Finite Group Databasebeta

← D61×#1495 #29646639

Subgroups — D61×#1495 #29646639

Order 15616.

1066 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D61C211yesmaximal, characteristic
2#431×D61C211yesmaximal, characteristic, complemented
3#423×D61C211yesmaximal, characteristic, complemented
4#21444285C211yesmaximal, characteristic, complemented
5#21444284C211yesmaximal, characteristic, complemented
6#21444283C212yesmaximal, complemented
7#21444282C211yesmaximal, characteristic, complemented
8#21444281C212yesmaximal, complemented
9Q8⋊C8×D61C212yesmaximal, complemented
10D4⋊C8×D61C212yesmaximal, complemented
11C61×#1495C211yesmaximal, characteristic, complemented
12C2×M16×D61—21no—
13#16840299C2211yescharacteristic
14#16840298C411yescharacteristic
15#16840297C411yescharacteristic
16#16840296C2211yescharacteristic
17#16840295—21no—
18#16840294C2211yescharacteristic
19#16840293C411yescharacteristic
20#16840292—21no—
21#16840291C411yescharacteristic
22#16840290—21no—
23#16840289—21no—
24#126×D61—21no—
25#125×D61C411yescharacteristic
26#124×D61C411yescharacteristic
27#123×D61—21no—
28C22⋊Q8×D61C411yescharacteristic
29#121×D61C411yescharacteristic
30C4×Q8×D61C2211yescharacteristic
31C4×D4×D61—21no—
32C4×D4×D61C2211yescharacteristic
33#117×D61—21no—
34C2×C42×D61C2211yescharacteristic
35#16839815C2211yescharacteristic, complemented
36#16839814—21no—
37#16839813C2212yescomplemented
38#16839812—21no—
39#16839786C2211yescharacteristic, complemented
40#16839785—21no—
41#16839784—21no—
42#16839784C2212yescomplemented
43C4⋊C8×D61—21no—
44C4⋊C8×D61—21no—
45C4⋊C8×D61C2212yes—
46C22⋊C8×D61—21no—
47C4×C8×D61C2212yes—
48#16839494C2212yescomplemented
49Q8⋊#92418C2212yescomplemented
50#16839492C2212yescomplemented
51#16839491C2212yescomplemented
52D4⋊#92418C2212yescomplemented
53#16839489C2212yescomplemented
54C61×#529C2211yescharacteristic
55C61×#431C2211yescharacteristic, complemented
56C61×#423C2211yescharacteristic, complemented
57C61×Q8⋊C8C2212yescomplemented
58C61×D4⋊C8C2212yescomplemented
59C2×Q8×D61C2×C411yescharacteristic
60C2×D4×D61—21no—
61C2×D4×D61C2×C411yescharacteristic
62C22×C4×D61—21no—
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C2×#11758194—21no—
67C2×#11758189—22no—
68M16×D61—44no—
69C2×C8×D61—22no—
70C2×C8×D61—22no—
71#14519772—21no—
72#14519772—21no—
73#14519772—21no—
74#14519771—21no—
75#14519770—21no—
76#14519770—21no—
77#14519770—21no—
78#14519769C2×C411yescharacteristic
79#14519768C2×C411yescharacteristic
80#14519768C2×C411yescharacteristic
81#14519767—21no—
82#14519767—21no—
83#14519766C2×C411yescharacteristic
84#14519765C2×C411yescharacteristic
85#14519764C2×C411yescharacteristic
86#14519763—21no—
87#14519763—21no—
88#14519762—21no—
89#14519762—21no—
90#14519761—21no—
91#14519760—21no—
92#14519759—21no—
93#14519759—21no—
94#14519758—21no—
95#14519757C2×C411yescharacteristic
96#14519756C2×C411yescharacteristic
97#14519755—21no—
98#14519754—21no—
99#14519753C2×C411yescharacteristic
100#14519752C2×C411yescharacteristic
101#14519751C2×C411yescharacteristic
