Finite Group Databasebeta

← C2×#22563917 #31024319

Subgroups — C2×#22563917 #31024319

Order 17152.

2726 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524033C211yesmaximal, characteristic, complemented
2C22×#14523999C211yesmaximal, characteristic
3#22563917C2116yesmaximal, direct product factor
4C2×#16863332C211yesmaximal, characteristic
5C2×#16863332C211yesmaximal, characteristic
6C2×#16863319C211yesmaximal, characteristic
7C2×#16863295C211yesmaximal, characteristic, complemented
8C2×#16863293C211yesmaximal, characteristic, complemented
9C2×#16863291C211yesmaximal, characteristic, complemented
10C2×#16863291C211yesmaximal, characteristic, complemented
11C2×#16863278C211yesmaximal, characteristic, complemented
12C2×#16863277C211yesmaximal, characteristic, complemented
13C2×#16863265C211yesmaximal, characteristic, complemented
14C2×#16863254C211yesmaximal, characteristic
15C2×C22⋊C4×Dic67C211yesmaximal, characteristic
16C2×#396×C67C211yesmaximal, characteristic
17C24×Dic67C2211yescharacteristic
18C2×#14524033—28no—
19C2×#14524033C2218yescomplemented
20C2×#14523999—28no—
21C2×#14523999C2218yes—
22C22×C4⋊Dic67C2211yescharacteristic
23C22×C4⋊Dic67C2211yescharacteristic
24C22×C4⋊Dic67C2211yescharacteristic
25C22×Dic67⋊C4C2211yescharacteristic
26C22×Dic67⋊C4C2211yescharacteristic
27C22×Dic67⋊C4C2211yescharacteristic
28C22×Dic67⋊C4C2211yescharacteristic
29C22×Dic67⋊C4C2211yescharacteristic
30C22×Dic67⋊C4C2211yescharacteristic
31C22×Dic67⋊C4C2211yescharacteristic
32C22×Dic67⋊C4C2211yescharacteristic
33C22×Dic67⋊C4C2211yescharacteristic
34C22×Dic67⋊C4C2211yescharacteristic
35C22×C22⋊Dic67C2211yescharacteristic
36C22×C22⋊Dic67C2211yescharacteristic
37C22×C22⋊Dic67C2211yescharacteristic
38C22×C4×Dic67C2211yescharacteristic
39C22×C4×Dic67C2211yescharacteristic
40C22×C4×Dic67C2211yescharacteristic
41C22×C4×Dic67C2211yescharacteristic
42#16863332C2218yes—
43#16863332C2218yes—
44#16863319C2218yes—
45#16863295C2218yescomplemented
46#16863293C2218yescomplemented
47#16863291C2218yescomplemented
48#16863291C2218yescomplemented
49#16863278C2218yescomplemented
50#16863277C2218yescomplemented
51#16863265C2218yescomplemented
52#16863254C2218yes—
53C22⋊C4×Dic67C2218yes—
54C2×C67⋊#95C2211yescharacteristic
55C2×C67⋊#95C2211yescharacteristic
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2211yescharacteristic
59C2×C67⋊#95C2211yescharacteristic
60C2×C67⋊#95C2211yescharacteristic
61C22×C4⋊C4×C67C2211yescharacteristic
62C22×C4⋊C4×C67C2211yescharacteristic
63C22×C4⋊C4×C67C2211yescharacteristic
64C22×C22⋊C4×C67C2211yescharacteristic
65C22×C22⋊C4×C67C2211yescharacteristic
66C22×C22⋊C4×C67C2211yescharacteristic
