Finite Group Databasebeta

← #29646673

Subgroups — #29646673

Order 15616.

1056 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459113C211yesmaximal, characteristic
2#431×D61C211yesmaximal, characteristic, complemented
3#423×D61C211yesmaximal, characteristic, complemented
4#21444285C211yesmaximal, characteristic, complemented
5#21444284C211yesmaximal, characteristic, complemented
6#21444282C211yesmaximal, characteristic, complemented
7#21444272C212yesmaximal, complemented
8#21444268C212yesmaximal, complemented
9#21444205C212yesmaximal, complemented
10#21444203C212yesmaximal, complemented
11C61×#1495C211yesmaximal, characteristic, complemented
12C2×M16×D61—21no—
13#16840318C411yescharacteristic
14#16840316C2211yescharacteristic
15#16840314C411yescharacteristic
16#16840311C411yescharacteristic
17#16840309C2211yescharacteristic
18#16840307C411yescharacteristic
19#16840297C411yescharacteristic
20#16840296C2211yescharacteristic
21#16840295—21no—
22#16840295—21no—
23#16840291C411yescharacteristic
24#16840290—21no—
25#16840289—21no—
26#16840275C411yescharacteristic
27#16840272C411yescharacteristic
28#16840271—21no—
29#16840270—21no—
30C4×#11758226C2211yescharacteristic
31#16840230—21no—
32C4×#11758224—21no—
33C4×#11758224C2211yescharacteristic
34C2×C42×D61C2211yescharacteristic
35#16839815C2211yescharacteristic
36#16839814—21no—
37#16839813C2212yes—
38#16839812—21no—
39#16839786C2211yescharacteristic
40#16839785—21no—
41#16839784—21no—
42#16839784C2212yes—
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
56C61×#423C2211yescharacteristic
57C61×Q8⋊C8C2212yescomplemented
58C61×D4⋊C8C2212yescomplemented
59C2×#11758226C2×C411yescharacteristic
60C2×#11758222—21no—
61C2×#11758224—21no—
62C2×#11758224C2×C411yescharacteristic
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#14519776C2×C411yescharacteristic
72#14519776C2×C411yescharacteristic
73#14519775C2×C411yescharacteristic
74#14519773C2×C411yescharacteristic
75#14519772—21no—
76#14519771—21no—
77#14519770—21no—
78#14519769C2×C411yescharacteristic
79#14519767—21no—
80#14519767—21no—
81#14519765C2×C411yescharacteristic
82#14519763—21no—
83#14519763—21no—
84#14519762—21no—
85#14519762—21no—
86#14519760—21no—
87#14519759—21no—
88#14519759—21no—
89#14519757C2×C411yescharacteristic
90#14519756C2×C411yescharacteristic
91#14519755—21no—
92#14519755—21no—
93#14519755—21no—
94#14519754—21no—
95#14519753C2×C411yescharacteristic
96#14519752C2×C411yescharacteristic
97#14519751C2×C411yescharacteristic
98#14519750—21no—
99#14519750—21no—
100#14519750—21no—
101#14519749—21no—
102#14519748C2×C411yescharacteristic
103#14519747—21no—
104#14519745—21no—
105Q8×Dic61C2×C411yescharacteristic
106C4×Dic122—21no—
107C4×Dic122C2311yescharacteristic
108#14519742—21no—
109#14519742—21no—
110#14519742—21no—
111#14519742C2×C411yescharacteristic
112C4×D244—21no—
113C4×D244C2311yescharacteristic
114D4×Dic61—21no—
115D4×Dic61C2×C411yescharacteristic
116#14519739—21no—
117#14519739—21no—
118#14519739—21no—
119#14519739C2×C411yescharacteristic
120C4×C22⋊D61—21no—
121C4×C22⋊D61—21no—
122C4×C22⋊D61—21no—
123#14519737—21no—
124#14519737—21no—
125#14519737—21no—
126#14519737—21no—
127#14519737—21no—
128#14519737—21no—
129#14519737—21no—
130#14519735—21no—
131#14519735—21no—
132#14519735C2×C411yescharacteristic
133#14519735C2×C411yescharacteristic
134#14519734—21no—
135#14519734—21no—
136#14519733—21no—
137#14519733—21no—
138#14519733—21no—
139C2×C4×Dic61—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×D61C22⋊C411yescharacteristic
180C2×Q8×C61C22×C411yescharacteristic
