Finite Group Databasebeta

← C2×#22569211 #31720313

Subgroups — C2×#22569211 #31720313

Order 17152.

2014 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863924C211yesmaximal, characteristic
2#22569211C2116yesmaximal, direct product factor
3C2×#16863525C211yesmaximal, characteristic, complemented
4C2×#16863520C211yesmaximal, characteristic, complemented
5C2×#16863473C211yesmaximal, characteristic, complemented
6C2×#16863471C211yesmaximal, characteristic, complemented
7C2×#16863471C211yesmaximal, characteristic, complemented
8C2×#16863466C211yesmaximal, characteristic, complemented
9C2×#16863464C211yesmaximal, characteristic, complemented
10C2×(C22⋊D67)⋊C8C211yesmaximal, characteristic, complemented
11C2×#16863458C211yesmaximal, characteristic, complemented
12C2×#16863447C211yesmaximal, characteristic, complemented
13C2×#16863352C211yesmaximal, characteristic, complemented
14C2×#16863350C211yesmaximal, characteristic, complemented
15C2×#16863348C211yesmaximal, characteristic, complemented
16C2×#433×C67C211yesmaximal, characteristic, complemented
17C22×#11761612C2211yescharacteristic
18C22×#11761611C2211yescharacteristic
19C22×#11761611C2211yescharacteristic
20C22×#11761611C2211yescharacteristic
21C23×C67⋊C8C2211yescharacteristic
22C22×C8×D67C2211yescharacteristic
23#16863924C418yes—
24#16863924C2218yes—
25C2×#14524038C411yescharacteristic
26C2×#14524036C411yescharacteristic
27C2×#14524033C411yescharacteristic
28C2×#14524029C411yescharacteristic
29C2×#14524028C411yescharacteristic
30C2×#14524025C411yescharacteristic
31C2×#14524021C411yescharacteristic
32C2×#14524016C411yescharacteristic
33C2×C4×Dic134C2211yescharacteristic
34C2×C4×D268C2211yescharacteristic
35C2×C4×C22⋊D67C2211yescharacteristic
36C2×C4×C22⋊D67C2211yescharacteristic
37C2×#14524000C2211yescharacteristic
38C2×C42×D67C2211yescharacteristic
39#16863525C2218yescomplemented
40#16863520C2218yescomplemented
41#16863473C2218yescomplemented
42#16863471C2218yescomplemented
43#16863471C2218yescomplemented
44#16863466C2218yescomplemented
45#16863464C2218yescomplemented
46(C22⋊D67)⋊C8C2218yescomplemented
47#16863458C2218yescomplemented
48#16863447C2218yescomplemented
49C2×Dic67⋊C8C2211yescharacteristic
50C2×Dic67⋊C8C2211yescharacteristic
51C2×Dic67⋊C8C2211yescharacteristic
52C2×Dic67⋊C8C2211yescharacteristic
53C2×(C2×D67)⋊C8C2211yescharacteristic
54C2×(C2×D67)⋊C8C2211yescharacteristic
55C2×(C2×D67)⋊C8C2211yescharacteristic
56C2×(C2×D67)⋊C8C2211yescharacteristic
57#16863352C2218yescomplemented
58#16863350C2218yescomplemented
59#16863348C2218yescomplemented
60C2×#14523954C2211yescharacteristic
61C2×#14523954C2211yescharacteristic
62C2×#14523953C2211yescharacteristic
