Finite Group Databasebeta

← C67×#18450 #30697701

Subgroups — C67×#18450 #30697701

Order 17152.

1096 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C67×#3537C211yesmaximal, characteristic, complemented
2C67×#3194C211yesmaximal, characteristic, complemented
3C67×#3186C211yesmaximal, characteristic, complemented
4C67×#2815C211yesmaximal, characteristic, complemented
5C67×#1612C212yesmaximal, complemented
6C67×#1607C212yesmaximal, complemented
7C67×#1600C212yesmaximal, complemented
8C67×#1595C212yesmaximal, complemented
9C67×#1516C211yesmaximal, characteristic, complemented
10C67×#1510C211yesmaximal, characteristic, complemented
11C67×#1471C211yesmaximal, characteristic, complemented
12#560×C67—22no—
13#553×C67—21no—
14#553×C67—21no—
15D42×C67—22no—
16D42×C67—21no—
17D42×C67—21no—
18#540×C67—21no—
19#538×C67—21no—
20#538×C67C2212yes—
21#535×C67—21no—
22#534×C67—21no—
23#534×C67C2212yes—
24#525×C67C2211yescharacteristic
25C2×#121×C67C2211yescharacteristic
26C2×#121×C67C2211yescharacteristic
27C2×#121×C67C2211yescharacteristic, complemented
28#483×C67C2211yescharacteristic, complemented
29#482×C67—21no—
30#480×C67—21no—
31#480×C67C2211yescharacteristic, complemented
32#480×C67C2212yescomplemented
33#469×C67—21no—
34#468×C67—21no—
35#466×C67—22no—
36#450×C67C2211yescharacteristic, complemented
37#449×C67—21no—
38#447×C67—21no—
39#447×C67C2211yescharacteristic, complemented
40#447×C67C2212yescomplemented
41#407×C67C2211yescharacteristic, complemented
42C2×C22⋊C8×C67C2211yescharacteristic, complemented
43#397×C67—21no—
44#397×C67C2212yescomplemented
45#392×C67—21no—
46#392×C67—22no—
47#392×C67C2212yescomplemented
48#381×C67C2211yescharacteristic, complemented
49#328×C67C2212yescomplemented
50#327×C67C2212yescomplemented
51#327×C67C2212yescomplemented
52#327×C67C2212yescomplemented
53#323×C67C2212yescomplemented
54#323×C67C2212yescomplemented
55C2×#41×C67D411yescharacteristic, complemented
56C22×D4×C67—22no—
57C22×D4×C67—21no—
58C22×D4×C67—21no—
59C22×D4×C67—22no—
60C22×D4×C67—21no—
61C22×D4×C67—22no—
62C22×D4×C67D412yes—
63C22×D4×C67D411yescharacteristic
64C22×D4×C67D411yescharacteristic, complemented
65C22×D4×C67C2311yescharacteristic
66C23×C4×C67C2311yescharacteristic
67C2×SD16×C67—21no—
68C2×D8×C67—21no—
69C2×D8×C67—22no—
70C2×M16×C67—21no—
71C22×C8×C67—21no—
72#127×C67—22no—
73#127×C67—21no—
74#126×C67—22no—
75#126×C67—22no—
76#125×C67—21no—
77#124×C67—22no—
78#123×C67—22no—
79#123×C67—21no—
80#123×C67—22no—
81#123×C67—22no—
82#123×C67—22no—
83C22⋊Q8×C67D411yescharacteristic, complemented
84C22⋊Q8×C67C2311yescharacteristic
85#121×C67—22no—
86#121×C67—21no—
87#121×C67—21no—
88#121×C67—22no—
89#121×C67—22no—
90#121×C67—22no—
91#121×C67—22no—
92#121×C67—21no—
93#121×C67—21no—
94#121×C67—21no—
95#121×C67—21no—
96#121×C67—21no—
97#121×C67—21no—
98#121×C67—22no—
99#121×C67—21no—
100#121×C67—21no—
101#121×C67—21no—
102#121×C67—21no—
