Finite Group Databasebeta

← C2×#22564596 #31024801

Subgroups — C2×#22564596 #31024801

Order 17152.

2398 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22564596C2116yesmaximal, direct product factor
2C2×C67⋊#401C211yesmaximal, characteristic, complemented
3C2×#16863338C211yesmaximal, characteristic, complemented
4C2×#16863335C211yesmaximal, characteristic, complemented
5C2×#16863334C211yesmaximal, characteristic, complemented
6C2×#16863282C211yesmaximal, characteristic, complemented
7C2×#16863279C211yesmaximal, characteristic, complemented
8C2×#16863277C211yesmaximal, characteristic, complemented
9C2×#16863271C211yesmaximal, characteristic
10C2×#16863263C211yesmaximal, characteristic, complemented
11C2×#16863257C211yesmaximal, characteristic
12C2×#16863257C211yesmaximal, characteristic
13C2×#16863254C211yesmaximal, characteristic
14C2×C4×C22⋊Dic67C211yesmaximal, characteristic
15C22×C67⋊#95C211yesmaximal, characteristic
16C2×#385×C67C211yesmaximal, characteristic
17C24×Dic67C2211yescharacteristic
18C24×Dic67C2211yescharacteristic
19C22×C4⋊Dic67C2211yescharacteristic
20C22×C4⋊Dic67C2211yescharacteristic
21C22×Dic67⋊C4C2211yescharacteristic
22C22×Dic67⋊C4C2211yescharacteristic
23C22×C22⋊Dic67C2211yescharacteristic
24C22×C22⋊Dic67C2211yescharacteristic
25C22×C4×Dic67C2211yescharacteristic
26C22×C4×Dic67C2211yescharacteristic
27C67⋊#401C2218yescomplemented
28#16863338C2218yescomplemented
29#16863335C2218yescomplemented
30#16863334C2218yescomplemented
31#16863282C2218yescomplemented
32#16863279C2218yescomplemented
33#16863277C2218yescomplemented
34#16863271C2218yes—
35#16863263C2218yescomplemented
36#16863257C2218yes—
37#16863257C2218yes—
38#16863254C2218yes—
39C4×C22⋊Dic67C2218yes—
40C2×C67⋊#95C2211yescharacteristic
41C2×C67⋊#95C2211yescharacteristic
42C2×C67⋊#95C2211yescharacteristic
43C2×C67⋊#95C2211yescharacteristic
44C2×C67⋊#95C2211yescharacteristic
45C2×C67⋊#95C2211yescharacteristic
46C2×C67⋊#95C2211yescharacteristic
47C2×C67⋊#95C2211yescharacteristic
48C2×C67⋊#95C2211yescharacteristic
49C2×C67⋊#95C2211yescharacteristic
50C2×C67⋊#95C2211yescharacteristic
51C2×C67⋊#95C2211yescharacteristic
52C2×C67⋊#95C2211yescharacteristic
53C2×C67⋊#95C2211yescharacteristic
54C2×C67⋊#95C2211yescharacteristic
55C2×C67⋊#95C2211yescharacteristic
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2218yes—
59C24×C4×C67C2211yescharacteristic
60C22×C4⋊C4×C67C2211yescharacteristic
61C22×C4⋊C4×C67C2211yescharacteristic
62C22×C22⋊C4×C67C2211yescharacteristic
63C22×C22⋊C4×C67C2211yescharacteristic
64#385×C67C2218yes—
65C2×#95×C67C2211yescharacteristic
66C2×#95×C67C2211yescharacteristic
67C23×Dic67—24no—
68C23×Dic67—24no—
69C23×Dic67—24no—
70C23×Dic67—24no—