67#396×C67C2218yes—
68C2×#95×C67C2211yescharacteristic
69C23×Dic67—24no—
70C23×Dic67—24no—
71C23×Dic67Q818yes—
72C23×Dic67C2311yescharacteristic
73C23×Dic67C2311yescharacteristic
74C23×Dic67C2311yescharacteristic
75C23×Dic67C2311yescharacteristic
76C23×Dic67C2311yescharacteristic
77C23×Dic67C2311yescharacteristic
78C23×Dic67C2314yes—
79C23×Dic67C2311yescharacteristic
80C23×Dic67C2311yescharacteristic
81#14524033—232no—
82#14523999—232no—
83C2×C4⋊Dic67—24no—
84C2×C4⋊Dic67—42no—
85C2×C4⋊Dic67—42no—
86C2×C4⋊Dic67C2314yes—
87C2×C4⋊Dic67C2314yes—
88C2×C4⋊Dic67C2314yes—
89C2×Dic67⋊C4—24no—
90C2×Dic67⋊C4—24no—
91C2×Dic67⋊C4—24no—
92C2×Dic67⋊C4—24no—
93C2×Dic67⋊C4—24no—
94C2×Dic67⋊C4—24no—
95C2×Dic67⋊C4—24no—
96C2×Dic67⋊C4—24no—
97C2×Dic67⋊C4—42no—
98C2×Dic67⋊C4D418yes—
99C2×Dic67⋊C4C2314yes—
100C2×Dic67⋊C4C2314yes—
101C2×Dic67⋊C4C2314yes—
102C2×Dic67⋊C4C2314yes—
103C2×Dic67⋊C4C2314yes—
104C2×Dic67⋊C4C2314yes—
105C2×Dic67⋊C4C2314yes—
106C2×Dic67⋊C4C2314yes—
107C2×Dic67⋊C4C2314yes—
108C2×Dic67⋊C4C2314yes—
109C2×C22⋊Dic67—24no—
110C2×C22⋊Dic67—24no—
111C2×C22⋊Dic67—42no—
112C2×C22⋊Dic67C2314yes—
113C2×C22⋊Dic67C2314yes—
114C2×C22⋊Dic67C2314yes—
115C2×C4×Dic67—24no—
116C2×C4×Dic67—24no—
117C2×C4×Dic67—24no—
118C2×C4×Dic67—24no—
119C2×C4×Dic67C2314yes—
120C2×C4×Dic67C2314yes—
121C2×C4×Dic67C2314yes—
122C2×C4×Dic67C2314yes—
123C67⋊#95C2314yes—
124C67⋊#95C2314yes—
125C67⋊#95C2314yes—
126C67⋊#95C2314yes—
127C67⋊#95C2314yes—
128C67⋊#95C2314yes—
129C67⋊#95C2314yes—
130C25×C67C2311yescharacteristic
131C23×C4×C67C2311yescharacteristic
132C23×C4×C67C2311yescharacteristic
133C23×C4×C67C2311yescharacteristic
134C23×C4×C67C2311yescharacteristic
135C23×C4×C67C2311yescharacteristic
136C23×C4×C67C2311yescharacteristic
137C2×C4⋊C4×C67—24no—
138C2×C4⋊C4×C67—24no—
139C2×C4⋊C4×C67—42no—
140C2×C4⋊C4×C67C2314yes—
141C2×C4⋊C4×C67C2314yes—
142C2×C4⋊C4×C67C2314yes—
143C2×C22⋊C4×C67—24no—
144C2×C22⋊C4×C67—24no—
145C2×C22⋊C4×C67—42no—
146C2×C22⋊C4×C67C2314yes—
147C2×C22⋊C4×C67C2314yes—
148C2×C22⋊C4×C67C2314yes—
149#95×C67C2314yes—
150C22×Dic67—22no—
151C22×Dic67—22no—
152C22×Dic67—22no—
153C22×Dic67—22no—
154C22×Dic67—22no—
155C22×Dic67—22no—
156C22×Dic67—232no—
157C22×Dic67—28no—
158C22×Dic67—28no—
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—22no—
168C22×Dic67—22no—
169C22×Dic67—22no—
170C22×Dic67—22no—
171C22×Dic67C2×D414yes—
172C22×Dic67C2×D414yes—
173C22×Dic67C2×Q814yes—
174C22×Dic67C2×Q8116yes—
175C22×Dic67C2×Q814yes—
176C22×Dic67#4114yes—
177C22×Dic67#4114yes—
178C22×Dic67C2412yes—
179C22×Dic67C2412yes—
180C22×Dic67C2412yes—
181C22×Dic67C2412yes—
182C22×Dic67C2412yes—
183C22×Dic67C2412yes—
