Finite Group Databasebeta

← C67×#18446 #30697697

Subgroups — C67×#18446 #30697697

Order 17152.

1032 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C67×#3534C211yesmaximal, characteristic, complemented
2C67×#3192C211yesmaximal, characteristic, complemented
3C67×#3188C211yesmaximal, characteristic, complemented
4C67×#2813C211yesmaximal, characteristic, complemented
5C67×#1618C211yesmaximal, characteristic, complemented
6C67×#1616C211yesmaximal, characteristic, complemented
7C67×#1615C211yesmaximal, characteristic, complemented
8C67×#1613C211yesmaximal, characteristic, complemented
9C67×#1600C211yesmaximal, characteristic, complemented
10C67×#1598C211yesmaximal, characteristic, complemented
11C67×#1597C211yesmaximal, characteristic, complemented
12C67×#1595C211yesmaximal, characteristic, complemented
13C67×#1519C211yesmaximal, characteristic, complemented
14C67×#1513C211yesmaximal, characteristic, complemented
15C67×#1468C211yesmaximal, characteristic, complemented
16#562×C67—21no—
17#560×C67—21no—
18#553×C67—21no—
19#551×C67—21no—
20#546×C67—21no—
21#546×C67—21no—
22#546×C67—21no—
23D42×C67—21no—
24#540×C67—21no—
25#539×C67—21no—
26#539×C67C2211yescharacteristic
27#538×C67—21no—
28#538×C67C2211yescharacteristic
29#537×C67C2211yescharacteristic
30#534×C67—21no—
31#534×C67C2211yescharacteristic
32#525×C67C2211yescharacteristic
33C2×#123×C67C2211yescharacteristic
34C2×#121×C67C2211yescharacteristic
35C2×#121×C67C2211yescharacteristic, complemented
36#484×C67C2211yescharacteristic, complemented
37#482×C67—21no—
38#481×C67—21no—
39#481×C67C2211yescharacteristic
40#481×C67C2211yescharacteristic, complemented
41#481×C67C2211yescharacteristic, complemented
42#469×C67—21no—
43#469×C67—21no—
44#466×C67—21no—
45#465×C67—21no—
46#450×C67C2211yescharacteristic, complemented
47#449×C67—21no—
48#447×C67—21no—
49#447×C67C2211yescharacteristic
50#447×C67C2211yescharacteristic, complemented
51#447×C67C2211yescharacteristic, complemented
52#407×C67C2211yescharacteristic, complemented
53C2×C22⋊C8×C67C2211yescharacteristic, complemented
54#400×C67C2211yescharacteristic, complemented
55#399×C67C2211yescharacteristic, complemented
56#396×C67—21no—
57#394×C67—21no—
58#394×C67—21no—
59#394×C67C2211yescharacteristic, complemented
60#392×C67—21no—
61#392×C67C2211yescharacteristic, complemented
62#380×C67C2211yescharacteristic, complemented
63#328×C67C2211yescharacteristic, complemented
64#328×C67C2211yescharacteristic, complemented
65#327×C67C2211yescharacteristic
66#327×C67C2211yescharacteristic
67#327×C67C2211yescharacteristic, complemented
68#327×C67C2211yescharacteristic, complemented
69#327×C67C2211yescharacteristic, complemented
70#327×C67C2211yescharacteristic, complemented
71#324×C67C2211yescharacteristic, complemented
72#324×C67C2211yescharacteristic, complemented
73#323×C67C2211yescharacteristic, complemented
74#323×C67C2211yescharacteristic, complemented
75C2×#41×C67—21no—
76C2×#41×C67D411yescharacteristic, complemented
77C22×D4×C67—21no—
78C22×D4×C67—21no—
79C22×D4×C67—21no—
80C22×D4×C67—21no—
81C22×D4×C67—21no—
