Finite Group Databasebeta

← #29647200

Subgroups — #29647200

Order 15616.

1194 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459111C211yesmaximal, characteristic
2#21454448C211yesmaximal, characteristic, complemented
3C2×#16839613C211yesmaximal, characteristic, complemented
4#21444343C212yesmaximal, complemented
5#21444341C212yesmaximal, complemented
6#21444324C211yesmaximal, characteristic, complemented
7#21444323C211yesmaximal, characteristic, complemented
8#21444321C211yesmaximal, characteristic, complemented
9#21444316C212yesmaximal, complemented
10#21444312C212yesmaximal, complemented
11C61×#1504C211yesmaximal, characteristic, complemented
12#16840315C411yescharacteristic, complemented
13#16840314C411yescharacteristic, complemented
14#16840314C2211yescharacteristic
15#16840308C411yescharacteristic, complemented
16#16840307C411yescharacteristic, complemented
17#16840307C2211yescharacteristic
18#16840298C411yescharacteristic, complemented
19#16840298C2211yescharacteristic
20#16840293C411yescharacteristic, complemented
21#16840293C2211yescharacteristic
22#16840292—21no—
23#16840292—21no—
24#16840289—21no—
25#16840289—21no—
26#16840273C2211yescharacteristic
27#16840268—21no—
28#16840268—21no—
29#41×Dic61C411yescharacteristic, complemented
30#16840230C411yescharacteristic, complemented
31C4×#11758224—21no—
32C4×#11758224—21no—
33C22×#11758196—21no—
34C22×C4×Dic61—21no—
35C22×C4×Dic61C2211yescharacteristic
36#16839816—21no—
37#16839816C2212yes—
38#16839812—21no—
39#16839812C2212yes—
40#16839785—21no—
41#16839726C2211yescharacteristic
42M16×Dic61—21no—
43#16839613—21no—
44#16839613—21no—
45#16839613C2212yes—
46#16839613C2212yes—
47C2×#14519684C2211yescharacteristic
48#16839500C2212yes—
49#16839499C2212yes—
50#16839498C2212yes—
51#16839497C2212yes—
52#16839496C2212yes—
53#16839495C2212yes—
54C61×#525C2211yescharacteristic
55C61×#407C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C61×#328C2212yes—
58C61×#327C2212yes—
59C2×#11758222C2×C411yescharacteristic
60C2×#11758224—21no—
61C2×#11758224—21no—
62C23×Dic61—21no—
63C23×Dic61D411yescharacteristic
64C23×Dic61D411yescharacteristic
65C2×#11758194—21no—
66#14519776C2×C411yescharacteristic, complemented
67#14519776C2×C411yescharacteristic, complemented
68#14519775C2×C411yescharacteristic, complemented
69#14519773C2×C411yescharacteristic, complemented
70#14519772—21no—
71#14519772—21no—
72#14519770—21no—
73#14519770—21no—
74#14519768C2×C411yescharacteristic, complemented
75#14519768C2×C411yescharacteristic, complemented
76#14519767—21no—
77#14519767—21no—
78#14519766C2×C411yescharacteristic, complemented
79#14519764C2×C411yescharacteristic, complemented
80#14519763—21no—
81#14519763—21no—
82#14519761—21no—
83#14519761—21no—
84#14519760—21no—
85#14519758—21no—
86#14519758—21no—
87#14519756C2×C411yescharacteristic
88#14519756C2311yescharacteristic
89#14519754—21no—
90#14519754—21no—
91#14519754—21no—
92#14519754—21no—
93#14519751C2×C411yescharacteristic
94#14519751C2311yescharacteristic
95#14519749—21no—
96#14519749—21no—
97#14519749—21no—
98#14519749—21no—
99#14519746—21no—
100Q8×Dic61C2×C411yescharacteristic, complemented
101Q8×Dic61C2×C411yescharacteristic, complemented
102C4×Dic122—21no—
