Finite Group Databasebeta

← C67×#18458 #30697709

Subgroups — C67×#18458 #30697709

Order 17152.

1036 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C67×#3558C211yesmaximal, characteristic, complemented
2C67×#3213C211yesmaximal, characteristic, complemented
3C67×#3211C211yesmaximal, characteristic, complemented
4C67×#2819C211yesmaximal, characteristic, complemented
5C67×#1606C212yesmaximal, complemented
6C67×#1601C212yesmaximal, complemented
7C67×#1600C212yesmaximal, complemented
8C67×#1595C212yesmaximal, complemented
9C67×#1517C211yesmaximal, characteristic, complemented
10C67×#1512C211yesmaximal, characteristic, complemented
11C67×#1469C211yesmaximal, characteristic, complemented
12#562×C67—21no—
13H(3,𝔽4)×C67—21no—
14#559×C67—21no—
15#548×C67—21no—
16#546×C67—21no—
17#546×C67—22no—
18D42×C67—21no—
19#542×C67—21no—
20#538×C67—22no—
21#538×C67C2212yes—
22#535×C67—21no—
23#534×C67C2212yes—
24#532×C67C2211yescharacteristic
25#529×C67C2211yescharacteristic
26C2×#124×C67C2211yescharacteristic
27C2×#124×C67C2211yescharacteristic, complemented
28#496×C67—21no—
29#495×C67—21no—
30#489×C67—21no—
31#488×C67—21no—
32#464×C67—21no—
33#463×C67—21no—
34#463×C67—22no—
35#451×C67C2211yescharacteristic, complemented
36#450×C67C2211yescharacteristic, complemented
37#448×C67C2211yescharacteristic
38#448×C67C2212yescomplemented
39#447×C67C2211yescharacteristic
40#447×C67C2212yescomplemented
41#432×C67C2211yescharacteristic, complemented
42#431×C67C2211yescharacteristic, complemented
43#394×C67—22no—
44#393×C67—21no—
45#393×C67C2212yescomplemented
46#392×C67—21no—
47#392×C67C2212yescomplemented
48#382×C67C2211yescharacteristic, complemented
49#328×C67C2212yescomplemented
50#327×C67C2212yes—
51#327×C67C2212yescomplemented
52#327×C67C2212yescomplemented
53#323×C67C2212yescomplemented
54#323×C67C2212yescomplemented
55C2×#41×C67—21no—
56C2×#41×C67—21no—
57C22×Q8×C67D411yescharacteristic
58C22×Q8×C67C2311yescharacteristic
59C22×D4×C67—21no—
60C22×D4×C67—22no—
61C22×D4×C67—22no—
62C22×D4×C67D411yescharacteristic
63C22×D4×C67C2311yescharacteristic
64C2×Q16×C67—21no—
65C2×SD16×C67—21no—
66C2×SD16×C67—21no—
67C2×SD16×C67—22no—
68C2×D8×C67—21no—
69C2×D8×C67—22no—
70C4⋊Q8×C67D411yescharacteristic, complemented
71#127×C67—21no—
72#127×C67D411yescharacteristic, complemented
73#126×C67—22no—
74#126×C67—21no—
75#125×C67D411yescharacteristic, complemented
76#124×C67—21no—
77#124×C67—22no—
78#124×C67—22no—
79#124×C67—22no—
80#124×C67—21no—
81#124×C67—21no—
82#124×C67—21no—
83#124×C67—21no—
84#124×C67—21no—
85#124×C67—21no—
86#124×C67—21no—
87#124×C67—21no—
88#124×C67—21no—
89#124×C67D411yescharacteristic, complemented
90#123×C67—22no—
91#123×C67—21no—
92#123×C67—22no—
93#123×C67—22no—
94#123×C67—22no—
95C22⋊Q8×C67—22no—