82C22×D4×C67D411yescharacteristic
83C22×D4×C67D411yescharacteristic, complemented
84C22×D4×C67C2311yescharacteristic
85C23×C4×C67C2311yescharacteristic
86C2×SD16×C67—21no—
87C2×D8×C67—21no—
88C2×D8×C67—21no—
89C2×D8×C67—21no—
90C2×M16×C67—21no—
91C22×C8×C67—21no—
92#127×C67—21no—
93#126×C67—21no—
94#126×C67—21no—
95#126×C67—21no—
96#126×C67—21no—
97#125×C67—21no—
98#125×C67—21no—
99#124×C67—21no—
100#124×C67—21no—
101#124×C67—21no—
102#123×C67—21no—
103#123×C67—21no—
104#123×C67—21no—
105#123×C67—21no—
106#123×C67—21no—
107#123×C67—21no—
108#123×C67—21no—
109#123×C67—21no—
110#123×C67—21no—
111#123×C67—21no—
112#123×C67—21no—
113#123×C67—21no—
114#123×C67—21no—
115#123×C67—21no—
116C22⋊Q8×C67—21no—
117C22⋊Q8×C67—21no—
118C22⋊Q8×C67—21no—
119C22⋊Q8×C67—21no—
120C22⋊Q8×C67—21no—
121C22⋊Q8×C67D411yescharacteristic, complemented
122C22⋊Q8×C67C2311yescharacteristic
123#121×C67—21no—
124#121×C67—21no—
125#121×C67—21no—
126#121×C67—21no—
127#121×C67—21no—
128#121×C67—21no—
129#121×C67—21no—
130#121×C67—21no—
131#121×C67—21no—
132#121×C67—21no—
133#121×C67—21no—
134#121×C67—21no—
135#121×C67—21no—
136#121×C67—21no—
137#121×C67—21no—
138#121×C67—21no—
139#121×C67—21no—
140#121×C67—21no—
141#121×C67—21no—
142#121×C67D411yescharacteristic, complemented
143#121×C67D411yescharacteristic, complemented
144#121×C67D411yescharacteristic, complemented
145#121×C67C2311yescharacteristic
146#121×C67C2311yescharacteristic
147#121×C67C2311yescharacteristic
148#120×C67—21no—
149#120×C67—21no—
150#120×C67—21no—
151#120×C67—21no—
152#120×C67—21no—
153#120×C67—21no—
154#120×C67—21no—
155#120×C67—21no—
156C4×D4×C67—21no—
157C4×D4×C67—21no—
158C4×D4×C67—21no—
159C4×D4×C67—21no—
160C4×D4×C67—21no—
161C4×D4×C67—21no—
162C4×D4×C67—21no—
163C4×D4×C67—21no—
164#117×C67—21no—
165#117×C67D411yescharacteristic, complemented
166C2×C4⋊C4×C67—21no—
167C2×C4⋊C4×C67—21no—
168C2×C4⋊C4×C67D411yescharacteristic
169C2×C4⋊C4×C67D411yescharacteristic, complemented
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C4⋊C4×C67C2311yescharacteristic
172C2×C22⋊C4×C67—21no—
173C2×C22⋊C4×C67—21no—
174C2×C22⋊C4×C67—21no—
175C2×C22⋊C4×C67—21no—
176C2×C22⋊C4×C67—21no—
177C2×C22⋊C4×C67—21no—
178C2×C22⋊C4×C67—21no—
179C2×C22⋊C4×C67—21no—
180C2×C22⋊C4×C67—21no—
181C2×C22⋊C4×C67D411yescharacteristic
182C2×C22⋊C4×C67D411yescharacteristic
183C2×C22⋊C4×C67C2311yescharacteristic
184#107×C67—21no—
185#106×C67—21no—
186#106×C67—21no—
187#106×C67—21no—
188#103×C67—21no—
189#102×C67—21no—
190#102×C67—21no—
191#102×C67—21no—
192#102×C67—21no—
193#102×C67—21no—
194#102×C67—21no—
195#102×C67—21no—
196C22⋊C8×C67—21no—
197C22⋊C8×C67—21no—
198C22⋊C8×C67C2311yescharacteristic
199C22⋊C8×C67C2311yescharacteristic
200C22⋊C8×C67C2311yescharacteristic
201C22⋊C8×C67C2311yescharacteristic
202#95×C67—21no—
203#95×C67—21no—
204#95×C67C2311yescharacteristic
205#95×C67C2311yescharacteristic
206C24×C67—21no—
207C24×C67—21no—
208C24×C67—21no—
209C24×C67C2×D411yescharacteristic
210C24×C67C2×D411yescharacteristic
211#41×C67—81no—
212#41×C67—81no—
213#41×C67—81no—
214C2×Q8×C67—21no—