63C2×C4×C67⋊C8C2211yescharacteristic
64C2×C4×C67⋊C8C2211yescharacteristic
65C2×C8×Dic67C2211yescharacteristic
66C2×C8×Dic67C2211yescharacteristic
67C2×C8×Dic67C2211yescharacteristic
68C2×#117×C67C2211yescharacteristic
69#433×C67C2218yescomplemented
70C2×C4⋊C8×C67C2211yescharacteristic
71C2×C4⋊C8×C67C2211yescharacteristic
72C2×C22⋊C8×C67C2211yescharacteristic
73C2×C22⋊C8×C67C2211yescharacteristic
74C2×#97×C67C2211yescharacteristic
75C2×C4×C8×C67C2211yescharacteristic
76C22×Dic134C2×C411yescharacteristic
77C22×D268C2×C411yescharacteristic
78C22×C22⋊D67C2×C411yescharacteristic
79C22×C22⋊D67C2×C411yescharacteristic
80C22×C4×D67C2×C411yescharacteristic
81C22×C4×D67C2×C411yescharacteristic
82C22×C4×D67C2311yescharacteristic
83C22×C4×D67C2311yescharacteristic
84C2×#11761612—24no—
85C2×#11761612C2314yes—
86C2×#11761611—24no—
87C2×#11761611—24no—
88C2×#11761611—24no—
89C2×#11761611C2314yes—
90C2×#11761611C2314yes—
91C2×#11761611C2314yes—
92C22×C67⋊C8—24no—
93C22×C67⋊C8C2311yescharacteristic
94C22×C67⋊C8C2311yescharacteristic
95C22×C67⋊C8C2314yes—
96C22×C67⋊C8C2311yescharacteristic
97C22×C67⋊C8C2311yescharacteristic
98C2×C8×D67—24no—
99C2×C8×D67C2314yes—
100#14524038C2×C418yes—
101#14524036C2×C418yes—
102#14524033C2×C418yes—
103#14524029C2×C418yes—
104#14524028C2×C418yes—
105#14524025C2×C418yes—
106#14524021C2×C418yes—
107#14524016C2×C418yes—
108C4×Dic134C2×C414yes—
109C4×Dic134C2314yes—
110C4×D268C2×C414yes—
111C4×D268C2314yes—
112C4×C22⋊D67C2×C414yes—
113C4×C22⋊D67C2×C414yes—
114C4×C22⋊D67C2314yes—
115C4×C22⋊D67C2314yes—
116#14524000C2×C414yes—
117#14524000C2314yes—
118C2×C4⋊Dic67C2×C411yescharacteristic
119C2×C4⋊Dic67C2×C411yescharacteristic
120C2×Dic67⋊C4C2×C411yescharacteristic
121C2×Dic67⋊C4C2×C411yescharacteristic
122C2×Dic67⋊C4C2×C411yescharacteristic
123C2×Dic67⋊C4C2×C411yescharacteristic
124C2×Dic67⋊C4C2×C411yescharacteristic
125C2×Dic67⋊C4C2×C411yescharacteristic
126C2×C22⋊Dic67C2×C411yescharacteristic
127C2×C22⋊Dic67C2×C411yescharacteristic
128C2×(C2×D67)⋊C4C2×C411yescharacteristic
129C2×(C2×D67)⋊C4C2×C411yescharacteristic
130C2×(C2×D67)⋊C4C2×C411yescharacteristic
131C2×(C2×D67)⋊C4C2×C411yescharacteristic
132C2×(C2×D67)⋊C4C2×C411yescharacteristic
133C2×(C2×D67)⋊C4C2×C411yescharacteristic
134C2×C4×Dic67C2×C411yescharacteristic
135C2×C4×Dic67C2×C411yescharacteristic
136C2×C4×Dic67C2311yescharacteristic
137C2×C4×Dic67C2311yescharacteristic
138C42×D67C2×C414yes—
139C42×D67C2314yes—
140Dic67⋊C8C2314yes—
141Dic67⋊C8C2314yes—
142Dic67⋊C8C2314yes—
143Dic67⋊C8C2314yes—
144(C2×D67)⋊C8C2314yes—
145(C2×D67)⋊C8C2314yes—
146(C2×D67)⋊C8C2314yes—
147(C2×D67)⋊C8C2314yes—
148#14523954C2314yes—
149#14523954C2314yes—
150#14523953C2314yes—
