21no—
488C2×SD16—21no—
489C2×SD16—22no—
490C2×SD16—21no—
491C2×D8—21no—
492C2×D8—21no—
493C2×D8—22no—
494C2×D8—21no—
495C2×M16—21no—
496C2×M16—21no—
497C4⋊Q8C23×C6711yescharacteristic
498C4⋊Q8C23×C6711yescharacteristic
499#127—21no—
500#127C23×C6711yescharacteristic
501#127C23×C6711yescharacteristic
502#126—22no—
503#126—21no—
504#125—21no—
505#125D4×C6711yescharacteristic
506#124—22no—
507#124—21no—
508#124D4×C6711yescharacteristic
509#124D4×C6712yes—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—21no—
514C22⋊Q8—21no—
515C22⋊Q8—22no—
516C22⋊Q8D4×C6711yescharacteristic
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—21no—
522#121—22no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—21no—
531#121D4×C6711yescharacteristic
532#120—22no—
533#120—22no—
534#120—22no—
535C4×Q8C23×C6711yescharacteristic
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4—21no—
548C4×D4D4×C6711yescharacteristic
549C4×D4D4×C6711yescharacteristic
550C4×D4C23×C6711yescharacteristic
551C4×D4C23×C6711yescharacteristic
552C4×D4C23×C6711yescharacteristic
553#117—21no—
554#117—21no—
555#117—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4D4×C6711yescharacteristic
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—21no—
561C2×C42C23×C6711yescharacteristic
562#107—21no—
563#106—21no—
564C4⋊C8—21no—
565C4⋊C8—21no—
566C4⋊C8—21no—
567C4⋊C8C23×C6711yescharacteristic
568C4⋊C8C23×C6711yescharacteristic
569C4⋊C8C23×C6711yescharacteristic
570C4⋊C8C23×C6711yescharacteristic
571#103—22no—
572#103—21no—
573#103—21no—
574#103—21no—
575#102—22no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#102—21no—
581C22⋊C8—21no—
582C4×C8C23×C6711yescharacteristic
583C4×C8C23×C6711yescharacteristic
584C24—22no—
585C24—21no—
586#41—42no—
587#41—42no—
588#41—81no—
589#41—81no—
590#41—82no—
591C2×Q8—21no—
592C2×Q8C2×D4×C6711yescharacteristic
593C2×Q8C2×D4×C6712yes—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—21no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—41no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—41no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—84no—
615C2×D4C2×D4×C6711yescharacteristic
616C2×D4C2×D4×C6711yescharacteristic
617C2×D4C2×D4×C6711yescharacteristic
618C2×D4C2×D4×C6712yes—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—21no—
628C22×C4—41no—
629C22×C4—81no—
630C22×C4—81no—
631C22×C4C2×D4×C6711yescharacteristic
632C22×C4C2×D4×C6711yescharacteristic
633C22×C4C2×D4×C6711yescharacteristic
634SD16—42no—
635SD16—42no—
636SD16—81no—
637SD16—82no—
638D8—42no—
639D8—42no—
640D8—81no—
641D8—82no—
642M16—42no—
643M16—81no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4C2×D4×C6711yescharacteristic
662C4⋊C4C2×D4×C6711yescharacteristic
663C4⋊C4C2×D4×C6711yescharacteristic
664C4⋊C4C2×D4×C6711yescharacteristic
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—22no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—22no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C42—22no—
684C42—21no—
685C42C2×D4×C6711yescharacteristic
686C42C2×D4×C6711yescharacteristic
687C42C2×D4×C6711yescharacteristic
688C42C24×C6711yescharacteristic
689C23—21no—
690C23—21no—
691C23—21no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—44no—
696C23—41no—
697C23—81no—
698C23—82no—
699C23—82no—
700C23#120×C6711yescharacteristic
701Q8—21no—
702Q8—21no—
703Q8—42no—
704Q8—41no—
