Finite Group Databasebeta

← #29646832

Subgroups — #29646832

Order 15616.

1112 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459113C211yesmaximal, characteristic
2C2×#16839784C211yesmaximal, characteristic, complemented
3C4×M16×D61C211yesmaximal, characteristic, complemented
4#21444272C212yesmaximal, complemented
5#21444268C212yesmaximal, complemented
6#21444257C212yesmaximal, complemented
7#21444255C212yesmaximal, complemented
8#21444233C211yesmaximal, characteristic, complemented
9#21444232C211yesmaximal, characteristic, complemented
10#21444230C211yesmaximal, characteristic, complemented
11C61×#1483C211yesmaximal, characteristic, complemented
12C22×#11758189—21no—
13C2×M16×D61—21no—
14#16840318C411yescharacteristic
15#16840316C2211yescharacteristic
16#16840314C411yescharacteristic
17#16840311C411yescharacteristic
18#16840309C2211yescharacteristic
19#16840307C411yescharacteristic
20#16840297C411yescharacteristic
21#16840296C2211yescharacteristic
22#16840295—21no—
23#16840295—21no—
24#16840291C411yescharacteristic
25#16840290—21no—
26#16840289—21no—
27#16840275C411yescharacteristic
28#16840272C411yescharacteristic
29#16840271—21no—
30#16840270—21no—
31C4×#11758226C2211yescharacteristic
32#16840230—21no—
33C4×#11758224—21no—
34C4×#11758224C2211yescharacteristic
35C2×C42×D61C2211yescharacteristic
36#16839784—21no—
37#16839784—21no—
38#16839784C2212yes—
39#16839784C2212yes—
40C2×C4⋊#92418C2211yescharacteristic
41C2×#14519706—21no—
42C4×#11758194C2211yescharacteristic
43#16839714—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
54C61×#529C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C4×M16×C61C2211yescharacteristic
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—
68C2×#11758189—22no—
69C2×#11758189—22no—
70C2×#11758189—44no—
71M16×D61—28no—
72C22×#92418—21no—
73C2×C8×D61—22no—
74#14519776C2×C411yescharacteristic
75#14519776C2×C411yescharacteristic
76#14519775C2×C411yescharacteristic
77#14519773C2×C411yescharacteristic
78#14519772—21no—
79#14519771—21no—
80#14519770—21no—
81#14519769C2×C411yescharacteristic
82#14519767—21no—
83#14519767—21no—
84#14519765C2×C411yescharacteristic
85#14519763—21no—
86#14519763—21no—
87#14519762—21no—
88#14519762—21no—
89#14519760—21no—
90#14519759—21no—
91#14519759—21no—
92#14519757C2×C411yescharacteristic
93#14519756C2×C411yescharacteristic
94#14519755—21no—
95#14519755—21no—
96#14519755—21no—
97#14519754—21no—
98#14519753C2×C411yescharacteristic
99#14519752C2×C411yescharacteristic
100#14519751C2×C411yescharacteristic
101#14519750—21no—
102#14519750—21no—
103#14519750—21no—
104#14519749—21no—
105#14519748C2×C411yescharacteristic
106#14519747—21no—
107#14519745—21no—
108Q8×Dic61C2×C411yescharacteristic
109C4×Dic122—21no—
110C4×Dic122C2311yescharacteristic
111#14519742—21no—
112#14519742—21no—
113#14519742—21no—
114#14519742C2×C411yescharacteristic
115C4×D244—21no—
116C4×D244C2311yescharacteristic
117D4×Dic61—21no—
118D4×Dic61C2×C411yescharacteristic
119#14519739—21no—
120#14519739—21no—
121#14519739—21no—
122#14519739C2×C411yescharacteristic
123C4×C22⋊D61—21no—
124C4×C22⋊D61—21no—
125C4×C22⋊D61—21no—
126#14519737—21no—
127#14519737—21no—
128#14519737—21no—
129#14519737—21no—
130#14519737—21no—
131#14519737—21no—
132#14519737—21no—
133#14519735—21no—
134#14519735—21no—
135#14519735C2×C411yescharacteristic
136#14519735C2×C411yescharacteristic