151C4×C67⋊C8C2314yes—
152C4×C67⋊C8C2314yes—
153C8×Dic67C2314yes—
154C8×Dic67C2314yes—
155C8×Dic67C2314yes—
156C23×C4×C67C2311yescharacteristic
157C22×C8×C67C2311yescharacteristic
158C22×C8×C67C2311yescharacteristic
159C22×C8×C67C2311yescharacteristic
160C22×C8×C67C2311yescharacteristic
161#117×C67C2×C414yes—
162#117×C67C2314yes—
163C2×C4⋊C4×C67C2×C411yescharacteristic
164C2×C4⋊C4×C67C2×C411yescharacteristic
165C2×C22⋊C4×C67C2×C411yescharacteristic
166C2×C22⋊C4×C67C2×C411yescharacteristic
167C2×C42×C67C2311yescharacteristic
168C2×C42×C67C2311yescharacteristic
169C4⋊C8×C67C2314yes—
170C4⋊C8×C67C2314yes—
171C22⋊C8×C67C2314yes—
172C22⋊C8×C67C2314yes—
173#97×C67C2314yes—
174C4×C8×C67C2314yes—
175C23×D67C22×C411yescharacteristic
176C23×D67C22×C411yescharacteristic
177C2×Dic134—24no—
178C2×Dic134C22×C414yes—
179C2×D268—42no—
180C2×D268C22×C414yes—
181C2×C22⋊D67—24no—
182C2×C22⋊D67—42no—
183C2×C22⋊D67C22×C414yes—
184C2×C22⋊D67C22×C414yes—
185C22×Dic67C22×C411yescharacteristic
186C22×Dic67C22×C411yescharacteristic
187C22×Dic67C22×C411yescharacteristic
188C22×Dic67C22×C411yescharacteristic
189C22×Dic67C22×C411yescharacteristic
190C22×Dic67C22×C411yescharacteristic
191C2×C4×D67—22no—
192C2×C4×D67—22no—
193C2×C4×D67—22no—
194C2×C4×D67—22no—
195C2×C4×D67—24no—
196C2×C4×D67—42no—
197C2×C4×D67C22×C412yes—
198C2×C4×D67C22×C414yes—
199C2×C4×D67C22×C412yes—
200C2×C4×D67C22×C414yes—
201C2×C4×D67C2412yes—
202C2×C4×D67C2412yes—
203#11761612—28no—
204#11761611—28no—
205#11761611—28no—
206#11761611—28no—
207C2×C67⋊C8—22no—
208C2×C67⋊C8—22no—
209C2×C67⋊C8—28no—
210C2×C67⋊C8#4114yes—
211C2×C67⋊C8#4114yes—
212C2×C67⋊C8C2412yes—
213C2×C67⋊C8C2412yes—
214C2×C67⋊C8C2412yes—
215C2×C67⋊C8C2412yes—
216C8×D67—28no—
217C4⋊Dic67C22×C414yes—
218C4⋊Dic67C22×C414yes—
219Dic67⋊C4C22×C414yes—
220Dic67⋊C4C22×C414yes—
221Dic67⋊C4C22×C414yes—
222Dic67⋊C4C22×C414yes—
223Dic67⋊C4C22×C414yes—
224Dic67⋊C4C22×C414yes—
225C22⋊Dic67C22×C414yes—
226C22⋊Dic67C22×C414yes—
227(C2×D67)⋊C4C22×C414yes—
228(C2×D67)⋊C4C22×C414yes—
229(C2×D67)⋊C4C22×C414yes—
230(C2×D67)⋊C4C22×C414yes—
231(C2×D67)⋊C4C22×C414yes—
232(C2×D67)⋊C4C22×C414yes—
233C4×Dic67C22×C412yes—
234C4×Dic67C22×C414yes—
235C4×Dic67C22×C414yes—
236C4×Dic67C22×C412yes—
237C4×Dic67C2412yes—
238C4×Dic67C2412yes—
239C24×C67C22×C411yescharacteristic
240C22×C4×C67—22no—
241C22×C4×C67—22no—
242C22×C4×C67C22×C411yescharacteristic
243C22×C4×C67C22×C411yescharacteristic
244C22×C4×C67C22×C411yescharacteristic
245C22×C4×C67C22×C411yescharacteristic
246C22×C4×C67C22×C411yescharacteristic
247C22×C4×C67C22×C412yes—
248C22×C4×C67C2412yes—
249C22×C4×C67C2411yescharacteristic
250C2×C8×C67—22no—
251C2×C8×C67—22no—
252C2×C8×C67—22no—