71C23×Dic67—24no—
72C23×Dic67—42no—
73C23×Dic67C2311yescharacteristic
74C23×Dic67C2311yescharacteristic
75C23×Dic67C2311yescharacteristic
76C23×Dic67C2311yescharacteristic
77C23×Dic67C2311yescharacteristic
78C23×Dic67C2311yescharacteristic
79C23×Dic67C2311yescharacteristic
80C23×Dic67C2314yes—
81C23×Dic67C2314yes—
82C23×Dic67C2311yescharacteristic
83C2×C4⋊Dic67—24no—
84C2×C4⋊Dic67—42no—
85C2×C4⋊Dic67C2314yes—
86C2×C4⋊Dic67C2314yes—
87C2×Dic67⋊C4—24no—
88C2×Dic67⋊C4—42no—
89C2×Dic67⋊C4C2314yes—
90C2×Dic67⋊C4C2314yes—
91C2×C22⋊Dic67—24no—
92C2×C22⋊Dic67—24no—
93C2×C22⋊Dic67C2314yes—
94C2×C22⋊Dic67C2314yes—
95C2×C4×Dic67—24no—
96C2×C4×Dic67—42no—
97C2×C4×Dic67C2314yes—
98C2×C4×Dic67C2314yes—
99C67⋊#95C2314yes—
100C67⋊#95C2314yes—
101C67⋊#95C2314yes—
102C67⋊#95C2314yes—
103C67⋊#95C2314yes—
104C67⋊#95C2314yes—
105C67⋊#95C2314yes—
106C67⋊#95C2314yes—
107C67⋊#95C2314yes—
108C67⋊#95C2314yes—
109C67⋊#95C2314yes—
110C67⋊#95C2314yes—
111C67⋊#95C2314yes—
112C67⋊#95C2314yes—
113C67⋊#95C2314yes—
114C67⋊#95C2314yes—
115C67⋊#95C2314yes—
116C67⋊#95C2314yes—
117C25×C67C2311yescharacteristic
118C23×C4×C67—24no—
119C23×C4×C67—24no—
120C23×C4×C67—42no—
121C23×C4×C67C2311yescharacteristic
122C23×C4×C67C2311yescharacteristic
123C23×C4×C67C2311yescharacteristic
124C23×C4×C67C2311yescharacteristic
125C23×C4×C67C2311yescharacteristic
126C23×C4×C67C2314yes—
127C23×C4×C67C2311yescharacteristic
128C2×C4⋊C4×C67—24no—
129C2×C4⋊C4×C67—42no—
130C2×C4⋊C4×C67C2314yes—
131C2×C4⋊C4×C67C2314yes—
132C2×C22⋊C4×C67—24no—
133C2×C22⋊C4×C67—24no—
134C2×C22⋊C4×C67C2314yes—
135C2×C22⋊C4×C67C2314yes—
136#95×C67C2314yes—
137#95×C67C2314yes—
138C22×Dic67—22no—
139C22×Dic67—22no—
140C22×Dic67—22no—
141C22×Dic67—22no—
142C22×Dic67—22no—
143C22×Dic67—22no—
144C22×Dic67—22no—
145C22×Dic67—22no—
146C22×Dic67—22no—
147C22×Dic67—22no—
148C22×Dic67—22no—
149C22×Dic67—28no—
150C22×Dic67—22no—
151C22×Dic67—22no—
152C22×Dic67—28no—
153C22×Dic67—22no—
154C22×Dic67—22no—
155C22×Dic67—28no—
156C22×Dic67—28no—
157C22×Dic67—22no—
158C22×Dic67—22no—
159C22×Dic67—22no—
160C22×Dic67—22no—
161C22×Dic67—22no—
162C22×Dic67—22no—
163C22×Dic67—22no—
164C22×Dic67—22no—
165C22×Dic67—28no—
166C22×Dic67—44no—
167C22×Dic67—416no—
168C22×Dic67—416no—
169C22×Dic67#4114yes—
170C22×Dic67C2412yes—
171C22×Dic67C2412yes—
172C22×Dic67C2412yes—
173C22×Dic67C2412yes—
174C22×Dic67C2412yes—
175C22×Dic67C2412yes—
176C22×Dic67C2412yes—
177C22×Dic67C2412yes—
178C4⋊Dic67—28no—
179C4⋊Dic67—44no—
180Dic67⋊C4—28no—
181Dic67⋊C4—44no—
182C22⋊Dic67—28no—
183C22⋊Dic67—28no—
184C4×Dic67—28no—
185C4×Dic67—44no—
186C24×C67—22no—
187C24×C67—22no—
188C24×C67—22no—
189C24×C67—22no—
190C24×C67#4114yes—
191C24×C67#4114yes—
192C24×C67#4114yes—
193C24×C67C2412yes—
