Finite Group Databasebeta

← #30872209

Subgroups — #30872209

Order 17152.

1174 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863468C211yesmaximal, characteristic
2#22563138C211yesmaximal, characteristic
3#22561183C211yesmaximal, characteristic, complemented
4#22561162C211yesmaximal, characteristic, complemented
5#22560643C211yesmaximal, characteristic, complemented
6#22560633C211yesmaximal, characteristic, complemented
7#22560522C211yesmaximal, characteristic, complemented
8#22560517C211yesmaximal, characteristic, complemented
9#22560299C211yesmaximal, characteristic, complemented
10#22560295C211yesmaximal, characteristic, complemented
11#22560224C211yesmaximal, characteristic, complemented
12#22560039C211yesmaximal, characteristic, complemented
13#22559928C211yesmaximal, characteristic, complemented
14C2×#16863158C211yesmaximal, characteristic, complemented
15C2×#554×C67C211yesmaximal, characteristic
16C22×#11761612C2211yescharacteristic
17C23×C67⋊C8C2211yescharacteristic
18C2×#14524002C2211yescharacteristic
19C22×C4⋊Dic67C2211yescharacteristic
20#16863468—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×#14523954C2211yescharacteristic
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#554×C67—24no—
50#554×C67C418yescomplemented
51C2×C4⋊Q8×C67C2211yescharacteristic
52C2×#125×C67—21no—
53C2×C22⋊Q8×C67—21no—
54C2×C22⋊Q8×C67—21no—
55C2×C22⋊Q8×C67C2211yescharacteristic
56C2×C22⋊Q8×C67C2211yescharacteristic
57C2×C4×Q8×C67C2211yescharacteristic
58C2×C4×D4×C67—21no—
59C2×C4×D4×C67C2211yescharacteristic
60C22×C4⋊C4×C67C2211yescharacteristic
61C22×C4⋊C4×C67C2211yescharacteristic
62C23×Dic67—21no—
63C2×#11761612—22no—
64C2×#11761612—22no—
65C2×#11761612—41no—
66C22×C67⋊C8—22no—
67C22×C67⋊C8—22no—
68C22×C67⋊C8—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—
94#14523954—22no—
95C67⋊#95—21no—
96C67⋊#95—21no—
97C67⋊#95—21no—
98C67⋊#95—21no—
99C67⋊#95—21no—
100C22×Q8×C67—21no—
101C22×Q8×C67C2311yescharacteristic
102C22×D4×C67D411yescharacteristic
103C23×C4×C67—21no—
104C23×C4×C67—21no—
105C23×C4×C67C2311yescharacteristic
106C23×C4×C67C2311yescharacteristic
107C4⋊Q8×C67—22no—
108C4⋊Q8×C67C2×C414yescomplemented
109#125×C67—28no—
110C22⋊Q8×C67—22no—
111C22⋊Q8×C67—22no—
112C22⋊Q8×C67—28no—
113C22⋊Q8×C67—28no—
114C22⋊Q8×C67C2×C414yes—
115C22⋊Q8×C67C2×C414yescomplemented
116C4×Q8×C67—22no—
117C4×Q8×C67C2×C414yescomplemented
118C4×D4×C67—28no—
119C4×D4×C67C2×C414yes—
120C4×D4×C67D414yes—
121C2×C4⋊C4×C67—21no—
122C2×C4⋊C4×C67—21no—
123C2×C4⋊C4×C67—22no—
124C2×C4⋊C4×C67—22no—
125C2×C4⋊C4×C67—21no—
126C2×C4⋊C4×C67—21no—
127C2×C4⋊C4×C67—21no—
128C2×C4⋊C4×C67—21no—
129C2×C4⋊C4×C67C2×C414yes—
130C2×C4⋊C4×C67C2×C414yescomplemented
131C2×C4⋊C4×C67D411yescharacteristic
132C2×C4⋊C4×C67C2311yescharacteristic
133C2×C4⋊C4×C67C2311yescharacteristic
134C2×C4⋊C4×C67C2311yescharacteristic