184C22×Dic67C2412yes—
185C22×Dic67C2412yes—
186C4⋊Dic67—28no—
187C4⋊Dic67—44no—
188C4⋊Dic67—44no—
189Dic67⋊C4—28no—
190Dic67⋊C4—28no—
191Dic67⋊C4—28no—
192Dic67⋊C4—28no—
193Dic67⋊C4—28no—
194Dic67⋊C4—28no—
195Dic67⋊C4—28no—
196Dic67⋊C4—28no—
197Dic67⋊C4—44no—
198Dic67⋊C4C2×D4116yes—
199C22⋊Dic67—28no—
200C22⋊Dic67—28no—
201C22⋊Dic67—44no—
202C4×Dic67—28no—
203C4×Dic67—28no—
204C4×Dic67—28no—
205C4×Dic67—28no—
206C24×C67—22no—
207C24×C67—22no—
208C24×C67—22no—
209C24×C67—22no—
210C24×C67—22no—
211C24×C67—22no—
212C24×C67C2×Q814yes—
213C24×C67C2412yes—
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×C67C2×D414yes—
232C22×C4×C67#4114yes—
233C22×C4×C67C2412yes—
234C22×C4×C67C2412yes—
235C22×C4×C67C2412yes—
236C22×C4×C67C2412yes—
237C22×C4×C67C2412yes—
238C22×C4×C67C2412yes—
239C4⋊C4×C67—28no—
240C4⋊C4×C67—28no—
241C4⋊C4×C67—44no—
242C22⋊C4×C67—28no—
243C22⋊C4×C67—28no—
244C22⋊C4×C67—44no—
245C23×C67—28no—
246C23×C67—28no—
247C23×C67—28no—
248C23×C67—22no—
249C23×C67—22no—
250C23×C67—22no—
251C23×C67—22no—
252C23×C67—22no—
253C23×C67—22no—
254C23×C67—44no—
255C23×C67—44no—
256C23×C67—44no—
257C23×C67—44no—
258C23×C67C22×D412yes—
259C23×C67C22×Q814yes—
260C23×C67C22×Q812yes—
261C23×C67C2×#4112yes—
262C23×C67C2×#4112yes—
263C23×C67C2×#4112yes—
264C23×C67H(5,𝔽2)12yes—
265C23×C672−1+412yes—
266C23×C67C2511yescharacteristic
267C2×C4×C67—28no—
268C2×C4×C67—28no—
269C2×C4×C67—22no—
270C2×C4×C67—22no—
271C2×C4×C67—22no—
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—44no—
286C2×C4×C67—44no—
287C2×C4×C67—44no—
288C2×C4×C67—44no—
289C2×C4×C67C22×D414yes—
290C2×C4×C67C2×#4114yes—
291C2×Dic67—28no—
292C2×Dic67—28no—
293C2×Dic67—28no—
294C2×Dic67—22no—
295C2×Dic67—22no—
296C2×Dic67—22no—
297C2×Dic67—22no—
298C2×Dic67—22no—
299C2×Dic67—22no—
300C2×Dic67—232no—
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—44no—
314C2×Dic67—44no—
315C2×Dic67—44no—
316C2×Dic67—44no—
317C2×Dic67C22⋊Q8116yes—
318C2×Dic67C22×D414yes—
319C2×Dic67C22×D414yes—
320C2×Dic67C22×Q814yes—
321C2×Dic67C22×Q814yes—
322C2×Dic67C2×#4114yes—
323C2×Dic67C2×#4114yes—
324C22×C67—24no—
325C22×C67—24no—
326C22×C67—24no—
327C22×C67—42no—
328C22×C67—416no—
329C22×C67—42no—
330C22×C67—42no—
331C22×C67—42no—
332C22×C67C2×C22⋊Q814yes—
333C22×C67#53314yes—
334C22×C67#54414yes—
335C22×C67#54714yes—
336C22×C67#55014yes—
337C22×C67#55214yes—
338C22×C67#55314yes—
339C22×C67C23×D411yescharacteristic
340C22×C67C23×Q811yescharacteristic
341C22×C67C22×#4111yescharacteristic
342C22×C67C22×#4111yescharacteristic
343C22×C67C22×#4111yescharacteristic
344C22×C67C2×H(5,𝔽2)11yescharacteristic
345C22×C67C2×2−1+411yescharacteristic
346C4×C67—24no—