194C24×C67C2411yescharacteristic
195C22×C4×C67—22no—
196C22×C4×C67—22no—
197C22×C4×C67—22no—
198C22×C4×C67—22no—
199C22×C4×C67—22no—
200C22×C4×C67—22no—
201C22×C4×C67—22no—
202C22×C4×C67—22no—
203C22×C4×C67—28no—
204C22×C4×C67—22no—
205C22×C4×C67—22no—
206C22×C4×C67—22no—
207C22×C4×C67—22no—
208C22×C4×C67—22no—
209C22×C4×C67—22no—
210C22×C4×C67—22no—
211C22×C4×C67—22no—
212C22×C4×C67—22no—
213C22×C4×C67—28no—
214C22×C4×C67—44no—
215C22×C4×C67—416no—
216C22×C4×C67#4114yes—
217C22×C4×C67C2412yes—
218C22×C4×C67C2412yes—
219C22×C4×C67C2412yes—
220C22×C4×C67C2412yes—
221C22×C4×C67C2412yes—
222C22×C4×C67C2412yes—
223C4⋊C4×C67—28no—
224C4⋊C4×C67—44no—
225C22⋊C4×C67—28no—
226C22⋊C4×C67—28no—
227C23×C67—28no—
228C23×C67—28no—
229C23×C67—28no—
230C23×C67—28no—
231C23×C67—28no—
232C23×C67—28no—
233C23×C67—22no—
234C23×C67—22no—
235C23×C67—22no—
236C23×C67—22no—
237C23×C67#126116yes—
238C23×C67C2×#4112yes—
239C23×C67C2×#4114yes—
240C23×C67C2×#4112yes—
241C23×C67C2×#4112yes—
242C23×C67C2×#4114yes—
243C23×C67C2×#4112yes—
244C23×C67C2×#4114yes—
245C23×C67C2×#4112yes—
246C23×C67H(5,𝔽2)12yes—
247C23×C672−1+412yes—
248C23×C67C2511yescharacteristic
249C2×C4×C67—28no—
250C2×C4×C67—22no—
251C2×C4×C67—22no—
252C2×C4×C67—22no—
253C2×C4×C67—22no—
254C2×C4×C67—22no—
255C2×C4×C67—22no—
256C2×C4×C67—22no—
257C2×C4×C67—22no—
258C2×C4×C67—22no—
259C2×C4×C67—22no—
260C2×C4×C67—22no—
261C2×C4×C67—22no—
262C2×C4×C67—22no—
263C2×C4×C67—22no—
264C2×C4×C67—22no—
265C2×C4×C67—22no—
266C2×C4×C67—22no—
267C2×C4×C67—416no—
268C2×C4×C67—44no—
269C2×C4×C67—44no—
270C2×C4×C67—44no—
271C2×C4×C67—44no—
272C2×C4×C67—44no—
273C2×C4×C67C2×#4114yes—
274C2×Dic67—28no—
275C2×Dic67—22no—
276C2×Dic67—22no—
277C2×Dic67—22no—
278C2×Dic67—22no—
279C2×Dic67—22no—
280C2×Dic67—22no—
281C2×Dic67—22no—
282C2×Dic67—22no—
283C2×Dic67—22no—
284C2×Dic67—22no—
285C2×Dic67—22no—
286C2×Dic67—22no—
287C2×Dic67—22no—
288C2×Dic67—22no—
289C2×Dic67—22no—
290C2×Dic67—22no—
291C2×Dic67—22no—
292C2×Dic67—22no—
293C2×Dic67—22no—
294C2×Dic67—22no—
295C2×Dic67—22no—
296C2×Dic67—22no—
297C2×Dic67—22no—
298C2×Dic67—416no—
299C2×Dic67—416no—
300C2×Dic67—44no—
301C2×Dic67—44no—
302C2×Dic67—44no—
303C2×Dic67—44no—
304C2×Dic67—44no—
305C2×Dic67—44no—
306C2×Dic67—44no—
307C2×Dic67C2×#4114yes—
308C22×C67—24no—
309C22×C67—24no—
310C22×C67—24no—
311C22×C67—24no—
312C22×C67—24no—
313C22×C67—24no—
314C22×C67—232no—
315C22×C67C2×#12618yes—
316C22×C67C2×#12614yes—
317C22×C67#52914yes—
318C22×C67#53914yes—
319C22×C67#55114yes—
320C22×C67#55114yes—
321C22×C67#55214yes—
322C22×C67#55214yes—
323C22×C67C22×#4111yescharacteristic
324C22×C67C22×#4111yescharacteristic
325C22×C67C22×#4111yescharacteristic
326C22×C67C22×#4111yescharacteristic