103#121×C67D412yescomplemented
104#121×C67D411yescharacteristic, complemented
105#121×C67C2312yes—
106#121×C67C2311yescharacteristic
107#120×C67—22no—
108#120×C67—22no—
109#120×C67—22no—
110#120×C67—21no—
111#120×C67—22no—
112#120×C67—22no—
113#120×C67—22no—
114C4×D4×C67—22no—
115C4×D4×C67—21no—
116C4×D4×C67—21no—
117C4×D4×C67—21no—
118C4×D4×C67—21no—
119C4×D4×C67—22no—
120#117×C67—21no—
121#117×C67D411yescharacteristic, complemented
122C2×C4⋊C4×C67D411yescharacteristic
123C2×C4⋊C4×C67D411yescharacteristic, complemented
124C2×C4⋊C4×C67C2311yescharacteristic
125C2×C22⋊C4×C67—21no—
126C2×C22⋊C4×C67—21no—
127C2×C22⋊C4×C67—21no—
128C2×C22⋊C4×C67—22no—
129C2×C22⋊C4×C67—22no—
130C2×C22⋊C4×C67C2312yes—
131#107×C67—22no—
132#107×C67—21no—
133#106×C67—21no—
134#103×C67—21no—
135#102×C67—21no—
136#102×C67—22no—
137#102×C67—21no—
138#102×C67—22no—
139#102×C67—21no—
140C22⋊C8×C67—21no—
141C22⋊C8×C67—21no—
142C22⋊C8×C67C2311yescharacteristic
143C22⋊C8×C67C2312yes—
144C22⋊C8×C67C2311yescharacteristic
145#95×C67—21no—
146#95×C67—22no—
147#95×C67C2312yes—
148C24×C67—22no—
149C24×C67—21no—
150C24×C67—21no—
151C24×C67C2×D412yes—
152C24×C67C2×D411yescharacteristic
153#41×C67—81no—
154C2×Q8×C67C2×D411yescharacteristic
155C2×D4×C67—22no—
156C2×D4×C67—21no—
157C2×D4×C67—21no—
158C2×D4×C67—22no—
159C2×D4×C67—22no—
160C2×D4×C67—22no—
161C2×D4×C67—22no—
162C2×D4×C67—22no—
163C2×D4×C67—22no—
164C2×D4×C67—21no—
165C2×D4×C67—22no—
166C2×D4×C67—22no—
167C2×D4×C67—21no—
168C2×D4×C67—21no—
169C2×D4×C67—21no—
170C2×D4×C67—21no—
171C2×D4×C67—21no—
172C2×D4×C67—41no—
173C2×D4×C67—41no—
174C2×D4×C67—81no—
175C2×D4×C67—81no—
176C2×D4×C67—82no—
177C2×D4×C67—81no—
178C2×D4×C67—82no—
179C2×D4×C67—82no—
180C2×D4×C67—82no—
181C2×D4×C67—82no—
182C2×D4×C67—82no—
183C2×D4×C67—82no—
184C2×D4×C67—82no—
185C2×D4×C67—82no—
186C2×D4×C67—84no—
187C2×D4×C67C2×D411yescharacteristic
188C2×D4×C67C2×D412yes—
189C22×C4×C67—22no—
190C22×C4×C67—22no—
191C22×C4×C67—21no—
192C22×C4×C67—21no—
193C22×C4×C67—21no—
194C22×C4×C67—22no—
195C22×C4×C67—81no—
196C22×C4×C67C2×D412yes—
197C22×C4×C67C2×D411yescharacteristic
198C22×C4×C67C2×D411yescharacteristic
199C22×C4×C67C2×D411yescharacteristic
200C22×C4×C67C2×D411yescharacteristic
201C22×C4×C67C2×D411yescharacteristic
202C22×C4×C67C2411yescharacteristic
203SD16×C67—81no—
204D8×C67—82no—
205D8×C67—81no—
206M16×C67—81no—
207C2×C8×C67—22no—
208C2×C8×C67—21no—
209C2×C8×C67—21no—
210C2×C8×C67—81no—
211C4⋊C4×C67—22no—
212C4⋊C4×C67—22no—
213C4⋊C4×C67—21no—
214C4⋊C4×C67—21no—
215C4⋊C4×C67—21no—
216C4⋊C4×C67—21no—
217C4⋊C4×C67—21no—
218C4⋊C4×C67—21no—
219C4⋊C4×C67—21no—
220C4⋊C4×C67C2×D411yescharacteristic
221C4⋊C4×C67C2×D412yes—
222C4⋊C4×C67C2×D411yescharacteristic
223C22⋊C4×C67—22no—
224C22⋊C4×C67—22no—
225C22⋊C4×C67—22no—
226C22⋊C4×C67—22no—
227C22⋊C4×C67—22no—
228C22⋊C4×C67—21no—
229C22⋊C4×C67—21no—
230C22⋊C4×C67—21no—
231C22⋊C4×C67—22no—