215C2×Q8×C67C2×D411yescharacteristic
216C2×D4×C67—21no—
217C2×D4×C67—21no—
218C2×D4×C67—21no—
219C2×D4×C67—21no—
220C2×D4×C67—21no—
221C2×D4×C67—21no—
222C2×D4×C67—21no—
223C2×D4×C67—21no—
224C2×D4×C67—21no—
225C2×D4×C67—21no—
226C2×D4×C67—21no—
227C2×D4×C67—21no—
228C2×D4×C67—21no—
229C2×D4×C67—21no—
230C2×D4×C67—21no—
231C2×D4×C67—21no—
232C2×D4×C67—21no—
233C2×D4×C67—21no—
234C2×D4×C67—21no—
235C2×D4×C67—41no—
236C2×D4×C67—41no—
237C2×D4×C67—81no—
238C2×D4×C67—81no—
239C2×D4×C67—81no—
240C2×D4×C67—81no—
241C2×D4×C67—81no—
242C2×D4×C67—81no—
243C2×D4×C67—81no—
244C2×D4×C67—81no—
245C2×D4×C67—81no—
246C2×D4×C67—81no—
247C2×D4×C67—81no—
248C2×D4×C67—81no—
249C2×D4×C67—82no—
250C2×D4×C67C2×D411yescharacteristic
251C2×D4×C67C2×D411yescharacteristic
252C2×D4×C67C2×D411yescharacteristic
253C22×C4×C67—21no—
254C22×C4×C67—21no—
255C22×C4×C67—21no—
256C22×C4×C67—21no—
257C22×C4×C67—21no—
258C22×C4×C67—21no—
259C22×C4×C67—21no—
260C22×C4×C67—21no—
261C22×C4×C67—21no—
262C22×C4×C67—21no—
263C22×C4×C67—81no—
264C22×C4×C67C2×D411yescharacteristic
265C22×C4×C67C2×D411yescharacteristic
266C22×C4×C67C2×D411yescharacteristic
267C22×C4×C67C2×D411yescharacteristic
268C22×C4×C67C2×D411yescharacteristic
269C22×C4×C67C2×D411yescharacteristic
270C22×C4×C67C2×D411yescharacteristic
271C22×C4×C67C2×D411yescharacteristic
272C22×C4×C67C2411yescharacteristic
273SD16×C67—81no—
274D8×C67—81no—
275D8×C67—81no—
276D8×C67—81no—
277M16×C67—81no—
278C2×C8×C67—21no—
279C2×C8×C67—21no—
280C2×C8×C67—21no—
281C2×C8×C67—21no—
282C2×C8×C67—81no—
283C4⋊C4×C67—21no—
284C4⋊C4×C67—21no—
285C4⋊C4×C67—21no—
286C4⋊C4×C67—21no—
287C4⋊C4×C67—21no—
288C4⋊C4×C67—21no—
289C4⋊C4×C67—21no—
290C4⋊C4×C67—21no—
291C4⋊C4×C67—21no—
292C4⋊C4×C67—21no—
293C4⋊C4×C67—21no—
294C4⋊C4×C67—21no—
295C4⋊C4×C67—21no—
296C4⋊C4×C67—21no—
297C4⋊C4×C67—21no—
298C4⋊C4×C67—81no—
299C4⋊C4×C67—81no—
300C4⋊C4×C67C2×D411yescharacteristic
301C4⋊C4×C67C2×D411yescharacteristic
302C4⋊C4×C67C2×D411yescharacteristic
303C4⋊C4×C67C2×D411yescharacteristic
304C22⋊C4×C67—21no—
305C22⋊C4×C67—21no—
306C22⋊C4×C67—21no—
307C22⋊C4×C67—21no—
308C22⋊C4×C67—21no—
309C22⋊C4×C67—21no—
310C22⋊C4×C67—21no—
311C22⋊C4×C67—21no—
312C22⋊C4×C67—21no—
313C22⋊C4×C67—21no—
314C22⋊C4×C67—21no—
315C22⋊C4×C67—21no—
316C22⋊C4×C67—21no—
317C22⋊C4×C67—21no—
318C22⋊C4×C67—21no—
319C22⋊C4×C67—21no—
320C22⋊C4×C67—21no—
321C22⋊C4×C67—21no—
322C22⋊C4×C67—21no—
323C22⋊C4×C67—21no—
324C22⋊C4×C67—21no—
325C22⋊C4×C67—21no—
326C22⋊C4×C67—21no—
327C22⋊C4×C67—21no—
328C22⋊C4×C67—21no—
329C22⋊C4×C67—41no—
330C22⋊C4×C67—41no—
331C22⋊C4×C67—81no—
332C22⋊C4×C67—81no—
333C22⋊C4×C67—81no—
334C22⋊C4×C67—81no—
335C22⋊C4×C67—81no—
336C42×C67—21no—
337C42×C67—21no—
338C42×C67—21no—
339C23×C67—21no—
340C23×C67—21no—
341C23×C67—21no—
342C23×C67—21no—
343C23×C67—21no—
344C23×C67—21no—
345C23×C67—21no—
346C23×C67—21no—
347C23×C67—41no—
348C23×C67—41no—
349C23×C67—42no—
350C23×C67—41no—
351C23×C67—41no—
352C23×C67—41no—
353C23×C67—41no—
354C23×C67—41no—
355C23×C67—41no—
356C23×C67—41no—
357C23×C67—41no—
358C23×C67—41no—
359C23×C67—81no—