327C22×C67C22×#4111yescharacteristic
328C22×C67C2×H(5,𝔽2)11yescharacteristic
329C22×C67C2×2−1+411yescharacteristic
330C4×C67—24no—
331C4×C67—42no—
332C4×C67—42no—
333C4×C67—42no—
334C4×C67—42no—
335C4×C67—42no—
336Dic67—24no—
337Dic67—42no—
338Dic67—42no—
339Dic67—42no—
340Dic67—42no—
341Dic67—42no—
342Dic67—42no—
343Dic67—42no—
344C2×#2493—671nomaximal, Sylow
345C2×C67—28no—
346C2×C67#249318yescomplemented
347C2×C67C22×#12611yescharacteristic
348C2×C67C2×#52911yescharacteristic
349C2×C67C2×#53911yescharacteristic
350C2×C67C2×#55111yescharacteristic
351C2×C67C2×#55111yescharacteristic
352C2×C67C2×#55211yescharacteristic
353C2×C67C2×#55211yescharacteristic
354#2493—6716no—
355C2×#401—671no—
356C2×#400—671no—
357C2×#400—671no—
358C2×#400—671no—
359C2×#387—671no—
360C2×#387—671no—
361C2×#387—671no—
362C2×#385—671no—
363C2×#385D6711yescharacteristic
364C2×#383—671no—
365C2×#381—671no—
366C2×#381—671no—
367C2×#380—671no—
368C2×C4×C22⋊C4—671no—
369C22×#95—671no—
370C67C2×#249311yescharacteristic, complemented, Sylow
371C24×C4—671no—
372C24×C4—671no—
373C24×C4C2×D6711yescharacteristic
374C22×C4⋊C4—671no—
375C22×C4⋊C4—671no—
376C22×C4⋊C4—671no—
377C22×C4⋊C4—671no—
378C22×C4⋊C4C2×D6711yescharacteristic
379C22×C4⋊C4C2×D6711yescharacteristic
380C22×C22⋊C4—671no—
381C22×C22⋊C4—671no—
382C22×C22⋊C4C2×D6711yescharacteristic
383C22×C22⋊C4C2×D6711yescharacteristic
384C22×C42—671no—
385C22×C42—671no—
386#401—678no—
387#400—678no—
388#400—678no—
389#400—678no—
390#387—678no—
391#387—678no—
392#387—678no—
393#385—678no—
394#385C2×D6718yes—
395#383—678no—
396#381—678no—
397#381—678no—
398#380—678no—
399C4×C22⋊C4—678no—
400C2×#95—671no—
401C2×#95—671no—
402C2×#95—671no—
403C2×#95—671no—
404C2×#95—671no—
405C2×#95—671no—
406C2×#95—671no—
407C2×#95—671no—
408C2×#95—671no—
409C2×#95—671no—
410C2×#95—671no—
411C2×#95—671no—
412C2×#95—671no—
413C2×#95—671no—
414C2×#95—671no—
415C2×#95—671no—
416C2×#95—678no—
417C2×#95—671no—
418C2×#95—671no—
419C2×#95C2×D6711yescharacteristic
420C2×#95C2×D6711yescharacteristic
421C25C22×D6711yescharacteristic
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—42no—
425C23×C4—2682no—
426C23×C4—674no—
427C23×C4—671no—
428C23×C4—674no—
429C23×C4—671no—
430C23×C4—671no—
431C23×C4—671no—
432C23×C4—671no—
433C23×C4—671no—
434C23×C4—671no—
435C23×C4—671no—
436C23×C4—1344no—
437C23×C4—1344no—
438C23×C4—1344no—
439C23×C4—1344no—
440C23×C4—1344no—
441C23×C4C22×D6711yescharacteristic
442C23×C4C22×D6711yescharacteristic
443C23×C4C22×D6711yescharacteristic
444C23×C4C22×D6711yescharacteristic
445C23×C4C22×D6711yescharacteristic
446C23×C4C22×D6714yes—
447C23×C4C22×D6711yescharacteristic
448C2×C4⋊C4—24no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—2682no—
