Finite Group Databasebeta

← C2×#22563287 #31015459

Subgroups — C2×#22563287 #31015459

Order 17152.

3094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524020C211yesmaximal, characteristic
2#22563287C2116yesmaximal, direct product factor
3C2×#16863302C211yesmaximal, characteristic, complemented
4C2×#16863300C211yesmaximal, characteristic, complemented
5C2×#16863283C211yesmaximal, characteristic, complemented
6C2×#16863283C211yesmaximal, characteristic, complemented
7C2×#16863280C211yesmaximal, characteristic, complemented
8C2×#16863279C211yesmaximal, characteristic, complemented
9C2×#16863271C211yesmaximal, characteristic
10C2×#16863269C211yesmaximal, characteristic
11C2×C4×Dic67⋊C4C211yesmaximal, characteristic, complemented
12C2×C4×C4⋊Dic67C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic67C211yesmaximal, characteristic
14C2×C22⋊C4×Dic67C211yesmaximal, characteristic
15C22×C67⋊#95C211yesmaximal, characteristic
16C2×C4×C22⋊C4×C67C211yesmaximal, characteristic
17C23×Dic134C2211yescharacteristic
18C24×Dic67C2211yescharacteristic
19C24×Dic67C2211yescharacteristic
20C2×#14524020C4116yescomplemented
21C2×#14524020C2218yes—
22C22×C4⋊Dic67C2211yescharacteristic
23C22×C4⋊Dic67C2211yescharacteristic
24C22×C4⋊Dic67C2211yescharacteristic
25C22×Dic67⋊C4C2211yescharacteristic
26C22×Dic67⋊C4C2211yescharacteristic
27C22×Dic67⋊C4C2211yescharacteristic
28C22×Dic67⋊C4C2211yescharacteristic
29C22×C22⋊Dic67C2211yescharacteristic
30C22×C22⋊Dic67C2211yescharacteristic
31C22×C4×Dic67C2211yescharacteristic
32C22×C4×Dic67C2211yescharacteristic
33C22×C4×Dic67C2211yescharacteristic
34C22×C4×Dic67C2211yescharacteristic
35#16863302C2218yescomplemented
36#16863300C2218yescomplemented
37#16863283C2218yescomplemented
38#16863283C2218yescomplemented
39#16863280C2218yescomplemented
40#16863279C2218yescomplemented
41#16863271C2218yes—
42#16863269C2218yes—
43C4×Dic67⋊C4C2218yescomplemented
44C4×C4⋊Dic67C2218yescomplemented
45C22⋊C4×Dic67C2218yes—
46C22⋊C4×Dic67C2218yes—
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—
59C2×C67⋊#95C2211yescharacteristic
60C24×C4×C67C2211yescharacteristic
61C22×C22⋊C4×C67C2211yescharacteristic
62C22×C22⋊C4×C67C2211yescharacteristic
63C22×C42×C67C2211yescharacteristic
64C22×C42×C67C2211yescharacteristic
65C4×C22⋊C4×C67C2218yes—
66C2×#95×C67C2211yescharacteristic
67C2×#95×C67C2211yescharacteristic
68C22×Dic134—42no—
69C22×Dic134—42no—
70C22×Dic134C2×C418yescomplemented
71C22×Dic134C2314yes—
72C23×Dic67—24no—
73C23×Dic67—24no—