137#14519734—21no—
138#14519734—21no—
139#14519733—21no—
140#14519733—21no—
141#14519733—21no—
142C2×C4×Dic61—21no—
143C2×C4×Dic61C2×C411yescharacteristic
144C2×C4×Dic61D411yescharacteristic
145C2×C4×Dic61D411yescharacteristic
146C42×D61—21no—
147C42×D61C2×C411yescharacteristic
148C42×D61C2×C411yescharacteristic
149C42×D61D411yescharacteristic
150C42×D61D411yescharacteristic
151C42×D61D411yescharacteristic
152C42×D61D411yescharacteristic
153C42×D61C2311yescharacteristic
154C42×D61C2311yescharacteristic
155C4⋊#92418—21no—
156C4⋊#92418C2312yes—
157#14519706—22no—
158#14519706—22no—
159#14519688—21no—
160#14519687—22no—
161C4×#92418C2312yes—
162C8×Dic61—22no—
163C2×M16×C61—21no—
164C22×C8×C61—21no—
165#126×C61—21no—
166#125×C61C2×C411yescharacteristic
167#124×C61C2×C411yescharacteristic
168#123×C61—21no—
169C22⋊Q8×C61C2×C411yescharacteristic
170#121×C61C2×C411yescharacteristic
171C4×Q8×C61C2311yescharacteristic
172C4×D4×C61—21no—
173C4×D4×C61C2311yescharacteristic
174#117×C61—21no—
175C2×C42×C61C2311yescharacteristic
176C4⋊C8×C61—21no—
177C4⋊C8×C61C2312yes—
178#97×C61—21no—
179C4×C8×C61C2312yes—
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—
191C2×C22⋊D61—21no—
192C2×C22⋊D61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61C22⋊C411yescharacteristic
196C22×Dic61C22⋊C411yescharacteristic
197C22×Dic61C22⋊C411yescharacteristic
198#11758226—42no—
199#11758224—42no—
200#11758224—44no—
201#11758222—42no—
202#11758222—42no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244C22×C411yescharacteristic
206C2×C4×D61—24no—
207C2×C4×D61—22no—
208C2×C4×D61—22no—
209C2×C4×D61—21no—
210C2×C4×D61—21no—
211C2×C4×D61—21no—
212C2×C4×D61—42no—
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×D61C22×C411yescharacteristic
221C2×C4×D61C2×D411yescharacteristic
222C2×C4×D61C2×D411yescharacteristic
223C2×C4×D61C2×D411yescharacteristic
224C2×C4×D61C2×D411yescharacteristic
225C2×Dic122—21no—
226C2×Dic122—21no—
227C2×Dic122C22×C411yescharacteristic
228M16×C61—24no—
229C2×C8×C61—22no—
230C2×C8×C61—22no—
231C2×C8×C61—42no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61C22×C411yescharacteristic
237C4⋊C4×C61C22×C411yescharacteristic
238C22⋊C4×C61—21no—
239C22⋊C4×C61—21no—
240C22⋊C4×C61—21no—
241C22⋊C4×C61—21no—
242C22⋊C4×C61—21no—
243C42×C61—21no—
244C42×C61C22×C411yescharacteristic
245C42×C61C2×D411yescharacteristic
246C42×C61C2×D411yescharacteristic
247C42×C61C2411yescharacteristic
248C22⋊Dic61—21no—
249C22⋊Dic61—21no—
250C22⋊Dic61—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—
260#11758198—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×Dic61—21no—
279C4×Dic61—21no—
280C4×Dic61C22⋊C411yescharacteristic
281C4×Dic61C22⋊C411yescharacteristic
282C4×Dic61C22⋊C411yescharacteristic
283C4×Dic61C22⋊C411yescharacteristic
284C4×Dic61C22⋊C411yescharacteristic
285C4×Dic61C22⋊C411yescharacteristic
286C4×Dic61C22×C411yescharacteristic
287C4×Dic61C22×C411yescharacteristic
288C4×Dic61C2×D411yescharacteristic
289C4×Dic61C2×D411yescharacteristic
290C4×Dic61C2×D411yescharacteristic
291C4×Dic61C2×D411yescharacteristic
292#11758194—24no—
293C2×#92418—22no—
294C2×#92418—22no—
295C2×#92418—42no—
296#11758189—28no—
297#11758189—44no—
298#11758189—44no—
299C8×D61—28no—
300C23×C61—21no—
301C23×C61C2×C22⋊C411yescharacteristic
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—21no—
305C22×D61—41no—
