Finite Group Databasebeta

← C2×#22570387 #31724056

Subgroups — C2×#22570387 #31724056

Order 17152.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863870C211yesmaximal, characteristic, complemented
2#22570387C2116yesmaximal, direct product factor
3C2×#16863734C211yesmaximal, characteristic, complemented
4C2×#16863717C211yesmaximal, characteristic, complemented
5C2×#16863683C211yesmaximal, characteristic, complemented
6C2×#16863673C211yesmaximal, characteristic, complemented
7C2×#16863608C211yesmaximal, characteristic, complemented
8C2×#16863608C211yesmaximal, characteristic, complemented
9C2×#16863546C211yesmaximal, characteristic, complemented
10C2×#16863529C211yesmaximal, characteristic
11C2×#16863506C211yesmaximal, characteristic, complemented
12C2×#16863494C211yesmaximal, characteristic, complemented
13C2×C4×#11761615C211yesmaximal, characteristic, complemented
14C2×C4×#11761613C211yesmaximal, characteristic, complemented
15C2×#16863457C211yesmaximal, characteristic, complemented
16C2×#542×C67C211yesmaximal, characteristic, complemented
17C23×D268C2211yescharacteristic
18C22×#11761615C2211yescharacteristic
19C22×#11761615C2211yescharacteristic
20C22×#11761613C2211yescharacteristic
21C22×#11761613C2211yescharacteristic
22#16863870—24no—
23#16863870C2218yescomplemented
24C2×C4×D268C2211yescharacteristic
25C2×C4×D268C2211yescharacteristic
26C2×C4×D268C2211yescharacteristic
27C2×C4×D268C2211yescharacteristic
28C2×#14524005—21no—
29C2×#14524005—21no—
30C2×#14524002C2211yescharacteristic
31C2×C22⋊C4×D67—21no—
32C2×C22⋊C4×D67—21no—
33#16863734C2218yescomplemented
34#16863717C2218yescomplemented
35#16863683C2218yescomplemented
36#16863673C2218yescomplemented
37#16863608C2218yescomplemented
38#16863608C2218yescomplemented
39#16863546C2218yescomplemented
40#16863529C2218yes—
41#16863506C2218yescomplemented
42#16863494C2218yescomplemented
43C4×#11761615C2218yescomplemented
44C4×#11761613C2218yescomplemented
45#16863457C2218yescomplemented
46C2×#14523976C2211yescharacteristic, complemented
47C2×#14523976C2211yescharacteristic, complemented
48C2×#14523974C2211yescharacteristic, complemented
49C2×#14523974C2211yescharacteristic, complemented
50C2×C4⋊(C67⋊C8)C2211yescharacteristic, complemented
51C2×C4⋊(C67⋊C8)C2211yescharacteristic, complemented
52C2×#14523967C2211yescharacteristic, complemented
53C2×#14523967C2211yescharacteristic, complemented
54C2×#14523964C2211yescharacteristic, complemented
55C2×#14523964C2211yescharacteristic, complemented
56C2×#14523963C2211yescharacteristic
57C2×#14523963C2211yescharacteristic
58C2×#14523963C2211yescharacteristic
59C2×#14523963C2211yescharacteristic
60C2×C22⋊(C67⋊C8)C2211yescharacteristic
61C2×C22⋊(C67⋊C8)C2211yescharacteristic
62C2×#14523954C2211yescharacteristic, complemented
63C2×C4×C67⋊C8C2211yescharacteristic, complemented
64#542×C67—24no—