74C23×Dic67—42no—
75C23×Dic67—42no—
76C23×Dic67—42no—
77C23×Dic67C2×C418yes—
78C23×Dic67C2311yescharacteristic
79C23×Dic67C2311yescharacteristic
80C23×Dic67C2311yescharacteristic
81C23×Dic67C2314yes—
82C23×Dic67C2311yescharacteristic
83C23×Dic67C2311yescharacteristic
84C23×Dic67C2311yescharacteristic
85C23×Dic67C2311yescharacteristic
86C23×Dic67C2311yescharacteristic
87C23×Dic67C2314yes—
88#14524020C2×C4164yescomplemented
89C2×C4⋊Dic67—24no—
90C2×C4⋊Dic67—42no—
91C2×C4⋊Dic67C2×C418yescomplemented
92C2×C4⋊Dic67C2314yes—
93C2×C4⋊Dic67C2314yes—
94C2×C4⋊Dic67C2314yes—
95C2×Dic67⋊C4—24no—
96C2×Dic67⋊C4—42no—
97C2×Dic67⋊C4C2×C418yescomplemented
98C2×Dic67⋊C4C2×C418yescomplemented
99C2×Dic67⋊C4C2314yes—
100C2×Dic67⋊C4C2314yes—
101C2×Dic67⋊C4C2314yes—
102C2×Dic67⋊C4C2314yes—
103C2×C22⋊Dic67—24no—
104C2×C22⋊Dic67C2×C418yes—
105C2×C22⋊Dic67C2314yes—
106C2×C22⋊Dic67C2314yes—
107C2×C4×Dic67—24no—
108C2×C4×Dic67—42no—
109C2×C4×Dic67—42no—
110C2×C4×Dic67—42no—
111C2×C4×Dic67C2314yes—
112C2×C4×Dic67C2314yes—
113C2×C4×Dic67C2314yes—
114C2×C4×Dic67C2314yes—
115C67⋊#95C2314yes—
116C67⋊#95C2314yes—
117C67⋊#95C2314yes—
118C67⋊#95C2314yes—
119C67⋊#95C2314yes—
120C67⋊#95C2314yes—
121C67⋊#95C2314yes—
122C67⋊#95C2314yes—
123C67⋊#95C2314yes—
124C67⋊#95C2314yes—
125C67⋊#95C2314yes—
126C67⋊#95C2314yes—
127C25×C67C2311yescharacteristic
128C23×C4×C67—24no—
129C23×C4×C67—24no—
130C23×C4×C67—42no—
131C23×C4×C67C2311yescharacteristic
132C23×C4×C67C2314yes—
133C23×C4×C67C2311yescharacteristic
134C23×C4×C67C2311yescharacteristic
135C23×C4×C67C2311yescharacteristic
136C23×C4×C67C2311yescharacteristic
137C23×C4×C67C2311yescharacteristic
138C2×C22⋊C4×C67C2×C418yes—
139C2×C22⋊C4×C67Q818yescomplemented
140C2×C22⋊C4×C67C2314yes—
141C2×C22⋊C4×C67C2314yes—
142C2×C42×C67—24no—
143C2×C42×C67—42no—
144C2×C42×C67C2314yes—
145C2×C42×C67C2314yes—
146#95×C67C2314yes—
147#95×C67C2314yes—
148C2×Dic134—416no—
149C2×Dic134—44no—
150C2×Dic134—44no—
151C2×Dic134C22×C4116yescomplemented
152C22×Dic67—22no—
153C22×Dic67—22no—
154C22×Dic67—22no—
155C22×Dic67—22no—
156C22×Dic67—22no—
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—22no—
166C22×Dic67—22no—
167C22×Dic67—28no—
168C22×Dic67—22no—
169C22×Dic67—22no—
170C22×Dic67—22no—
171C22×Dic67—22no—
172C22×Dic67—28no—
173C22×Dic67—416no—
174C22×Dic67—44no—
175C22×Dic67—44no—
176C22×Dic67—44no—
177C22×Dic67—416no—
178C22×Dic67C22×C414yes—
179C22×Dic67C22×C414yes—
180C22×Dic67C22×C414yes—
181C22×Dic67C22×C414yes—
182C22×Dic67C22×C4116yes—
183C22×Dic67#4114yes—
