Finite Group Databasebeta

← #30872239

Subgroups — #30872239

Order 17152.

1130 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863474C211yesmaximal, characteristic
2#22563138C211yesmaximal, characteristic
3#22561175C211yesmaximal, characteristic, complemented
4#22561167C211yesmaximal, characteristic, complemented
5#22560643C211yesmaximal, characteristic, complemented
6#22560643C211yesmaximal, characteristic, complemented
7#22560522C211yesmaximal, characteristic, complemented
8#22560517C211yesmaximal, characteristic, complemented
9#22560304C211yesmaximal, characteristic, complemented
10#22560299C211yesmaximal, characteristic, complemented
11#22560224C211yesmaximal, characteristic, complemented
12C4×#14523967C211yesmaximal, characteristic, complemented
13#22559930C211yesmaximal, characteristic, complemented
14#22559928C211yesmaximal, characteristic, complemented
15C2×#552×C67C211yesmaximal, characteristic
16C22×#11761612C2211yescharacteristic
17C22×#11761612C2211yescharacteristic
18C2×#14524002C2211yescharacteristic
19C22×C4⋊Dic67C2211yescharacteristic
20#16863474—24no—
21C2×C4⋊(C67⋊C8)C2211yescharacteristic
22C2×#14523967C2211yescharacteristic
23C2×#14523967C2211yescharacteristic
24C2×#14523967C2211yescharacteristic
25C2×#14523967C2211yescharacteristic
26C2×C22⋊(C67⋊C8)C2211yescharacteristic
27C2×C22⋊(C67⋊C8)C2211yescharacteristic
28C2×C4×C67⋊C8C2211yescharacteristic
29#16863289—21no—
30#16863282—21no—
31#16863276—21no—
32#16863262C2211yescharacteristic
33#16863256C2211yescharacteristic
34#16863256C2211yescharacteristic
35C4×C4⋊Dic67C2211yescharacteristic
36C22⋊C4×Dic67—21no—
37#16863158C2211yescharacteristic
38#16863158C2211yescharacteristic
39#16863158C2211yescharacteristic
40#16863158C2211yescharacteristic
41#16863158C2211yescharacteristic
42#16863158C2211yescharacteristic
43#16863158C2211yescharacteristic
44#16863158C2211yescharacteristic
45#16863158C2211yescharacteristic
46#16863158C2211yescharacteristic
47#16863158C2211yescharacteristic
48#16863158C2211yescharacteristic
49#552×C67—24no—
50#552×C67C418yescomplemented
51C2×#126×C67—21no—
52C2×#125×C67—21no—
53C2×#125×C67C2211yescharacteristic
54C2×#123×C67—21no—
55C2×C22⋊Q8×C67C2211yescharacteristic
56C2×C22⋊Q8×C67C2211yescharacteristic
57C2×C4×Q8×C67C2211yescharacteristic
58C2×C4×D4×C67C2211yescharacteristic
59C2×#117×C67—21no—
60C2×#117×C67C2211yescharacteristic
61C22×C4⋊C4×C67C2211yescharacteristic
62C23×Dic67—21no—
63C2×#11761612—22no—
64C2×#11761612—22no—
65C2×#11761612—22no—
66C2×#11761612—22no—
67C2×#11761612—41no—
68C2×#11761612—41no—
69C22×C67⋊C8C2311yescharacteristic
70C22×C67⋊C8C2311yescharacteristic
71C22×C67⋊C8C2311yescharacteristic
72C22×C67⋊C8C2311yescharacteristic
