Finite Group Databasebeta

← C2×#22563286 #31015458

Subgroups — C2×#22563286 #31015458

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×#14524021C211yesmaximal, characteristic
2#22563286C2116yesmaximal, direct product factor
3C2×#16863301C211yesmaximal, characteristic, complemented
4C2×#16863300C211yesmaximal, characteristic, complemented
5C2×#16863283C211yesmaximal, characteristic, complemented
6C2×#16863278C211yesmaximal, characteristic, complemented
7C2×#16863278C211yesmaximal, characteristic, complemented
8C2×#16863270C211yesmaximal, characteristic
9C2×#16863267C211yesmaximal, characteristic
10C2×C4⋊C4×Dic67C211yesmaximal, characteristic, complemented
11C2×C4×Dic67⋊C4C211yesmaximal, characteristic, complemented
12C2×C4×(C2×D67)⋊C4C211yesmaximal, characteristic
13C2×#16863243C211yesmaximal, characteristic
14C2×#16863243C211yesmaximal, characteristic
15C2×#95×D67C211yesmaximal, characteristic
16C2×#387×C67C211yesmaximal, characteristic, complemented
17C23×Dic134C2211yescharacteristic
18C23×C4×D67C2211yescharacteristic
19C23×C4×D67C2211yescharacteristic
20C23×C4×D67C2211yescharacteristic
21C2×#14524021C4116yescomplemented
22C2×#14524021C2218yes—
23C22×C4⋊Dic67C2211yescharacteristic
24C22×Dic67⋊C4C2211yescharacteristic
25C22×Dic67⋊C4C2211yescharacteristic
26C22×Dic67⋊C4C2211yescharacteristic
27C22×Dic67⋊C4C2211yescharacteristic
28C22×(C2×D67)⋊C4C2211yescharacteristic
29C22×(C2×D67)⋊C4C2211yescharacteristic
30C22×(C2×D67)⋊C4C2211yescharacteristic
31C22×(C2×D67)⋊C4C2211yescharacteristic
32C22×C4×Dic67C2211yescharacteristic
33C22×C4×Dic67C2211yescharacteristic
34C22×C4×Dic67C2211yescharacteristic
35C22×C4×Dic67C2211yescharacteristic
36C22×C4×Dic67C2211yescharacteristic
37#16863301C2218yescomplemented
38#16863300C2218yescomplemented
39#16863283C2218yescomplemented
40#16863278C2218yescomplemented
41#16863278C2218yescomplemented
42#16863270C2218yes—
43#16863267C2218yes—
44C4⋊C4×Dic67C2218yescomplemented
45C4×Dic67⋊C4C2218yescomplemented
46C4×(C2×D67)⋊C4C2218yes—
47#16863243C2218yes—
48#16863243C2218yes—
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⋊#95C2211yescharacteristic
59#95×D67C2218yes—
60C22×C4⋊C4×C67C2211yescharacteristic
61C22×C4⋊C4×C67C2211yescharacteristic
62C22×C42×C67C2211yescharacteristic
63#387×C67C2218yescomplemented
64C2×#95×C67C2211yescharacteristic
65C2×#95×C67C2211yescharacteristic
66C2×#95×C67C2211yescharacteristic
67C2×#95×C67C2211yescharacteristic
68C24×D67C2311yescharacteristic
69C22×Dic134—42no—
70C22×Dic134—42no—
71C22×Dic134C2×C418yescomplemented
72C22×Dic134C2314yes—
73C23×Dic67C2311yescharacteristic
74C23×Dic67C2311yescharacteristic
75C23×Dic67C2311yescharacteristic