96C22⋊Q8×C67—21no—
97C22⋊Q8×C67—22no—
98C22⋊Q8×C67C2311yescharacteristic
99#121×C67—22no—
100#121×C67—22no—
101#121×C67—22no—
102#121×C67—21no—
103#121×C67—22no—
104#121×C67—21no—
105#121×C67—22no—
106#121×C67C2311yescharacteristic
107#121×C67C2312yes—
108#120×C67—22no—
109#120×C67—22no—
110#120×C67—22no—
111#120×C67—22no—
112#120×C67—22no—
113C4×Q8×C67—21no—
114C4×Q8×C67D411yescharacteristic, complemented
115C4×D4×C67—22no—
116C4×D4×C67—21no—
117C4×D4×C67—21no—
118C4×D4×C67—22no—
119C4×D4×C67—21no—
120C4×D4×C67D411yescharacteristic, complemented
121C4×D4×C67D412yescomplemented
122#117×C67—21no—
123C2×C4⋊C4×C67—21no—
124C2×C22⋊C4×C67—22no—
125C2×C22⋊C4×C67—21no—
126C2×C22⋊C4×C67—21no—
127C2×C22⋊C4×C67—22no—
128C2×C22⋊C4×C67—22no—
129C2×C22⋊C4×C67D412yes—
130C2×C22⋊C4×C67C2312yes—
131C2×C42×C67C2311yescharacteristic
132C4⋊C8×C67—21no—
133C4⋊C8×C67—21no—
134#103×C67—21no—
135#103×C67—22no—
136#103×C67—21no—
137#102×C67—21no—
138#102×C67—22no—
139#102×C67—21no—
140C22⋊C8×C67C2311yescharacteristic
141C22⋊C8×C67C2312yes—
142C22⋊C8×C67C2311yescharacteristic
143#97×C67—21no—
144C4×C8×C67—21no—
145#95×C67—21no—
146#95×C67—22no—
147#95×C67C2312yes—
148C24×C67—22no—
149C24×C67—21no—
150C24×C67C2×D412yes—
151#41×C67—81no—
152#41×C67—81no—
153#41×C67—82no—
154C2×Q8×C67—21no—
155C2×Q8×C67—21no—
156C2×Q8×C67—21no—
157C2×Q8×C67—21no—
158C2×Q8×C67—21no—
159C2×Q8×C67—81no—
160C2×Q8×C67—81no—
161C2×Q8×C67C2×D411yescharacteristic
162C2×D4×C67—22no—
163C2×D4×C67—21no—
164C2×D4×C67—22no—
165C2×D4×C67—22no—
166C2×D4×C67—22no—
167C2×D4×C67—22no—
168C2×D4×C67—22no—
169C2×D4×C67—21no—
170C2×D4×C67—21no—
171C2×D4×C67—21no—
172C2×D4×C67—21no—
173C2×D4×C67—21no—
174C2×D4×C67—21no—
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×C67C2×D411yescharacteristic
184C2×D4×C67C2×D412yes—
185C22×C4×C67—22no—
186C22×C4×C67—22no—
187C22×C4×C67—21no—
188C22×C4×C67—22no—
189C22×C4×C67—21no—
190C22×C4×C67—22no—
191C22×C4×C67C2×D411yescharacteristic
192C22×C4×C67C2×D412yes—
193C22×C4×C67C2×D411yescharacteristic
194C22×C4×C67C2411yescharacteristic
195Q16×C67—81no—
196SD16×C67—82no—
197SD16×C67—81no—
198SD16×C67—81no—
199D8×C67—82no—
200D8×C67—81no—
201C2×C8×C67—22no—
202C2×C8×C67—21no—
203C2×C8×C67—21no—
204C4⋊C4×C67—22no—
205C4⋊C4×C67—22no—
206C4⋊C4×C67—21no—
207C4⋊C4×C67—21no—
208C4⋊C4×C67—21no—
209C4⋊C4×C67—21no—
210C4⋊C4×C67—21no—
211C4⋊C4×C67—81no—
212C4⋊C4×C67C2×D412yes—
213C4⋊C4×C67C2×D411yescharacteristic
214C4⋊C4×C67C2×D411yescharacteristic
215C22⋊C4×C67—22no—
216C22⋊C4×C67—22no—
217C22⋊C4×C67—22no—
218C22⋊C4×C67—22no—
219C22⋊C4×C67—22no—
220C22⋊C4×C67—21no—
221C22⋊C4×C67—21no—
222C22⋊C4×C67—22no—
223C22⋊C4×C67—22no—
224C22⋊C4×C67—21no—
225C22⋊C4×C67—21no—
226C22⋊C4×C67—22no—
227C22⋊C4×C67—22no—
228C22⋊C4×C67—22no—