73#14524002—22no—
74#14524002—41no—
75C2×C4⋊Dic67—22no—
76C2×C4⋊Dic67—21no—
77C2×C4⋊Dic67—41no—
78C2×C4⋊Dic67C2311yescharacteristic
79C2×C4⋊Dic67C2311yescharacteristic
80C2×C4⋊Dic67C2311yescharacteristic
81C2×C4⋊Dic67C2311yescharacteristic
82C2×C22⋊Dic67—21no—
83C2×C22⋊Dic67—21no—
84C2×C22⋊Dic67—21no—
85C2×C4×Dic67—21no—
86C2×C4×Dic67—21no—
87C4⋊(C67⋊C8)—22no—
88#14523967—22no—
89#14523967—22no—
90#14523967—41no—
91#14523967—41no—
92C22⋊(C67⋊C8)—22no—
93C22⋊(C67⋊C8)—22no—
94C4×C67⋊C8—22no—
95C67⋊#95—21no—
96C67⋊#95—21no—
97C67⋊#95—21no—
98C67⋊#95—21no—
99C67⋊#95—21no—
100C22×Q8×C67C2311yescharacteristic
101C22×D4×C67D411yescharacteristic
102C23×C4×C67—21no—
103C23×C4×C67C2311yescharacteristic
104C23×C4×C67C2311yescharacteristic
105#126×C67—28no—
106#125×C67—28no—
107#125×C67—22no—
108#125×C67C2×C414yescomplemented
109#123×C67—28no—
110C22⋊Q8×C67—22no—
111C22⋊Q8×C67—22no—
112C22⋊Q8×C67C2×C414yes—
113C22⋊Q8×C67C2×C414yescomplemented
114C4×Q8×C67—22no—
115C4×Q8×C67C2×C414yescomplemented
116C4×D4×C67C2×C414yes—
117C4×D4×C67D414yes—
118#117×C67—22no—
119#117×C67—28no—
120#117×C67C2×C414yes—
121C2×C4⋊C4×C67—21no—
122C2×C4⋊C4×C67—22no—
123C2×C4⋊C4×C67—21no—
124C2×C4⋊C4×C67—21no—
125C2×C4⋊C4×C67—21no—
126C2×C4⋊C4×C67—21no—
127C2×C4⋊C4×C67—21no—
128C2×C4⋊C4×C67C2×C414yescomplemented
129C2×C4⋊C4×C67D411yescharacteristic
130C2×C4⋊C4×C67C2311yescharacteristic
131C2×C4⋊C4×C67C2311yescharacteristic
132C2×C4⋊C4×C67C2311yescharacteristic
133C2×C22⋊C4×C67—21no—
134C2×C22⋊C4×C67—21no—
135C2×C22⋊C4×C67—21no—
136C2×C22⋊C4×C67D411yescharacteristic
137C2×C22⋊C4×C67D411yescharacteristic
138C2×C42×C67—21no—
139C2×C42×C67—21no—
140C2×C42×C67C2311yescharacteristic
141C22×Dic67—21no—
142C22×Dic67—21no—
143C22×Dic67—21no—
144C22×Dic67—21no—
145C22×Dic67—42no—
146C22×Dic67—42no—
147C22×Dic67—81no—
148#11761612—44no—
149#11761612—44no—
150C2×C67⋊C8—21no—
151C2×C67⋊C8—21no—
152C2×C67⋊C8—21no—
153C2×C67⋊C8—21no—
154C2×C67⋊C8—21no—
155C2×C67⋊C8—21no—
156C2×C67⋊C8—21no—
157C2×C67⋊C8—21no—
158C2×C67⋊C8—21no—
159C2×C67⋊C8—21no—
160C2×C67⋊C8—21no—
161C2×C67⋊C8#4112yes—
162C4⋊Dic67—21no—
163C4⋊Dic67—21no—
164C4⋊Dic67—21no—
165C4⋊Dic67—21no—
166C4⋊Dic67—21no—
167C4⋊Dic67—21no—
168C4⋊Dic67—21no—
169C4⋊Dic67—42no—
170C4⋊Dic67#4112yes—
171C22⋊Dic67—42no—
172C22⋊Dic67—42no—
173C22⋊Dic67—81no—
174C4×Dic67—42no—
175C4×Dic67—81no—
176C24×C67C2×D411yescharacteristic
177C24×C67C2×D411yescharacteristic
178C2×Q8×C67—21no—
179C2×Q8×C67—21no—
180C2×Q8×C67—21no—
181C2×Q8×C67—21no—
182C2×Q8×C67—21no—
183C2×Q8×C67C22×C412yes—
184C2×D4×C67—41no—
185C2×D4×C67—41no—
186C2×D4×C67C22⋊C414yes—
187C22×C4×C67—21no—
188C22×C4×C67—21no—
189C22×C4×C67—21no—
190C22×C4×C67—21no—