347C4×C67—24no—
348C4×C67—42no—
349C4×C67—42no—
350C4×C67—42no—
351C4×C67—42no—
352Dic67—24no—
353Dic67—24no—
354Dic67—24no—
355Dic67—42no—
356Dic67—42no—
357Dic67—42no—
358Dic67—42no—
359Dic67C2×C22⋊Q818yes—
360C2×#2441—671nomaximal, Sylow
361C2×C67—44no—
362C2×C67#244118yescomplemented
363C2×C67C22×C22⋊Q811yescharacteristic
364C2×C67C2×#53311yescharacteristic
365C2×C67C2×#54411yescharacteristic
366C2×C67C2×#54711yescharacteristic
367C2×C67C2×#55011yescharacteristic
368C2×C67C2×#55211yescharacteristic
369C2×C67C2×#55311yescharacteristic
370C22×#125—671no—
371C22×#117—671no—
372#2441—6716no—
373C2×#399—671no—
374C2×#399—671no—
375C2×#396—671no—
376C2×#396D6711yescharacteristic
377C2×#389—671no—
378C2×#389—671no—
379C2×#389—671no—
380C2×#389—671no—
381C2×#387—671no—
382C2×#387—671no—
383C2×#384—671no—
384C2×#380—671no—
385C2×C4×C22⋊C4—671no—
386C67C2×#244111yescharacteristic, complemented, Sylow
387C24×C4—671no—
388C2×#125—678no—
389C2×#125—1348no—
390C2×#117—678no—
391C2×#117—1348no—
392C22×C4⋊C4—671no—
393C22×C4⋊C4—671no—
394C22×C4⋊C4—671no—
395C22×C4⋊C4—671no—
396C22×C4⋊C4—671no—
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×C4⋊C4—671no—
405C22×C4⋊C4C2×D6711yescharacteristic
406C22×C4⋊C4C2×D6711yescharacteristic
407C22×C4⋊C4C2×D6711yescharacteristic
408C22×C22⋊C4—671no—
409C22×C22⋊C4—671no—
410C22×C22⋊C4—671no—
411C22×C22⋊C4C2×D6711yescharacteristic
412C22×C22⋊C4C2×D6711yescharacteristic
413C22×C22⋊C4C2×D6711yescharacteristic
414C22×C42—671no—
415C22×C42—671no—
416C22×C42—671no—
417C22×C42—671no—
418#399—678no—
419#399—678no—
420#396—678no—
421#396C2×D6718yes—
422#389—678no—
423#389—678no—
424#389—678no—
425#389—678no—
426#387—678no—
427#387—678no—
428#384—678no—
429#380—678no—
430C4×C22⋊C4—678no—
431C2×#95—671no—
432C2×#95—671no—
433C2×#95—671no—
434C2×#95—671no—
435C2×#95—671no—
436C2×#95—671no—
437C2×#95—671no—
438C2×#95C2×D6711yescharacteristic
439C25C22×D6711yescharacteristic
440C23×C4—671no—
441C23×C4—678no—
442C23×C4—674no—
443C23×C4—671no—
444C23×C4—671no—
445C23×C4—671no—
446C23×C4—671no—
447C23×C4—671no—
448C23×C4—671no—
449C23×C4—671no—
450C23×C4—1344no—
451C23×C4—1344no—
452C23×C4C22×D6711yescharacteristic
453C23×C4C22×D6711yescharacteristic
454C23×C4C22×D6711yescharacteristic
455C23×C4C22×D6711yescharacteristic
456C23×C4C22×D6711yescharacteristic
457C23×C4C22×D6711yescharacteristic
458#125—13432no—
459#117—13432no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—2682no—
464C2×C4⋊C4—2682no—
465C2×C4⋊C4—2682no—
466C2×C4⋊C4—674no—
467C2×C4⋊C4—674no—
468C2×C4⋊C4—674no—
469C2×C4⋊C4—678no—
470C2×C4⋊C4—674no—
471C2×C4⋊C4—674no—
472C2×C4⋊C4—674no—
473C2×C4⋊C4—674no—