232C22⋊C4×C67—21no—
233C22⋊C4×C67—22no—
234C22⋊C4×C67—22no—
235C22⋊C4×C67—22no—
236C22⋊C4×C67—21no—
237C22⋊C4×C67—41no—
238C22⋊C4×C67—41no—
239C22⋊C4×C67—82no—
240C22⋊C4×C67—82no—
241C22⋊C4×C67—81no—
242C42×C67—22no—
243C42×C67—21no—
244C23×C67—22no—
245C23×C67—22no—
246C23×C67—22no—
247C23×C67—21no—
248C23×C67—22no—
249C23×C67—22no—
250C23×C67—41no—
251C23×C67—41no—
252C23×C67—42no—
253C23×C67—42no—
254C23×C67—42no—
255C23×C67—41no—
256C23×C67—41no—
257C23×C67—42no—
258C23×C67—41no—
259C23×C67—42no—
260C23×C67—81no—
261C23×C67—81no—
262C23×C67—82no—
263C23×C67—82no—
264C23×C67—82no—
265C23×C67#12011yescharacteristic
266C23×C67#12011yescharacteristic
267C23×C67C22×D411yescharacteristic
268Q8×C67—41no—
269D4×C67—42no—
270D4×C67—41no—
271D4×C67—42no—
272D4×C67—42no—
273D4×C67—42no—
274D4×C67—41no—
275D4×C67—41no—
276D4×C67—44no—
277D4×C67—42no—
278D4×C67—42no—
279D4×C67—42no—
280D4×C67—42no—
281D4×C67—81no—
282D4×C67—82no—
283D4×C67—82no—
284D4×C67—81no—
285D4×C67—82no—
286D4×C67—82no—
287D4×C67—82no—
288D4×C67—82no—
289D4×C67—82no—
290D4×C67—82no—
291D4×C67—82no—
292D4×C67—88no—
293C2×C4×C67—21no—
294C2×C4×C67—22no—
295C2×C4×C67—22no—
296C2×C4×C67—21no—
297C2×C4×C67—21no—
298C2×C4×C67—41no—
299C2×C4×C67—41no—
300C2×C4×C67—41no—
301C2×C4×C67—41no—
302C2×C4×C67—41no—
303C2×C4×C67—41no—
304C2×C4×C67—42no—
305C2×C4×C67—42no—
306C2×C4×C67—42no—
307C2×C4×C67—42no—
308C2×C4×C67—41no—
309C2×C4×C67—42no—
310C2×C4×C67—42no—
311C2×C4×C67—81no—
312C2×C4×C67—82no—
313C2×C4×C67—82no—
314C2×C4×C67#12011yescharacteristic
315C2×C4×C67#12011yescharacteristic
316C2×C4×C67C22×D411yescharacteristic
317C2×C4×C67C22×D411yescharacteristic
318C8×C67—42no—
319C8×C67—41no—
320C8×C67—41no—
321C22×C67—21no—
322C22×C67—21no—
323C22×C67—21no—
324C22×C67—21no—
325C22×C67—21no—
326C22×C67—21no—
327C22×C67—21no—
328C22×C67—21no—
329C22×C67—42no—
330C22×C67—42no—
331C22×C67—41no—
332C22×C67—42no—
333C22×C67—42no—
334C22×C67—41no—
335C22×C67—41no—
336C22×C67—42no—
337C22×C67—42no—
338C22×C67—82no—
339C22×C67—82no—
340C22×C67—82no—
341C22×C67—82no—
342C22×C67—82no—
343C22×C67—81no—
344C22×C67—81no—
345C22×C67—81no—
346C22×C67—162no—
347C22×C67—164no—
348C22×C67C2×#12011yescharacteristic
349C22×C67#57612yes—
350C4×C67—21no—
351C4×C67—21no—
352C4×C67—21no—
353C4×C67—21no—
354C4×C67—42no—
355C4×C67—41no—
356C4×C67—42no—
357C4×C67—41no—
358C4×C67—41no—
359C4×C67—82no—
360C4×C67—81no—
361#18450C6711yesmaximal, characteristic, direct product factor, Sylow
362C2×C67—22no—
363C2×C67—41no—
364C2×C67—41no—
365C2×C67—82no—
366C2×C67—82no—
367C2×C67—81no—
368C2×C67—161no—
369C2×C67#300811yescharacteristic
370C2×C67#301911yescharacteristic
371C2×C67#302611yescharacteristic
372#3537C2×C6711yescharacteristic, complemented
373#3194C2×C6711yescharacteristic, complemented
374#3186C2×C6711yescharacteristic, complemented
375#2815C2×C6711yescharacteristic, complemented
376#1612C2×C6712yescomplemented
