Finite Group Databasebeta

← #29646826

Subgroups — #29646826

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#21459112C211yesmaximal, characteristic
2#21454451C211yesmaximal, characteristic, complemented
3C4×M16×D61C211yesmaximal, characteristic, complemented
4#21444278C212yesmaximal, complemented
5#21444276C212yesmaximal, complemented
6#21444259C211yesmaximal, characteristic, complemented
7#21444258C211yesmaximal, characteristic, complemented
8#21444256C211yesmaximal, characteristic, complemented
9#21444238C212yesmaximal, complemented
10#21444234C212yesmaximal, complemented
11C61×#1489C211yesmaximal, characteristic, complemented
12C2×M16×D61—21no—
13#16840316C411yescharacteristic
14#16840316C2211yescharacteristic
15#16840315C411yescharacteristic
16#16840309C411yescharacteristic
17#16840309C2211yescharacteristic
18#16840308C411yescharacteristic
19#16840299C411yescharacteristic
20#16840299C2211yescharacteristic
21#16840294C411yescharacteristic
22#16840294C2211yescharacteristic
23#16840292—21no—
24#16840292—21no—
25#16840290—21no—
26#16840290—21no—
27#16840274C411yescharacteristic
28#16840271—21no—
29#16840271—21no—
30#16840269C411yescharacteristic
31C4×#11758222—21no—
32C4×#11758222—21no—
33C4×#11758222C2211yescharacteristic
34C2×C42×D61C2211yescharacteristic
35#16839818—21no—
36#16839818C2212yes—
37#16839814—21no—
38#16839814C2212yes—
39#16839786C2211yescharacteristic
40#16839725—21no—
41C4×#11758194C2211yescharacteristic
42#16839714—21no—
43M16×Dic61—21no—
44M16×Dic61—21no—
45C4×#11758189C2212yes—
46#97×D61—21no—
47C4×C8×D61C2212yes—
48#16839494C2212yescomplemented
49Q8⋊#92418C2212yescomplemented
50#16839492C2212yescomplemented
51#16839491C2212yescomplemented
52D4⋊#92418C2212yescomplemented
53#16839489C2212yescomplemented
54C4×#41×C61C2211yescharacteristic
55C61×#423C2211yescharacteristic
56C4×M16×C61C2211yescharacteristic
57C61×Q8⋊C8C2212yescomplemented
58C61×D4⋊C8C2212yescomplemented
59C2×#11758222—21no—
60C2×#11758222—21no—
61C2×#11758222C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C2×#11758194—21no—
66C2×#11758194—21no—
67C2×#11758189—22no—
68M16×D61—28no—
69C2×C8×D61—22no—
70#14519776C2×C411yescharacteristic
71#14519776C2×C411yescharacteristic
72#14519775C2×C411yescharacteristic
73#14519773C2×C411yescharacteristic
74#14519772—21no—
75#14519772—21no—
76#14519770—21no—
77#14519770—21no—
78#14519768C2×C411yescharacteristic
79#14519768C2×C411yescharacteristic
80#14519767—21no—
81#14519767—21no—
82#14519766C2×C411yescharacteristic
83#14519764C2×C411yescharacteristic
84#14519763—21no—
85#14519763—21no—
86#14519762—21no—
87#14519762—21no—
88#14519761—21no—
89#14519759—21no—
90#14519759—21no—
91#14519758—21no—
92#14519757C2×C411yescharacteristic
93#14519757C2×C411yescharacteristic
94#14519755—21no—
95#14519755—21no—
96#14519754—21no—
97#14519754—21no—
98#14519753C2×C411yescharacteristic
99#14519753C2×C411yescharacteristic
100#14519752C2×C411yescharacteristic
101#14519752C2×C411yescharacteristic
102#14519750—21no—
103#14519750—21no—
104#14519749—21no—
105#14519749—21no—
106#14519748C2×C411yescharacteristic
107#14519748C2×C411yescharacteristic
108#14519747—21no—
109#14519745—21no—
110C4×Dic122—21no—
111C4×Dic122—21no—
112C4×Dic122—21no—