306C22×D61C2×C22⋊C411yescharacteristic
307C22×D61C2×C22⋊C411yescharacteristic
308Q8×C61—22no—
309D4×C61—22no—
310D4×C61—42no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61C2×C22⋊C411yescharacteristic
321C2×C4×C61C2×C22⋊C411yescharacteristic
322C2×C4×C61C2×C22⋊C411yescharacteristic
323C2×C4×C61C23×C411yescharacteristic
324C2×C4×C61C22×D411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C22⋊D61—42no—
327C22⋊D61—42no—
328C22⋊D61—42no—
329C22⋊D61—42no—
330C22⋊D61—42no—
331C2×Dic61—22no—
332C2×Dic61—21no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—41no—
336C2×Dic61—42no—
337C2×Dic61—42no—
338C2×Dic61#10414yes—
339C2×Dic61C2×C22⋊C411yescharacteristic
340C2×Dic61C2×C22⋊C411yescharacteristic
341C2×Dic61C2×C22⋊C411yescharacteristic
342C2×Dic61C2×C22⋊C411yescharacteristic
343C2×Dic61C2×C22⋊C411yescharacteristic
344C2×Dic61C2×C22⋊C411yescharacteristic
345D244—22no—
346D244—42no—
347D244—42no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—21no—
352C4×D61—21no—
353C4×D61—22no—
354C4×D61—22no—
355C4×D61—22no—
356C4×D61—22no—
357C4×D61—22no—
358C4×D61—41no—
359C4×D61—41no—
360C4×D61—42no—
361C4×D61—41no—
362C4×D61—41no—
363C4×D61—42no—
364C4×D61AGL(1,ℤ/8)12yes—
365C4×D61#13712yes—
366Dic122—22no—
367Dic122—42no—
368Dic122—42no—
369C8×C61—24no—
370C8×C61—42no—
371#92418—24no—
372#92418—42no—
373#17504—611nomaximal, Sylow
374C22×C61—21no—
375C22×C61—21no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61C2×#10412yes—
380C22×C61C22×C22⋊C411yescharacteristic
381C2×D61—21no—
382C2×D61—21no—
383C2×D61—21no—
384C2×D61—21no—
385C2×D61—21no—
386C2×D61—44no—
387C2×D61—41no—
388C2×D61—41no—
389C2×D61—41no—
390C2×D61#41712yes—
391C4×C61—21no—
392C4×C61—21no—
393C4×C61—21no—
394C4×C61—21no—
395C4×C61—41no—
396C4×C61—41no—
397C4×C61—41no—
398C4×C61#56812yes—
399C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
400C4×C61C2×#13711yescharacteristic
401Dic61—21no—
402Dic61—21no—
403Dic61—21no—
404Dic61—41no—
405Dic61—41no—
406Dic61—41no—
407Dic61#41712yes—
408Dic61C2×#10412yes—
409Dic61C2×#10412yes—
410#3444—611no—
411C2×#423—611no—
412C2×C4×M16—611no—
413#1493—612no—
414#1492—612no—
415#1489—612no—
416#1489—612no—
417#1483—611no—
418#1483—611no—
419#1483—611no—
420#1483D6111yescharacteristic, complemented
421C2×C61—22no—
422C2×C61—81no—
423C2×C61#287911yescharacteristic
424C2×C61C2×#41711yescharacteristic
425C2×C61C22×#10411yescharacteristic
426D61—22no—
427D61—41no—
428D61—81no—
429C22×M16—1221no—
430C22×M16—1221no—
431#533—611no—
432#533—611no—
433#533—611no—
434#532—611no—
435#532—611no—
436#532—611no—
437#529—611no—
438#529—611no—
439#529—611no—
440#529—1221no—
441#529—1221no—
442#529—1221no—
443#529—1221no—
444#529C2×D6111yescharacteristic
445#525—611no—
446#525—611no—
447#525—1221no—
448#525—1221no—
449C4×#41—611no—
450C4×#41—611no—
451C4×#41—1221no—
452C4×#41—1221no—
453C22×C42—611no—
454#423—612no—
455#423—612no—
456#423—1221no—
457#423—1221no—
458C2×C4⋊C8—611no—
459C2×C4⋊C8—1221no—
460C2×C4⋊C8C2×D6111yescharacteristic
461C4×M16—611no—
462C4×M16—612no—
463C4×M16—1221no—
464C4×M16—1221no—
465C4×M16C2×D6111yescharacteristic
466C2×#97—1221no—
467C2×C4×C8—612no—
468Q8⋊C8—612no—
469Q8⋊C8—612no—
470Q8⋊C8—612no—
471Q8⋊C8C2×D6112yescomplemented
472D4⋊C8—612no—
473D4⋊C8—612no—
474D4⋊C8—612no—
475D4⋊C8C2×D6112yescomplemented
476C61#1750411yescharacteristic, complemented, Sylow
477C2×#41—611no—