181C2×D4×C61—21no—
182C2×D4×C61C22×C411yescharacteristic
183C22×C4×C61—21no—
184C22×C4×C61C22×C411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C2×C22⋊D61—21no—
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61C22⋊C411yescharacteristic
195C22×Dic61C22⋊C411yescharacteristic
196C22×Dic61C22⋊C411yescharacteristic
197#11758226—24no—
198#11758224—24no—
199#11758224—44no—
200#11758222—42no—
201#11758222—42no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244C22×C411yescharacteristic
205C2×C4×D61—24no—
206C2×C4×D61—22no—
207C2×C4×D61—22no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—42no—
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×D61C22×C411yescharacteristic
220C2×C4×D61C2×D411yescharacteristic
221C2×C4×D61C2×D411yescharacteristic
222C2×C4×D61C2×D411yescharacteristic
223C2×C4×D61C2×D411yescharacteristic
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122C22×C411yescharacteristic
227M16×C61—42no—
228C2×C8×C61—22no—
229C2×C8×C61—22no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61C22×C411yescharacteristic
235C4⋊C4×C61C22×C411yescharacteristic
236C22⋊C4×C61—21no—
237C22⋊C4×C61—21no—
238C22⋊C4×C61—21no—
239C22⋊C4×C61—21no—
240C22⋊C4×C61—21no—
241C42×C61—21no—
242C42×C61C22×C411yescharacteristic
243C42×C61C2×D411yescharacteristic
244C42×C61C2×D411yescharacteristic
245C42×C61C2411yescharacteristic
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⋊Dic61C22×C411yescharacteristic
262C4⋊Dic61C22×C411yescharacteristic
263#11758196—21no—
264#11758196—21no—
265#11758196—21no—
266#11758196—21no—
267#11758196—21no—
268#11758196—21no—
269#11758196—21no—
270#11758196—21no—
271#11758196—21no—
272#11758196—21no—
273C4×Dic61—21no—
274C4×Dic61—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—21no—
301C22×D61—41no—
302C22×D61C2×C22⋊C411yescharacteristic
303C22×D61C2×C22⋊C411yescharacteristic
304Q8×C61—22no—
305D4×C61—22no—
306D4×C61—42no—
307C2×C4×C61—22no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61C2×C22⋊C411yescharacteristic
317C2×C4×C61C2×C22⋊C411yescharacteristic
318C2×C4×C61C2×C22⋊C411yescharacteristic
319C2×C4×C61C23×C411yescharacteristic
320C2×C4×C61C22×D411yescharacteristic
321C2×C4×C61C22×D411yescharacteristic
322C22⋊D61—42no—
323C22⋊D61—42no—
324C22⋊D61—42no—
325C22⋊D61—42no—
326C22⋊D61—42no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—21no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—42no—
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—
343D244—42no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—21no—
348C4×D61—21no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—22no—
353C4×D61—41no—
354C4×D61—41no—
355C4×D61—42no—
356C4×D61—41no—
357C4×D61—41no—
358C4×D61—42no—
359C4×D61#13114yes—
360C4×D61AGL(1,ℤ/8)12yes—
361C4×D61#13712yes—
362Dic122—22no—
363Dic122—42no—
364Dic122—42no—
365C8×C61—42no—
366C8×C61—42no—
367#92418—42no—
368#92418—42no—
369#17481—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—21no—
381C2×D61—44no—
382C2×D61—41no—
383C2×D61—41no—
384C2×D61—41no—
385C2×D61#40812yes—
386C2×D61#41712yes—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—21no—
390C4×C61—21no—
391C4×C61—41no—
392C4×C61—41no—
393C4×C61—41no—
394C4×C61C2×#13112yes—
395C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
396C4×C61C2×#13711yescharacteristic
397Dic61—21no—
398Dic61—21no—
399Dic61—21no—
400Dic61—41no—
401Dic61—41no—
402Dic61—41no—
403Dic61#40812yes—
404Dic61#41712yes—
405Dic61#42112yes—
406#3444—611no—
407C2×#431—611no—
408C2×#423—611no—
409#1495—611no—
410#1495—611no—
411#1495—611no—