191C22×C4×C67—21no—
192C22×C4×C67—21no—
193C22×C4×C67—21no—
194C22×C4×C67—21no—
195C22×C4×C67—24no—
196C22×C4×C67—21no—
197C22×C4×C67—21no—
198C22×C4×C67—21no—
199C22×C4×C67—21no—
200C22×C4×C67—42no—
201C22×C4×C67—42no—
202C22×C4×C67C22×C412yes—
203C22×C4×C67C22×C412yes—
204C22×C4×C67C2×D411yescharacteristic
205C22×C4×C67C2×D411yescharacteristic
206C22×C4×C67C2×D411yescharacteristic
207C22×C4×C67C2×D411yescharacteristic
208C22×C4×C67C2×D412yes—
209C22×C4×C67C2×D412yes—
210C22×C4×C67C2411yescharacteristic
211C4⋊C4×C67—24no—
212C4⋊C4×C67—24no—
213C4⋊C4×C67—24no—
214C4⋊C4×C67—24no—
215C4⋊C4×C67—24no—
216C4⋊C4×C67—24no—
217C4⋊C4×C67—21no—
218C4⋊C4×C67—21no—
219C4⋊C4×C67—21no—
220C4⋊C4×C67C22⋊C414yes—
221C4⋊C4×C67C22×C412yes—
222C4⋊C4×C67C22×C412yes—
223C4⋊C4×C67C22×C412yes—
224C22⋊C4×C67—24no—
225C22⋊C4×C67—24no—
226C22⋊C4×C67—24no—
227C22⋊C4×C67C22⋊C414yes—
228C22⋊C4×C67C22⋊C414yes—
229C42×C67—24no—
230C42×C67—24no—
231C42×C67C22×C412yes—
232C42×C67C2×D412yes—
233C23×C67—21no—
234C23×C67—21no—
235C23×C67—21no—
236C23×C67—21no—
237C23×C67—21no—
238C23×C67—21no—
239C23×C67—21no—
240C23×C67—21no—
241C23×C67—21no—
242C23×C67—21no—
243C23×C67—21no—
244C23×C67—21no—
245C23×C67C2×C22⋊C412yes—
246C23×C67C2×C22⋊C412yes—
247C23×C67C22×D411yescharacteristic
248Q8×C67—22no—
249Q8×C67—22no—
250Q8×C67—41no—
251Q8×C67—41no—
252D4×C67—44no—
253C2×C4×C67—21no—
254C2×C4×C67—21no—
255C2×C4×C67—21no—
256C2×C4×C67—21no—
257C2×C4×C67—21no—
258C2×C4×C67—21no—
259C2×C4×C67—21no—
260C2×C4×C67—21no—
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—22no—
268C2×C4×C67—22no—
269C2×C4×C67—22no—
270C2×C4×C67—22no—
271C2×C4×C67—22no—
272C2×C4×C67—22no—
273C2×C4×C67—48no—
274C2×C4×C67—41no—
275C2×C4×C67—41no—
276C2×C4×C67—41no—
277C2×C4×C67—41no—
278C2×C4×C67—41no—
279C2×C4×C67—41no—
280C2×C4×C67—41no—
281C2×C4×C67—41no—
282C2×C4×C67C2×C22⋊C412yes—
283C2×C4×C67C2×C22⋊C412yes—
284C2×C4×C67C2×C22⋊C412yes—
285C2×C4×C67C2×C22⋊C412yes—
286C2×C4×C67C23×C411yescharacteristic
287C2×C4×C67C22×D411yescharacteristic
288C2×C4×C67C2×#4111yescharacteristic
289C2×C4×C67C2×#4111yescharacteristic
290C2×C4×C67H(5,𝔽2)11yescharacteristic
291C2×C4×C672−1+411yescharacteristic
292C2×Dic67—22no—
293C2×Dic67—41no—
294C2×Dic67—41no—
295C2×Dic67—41no—
296C2×Dic67—41no—
297C2×Dic67—41no—
298C2×Dic67—41no—
299C2×Dic67—41no—
300C2×Dic67—41no—
301C2×Dic67—41no—
302C2×Dic67—41no—
303C2×Dic67—41no—
304C2×Dic67—84no—
305C67⋊C8—22no—
306C67⋊C8—41no—
307C67⋊C8—41no—
308C67⋊C8—41no—
309C22×C67—22no—
310C22×C67—22no—
311C22×C67—22no—
312C22×C67—22no—
313C22×C67—22no—
314C22×C67—22no—
315C22×C67—41no—
316C22×C67—41no—
317C22×C67—41no—
318C22×C67—41no—
319C22×C67—41no—
320C22×C67—41no—
321C22×C67—41no—