184C22×Dic67C2412yes—
185C22×Dic67C2412yes—
186C22×Dic67C2412yes—
187C22×Dic67C2412yes—
188C22×Dic67C2412yes—
189C22×Dic67C2412yes—
190C22×Dic67C2412yes—
191C22×Dic67C2412yes—
192C4⋊Dic67—28no—
193C4⋊Dic67—44no—
194C4⋊Dic67C22×C4116yescomplemented
195Dic67⋊C4—28no—
196Dic67⋊C4—44no—
197Dic67⋊C4C22×C4116yescomplemented
198Dic67⋊C4C22×C4116yescomplemented
199C22⋊Dic67—28no—
200C22⋊Dic67C22×C4116yes—
201C4×Dic67—28no—
202C4×Dic67—44no—
203C4×Dic67—44no—
204C4×Dic67—44no—
205C24×C67—22no—
206C24×C67—22no—
207C24×C67—22no—
208C24×C67—22no—
209C24×C67C22×C414yes—
210C24×C67C2×Q814yes—
211C24×C67#4114yes—
212C24×C67C2412yes—
213C24×C67C2411yescharacteristic
214C22×C4×C67—22no—
215C22×C4×C67—22no—
216C22×C4×C67—22no—
217C22×C4×C67—22no—
218C22×C4×C67—22no—
219C22×C4×C67—22no—
220C22×C4×C67—22no—
221C22×C4×C67—22no—
222C22×C4×C67—22no—
223C22×C4×C67—22no—
224C22×C4×C67—22no—
225C22×C4×C67—28no—
226C22×C4×C67—22no—
227C22×C4×C67—22no—
228C22×C4×C67—28no—
229C22×C4×C67—44no—
230C22×C4×C67—416no—
231C22×C4×C67C22×C414yes—
232C22×C4×C67C22×C414yes—
233C22×C4×C67C2×Q814yes—
234C22×C4×C67C2×Q814yes—
235C22×C4×C67#4114yes—
236C22×C4×C67C2412yes—
237C22×C4×C67C2412yes—
238C22×C4×C67C2412yes—
239C22×C4×C67C2412yes—
240C22×C4×C67C2412yes—
241C22×C4×C67C2412yes—
242C22⋊C4×C67C22×C4116yes—
243C22⋊C4×C67C2×Q8116yescomplemented
244C42×C67—28no—
245C42×C67—44no—
246C23×C67—28no—
247C23×C67—28no—
248C23×C67—28no—
249C23×C67—28no—
250C23×C67—28no—
251C23×C67—28no—
252C23×C67—22no—
253C23×C67—22no—
254C23×C67—22no—
255C23×C67—22no—
256C23×C67C4×Q8116yes—
257C23×C67C23×C414yes—
258C23×C67C23×C412yes—
259C23×C67C22×Q814yes—
260C23×C67C22×Q812yes—
261C23×C67C2×#4112yes—
262C23×C67C2×#4112yes—
263C23×C67C2×#4114yes—
264C23×C67C2×#4112yes—
265C23×C67H(5,𝔽2)12yes—
266C23×C67H(5,𝔽2)12yes—
267C23×C67C2511yescharacteristic
268C2×C4×C67—28no—
269C2×C4×C67—28no—
270C2×C4×C67—28no—
271C2×C4×C67—28no—
272C2×C4×C67—28no—
273C2×C4×C67—22no—
274C2×C4×C67—22no—
275C2×C4×C67—22no—
276C2×C4×C67—22no—
277C2×C4×C67—22no—
278C2×C4×C67—22no—
279C2×C4×C67—22no—
280C2×C4×C67—22no—
281C2×C4×C67—22no—
282C2×C4×C67—22no—
283C2×C4×C67—22no—
284C2×C4×C67—22no—
285C2×C4×C67—22no—
286C2×C4×C67—416no—
287C2×C4×C67—44no—
288C2×C4×C67C23×C414yes—
289C2×C4×C67C23×C414yes—
290C2×C4×C67C22×Q814yes—
291C2×C4×C67C22×Q814yes—
292C2×C4×C67C2×#4114yes—
293C2×Dic67—28no—
294C2×Dic67—28no—
295C2×Dic67—28no—
296C2×Dic67—28no—
297C2×Dic67—28no—
298C2×Dic67—22no—
299C2×Dic67—22no—
300C2×Dic67—22no—
301C2×Dic67—22no—