103C4×Dic122—21no—
104#14519742—21no—
105#14519742—21no—
106#14519742C2×C411yescharacteristic, complemented
107#14519742C2×C411yescharacteristic, complemented
108D4×Dic61—21no—
109D4×Dic61—21no—
110D4×Dic61—21no—
111D4×Dic61—21no—
112D4×Dic61C2×C411yescharacteristic, complemented
113D4×Dic61C2×C411yescharacteristic, complemented
114#14519739C2×C411yescharacteristic, complemented
115#14519739C2×C411yescharacteristic, complemented
116C4×C22⋊D61—21no—
117C4×C22⋊D61—21no—
118C4×C22⋊D61—21no—
119C4×C22⋊D61—21no—
120#14519737—21no—
121#14519737—21no—
122#14519737—21no—
123#14519737—21no—
124#14519737—21no—
125#14519737—21no—
126#14519736—21no—
127#14519736C2×C411yescharacteristic
128#14519735—21no—
129#14519735—21no—
130#14519734—21no—
131#14519733—21no—
132#14519733—21no—
133#14519733—21no—
134#14519733—21no—
135C2×#11758196—28no—
136C2×#11758196—22no—
137C2×#11758196—22no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61—22no—
140C2×C4×Dic61—22no—
141C2×C4×Dic61—44no—
142C2×C4×Dic61C2×C411yescharacteristic
143C2×C4×Dic61C2×C411yescharacteristic
144C2×C4×Dic61C2×C411yescharacteristic
145C2×C4×Dic61C2×C411yescharacteristic
146C2×C4×Dic61D411yescharacteristic
147C2×C4×Dic61D411yescharacteristic
148C2×C4×Dic61D411yescharacteristic
149C2×C4×Dic61D411yescharacteristic
150C2×C4×Dic61D411yescharacteristic
151C2×C4×Dic61D411yescharacteristic
152C2×C4×Dic61C2311yescharacteristic
153C2×C4×Dic61C2311yescharacteristic
154C42×D61—21no—
155#14519706—22no—
156#14519706—22no—
157C22⋊#92418—21no—
158C22⋊#92418C2312yes—
159#14519687—22no—
160C8×Dic61—22no—
161#14519684—21no—
162#14519684C2312yes—
163C2×#41×C61C2×C411yescharacteristic
164C23×C4×C61—21no—
165C23×C4×C61C2311yescharacteristic
166C2×M16×C61—21no—
167#123×C61—21no—
168C22⋊Q8×C61C2×C411yescharacteristic
169C22⋊Q8×C61C2311yescharacteristic
170#121×C61C2×C411yescharacteristic
171#121×C61C2311yescharacteristic
172#120×C61—21no—
173C4×D4×C61—21no—
174C4×D4×C61—21no—
175#117×C61C2×C411yescharacteristic
176C22⋊C8×C61—21no—
177C22⋊C8×C61C2312yes—
178#95×C61—21no—
179#95×C61C2312yes—
180C24×C61C2×D411yescharacteristic
181#41×C61—42no—
182C2×Q8×C61C22×C411yescharacteristic
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61C22×C411yescharacteristic
187C22×C4×C61—24no—
188C22×C4×C61—22no—
189C22×C4×C61—21no—
190C22×C4×C61—42no—
191C22×C4×C61—42no—
192C22×C4×C61—42no—
193C22×C4×C61C22×C411yescharacteristic
194C22×C4×C61C22×C411yescharacteristic
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2411yescharacteristic
199C2×C22⋊D61—21no—
200C2×C22⋊D61—21no—
201C2×C22⋊D61—21no—
202C2×C22⋊D61—21no—
203C2×C22⋊D61—21no—
204C22×Dic61—24no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—24no—
208C22×Dic61—22no—
209C22×Dic61—21no—
210C22×Dic61—21no—
211C22×Dic61—42no—
212C22×Dic61—42no—
213C22×Dic61C22⋊C411yescharacteristic
214C22×Dic61C22⋊C411yescharacteristic
215C22×Dic61C22⋊C411yescharacteristic
216C22×Dic61C22⋊C411yescharacteristic
217C22×Dic61C22⋊C411yescharacteristic
218C22×Dic61C22⋊C411yescharacteristic
219C22×Dic61C22⋊C411yescharacteristic
220C22×Dic61C22⋊C411yescharacteristic
221C22×Dic61C2×D411yescharacteristic
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225#11758224—44no—
226#11758224—42no—