102#14519750—21no—
103#14519749—21no—
104#14519748C2×C411yescharacteristic
105Q8×Dic61C2×C411yescharacteristic
106C4×Dic122—21no—
107C4×Dic122C2311yescharacteristic
108#14519742—21no—
109#14519742C2×C411yescharacteristic
110C4×D244—21no—
111C4×D244C2311yescharacteristic
112D4×Dic61—21no—
113D4×Dic61C2×C411yescharacteristic
114#14519739—21no—
115#14519739C2×C411yescharacteristic
116C4×C22⋊D61—21no—
117C4×C22⋊D61—21no—
118C4×C22⋊D61—21no—
119#14519737—21no—
120#14519737—21no—
121#14519737—21no—
122#14519736—21no—
123#14519735—21no—
124#14519735—21no—
125#14519734—21no—
126#14519734—21no—
127#14519733—21no—
128#14519733—21no—
129C4⋊C4×D61—21no—
130C4⋊C4×D61—21no—
131C4⋊C4×D61—21no—
132C4⋊C4×D61—21no—
133C4⋊C4×D61C2×C411yescharacteristic
134C4⋊C4×D61C2×C411yescharacteristic
135C22⋊C4×D61—21no—
136C22⋊C4×D61—21no—
137C22⋊C4×D61—21no—
138C22⋊C4×D61—21no—
139C22⋊C4×D61—21no—
140C2×C4×Dic61C2×C411yescharacteristic
141C2×C4×Dic61D411yescharacteristic
142C2×C4×Dic61D411yescharacteristic
143C42×D61—21no—
144C42×D61C2×C411yescharacteristic
145C42×D61C2×C411yescharacteristic
146C42×D61D411yescharacteristic
147C42×D61D411yescharacteristic
148C42×D61D411yescharacteristic
149C42×D61D411yescharacteristic
150C42×D61C2311yescharacteristic
151C42×D61C2311yescharacteristic
152C4⋊#92418—21no—
153C4⋊#92418—21no—
154C4⋊#92418C2312yes—
155#14519706—22no—
156#14519706—22no—
157#14519706—22no—
158C22⋊#92418—21no—
159#14519689—22no—
160C4×#92418C2312yes—
161C8×Dic61—22no—
162C2×M16×C61—21no—
163#126×C61—21no—
164#125×C61C2×C411yescharacteristic
165#124×C61C2×C411yescharacteristic
166#123×C61—21no—
167C22⋊Q8×C61C2×C411yescharacteristic
168#121×C61C2×C411yescharacteristic
169C4×Q8×C61C2311yescharacteristic
170C4×D4×C61—21no—
171C4×D4×C61C2311yescharacteristic
172#117×C61—21no—
173C2×C42×C61C2311yescharacteristic
174C4⋊C8×C61—21no—
175C4⋊C8×C61—21no—
176C4⋊C8×C61C2312yes—
177C22⋊C8×C61—21no—
178C4×C8×C61C2312yes—
179C23×D61—21no—
180C23×D61C22⋊C411yescharacteristic
181C2×Q8×C61C22×C411yescharacteristic
182C2×D4×C61—21no—
183C2×D4×C61C22×C411yescharacteristic
184C22×C4×C61—21no—
185C22×C4×C61C22×C411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C22×Dic61—21no—
192C22×Dic61C22⋊C411yescharacteristic
193C22×Dic61C22⋊C411yescharacteristic
194C22×Dic61C22⋊C411yescharacteristic
195Q8×D61—24no—
196D4×D61—24no—
197D4×D61—44no—
198C2×D244—21no—
199C2×D244C22×C411yescharacteristic
200C2×C4×D61—24no—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61—42no—
211C2×C4×D61C22⋊C411yescharacteristic
212C2×C4×D61C22⋊C411yescharacteristic
213C2×C4×D61C22⋊C411yescharacteristic
214C2×C4×D61C22⋊C411yescharacteristic
215C2×C4×D61C22⋊C411yescharacteristic
216C2×C4×D61C22⋊C411yescharacteristic
217C2×C4×D61C22×C411yescharacteristic
218C2×C4×D61C22×C411yescharacteristic
219C2×C4×D61C2×D411yescharacteristic
220C2×C4×D61C2×D411yescharacteristic
221C2×C4×D61C2×D411yescharacteristic
222C2×C4×D61C2×D411yescharacteristic
223C2×Dic122—21no—
224C2×Dic122C22×C411yescharacteristic
225M16×C61—42no—
226C2×C8×C61—22no—