76C23×Dic67C2311yescharacteristic
77C23×Dic67C2311yescharacteristic
78C23×Dic67C2311yescharacteristic
79C23×Dic67C2311yescharacteristic
80C22×C4×D67—24no—
81C22×C4×D67—24no—
82C22×C4×D67—24no—
83C22×C4×D67—24no—
84C22×C4×D67—42no—
85C22×C4×D67—42no—
86C22×C4×D67—42no—
87C22×C4×D67—42no—
88C22×C4×D67C2×C418yes—
89C22×C4×D67C2314yes—
90C22×C4×D67C2314yes—
91C22×C4×D67C2314yes—
92#14524021C2×C4164yescomplemented
93C2×C4⋊Dic67—24no—
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×(C2×D67)⋊C4—24no—
104C2×(C2×D67)⋊C4C2×C418yes—
105C2×(C2×D67)⋊C4C2×C418yes—
106C2×(C2×D67)⋊C4Q818yescomplemented
107C2×(C2×D67)⋊C4C2314yes—
108C2×(C2×D67)⋊C4C2314yes—
109C2×(C2×D67)⋊C4C2314yes—
110C2×(C2×D67)⋊C4C2314yes—
111C2×C4×Dic67—24no—
112C2×C4×Dic67—24no—
113C2×C4×Dic67—42no—
114C2×C4×Dic67—42no—
115C2×C4×Dic67—42no—
116C2×C4×Dic67C2314yes—
117C2×C4×Dic67C2314yes—
118C2×C4×Dic67C2314yes—
119C2×C4×Dic67C2314yes—
120C2×C4×Dic67C2314yes—
121C67⋊#95C2314yes—
122C67⋊#95C2314yes—
123C67⋊#95C2314yes—
124C67⋊#95C2314yes—
125C67⋊#95C2314yes—
126C67⋊#95C2314yes—
127C67⋊#95C2314yes—
128C67⋊#95C2314yes—
129C67⋊#95C2314yes—
130C67⋊#95C2314yes—
131C23×C4×C67C2311yescharacteristic
132C23×C4×C67C2311yescharacteristic
133C23×C4×C67C2311yescharacteristic
134C23×C4×C67C2311yescharacteristic
135C23×C4×C67C2311yescharacteristic
136C23×C4×C67C2311yescharacteristic
137C23×C4×C67C2311yescharacteristic
138C2×C4⋊C4×C67—42no—
139C2×C4⋊C4×C67C2×C418yescomplemented
140C2×C4⋊C4×C67C2314yes—
141C2×C4⋊C4×C67C2314yes—
142C2×C42×C67—42no—
143C2×C42×C67C2314yes—
144#95×C67C2314yes—
145#95×C67C2314yes—
146#95×C67C2314yes—
147#95×C67C2314yes—
148C23×D67—22no—
149C23×D67—22no—
150C23×D67—22no—
151C23×D67—22no—
152C23×D67C22×C414yes—
153C23×D67C2×Q814yes—
154C23×D67#4114yes—
155C23×D67C2412yes—
156C2×Dic134—416no—
157C2×Dic134—44no—
158C2×Dic134—44no—
159C2×Dic134C22×C4116yescomplemented
160C22×Dic67—22no—
161C22×Dic67—22no—
162C22×Dic67—22no—
163C22×Dic67—22no—
164C22×Dic67—22no—
165C22×Dic67—22no—
166C22×Dic67—22no—
167C22×Dic67—22no—
168C22×Dic67—22no—
169C22×Dic67—22no—
170C22×Dic67—22no—
171C22×Dic67—22no—
172C22×Dic67—22no—
173C22×Dic67—22no—
174C22×Dic67—22no—
175C22×Dic67C22×C414yes—
176C22×Dic67C22×C414yes—
177C22×Dic67C22×C414yes—
178C22×Dic67C2×Q814yes—
179C22×Dic67#4114yes—
180C22×Dic67#4114yes—
181C22×Dic67C2412yes—
182C22×Dic67C2412yes—
183C22×Dic67C2412yes—
184C22×Dic67C2412yes—
185C22×Dic67C2412yes—
186C22×Dic67C2412yes—
187C22×Dic67C2412yes—
188C2×C4×D67—28no—
189C2×C4×D67—28no—
190C2×C4×D67—28no—
191C2×C4×D67—28no—
192C2×C4×D67—416no—
193C2×C4×D67—44no—
194C2×C4×D67—44no—
195C2×C4×D67—44no—
196C2×C4×D67—44no—
197C2×C4×D67—416no—
198C2×C4×D67—416no—