451C2×C4⋊C4—2682no—
452C2×C4⋊C4—674no—
453C2×C4⋊C4—674no—
454C2×C4⋊C4—674no—
455C2×C4⋊C4—674no—
456C2×C4⋊C4—1344no—
457C2×C4⋊C4—1344no—
458C2×C4⋊C4C22×D6714yes—
459C2×C4⋊C4C22×D6714yes—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—674no—
463C2×C22⋊C4—674no—
464C2×C22⋊C4—1344no—
465C2×C22⋊C4—1344no—
466C2×C22⋊C4C22×D6714yes—
467C2×C22⋊C4C22×D6714yes—
468C2×C42—2682no—
469C2×C42—674no—
470C2×C42—674no—
471C2×C42—1344no—
472#95—674no—
473#95—674no—
474#95—674no—
475#95—674no—
476#95—674no—
477#95—674no—
478#95—674no—
479#95—674no—
480#95—674no—
481#95—674no—
482#95—674no—
483#95—674no—
484#95—674no—
485#95—674no—
486#95—674no—
487#95—674no—
488#95—674no—
489#95—674no—
490#95C22×D6714yes—
491#95C22×D6714yes—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24#1176162714yes—
497C24#1176162814yes—
498C24#1176162914yes—
499C24C23×D6712yes—
500C24C23×D6711yescharacteristic
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—28no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—28no—
520C22×C4—44no—
521C22×C4—416no—
522C22×C4—26816no—
523C22×C4—26816no—
524C22×C4—2684no—
525C22×C4—674no—
526C22×C4—672no—
527C22×C4—672no—
528C22×C4—672no—
529C22×C4—672no—
530C22×C4—672no—
531C22×C4—672no—
532C22×C4—672no—
533C22×C4—672no—
534C22×C4—1348no—
535C22×C4—1342no—
536C22×C4—1342no—
537C22×C4—1342no—
538C22×C4—1342no—
539C22×C4—1342no—
540C22×C4—1348no—
541C22×C4—1342no—
542C22×C4—1342no—
543C22×C4—1342no—
544C22×C4—1342no—
545C22×C4—1348no—
546C22×C4—1342no—
547C22×C4—1342no—
548C22×C4—1342no—
549C22×C4—1342no—
550C22×C4—1342no—
551C22×C4—1348no—
552C22×C4—1342no—
553C22×C4—1342no—
554C22×C4—1348no—
555C22×C4—1342no—
556C22×C4—1342no—
557C22×C4—1342no—
558C22×C4—1342no—
559C22×C4—1342no—
560C22×C4—1342no—
561C22×C4—1342no—
562C22×C4#1176162714yes—
563C22×C4C23×D6712yes—
564C22×C4C23×D6712yes—
565C22×C4C23×D6712yes—
566C22×C4C23×D6712yes—
567C22×C4C23×D6712yes—
568C22×C4C23×D6712yes—
569C4⋊C4—28no—
570C4⋊C4—44no—
571C4⋊C4—2684no—
572C4⋊C4—2684no—
573C4⋊C4—1348no—
574C4⋊C4—1348no—
575C22⋊C4—28no—
576C22⋊C4—28no—
577C22⋊C4—1348no—
578C22⋊C4—1348no—
579C42—2684no—
580C42—1348no—
581C23—28no—
582C23—28no—
583C23—28no—
584C23—28no—
585C23—28no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—28no—
591C23#14524038116yes—
592C23#41×D6712yes—
593C23C2×#1176162714yes—
594C23C2×#1176162712yes—
595C23C2×#1176162712yes—
596C23C2×#1176162814yes—
597C23C2×#1176162812yes—
598C23C2×#1176162914yes—
599C23C2×#1176162912yes—
600C23#1452408812yes—
601C23#1452409012yes—
602C23C24×D6711yescharacteristic
603C2×C4—28no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—416no—
622C2×C4—44no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—44no—