229C22⋊C4×C67—21no—
230C22⋊C4×C67—22no—
231C22⋊C4×C67—41no—
232C22⋊C4×C67—41no—
233C22⋊C4×C67—41no—
234C22⋊C4×C67—41no—
235C22⋊C4×C67—82no—
236C22⋊C4×C67—82no—
237C42×C67—22no—
238C42×C67—21no—
239C42×C67C2×D411yescharacteristic
240C42×C67C2×D411yescharacteristic
241C42×C67C2×D411yescharacteristic
242C42×C67C2×D411yescharacteristic
243C23×C67—22no—
244C23×C67—21no—
245C23×C67—22no—
246C23×C67—22no—
247C23×C67—22no—
248C23×C67—42no—
249C23×C67—42no—
250C23×C67—42no—
251C23×C67—42no—
252C23×C67—41no—
253C23×C67—41no—
254C23×C67—41no—
255C23×C67—82no—
256C23×C67—82no—
257C23×C67—82no—
258C23×C67C22×D411yescharacteristic
259Q8×C67—41no—
260Q8×C67—42no—
261Q8×C67—42no—
262Q8×C67—41no—
263Q8×C67—41no—
264Q8×C67—81no—
265Q8×C67—81no—
266D4×C67—42no—
267D4×C67—41no—
268D4×C67—42no—
269D4×C67—42no—
270D4×C67—42no—
271D4×C67—41no—
272D4×C67—41no—
273D4×C67—41no—
274D4×C67—42no—
275D4×C67—41no—
276D4×C67—42no—
277D4×C67—81no—
278D4×C67—81no—
279D4×C67—82no—
280D4×C67—82no—
281D4×C67—82no—
282D4×C67—82no—
283D4×C67—82no—
284D4×C67—88no—
285C2×C4×C67—21no—
286C2×C4×C67—21no—
287C2×C4×C67—21no—
288C2×C4×C67—22no—
289C2×C4×C67—22no—
290C2×C4×C67—21no—
291C2×C4×C67—21no—
292C2×C4×C67—41no—
293C2×C4×C67—41no—
294C2×C4×C67—42no—
295C2×C4×C67—42no—
296C2×C4×C67—42no—
297C2×C4×C67—42no—
298C2×C4×C67—42no—
299C2×C4×C67—41no—
300C2×C4×C67—42no—
301C2×C4×C67—82no—
302C2×C4×C67—82no—
303C2×C4×C67—82no—
304C2×C4×C67#12011yescharacteristic
305C2×C4×C67#12011yescharacteristic
306C2×C4×C67#12011yescharacteristic
307C2×C4×C67#12011yescharacteristic
308C2×C4×C67C22×D411yescharacteristic
309C2×C4×C67C22×D411yescharacteristic
310C8×C67—42no—
311C8×C67—41no—
312C8×C67—41no—
313C22×C67—21no—
314C22×C67—21no—
315C22×C67—42no—
316C22×C67—42no—
317C22×C67—41no—
318C22×C67—41no—
319C22×C67—42no—
320C22×C67—42no—
321C22×C67—42no—
322C22×C67—41no—
323C22×C67—42no—
324C22×C67—82no—
325C22×C67—82no—
326C22×C67—82no—
327C22×C67—82no—
328C22×C67—81no—
329C22×C67—81no—
330C22×C67—81no—
331C22×C67—164no—
332C22×C67C2×#12011yescharacteristic
333C22×C67#57611yescharacteristic
334C22×C67#57711yescharacteristic
335C4×C67—21no—
336C4×C67—21no—
337C4×C67—21no—
338C4×C67—21no—
339C4×C67—21no—
340C4×C67—21no—
341C4×C67—41no—
342C4×C67—42no—
343C4×C67—41no—
344C4×C67—42no—
345C4×C67—41no—
346C4×C67—82no—
347C4×C67—81no—
348#18458C6711yesmaximal, characteristic, direct product factor, Sylow
349C2×C67—21no—
350C2×C67—21no—
351C2×C67—82no—
352C2×C67—82no—
353C2×C67—81no—
354C2×C67—161no—
355C2×C67#301211yescharacteristic
356C2×C67#301911yescharacteristic
357C2×C67#302711yescharacteristic
358#3558C2×C6711yescharacteristic, complemented
359#3213C2×C6711yescharacteristic, complemented
360#3211C2×C6711yescharacteristic, complemented