199C2×C4×D67C22×C4116yes—
200C4⋊Dic67—28no—
201Dic67⋊C4—28no—
202Dic67⋊C4—44no—
203Dic67⋊C4C22×C4116yescomplemented
204Dic67⋊C4C22×C4116yescomplemented
205(C2×D67)⋊C4—28no—
206(C2×D67)⋊C4C22×C4116yes—
207(C2×D67)⋊C4C22×C4116yes—
208(C2×D67)⋊C4C2×Q8116yescomplemented
209C4×Dic67—28no—
210C4×Dic67—28no—
211C4×Dic67—44no—
212C4×Dic67—44no—
213C4×Dic67—44no—
214C24×C67C2411yescharacteristic
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—22no—
226C22×C4×C67—22no—
227C22×C4×C67—22no—
228C22×C4×C67—22no—
229C22×C4×C67—22no—
230C22×C4×C67—22no—
231C22×C4×C67—22no—
232C22×C4×C67C22×C414yes—
233C22×C4×C67C22×C414yes—
234C22×C4×C67C22×C414yes—
235C22×C4×C67C2×Q814yes—
236C22×C4×C67C2412yes—
237C22×C4×C67C2412yes—
238C22×C4×C67C2412yes—
239C22×C4×C67C2412yes—
240C22×C4×C67C2412yes—
241C22×C4×C67C2412yes—
242C22×C4×C67C2412yes—
243C4⋊C4×C67—44no—
244C4⋊C4×C67C22×C4116yescomplemented
245C42×C67—44no—
246C23×C67C23×C412yes—
247C23×C67C22×Q812yes—
248C23×C67C2×#4112yes—
249C23×C67C2×#4112yes—
250C23×C67C2×#4112yes—
251C23×C67H(5,𝔽2)12yes—
252C23×C67H(5,𝔽2)12yes—
253C23×C67C2511yescharacteristic
254C22×D67—28no—
255C22×D67—28no—
256C22×D67—28no—
257C22×D67—28no—
258C22×D67—28no—
259C22×D67—28no—
260C22×D67—22no—
261C22×D67—22no—
262C22×D67—22no—
263C22×D67—22no—
264C22×D67C4×Q8116yes—
265C22×D67C23×C414yes—
266C22×D67C22×Q814yes—
267C22×D67C2×#4114yes—
268C2×C4×C67—28no—
269C2×C4×C67—28no—
270C2×C4×C67—28no—
271C2×C4×C67—28no—
272C2×C4×C67—22no—
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—22no—
287C2×C4×C67—22no—
288C2×C4×C67—22no—
289C2×C4×C67—44no—
290C2×C4×C67—44no—
291C2×C4×C67—44no—
292C2×C4×C67C23×C414yes—
293C2×C4×C67C23×C414yes—
294C2×C4×C67C23×C414yes—
295C2×C4×C67C22×Q814yes—
296C2×Dic67—28no—
297C2×Dic67—28no—
298C2×Dic67—28no—
299C2×Dic67—28no—
300C2×Dic67—28no—
301C2×Dic67—28no—
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—44no—
318C2×Dic67C23×C414yes—
319C2×Dic67C23×C414yes—
320C2×Dic67C23×C414yes—
321C2×Dic67C22×Q814yes—
322C2×Dic67C2×#4114yes—
323C2×Dic67C2×#4114yes—
324C4×D67—416no—
325C4×D67—416no—
326C4×D67—416no—
327Dic134—416no—
328C22×C67C2×C4×Q814yes—
329C22×C67C4×#4114yes—
330C22×C67#51814yes—
331C22×C67#55114yes—
332C22×C67#55114yes—
333C22×C67#55414yes—
334C22×C67#55414yes—
335C22×C67C24×C411yescharacteristic
336C22×C67C23×Q811yescharacteristic
337C22×C67C22×#4111yescharacteristic
338C22×C67C22×#4111yescharacteristic
339C22×C67C22×#4111yescharacteristic
340C22×C67C2×H(5,𝔽2)11yescharacteristic
341C22×C67C2×H(5,𝔽2)11yescharacteristic
342C2×D67—232no—
343C2×D67—24no—
344C2×D67—24no—
345C2×D67—24no—
346C2×D67—24no—
347C2×D67—24no—
348C2×D67—24no—
349C2×D67C2×C4×Q818yes—
350C4×C67—24no—