302C2×Dic67—22no—
303C2×Dic67—22no—
304C2×Dic67—22no—
305C2×Dic67—22no—
306C2×Dic67—22no—
307C2×Dic67—22no—
308C2×Dic67—22no—
309C2×Dic67—22no—
310C2×Dic67—22no—
311C2×Dic67—22no—
312C2×Dic67—22no—
313C2×Dic67—22no—
314C2×Dic67—22no—
315C2×Dic67—22no—
316C2×Dic67—22no—
317C2×Dic67—416no—
318C2×Dic67—416no—
319C2×Dic67—44no—
320C2×Dic67—44no—
321C2×Dic67—44no—
322C2×Dic67C23×C414yes—
323C2×Dic67C23×C414yes—
324C2×Dic67C23×C414yes—
325C2×Dic67C23×C414yes—
326C2×Dic67C2×#4114yes—
327Dic134—416no—
328C22×C67—232no—
329C22×C67—24no—
330C22×C67—24no—
331C22×C67—24no—
332C22×C67—24no—
333C22×C67—24no—
334C22×C67—24no—
335C22×C67C2×C4×Q818yes—
336C22×C67C2×C4×Q814yes—
337C22×C67C4×#4114yes—
338C22×C67#51814yes—
339C22×C67#55114yes—
340C22×C67#55114yes—
341C22×C67#55414yes—
342C22×C67#55414yes—
343C22×C67C24×C411yescharacteristic
344C22×C67C23×Q811yescharacteristic
345C22×C67C22×#4111yescharacteristic
346C22×C67C22×#4111yescharacteristic
347C22×C67C22×#4111yescharacteristic
348C22×C67C2×H(5,𝔽2)11yescharacteristic
349C22×C67C2×H(5,𝔽2)11yescharacteristic
350C4×C67—24no—
351C4×C67—24no—
352C4×C67—24no—
353C4×C67—24no—
354C4×C67—24no—
355C4×C67—42no—
356Dic67—24no—
357Dic67—24no—
358Dic67—24no—
359Dic67—24no—
360Dic67—24no—
361Dic67—42no—
362Dic67—42no—
363Dic67—42no—
364C2×#2368—671nomaximal, Sylow
365C2×C67—28no—
366C2×C67#236818yescomplemented
367C2×C67C22×C4×Q811yescharacteristic
368C2×C67C2×C4×#4111yescharacteristic
369C2×C67C2×#51811yescharacteristic
370C2×C67C2×#55111yescharacteristic
371C2×C67C2×#55111yescharacteristic
372C2×C67C2×#55411yescharacteristic
373C2×C67C2×#55411yescharacteristic
374C22×C22⋊Q8—671no—
375#2368—6716no—
376C2×#391—671no—
377C2×#391—671no—
378C2×#387—671no—
379C2×#387—671no—
380C2×#387—671no—
381C2×#387—671no—
382C2×#385—671no—
383C2×#385—671no—
384C2×C4×C4⋊C4—671no—
385C2×C4×C4⋊C4—671no—
386C2×C4×C22⋊C4—671no—
387C2×C4×C22⋊C4—671no—
388C2×C4×C22⋊C4D6711yescharacteristic
389C22×#95—671no—
390C67C2×#236811yescharacteristic, complemented, Sylow
391C23×Q8—671no—
392C24×C4—671no—
393C24×C4—671no—
394C24×C4C2×D6711yescharacteristic
395C2×C22⋊Q8—6716no—
396C2×C22⋊Q8—678no—
397C22×C4⋊C4—671no—
398C22×C4⋊C4—671no—
399C22×C4⋊C4—671no—
400C22×C4⋊C4—671no—
401C22×C4⋊C4—671no—
402C22×C4⋊C4—671no—
403C22×C4⋊C4—671no—
404C22×C22⋊C4—671no—
405C22×C22⋊C4—671no—
406C22×C22⋊C4C2×D6711yescharacteristic
407C22×C22⋊C4C2×D6711yescharacteristic
408C22×C42—671no—
409C22×C42—671no—
410C22×C42—671no—
411C22×C42—671no—
412C22×C42C2×D6711yescharacteristic