65#542×C67C2218yescomplemented
66C2×C4⋊Q8×C67C2211yescharacteristic, complemented
67C2×#126×C67—21no—
68C2×#124×C67—21no—
69C2×#124×C67C2211yescharacteristic, complemented
70C2×#123×C67—21no—
71C2×C22⋊Q8×C67—21no—
72C2×C22⋊Q8×C67C2211yescharacteristic
73C2×#121×C67C2211yescharacteristic
74C2×C4×Q8×C67C2211yescharacteristic, complemented
75C2×C4×D4×C67C2211yescharacteristic, complemented
76C2×#117×C67C2211yescharacteristic
77C24×D67—21no—
78C22×D268—24no—
79C22×D268—24no—
80C22×D268—21no—
81C22×D268—22no—
82C22×D268C2314yes—
83C22×D268C2311yescharacteristic
84C22×D268C2311yescharacteristic
85C22×C4×D67—21no—
86C22×C4×D67—21no—
87C22×C4×D67—21no—
88C22×C4×D67—21no—
89C2×#11761615—24no—
90C2×#11761615—24no—
91C2×#11761615C2314yes—
92C2×#11761615C2314yes—
93C2×#11761613—24no—
94C2×#11761613—24no—
95C2×#11761613C2314yes—
96C2×#11761613C2314yes—
97C22×C67⋊C8C2311yescharacteristic
98C22×C67⋊C8C2311yescharacteristic
99C22×C67⋊C8C2311yescharacteristic
100C22×C67⋊C8C2311yescharacteristic
101C4×D268—22no—
102C4×D268—22no—
103C4×D268—22no—
104C4×D268—22no—
105C4×D268C2314yes—
106C4×D268C2314yes—
107C4×D268C2314yes—
108C4×D268C2314yes—
109#14524005—28no—
110#14524005—28no—
111#14524002—22no—
112#14524002C2314yes—
113C2×C4⋊Dic67C2311yescharacteristic
114C2×C4⋊Dic67C2311yescharacteristic
115C2×C22⋊Dic67—21no—
116C2×(C2×D67)⋊C4—21no—
117C2×(C2×D67)⋊C4—21no—
118C2×(C2×D67)⋊C4—21no—
119C2×(C2×D67)⋊C4—21no—
120C22⋊C4×D67—28no—
121C22⋊C4×D67—28no—
122C2×C4×Dic67—21no—
123#14523976C2314yescomplemented
124#14523976C2314yescomplemented
125#14523974C2314yescomplemented
126#14523974C2314yescomplemented
127C4⋊(C67⋊C8)C2314yescomplemented
128C4⋊(C67⋊C8)C2314yescomplemented
129#14523967C2314yescomplemented
130#14523967C2314yescomplemented
131#14523964C2314yescomplemented
132#14523964C2314yescomplemented
133#14523963C2314yes—
134#14523963C2314yes—
135#14523963C2314yes—
136#14523963C2314yes—
137C22⋊(C67⋊C8)C2314yes—
138C22⋊(C67⋊C8)C2314yes—
139#14523954C2314yescomplemented
140C4×C67⋊C8C2314yescomplemented
141C22×Q8×C67—21no—
142C22×Q8×C67C2311yescharacteristic
143C22×D4×C67—21no—
144C22×D4×C67C2311yescharacteristic
145C23×C4×C67—21no—
146C23×C4×C67C2311yescharacteristic
147C4⋊Q8×C67—22no—
148C4⋊Q8×C67C2314yescomplemented
149#126×C67—28no—
150#124×C67—28no—
151#124×C67—22no—
152#124×C67C2314yescomplemented
153#123×C67—28no—
154C22⋊Q8×C67—22no—
155C22⋊Q8×C67—28no—
156C22⋊Q8×C67C2314yes—
157#121×C67—22no—
158#121×C67C2314yes—
159C4×Q8×C67—22no—
160C4×Q8×C67C2314yescomplemented
161C4×D4×C67—22no—
162C4×D4×C67C2314yescomplemented
163#117×C67D414yes—
164#117×C67C2314yes—
165C2×C4⋊C4×C67—21no—
166C2×C4⋊C4×C67—21no—
167C2×C4⋊C4×C67—21no—
168C2×C4⋊C4×C67D411yescharacteristic
169C2×C4⋊C4×C67D411yescharacteristic
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C4⋊C4×C67C2311yescharacteristic
172C2×C22⋊C4×C67—21no—