377#1607C2×C6712yescomplemented
378#1600C2×C6712yescomplemented
379#1595C2×C6712yescomplemented
380#1516C2×C6711yescharacteristic, complemented
381#1510C2×C6711yescharacteristic, complemented
382#1471C2×C6711yescharacteristic, complemented
383C67#1845011yescharacteristic, direct product factor, Sylow
384#560—22no—
385#553—21no—
386#553—21no—
387D42—22no—
388D42—21no—
389D42—21no—
390#540—21no—
391#538—21no—
392#538C22×C6712yes—
393#535—21no—
394#534—21no—
395#534C22×C6712yes—
396#525C22×C6711yescharacteristic
397C2×#121C22×C6711yescharacteristic
398C2×#121C22×C6711yescharacteristic
399C2×#121C22×C6711yescharacteristic, complemented
400#483C22×C6711yescharacteristic, complemented
401#482—21no—
402#480—21no—
403#480C22×C6711yescharacteristic, complemented
404#480C22×C6712yescomplemented
405#469—21no—
406#468—21no—
407#466—22no—
408#450C22×C6711yescharacteristic, complemented
409#449—21no—
410#447—21no—
411#447C22×C6711yescharacteristic, complemented
412#447C22×C6712yescomplemented
413#407C22×C6711yescharacteristic, complemented
414C2×C22⋊C8C22×C6711yescharacteristic, complemented
415#397—21no—
416#397C22×C6712yescomplemented
417#392—21no—
418#392—22no—
419#392C22×C6712yescomplemented
420#381C22×C6711yescharacteristic, complemented
421#328C22×C6712yescomplemented
422#327C22×C6712yescomplemented
423#327C22×C6712yescomplemented
424#327C22×C6712yescomplemented
425#323C22×C6712yescomplemented
426#323C22×C6712yescomplemented
427C2×#41D4×C6711yescharacteristic, complemented
428C22×D4—22no—
429C22×D4—21no—
430C22×D4—21no—
431C22×D4—22no—
432C22×D4—21no—
433C22×D4—22no—
434C22×D4D4×C6712yes—
435C22×D4D4×C6711yescharacteristic
436C22×D4D4×C6711yescharacteristic, complemented
437C22×D4C23×C6711yescharacteristic
438C23×C4C23×C6711yescharacteristic
439C2×SD16—21no—
440C2×D8—22no—
441C2×D8—21no—
442C2×M16—21no—
443C22×C8—21no—
444#127—22no—
445#127—21no—
446#126—22no—
447#126—22no—
448#125—21no—
449#124—22no—
450#123—22no—
451#123—21no—
452#123—22no—
453#123—22no—
454#123—22no—
455C22⋊Q8D4×C6711yescharacteristic, complemented
456C22⋊Q8C23×C6711yescharacteristic
457#121—22no—
458#121—21no—
459#121—21no—
460#121—22no—
461#121—22no—
462#121—22no—
463#121—22no—
464#121—21no—
465#121—21no—
466#121—21no—
467#121—21no—
468#121—21no—
469#121—21no—
470#121—22no—
471#121—21no—
472#121—21no—
473#121—21no—
474#121—21no—
475#121D4×C6712yescomplemented
476#121D4×C6711yescharacteristic, complemented
477#121C23×C6712yes—
478#121C23×C6711yescharacteristic
479#120—22no—
480#120—22no—
481#120—22no—
482#120—21no—
483#120—22no—
484#120—22no—
485#120—22no—
486C4×D4—22no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4—21no—
491C4×D4—22no—
492#117—21no—
493#117D4×C6711yescharacteristic, complemented
494C2×C4⋊C4D4×C6711yescharacteristic
495C2×C4⋊C4D4×C6711yescharacteristic, complemented
496C2×C4⋊C4C23×C6711yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4C23×C6712yes—