413C22×C42C2×D6711yescharacteristic
414#391—678no—
415#391—678no—
416#387—678no—
417#387—678no—
418#387—678no—
419#387—678no—
420#385—678no—
421#385—678no—
422C4×C4⋊C4—678no—
423C4×C4⋊C4—678no—
424C4×C22⋊C4—678no—
425C4×C22⋊C4—678no—
426C4×C22⋊C4C2×D6718yes—
427C2×#95—678no—
428C2×#95—671no—
429C2×#95—671no—
430C2×#95—671no—
431C2×#95—671no—
432C2×#95—671no—
433C2×#95—671no—
434C2×#95—671no—
435C2×#95—671no—
436C2×#95—671no—
437C2×#95—671no—
438C2×#95—671no—
439C2×#95—671no—
440C2×#95C2×D6711yescharacteristic
441C2×#95C2×D6711yescharacteristic
442C25C22×D6711yescharacteristic
443C22×Q8—2682no—
444C22×Q8—2682no—
445C22×Q8—678no—
446C22×Q8—674no—
447C23×C4—24no—
448C23×C4—24no—
449C23×C4—42no—
450C23×C4—2682no—
451C23×C4—2682no—
452C23×C4—2682no—
453C23×C4—678no—
454C23×C4—674no—
455C23×C4—674no—
456C23×C4—671no—
457C23×C4—671no—
458C23×C4—671no—
459C23×C4—671no—
460C23×C4—671no—
461C23×C4—671no—
462C23×C4—671no—
463C23×C4—671no—
464C23×C4—1344no—
465C23×C4—1344no—
466C23×C4C22×D6711yescharacteristic
467C23×C4C22×D6714yes—
468C23×C4C22×D6711yescharacteristic
469C23×C4C22×D6711yescharacteristic
470C23×C4C22×D6711yescharacteristic
471C23×C4C22×D6711yescharacteristic
472C23×C4C22×D6711yescharacteristic
473C22⋊Q8—6764no—
474C2×C4⋊C4—2682no—
475C2×C4⋊C4—2682no—
476C2×C4⋊C4—674no—
477C2×C4⋊C4—674no—
478C2×C4⋊C4—678no—
479C2×C4⋊C4—678no—
480C2×C4⋊C4—678no—
481C2×C4⋊C4—674no—
482C2×C4⋊C4—674no—
483C2×C4⋊C4—674no—
484C2×C4⋊C4—674no—
485C2×C4⋊C4—674no—
486C2×C4⋊C4—1344no—
487C2×C4⋊C4—1344no—
488C2×C22⋊C4—678no—
489C2×C22⋊C4—674no—
490C2×C22⋊C4—674no—
491C2×C22⋊C4—1344no—
492C2×C22⋊C4Dic13418yescomplemented
493C2×C22⋊C4C4×D6718yes—
494C2×C22⋊C4C22×D6714yes—
495C2×C22⋊C4C22×D6714yes—
496C2×C42—24no—
497C2×C42—42no—
498C2×C42—2682no—
499C2×C42—2682no—
500C2×C42—2682no—
501C2×C42—674no—
502C2×C42—674no—
503C2×C42—674no—
504C2×C42—674no—
505C2×C42—1344no—
506C2×C42C22×D6714yes—
507C2×C42C22×D6714yes—
508#95—674no—
509#95—674no—
510#95—674no—
511#95—674no—
512#95—674no—
513#95—674no—
514#95—674no—
515#95—674no—
516#95—674no—
517#95—674no—
518#95—674no—
519#95—674no—
520#95C22×D6714yes—
521#95C22×D6714yes—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24C2×C4×D6714yes—
527C24C2×Dic13414yes—
528C24#1176162814yes—
529C24C23×D6712yes—
530C24C23×D6711yescharacteristic
531C2×Q8—26816no—
532C2×Q8—2684no—
533C2×Q8—2684no—
534C2×Q8—6716no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—28no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—28no—
550C22×C4—44no—