227C2×C8×C61—22no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61C22×C411yescharacteristic
233C4⋊C4×C61C22×C411yescharacteristic
234C22⋊C4×C61—21no—
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C22⋊C4×C61—21no—
238C22⋊C4×C61—21no—
239C42×C61—21no—
240C42×C61C22×C411yescharacteristic
241C42×C61C2×D411yescharacteristic
242C42×C61C2×D411yescharacteristic
243C42×C61C2411yescharacteristic
244C22⋊Dic61—21no—
245C22⋊Dic61—21no—
246C22⋊Dic61—21no—
247C22⋊Dic61—21no—
248C22⋊Dic61—21no—
249#11758198—21no—
250#11758198—21no—
251#11758198—21no—
252#11758198—21no—
253#11758198—21no—
254#11758198—21no—
255#11758198—21no—
256#11758198—21no—
257#11758198—21no—
258#11758198—21no—
259C4⋊Dic61—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61C22×C411yescharacteristic
264C4⋊Dic61C22×C411yescharacteristic
265#11758196—21no—
266#11758196—21no—
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273#11758196—21no—
274#11758196—21no—
275C4×Dic61—21no—
276C4×Dic61—21no—
277C4×Dic61—21no—
278C4×Dic61C22⋊C411yescharacteristic
279C4×Dic61C22⋊C411yescharacteristic
280C4×Dic61C22⋊C411yescharacteristic
281C4×Dic61C22⋊C411yescharacteristic
282C4×Dic61C22⋊C411yescharacteristic
283C4×Dic61C22⋊C411yescharacteristic
284C4×Dic61C22×C411yescharacteristic
285C4×Dic61C22×C411yescharacteristic
286C4×Dic61C2×D411yescharacteristic
287C4×Dic61C2×D411yescharacteristic
288C4×Dic61C2×D411yescharacteristic
289C4×Dic61C2×D411yescharacteristic
290#11758194—42no—
291C2×#92418—22no—
292C2×#92418—22no—
293#11758189—44no—
294C8×D61—44no—
295C8×D61—44no—
296C23×C61—21no—
297C23×C61C2×C22⋊C411yescharacteristic
298C22×D61—22no—
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—21no—
302C22×D61—42no—
303C22×D61—42no—
304C22×D61—42no—
305C22×D61C2×C22⋊C411yescharacteristic
306C22×D61C2×C22⋊C411yescharacteristic
307Q8×C61—22no—
308D4×C61—22no—
309D4×C61—42no—
310C2×C4×C61—22no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61C2×C22⋊C411yescharacteristic
320C2×C4×C61C2×C22⋊C411yescharacteristic
321C2×C4×C61C2×C22⋊C411yescharacteristic
322C2×C4×C61C23×C411yescharacteristic
323C2×C4×C61C22×D411yescharacteristic
324C2×C4×C61C22×D411yescharacteristic
325C22⋊D61—42no—
326C22⋊D61—42no—
327C22⋊D61—42no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—41no—
334C2×Dic61—42no—
335C2×Dic61C2×C22⋊C411yescharacteristic
336C2×Dic61C2×C22⋊C411yescharacteristic
337C2×Dic61C2×C22⋊C411yescharacteristic
338C2×Dic61C2×C22⋊C411yescharacteristic
339C2×Dic61C2×C22⋊C411yescharacteristic
340C2×Dic61C2×C22⋊C411yescharacteristic
341D244—22no—
342D244—42no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—21no—
349C4×D61—21no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—41no—
353C4×D61—41no—
354C4×D61—42no—
355C4×D61—42no—
356C4×D61—42no—
357C4×D61—41no—
358C4×D61—41no—
359C4×D61—42no—
360C4×D61#13114yes—
361C4×D61AGL(1,ℤ/8)12yes—
362C4×D61#13712yes—
363Dic122—22no—
364Dic122—42no—
365C8×C61—42no—
366C8×C61—42no—
367#92418—42no—
368#92418—42no—
369C2×#1495—611nomaximal, Sylow
370C22×C61—21no—
371C22×C61—21no—