322C22×C67—41no—
323C22×C67C22×C22⋊C411yescharacteristic
324C22×C67#54611yescharacteristic
325C22×C67#54711yescharacteristic
326C22×C67#57511yescharacteristic
327C22×C67#57511yescharacteristic
328C22×C67#57711yescharacteristic
329C22×C67#57811yescharacteristic
330C4×C67—22no—
331C4×C67—22no—
332C4×C67—22no—
333C4×C67—22no—
334C4×C67—42no—
335C4×C67—42no—
336C4×C67—42no—
337C4×C67—42no—
338C4×C67C4×#4111yescharacteristic
339C4×C67#52011yescharacteristic
340C4×C67#54611yescharacteristic
341C4×C67#54711yescharacteristic
342Dic67—42no—
343Dic67—81no—
344Dic67—81no—
345Dic67—81no—
346#22499—671nomaximal, Sylow
347C2×C67—42no—
348C2×C67—42no—
349C2×C67#233911yescharacteristic
350C2×C67#289611yescharacteristic
351C2×C67#289811yescharacteristic
352C2×C67#332311yescharacteristic
353C2×C67#332711yescharacteristic
354C2×C67#335111yescharacteristic
355C2×C67#335211yescharacteristic
356C2×#552D6711yescharacteristic
357C2×#436—671no—
358#2352—671no—
359#1991—671no—
360#1989—671no—
361#1894—671no—
362#1894—671no—
363#1873—671no—
364#1872—671no—
365#1825—671no—
366#1824—671no—
367#1805—671no—
368C4×#103—671no—
369#1736—671no—
370#1736—671no—
371C67#2249911yescharacteristic, complemented, Sylow
372C22×M16—671no—
373C22×M16—671no—
374#552—24no—
375#552Dic6718yescomplemented
376C2×#126—21no—
377C2×#125—21no—
378C2×#125C2×D6711yescharacteristic
379C2×#123—21no—
380C2×C22⋊Q8C2×D6711yescharacteristic
381C2×C22⋊Q8C2×D6711yescharacteristic
382C2×C4×Q8C2×D6711yescharacteristic
383C2×C4×D4C2×D6711yescharacteristic
384C2×#117—21no—
385C2×#117—671no—
386C2×#117C2×D6711yescharacteristic
387C22×C4⋊C4—671no—
388C22×C4⋊C4C2×D6711yescharacteristic
389#436—1344no—
390C2×C4⋊C8—671no—
391C2×#103—671no—
392C2×#103—671no—
393C2×#103—671no—
394C2×#103—671no—
395C2×C22⋊C8—671no—
396C2×C22⋊C8—671no—
397C2×C4×C8—671no—
398#388—1341no—
399#387—1341no—
400#386—1341no—
401#382—671no—
402#380—671no—
403#380—671no—
404C4×C4⋊C4—671no—
405C4×C22⋊C4—1341no—
406#340—671no—
407#340—671no—
408#340—671no—
409#340—671no—
410#340—671no—
411#340—671no—
412#340—671no—
413#340—671no—
414#340—671no—
415#340—671no—
416#340—671no—
417#340—671no—
418C22×Q8C22×D6711yescharacteristic
419C22×D4C22⋊D6711yescharacteristic
420C23×C4—21no—
421C23×C4—1341no—
422C23×C4C22×D6711yescharacteristic
423C23×C4C22×D6711yescharacteristic
424C2×M16—2681no—
425C2×M16—2681no—
426C2×M16—1342no—
427C2×M16—1342no—
428C2×M16—1342no—
429C2×M16—1342no—
430C22×C8—671no—
431C22×C8—671no—
432C22×C8—671no—
433C22×C8—671no—
434#126—28no—
435#125—28no—
436#125—22no—
437#125C2×Dic6714yescomplemented
438#123—28no—
439C22⋊Q8—22no—
440C22⋊Q8—22no—
441C22⋊Q8C2×Dic6714yes—
442C22⋊Q8C2×Dic6714yescomplemented
443C4×Q8—22no—