551C22×C4—416no—
552C22×C4—26816no—
553C22×C4—2684no—
554C22×C4—26816no—
555C22×C4—2684no—
556C22×C4—2684no—
557C22×C4—6716no—
558C22×C4—674no—
559C22×C4—674no—
560C22×C4—674no—
561C22×C4—674no—
562C22×C4—674no—
563C22×C4—672no—
564C22×C4—672no—
565C22×C4—672no—
566C22×C4—672no—
567C22×C4—672no—
568C22×C4—672no—
569C22×C4—672no—
570C22×C4—672no—
571C22×C4—1348no—
572C22×C4—1342no—
573C22×C4—1342no—
574C22×C4—1342no—
575C22×C4—1342no—
576C22×C4—1342no—
577C22×C4—1342no—
578C22×C4—1348no—
579C22×C4—1342no—
580C22×C4—1342no—
581C22×C4—1342no—
582C22×C4—1342no—
583C22×C4—1342no—
584C22×C4—1342no—
585C22×C4—1342no—
586C22×C4—1342no—
587C22×C4—1342no—
588C22×C4—1342no—
589C22×C4—1342no—
590C22×C4—1342no—
591C22×C4—1342no—
592C22×C4C2×C4×D6714yes—
593C22×C4C2×C4×D6714yes—
594C22×C4C2×Dic13414yes—
595C22×C4C2×Dic13414yes—
596C22×C4#1176162714yes—
597C22×C4C23×D6712yes—
598C22×C4C23×D6712yes—
599C22×C4C23×D6712yes—
600C22×C4C23×D6712yes—
601C22×C4C23×D6712yes—
602C22×C4C23×D6712yes—
603C4⋊C4—2684no—
604C4⋊C4—2684no—
605C4⋊C4—6716no—
606C4⋊C4—6716no—
607C4⋊C4—6716no—
608C4⋊C4—1348no—
609C4⋊C4—1348no—
610C22⋊C4—6716no—
611C22⋊C4—1348no—
612C22⋊C4C2×C4×D67116yes—
613C22⋊C4C2×Dic134116yescomplemented
614C42—28no—
615C42—44no—
616C42—2684no—
617C42—2684no—
618C42—2684no—
619C42—1348no—
620C23—28no—
621C23—28no—
622C23—28no—
623C23—28no—
624C23—28no—
625C23—28no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23C4×Dic134116yes—
631C23C22×C4×D6714yes—
632C23C22×C4×D6712yes—
633C23C22×Dic13414yes—
634C23C22×Dic13412yes—
635C23#41×D6712yes—
636C23C2×#1176162712yes—
637C23C2×#1176162814yes—
638C23C2×#1176162812yes—
639C23#1452408812yes—
640C23#1452408912yes—
641C23C24×D6711yescharacteristic
642Q8—26816no—
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—416no—
662C2×C4—44no—
663C2×C4—2684no—
664C2×C4—2684no—
665C2×C4—2684no—
666C2×C4—26816no—
667C2×C4—26816no—
668C2×C4—674no—
669C2×C4—674no—
670C2×C4—674no—
671C2×C4—674no—
672C2×C4—674no—
673C2×C4—1342no—
674C2×C4—1342no—
675C2×C4—1342no—
676C2×C4—1342no—
677C2×C4—1342no—
678C2×C4—1342no—
679C2×C4—1342no—
680C2×C4—1342no—
681C2×C4—1342no—
682C2×C4—1348no—
683C2×C4—1348no—
684C2×C4—1348no—
685C2×C4—1348no—
686C2×C4—1348no—
687C2×C4—1342no—
688C2×C4—1342no—
689C2×C4—1342no—
690C2×C4—1342no—
691C2×C4—1342no—
692C2×C4—1342no—
693C2×C4—1342no—
694C2×C4—1342no—
695C2×C4—1342no—
696C2×C4—1342no—
697C2×C4C22×C4×D6714yes—
698C2×C4C22×C4×D6714yes—
699C2×C4C22×Dic13414yes—
700C2×C4C22×Dic13414yes—