412#1495D6111yescharacteristic, complemented
413#1493—612no—
414#1492—612no—
415#1477—612no—
416#1477—612no—
417C2×C61—41no—
418C2×C61—81no—
419C2×C61C2×#40811yescharacteristic
420C2×C61C2×#41711yescharacteristic
421C2×C61C2×#42111yescharacteristic
422D61—22no—
423D61—22no—
424D61—81no—
425C22×M16—1221no—
426#533—611no—
427#533—611no—
428#533—611no—
429#532—611no—
430#532—611no—
431#532—611no—
432#529—611no—
433#529—611no—
434#529—611no—
435#529—1221no—
436#529—1221no—
437#529—1221no—
438#529—1221no—
439#529C2×D6111yescharacteristic
440#525—611no—
441#525—611no—
442#525—1221no—
443#525—1221no—
444C4×#41—611no—
445C4×#41—611no—
446C4×#41—1221no—
447C4×#41—1221no—
448C22×C42—611no—
449#431—611no—
450#431—612no—
451#431—1221no—
452#431—1221no—
453#431C2×D6111yescharacteristic
454#423—611no—
455#423—612no—
456#423—1221no—
457#423—1221no—
458#423C2×D6111yescharacteristic
459C2×C4⋊C8—612no—
460C2×C4⋊C8—1221no—
461C2×C4⋊C8—1221no—
462C2×C22⋊C8—1221no—
463C2×C4×C8—612no—
464Q8⋊C8—612no—
465Q8⋊C8—612no—
466Q8⋊C8—612no—
467Q8⋊C8C2×D6112yescomplemented
468D4⋊C8—612no—
469D4⋊C8—612no—
470D4⋊C8—612no—
471D4⋊C8C2×D6112yescomplemented
472C61#1748111yescharacteristic, complemented, Sylow
473C2×#41—611no—
474C2×#41—611no—
475C2×#41—1221no—
476C2×#41—1221no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—611no—
480C2×M16—21no—
481C2×M16—1222no—
482C2×M16—1221no—
483C2×M16—2444no—
484C22×C8—1222no—
485C22×C8—1222no—
486C4⋊Q8—611no—
487C4⋊Q8—611no—
488C4⋊Q8—611no—
489#127—611no—
490#126—21no—
491#126—1221no—
492#126—1221no—
493#126—1221no—
494#125—611no—
495#125—1221no—
496#125—1221no—
497#125C4×D6111yescharacteristic
498#124—611no—
499#124—1221no—
500#124—1221no—
501#124C4×D6111yescharacteristic
502#123—21no—
503#123—1221no—
504#123—1221no—
505#123—1221no—
506#123—1221no—
507#123—1221no—
508C22⋊Q8—611no—
509C22⋊Q8—611no—
510C22⋊Q8—611no—
511C22⋊Q8—1221no—
512C22⋊Q8—1221no—
513C22⋊Q8—1221no—
514C22⋊Q8—1221no—
515C22⋊Q8C4×D6111yescharacteristic
516#121—611no—
517#121—611no—
518#121—611no—
519#121—1221no—
520#121—1221no—
521#121—1221no—
522#121—1221no—
523#121C4×D6111yescharacteristic
524#120—1221no—
525#120—1221no—
526C4×Q8—611no—
527C4×Q8—611no—
528C4×Q8—611no—
529C4×Q8—1221no—
530C4×Q8—1221no—
531C4×Q8—1221no—
532C4×Q8—1221no—
533C4×Q8C22×D6111yescharacteristic
534C4×D4—21no—
535C4×D4—611no—
536C4×D4—611no—
537C4×D4—611no—
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×D4—1221no—
547C4×D4—1221no—
548C4×D4—1221no—
549C4×D4—1221no—
550C4×D4—1221no—
551C4×D4—1221no—
552C4×D4—1221no—
553C4×D4C22×D6111yescharacteristic
554#117—21no—
555#117—611no—
556#117—611no—
557#117—1221no—
558#117—1221no—
559#117—1221no—
560#117—1221no—
561#117—1221no—
562#117—1221no—
563#117—1221no—
564C2×C42—611no—
565C2×C42—611no—
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—1221no—
576C2×C42—1221no—
577C2×C42C22×D6111yescharacteristic
578C4⋊C8—21no—
579C4⋊C8—21no—
580C4⋊C8—612no—
581C4⋊C8—1222no—
582C4⋊C8—1222no—
583C4⋊C8—1222no—
584C4⋊C8—1221no—
585C4⋊C8—1221no—
586C4⋊C8C22×D6112yes—
587C22⋊C8—21no—
588C22⋊C8—1222no—
589C22⋊C8—1221no—
590C4×C8—612no—
591C4×C8—1222no—
592C4×C8C22×D6112yes—
593C24—611no—
594#41—1224no—
595#41—1224no—
596#41—2442no—
597#41—2442no—
598#41—2444no—
599C2×Q8—611no—
600C2×Q8—1221no—
601C2×Q8—1221no—
602C2×Q8C2×C4×D6111yescharacteristic
603C2×D4—21no—
604C2×D4—611no—
605C2×D4—1221no—
606C2×D4—1221no—
607C2×D4—1221no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4C2×C4×D6111yescharacteristic
613C22×C4—21no—
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—611no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—1222no—