478C2×#41—611no—
479C2×#41—1221no—
480C2×#41—1221no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C2×M16—21no—
485C2×M16—1222no—
486C2×M16—1222no—
487C2×M16—1222no—
488C2×M16—1228no—
489C2×M16—1221no—
490C2×M16—2444no—
491C22×C8—21no—
492C22×C8—1222no—
493C22×C8—1221no—
494C4⋊Q8—611no—
495C4⋊Q8—611no—
496C4⋊Q8—611no—
497#127—611no—
498#126—21no—
499#126—1221no—
500#126—1221no—
501#126—1221no—
502#125—611no—
503#125—1221no—
504#125—1221no—
505#125C4×D6111yescharacteristic
506#124—611no—
507#124—1221no—
508#124—1221no—
509#124C4×D6111yescharacteristic
510#123—21no—
511#123—1221no—
512#123—1221no—
513#123—1221no—
514#123—1221no—
515#123—1221no—
516C22⋊Q8—611no—
517C22⋊Q8—611no—
518C22⋊Q8—611no—
519C22⋊Q8—1221no—
520C22⋊Q8—1221no—
521C22⋊Q8—1221no—
522C22⋊Q8—1221no—
523C22⋊Q8C4×D6111yescharacteristic
524#121—611no—
525#121—611no—
526#121—611no—
527#121—1221no—
528#121—1221no—
529#121—1221no—
530#121—1221no—
531#121C4×D6111yescharacteristic
532#120—1221no—
533#120—1221no—
534C4×Q8—611no—
535C4×Q8—611no—
536C4×Q8—611no—
537C4×Q8—1221no—
538C4×Q8—1221no—
539C4×Q8—1221no—
540C4×Q8—1221no—
541C4×Q8C22×D6111yescharacteristic
542C4×D4—21no—
543C4×D4—611no—
544C4×D4—611no—
545C4×D4—611no—
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×D4—1221no—
555C4×D4—1221no—
556C4×D4—1221no—
557C4×D4—1221no—
558C4×D4—1221no—
559C4×D4—1221no—
560C4×D4—1221no—
561C4×D4C22×D6111yescharacteristic
562#117—21no—
563#117—611no—
564#117—611no—
565#117—1221no—
566#117—1221no—
567#117—1221no—
568#117—1221no—
569#117—1221no—
570#117—1221no—
571#117—1221no—
572C2×C42—611no—
573C2×C42—611no—
574C2×C42—611no—
575C2×C42—611no—
576C2×C42—611no—
577C2×C42—611no—
578C2×C42—611no—
579C2×C42—611no—
580C2×C42—611no—
581C2×C42—611no—
582C2×C42—611no—
583C2×C42—1221no—
584C2×C42—1221no—
585C2×C42C22×D6111yescharacteristic
586C4⋊C8—21no—
587C4⋊C8—612no—
588C4⋊C8—1222no—
589C4⋊C8—1222no—
590C4⋊C8—1221no—
591C4⋊C8C22×D6112yes—
592#97—21no—
593#97—1222no—
594#97—1221no—
595C4×C8—612no—
596C4×C8—1222no—
597C4×C8C22×D6112yes—
598C24—611no—
599#41—2442no—
600#41—2442no—
601#41—2444no—
602#41—2442no—
603#41—2442no—
604C2×Q8—611no—
605C2×Q8—1221no—
606C2×Q8—1221no—
607C2×Q8C2×C4×D6111yescharacteristic
608C2×D4—21no—
609C2×D4—611no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4—1221no—
614C2×D4—1221no—
615C2×D4—1221no—
616C2×D4—1221no—
617C2×D4C2×C4×D6111yescharacteristic
618C22×C4—21no—
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—611no—
633C22×C4—611no—
634C22×C4—1224no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4—2442no—
643C22×C4C2×C4×D6111yescharacteristic
644C22×C4D4×D6111yescharacteristic
645C22×C4D4×D6111yescharacteristic
646M16—24no—
647M16—1228no—
648M16—1224no—
649M16—2444no—
650M16—2444no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—42no—
654C2×C8—1228no—
655C2×C8—1222no—
656C2×C8—1222no—
657C2×C8—2442no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—611no—
663C4⋊C4—611no—
664C4⋊C4—1221no—
665C4⋊C4—1221no—
666C4⋊C4—1221no—
667C4⋊C4—1221no—
668C4⋊C4—1221no—
669C4⋊C4—1221no—
670C4⋊C4—1221no—
671C4⋊C4—1221no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4C2×C4×D6111yescharacteristic
677C4⋊C4C2×C4×D6111yescharacteristic
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—1221no—
684C22⋊C4—1221no—
685C22⋊C4—1221no—
686C22⋊C4—1221no—
687C22⋊C4—1221no—
688C22⋊C4—1221no—
689C22⋊C4—1221no—