253C2×C8×C67—22no—
254C2×C8×C67C2412yes—
255C2×C8×C67C2412yes—
256C2×C8×C67C2412yes—
257C2×C8×C67C2412yes—
258C4⋊C4×C67C22×C414yes—
259C4⋊C4×C67C22×C414yes—
260C22⋊C4×C67C22×C414yes—
261C22⋊C4×C67C22×C414yes—
262C42×C67C22×C412yes—
263C42×C67C22×C412yes—
264C42×C67C2412yes—
265C42×C67C2412yes—
266C23×C67—22no—
267C23×C67—22no—
268C23×C67—22no—
269C23×C67C23×C412yes—
270C23×C67C23×C411yescharacteristic
271C22×D67—22no—
272C22×D67—22no—
273C22×D67—22no—
274C22×D67—22no—
275C22×D67—22no—
276C22×D67—22no—
277C22×D67C23×C412yes—
278C22×D67C23×C412yes—
279C2×C4×C67—22no—
280C2×C4×C67—22no—
281C2×C4×C67—22no—
282C2×C4×C67—22no—
283C2×C4×C67—22no—
284C2×C4×C67—24no—
285C2×C4×C67—22no—
286C2×C4×C67—22no—
287C2×C4×C67C23×C412yes—
288C2×C4×C67C23×C412yes—
289C2×C4×C67C23×C412yes—
290C2×C4×C67C23×C412yes—
291C2×C4×C67C23×C412yes—
292C2×C4×C67C23×C411yescharacteristic
293C2×C4×C67C2×#4112yes—
294C2×C4×C67C2×#4112yes—
295C2×C4×C67C2511yescharacteristic
296C22⋊D67—28no—
297C22⋊D67—44no—
298C2×Dic67—22no—
299C2×Dic67—22no—
300C2×Dic67—22no—
301C2×Dic67—22no—
302C2×Dic67—22no—
303C2×Dic67#13114yes—
304C2×Dic67C23×C412yes—
305C2×Dic67C23×C412yes—
306C2×Dic67C23×C412yes—
307C2×Dic67C23×C412yes—
308C2×Dic67C23×C412yes—
309C2×Dic67C23×C412yes—
310D268—44no—
311C4×D67—24no—
312C4×D67—24no—
313C4×D67—22no—
314C4×D67—22no—
315C4×D67—22no—
316C4×D67—22no—
317C4×D67—28no—
318C4×D67—44no—
319Dic134—28no—
320C8×C67—22no—
321C8×C67—22no—
322C8×C67—22no—
323C8×C67—22no—
324C67⋊C8—22no—
325C67⋊C8—22no—
326C67⋊C8C2×#4114yes—
327C67⋊C8C2×#4114yes—
328C22×C67—22no—
329C22×C67—22no—
330C22×C67—22no—
331C22×C67—44no—
332C22×C67C4×#4112yes—
333C22×C67C2×#13112yes—
334C22×C67#56812yes—
335C22×C67C24×C411yescharacteristic
336C2×D67—22no—
337C2×D67—22no—
338C2×D67—22no—
339C2×D67—22no—
340C2×D67—22no—
341C2×D67—22no—
342C2×D67—44no—
343C2×D67—44no—
344C4×C67—22no—
345C4×C67—22no—
346C4×C67—22no—
347C4×C67—22no—
348C4×C67—22no—
349C4×C67C4×#4112yes—
350C4×C67C22×#4111yescharacteristic
351C4×C67C22×#4111yescharacteristic
352Dic67—22no—
353Dic67—22no—
354Dic67—22no—
355Dic67—22no—
356Dic67—22no—
357Dic67C2×#13114yes—
358C2×#2969—671nomaximal, Sylow
359C2×C67—42no—
360C2×C67#296914yescomplemented
361C2×C67C2×C4×#4111yescharacteristic
362C2×C67C22×#13111yescharacteristic
363C2×C67C2×#56811yescharacteristic
364D67—42no—
365D67—42no—
366C2×#529—671no—
367#2969—6716no—
368C2×#446—671no—
369C2×C8×Q8—671no—
370C2×#436—671no—
371C2×#436—671no—
372C2×#436—671no—
373C2×#435—671no—
374C2×#435—671no—
375C2×C8×D4—671no—
376C2×#433—671no—
377C2×#433D6711yescharacteristic, complemented
378C2×#431—671no—
379C2×#405—671no—
380C2×#405—671no—
381C2×C4×M16—671no—