705Q8—41no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—44no—
715D4—42no—
716D4—44no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—82no—
726D4—82no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4AGL(1,ℤ/8)×C6712yes—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—82no—
752C2×C4—82no—
753C2×C4—81no—
754C2×C4—82no—
755C2×C4—82no—
756C2×C4#120×C6711yescharacteristic
757C2×C4#120×C6711yescharacteristic
758C2×C4#120×C6711yescharacteristic
759C2×C4C22×D4×C6711yescharacteristic
760C2×C4C22×D4×C6711yescharacteristic
761C2×C4C22×D4×C6711yescharacteristic
762C8—41no—
763C8—41no—
764C8—41no—
765C8—41no—
766C8—41no—
767C8—41no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—22no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—42no—
783C22—84no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—164no—
788C22C2×#120×C6711yescharacteristic
789C4—21no—
790C4—21no—
791C4—21no—
792C4—21no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—42no—
798C4—41no—
799C4—81no—
800C4C2×AGL(1,ℤ/8)×C6711yescharacteristic
801C4#575×C6711yescharacteristic
802C4#576×C6711yescharacteristic
803C4#577×C6711yescharacteristic
804C2—41no—
805C2—42no—
806C2—81no—
807C2—81no—
808C2—82no—
809C2—161no—
810C2C67×#300611yescharacteristic
811C2C67×#301211yescharacteristic
812C2C67×#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×#3251C2semidirect
3. C67×#3207C2semidirect
4. C67×#3036C2semidirect
5. C67×#1646C2semidirect
6. C67×#1643C2semidirect
7. C67×#1642C2semidirect
8. C67×#1639C2semidirect
9. C67×#1624C2semidirect
10. C67×#1622C2semidirect
11. C67×#1621C2semidirect
12. C67×#1619C2semidirect
13. C67×#1560C2semidirect
14. C67×#1495C2semidirect
15. C67×#1486C2semidirect
29. #532×C67C22semidirect
35. #493×C67C22semidirect
36. #492×C67C22semidirect
37. #487×C67C22semidirect
38. #486×C67C22semidirect
40. #475×C67C22semidirect
41. #474×C67C22semidirect
49. #461×C67C22semidirect
50. #460×C67C22semidirect
52. #459×C67C22semidirect
53. #459×C67C22semidirect
55. #431×C67C22semidirect
56. #423×C67C22semidirect
57. #423×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
397. #18810C67direct (N × H)
407. #3519C2×C67semidirect
408. #3251C2×C67semidirect
409. #3207C2×C67semidirect
410. #3036C2×C67semidirect
411. #1646C2×C67semidirect
412. #1643C2×C67semidirect
413. #1642C2×C67semidirect
414. #1639C2×C67semidirect
415. #1624C2×C67semidirect
416. #1622C2×C67semidirect
417. #1621C2×C67semidirect
418. #1619C2×C67semidirect
419. #1560C2×C67semidirect
420. #1495C2×C67semidirect
421. #1486C2×C67semidirect
422. C67#18810direct (N × H)
436. #532C22×C67semidirect
442. #493C22×C67semidirect
443. #492C22×C67semidirect
444. #487C22×C67semidirect
445. #486C22×C67semidirect
447. #475C22×C67semidirect
448. #474C22×C67semidirect
456. #461C22×C67semidirect
457. #460C22×C67semidirect
459. #459C22×C67semidirect
460. #459C22×C67semidirect
462. #431C22×C67semidirect
463. #423C22×C67semidirect
464. #423C22×C67semidirect
466. #333C22×C67semidirect
467. #333C22×C67semidirect
468. #331C22×C67semidirect
469. #331C22×C67semidirect
470. Q8⋊C8C22×C67semidirect
471. Q8⋊C8C22×C67semidirect
474. D4⋊C8C22×C67semidirect
475. D4⋊C8C22×C67semidirect
476. D4⋊C8C22×C67semidirect
477. 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×#32512
C67×#32072
C67×#30362
C67×#16462
C67×#16432
C67×#16422
C67×#16392
C67×#16242
C67×#16222
C67×#16212
C67×#16192
C67×#15602
C67×#14952
C67×#14862
#1881067