113C4×Dic122—21no—
114C4×Dic122C2×C411yescharacteristic
115C4×Dic122C2311yescharacteristic
116C4×D244—21no—
117C4×D244—21no—
118C4×D244—21no—
119C4×D244—21no—
120C4×D244C2×C411yescharacteristic
121C4×D244C2311yescharacteristic
122C4×C22⋊D61—21no—
123C4×C22⋊D61—21no—
124C4×C22⋊D61—21no—
125C4×C22⋊D61—21no—
126C4×C22⋊D61—21no—
127C4×C22⋊D61—21no—
128C4×C22⋊D61—21no—
129C4×C22⋊D61—21no—
130C4×C22⋊D61—21no—
131C4×C22⋊D61—21no—
132#14519736—21no—
133#14519736—21no—
134#14519736C2×C411yescharacteristic
135#14519734—21no—
136#14519734—21no—
137#14519734—21no—
138#14519734—21no—
139#14519734—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⋊#92418C2312yes—
154#14519689—22no—
155#14519689—22no—
156#14519688—21no—
157#14519687—22no—
158#14519687—22no—
159C4×#92418C2312yes—
160C8×Dic61—22no—
161C8×Dic61—22no—
162C2×#41×C61C2×C411yescharacteristic
163C2×M16×C61—21no—
164C2×M16×C61—21no—
165C4×Q8×C61C2×C411yescharacteristic
166C4×Q8×C61C2311yescharacteristic
167C4×D4×C61—21no—
168C4×D4×C61—21no—
169C4×D4×C61C2×C411yescharacteristic
170C4×D4×C61C2311yescharacteristic
171#117×C61—21no—
172#117×C61C2×C411yescharacteristic
173C2×C42×C61—21no—
174C2×C42×C61C2311yescharacteristic
175C4⋊C8×C61—21no—
176C4⋊C8×C61C2312yes—
177#97×C61—21no—
178C4×C8×C61C2312yes—
179C23×D61C22⋊C411yescharacteristic
180#41×C61—42no—
181C2×Q8×C61C22×C411yescharacteristic
182C2×D4×C61—21no—
183C2×D4×C61C22×C411yescharacteristic
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61C22×C411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C2×C22⋊D61—21no—
193C2×C22⋊D61—21no—
194C2×C22⋊D61—21no—
195C22×Dic61C22⋊C411yescharacteristic
196C22×Dic61C22⋊C411yescharacteristic
197C22×Dic61C22⋊C411yescharacteristic
198#11758222—42no—
199#11758222—42no—
200#11758222—42no—
201#11758222—44no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244C22×C411yescharacteristic
205C2×C4×D61—24no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—42no—
210C2×C4×D61—41no—
211C2×C4×D61—41no—
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—24no—
228M16×C61—42no—
229C2×C8×C61—22no—
230C2×C8×C61—22no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61C22×C411yescharacteristic
234C4⋊C4×C61C22×C411yescharacteristic
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C22⋊C4×C61—21no—
238C42×C61—21no—
239C42×C61—21no—
240C42×C61—21no—
241C42×C61C22×C411yescharacteristic
242C42×C61C2×D411yescharacteristic
243C42×C61C2×D411yescharacteristic
244C42×C61C2411yescharacteristic
245C22⋊Dic61—21no—
246C22⋊Dic61—21no—
247C22⋊Dic61—21no—
248C22⋊Dic61—21no—
249C22⋊Dic61—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—
259#11758198—21no—
260C4⋊Dic61—21no—
261C4⋊Dic61—21no—
262C4⋊Dic61—21no—
263C4⋊Dic61—21no—
264C4⋊Dic61C22×C411yescharacteristic
265C4⋊Dic61C22×C411yescharacteristic
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—
275#11758196—21no—
276C4×Dic61—21no—
277C4×Dic61—21no—
278C4×Dic61—21no—
279C4×Dic61C22⋊C411yescharacteristic
280C4×Dic61C22⋊C411yescharacteristic
281C4×Dic61C22⋊C411yescharacteristic
282C4×Dic61C22⋊C411yescharacteristic
283C4×Dic61C22⋊C411yescharacteristic
284C4×Dic61C22⋊C411yescharacteristic
285C4×Dic61C22×C411yescharacteristic
286C4×Dic61C22×C411yescharacteristic
287C4×Dic61C2×D411yescharacteristic