351C4×C67—24no—
352C4×C67—24no—
353C4×C67—24no—
354C4×C67—42no—
355C4×C67—42no—
356C4×C67—42no—
357Dic67—24no—
358Dic67—24no—
359Dic67—24no—
360Dic67—24no—
361Dic67—24no—
362Dic67—24no—
363Dic67—42no—
364C2×#2368—671nomaximal, Sylow
365C2×C67#236818yescomplemented
366C2×C67C22×C4×Q811yescharacteristic
367C2×C67C2×C4×#4111yescharacteristic
368C2×C67C2×#51811yescharacteristic
369C2×C67C2×#55111yescharacteristic
370C2×C67C2×#55111yescharacteristic
371C2×C67C2×#55411yescharacteristic
372C2×C67C2×#55411yescharacteristic
373D67—28no—
374C22×C22⋊Q8—671no—
375#2368—6716no—
376C2×#391—671no—
377C2×#391—671no—
378C2×#387—671no—
379C2×#387—671no—
380C2×#387—671no—
381C2×#387D6711yescharacteristic, complemented
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⋊C4—671no—
389C22×#95—671no—
390C67C2×#236811yescharacteristic, complemented, Sylow
391C23×Q8—671no—
392C24×C4—671no—
393C24×C4—671no—
394C24×C4—671no—
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⋊C4C2×D6711yescharacteristic
403C22×C4⋊C4C2×D6711yescharacteristic
404C22×C22⋊C4—671no—
405C22×C22⋊C4—671no—
406C22×C22⋊C4—671no—
407C22×C22⋊C4—671no—
408C22×C42—671no—
409C22×C42—671no—
410C22×C42—671no—
411C22×C42—671no—
412C22×C42—671no—
413C22×C42C2×D6711yescharacteristic
414#391—678no—
415#391—678no—
416#387—678no—
417#387—678no—
418#387—678no—
419#387C2×D6718yescomplemented
420#385—678no—
421#385—678no—
422C4×C4⋊C4—678no—
423C4×C4⋊C4—678no—
424C4×C22⋊C4—678no—
425C4×C22⋊C4—678no—
426C4×C22⋊C4—678no—
427C2×#95—671no—
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—678no—
438C2×#95C2×D6711yescharacteristic
439C2×#95C2×D6711yescharacteristic
440C2×#95C2×D6711yescharacteristic
441C2×#95C2×D6711yescharacteristic
442C25—671no—
443C22×Q8—2682no—
444C22×Q8—2682no—
445C22×Q8—678no—
446C22×Q8—674no—
447C23×C4—2682no—
448C23×C4—2682no—
449C23×C4—2682no—
450C23×C4—2682no—
451C23×C4—678no—
452C23×C4—674no—
453C23×C4—674no—
454C23×C4—674no—
455C23×C4—671no—
456C23×C4—671no—
457C23×C4—671no—
458C23×C4—671no—
459C23×C4—671no—
460C23×C4—671no—
461C23×C4—671no—
462C23×C4—1344no—
463C23×C4—1344no—
464C23×C4—1344no—
465C23×C4—1344no—
466C23×C4C22×D6711yescharacteristic
467C23×C4C22×D6711yescharacteristic
468C23×C4C22×D6711yescharacteristic
469C23×C4C22×D6711yescharacteristic
470C23×C4C22×D6711yescharacteristic
471C23×C4C22×D6711yescharacteristic
472C23×C4C22×D6711yescharacteristic
473C22⋊Q8—6764no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—2682no—
476C2×C4⋊C4—674no—
477C2×C4⋊C4—678no—
478C2×C4⋊C4—678no—
479C2×C4⋊C4—674no—
480C2×C4⋊C4—674no—
481C2×C4⋊C4—674no—
482C2×C4⋊C4—674no—
483C2×C4⋊C4—1344no—
484C2×C4⋊C4—1344no—
485C2×C4⋊C4C4×D6718yescomplemented
486C2×C4⋊C4C22×D6714yes—