135C2×C22⋊C4×C67—21no—
136C2×C22⋊C4×C67—21no—
137C2×C22⋊C4×C67D411yescharacteristic
138C2×C22⋊C4×C67D411yescharacteristic
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—
149C2×C67⋊C8—21no—
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—44no—
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—24no—
179C2×Q8×C67—21no—
180C2×Q8×C67—21no—
181C2×Q8×C67—21no—
182C2×Q8×C67—21no—
183C2×Q8×C67—21no—
184C2×Q8×C67—81no—
185C2×Q8×C67—81no—
186C2×Q8×C67C22×C412yes—
187C2×D4×C67—22no—
188C2×D4×C67—22no—
189C2×D4×C67C22⋊C414yes—
190C22×C4×C67—21no—
191C22×C4×C67—21no—
192C22×C4×C67—21no—
193C22×C4×C67—21no—
194C22×C4×C67—21no—
195C22×C4×C67—21no—
196C22×C4×C67—21no—
197C22×C4×C67—21no—
198C22×C4×C67—21no—
199C22×C4×C67—21no—
200C22×C4×C67—21no—
201C22×C4×C67—21no—
202C22×C4×C67—24no—
203C22×C4×C67—24no—
204C22×C4×C67—81no—
205C22×C4×C67—81no—
206C22×C4×C67—81no—
207C22×C4×C67—81no—
208C22×C4×C67C22×C412yes—
209C22×C4×C67C22×C412yes—
210C22×C4×C67C2×D411yescharacteristic
211C22×C4×C67C2×D411yescharacteristic
212C22×C4×C67C2×D411yescharacteristic
213C22×C4×C67C2×D411yescharacteristic
214C22×C4×C67C2×D412yes—
215C22×C4×C67C2×D412yes—
216C22×C4×C67C2411yescharacteristic
217C4⋊C4×C67—24no—
218C4⋊C4×C67—24no—
219C4⋊C4×C67—24no—
220C4⋊C4×C67—24no—
221C4⋊C4×C67—24no—
222C4⋊C4×C67—24no—
223C4⋊C4×C67—21no—
224C4⋊C4×C67—21no—
225C4⋊C4×C67—21no—
226C4⋊C4×C67C22⋊C414yes—
227C4⋊C4×C67C22×C412yes—
228C4⋊C4×C67C22×C412yes—
229C4⋊C4×C67C22×C412yes—
230C22⋊C4×C67—24no—
231C22⋊C4×C67—24no—
232C22⋊C4×C67C22⋊C414yes—
233C22⋊C4×C67C22⋊C414yes—
234C42×C67—24no—
235C42×C67C22×C412yes—
236C42×C67C2×D412yes—
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×C67—21no—
246C23×C67—21no—
247C23×C67C2×C22⋊C412yes—
248C23×C67C2×C22⋊C412yes—
249C23×C67#13712yes—
250C23×C67#13712yes—
251C23×C67C22×D411yescharacteristic
252Q8×C67—22no—
253Q8×C67—22no—
254Q8×C67—41no—
255Q8×C67—41no—
256Q8×C67—84no—
257D4×C67—28no—
258C2×C4×C67—21no—
259C2×C4×C67—21no—
260C2×C4×C67—21no—
261C2×C4×C67—21no—
262C2×C4×C67—21no—
263C2×C4×C67—21no—
264C2×C4×C67—21no—
265C2×C4×C67—21no—
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—22no—
274C2×C4×C67—22no—
275C2×C4×C67—22no—
276C2×C4×C67—22no—
277C2×C4×C67—22no—
278C2×C4×C67—41no—
279C2×C4×C67—41no—
280C2×C4×C67—41no—
281C2×C4×C67—41no—
282C2×C4×C67—41no—
283C2×C4×C67—41no—
284C2×C4×C67—41no—
285C2×C4×C67—41no—
286C2×C4×C67—84no—
287C2×C4×C67—84no—
288C2×C4×C67C2×C22⋊C412yes—
289C2×C4×C67C2×C22⋊C412yes—
290C2×C4×C67C2×C22⋊C412yes—
291C2×C4×C67C2×C22⋊C412yes—
292C2×C4×C67C23×C411yescharacteristic
293C2×C4×C67C22×D411yescharacteristic
294C2×C4×C67C2×#4111yescharacteristic
295C2×C4×C67C2×#4111yescharacteristic
296C2×C4×C67H(5,𝔽2)11yescharacteristic
297C2×C4×C672−1+411yescharacteristic
298C2×Dic67—22no—
299C2×Dic67—41no—
300C2×Dic67—41no—