288C4×Dic61C2×D411yescharacteristic
289C4×Dic61C2×D411yescharacteristic
290C4×Dic61C2×D411yescharacteristic
291#11758194—24no—
292#11758194—42no—
293C2×#92418—22no—
294C2×#92418—22no—
295#11758189—28no—
296C8×D61—28no—
297C23×C61—21no—
298C23×C61C2×C22⋊C411yescharacteristic
299C22×D61—22no—
300C22×D61—21no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61C2×C22⋊C411yescharacteristic
304C22×D61C2×C22⋊C411yescharacteristic
305Q8×C61—22no—
306D4×C61—22no—
307D4×C61—42no—
308C2×C4×C61—22no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—22no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—42no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—42no—
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—
328C22⋊D61—42no—
329C22⋊D61—42no—
330C2×Dic61—22no—
331C2×Dic61—21no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—41no—
335C2×Dic61—41no—
336C2×Dic61C2×C22⋊C411yescharacteristic
337C2×Dic61C2×C22⋊C411yescharacteristic
338C2×Dic61C2×C22⋊C411yescharacteristic
339C2×Dic61C2×C22⋊C411yescharacteristic
340C2×Dic61C2×C22⋊C411yescharacteristic
341C2×Dic61C2×C22⋊C411yescharacteristic
342D244—22no—
343D244—42no—
344D244—42no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—21no—
349C4×D61—21no—
350C4×D61—21no—
351C4×D61—21no—
352C4×D61—22no—
353C4×D61—22no—
354C4×D61—41no—
355C4×D61—41no—
356C4×D61—41no—
357C4×D61—41no—
358C4×D61—42no—
359C4×D61—41no—
360C4×D61—41no—
361C4×D61—42no—
362C4×D61#10414yes—
363Dic122—22no—
364Dic122—42no—
365Dic122—42no—
366C8×C61—24no—
367C8×C61—42no—
368#92418—24no—
369#92418—42no—
370#17503—611nomaximal, Sylow
371C22×C61—21no—
372C22×C61—21no—
373C22×C61—21no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61C22×C22⋊C411yescharacteristic
378C2×D61—21no—
379C2×D61—21no—
380C2×D61—21no—
381C2×D61—21no—
382C2×D61—21no—
383C2×D61—44no—
384C2×D61—41no—
385C2×D61—41no—
386C2×D61—41no—
387C2×D61C2×#10412yes—
388C4×C61—21no—
389C4×C61—21no—
390C4×C61—21no—
391C4×C61—41no—
392C4×C61—41no—
393C4×C61—41no—
394C4×C61C2×#10412yes—
395C4×C61#56812yes—
396C4×C61#57511yescharacteristic
397C4×C61#57511yescharacteristic
398Dic61—21no—
399Dic61—21no—
400Dic61—21no—
401Dic61—21no—
402Dic61—21no—
403Dic61—41no—
404Dic61—41no—
405Dic61—41no—
406Dic61C2×#10412yes—
407#3444—611no—
408#2920—611no—
409C2×C4×M16—611no—
410#1494—612no—
411#1494—612no—
412#1489—611no—
413#1489—611no—
414#1489—611no—
415#1489D6111yescharacteristic, complemented
416#1485—612no—
417#1484—612no—
418C2×C61—41no—
419C2×C61—81no—
420C2×C61#287911yescharacteristic
421C2×C61#289611yescharacteristic
422C2×C61C22×#10411yescharacteristic
423D61—22no—
424D61—41no—
425D61—81no—
426C22×M16—1221no—
427#533—611no—
428#533—611no—
429#533—611no—
430#532—611no—
431#532—611no—
432#532—611no—
433#529—611no—
434#529—611no—
435#529—611no—
436#529—611no—
437#529—1221no—
438#529—1221no—
439#529—1221no—
440#529—1221no—
441#525—611no—
442#525—611no—
443#525—1221no—
444#525—1221no—
445C4×#41—611no—
446C4×#41—1221no—
447C4×#41—1221no—
448C4×#41C2×D6111yescharacteristic
449C22×C42—611no—
450#432—612no—
451#432—1221no—
452#431—612no—
453#431—1221no—
454#423—611no—
455#423C2×D6111yescharacteristic
456#407—1221no—
457C4×M16—611no—
458C4×M16—612no—
459C4×M16—1221no—