487C2×C4⋊C4C22×D6714yes—
488C2×C22⋊C4—678no—
489C2×C22⋊C4—678no—
490C2×C22⋊C4—678no—
491C2×C22⋊C4—674no—
492C2×C22⋊C4—674no—
493C2×C22⋊C4—674no—
494C2×C22⋊C4—674no—
495C2×C22⋊C4—1344no—
496C2×C42—42no—
497C2×C42—2682no—
498C2×C42—2682no—
499C2×C42—2682no—
500C2×C42—674no—
501C2×C42—674no—
502C2×C42—674no—
503C2×C42—674no—
504C2×C42—674no—
505C2×C42—1344no—
506C2×C42—1344no—
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#95C22×D6714yes—
519#95C22×D6714yes—
520#95C22×D6714yes—
521#95C22×D6714yes—
522C24—674no—
523C24—674no—
524C24—674no—
525C24—672no—
526C24—1342no—
527C24—1342no—
528C24—1342no—
529C24—1342no—
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—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—26816no—
553C22×C4—2684no—
554C22×C4—2684no—
555C22×C4—2684no—
556C22×C4—2684no—
557C22×C4—26816no—
558C22×C4—26816no—
559C22×C4—6716no—
560C22×C4—674no—
561C22×C4—674no—
562C22×C4—674no—
563C22×C4—674no—
564C22×C4—674no—
565C22×C4—674no—
566C22×C4—672no—
567C22×C4—672no—
568C22×C4—672no—
569C22×C4—672no—
570C22×C4—672no—
571C22×C4—672no—
572C22×C4—672no—
573C22×C4—1348no—
574C22×C4—1348no—
575C22×C4—1348no—
576C22×C4—1348no—
577C22×C4—1342no—
578C22×C4—1342no—
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×C4×D6714yes—
595C22×C4Q8×D6714yes—
596C22×C4C23×D6712yes—
597C22×C4C23×D6712yes—
598C22×C4C23×D6712yes—
599C22×C4C23×D6712yes—
600C22×C4C23×D6712yes—
601C22×C4C23×D6712yes—
602C22×C4C23×D6712yes—
603C4⋊C4—44no—
604C4⋊C4—2684no—
605C4⋊C4—6716no—
606C4⋊C4—6716no—
607C4⋊C4—1348no—
608C4⋊C4—1348no—
609C4⋊C4C2×C4×D67116yescomplemented
610C22⋊C4—6716no—
611C22⋊C4—6716no—
612C22⋊C4—6716no—
613C22⋊C4—1348no—
614C42—44no—
615C42—2684no—
616C42—2684no—
617C42—2684no—
618C42—1348no—
619C42—1348no—
620C23—6716no—
621C23—674no—
622C23—674no—
623C23—674no—
624C23—1348no—
625C23—1348no—
626C23—1348no—
627C23—1348no—
628C23—1348no—
629C23—1348no—
630C23—1342no—
631C23—1342no—
632C23—1342no—
633C23—1342no—
634C23C22×C4×D6712yes—
635C23C2×Q8×D6712yes—
636C23#41×D6712yes—
637C23#41×D6712yes—
638C23#41×D6712yes—
639C23#1452408812yes—
640C23#1452408912yes—
641C23C24×D6711yescharacteristic
642Q8—26816no—
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—22no—
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—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—26816no—
668C2×C4—26816no—
669C2×C4—26816no—
670C2×C4—2684no—
671C2×C4—674no—
672C2×C4—674no—
673C2×C4—674no—
674C2×C4—674no—
675C2×C4—674no—
676C2×C4—674no—
677C2×C4—1342no—
678C2×C4—1342no—
679C2×C4—1342no—
680C2×C4—1348no—
681C2×C4—1348no—
682C2×C4—1348no—
683C2×C4—1348no—
684C2×C4—1348no—
685C2×C4—1348no—
686C2×C4—1342no—