382C67C2×#296911yescharacteristic, complemented, Sylow
383C22×M16—671no—
384C22×M16—671no—
385C22×M16—671no—
386C22×M16—671no—
387C23×C8—671no—
388C23×C8—671no—
389#529—678no—
390#529—678no—
391C2×#126—671no—
392C2×#126—671no—
393C2×#125—671no—
394C2×#124—671no—
395C2×#123—671no—
396C2×#123—671no—
397C2×C22⋊Q8—671no—
398C2×#121—671no—
399C2×C4×Q8—671no—
400C2×C4×D4—671no—
401C2×C4×D4—671no—
402C2×C4×D4—671no—
403C2×#117—671no—
404C2×#117C2×D6711yescharacteristic
405C22×C42—671no—
406#446—678no—
407C8×Q8—678no—
408#436—678no—
409#436—678no—
410#436—678no—
411#435—678no—
412#435—678no—
413C8×D4—678no—
414#433—678no—
415#433C2×D6718yescomplemented
416#431—678no—
417C2×C4⋊C8—671no—
418C2×C4⋊C8—671no—
419C2×C4⋊C8—671no—
420C2×C4⋊C8—671no—
421C2×C4⋊C8C2×D6711yescharacteristic
422C2×C4⋊C8C2×D6711yescharacteristic
423C2×C22⋊C8—671no—
424C2×C22⋊C8—671no—
425C2×C22⋊C8—671no—
426C2×C22⋊C8—671no—
427C2×C22⋊C8C2×D6711yescharacteristic
428C2×C22⋊C8C2×D6711yescharacteristic
429#405—678no—
430#405—678no—
431C4×M16—678no—
432C2×#97—671no—
433C2×#97—671no—
434C2×#97—671no—
435C2×#97C2×D6711yescharacteristic
436C2×C4×C8—671no—
437C2×C4×C8—671no—
438C2×C4×C8—671no—
439C2×C4×C8—671no—
440C2×C4×C8—671no—
441C2×C4×C8C2×D6711yescharacteristic
442C22×Q8—671no—
443C22×D4—671no—
444C22×D4—671no—
445C22×D4—671no—
446C23×C4—671no—
447C23×C4—671no—
448C23×C4—671no—
449C23×C4—671no—
450C23×C4C22×D6711yescharacteristic
451C2×M16—674no—
452C2×M16—674no—
453C2×M16—674no—
454C2×M16—674no—
455C2×M16—1344no—
456C2×M16—1344no—
457C2×M16—1344no—
458C2×M16—1344no—
459C22×C8—671no—
460C22×C8—671no—
461C22×C8—674no—
462C22×C8—671no—
463C22×C8—671no—
464C22×C8—674no—
465C22×C8—1344no—
466C22×C8—1344no—
467C22×C8C22×D6711yescharacteristic
468C22×C8C22×D6711yescharacteristic
469C22×C8C22×D6711yescharacteristic
470C22×C8C22×D6711yescharacteristic
471#126—678no—
472#126—678no—
473#125—678no—
474#124—678no—
475#123—678no—
476#123—678no—
477C22⋊Q8—678no—
478#121—678no—
479C4×Q8—674no—
480C4×Q8—674no—
481C4×D4—674no—
482C4×D4—674no—
483C4×D4—674no—
484C4×D4—674no—
485C4×D4—674no—
486C4×D4—674no—
487#117—674no—
488#117—674no—
489#117C4×D6714yes—
490#117C22×D6714yes—
491C2×C4⋊C4—671no—
492C2×C4⋊C4—671no—
493C2×C4⋊C4—671no—
494C2×C4⋊C4—671no—
495C2×C4⋊C4—671no—
496C2×C4⋊C4—671no—
497C2×C4⋊C4—671no—
498C2×C4⋊C4—671no—
499C2×C4⋊C4C4×D6711yescharacteristic
500C2×C4⋊C4C4×D6711yescharacteristic
501C2×C22⋊C4—671no—
502C2×C22⋊C4—671no—
503C2×C22⋊C4—671no—
504C2×C22⋊C4—671no—
505C2×C22⋊C4—671no—
506C2×C22⋊C4—671no—
507C2×C22⋊C4—671no—
508C2×C22⋊C4—671no—
509C2×C22⋊C4C4×D6711yescharacteristic
510C2×C22⋊C4C4×D6711yescharacteristic
511C2×C42—671no—
512C2×C42—671no—
513C2×C42—671no—
514C2×C42—671no—