460C4×M16—1221no—
461C4×M16—1221no—
462C4×M16C2×D6111yescharacteristic
463C2×#97—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
473C61#1750311yescharacteristic, complemented, Sylow
474C2×#41—611no—
475C2×#41—1221no—
476C2×#41—1221no—
477C2×#41C4×D6111yescharacteristic
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—611no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—1222no—
484C2×M16—1228no—
485C2×M16—1221no—
486C2×M16—1221no—
487C22×C8—1222no—
488C4⋊Q8—611no—
489C4⋊Q8—611no—
490C4⋊Q8—611no—
491#127—611no—
492#126—1221no—
493#126—1221no—
494#126—1221no—
495#126—1221no—
496#125—611no—
497#125—611no—
498#125—1221no—
499#125—1221no—
500#124—611no—
501#124—611no—
502#124—1221no—
503#124—1221no—
504#123—1221no—
505#123—1221no—
506#123—1221no—
507#123—1221no—
508#123—1221no—
509#123—1221no—
510C22⋊Q8—611no—
511C22⋊Q8—611no—
512C22⋊Q8—611no—
513C22⋊Q8—611no—
514C22⋊Q8—1221no—
515C22⋊Q8—1221no—
516C22⋊Q8—1221no—
517C22⋊Q8—1221no—
518#121—611no—
519#121—611no—
520#121—611no—
521#121—611no—
522#121—1221no—
523#121—1221no—
524#121—1221no—
525#121—1221no—
526#120—1221no—
527#120—1221no—
528C4×Q8—611no—
529C4×Q8—611no—
530C4×Q8—1221no—
531C4×Q8—1221no—
532C4×Q8—1221no—
533C4×Q8—1221no—
534C4×Q8C4×D6111yescharacteristic
535C4×Q8C22×D6111yescharacteristic
536C4×D4—21no—
537C4×D4—21no—
538C4×D4—611no—
539C4×D4—611no—
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×D4—1221no—
554C4×D4C4×D6111yescharacteristic
555C4×D4C22×D6111yescharacteristic
556#117—21no—
557#117—611no—
558#117—1221no—
559#117—1221no—
560#117—1221no—
561#117—1221no—
562#117—1221no—
563#117—1221no—
564#117—1221no—
565#117C4×D6111yescharacteristic
566C2×C42—21no—
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—611no—
578C2×C42—1221no—
579C2×C42C22×D6111yescharacteristic
580C4⋊C8—21no—
581C4⋊C8—612no—
582C4⋊C8—1221no—
583C4⋊C8C22×D6112yes—
584C22⋊C8—1222no—
585C22⋊C8—1222no—
586#97—21no—
587#97—1222no—
588#97—1222no—
589#97—1221no—
590C4×C8—612no—
591C4×C8—1222no—
592C4×C8—1222no—
593C4×C8C22×D6112yes—
594C24—611no—
595#41—42no—
596#41—2442no—
597#41—2444no—
598#41—2442no—
599#41—2442no—
600C2×Q8—611no—
601C2×Q8—1221no—
602C2×Q8—1221no—
603C2×Q8C2×C4×D6111yescharacteristic
604C2×D4—21no—
605C2×D4—611no—
606C2×D4—1221no—
607C2×D4—1221no—
608C2×D4—1221no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4C2×C4×D6111yescharacteristic
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
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—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—1224no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1221no—
636C22×C4—2442no—
637C22×C4—2441no—
638C22×C4—2441no—
639C22×C4C2×C4×D6111yescharacteristic
640C22×C4D4×D6111yescharacteristic
641C22×C4D4×D6111yescharacteristic
642M16—24no—
643M16—42no—
644M16—1228no—
645M16—1224no—
646M16—2442no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—1228no—
650C2×C8—1222no—
651C2×C8—1222no—
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⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4C2×C4×D6111yescharacteristic
671C4⋊C4C2×C4×D6111yescharacteristic
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—
688C22⋊C4—1221no—
689C22⋊C4—1221no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—611no—