372C22×C61—21no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61C22×C22⋊C411yescharacteristic
377C2×D61—21no—
378C2×D61—21no—
379C2×D61—21no—
380C2×D61—44no—
381C2×D61—41no—
382C2×D61—41no—
383C2×D61—41no—
384C2×D61—84no—
385C2×D61#40812yes—
386C2×D61#41712yes—
387C2×D61#42112yes—
388C4×C61—21no—
389C4×C61—21no—
390C4×C61—21no—
391C4×C61—21no—
392C4×C61—41no—
393C4×C61—41no—
394C4×C61—41no—
395C4×C61C2×#13112yes—
396C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
397C4×C61C2×#13711yescharacteristic
398Dic61—21no—
399Dic61—21no—
400Dic61—21no—
401Dic61—21no—
402Dic61—41no—
403Dic61—41no—
404Dic61—41no—
405Dic61#40812yes—
406Dic61#41712yes—
407C2×#529—611no—
408C2×#431—611no—
409C2×#423—611no—
410#1495—611no—
411#1495—611no—
412#1495—612no—
413#1495—612no—
414#1495—611no—
415#1495D6111yescharacteristic, direct product factor
416C2×Q8⋊C8—612no—
417C2×D4⋊C8—612no—
418C2×C61—41no—
419C2×C61—81no—
420C2×C61C2×#40811yescharacteristic
421C2×C61C2×#41711yescharacteristic
422C2×C61C2×#42111yescharacteristic
423D61—41no—
424D61—81no—
425D61#149514yesdirect product factor
426C22×M16—1221no—
427#529—611no—
428#529—611no—
429#529—611no—
430#529—611no—
431#529—611no—
432#529—611no—
433#529—611no—
434#529—1221no—
435#529—1221no—
436#529—1221no—
437#529—1221no—
438#529C2×D6111yescharacteristic
439C2×#126—1221no—
440C2×#125—611no—
441C2×#124—611no—
442C2×#123—1221no—
443C2×C22⋊Q8—611no—
444C2×#121—611no—
445C2×C4×Q8—611no—
446C2×C4×D4—611no—
447C2×C4×D4—1221no—
448C2×#117—1221no—
449C22×C42—611no—
450#431—611no—
451#431—612no—
452#431—1221no—
453#431—1221no—
454#431C2×D6111yescharacteristic, complemented
455#423—611no—
456#423—612no—
457#423—1221no—
458#423—1221no—
459#423C2×D6111yescharacteristic, complemented
460C2×C4⋊C8—612no—
461C2×C4⋊C8—1221no—
462C2×C4⋊C8—1221no—
463C2×C22⋊C8—1221no—
464C2×C4×C8—612no—
465Q8⋊C8—612no—
466Q8⋊C8—612no—
467Q8⋊C8—612no—
468Q8⋊C8C2×D6112yescomplemented
469D4⋊C8—612no—
470D4⋊C8—612no—
471D4⋊C8—612no—
472D4⋊C8C2×D6112yescomplemented
473C61C2×#149511yescharacteristic, complemented, Sylow
474C22×Q8—611no—
475C22×D4—611no—
476C22×D4—1221no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—1221no—
481C2×M16—21no—
482C2×M16—1222no—
483C2×M16—1221no—
484C2×M16—2444no—
485C22×C8—1222no—
486C22×C8—1222no—
487#126—21no—
488#126—1221no—
489#126—1221no—
490#126—1221no—
491#126—1221no—
492#126—1221no—
493#126—1221no—
494#126—1221no—
495#125—611no—
496#125—611no—
497#125—611no—
498#125—1221no—
499#125—1221no—
500#125C4×D6111yescharacteristic
501#124—611no—
502#124—611no—
503#124—611no—
504#124—1221no—
505#124—1221no—
506#124C4×D6111yescharacteristic
507#123—21no—
508#123—1221no—
509#123—1221no—
510#123—1221no—
511#123—1221no—
512#123—1221no—
513#123—1221no—
514#123—1221no—
515C22⋊Q8—611no—
516C22⋊Q8—611no—
517C22⋊Q8—611no—
518C22⋊Q8—1221no—
519C22⋊Q8—1221no—
520C22⋊Q8C4×D6111yescharacteristic
521#121—611no—
522#121—611no—
523#121—611no—
524#121—1221no—
525#121—1221no—
526#121C4×D6111yescharacteristic
527C4×Q8—611no—
528C4×Q8—611no—
529C4×Q8—611no—
530C4×Q8—1221no—