173C2×C22⋊C4×C67—21no—
174C2×C22⋊C4×C67—21no—
175C2×C22⋊C4×C67—21no—
176C2×C22⋊C4×C67—21no—
177C2×C22⋊C4×C67D411yescharacteristic
178C2×C22⋊C4×C67D411yescharacteristic
179C2×C42×C67—21no—
180C2×C42×C67C2311yescharacteristic
181C2×C42×C67C2311yescharacteristic
182C23×D67—21no—
183C23×D67—21no—
184C23×D67—28no—
185C23×D67—24no—
186C23×D67—82no—
187C23×D67—82no—
188C2×D268—28no—
189C2×D268—216no—
190C2×D268—24no—
191C2×D268—21no—
192C2×D268—21no—
193C2×D268—22no—
194C2×D268—22no—
195C2×D268—28no—
196C2×D268—28no—
197C2×D268#4114yes—
198C2×D268#4114yes—
199C2×D268C2412yes—
200C2×D268C2412yes—
201C22×Dic67—21no—
202C22×Dic67—21no—
203C2×C4×D67—24no—
204C2×C4×D67—24no—
205C2×C4×D67—24no—
206C2×C4×D67—24no—
207C2×C4×D67—82no—
208C2×C4×D67—82no—
209C2×C4×D67—82no—
210C2×C4×D67—82no—
211#11761615—28no—
212#11761615—28no—
213#11761613—28no—
214#11761613—28no—
215C2×C67⋊C8—22no—
216C2×C67⋊C8—22no—
217C2×C67⋊C8—22no—
218C2×C67⋊C8—22no—
219C2×C67⋊C8C2412yes—
220C2×C67⋊C8C2412yes—
221C2×C67⋊C8C2412yes—
222C2×C67⋊C8C2412yes—
223C4⋊Dic67—21no—
224C4⋊Dic67—21no—
225C4⋊Dic67C2412yes—
226C4⋊Dic67C2412yes—
227C22⋊Dic67—24no—
228(C2×D67)⋊C4—24no—
229(C2×D67)⋊C4—24no—
230(C2×D67)⋊C4—24no—
231(C2×D67)⋊C4—24no—
232C4×Dic67—24no—
233C24×C67—21no—
234C24×C67C2×D411yescharacteristic
235C2×Q8×C67—21no—
236C2×Q8×C67—24no—
237C2×Q8×C67—22no—
238C2×Q8×C67—22no—
239C2×Q8×C67—82no—
240C2×Q8×C67C2412yes—
241C2×D4×C67—24no—
242C2×D4×C67—21no—
243C2×D4×C67—22no—
244C2×D4×C67—22no—
245C2×D4×C67—82no—
246C2×D4×C67C2412yes—
247C22×C4×C67—22no—
248C22×C4×C67—22no—
249C22×C4×C67—21no—
250C22×C4×C67—21no—
251C22×C4×C67—21no—
252C22×C4×C67—24no—
253C22×C4×C67—82no—
254C22×C4×C67C2×D411yescharacteristic
255C22×C4×C67C2×D411yescharacteristic
256C22×C4×C67C2×D411yescharacteristic
257C22×C4×C67C2×D411yescharacteristic
258C22×C4×C67C2×D411yescharacteristic
259C22×C4×C67C2×D412yes—
260C22×C4×C67C2412yes—
261C22×C4×C67C2411yescharacteristic
262C4⋊C4×C67—24no—
263C4⋊C4×C67—24no—
264C4⋊C4×C67—24no—
265C4⋊C4×C67—21no—
266C4⋊C4×C67—21no—
267C4⋊C4×C67C2×D414yes—
268C4⋊C4×C67C2×D414yes—
269C4⋊C4×C67C2412yes—
270C4⋊C4×C67C2412yes—
271C22⋊C4×C67—24no—
272C22⋊C4×C67—24no—
273C22⋊C4×C67—24no—
274C22⋊C4×C67—24no—
275C22⋊C4×C67—24no—
276C22⋊C4×C67C2×D414yes—
277C22⋊C4×C67C2×D414yes—
278C42×C67—24no—
279C42×C67C2×D412yes—
280C42×C67C2×D412yes—
281C42×C67C2412yes—
282C42×C67C2412yes—
283C23×C67—22no—
284C23×C67—22no—
285C23×C67—22no—
286C23×C67—22no—
287C23×C67—42no—
288C23×C67—42no—
289C23×C67—42no—
290C23×C67C22×D412yes—
291C23×C67C22×D411yescharacteristic
292C22×D67—24no—
293C22×D67—24no—
294C22×D67—22no—
295C22×D67—22no—
296C22×D67—216no—
297C22×D67—42no—
298C22×D67—42no—
299C22×D67—42no—
300C22×D67—42no—
301C22×D67—84no—
302C22×D67—84no—
303C22×D67—816no—
304Q8×C67—22no—
305Q8×C67—22no—
306Q8×C67—42no—
307Q8×C67—84no—
308D4×C67—22no—
309D4×C67—22no—