626C2×C4—44no—
627C2×C4—2684no—
628C2×C4—2684no—
629C2×C4—2684no—
630C2×C4—26816no—
631C2×C4—2684no—
632C2×C4—2684no—
633C2×C4—2684no—
634C2×C4—2684no—
635C2×C4—26816no—
636C2×C4—674no—
637C2×C4—1342no—
638C2×C4—1342no—
639C2×C4—1342no—
640C2×C4—1342no—
641C2×C4—1342no—
642C2×C4—1342no—
643C2×C4—1342no—
644C2×C4—1342no—
645C2×C4—1342no—
646C2×C4—1342no—
647C2×C4—1342no—
648C2×C4—1342no—
649C2×C4—1342no—
650C2×C4—1342no—
651C2×C4—1342no—
652C2×C4—1342no—
653C2×C4—1342no—
654C2×C4—1342no—
655C2×C4—1342no—
656C2×C4—1342no—
657C2×C4—1342no—
658C2×C4—1348no—
659C2×C4—1342no—
660C2×C4—1342no—
661C2×C4C2×#1176162714yes—
662C22—24no—
663C22—24no—
664C22—24no—
665C22—24no—
666C22—24no—
667C22—24no—
668C22—232no—
669C22C2×#1452403818yes—
670C22C2×#1452403814yes—
671C22#1686392614yes—
672C22#1686398814yes—
673C22#1686407314yes—
674C22#1686407714yes—
675C22#1686408314yes—
676C22#1686408814yes—
677C22C2×#41×D6711yescharacteristic
678C22C22×#1176162711yescharacteristic
679C22C22×#1176162711yescharacteristic
680C22C22×#1176162811yescharacteristic
681C22C22×#1176162911yescharacteristic
682C22C2×#1452408811yescharacteristic
683C22C2×#1452409011yescharacteristic
684C4—24no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—2682no—
691C4—2682no—
692C4—2682no—
693C4—2682no—
694C4—2682no—
695C4—2682no—
696C4—2682no—
697C4—1344no—
698C2—28no—
699C2#2256459618yesdirect product factor
700C2C22×#1452403811yescharacteristic
701C2C2×#1686392611yescharacteristic
702C2C2×#1686398811yescharacteristic
703C2C2×#1686407311yescharacteristic
704C2C2×#1686407711yescharacteristic
705C2C2×#1686408311yescharacteristic
706C2C2×#1686408811yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×#385×C67C2
socleC24×C67C24
prime radicalC25×C67C23
hypercenterC2×#385D67
hypocenterC67C2×#2493
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. #22564596C2direct (N × H)
2. C2×C67⋊#401C2semidirect
3. C2×#16863338C2semidirect
4. C2×#16863335C2semidirect
5. C2×#16863334C2semidirect
6. C2×#16863282C2semidirect
7. C2×#16863279C2semidirect
8. C2×#16863277C2semidirect
10. C2×#16863263C2semidirect
27. C67⋊#401C22semidirect
28. #16863338C22semidirect
29. #16863335C22semidirect
30. #16863334C22semidirect
31. #16863282C22semidirect
32. #16863279C22semidirect
33. #16863277C22semidirect
35. #16863263C22semidirect
346. C2×C67#2493semidirect
370. C67C2×#2493semidirect
699. C2#22564596direct (N × H)

Maximal subgroups

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

subgroupindex
#225645962
C2×C67⋊#4012
C2×#168633382
C2×#168633352
C2×#168633342
C2×#168632822
C2×#168632792
C2×#168632772
C2×#168632712
C2×#168632632
C2×#168632572
C2×#168632542
C2×C4×C22⋊Dic672
C22×C67⋊#952
C2×#385×C672
C2×#249367