515C2×C42—674no—
516C2×C42—674no—
517C2×C42C22×D6711yescharacteristic
518C2×C42C22×D6711yescharacteristic
519C4⋊C8—674no—
520C4⋊C8—674no—
521C4⋊C8—674no—
522C4⋊C8—674no—
523C4⋊C8C22×D6714yes—
524C4⋊C8C22×D6714yes—
525C22⋊C8—674no—
526C22⋊C8—674no—
527C22⋊C8—674no—
528C22⋊C8—674no—
529C22⋊C8C22×D6714yes—
530C22⋊C8C22×D6714yes—
531#97—674no—
532#97—674no—
533#97—674no—
534#97C22×D6714yes—
535C4×C8—674no—
536C4×C8—674no—
537C4×C8—674no—
538C4×C8—674no—
539C4×C8—674no—
540C4×C8C22×D6714yes—
541C24—671no—
542C24—671no—
543C24C2×C4×D6711yescharacteristic
544C2×Q8—674no—
545C2×Q8—1344no—
546C2×D4—2682no—
547C2×D4—2682no—
548C2×D4—674no—
549C2×D4—674no—
550C2×D4—674no—
551C2×D4—1344no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—2682no—
555C22×C4—674no—
556C22×C4—671no—
557C22×C4—671no—
558C22×C4—671no—
559C22×C4—671no—
560C22×C4—671no—
561C22×C4—671no—
562C22×C4—672no—
563C22×C4—674no—
564C22×C4—672no—
565C22×C4—672no—
566C22×C4—672no—
567C22×C4—1344no—
568C22×C4—1342no—
569C22×C4—1342no—
570C22×C4—1342no—
571C22×C4—1342no—
572C22×C4C2×C4×D6711yescharacteristic
573C22×C4C2×C4×D6711yescharacteristic
574C22×C4C2×C4×D6711yescharacteristic
575C22×C4C2×C4×D6711yescharacteristic
576C22×C4C2×C4×D6711yescharacteristic
577C22×C4C2×C4×D6712yes—
578C22×C4C23×D6712yes—
579C22×C4C23×D6711yescharacteristic
580M16—1348no—
581M16—1348no—
582M16—1348no—
583M16—1348no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—674no—
589C2×C8—674no—
590C2×C8—672no—
591C2×C8—672no—
592C2×C8—672no—
593C2×C8—672no—
594C2×C8—1348no—
595C2×C8—1348no—
596C2×C8—1342no—
597C2×C8—1342no—
598C2×C8C23×D6712yes—
599C2×C8C23×D6712yes—
600C2×C8C23×D6712yes—
601C2×C8C23×D6712yes—
602C4⋊C4—674no—
603C4⋊C4—674no—
604C4⋊C4—674no—
605C4⋊C4—674no—
606C4⋊C4—674no—
607C4⋊C4—674no—
608C4⋊C4—674no—
609C4⋊C4—674no—
610C4⋊C4C2×C4×D6714yes—
611C4⋊C4C2×C4×D6714yes—
612C22⋊C4—674no—
613C22⋊C4—674no—
614C22⋊C4—674no—
615C22⋊C4—674no—
616C22⋊C4—674no—
617C22⋊C4—674no—
618C22⋊C4—674no—
619C22⋊C4—674no—
620C22⋊C4C2×C4×D6714yes—
621C22⋊C4C2×C4×D6714yes—
622C42—672no—
623C42—674no—
624C42—674no—
625C42—672no—
626C42—672no—
627C42—672no—
628C42C2×C4×D6712yes—
629C42C2×C4×D6712yes—
630C42C23×D6712yes—
631C42C23×D6712yes—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—672no—
636C23—672no—
637C23—1342no—
638C23—1342no—
639C23—1342no—
640C23—1342no—
641C23—1342no—
642C23—1342no—
643C23C22×C4×D6712yes—
644C23C22×C4×D6711yescharacteristic
645Q8—1348no—
646D4—2684no—
647D4—2684no—
648D4—1348no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—2684no—
658C2×C4—674no—
659C2×C4—672no—
660C2×C4—672no—
661C2×C4—672no—
662C2×C4—672no—
663C2×C4—672no—
664C2×C4—672no—
665C2×C4—1348no—