310D4×C67—42no—
311D4×C67—84no—
312C2×C4×C67—22no—
313C2×C4×C67—22no—
314C2×C4×C67—22no—
315C2×C4×C67—22no—
316C2×C4×C67—22no—
317C2×C4×C67—24no—
318C2×C4×C67—22no—
319C2×C4×C67—22no—
320C2×C4×C67—22no—
321C2×C4×C67—22no—
322C2×C4×C67—22no—
323C2×C4×C67—42no—
324C2×C4×C67—42no—
325C2×C4×C67—42no—
326C2×C4×C67—84no—
327C2×C4×C67C22×D412yes—
328C2×C4×C67C22×D412yes—
329C2×C4×C67C22×D412yes—
330C2×C4×C67C22×D412yes—
331C2×C4×C67C22×D412yes—
332C2×C4×C67C22×D411yescharacteristic
333C2×C4×C67C2×#4112yes—
334C2×C4×C67C2×#4112yes—
335C2×C4×C67C2511yescharacteristic
336C2×Dic67—22no—
337C2×Dic67—22no—
338C2×Dic67—42no—
339C2×Dic67—42no—
340D268—216no—
341D268—24no—
342D268—24no—
343D268—22no—
344D268—22no—
345D268C2×#4114yes—
346D268C2×#4114yes—
347C4×D67—84no—
348C4×D67—84no—
349C4×D67—84no—
350C4×D67—84no—
351C67⋊C8—22no—
352C67⋊C8—22no—
353C67⋊C8—22no—
354C67⋊C8—22no—
355C22×C67—22no—
356C22×C67—22no—
357C22×C67—22no—
358C22×C67—44no—
359C22×C67—42no—
360C22×C67—42no—
361C22×C67—42no—
362C22×C67—84no—
363C22×C67#52512yes—
364C22×C67#57612yes—
365C22×C67#57712yes—
366C22×C67C23×D411yescharacteristic
367C2×D67—24no—
368C2×D67—24no—
369C2×D67—48no—
370C2×D67—48no—
371C2×D67—42no—
372C2×D67—42no—
373C2×D67—42no—
374C2×D67—42no—
375C2×D67—816no—
376C4×C67—22no—
377C4×C67—22no—
378C4×C67—22no—
379C4×C67—22no—
380C4×C67—22no—
381C4×C67—42no—
382C4×C67—42no—
383C4×C67—42no—
384C4×C67#52512yes—
385C4×C67C22×#4111yescharacteristic
386C4×C67C22×#4111yescharacteristic
387Dic67—42no—
388Dic67—42no—
389C2×#3118—671nomaximal, Sylow
390C2×C67—42no—
391C2×C67—82no—
392C2×C67#311814yescomplemented
393C2×C67C2×#52511yescharacteristic
394C2×C67C2×#57611yescharacteristic
395C2×C67C2×#57711yescharacteristic
396D67—44no—
397D67—44no—
398C2×#542D6711yescharacteristic, complemented
399C2×#518—671no—
400#3118—6716no—
401C2×#485—671no—
402C2×#482—671no—
403C2×#476—671no—
404C2×#474—671no—
405C2×#463—671no—
406C2×#463—671no—
407C2×#450—671no—
408C2×#447—671no—
409C2×#442—671no—
410C2×#440—671no—
411C2×C4×SD16—671no—
412C2×C4×D8—671no—
413C2×#433—671no—
414C67C2×#311811yescharacteristic, complemented, Sylow
415C23×D4—671no—
416C22×SD16—671no—
417C22×SD16—671no—
418C22×D8—671no—
419C22×D8—671no—
420#542—24no—
421#542C2×D6718yescomplemented
422C2×C4⋊Q8C2×D6711yescharacteristic, complemented
423C2×#126—21no—
424C2×#124—21no—
425C2×#124C2×D6711yescharacteristic, complemented
426C2×#123—21no—
427C2×C22⋊Q8—21no—
428C2×C22⋊Q8C2×D6711yescharacteristic
429C2×#121C2×D6711yescharacteristic
430#518—678no—
431#518—1344no—
432C2×C4×Q8C2×D6711yescharacteristic, complemented
433C2×C4×D4—671no—
434C2×C4×D4—671no—
435C2×C4×D4—671no—
436C2×C4×D4—671no—
437C2×C4×D4—1341no—
438C2×C4×D4—1341no—
439C2×C4×D4C2×D6711yescharacteristic, complemented
440C2×#117—671no—
441C2×#117C2×D6711yescharacteristic
442C22×C22⋊C4—1341no—
443C22×C22⋊C4—1341no—