301C2×Dic67—41no—
302C2×Dic67—41no—
303C2×Dic67—41no—
304C2×Dic67—41no—
305C2×Dic67—41no—
306C2×Dic67—41no—
307C2×Dic67—41no—
308C2×Dic67—41no—
309C2×Dic67—41no—
310C2×Dic67—84no—
311C67⋊C8—22no—
312C67⋊C8—41no—
313C67⋊C8—41no—
314C67⋊C8—41no—
315C22×C67—22no—
316C22×C67—22no—
317C22×C67—22no—
318C22×C67—22no—
319C22×C67—22no—
320C22×C67—22no—
321C22×C67—22no—
322C22×C67—22no—
323C22×C67—22no—
324C22×C67—41no—
325C22×C67—41no—
326C22×C67—41no—
327C22×C67—41no—
328C22×C67#41914yes—
329C22×C67C22×C22⋊C411yescharacteristic
330C22×C67#54611yescharacteristic
331C22×C67#54711yescharacteristic
332C22×C67C2×#13711yescharacteristic
333C22×C67C2×#13711yescharacteristic
334C22×C67#57611yescharacteristic
335C22×C67#57711yescharacteristic
336C4×C67—22no—
337C4×C67—22no—
338C4×C67—22no—
339C4×C67—22no—
340C4×C67—42no—
341C4×C67—42no—
342C4×C67—42no—
343C4×C67—42no—
344C4×C67C4×#4111yescharacteristic
345C4×C67#52011yescharacteristic
346C4×C67#54611yescharacteristic
347C4×C67#54711yescharacteristic
348Dic67—42no—
349Dic67—81no—
350Dic67—81no—
351Dic67—81no—
352#22497—671nomaximal, Sylow
353C2×C67—24no—
354C2×C67—42no—
355C2×C67#233911yescharacteristic
356C2×C67C2×#41911yescharacteristic
357C2×C67#289711yescharacteristic
358C2×C67#331411yescharacteristic
359C2×C67#331611yescharacteristic
360C2×C67#334411yescharacteristic
361C2×C67#334611yescharacteristic
362C2×#554D6711yescharacteristic
363C2×#435—671no—
364#2352—671no—
365#1993—671no—
366#1988—671no—
367#1894—671no—
368#1892—671no—
369#1873—671no—
370#1872—671no—
371#1824—671no—
372#1823—671no—
373#1805—671no—
374#1763—671no—
375#1736—671no—
376C2×#340—671no—
377C67#2249711yescharacteristic, complemented, Sylow
378C22×M16—671no—
379C23×C8—671no—
380#554—24no—
381#554Dic6718yescomplemented
382C2×C4⋊Q8C2×D6711yescharacteristic
383C2×#125—21no—
384C2×C22⋊Q8—21no—
385C2×C22⋊Q8—21no—
386C2×C22⋊Q8C2×D6711yescharacteristic
387C2×C22⋊Q8C2×D6711yescharacteristic
388C2×C4×Q8C2×D6711yescharacteristic
389C2×C4×D4—21no—
390C2×C4×D4C2×D6711yescharacteristic
391C2×#117—671no—
392C22×C4⋊C4—671no—
393C22×C4⋊C4C2×D6711yescharacteristic
394C22×C4⋊C4C2×D6711yescharacteristic
395#435—1344no—
396C2×C4⋊C8—671no—
397C2×#103—671no—
398C2×#103—671no—
399C2×#103—671no—
400C2×#103—671no—
401C2×C22⋊C8—671no—
402C2×C22⋊C8—671no—
403C2×#97—671no—
404#388—1341no—
405#387—1341no—
406#386—1341no—
407#382—671no—
408#380—671no—
409#380—671no—
410C4×C4⋊C4—671no—
411C4×C22⋊C4—1341no—
412#340—671no—
413#340—671no—
414#340—671no—
415#340—671no—
416#340—671no—
417#340—671no—
418#340—671no—
419#340—671no—
420#340—671no—
421#340—671no—
422#340—671no—
423#340—671no—
424C22×Q8—21no—
425C22×Q8C22×D6711yescharacteristic
426C22×D4C22⋊D6711yescharacteristic
427C23×C4—21no—
428C23×C4—21no—
429C23×C4—1341no—
430C23×C4C22×D6711yescharacteristic
431C23×C4C22×D6711yescharacteristic