690C22⋊C4—1221no—
691C22⋊C4—1221no—
692C22⋊C4—1221no—
693C22⋊C4—1221no—
694C22⋊C4—1221no—
695C22⋊C4—1221no—
696C42—21no—
697C42—611no—
698C42—611no—
699C42—611no—
700C42—611no—
701C42—611no—
702C42—611no—
703C42—611no—
704C42—611no—
705C42—611no—
706C42—611no—
707C42—611no—
708C42—611no—
709C42—1221no—
710C42—1221no—
711C42—1221no—
712C42—1221no—
713C42—1221no—
714C42C2×C4×D6111yescharacteristic
715C42D4×D6111yescharacteristic
716C42D4×D6111yescharacteristic
717C42C23×D6111yescharacteristic
718C23—21no—
719C23—611no—
720C23—611no—
721C23—1222no—
722C23—1222no—
723C23—1221no—
724C23—2441no—
725C23C22⋊C4×D6111yescharacteristic
726Q8—22no—
727Q8—1222no—
728Q8—2442no—
729Q8—2442no—
730D4—22no—
731D4—42no—
732D4—1222no—
733D4—2442no—
734D4—2442no—
735D4—2442no—
736D4—2442no—
737D4—2442no—
738D4—2442no—
739D4—2442no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—611no—
750C2×C4—611no—
751C2×C4—611no—
752C2×C4—614no—
753C2×C4—612no—
754C2×C4—612no—
755C2×C4—611no—
756C2×C4—611no—
757C2×C4—611no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1221no—
768C2×C4—1221no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2442no—
775C2×C4—2442no—
776C2×C4—2442no—
777C2×C4—2441no—
778C2×C4—2442no—
779C2×C4—2441no—
780C2×C4—2441no—
781C2×C4C22⋊C4×D6111yescharacteristic
782C2×C4C22⋊C4×D6111yescharacteristic
783C2×C4C22⋊C4×D6111yescharacteristic
784C2×C4C22×C4×D6111yescharacteristic
785C2×C4C2×D4×D6111yescharacteristic
786C2×C4C2×D4×D6111yescharacteristic
787C8—24no—
788C8—42no—
789C8—1224no—
790C8—2442no—
791C22—21no—
792C22—21no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—612no—
797C22—1221no—
798C22—1221no—
799C22—1221no—
800C22—1221no—
801C22—1221no—
802C22—2444no—
803C22—2441no—
804C22—2441no—
805C22—2441no—
806C22#104×D6112yes—
807C22C2×C22⋊C4×D6111yescharacteristic
808C4—21no—
809C4—21no—
810C4—21no—
811C4—21no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—612no—
816C4—612no—
817C4—612no—
818C4—1221no—
819C4—1221no—
820C4—1221no—
821C4—2441no—
822C4—2441no—
823C4—2441no—
824C4#1684052712yes—
825C4AGL(1,ℤ/8)×D6111yescharacteristic
826C4#137×D6111yescharacteristic
827C2—22no—
828C2—81no—
829C2—1222no—
830C2—4881no—
831C2—2441no—
832C2#2145426111yescharacteristic
833C2#417×D6111yescharacteristic
834C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1483C2
socleC22×C61C22×C22⋊C4
prime radical#21459113C2
cosocleC42×C61C24
hypercenter#1483D61
hypocenterC61#17504
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1483

Complements

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

NH ≅ G/Ntype
2. C2×#16839784C2semidirect
3. C4×M16×D61C2semidirect
4. #21444272C2semidirect
5. #21444268C2semidirect
6. #21444257C2semidirect
7. #21444255C2semidirect
8. #21444233C2semidirect
9. #21444232C2semidirect
10. #21444230C2semidirect
11. C61×#1483C2semidirect
48. #16839494C22semidirect
49. Q8⋊#92418C22semidirect
50. #16839492C22semidirect
51. #16839491C22semidirect
52. D4⋊#92418C22semidirect
53. #16839489C22semidirect
57. C61×Q8⋊C8C22semidirect
58. C61×D4⋊C8C22semidirect
420. #1483D61semidirect
471. Q8⋊C8C2×D61semidirect
475. D4⋊C8C2×D61semidirect
476. C61#17504semidirect

Maximal subgroups

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

subgroupindex
#214591132
C2×#168397842
C4×M16×D612
#214442722
#214442682
#214442572
#214442552
#214442332
#214442322
#214442302
C61×#14832
#1750461