444#485—678no—
445#482—678no—
446#476—678no—
447#474—678no—
448#463—678no—
449#463—678no—
450#450—678no—
451#447—678no—
452#442—678no—
453#440—678no—
454C4×SD16—678no—
455C4×D8—678no—
456#433—678no—
457C2×#107—671no—
458C2×#107—671no—
459C2×#106—671no—
460C2×#106—671no—
461C2×C4⋊C8—671no—
462C2×C4⋊C8—671no—
463C2×#103—671no—
464C2×#103—671no—
465C2×#102—671no—
466C2×#102—671no—
467C2×#102—671no—
468C2×#102—671no—
469C2×#102—671no—
470C2×#102—671no—
471C2×C22⋊C8—671no—
472C2×C22⋊C8—671no—
473C2×#97—671no—
474C2×C4×C8—671no—
475C25—1341no—
476C22×Q8—21no—
477C22×Q8C22×D6711yescharacteristic
478C22×D4—21no—
479C22×D4—671no—
480C22×D4—671no—
481C22×D4—674no—
482C22×D4—1344no—
483C22×D4—1344no—
484C22×D4—1341no—
485C22×D4—1342no—
486C22×D4C22×D6711yescharacteristic
487C23×C4—21no—
488C23×C4—1341no—
489C23×C4—1341no—
490C23×C4—1341no—
491C23×C4—1341no—
492C23×C4C22×D6711yescharacteristic
493C2×SD16—674no—
494C2×SD16—674no—
495C2×SD16—1344no—
496C2×SD16—1344no—
497C2×D8—674no—
498C2×D8—674no—
499C2×D8—1344no—
500C2×D8—1344no—
501C22×C8—671no—
502C22×C8—671no—
503C22×C8—671no—
504C22×C8—671no—
505C4⋊Q8—22no—
506C4⋊Q8C22×D6714yescomplemented
507#126—28no—
508#124—28no—
509#124—22no—
510#124C22×D6714yescomplemented
511#123—28no—
512C22⋊Q8—22no—
513C22⋊Q8—28no—
514C22⋊Q8C22×D6714yes—
515#121—22no—
516#121C22×D6714yes—
517C4×Q8—22no—
518C4×Q8C22×D6714yescomplemented
519C4×D4—22no—
520C4×D4—674no—
521C4×D4—674no—
522C4×D4—674no—
523C4×D4—674no—
524C4×D4—1348no—
525C4×D4—1348no—
526C4×D4—1342no—
527C4×D4—1342no—
528C4×D4—1342no—
529C4×D4—1342no—
530C4×D4C22×D6714yescomplemented
531#117—674no—
532#117—1342no—
533#117C22⋊D6714yes—
534#117C22×D6714yes—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—671no—
539C2×C4⋊C4—671no—
540C2×C4⋊C4C22⋊D6711yescharacteristic
541C2×C4⋊C4C22⋊D6711yescharacteristic
542C2×C4⋊C4C22×D6711yescharacteristic
543C2×C4⋊C4C22×D6711yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—1341no—
550C2×C22⋊C4—1341no—
551C2×C22⋊C4—1341no—
552C2×C22⋊C4—1341no—
553C2×C22⋊C4—1341no—
554C2×C22⋊C4—1348no—
555C2×C22⋊C4—1348no—
556C2×C22⋊C4C22⋊D6711yescharacteristic
557C2×C22⋊C4C22⋊D6711yescharacteristic
558C2×C42—21no—
559C2×C42—1341no—
560C2×C42C22×D6711yescharacteristic
561C2×C42C22×D6711yescharacteristic
562#107—674no—
563#107—674no—
564#106—674no—
565#106—674no—
566C4⋊C8—674no—
567C4⋊C8—674no—
568#103—674no—
569#103—674no—
570#102—674no—
571#102—674no—
572#102—674no—
573#102—674no—
574#102—674no—
575#102—674no—
576C22⋊C8—674no—
577C22⋊C8—674no—
578#97—674no—
579C4×C8—674no—
580C24—21no—
581C24—5362no—
582C24—5362no—
583C24—1348no—
584C24—1341no—
585C24—1341no—
586C24—1344no—
587C24C2×C22⋊D6711yescharacteristic
588C2×Q8—21no—
589C2×Q8—24no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—82no—
593C2×Q8C23×D6712yes—
594C2×D4—24no—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—82no—