227#11758224—42no—
228#11758222—42no—
229C2×D244C22×C411yescharacteristic
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122C22×C411yescharacteristic
236M16×C61—42no—
237C2×C8×C61—22no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61C22×C411yescharacteristic
241C4⋊C4×C61C22×C411yescharacteristic
242C22⋊C4×C61—21no—
243C22⋊C4×C61—21no—
244C22⋊C4×C61—21no—
245C22⋊C4×C61—21no—
246C22⋊C4×C61—21no—
247C42×C61—21no—
248C22⋊Dic61—21no—
249C22⋊Dic61—21no—
250C22⋊Dic61—21no—
251C22⋊Dic61—21no—
252C22⋊Dic61—21no—
253C22⋊Dic61—21no—
254C22⋊Dic61—21no—
255#11758198—21no—
256#11758198—21no—
257#11758198—21no—
258#11758198—21no—
259#11758198—21no—
260#11758198—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61C22×C411yescharacteristic
266C4⋊Dic61C22×C411yescharacteristic
267#11758196—28no—
268#11758196—28no—
269#11758196—21no—
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273#11758196—21no—
274#11758196—21no—
275#11758196—21no—
276#11758196—21no—
277#11758196—21no—
278#11758196—21no—
279C4×Dic61—21no—
280C4×Dic61—21no—
281C4×Dic61—21no—
282C4×Dic61—21no—
283C4×Dic61—21no—
284C4×Dic61—44no—
285C4×Dic61—44no—
286C4×Dic61C22⋊C411yescharacteristic
287C4×Dic61C22⋊C411yescharacteristic
288C4×Dic61C22⋊C411yescharacteristic
289C4×Dic61C22⋊C411yescharacteristic
290C4×Dic61C22⋊C411yescharacteristic
291C4×Dic61C22⋊C411yescharacteristic
292C4×Dic61C22⋊C411yescharacteristic
293C4×Dic61C22⋊C411yescharacteristic
294C4×Dic61C22×C411yescharacteristic
295C4×Dic61C22×C411yescharacteristic
296C4×Dic61C22×C411yescharacteristic
297C4×Dic61C22×C411yescharacteristic
298C4×Dic61C2×D411yescharacteristic
299C4×Dic61C2×D411yescharacteristic
300C4×Dic61C2×D411yescharacteristic
301C4×Dic61C2×D411yescharacteristic
302#11758194—42no—
303C2×#92418—22no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—21no—
309C23×C61C2×C22⋊C411yescharacteristic
310C23×C61C2×C22⋊C411yescharacteristic
311C23×C61C22×D411yescharacteristic
312C22×D61—21no—
313Q8×C61—41no—
314D4×C61—41no—
315D4×C61—41no—
316D4×C61—41no—
317D4×C61—42no—
318D4×C61—42no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—24no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—42no—
330C2×C4×C61—48no—
331C2×C4×C61—42no—
332C2×C4×C61—42no—
333C2×C4×C61C2×C22⋊C411yescharacteristic
334C2×C4×C61C2×C22⋊C411yescharacteristic
335C2×C4×C61C23×C411yescharacteristic
336C2×C4×C61C22×D411yescharacteristic
337C22⋊D61—41no—
338C22⋊D61—41no—
339C22⋊D61—42no—
340C22⋊D61—42no—
341C22⋊D61—42no—
342C22⋊D61—42no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—24no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—48no—
359C2×Dic61—42no—
360C2×Dic61—42no—
361C2×Dic61—42no—
362C2×Dic61—42no—
363C2×Dic61#10414yes—
364C2×Dic61C2×C22⋊C411yescharacteristic
365C2×Dic61C2×C22⋊C411yescharacteristic
366C2×Dic61C2×C22⋊C411yescharacteristic
367C2×Dic61C2×C22⋊C411yescharacteristic
368C2×Dic61C2×C22⋊C411yescharacteristic
369C2×Dic61C2×C22⋊C411yescharacteristic
370C2×Dic61C2×C22⋊C411yescharacteristic
371C2×Dic61C2×C22⋊C411yescharacteristic
372C2×Dic61AGL(1,ℤ/8)12yes—
373C2×Dic61#13712yes—
374D244—41no—
375C4×D61—42no—
376C4×D61—42no—
377C4×D61—42no—
378Dic122—42no—
379Dic122—42no—
380Dic122—41no—
381C8×C61—42no—
382#92418—42no—