360C23×C67—81no—
361C23×C67—81no—
362C23×C67—81no—
363C23×C67—81no—
364C23×C67#12011yescharacteristic
365C23×C67#12011yescharacteristic
366C23×C67C22×D411yescharacteristic
367Q8×C67—41no—
368Q8×C67—81no—
369D4×C67—41no—
370D4×C67—41no—
371D4×C67—41no—
372D4×C67—41no—
373D4×C67—41no—
374D4×C67—41no—
375D4×C67—41no—
376D4×C67—42no—
377D4×C67—42no—
378D4×C67—41no—
379D4×C67—41no—
380D4×C67—41no—
381D4×C67—41no—
382D4×C67—41no—
383D4×C67—41no—
384D4×C67—81no—
385D4×C67—81no—
386D4×C67—81no—
387D4×C67—81no—
388D4×C67—81no—
389D4×C67—81no—
390D4×C67—81no—
391D4×C67—81no—
392D4×C67—81no—
393D4×C67—81no—
394D4×C67—81no—
395D4×C67—81no—
396D4×C67—82no—
397D4×C67—82no—
398D4×C67—84no—
399C2×C4×C67—21no—
400C2×C4×C67—21no—
401C2×C4×C67—21no—
402C2×C4×C67—21no—
403C2×C4×C67—21no—
404C2×C4×C67—21no—
405C2×C4×C67—21no—
406C2×C4×C67—21no—
407C2×C4×C67—21no—
408C2×C4×C67—21no—
409C2×C4×C67—41no—
410C2×C4×C67—41no—
411C2×C4×C67—41no—
412C2×C4×C67—41no—
413C2×C4×C67—41no—
414C2×C4×C67—41no—
415C2×C4×C67—41no—
416C2×C4×C67—41no—
417C2×C4×C67—41no—
418C2×C4×C67—41no—
419C2×C4×C67—41no—
420C2×C4×C67—41no—
421C2×C4×C67—41no—
422C2×C4×C67—41no—
423C2×C4×C67—41no—
424C2×C4×C67—41no—
425C2×C4×C67—41no—
426C2×C4×C67—81no—
427C2×C4×C67—81no—
428C2×C4×C67—81no—
429C2×C4×C67—81no—
430C2×C4×C67—81no—
431C2×C4×C67—81no—
432C2×C4×C67—81no—
433C2×C4×C67#12011yescharacteristic
434C2×C4×C67#12011yescharacteristic
435C2×C4×C67C22×D411yescharacteristic
436C2×C4×C67C22×D411yescharacteristic
437C8×C67—41no—
438C8×C67—41no—
439C8×C67—41no—
440C8×C67—41no—
441C22×C67—21no—
442C22×C67—21no—
443C22×C67—21no—
444C22×C67—21no—
445C22×C67—21no—
446C22×C67—21no—
447C22×C67—21no—
448C22×C67—21no—
449C22×C67—41no—
450C22×C67—41no—
451C22×C67—41no—
452C22×C67—41no—
453C22×C67—41no—
454C22×C67—41no—
455C22×C67—41no—
456C22×C67—41no—
457C22×C67—41no—
458C22×C67—41no—
459C22×C67—41no—
460C22×C67—41no—
461C22×C67—81no—
462C22×C67—81no—
463C22×C67—81no—
464C22×C67—81no—
465C22×C67—81no—
466C22×C67—81no—
467C22×C67—81no—
468C22×C67—81no—
469C22×C67—81no—
470C22×C67—81no—
471C22×C67—81no—
472C22×C67—162no—
473C22×C67—162no—
474C22×C67C2×#12011yescharacteristic
475C22×C67#57611yescharacteristic
476C22×C67#57711yescharacteristic
477C4×C67—21no—
478C4×C67—21no—
479C4×C67—21no—
480C4×C67—21no—
481C4×C67—41no—
482C4×C67—41no—
483C4×C67—41no—
484C4×C67—41no—
485C4×C67—41no—
486C4×C67—41no—
487C4×C67—41no—
488C4×C67—41no—
489C4×C67—81no—
490C4×C67—81no—
491C4×C67—81no—
492#18446C6711yesmaximal, characteristic, direct product factor, Sylow
493C2×C67—21no—
494C2×C67—21no—
495C2×C67—41no—
496C2×C67—41no—
497C2×C67—81no—
498C2×C67—81no—
499C2×C67—81no—
500C2×C67—81no—
501C2×C67—161no—
502C2×C67#301211yescharacteristic
503C2×C67#302111yescharacteristic
504C2×C67#302611yescharacteristic
505#3534C2×C6711yescharacteristic, complemented
506#3192C2×C6711yescharacteristic, complemented
507#3188C2×C6711yescharacteristic, complemented
508#2813C2×C6711yescharacteristic, complemented
509#1618C2×C6711yescharacteristic, complemented
510#1616C2×C6711yescharacteristic, complemented