361#2819C2×C6711yescharacteristic, complemented
362#1606C2×C6712yescomplemented
363#1601C2×C6712yescomplemented
364#1600C2×C6712yescomplemented
365#1595C2×C6712yescomplemented
366#1517C2×C6711yescharacteristic, complemented
367#1512C2×C6711yescharacteristic, complemented
368#1469C2×C6711yescharacteristic, complemented
369C67#1845811yescharacteristic, direct product factor, Sylow
370#562—21no—
371H(3,𝔽4)—21no—
372#559—21no—
373#548—21no—
374#546—21no—
375#546—22no—
376D42—21no—
377#542—21no—
378#538—22no—
379#538C22×C6712yes—
380#535—21no—
381#534C22×C6712yes—
382#532C22×C6711yescharacteristic
383#529C22×C6711yescharacteristic
384C2×#124C22×C6711yescharacteristic
385C2×#124C22×C6711yescharacteristic, complemented
386#496—21no—
387#495—21no—
388#489—21no—
389#488—21no—
390#464—21no—
391#463—21no—
392#463—22no—
393#451C22×C6711yescharacteristic, complemented
394#450C22×C6711yescharacteristic, complemented
395#448C22×C6711yescharacteristic
396#448C22×C6712yescomplemented
397#447C22×C6711yescharacteristic
398#447C22×C6712yescomplemented
399#432C22×C6711yescharacteristic, complemented
400#431C22×C6711yescharacteristic, complemented
401#394—22no—
402#393—21no—
403#393C22×C6712yescomplemented
404#392—21no—
405#392C22×C6712yescomplemented
406#382C22×C6711yescharacteristic, complemented
407#328C22×C6712yescomplemented
408#327C22×C6712yes—
409#327C22×C6712yescomplemented
410#327C22×C6712yescomplemented
411#323C22×C6712yescomplemented
412#323C22×C6712yescomplemented
413C2×#41—21no—
414C2×#41—21no—
415C22×Q8D4×C6711yescharacteristic
416C22×Q8C23×C6711yescharacteristic
417C22×D4—21no—
418C22×D4—22no—
419C22×D4—22no—
420C22×D4D4×C6711yescharacteristic
421C22×D4C23×C6711yescharacteristic
422C2×Q16—21no—
423C2×SD16—21no—
424C2×SD16—21no—
425C2×SD16—22no—
426C2×D8—21no—
427C2×D8—22no—
428C4⋊Q8D4×C6711yescharacteristic, complemented
429#127—21no—
430#127D4×C6711yescharacteristic, complemented
431#126—22no—
432#126—21no—
433#125D4×C6711yescharacteristic, complemented
434#124—21no—
435#124—22no—
436#124—22no—
437#124—22no—
438#124—21no—
439#124—21no—
440#124—21no—
441#124—21no—
442#124—21no—
443#124—21no—
444#124—21no—
445#124—21no—
446#124—21no—
447#124D4×C6711yescharacteristic, complemented
448#123—22no—
449#123—21no—
450#123—22no—
451#123—22no—
452#123—22no—
453C22⋊Q8—22no—
454C22⋊Q8—21no—
455C22⋊Q8—22no—
456C22⋊Q8C23×C6711yescharacteristic
457#121—22no—
458#121—22no—
459#121—22no—
460#121—21no—
461#121—22no—
462#121—21no—
463#121—22no—
464#121C23×C6711yescharacteristic
465#121C23×C6712yes—
466#120—22no—
467#120—22no—
468#120—22no—
469#120—22no—
470#120—22no—
471C4×Q8—21no—
472C4×Q8D4×C6711yescharacteristic, complemented
473C4×D4—22no—
474C4×D4—21no—
475C4×D4—21no—
476C4×D4—22no—
477C4×D4—21no—
478C4×D4D4×C6711yescharacteristic, complemented