444C4×Q8C2×Dic6714yescomplemented
445C4×D4C2×Dic6714yes—
446C4×D4C22⋊D6714yes—
447#117—22no—
448#117—28no—
449#117—2681no—
450#117—1342no—
451#117C2×Dic6714yes—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—2681no—
460C2×C4⋊C4—671no—
461C2×C4⋊C4—671no—
462C2×C4⋊C4—671no—
463C2×C4⋊C4—671no—
464C2×C4⋊C4—1341no—
465C2×C4⋊C4—1342no—
466C2×C4⋊C4C2×Dic6714yescomplemented
467C2×C4⋊C4C22⋊D6711yescharacteristic
468C2×C4⋊C4C22×D6711yescharacteristic
469C2×C4⋊C4C22×D6711yescharacteristic
470C2×C4⋊C4C22×D6711yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—1341no—
475C2×C22⋊C4—1341no—
476C2×C22⋊C4—1341no—
477C2×C22⋊C4C22⋊D6711yescharacteristic
478C2×C22⋊C4C22⋊D6711yescharacteristic
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—1341no—
482C2×C42—1341no—
483C2×C42C22×D6711yescharacteristic
484C4⋊C8—1342no—
485#103—2681no—
486#103—2681no—
487#103—1342no—
488#103—1342no—
489C22⋊C8—1342no—
490C22⋊C8—1342no—
491C4×C8—1342no—
492#95—1341no—
493#95—1341no—
494#95—1341no—
495#95—1341no—
496#95—1341no—
497C24C2×C22⋊D6711yescharacteristic
498C24C2×C22⋊D6711yescharacteristic
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8C22×Dic6712yes—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4C22⋊Dic6714yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—24no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—2682no—
524C22×C4—2682no—
525C22×C4—5361no—
526C22×C4—1341no—
527C22×C4—1341no—
528C22×C4—1341no—
529C22×C4—1341no—
530C22×C4C22×Dic6712yes—
531C22×C4C22×Dic6712yes—
532C22×C4C2×C22⋊D6711yescharacteristic
533C22×C4C2×C22⋊D6711yescharacteristic
534C22×C4C2×C22⋊D6711yescharacteristic
535C22×C4C2×C22⋊D6711yescharacteristic
536C22×C4C2×C22⋊D6712yes—
537C22×C4C2×C22⋊D6712yes—
538C22×C4C23×D6711yescharacteristic
539M16—2684no—
540M16—2684no—
541C2×C8—672no—
542C2×C8—1341no—
543C2×C8—1341no—
544C2×C8—1341no—
545C2×C8—1341no—
546C2×C8—1341no—
547C2×C8—1341no—
548C2×C8—1341no—
549C2×C8—1341no—
550C2×C8—1341no—
551C2×C8—1341no—
552C2×C8—1341no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—2682no—
563C4⋊C4—672no—
564C4⋊C4—1341no—
565C4⋊C4—1341no—
566C4⋊C4—1341no—
567C4⋊C4—1341no—
568C4⋊C4—1341no—
569C4⋊C4—1341no—
570C4⋊C4—1341no—
571C4⋊C4C22⋊Dic6714yes—
572C4⋊C4C22×Dic6712yes—
573C4⋊C4C22×Dic6712yes—
574C4⋊C4C22×Dic6712yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—2682no—
579C22⋊C4—2682no—
580C22⋊C4—5361no—
581C22⋊C4C22⋊Dic6714yes—
582C22⋊C4C22⋊Dic6714yes—
583C42—24no—
584C42—24no—
585C42—2682no—
586C42—5361no—
587C42C22×Dic6712yes—
588C42C2×C22⋊D6712yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23C2×C22⋊Dic6712yes—
602C23C2×C22⋊Dic6712yes—
603C23C22×C22⋊D6711yescharacteristic
604Q8—22no—
605Q8—22no—