511#1615C2×C6711yescharacteristic, complemented
512#1613C2×C6711yescharacteristic, complemented
513#1600C2×C6711yescharacteristic, complemented
514#1598C2×C6711yescharacteristic, complemented
515#1597C2×C6711yescharacteristic, complemented
516#1595C2×C6711yescharacteristic, complemented
517#1519C2×C6711yescharacteristic, complemented
518#1513C2×C6711yescharacteristic, complemented
519#1468C2×C6711yescharacteristic, complemented
520C67#1844611yescharacteristic, direct product factor, Sylow
521#562—21no—
522#560—21no—
523#553—21no—
524#551—21no—
525#546—21no—
526#546—21no—
527#546—21no—
528D42—21no—
529#540—21no—
530#539—21no—
531#539C22×C6711yescharacteristic
532#538—21no—
533#538C22×C6711yescharacteristic
534#537C22×C6711yescharacteristic
535#534—21no—
536#534C22×C6711yescharacteristic
537#525C22×C6711yescharacteristic
538C2×#123C22×C6711yescharacteristic
539C2×#121C22×C6711yescharacteristic
540C2×#121C22×C6711yescharacteristic, complemented
541#484C22×C6711yescharacteristic, complemented
542#482—21no—
543#481—21no—
544#481C22×C6711yescharacteristic
545#481C22×C6711yescharacteristic, complemented
546#481C22×C6711yescharacteristic, complemented
547#469—21no—
548#469—21no—
549#466—21no—
550#465—21no—
551#450C22×C6711yescharacteristic, complemented
552#449—21no—
553#447—21no—
554#447C22×C6711yescharacteristic
555#447C22×C6711yescharacteristic, complemented
556#447C22×C6711yescharacteristic, complemented
557#407C22×C6711yescharacteristic, complemented
558C2×C22⋊C8C22×C6711yescharacteristic, complemented
559#400C22×C6711yescharacteristic, complemented
560#399C22×C6711yescharacteristic, complemented
561#396—21no—
562#394—21no—
563#394—21no—
564#394C22×C6711yescharacteristic, complemented
565#392—21no—
566#392C22×C6711yescharacteristic, complemented
567#380C22×C6711yescharacteristic, complemented
568#328C22×C6711yescharacteristic, complemented
569#328C22×C6711yescharacteristic, complemented
570#327C22×C6711yescharacteristic
571#327C22×C6711yescharacteristic
572#327C22×C6711yescharacteristic, complemented
573#327C22×C6711yescharacteristic, complemented
574#327C22×C6711yescharacteristic, complemented
575#327C22×C6711yescharacteristic, complemented
576#324C22×C6711yescharacteristic, complemented
577#324C22×C6711yescharacteristic, complemented
578#323C22×C6711yescharacteristic, complemented
579#323C22×C6711yescharacteristic, complemented
580C2×#41—21no—
581C2×#41D4×C6711yescharacteristic, complemented
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4D4×C6711yescharacteristic
588C22×D4D4×C6711yescharacteristic, complemented
589C22×D4C23×C6711yescharacteristic
590C23×C4C23×C6711yescharacteristic
591C2×SD16—21no—
592C2×D8—21no—
593C2×D8—21no—
594C2×D8—21no—
595C2×M16—21no—
596C22×C8—21no—
597#127—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#123—21no—
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620#123—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8D4×C6711yescharacteristic, complemented
627C22⋊Q8C23×C6711yescharacteristic
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121D4×C6711yescharacteristic, complemented