383#17546—611nomaximal, Sylow
384C22×C61—24no—
385C22×C61—24no—
386C22×C61—21no—
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61#41012yes—
396C22×C61C2×#10412yes—
397C22×C61C22×C22⋊C411yescharacteristic
398C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
399C22×C61C2×#13711yescharacteristic
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—41no—
403C4×C61—21no—
404C4×C61—21no—
405C4×C61—21no—
406C4×C61—21no—
407C4×C61—44no—
408C4×C61—41no—
409C4×C61—41no—
410C4×C61—41no—
411Dic61—21no—
412Dic61—21no—
413Dic61—21no—
414Dic61—21no—
415Dic61—44no—
416Dic61—41no—
417Dic61—41no—
418Dic61—41no—
419Dic61#41712yes—
420Dic61#41712yes—
421Dic61C2×#10412yes—
422Dic61C2×#10412yes—
423#3444—611no—
424#2920—611no—
425C2×C4×C4⋊C4—611no—
426#1509—612no—
427#1509—612no—
428#1504—611no—
429#1504—611no—
430#1504—611no—
431#1504D6111yescharacteristic, complemented
432#1503—612no—
433#1502—612no—
434C2×C61—21no—
435C2×C61—21no—
436C2×C61—22no—
437C2×C61—22no—
438C2×C61—81no—
439C2×C61C2×#41011yescharacteristic
440C2×C61C2×#41711yescharacteristic
441C2×C61C22×#10411yescharacteristic
442D61—81no—
443#533—611no—
444#533—611no—
445#533—611no—
446#532—611no—
447#532—611no—
448#532—611no—
449#529—611no—
450#529—611no—
451#529—611no—
452#529—611no—
453#529—1221no—
454#529—1221no—
455#529—1221no—
456#529—1221no—
457#525—611no—
458#525—1221no—
459#525—1221no—
460#525C2×D6111yescharacteristic
461C4×#41—611no—
462C4×#41—611no—
463C4×#41—1221no—
464C4×#41—1221no—
465C22×C4⋊C4—1221no—
466C22×C42—611no—
467C22×C42—1221no—
468#432—612no—
469#432—1221no—
470#431—612no—
471#431—1221no—
472#423—1221no—
473#407—611no—
474#407C2×D6111yescharacteristic
475C4×M16—1221no—
476C4×C4⋊C4—612no—
477C4×C4⋊C4—612no—
478C4×C4⋊C4—1221no—
479C4×C4⋊C4—1221no—
480C2×#95—611no—
481C2×#95C2×D6111yescharacteristic
482#328—612no—
483#328—612no—
484#328—612no—
485#328C2×D6112yes—
486#327—612no—
487#327—612no—
488#327—612no—
489#327C2×D6112yes—
490C61#1754611yescharacteristic, complemented, Sylow
491C2×#41—611no—
492C2×#41—1221no—
493C2×#41—1221no—
494C2×#41C4×D6111yescharacteristic
495C23×C4—21no—
496C23×C4—611no—
497C23×C4—611no—
498C23×C4—1221no—
499C23×C4C22×D6111yescharacteristic
500C2×M16—21no—
501C2×M16—1221no—
502C4⋊Q8—611no—
503C4⋊Q8—611no—
504C4⋊Q8—611no—
505#127—611no—
506#126—1221no—
507#126—1221no—
508#126—1221no—
509#126—1221no—
510#125—611no—
511#125—611no—
512#125—1221no—
513#125—1221no—
514#124—611no—
515#124—611no—
516#124—1221no—
517#124—1221no—
518#123—21no—
519#123—1221no—
520#123—1221no—
521#123—1221no—
522#123—1221no—
523#123—1221no—
524C22⋊Q8—611no—
525C22⋊Q8—611no—
526C22⋊Q8—1221no—
527C22⋊Q8—1221no—
528C22⋊Q8—1221no—
529C22⋊Q8—1221no—
530C22⋊Q8C4×D6111yescharacteristic
531C22⋊Q8C22×D6111yescharacteristic
532#121—611no—
533#121—611no—
534#121—1221no—
535#121—1221no—
536#121—1221no—
537#121—1221no—
538#121C4×D6111yescharacteristic
539#121C22×D6111yescharacteristic
540#120—21no—
541#120—1221no—
542C4×Q8—611no—
543C4×Q8—611no—
544C4×Q8—611no—
545C4×Q8—611no—
546C4×Q8—1221no—
547C4×Q8—1221no—
548C4×Q8—1221no—
549C4×Q8—1221no—
550C4×D4—21no—
551C4×D4—21no—
552C4×D4—611no—
553C4×D4—611no—
554C4×D4—611no—
555C4×D4—611no—
556C4×D4—1221no—
557C4×D4—1221no—
558C4×D4—1221no—