503#107—22no—
504#107—21no—
505#106—21no—
506#103—21no—
507#102—22no—
508#102—21no—
509#102—22no—
510#102—21no—
511#102—21no—
512C22⋊C8—21no—
513C22⋊C8—21no—
514C22⋊C8C23×C6711yescharacteristic
515C22⋊C8C23×C6711yescharacteristic
516C22⋊C8C23×C6712yes—
517#95—21no—
518#95—22no—
519#95C23×C6712yes—
520C24—22no—
521C24—21no—
522C24—21no—
523C24C2×D4×C6712yes—
524C24C2×D4×C6711yescharacteristic
525#41—81no—
526C2×Q8C2×D4×C6711yescharacteristic
527C2×D4—22no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—21no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—41no—
545C2×D4—41no—
546C2×D4—81no—
547C2×D4—81no—
548C2×D4—82no—
549C2×D4—81no—
550C2×D4—82no—
551C2×D4—82no—
552C2×D4—82no—
553C2×D4—82no—
554C2×D4—82no—
555C2×D4—82no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4—84no—
559C2×D4C2×D4×C6711yescharacteristic
560C2×D4C2×D4×C6712yes—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—81no—
568C22×C4C2×D4×C6712yes—
569C22×C4C2×D4×C6711yescharacteristic
570C22×C4C2×D4×C6711yescharacteristic
571C22×C4C2×D4×C6711yescharacteristic
572C22×C4C2×D4×C6711yescharacteristic
573C22×C4C2×D4×C6711yescharacteristic
574C22×C4C24×C6711yescharacteristic
575SD16—81no—
576D8—82no—
577D8—81no—
578M16—81no—
579C2×C8—22no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—81no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4C2×D4×C6711yescharacteristic
593C4⋊C4C2×D4×C6712yes—
594C4⋊C4C2×D4×C6711yescharacteristic
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—22no—
604C22⋊C4—21no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—21no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C22⋊C4—82no—
612C22⋊C4—82no—
613C22⋊C4—81no—
614C42—22no—
615C42—21no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—21no—
620C23—22no—
621C23—22no—
622C23—41no—
623C23—41no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—41no—
628C23—41no—
629C23—42no—
630C23—41no—
631C23—42no—
632C23—81no—
633C23—81no—
634C23—82no—
635C23—82no—
636C23—82no—
637C23#120×C6711yescharacteristic
638C23#120×C6711yescharacteristic
639C23C22×D4×C6711yescharacteristic
640Q8—41no—
641D4—42no—
642D4—41no—
643D4—42no—
644D4—42no—
645D4—42no—
646D4—41no—
647D4—41no—
648D4—44no—
649D4—42no—
650D4—42no—
651D4—42no—
652D4—42no—
653D4—81no—
654D4—82no—
655D4—82no—
656D4—81no—
657D4—82no—
658D4—82no—
659D4—82no—
660D4—82no—
661D4—82no—
662D4—82no—
663D4—82no—
664D4—88no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—81no—
684C2×C4—82no—
685C2×C4—82no—
686C2×C4#120×C6711yescharacteristic
687C2×C4#120×C6711yescharacteristic
688C2×C4C22×D4×C6711yescharacteristic
689C2×C4C22×D4×C6711yescharacteristic
690C8—42no—
691C8—41no—
692C8—41no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—42no—
702C22—42no—
703C22—41no—
704C22—41no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—41no—
710C22—82no—
711C22—82no—
712C22—82no—