432C2×M16—2681no—
433C2×M16—1342no—
434C2×M16—1342no—
435C22×C8—2681no—
436C22×C8—671no—
437C22×C8—671no—
438C22×C8—671no—
439C22×C8—671no—
440C22×C8—1342no—
441C22×C8—1342no—
442C4⋊Q8—22no—
443C4⋊Q8C2×Dic6714yescomplemented
444#125—28no—
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C22⋊Q8—28no—
448C22⋊Q8—28no—
449C22⋊Q8C2×Dic6714yes—
450C22⋊Q8C2×Dic6714yescomplemented
451C4×Q8—22no—
452C4×Q8C2×Dic6714yescomplemented
453C4×D4—28no—
454C4×D4C2×Dic6714yes—
455C4×D4C22⋊D6714yes—
456#117—2681no—
457#117—1342no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—2681no—
467C2×C4⋊C4—671no—
468C2×C4⋊C4—671no—
469C2×C4⋊C4—671no—
470C2×C4⋊C4—671no—
471C2×C4⋊C4—1341no—
472C2×C4⋊C4—1342no—
473C2×C4⋊C4C2×Dic6714yes—
474C2×C4⋊C4C2×Dic6714yescomplemented
475C2×C4⋊C4C22⋊D6711yescharacteristic
476C2×C4⋊C4C22×D6711yescharacteristic
477C2×C4⋊C4C22×D6711yescharacteristic
478C2×C4⋊C4C22×D6711yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—1341no—
482C2×C22⋊C4—1341no—
483C2×C22⋊C4—1341no—
484C2×C22⋊C4C22⋊D6711yescharacteristic
485C2×C22⋊C4C22⋊D6711yescharacteristic
486C2×C42—21no—
487C2×C42—1341no—
488C2×C42—1341no—
489C2×C42C22×D6711yescharacteristic
490C4⋊C8—1342no—
491#103—2681no—
492#103—2681no—
493#103—1342no—
494#103—1342no—
495C22⋊C8—1342no—
496C22⋊C8—1342no—
497#97—1342no—
498#95—1341no—
499#95—1341no—
500#95—1341no—
501#95—1341no—
502#95—1341no—
503C24C2×C22⋊D6711yescharacteristic
504C24C2×C22⋊D6711yescharacteristic
505C2×Q8—24no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—81no—
512C2×Q8—81no—
513C2×Q8C22×Dic6712yes—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4C22⋊Dic6714yes—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4—2682no—
536C22×C4—2682no—
537C22×C4—5361no—
538C22×C4—1341no—
539C22×C4—1341no—
540C22×C4—1341no—
541C22×C4—1341no—
542C22×C4C22×Dic6712yes—
543C22×C4C22×Dic6712yes—
544C22×C4C2×C22⋊D6711yescharacteristic
545C22×C4C2×C22⋊D6711yescharacteristic
546C22×C4C2×C22⋊D6711yescharacteristic
547C22×C4C2×C22⋊D6711yescharacteristic
548C22×C4C2×C22⋊D6712yes—
549C22×C4C2×C22⋊D6712yes—
550C22×C4C23×D6711yescharacteristic
551M16—2684no—
552C2×C8—2684no—
553C2×C8—672no—
554C2×C8—1341no—
555C2×C8—1341no—
556C2×C8—1341no—
557C2×C8—1341no—
558C2×C8—1341no—
559C2×C8—1341no—
560C2×C8—1341no—
561C2×C8—1341no—
562C2×C8—1341no—
563C2×C8—1341no—
564C2×C8—1341no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—2682no—
575C4⋊C4—672no—
576C4⋊C4—1341no—
577C4⋊C4—1341no—
578C4⋊C4—1341no—
579C4⋊C4—1341no—
580C4⋊C4—1341no—
581C4⋊C4—1341no—
582C4⋊C4—1341no—
583C4⋊C4C22⋊Dic6714yes—
584C4⋊C4C22×Dic6712yes—
585C4⋊C4C22×Dic6712yes—
586C4⋊C4C22×Dic6712yes—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C22⋊C4—2682no—
590C22⋊C4—2682no—
591C22⋊C4—5361no—
592C22⋊C4C22⋊Dic6714yes—
593C22⋊C4C22⋊Dic6714yes—
594C42—24no—
595C42—2682no—
596C42—5361no—