606Q8—41no—
607Q8—41no—
608D4—44no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—48no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—2681no—
639C2×C4—2681no—
640C2×C4—2681no—
641C2×C4—2681no—
642C2×C4—2681no—
643C2×C4—2681no—
644C2×C4—2681no—
645C2×C4—2681no—
646C2×C4—2681no—
647C2×C4—2681no—
648C2×C4—2681no—
649C2×C4—5364no—
650C2×C4—1342no—
651C2×C4C2×C22⋊Dic6712yes—
652C2×C4C2×C22⋊Dic6712yes—
653C2×C4C2×C22⋊Dic6712yes—
654C2×C4C2×C22⋊Dic6712yes—
655C2×C4C23×Dic6711yescharacteristic
656C2×C4C22×C22⋊D6711yescharacteristic
657C2×C4#41×D6711yescharacteristic
658C2×C4#41×D6711yescharacteristic
659C2×C4#1452408911yescharacteristic
660C2×C4#1452409011yescharacteristic
661C8—2681no—
662C8—2681no—
663C8—2681no—
664C8—1342no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22C22×C22⋊Dic6711yescharacteristic
680C22#1686403411yescharacteristic
681C22#1686404511yescharacteristic
682C22#1686419411yescharacteristic
683C22#1686419411yescharacteristic
684C22#1686420411yescharacteristic
685C22#1686421111yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—42no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—2682no—
695C4—5361no—
696C4—5361no—
697C4—5361no—
698C4#41×Dic6711yescharacteristic
699C4#1686387911yescharacteristic
700C4#1686403411yescharacteristic
701C4#1686404511yescharacteristic
702C2—42no—
703C2—42no—
704C2#2256303911yescharacteristic
705C2#2256872811yescharacteristic
706C2#2256874211yescharacteristic
707C2#2257241911yescharacteristic
708C2#2257247111yescharacteristic
709C2#2257276911yescharacteristic
710C2#2257277811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC2×#552×C67C2
socleC23×C67C22×D4
prime radicalC22×D4×C67D4
cosocleC22×C4×C67C24
hypercenterC2×#552D67
hypocenterC67#22499
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
3. #22561175C2semidirect
4. #22561167C2semidirect
5. #22560643C2semidirect
6. #22560643C2semidirect
7. #22560522C2semidirect
8. #22560517C2semidirect
9. #22560304C2semidirect
10. #22560299C2semidirect
11. #22560224C2semidirect
12. C4×#14523967C2semidirect
13. #22559930C2semidirect
14. #22559928C2semidirect
50. #552×C67C4semidirect
108. #125×C67C2×C4semidirect
113. C22⋊Q8×C67C2×C4semidirect
115. C4×Q8×C67C2×C4semidirect
128. C2×C4⋊C4×C67C2×C4semidirect
371. C67#22499semidirect
375. #552Dic67semidirect
437. #125C2×Dic67semidirect
442. C22⋊Q8C2×Dic67semidirect
444. C4×Q8C2×Dic67semidirect
466. C2×C4⋊C4C2×Dic67semidirect

Maximal subgroups

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

subgroupindex
C2×#168634742
#225631382
#225611752
#225611672
#225606432
#225605222
#225605172
#225603042
#225602992
#225602242
C4×#145239672
#225599302
#225599282
C2×#552×C672
#2249967