666C2×C4—1342no—
667C2×C4—1342no—
668C2×C4—1342no—
669C2×C4—1342no—
670C2×C4—1342no—
671C2×C4—1344no—
672C2×C4—1344no—
673C2×C4—1342no—
674C2×C4—1342no—
675C2×C4—1342no—
676C2×C4—1342no—
677C2×C4C22×C4×D6712yes—
678C2×C4C22×C4×D6712yes—
679C2×C4C22×C4×D6712yes—
680C2×C4C22×C4×D6712yes—
681C2×C4C22×C4×D6712yes—
682C2×C4C22×C4×D6711yescharacteristic
683C2×C4#41×D6712yes—
684C2×C4#41×D6712yes—
685C2×C4C24×D6711yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—22no—
690C8—674no—
691C8—674no—
692C8—1342no—
693C8—1342no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—44no—
698C22—2684no—
699C22—2684no—
700C22—1342no—
701C22—1342no—
702C22—1342no—
703C22—1342no—
704C22—1342no—
705C22—1342no—
706C22#1686386412yes—
707C22#131×D6712yes—
708C22#1686416112yes—
709C22C23×C4×D6711yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—674no—
716C4—1342no—
717C4—1342no—
718C4—1342no—
719C4—1342no—
720C4—1342no—
721C4#1686386412yes—
722C4C2×#41×D6711yescharacteristic
723C4C2×#41×D6711yescharacteristic
724C2—42no—
725C2—2682no—
726C2—2682no—
727C2#2256921114yesdirect product factor
728C2C2×#1686386411yescharacteristic
729C2C2×#131×D6711yescharacteristic
730C2C2×#1686416111yescharacteristic
subgroupG/H
centerC22×C4C23×D67
commutatorC22×C67C24×C4
FrattiniC2×C4C24×D67
FittingC2×#433×C67C2
socleC23×C67C23×C4
prime radicalC2×#14524016C4
cosocleC2×C4×C67C25
hypercenterC2×#433D67
hypocenterC67C2×#2969
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #22569211C2direct (N × H)
3. C2×#16863525C2semidirect
4. C2×#16863520C2semidirect
5. C2×#16863473C2semidirect
6. C2×#16863471C2semidirect
7. C2×#16863471C2semidirect
8. C2×#16863466C2semidirect
9. C2×#16863464C2semidirect
10. C2×(C22⋊D67)⋊C8C2semidirect
11. C2×#16863458C2semidirect
12. C2×#16863447C2semidirect
13. C2×#16863352C2semidirect
14. C2×#16863350C2semidirect
15. C2×#16863348C2semidirect
16. C2×#433×C67C2semidirect
39. #16863525C22semidirect
40. #16863520C22semidirect
41. #16863473C22semidirect
42. #16863471C22semidirect
43. #16863471C22semidirect
44. #16863466C22semidirect
45. #16863464C22semidirect
46. (C22⋊D67)⋊C8C22semidirect
47. #16863458C22semidirect
48. #16863447C22semidirect
57. #16863352C22semidirect
58. #16863350C22semidirect
59. #16863348C22semidirect
69. #433×C67C22semidirect
360. C2×C67#2969semidirect
377. C2×#433D67semidirect
382. C67C2×#2969semidirect
415. #433C2×D67semidirect
727. C2#22569211direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168639242
#225692112
C2×#168635252
C2×#168635202
C2×#168634732
C2×#168634712
C2×#168634662
C2×#168634642
C2×(C22⋊D67)⋊C82
C2×#168634582
C2×#168634472
C2×#168633522
C2×#168633502
C2×#168633482
C2×#433×C672
C2×#296967