531C4×Q8—1221no—
532C4×Q8C22×D6111yescharacteristic
533C4×D4—21no—
534C4×D4—611no—
535C4×D4—611no—
536C4×D4—611no—
537C4×D4—1221no—
538C4×D4—1221no—
539C4×D4—1221no—
540C4×D4—1221no—
541C4×D4—1221no—
542C4×D4—1221no—
543C4×D4—1221no—
544C4×D4—1221no—
545C4×D4—1221no—
546C4×D4C22×D6111yescharacteristic
547#117—21no—
548#117—1221no—
549#117—1221no—
550#117—1221no—
551#117—1221no—
552#117—1221no—
553#117—1221no—
554#117—1221no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—611no—
557C2×C4⋊C4—1221no—
558C2×C4⋊C4—1221no—
559C2×C4⋊C4—1221no—
560C2×C4⋊C4—1221no—
561C2×C22⋊C4—1221no—
562C2×C22⋊C4—1221no—
563C2×C22⋊C4—1221no—
564C2×C22⋊C4—1221no—
565C2×C22⋊C4—1221no—
566C2×C42—611no—
567C2×C42—611no—
568C2×C42—611no—
569C2×C42—611no—
570C2×C42—611no—
571C2×C42—611no—
572C2×C42—611no—
573C2×C42—611no—
574C2×C42—611no—
575C2×C42—611no—
576C2×C42—611no—
577C2×C42—1221no—
578C2×C42C22×D6111yescharacteristic
579C4⋊C8—21no—
580C4⋊C8—21no—
581C4⋊C8—612no—
582C4⋊C8—1222no—
583C4⋊C8—1222no—
584C4⋊C8—1222no—
585C4⋊C8—1221no—
586C4⋊C8—1221no—
587C4⋊C8C22×D6112yes—
588C22⋊C8—21no—
589C22⋊C8—1222no—
590C22⋊C8—1221no—
591C4×C8—612no—
592C4×C8—1222no—
593C4×C8C22×D6112yes—
594C24—611no—
595C24—1221no—
596C2×Q8—611no—
597C2×Q8—1221no—
598C2×Q8—1224no—
599C2×Q8C2×C4×D6111yescharacteristic
600C2×D4—21no—
601C2×D4—611no—
602C2×D4—1221no—
603C2×D4—1224no—
604C2×D4—1221no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4—2444no—
608C2×D4C2×C4×D6111yescharacteristic
609C22×C4—21no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—611no—
625C22×C4—1222no—
626C22×C4—1224no—
627C22×C4—1222no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—2442no—
635C22×C4—2442no—
636C22×C4—2442no—
637C22×C4C2×C4×D6111yescharacteristic
638C22×C4D4×D6111yescharacteristic
639C22×C4D4×D6111yescharacteristic
640M16—42no—
641M16—2444no—
642M16—2442no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—1222no—
646C2×C8—1222no—
647C2×C8—2444no—
648C2×C8—2444no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—611no—
654C4⋊C4—611no—
655C4⋊C4—1221no—
656C4⋊C4—1221no—
657C4⋊C4—1221no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C4⋊C4—1221no—
663C4⋊C4—1221no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4—1221no—
669C4⋊C4C2×C4×D6111yescharacteristic
670C4⋊C4C2×C4×D6111yescharacteristic
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—1221no—
677C22⋊C4—1221no—
678C22⋊C4—1221no—
679C22⋊C4—1221no—
680C22⋊C4—1221no—
681C22⋊C4—1221no—
682C22⋊C4—1221no—
683C22⋊C4—1221no—
684C22⋊C4—1221no—
685C22⋊C4—1221no—
686C22⋊C4—1221no—
687C22⋊C4—1221no—
688C22⋊C4—1221no—
689C22⋊C4—1221no—
690C22⋊C4—1221no—
691C42—21no—
692C42—611no—
693C42—611no—
694C42—611no—
695C42—611no—
696C42—611no—
697C42—611no—
698C42—611no—
699C42—611no—
700C42—611no—
701C42—611no—
702C42—611no—
703C42—611no—
704C42—1221no—
705C42—1221no—
706C42—1221no—
707C42C2×C4×D6111yescharacteristic
708C42D4×D6111yescharacteristic
709C42D4×D6111yescharacteristic
710C42C23×D6111yescharacteristic
711C23—21no—
712C23—611no—
713C23—611no—
714C23—1222no—