713C22—82no—
714C22—82no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—162no—
719C22—164no—
720C22C2×#120×C6711yescharacteristic
721C22#576×C6712yes—
722C4—21no—
723C4—21no—
724C4—21no—
725C4—21no—
726C4—42no—
727C4—41no—
728C4—41no—
729C4—42no—
730C4—41no—
731C4—82no—
732C4—81no—
733C2—22no—
734C2—41no—
735C2—41no—
736C2—82no—
737C2—82no—
738C2—81no—
739C2—161no—
740C2C67×#300811yescharacteristic
741C2C67×#301911yescharacteristic
742C2C67×#302611yescharacteristic
subgroupG/H
center, socleC22×C67C2×#120
commutator, Frattini, cosocleC22×C4C24×C67
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C67 ◁ C23×C4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
1. C67×#3537C2semidirect
2. C67×#3194C2semidirect
3. C67×#3186C2semidirect
4. C67×#2815C2semidirect
5. C67×#1612C2semidirect
6. C67×#1607C2semidirect
7. C67×#1600C2semidirect
8. C67×#1595C2semidirect
9. C67×#1516C2semidirect
10. C67×#1510C2semidirect
11. C67×#1471C2semidirect
27. C2×#121×C67C22semidirect
28. #483×C67C22semidirect
31. #480×C67C22semidirect
32. #480×C67C22semidirect
36. #450×C67C22semidirect
39. #447×C67C22semidirect
40. #447×C67C22semidirect
41. #407×C67C22semidirect
42. C2×C22⋊C8×C67C22semidirect
44. #397×C67C22semidirect
47. #392×C67C22semidirect
48. #381×C67C22semidirect
49. #328×C67C22semidirect
50. #327×C67C22semidirect
51. #327×C67C22semidirect
52. #327×C67C22semidirect
53. #323×C67C22semidirect
54. #323×C67C22semidirect
55. C2×#41×C67D4semidirect
64. C22×D4×C67D4semidirect
83. C22⋊Q8×C67D4semidirect
103. #121×C67D4semidirect
104. #121×C67D4semidirect
121. #117×C67D4semidirect
123. C2×C4⋊C4×C67D4semidirect
361. #18450C67direct (N × H)
372. #3537C2×C67semidirect
373. #3194C2×C67semidirect
374. #3186C2×C67semidirect
375. #2815C2×C67semidirect
376. #1612C2×C67semidirect
377. #1607C2×C67semidirect
378. #1600C2×C67semidirect
379. #1595C2×C67semidirect
380. #1516C2×C67semidirect
381. #1510C2×C67semidirect
382. #1471C2×C67semidirect
383. C67#18450direct (N × H)
399. C2×#121C22×C67semidirect
400. #483C22×C67semidirect
403. #480C22×C67semidirect
404. #480C22×C67semidirect
408. #450C22×C67semidirect
411. #447C22×C67semidirect
412. #447C22×C67semidirect
413. #407C22×C67semidirect
414. C2×C22⋊C8C22×C67semidirect
416. #397C22×C67semidirect
419. #392C22×C67semidirect
420. #381C22×C67semidirect
421. #328C22×C67semidirect
422. #327C22×C67semidirect
423. #327C22×C67semidirect
424. #327C22×C67semidirect
425. #323C22×C67semidirect
426. #323C22×C67semidirect
427. C2×#41D4×C67semidirect
436. C22×D4D4×C67semidirect
455. C22⋊Q8D4×C67semidirect
475. #121D4×C67semidirect
476. #121D4×C67semidirect
493. #117D4×C67semidirect
495. C2×C4⋊C4D4×C67semidirect

Maximal subgroups

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

subgroupindex
C67×#35372
C67×#31942
C67×#31862
C67×#28152
C67×#16122
C67×#16072
C67×#16002
C67×#15952
C67×#15162
C67×#15102
C67×#14712
#1845067