701C2×C4C2×#1176162714yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—232no—
709C22C2×C4×Dic13418yes—
710C22C2×C4×Dic13414yes—
711C22C4×#1176162714yes—
712C22#1686386814yes—
713C22#1686407014yes—
714C22#1686407214yes—
715C22#1686410314yes—
716C22#1686410514yes—
717C22C23×C4×D6711yescharacteristic
718C22C23×Dic13411yescharacteristic
719C22C2×#41×D6711yescharacteristic
720C22C22×#1176162711yescharacteristic
721C22C22×#1176162811yescharacteristic
722C22C2×#1452408811yescharacteristic
723C22C2×#1452408911yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—24no—
729C4—42no—
730C4—2682no—
731C4—2682no—
732C4—2682no—
733C4—1344no—
734C4—1344no—
735C4—1344no—
736C4—1344no—
737C4—1344no—
738C2—28no—
739C2#2256328718yesdirect product factor
740C2C22×C4×Dic13411yescharacteristic
741C2C2×C4×#1176162711yescharacteristic
742C2C2×#1686386811yescharacteristic
743C2C2×#1686407011yescharacteristic
744C2C2×#1686407211yescharacteristic
745C2C2×#1686410311yescharacteristic
746C2C2×#1686410511yescharacteristic
subgroupG/H
centerC24C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC2×C4×C22⋊C4×C67C2
socleC24×C67C24
prime radicalC25×C67C23
cosocleC23×C67C25
hypercenterC2×C4×C22⋊C4D67
hypocenterC67C2×#2368
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #22563287C2direct (N × H)
3. C2×#16863302C2semidirect
4. C2×#16863300C2semidirect
5. C2×#16863283C2semidirect
6. C2×#16863283C2semidirect
7. C2×#16863280C2semidirect
8. C2×#16863279C2semidirect
11. C2×C4×Dic67⋊C4C2semidirect
12. C2×C4×C4⋊Dic67C2semidirect
20. C2×#14524020C4semidirect
35. #16863302C22semidirect
36. #16863300C22semidirect
37. #16863283C22semidirect
38. #16863283C22semidirect
39. #16863280C22semidirect
40. #16863279C22semidirect
43. C4×Dic67⋊C4C22semidirect
44. C4×C4⋊Dic67C22semidirect
70. C22×Dic134C2×C4semidirect
88. #14524020C2×C4semidirect
91. C2×C4⋊Dic67C2×C4semidirect
97. C2×Dic67⋊C4C2×C4semidirect
98. C2×Dic67⋊C4C2×C4semidirect
139. C2×C22⋊C4×C67Q8semidirect
151. C2×Dic134C22×C4semidirect
194. C4⋊Dic67C22×C4semidirect
197. Dic67⋊C4C22×C4semidirect
198. Dic67⋊C4C22×C4semidirect
243. C22⋊C4×C67C2×Q8semidirect
366. C2×C67#2368semidirect
390. C67C2×#2368semidirect
492. C2×C22⋊C4Dic134semidirect
613. C22⋊C4C2×Dic134semidirect
739. C2#22563287direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240202
#225632872
C2×#168633022
C2×#168633002
C2×#168632832
C2×#168632802
C2×#168632792
C2×#168632712
C2×#168632692
C2×C4×Dic67⋊C42
C2×C4×C4⋊Dic672
C2×C22⋊C4×Dic672
C22×C67⋊#952
C2×C4×C22⋊C4×C672
C2×#236867