648#121D4×C6711yescharacteristic, complemented
649#121D4×C6711yescharacteristic, complemented
650#121C23×C6711yescharacteristic
651#121C23×C6711yescharacteristic
652#121C23×C6711yescharacteristic
653#120—21no—
654#120—21no—
655#120—21no—
656#120—21no—
657#120—21no—
658#120—21no—
659#120—21no—
660#120—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669#117—21no—
670#117D4×C6711yescharacteristic, complemented
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4D4×C6711yescharacteristic
674C2×C4⋊C4D4×C6711yescharacteristic, complemented
675C2×C4⋊C4C23×C6711yescharacteristic
676C2×C4⋊C4C23×C6711yescharacteristic
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4D4×C6711yescharacteristic
687C2×C22⋊C4D4×C6711yescharacteristic
688C2×C22⋊C4C23×C6711yescharacteristic
689#107—21no—
690#106—21no—
691#106—21no—
692#106—21no—
693#103—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700#102—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8C23×C6711yescharacteristic
704C22⋊C8C23×C6711yescharacteristic
705C22⋊C8C23×C6711yescharacteristic
706C22⋊C8C23×C6711yescharacteristic
707#95—21no—
708#95—21no—
709#95C23×C6711yescharacteristic
710#95C23×C6711yescharacteristic
711C24—21no—
712C24—21no—
713C24—21no—
714C24C2×D4×C6711yescharacteristic
715C24C2×D4×C6711yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C2×D4×C6711yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—41no—
741C2×D4—41no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—82no—
755C2×D4C2×D4×C6711yescharacteristic
756C2×D4C2×D4×C6711yescharacteristic
757C2×D4C2×D4×C6711yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—81no—
769C22×C4C2×D4×C6711yescharacteristic
770C22×C4C2×D4×C6711yescharacteristic
771C22×C4C2×D4×C6711yescharacteristic
772C22×C4C2×D4×C6711yescharacteristic
773C22×C4C2×D4×C6711yescharacteristic
774C22×C4C2×D4×C6711yescharacteristic
775C22×C4C2×D4×C6711yescharacteristic
776C22×C4C2×D4×C6711yescharacteristic
777C22×C4C24×C6711yescharacteristic
778SD16—81no—
779D8—81no—
780D8—81no—
781D8—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—81no—
804C4⋊C4—81no—
805C4⋊C4C2×D4×C6711yescharacteristic
806C4⋊C4C2×D4×C6711yescharacteristic
807C4⋊C4C2×D4×C6711yescharacteristic
808C4⋊C4C2×D4×C6711yescharacteristic
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—21no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—81no—
837C22⋊C4—81no—
838C22⋊C4—81no—
839C22⋊C4—81no—
840C22⋊C4—81no—
841C42—21no—
842C42—21no—
843C42—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23#120×C6711yescharacteristic
870C23#120×C6711yescharacteristic
871C23C22×D4×C6711yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—81no—
901D4—82no—
902D4—82no—
903D4—84no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4#120×C6711yescharacteristic
939C2×C4#120×C6711yescharacteristic
940C2×C4C22×D4×C6711yescharacteristic
941C2×C4C22×D4×C6711yescharacteristic
942C8—41no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×#120×C6711yescharacteristic
980C22#576×C6711yescharacteristic