559C4×D4—1221no—
560C4×D4—1221no—
561C4×D4—1221no—
562C4×D4—1221no—
563C4×D4—1221no—
564C4×D4—1221no—
565C4×D4—1221no—
566C4×D4—1221no—
567C4×D4—1221no—
568C4×D4—1221no—
569C4×D4—1221no—
570#117—611no—
571#117—1221no—
572#117—1221no—
573#117—1221no—
574#117—1221no—
575#117—1221no—
576#117—1221no—
577#117—1221no—
578#117—1221no—
579#117C4×D6111yescharacteristic
580C2×C4⋊C4—1222no—
581C2×C4⋊C4—1222no—
582C2×C4⋊C4—1228no—
583C2×C42—611no—
584C2×C42—611no—
585C2×C42—611no—
586C2×C42—611no—
587C2×C42—611no—
588C2×C42—611no—
589C2×C42—611no—
590C2×C42—611no—
591C2×C42—611no—
592C2×C42—611no—
593C2×C42—611no—
594C2×C42—611no—
595C2×C42—1221no—
596C2×C42—1221no—
597C2×C42—1222no—
598C2×C42—1222no—
599C2×C42—2444no—
600C4⋊C8—1222no—
601C4⋊C8—1222no—
602C22⋊C8—21no—
603C22⋊C8—612no—
604C22⋊C8—1221no—
605C22⋊C8C22×D6112yes—
606#97—1222no—
607C4×C8—1222no—
608#95—21no—
609#95—612no—
610#95—1221no—
611#95C22×D6112yes—
612C24D4×D6111yescharacteristic
613#41—42no—
614#41—2442no—
615#41—2444no—
616#41—2442no—
617#41—2442no—
618C2×Q8—611no—
619C2×Q8—1221no—
620C2×Q8—1221no—
621C2×Q8C2×C4×D6111yescharacteristic
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—611no—
626C2×D4—1221no—
627C2×D4—1221no—
628C2×D4—1221no—
629C2×D4—1221no—
630C2×D4—1221no—
631C2×D4C2×C4×D6111yescharacteristic
632C22×C4—24no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—611no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—611no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—611no—
650C22×C4—1221no—
651C22×C4—1221no—
652C22×C4—1222no—
653C22×C4—1224no—
654C22×C4—1222no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1224no—
658C22×C4—1222no—
659C22×C4—1221no—
660C22×C4—2442no—
661C22×C4—2442no—
662C22×C4C2×C4×D6111yescharacteristic
663C22×C4C2×C4×D6111yescharacteristic
664C22×C4D4×D6111yescharacteristic
665C22×C4D4×D6111yescharacteristic
666C22×C4D4×D6111yescharacteristic
667C22×C4C23×D6111yescharacteristic
668M16—42no—
669M16—2442no—
670C2×C8—22no—
671C2×C8—1222no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—611no—
675C4⋊C4—611no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—1221no—
681C4⋊C4—1221no—
682C4⋊C4—1221no—
683C4⋊C4—1221no—
684C4⋊C4—1221no—
685C4⋊C4—1221no—
686C4⋊C4—1221no—
687C4⋊C4—1221no—
688C4⋊C4—1228no—
689C4⋊C4—1228no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4C2×C4×D6111yescharacteristic
693C4⋊C4C2×C4×D6111yescharacteristic
694C22⋊C4—21no—
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—1221no—
700C22⋊C4—1221no—
701C22⋊C4—1221no—
702C22⋊C4—1221no—
703C22⋊C4—1221no—
704C22⋊C4—1221no—
705C22⋊C4—1221no—
706C22⋊C4—1221no—
707C22⋊C4—1221no—
708C22⋊C4—1221no—
709C22⋊C4—1221no—
710C22⋊C4—1221no—
711C22⋊C4—1221no—
712C42—21no—
713C42—611no—
714C42—611no—
715C42—611no—
716C42—611no—
717C42—611no—
718C42—611no—
719C42—611no—
720C42—611no—
721C42—611no—
722C42—611no—
723C42—611no—
724C42—611no—
725C42—611no—
726C42—611no—
727C42—611no—
728C42—611no—
729C42—1221no—
730C42—1221no—
731C42—1221no—
732C42—1221no—
733C42—1221no—
734C42—2444no—
735C42—2444no—
736C23—22no—
737C23—22no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—1221no—
742C23C22⋊C4×D6111yescharacteristic
743C23C22⋊C4×D6111yescharacteristic