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×C4—1342no—
698C2×C4C22×C4×D6714yes—
699C2×C4C22×C4×D6714yes—
700C2×C4C22×C4×D6714yes—
701C2×C4C2×Q8×D6714yes—
702C22—678no—
703C22—1344no—
704C22—1344no—
705C22—1344no—
706C22—1344no—
707C22—1344no—
708C22—1344no—
709C22—13432no—
710C22C4×Q8×D6714yes—
711C22#1686386414yes—
712C22#1686386814yes—
713C22#1686407114yes—
714C22#1686407414yes—
715C22#1686410014yes—
716C22#1686410214yes—
717C22C23×C4×D6711yescharacteristic
718C22C22×Q8×D6711yescharacteristic
719C22C2×#41×D6711yescharacteristic
720C22C2×#41×D6711yescharacteristic
721C22C2×#41×D6711yescharacteristic
722C22C2×#1452408811yescharacteristic
723C22C2×#1452408911yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—2682no—
732C4—1344no—
733C4—1344no—
734C4—1344no—
735C4—1344no—
736C4—1344no—
737C4—1344no—
738C2—1348no—
739C2#2256328618yesdirect product factor
740C2C2×C4×Q8×D6711yescharacteristic
741C2C2×#1686386411yescharacteristic
742C2C2×#1686386811yescharacteristic
743C2C2×#1686407111yescharacteristic
744C2C2×#1686407411yescharacteristic
745C2C2×#1686410011yescharacteristic
746C2C2×#1686410211yescharacteristic
subgroupG/H
centerC24C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC2×#387×C67C2
socleC24×C67C24
prime radicalC24×D67C23
cosocleC23×C67C25
hypercenterC2×#387D67
hypocenterC67C2×#2368
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #22563286C2direct (N × H)
3. C2×#16863301C2semidirect
4. C2×#16863300C2semidirect
5. C2×#16863283C2semidirect
6. C2×#16863278C2semidirect
7. C2×#16863278C2semidirect
10. C2×C4⋊C4×Dic67C2semidirect
11. C2×C4×Dic67⋊C4C2semidirect
16. C2×#387×C67C2semidirect
21. C2×#14524021C4semidirect
37. #16863301C22semidirect
38. #16863300C22semidirect
39. #16863283C22semidirect
40. #16863278C22semidirect
41. #16863278C22semidirect
44. C4⋊C4×Dic67C22semidirect
45. C4×Dic67⋊C4C22semidirect
63. #387×C67C22semidirect
71. C22×Dic134C2×C4semidirect
92. #14524021C2×C4semidirect
97. C2×Dic67⋊C4C2×C4semidirect
98. C2×Dic67⋊C4C2×C4semidirect
106. C2×(C2×D67)⋊C4Q8semidirect
139. C2×C4⋊C4×C67C2×C4semidirect
159. C2×Dic134C22×C4semidirect
203. Dic67⋊C4C22×C4semidirect
204. Dic67⋊C4C22×C4semidirect
208. (C2×D67)⋊C4C2×Q8semidirect
244. C4⋊C4×C67C22×C4semidirect
365. C2×C67#2368semidirect
381. C2×#387D67semidirect
390. C67C2×#2368semidirect
419. #387C2×D67semidirect
485. C2×C4⋊C4C4×D67semidirect
609. C4⋊C4C2×C4×D67semidirect
739. C2#22563286direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240212
#225632862
C2×#168633012
C2×#168633002
C2×#168632832
C2×#168632782
C2×#168632702
C2×#168632672
C2×C4⋊C4×Dic672
C2×C4×Dic67⋊C42
C2×C4×(C2×D67)⋊C42
C2×#168632432
C2×#95×D672
C2×#387×C672
C2×#236867