981C22#577×C6711yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—41no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—81no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2C67×#301211yescharacteristic
1007C2C67×#302111yescharacteristic
1008C2C67×#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×#3534C2semidirect
2. C67×#3192C2semidirect
3. C67×#3188C2semidirect
4. C67×#2813C2semidirect
5. C67×#1618C2semidirect
6. C67×#1616C2semidirect
7. C67×#1615C2semidirect
8. C67×#1613C2semidirect
9. C67×#1600C2semidirect
10. C67×#1598C2semidirect
11. C67×#1597C2semidirect
12. C67×#1595C2semidirect
13. C67×#1519C2semidirect
14. C67×#1513C2semidirect
15. C67×#1468C2semidirect
35. C2×#121×C67C22semidirect
36. #484×C67C22semidirect
40. #481×C67C22semidirect
41. #481×C67C22semidirect
46. #450×C67C22semidirect
50. #447×C67C22semidirect
51. #447×C67C22semidirect
52. #407×C67C22semidirect
53. C2×C22⋊C8×C67C22semidirect
54. #400×C67C22semidirect
55. #399×C67C22semidirect
59. #394×C67C22semidirect
61. #392×C67C22semidirect
62. #380×C67C22semidirect
63. #328×C67C22semidirect
64. #328×C67C22semidirect
67. #327×C67C22semidirect
68. #327×C67C22semidirect
69. #327×C67C22semidirect
70. #327×C67C22semidirect
71. #324×C67C22semidirect
72. #324×C67C22semidirect
73. #323×C67C22semidirect
74. #323×C67C22semidirect
76. C2×#41×C67D4semidirect
83. C22×D4×C67D4semidirect
121. C22⋊Q8×C67D4semidirect
142. #121×C67D4semidirect
143. #121×C67D4semidirect
144. #121×C67D4semidirect
165. #117×C67D4semidirect
169. C2×C4⋊C4×C67D4semidirect
492. #18446C67direct (N × H)
505. #3534C2×C67semidirect
506. #3192C2×C67semidirect
507. #3188C2×C67semidirect
508. #2813C2×C67semidirect
509. #1618C2×C67semidirect
510. #1616C2×C67semidirect
511. #1615C2×C67semidirect
512. #1613C2×C67semidirect
513. #1600C2×C67semidirect
514. #1598C2×C67semidirect
515. #1597C2×C67semidirect
516. #1595C2×C67semidirect
517. #1519C2×C67semidirect
518. #1513C2×C67semidirect
519. #1468C2×C67semidirect
520. C67#18446direct (N × H)
540. C2×#121C22×C67semidirect
541. #484C22×C67semidirect
545. #481C22×C67semidirect
546. #481C22×C67semidirect
551. #450C22×C67semidirect
555. #447C22×C67semidirect
556. #447C22×C67semidirect
557. #407C22×C67semidirect
558. C2×C22⋊C8C22×C67semidirect
559. #400C22×C67semidirect
560. #399C22×C67semidirect
564. #394C22×C67semidirect
566. #392C22×C67semidirect
567. #380C22×C67semidirect
568. #328C22×C67semidirect
569. #328C22×C67semidirect
572. #327C22×C67semidirect
573. #327C22×C67semidirect
574. #327C22×C67semidirect
575. #327C22×C67semidirect
576. #324C22×C67semidirect
577. #324C22×C67semidirect
578. #323C22×C67semidirect
579. #323C22×C67semidirect
581. C2×#41D4×C67semidirect
588. C22×D4D4×C67semidirect
626. C22⋊Q8D4×C67semidirect
647. #121D4×C67semidirect
648. #121D4×C67semidirect
649. #121D4×C67semidirect
670. #117D4×C67semidirect
674. 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×#35342
C67×#31922
C67×#31882
C67×#28132
C67×#16182
C67×#16162
C67×#16152
C67×#16132
C67×#16002
C67×#15982
C67×#15972
C67×#15952
C67×#15192
C67×#15132
C67×#14682
#1844667