474C2×C4⋊C4—674no—
475C2×C4⋊C4—674no—
476C2×C4⋊C4—674no—
477C2×C4⋊C4—674no—
478C2×C4⋊C4—674no—
479C2×C4⋊C4—674no—
480C2×C4⋊C4—1344no—
481C2×C4⋊C4—1344no—
482C2×C4⋊C4—1344no—
483C2×C4⋊C4—1344no—
484C2×C4⋊C4—1344no—
485C2×C4⋊C4—1344no—
486C2×C4⋊C4—1344no—
487C2×C4⋊C4—1344no—
488C2×C4⋊C4—1344no—
489C2×C4⋊C4C22×D6714yes—
490C2×C4⋊C4C22×D6714yes—
491C2×C4⋊C4C22×D6714yes—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—2682no—
496C2×C22⋊C4—674no—
497C2×C22⋊C4—674no—
498C2×C22⋊C4—674no—
499C2×C22⋊C4—1344no—
500C2×C22⋊C4—1344no—
501C2×C22⋊C4C22×D6714yes—
502C2×C22⋊C4C22×D6714yes—
503C2×C22⋊C4C22×D6714yes—
504C2×C42—674no—
505C2×C42—674no—
506C2×C42—674no—
507C2×C42—674no—
508C2×C42—1344no—
509C2×C42—1344no—
510C2×C42—1344no—
511C2×C42—1344no—
512#95—674no—
513#95—674no—
514#95—674no—
515#95—674no—
516#95—674no—
517#95—674no—
518#95—674no—
519#95C22×D6714yes—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24Q8×D6714yes—
527C24C23×D6712yes—
528C24C23×D6711yescharacteristic
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
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—674no—
546C22×C4—674no—
547C22×C4—674no—
548C22×C4—672no—
549C22×C4—674no—
550C22×C4—6716no—
551C22×C4—674no—
552C22×C4—674no—
553C22×C4—672no—
554C22×C4—672no—
555C22×C4—672no—
556C22×C4—672no—
557C22×C4—672no—
558C22×C4—672no—
559C22×C4—672no—
560C22×C4—1342no—
561C22×C4—1342no—
562C22×C4—1342no—
563C22×C4—1342no—
564C22×C4—1342no—
565C22×C4—1342no—
566C22×C4—1342no—
567C22×C4—1342no—
568C22×C4—1342no—
569C22×C4—1342no—
570C22×C4—1342no—
571C22×C4—1342no—
572C22×C4—1348no—
573C22×C4—13432no—
574C22×C4—1348no—
575C22×C4—1342no—
576C22×C4—1342no—
577C22×C4—1342no—
578C22×C4—1342no—
579C22×C4—1342no—
580C22×C4—1342no—
581C22×C4D4×D6714yes—
582C22×C4#1176162714yes—
583C22×C4C23×D6712yes—
584C22×C4C23×D6712yes—
585C22×C4C23×D6712yes—
586C22×C4C23×D6712yes—
587C22×C4C23×D6712yes—
588C22×C4C23×D6712yes—
589C4⋊C4—28no—
590C4⋊C4—28no—
591C4⋊C4—44no—
592C4⋊C4—2684no—
593C4⋊C4—2684no—
594C4⋊C4—2684no—
595C4⋊C4—6716no—
596C4⋊C4—1348no—
597C4⋊C4—1348no—
598C4⋊C4—1348no—
599C4⋊C4—1348no—
600C4⋊C4—1348no—
601C4⋊C4—1348no—
602C4⋊C4—1348no—
603C4⋊C4—1348no—
604C4⋊C4—1348no—
605C22⋊C4—28no—
606C22⋊C4—28no—
607C22⋊C4—44no—
608C22⋊C4—2684no—
609C22⋊C4—1348no—
610C22⋊C4—1348no—
611C42—1348no—
612C42—1348no—
613C42—1348no—
614C42—1348no—
615C23—28no—
616C23—28no—
617C23—28no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—44no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23C2×D4×D6712yes—
629C23C2×Q8×D6714yes—
630C23C2×Q8×D6712yes—
631C23#41×D6712yes—
632C23#41×D6712yes—
633C23C2×#1176162712yes—
634C23#1452408812yes—