597C42C22×Dic6712yes—
598C42C2×C22⋊D6712yes—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23C2×C22⋊Dic6712yes—
610C23C2×C22⋊Dic6712yes—
611C23#1452407412yes—
612C23#1452407412yes—
613C23C22×C22⋊D6711yescharacteristic
614Q8—22no—
615Q8—22no—
616Q8—41no—
617Q8—41no—
618Q8—84no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—84no—
649C2×C4—84no—
650C2×C4—2681no—
651C2×C4—2681no—
652C2×C4—2681no—
653C2×C4—2681no—
654C2×C4—2681no—
655C2×C4—2681no—
656C2×C4—2681no—
657C2×C4—2681no—
658C2×C4—2681no—
659C2×C4—2681no—
660C2×C4—2681no—
661C2×C4—5364no—
662C2×C4—1342no—
663C2×C4C2×C22⋊Dic6712yes—
664C2×C4C2×C22⋊Dic6712yes—
665C2×C4C2×C22⋊Dic6712yes—
666C2×C4C2×C22⋊Dic6712yes—
667C2×C4C23×Dic6711yescharacteristic
668C2×C4C22×C22⋊D6711yescharacteristic
669C2×C4#41×D6711yescharacteristic
670C2×C4#41×D6711yescharacteristic
671C2×C4#1452408911yescharacteristic
672C2×C4#1452409011yescharacteristic
673C8—2681no—
674C8—2681no—
675C8—2681no—
676C8—1342no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#1686340514yes—
691C22C22×C22⋊Dic6711yescharacteristic
692C22#1686403411yescharacteristic
693C22#1686404511yescharacteristic
694C22C2×#1452407411yescharacteristic
695C22C2×#1452407411yescharacteristic
696C22#1686419911yescharacteristic
697C22#1686420711yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—2682no—
707C4—5361no—
708C4—5361no—
709C4—5361no—
710C4#41×Dic6711yescharacteristic
711C4#1686387911yescharacteristic
712C4#1686403411yescharacteristic
713C4#1686404511yescharacteristic
714C2—24no—
715C2—42no—
716C2#2256303911yescharacteristic
717C2C2×#1686340511yescharacteristic
718C2#2256873511yescharacteristic
719C2#2257228411yescharacteristic
720C2#2257231411yescharacteristic
721C2#2257265811yescharacteristic
722C2#2257268811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC2×#554×C67C2
socleC23×C67C22×D4
prime radicalC22×D4×C67D4
cosocleC22×C4×C67C24
hypercenterC2×#554D67
hypocenterC67#22497
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
3. #22561183C2semidirect
4. #22561162C2semidirect
5. #22560643C2semidirect
6. #22560633C2semidirect
7. #22560522C2semidirect
8. #22560517C2semidirect
9. #22560299C2semidirect
10. #22560295C2semidirect
11. #22560224C2semidirect
12. #22560039C2semidirect
13. #22559928C2semidirect
14. C2×#16863158C2semidirect
50. #554×C67C4semidirect
108. C4⋊Q8×C67C2×C4semidirect
115. C22⋊Q8×C67C2×C4semidirect
117. C4×Q8×C67C2×C4semidirect
130. C2×C4⋊C4×C67C2×C4semidirect
377. C67#22497semidirect
381. #554Dic67semidirect
443. C4⋊Q8C2×Dic67semidirect
450. C22⋊Q8C2×Dic67semidirect
452. C4×Q8C2×Dic67semidirect
474. 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×#168634682
#225631382
#225611832
#225611622
#225606432
#225606332
#225605222
#225605172
#225602992
#225602952
#225602242
#225600392
#225599282
C2×#168631582
C2×#554×C672
#2249767