694C42—611no—
695C42—611no—
696C42—611no—
697C42—611no—
698C42—611no—
699C42—611no—
700C42—611no—
701C42—611no—
702C42—611no—
703C42—611no—
704C42—611no—
705C42—1221no—
706C42—1221no—
707C42—1221no—
708C42C2×C4×D6111yescharacteristic
709C42D4×D6111yescharacteristic
710C42D4×D6111yescharacteristic
711C42C23×D6111yescharacteristic
712C23—21no—
713C23—611no—
714C23—611no—
715C23—1222no—
716C23—1221no—
717C23—2441no—
718C23—2441no—
719C23C22⋊C4×D6111yescharacteristic
720Q8—22no—
721Q8—1222no—
722Q8—2442no—
723Q8—2442no—
724D4—22no—
725D4—42no—
726D4—1222no—
727D4—2442no—
728D4—2442no—
729D4—2442no—
730D4—2442no—
731D4—2442no—
732D4—2442no—
733D4—2442no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—611no—
746C2×C4—614no—
747C2×C4—611no—
748C2×C4—611no—
749C2×C4—611no—
750C2×C4—611no—
751C2×C4—611no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1221no—
759C2×C4—1221no—
760C2×C4—1221no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—2441no—
766C2×C4—2441no—
767C2×C4—2441no—
768C2×C4—2441no—
769C2×C4—2442no—
770C2×C4—2441no—
771C2×C4—2441no—
772C2×C4—2442no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4C22⋊C4×D6111yescharacteristic
776C2×C4C22⋊C4×D6111yescharacteristic
777C2×C4C22⋊C4×D6111yescharacteristic
778C2×C4C22×C4×D6111yescharacteristic
779C2×C4C2×D4×D6111yescharacteristic
780C2×C4C2×D4×D6111yescharacteristic
781C8—24no—
782C8—42no—
783C8—1224no—
784C8—2442no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—612no—
792C22—1221no—
793C22—1221no—
794C22—1221no—
795C22—1221no—
796C22—1221no—
797C22—2444no—
798C22—2441no—
799C22—2441no—
800C22—2441no—
801C22C2×C22⋊C4×D6111yescharacteristic
802C4—21no—
803C4—21no—
804C4—21no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—612no—
809C4—1221no—
810C4—1221no—
811C4—1221no—
812C4—1221no—
813C4—1221no—
814C4—2441no—
815C4—2441no—
816C4—2441no—
817C4#104×D6112yes—
818C4#1684052812yes—
819C4#1684055811yescharacteristic
820C4#1684056111yescharacteristic
821C2—41no—
822C2—81no—
823C2—1222no—
824C2—4881no—
825C2—2441no—
826C2#2145426211yescharacteristic
827C2#2145433511yescharacteristic
828C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1489C2
socleC22×C61C22×C22⋊C4
prime radical#21459112C2
cosocleC42×C61C24
hypercenter#1489D61
hypocenterC61#17503
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1489

Complements

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

NH ≅ G/Ntype
2. #21454451C2semidirect
3. C4×M16×D61C2semidirect
4. #21444278C2semidirect
5. #21444276C2semidirect
6. #21444259C2semidirect
7. #21444258C2semidirect
8. #21444256C2semidirect
9. #21444238C2semidirect
10. #21444234C2semidirect
11. C61×#1489C2semidirect
48. #16839494C22semidirect
49. Q8⋊#92418C22semidirect
50. #16839492C22semidirect
51. #16839491C22semidirect
52. D4⋊#92418C22semidirect
53. #16839489C22semidirect
57. C61×Q8⋊C8C22semidirect
58. C61×D4⋊C8C22semidirect
415. #1489D61semidirect
468. Q8⋊C8C2×D61semidirect
472. D4⋊C8C2×D61semidirect
473. C61#17503semidirect

Maximal subgroups

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

subgroupindex
#214591122
#214544512
C4×M16×D612
#214442782
#214442762
#214442592
#214442582
#214442562
#214442382
#214442342
C61×#14892
#1750361