479C4×D4D4×C6712yescomplemented
480#117—21no—
481C2×C4⋊C4—21no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4D4×C6712yes—
488C2×C22⋊C4C23×C6712yes—
489C2×C42C23×C6711yescharacteristic
490C4⋊C8—21no—
491C4⋊C8—21no—
492#103—21no—
493#103—22no—
494#103—21no—
495#102—21no—
496#102—22no—
497#102—21no—
498C22⋊C8C23×C6712yes—
499C22⋊C8C23×C6711yescharacteristic
500C22⋊C8C23×C6711yescharacteristic
501#97—21no—
502C4×C8—21no—
503#95—21no—
504#95—22no—
505#95C23×C6712yes—
506C24—22no—
507C24—21no—
508C24C2×D4×C6712yes—
509#41—81no—
510#41—81no—
511#41—82no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—81no—
518C2×Q8—81no—
519C2×Q8C2×D4×C6711yescharacteristic
520C2×D4—22no—
521C2×D4—21no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—81no—
534C2×D4—82no—
535C2×D4—81no—
536C2×D4—82no—
537C2×D4—82no—
538C2×D4—82no—
539C2×D4—82no—
540C2×D4—82no—
541C2×D4C2×D4×C6711yescharacteristic
542C2×D4C2×D4×C6712yes—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4C2×D4×C6711yescharacteristic
550C22×C4C2×D4×C6712yes—
551C22×C4C2×D4×C6711yescharacteristic
552C22×C4C24×C6711yescharacteristic
553Q16—81no—
554SD16—82no—
555SD16—81no—
556SD16—81no—
557D8—82no—
558D8—81no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—22no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—81no—
570C4⋊C4C2×D4×C6712yes—
571C4⋊C4C2×D4×C6711yescharacteristic
572C4⋊C4C2×D4×C6711yescharacteristic
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—21no—
583C22⋊C4—21no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—21no—
588C22⋊C4—22no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C22⋊C4—82no—
594C22⋊C4—82no—
595C42—22no—
596C42—21no—
597C42C2×D4×C6711yescharacteristic
598C42C2×D4×C6711yescharacteristic
599C42C2×D4×C6711yescharacteristic
600C42C2×D4×C6711yescharacteristic
601C23—22no—
602C23—21no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—82no—
614C23—82no—
615C23—82no—
616C23C22×D4×C6711yescharacteristic
617Q8—41no—
618Q8—42no—
619Q8—42no—
620Q8—41no—
621Q8—41no—
622Q8—81no—
623Q8—81no—
624D4—42no—
625D4—41no—
626D4—42no—
627D4—42no—
628D4—42no—
629D4—41no—
630D4—41no—
631D4—41no—
632D4—42no—
633D4—41no—
634D4—42no—
635D4—81no—
636D4—81no—
637D4—82no—
638D4—82no—
639D4—82no—
640D4—82no—
641D4—82no—
642D4—88no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—82no—
660C2×C4—82no—
661C2×C4—82no—
662C2×C4#120×C6711yescharacteristic
663C2×C4#120×C6711yescharacteristic
664C2×C4#120×C6711yescharacteristic
665C2×C4#120×C6711yescharacteristic
666C2×C4C22×D4×C6711yescharacteristic
667C2×C4C22×D4×C6711yescharacteristic
668C8—42no—
669C8—41no—
670C8—41no—
671C22—21no—
672C22—21no—
673C22—42no—
674C22—42no—
675C22—41no—
676C22—41no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—41no—