635C23#1452409012yes—
636C23C24×D6711yescharacteristic
637C2×C4—28no—
638C2×C4—28no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
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—44no—
656C2×C4—44no—
657C2×C4—44no—
658C2×C4—44no—
659C2×C4—2684no—
660C2×C4—2684no—
661C2×C4—2684no—
662C2×C4—2684no—
663C2×C4—6716no—
664C2×C4—674no—
665C2×C4—674no—
666C2×C4—674no—
667C2×C4—674no—
668C2×C4—674no—
669C2×C4—674no—
670C2×C4—1342no—
671C2×C4—1342no—
672C2×C4—1342no—
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—13432no—
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×C4C2×D4×D6714yes—
693C2×C4C2×#1176162714yes—
694C22—24no—
695C22—24no—
696C22—24no—
697C22—416no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22C22⋊Q8×D6714yes—
703C22#1686394814yes—
704C22#1686402514yes—
705C22#1686404614yes—
706C22#1686406414yes—
707C22#1686408214yes—
708C22#1686408914yes—
709C22C22×D4×D6711yescharacteristic
710C22C22×Q8×D6711yescharacteristic
711C22C2×#41×D6711yescharacteristic
712C22C2×#41×D6711yescharacteristic
713C22C22×#1176162711yescharacteristic
714C22C2×#1452408811yescharacteristic
715C22C2×#1452409011yescharacteristic
716C4—24no—
717C4—24no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—2682no—
723C4—2682no—
724C4—2682no—
725C4—2682no—
726C4—678no—
727C4—1344no—
728C4—1344no—
729C4—1344no—
730C2—44no—
731C2#2256391718yesdirect product factor
732C2C2×C22⋊Q8×D6711yescharacteristic
733C2C2×#1686394811yescharacteristic
734C2C2×#1686402511yescharacteristic
735C2C2×#1686404611yescharacteristic
736C2C2×#1686406411yescharacteristic
737C2C2×#1686408211yescharacteristic
738C2C2×#1686408911yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×#396×C67C2
socleC24×C67C24
prime radicalC25×C67C23
hypercenterC2×#396D67
hypocenterC67C2×#2441
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#14524033C2semidirect
3. #22563917C2direct (N × H)
7. C2×#16863295C2semidirect
8. C2×#16863293C2semidirect
9. C2×#16863291C2semidirect
10. C2×#16863291C2semidirect
11. C2×#16863278C2semidirect
12. C2×#16863277C2semidirect
13. C2×#16863265C2semidirect
19. C2×#14524033C22semidirect
45. #16863295C22semidirect
46. #16863293C22semidirect
47. #16863291C22semidirect
48. #16863291C22semidirect
49. #16863278C22semidirect
50. #16863277C22semidirect
51. #16863265C22semidirect
362. C2×C67#2441semidirect
386. C67C2×#2441semidirect
731. C2#22563917direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240332
C22×#145239992
#225639172
C2×#168633322
C2×#168633192
C2×#168632952
C2×#168632932
C2×#168632912
C2×#168632782
C2×#168632772
C2×#168632652
C2×#168632542
C2×C22⋊C4×Dic672
C2×#396×C672
C2×#244167