599C2×D4—674no—
600C2×D4—674no—
601C2×D4—672no—
602C2×D4—672no—
603C2×D4—1348no—
604C2×D4—1348no—
605C2×D4—1348no—
606C2×D4—13416no—
607C2×D4—1344no—
608C2×D4—1341no—
609C2×D4—1341no—
610C2×D4—1342no—
611C2×D4—1342no—
612C2×D4C23×D6712yes—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—24no—
619C22×C4—82no—
620C22×C4—5362no—
621C22×C4—5362no—
622C22×C4—5362no—
623C22×C4—5362no—
624C22×C4—1341no—
625C22×C4—1341no—
626C22×C4—1344no—
627C22×C4—1344no—
628C22×C4—1344no—
629C22×C4—1344no—
630C22×C4C2×C22⋊D6712yes—
631C22×C4C2×C22⋊D6711yescharacteristic
632C22×C4C2×C22⋊D6711yescharacteristic
633C22×C4C2×C22⋊D6711yescharacteristic
634C22×C4C2×C22⋊D6711yescharacteristic
635C22×C4C2×C22⋊D6711yescharacteristic
636C22×C4C23×D6712yes—
637C22×C4C23×D6711yescharacteristic
638SD16—1348no—
639SD16—1348no—
640D8—1348no—
641D8—1348no—
642C2×C8—672no—
643C2×C8—672no—
644C2×C8—672no—
645C2×C8—672no—
646C2×C8—1342no—
647C2×C8—1342no—
648C2×C8—1342no—
649C2×C8—1342no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—672no—
656C4⋊C4—672no—
657C4⋊C4—1341no—
658C4⋊C4—1341no—
659C4⋊C4C2×C22⋊D6714yes—
660C4⋊C4C2×C22⋊D6714yes—
661C4⋊C4C23×D6712yes—
662C4⋊C4C23×D6712yes—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—1344no—
669C22⋊C4—1344no—
670C22⋊C4—1344no—
671C22⋊C4—1344no—
672C22⋊C4—1344no—
673C22⋊C4C2×C22⋊D6714yes—
674C22⋊C4C2×C22⋊D6714yes—
675C42—24no—
676C42—1344no—
677C42C2×C22⋊D6712yes—
678C42C2×C22⋊D6712yes—
679C42C23×D6712yes—
680C42C23×D6712yes—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—2682no—
689C23—2682no—
690C23—2682no—
691C23—2682no—
692C23—5364no—
693C23—5364no—
694C23—53616no—
695C23—13416no—
696C23—1344no—
697C23—1344no—
698C23—1342no—
699C23—1342no—
700C23C22×C22⋊D6712yes—
701C23C22×C22⋊D6711yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—42no—
705Q8—84no—
706D4—22no—
707D4—22no—
708D4—42no—
709D4—84no—
710D4—674no—
711D4—674no—
712D4—13416no—
713D4—1344no—
714D4—1344no—
715D4—1342no—
716D4—1342no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—84no—
732C2×C4—2682no—
733C2×C4—2682no—
734C2×C4—5364no—
735C2×C4—5364no—
736C2×C4—5364no—
737C2×C4—5364no—
738C2×C4—1342no—
739C2×C4—1342no—
740C2×C4C22×C22⋊D6712yes—
741C2×C4C22×C22⋊D6712yes—
742C2×C4C22×C22⋊D6712yes—
743C2×C4C22×C22⋊D6712yes—
744C2×C4C22×C22⋊D6712yes—
745C2×C4C22×C22⋊D6711yescharacteristic
746C2×C4#41×D6712yes—
747C2×C4#41×D6712yes—
748C2×C4C24×D6711yescharacteristic
749C8—1342no—
750C8—1342no—
751C8—1342no—
752C8—1342no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22—2682no—
762C22—2682no—
763C22—2682no—
764C22—2682no—
765C22—2688no—
766C22—2688no—
767C22—53616no—
768C22—1344no—
769C22—1344no—
770C22#1686390312yes—
771C22#1686419912yes—
772C22#1686420412yes—
773C22C23×C22⋊D6711yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—2682no—
783C4—2682no—
784C4#1686390312yes—