744C23C2×D4×D6111yescharacteristic
745Q8—41no—
746Q8—2441no—
747Q8—2442no—
748Q8—2442no—
749D4—41no—
750D4—42no—
751D4—42no—
752D4—41no—
753D4—41no—
754D4—2441no—
755D4—2442no—
756D4—2442no—
757D4—2442no—
758D4—2442no—
759D4—2441no—
760D4—2441no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—48no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—611no—
776C2×C4—611no—
777C2×C4—611no—
778C2×C4—611no—
779C2×C4—614no—
780C2×C4—612no—
781C2×C4—612no—
782C2×C4—611no—
783C2×C4—611no—
784C2×C4—611no—
785C2×C4—611no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—1222no—
791C2×C4—1222no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1224no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—2442no—
802C2×C4—2442no—
803C2×C4—2442no—
804C2×C4—2442no—
805C2×C4—2442no—
806C2×C4—2448no—
807C2×C4—2442no—
808C2×C4—2442no—
809C2×C4C22⋊C4×D6111yescharacteristic
810C2×C4C22⋊C4×D6111yescharacteristic
811C2×C4C22×C4×D6111yescharacteristic
812C2×C4C2×D4×D6111yescharacteristic
813C8—42no—
814C8—2442no—
815C22—24no—
816C22—24no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—2441no—
827C22—2441no—
828C22—2441no—
829C22#1683973412yes—
830C22#104×D6112yes—
831C22C2×C22⋊C4×D6111yescharacteristic
832C22AGL(1,ℤ/8)×D6111yescharacteristic
833C22#137×D6111yescharacteristic
834C4—21no—
835C4—21no—
836C4—21no—
837C4—21no—
838C4—44no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—612no—
843C4—612no—
844C4—612no—
845C4—612no—
846C4—1221no—
847C4—1221no—
848C4—1221no—
849C4—1221no—
850C4—2444no—
851C4—2441no—
852C4—2441no—
853C4—2441no—
854C2—21no—
855C2—22no—
856C2—22no—
857C2—21no—
858C2—81no—
859C2—4881no—
860C2C2×#1683973411yescharacteristic
861C2#417×D6111yescharacteristic
862C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1504C2
socleC22×C61C22×C22⋊C4
prime radical#21459111C2
cosocleC22×C4×C61C24
hypercenter#1504D61
hypocenterC61#17546
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1504

Complements

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

NH ≅ G/Ntype
2. #21454448C2semidirect
3. C2×#16839613C2semidirect
4. #21444343C2semidirect
5. #21444341C2semidirect
6. #21444324C2semidirect
7. #21444323C2semidirect
8. #21444321C2semidirect
9. #21444316C2semidirect
10. #21444312C2semidirect
11. C61×#1504C2semidirect
12. #16840315C4semidirect
13. #16840314C4semidirect
15. #16840308C4semidirect
16. #16840307C4semidirect
18. #16840298C4semidirect
20. #16840293C4semidirect
29. #41×Dic61C4semidirect
30. #16840230C4semidirect
66. #14519776C2×C4semidirect
67. #14519776C2×C4semidirect
68. #14519775C2×C4semidirect
69. #14519773C2×C4semidirect
74. #14519768C2×C4semidirect
75. #14519768C2×C4semidirect
78. #14519766C2×C4semidirect
79. #14519764C2×C4semidirect
100. Q8×Dic61C2×C4semidirect
101. Q8×Dic61C2×C4semidirect
106. #14519742C2×C4semidirect
107. #14519742C2×C4semidirect
112. D4×Dic61C2×C4semidirect
113. D4×Dic61C2×C4semidirect
114. #14519739C2×C4semidirect
115. #14519739C2×C4semidirect
431. #1504D61semidirect
490. C61#17546semidirect

Maximal subgroups

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

subgroupindex
#214591112
#214544482
C2×#168396132
#214443432
#214443412
#214443242
#214443232
#214443212
#214443162
#214443122
C61×#15042
#1754661