715C23—1222no—
716C23—1222no—
717C23—1221no—
718C23—2442no—
719C23—2442no—
720C23—2442no—
721C23C22⋊C4×D6111yescharacteristic
722Q8—22no—
723Q8—1222no—
724Q8—2442no—
725D4—22no—
726D4—42no—
727D4—1222no—
728D4—2442no—
729D4—2442no—
730D4—2442no—
731D4—2442no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—611no—
742C2×C4—611no—
743C2×C4—614no—
744C2×C4—612no—
745C2×C4—612no—
746C2×C4—611no—
747C2×C4—611no—
748C2×C4—611no—
749C2×C4—611no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1221no—
760C2×C4—1221no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—1221no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—2442no—
767C2×C4—2442no—
768C2×C4—2442no—
769C2×C4—2442no—
770C2×C4—2442no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4C22⋊C4×D6111yescharacteristic
775C2×C4C22⋊C4×D6111yescharacteristic
776C2×C4C22⋊C4×D6111yescharacteristic
777C2×C4C22×C4×D6111yescharacteristic
778C2×C4C2×D4×D6111yescharacteristic
779C2×C4C2×D4×D6111yescharacteristic
780C8—42no—
781C8—42no—
782C8—2442no—
783C8—2442no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—612no—
791C22—612no—
792C22—612no—
793C22—1221no—
794C22—1221no—
795C22—1221no—
796C22—4884no—
797C22—2444no—
798C22—2441no—
799C22—2441no—
800C22—2441no—
801C22C2×C22⋊C4×D6111yescharacteristic
802C4—21no—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—612no—
810C4—612no—
811C4—1221no—
812C4—1221no—
813C4—1221no—
814C4—1221no—
815C4—2441no—
816C4—2441no—
817C4—2441no—
818C4#131×D6112yes—
819C4AGL(1,ℤ/8)×D6111yescharacteristic
820C4#137×D6111yescharacteristic
821C2—41no—
822C2—81no—
823C2—614no—
824C2—4881no—
825C2—2441no—
826C2#408×D6111yescharacteristic
827C2#417×D6111yescharacteristic
828C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1495C2
socleC22×C61C22×C22⋊C4
prime radical#121×D61C4
cosocleC42×C61C24
hypercenter#1495D61
hypocenterC61C2×#1495
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1495

Complements

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

NH ≅ G/Ntype
2. #431×D61C2semidirect
3. #423×D61C2semidirect
4. #21444285C2semidirect
5. #21444284C2semidirect
6. #21444283C2semidirect
7. #21444282C2semidirect
8. #21444281C2semidirect
9. Q8⋊C8×D61C2semidirect
10. D4⋊C8×D61C2semidirect
11. C61×#1495C2semidirect
35. #16839815C22semidirect
37. #16839813C22semidirect
39. #16839786C22semidirect
42. #16839784C22semidirect
48. #16839494C22semidirect
49. Q8⋊#92418C22semidirect
50. #16839492C22semidirect
51. #16839491C22semidirect
52. D4⋊#92418C22semidirect
53. #16839489C22semidirect
55. C61×#431C22semidirect
56. C61×#423C22semidirect
57. C61×Q8⋊C8C22semidirect
58. C61×D4⋊C8C22semidirect
415. #1495D61direct (N × H)
425. D61#1495direct (N × H)
454. #431C2×D61semidirect
459. #423C2×D61semidirect
468. Q8⋊C8C2×D61semidirect
472. D4⋊C8C2×D61semidirect
473. C61C2×#1495semidirect

Maximal subgroups

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

subgroupindex
#529×D612
#431×D612
#423×D612
#214442852
#214442842
#214442832
#214442822
#214442812
Q8⋊C8×D612
D4⋊C8×D612
C61×#14952
C2×#149561