630C22×C4—1224no—
631C22×C4—1222no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—1221no—
637C22×C4—2442no—
638C22×C4C2×C4×D6111yescharacteristic
639C22×C4D4×D6111yescharacteristic
640C22×C4D4×D6111yescharacteristic
641M16—42no—
642M16—2444no—
643M16—2442no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—1222no—
647C2×C8—1222no—
648C2×C8—2444no—
649C2×C8—2444no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—611no—
655C4⋊C4—611no—
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⋊C4C2×C4×D6111yescharacteristic
669C4⋊C4C2×C4×D6111yescharacteristic
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—1221no—
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—
688C42—21no—
689C42—611no—
690C42—611no—
691C42—611no—
692C42—611no—
693C42—611no—
694C42—611no—
695C42—611no—
696C42—611no—
697C42—611no—
698C42—611no—
699C42—611no—
700C42—611no—
701C42—1221no—
702C42—1221no—
703C42—1221no—
704C42—1221no—
705C42—1221no—
706C42C2×C4×D6111yescharacteristic
707C42D4×D6111yescharacteristic
708C42D4×D6111yescharacteristic
709C42C23×D6111yescharacteristic
710C23—21no—
711C23—611no—
712C23—611no—
713C23—1222no—
714C23—1222no—
715C23—1221no—
716C23—2441no—
717C23C22⋊C4×D6111yescharacteristic
718Q8—22no—
719Q8—1222no—
720Q8—2442no—
721Q8—2442no—
722D4—22no—
723D4—42no—
724D4—1222no—
725D4—2442no—
726D4—2442no—
727D4—2442no—
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—611no—
744C2×C4—614no—
745C2×C4—612no—
746C2×C4—612no—
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—1222no—
760C2×C4—1221no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4—2442no—
768C2×C4—2442no—
769C2×C4—2442no—
770C2×C4—2442no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4C22⋊C4×D6111yescharacteristic
774C2×C4C22⋊C4×D6111yescharacteristic
775C2×C4C22⋊C4×D6111yescharacteristic
776C2×C4C22×C4×D6111yescharacteristic
777C2×C4C2×D4×D6111yescharacteristic
778C2×C4C2×D4×D6111yescharacteristic
779C8—42no—
780C8—42no—
781C8—2442no—
782C8—2442no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—612no—
790C22—612no—
791C22—1221no—
792C22—1221no—
793C22—1221no—
794C22—1221no—
795C22—2444no—
796C22—2441no—
797C22—2441no—
798C22—2441no—
799C22C2×C22⋊C4×D6111yescharacteristic
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—612no—
808C4—612no—
809C4—612no—
810C4—1221no—
811C4—1221no—
812C4—1221no—
813C4—2441no—
814C4—2441no—
815C4—2441no—
816C4#131×D6112yes—
817C4AGL(1,ℤ/8)×D6111yescharacteristic
818C4#137×D6111yescharacteristic
819C2—41no—
820C2—81no—
821C2—1222no—
822C2—1222no—
823C2—4881no—
824C2#408×D6111yescharacteristic
825C2#417×D6111yescharacteristic
826C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1495C2
socleC22×C61C22×C22⋊C4
prime radical#21459113C2
cosocleC42×C61C24
hypercenter#1495D61
hypocenterC61#17481
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. #21444282C2semidirect
7. #21444272C2semidirect
8. #21444268C2semidirect
9. #21444205C2semidirect
10. #21444203C2semidirect
11. C61×#1495C2semidirect
48. #16839494C22semidirect
49. Q8⋊#92418C22semidirect
50. #16839492C22semidirect
51. #16839491C22semidirect
52. D4⋊#92418C22semidirect
53. #16839489C22semidirect
57. C61×Q8⋊C8C22semidirect
58. C61×D4⋊C8C22semidirect
412. #1495D61semidirect
467. Q8⋊C8C2×D61semidirect
471. D4⋊C8C2×D61semidirect
472. C61#17481semidirect

Maximal subgroups

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

subgroupindex
#214591132
#431×D612
#423×D612
#214442852
#214442842
#214442822
#214442722
#214442682
#214442052
#214442032
C61×#14952
#1748161