681C22—42no—
682C22—82no—
683C22—82no—
684C22—82no—
685C22—82no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—164no—
690C22C2×#120×C6711yescharacteristic
691C22#576×C6711yescharacteristic
692C22#577×C6711yescharacteristic
693C4—21no—
694C4—21no—
695C4—21no—
696C4—21no—
697C4—21no—
698C4—21no—
699C4—41no—
700C4—42no—
701C4—41no—
702C4—42no—
703C4—41no—
704C4—82no—
705C4—81no—
706C2—21no—
707C2—21no—
708C2—82no—
709C2—81no—
710C2—82no—
711C2—161no—
712C2C67×#301211yescharacteristic
713C2C67×#301911yescharacteristic
714C2C67×#302711yescharacteristic
subgroupG/H
center, socleC22×C67C2×#120
commutator, Frattini, cosocleC22×C4C24×C67
LCSG ▷ C22×C4 ▷ 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×#3558C2semidirect
2. C67×#3213C2semidirect
3. C67×#3211C2semidirect
4. C67×#2819C2semidirect
5. C67×#1606C2semidirect
6. C67×#1601C2semidirect
7. C67×#1600C2semidirect
8. C67×#1595C2semidirect
9. C67×#1517C2semidirect
10. C67×#1512C2semidirect
11. C67×#1469C2semidirect
27. C2×#124×C67C22semidirect
35. #451×C67C22semidirect
36. #450×C67C22semidirect
38. #448×C67C22semidirect
40. #447×C67C22semidirect
41. #432×C67C22semidirect
42. #431×C67C22semidirect
45. #393×C67C22semidirect
47. #392×C67C22semidirect
48. #382×C67C22semidirect
49. #328×C67C22semidirect
51. #327×C67C22semidirect
52. #327×C67C22semidirect
53. #323×C67C22semidirect
54. #323×C67C22semidirect
70. C4⋊Q8×C67D4semidirect
72. #127×C67D4semidirect
75. #125×C67D4semidirect
89. #124×C67D4semidirect
114. C4×Q8×C67D4semidirect
120. C4×D4×C67D4semidirect
121. C4×D4×C67D4semidirect
348. #18458C67direct (N × H)
358. #3558C2×C67semidirect
359. #3213C2×C67semidirect
360. #3211C2×C67semidirect
361. #2819C2×C67semidirect
362. #1606C2×C67semidirect
363. #1601C2×C67semidirect
364. #1600C2×C67semidirect
365. #1595C2×C67semidirect
366. #1517C2×C67semidirect
367. #1512C2×C67semidirect
368. #1469C2×C67semidirect
369. C67#18458direct (N × H)
385. C2×#124C22×C67semidirect
393. #451C22×C67semidirect
394. #450C22×C67semidirect
396. #448C22×C67semidirect
398. #447C22×C67semidirect
399. #432C22×C67semidirect
400. #431C22×C67semidirect
403. #393C22×C67semidirect
405. #392C22×C67semidirect
406. #382C22×C67semidirect
407. #328C22×C67semidirect
409. #327C22×C67semidirect
410. #327C22×C67semidirect
411. #323C22×C67semidirect
412. #323C22×C67semidirect
428. C4⋊Q8D4×C67semidirect
430. #127D4×C67semidirect
433. #125D4×C67semidirect
447. #124D4×C67semidirect
472. C4×Q8D4×C67semidirect
478. C4×D4D4×C67semidirect
479. C4×D4D4×C67semidirect

Maximal subgroups

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

subgroupindex
C67×#35582
C67×#32132
C67×#32112
C67×#28192
C67×#16062
C67×#16012
C67×#16002
C67×#15952
C67×#15172
C67×#15122
C67×#14692
#1845867