785C4C2×#41×D6711yescharacteristic
786C4C2×#41×D6711yescharacteristic
787C2—42no—
788C2—82no—
789C2—2684no—
790C2—2684no—
791C2#2257038714yesdirect product factor
792C2C2×#1686390311yescharacteristic
793C2C2×#1686419911yescharacteristic
794C2C2×#1686420411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#542×C67C2
socleC23×C67C22×D4
prime radicalC2×#16863529C2
hypercenterC2×#542D67
hypocenterC67C2×#3118
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16863870C2semidirect
2. #22570387C2direct (N × H)
3. C2×#16863734C2semidirect
4. C2×#16863717C2semidirect
5. C2×#16863683C2semidirect
6. C2×#16863673C2semidirect
7. C2×#16863608C2semidirect
8. C2×#16863608C2semidirect
9. C2×#16863546C2semidirect
11. C2×#16863506C2semidirect
12. C2×#16863494C2semidirect
13. C2×C4×#11761615C2semidirect
14. C2×C4×#11761613C2semidirect
15. C2×#16863457C2semidirect
16. C2×#542×C67C2semidirect
23. #16863870C22semidirect
33. #16863734C22semidirect
34. #16863717C22semidirect
35. #16863683C22semidirect
36. #16863673C22semidirect
37. #16863608C22semidirect
38. #16863608C22semidirect
39. #16863546C22semidirect
41. #16863506C22semidirect
42. #16863494C22semidirect
43. C4×#11761615C22semidirect
44. C4×#11761613C22semidirect
45. #16863457C22semidirect
46. C2×#14523976C22semidirect
47. C2×#14523976C22semidirect
48. C2×#14523974C22semidirect
49. C2×#14523974C22semidirect
50. C2×C4⋊(C67⋊C8)C22semidirect
51. C2×C4⋊(C67⋊C8)C22semidirect
52. C2×#14523967C22semidirect
53. C2×#14523967C22semidirect
54. C2×#14523964C22semidirect
55. C2×#14523964C22semidirect
62. C2×#14523954C22semidirect
63. C2×C4×C67⋊C8C22semidirect
65. #542×C67C22semidirect
66. C2×C4⋊Q8×C67C22semidirect
69. C2×#124×C67C22semidirect
74. C2×C4×Q8×C67C22semidirect
75. C2×C4×D4×C67C22semidirect
123. #14523976C23semidirect
124. #14523976C23semidirect
125. #14523974C23semidirect
126. #14523974C23semidirect
127. C4⋊(C67⋊C8)C23semidirect
128. C4⋊(C67⋊C8)C23semidirect
129. #14523967C23semidirect
130. #14523967C23semidirect
131. #14523964C23semidirect
132. #14523964C23semidirect
139. #14523954C23semidirect
140. C4×C67⋊C8C23semidirect
148. C4⋊Q8×C67C23semidirect
152. #124×C67C23semidirect
160. C4×Q8×C67C23semidirect
162. C4×D4×C67C23semidirect
392. C2×C67#3118semidirect
398. C2×#542D67semidirect
414. C67C2×#3118semidirect
421. #542C2×D67semidirect
422. C2×C4⋊Q8C2×D67semidirect
425. C2×#124C2×D67semidirect
432. C2×C4×Q8C2×D67semidirect
439. C2×C4×D4C2×D67semidirect
506. C4⋊Q8C22×D67semidirect
510. #124C22×D67semidirect
518. C4×Q8C22×D67semidirect
530. C4×D4C22×D67semidirect
791. C2#22570387direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168638702
#225703872
C2×#168637342
C2×#168637172
C2×#168636832
C2×#168636732
C2×#168636082
C2×#168635462
C2×#168635292
C2×#168635062
C2×#168634942
C2×C4×#117616152
C2×C4×#117616132
C2×#168634572
C2×#542×C672
C2×#311867