Finite Group Databasebeta

← #29646545

Subgroups — #29646545

Order 15616.

1096 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459112C211yesmaximal, characteristic
2#431×D61C211yesmaximal, characteristic, complemented
3C2×C4×#11758189C211yesmaximal, characteristic, complemented
4#21444238C212yesmaximal, complemented
5#21444234C212yesmaximal, complemented
6#21444231C212yesmaximal, complemented
7#21444229C212yesmaximal, complemented
8#21444202C211yesmaximal, characteristic, complemented
9#21444201C211yesmaximal, characteristic, complemented
10#21444199C211yesmaximal, characteristic, complemented
11C61×#1476C211yesmaximal, characteristic, complemented
12C22×#11758189—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#16839815C2211yescharacteristic
36#16839814C2212yes—
37#16839813—21no—
38#16839812—21no—
39C4⋊C8×D61C2212yes—
40C22⋊C8×D61—21no—
41C4×#11758189—21no—
42C4×#11758189—21no—
43C4×#11758189C2212yes—
44C4×#11758189C2212yes—
45C2×#14519687—21no—
46C2×C4×#92418C2211yescharacteristic
47C4×C8×D61—21no—
48#16839494C2212yescomplemented
49Q8⋊#92418C2212yescomplemented
50#16839492C2212yescomplemented
51#16839491C2212yescomplemented
52D4⋊#92418C2212yescomplemented
53#16839489C2212yescomplemented
54C4×#41×C61C2211yescharacteristic
55C61×#431C2211yescharacteristic
56C2×C4×C8×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×#11758189—28no—
66C2×#11758189—22no—
67C2×#11758189—22no—
68C22×#92418—21no—
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⋊#92418C2312yes—
153#14519706—22no—
154C22⋊#92418—21no—
155#14519689—22no—
156#14519687—22no—
157#14519687—22no—
158C4×#92418—21no—
159C4×#92418—21no—
160C4×#92418C2312yes—
161C8×Dic61—22no—
162C2×#41×C61C2×C411yescharacteristic
163C22×C8×C61—21no—
164C4×Q8×C61C2×C411yescharacteristic
165C4×Q8×C61C2311yescharacteristic
166C4×D4×C61—21no—
167C4×D4×C61—21no—
168C4×D4×C61C2×C411yescharacteristic
169C4×D4×C61C2311yescharacteristic
170#117×C61—21no—
171#117×C61C2×C411yescharacteristic
172C2×C42×C61—21no—
173C2×C42×C61C2311yescharacteristic
174C4⋊C8×C61C2312yes—
175C22⋊C8×C61—21no—
176C4×C8×C61—21no—
177C4×C8×C61—21no—
178C4×C8×C61C2312yes—
179C23×D61C22⋊C411yescharacteristic
180#41×C61—22no—
181#41×C61—22no—
182C2×Q8×C61C22×C411yescharacteristic
183C2×D4×C61—21no—
184C2×D4×C61C22×C411yescharacteristic
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61C22×C411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C2×C22⋊D61—21no—
192C2×C22⋊D61—21no—
193C2×C22⋊D61—21no—
194C2×C22⋊D61—21no—
195C2×C22⋊D61—21no—
196C22×Dic61C22⋊C411yescharacteristic
197C22×Dic61C22⋊C411yescharacteristic
198C22×Dic61C22⋊C411yescharacteristic
199#11758222—22no—
200#11758222—22no—
201#11758222—44no—
202#11758222—44no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244C22×C411yescharacteristic
206C2×C4×D61—22no—
207C2×C4×D61—22no—
208C2×C4×D61—24no—
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
228C2×C8×C61—24no—
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
291C2×#92418—24no—
292C2×#92418—22no—
293C2×#92418—22no—
294#11758189—28no—
295#11758189—28no—
296C8×D61—44no—
297C23×C61—21no—
298C23×C61C2×C22⋊C411yescharacteristic
299C22×D61—22no—
300C22×D61—22no—
301C22×D61—21no—
302C22×D61—41no—
303C22×D61C2×C22⋊C411yescharacteristic
304C22×D61C2×C22⋊C411yescharacteristic
305Q8×C61—21no—
306Q8×C61—21no—
307D4×C61—21no—
308D4×C61—21no—
309D4×C61—42no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61C2×C22⋊C411yescharacteristic
319C2×C4×C61C2×C22⋊C411yescharacteristic
320C2×C4×C61C2×C22⋊C411yescharacteristic
321C2×C4×C61#13112yes—
322C2×C4×C61#13112yes—
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—22no—
333C2×Dic61—21no—
334C2×Dic61—21no—
335C2×Dic61—21no—
336C2×Dic61—41no—
337C2×Dic61C2×C22⋊C411yescharacteristic
338C2×Dic61C2×C22⋊C411yescharacteristic
339C2×Dic61C2×C22⋊C411yescharacteristic
340C2×Dic61C2×C22⋊C411yescharacteristic
341C2×Dic61C2×C22⋊C411yescharacteristic
342C2×Dic61C2×C22⋊C411yescharacteristic
343D244—21no—
344D244—21no—
345D244—42no—
346D244—42no—
347C4×D61—22no—
348C4×D61—21no—
349C4×D61—21no—
350C4×D61—21no—
351C4×D61—21no—
352C4×D61—22no—
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—42no—
362C4×D61—42no—
363C4×D61#10414yes—
364Dic122—21no—
365Dic122—21no—
366Dic122—42no—
367Dic122—42no—
368C8×C61—24no—
369C8×C61—42no—
370#92418—24no—
371#92418—42no—
372#17462—611nomaximal, Sylow
373C22×C61—21no—
374C22×C61—21no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61#40812yes—
379C22×C61C22×C22⋊C411yescharacteristic
380C2×D61—21no—
381C2×D61—21no—
382C2×D61—21no—
383C2×D61—21no—
384C2×D61—21no—
385C2×D61—44no—
386C2×D61—41no—
387C2×D61—41no—
388C2×D61—41no—
389C2×D61C2×#10412yes—
390C4×C61—21no—
391C4×C61—21no—
392C4×C61—41no—
393C4×C61—41no—
394C4×C61—41no—
395C4×C61#40812yes—
396C4×C61C2×#10412yes—
397C4×C61C2×#13111yescharacteristic
398C4×C61C2×#13111yescharacteristic
399C4×C61#57512yes—
400Dic61—21no—
401Dic61—21no—
402Dic61—21no—
403Dic61—21no—
404Dic61—21no—
405Dic61—41no—
406Dic61—41no—
407Dic61—41no—
408Dic61C2×#10412yes—
409#3444—611no—
410C2×#431—611no—
411C2×C4×M16—611no—
412#1485—612no—
413#1484—612no—
414#1483—612no—
415#1483—612no—
416#1476—611no—
417#1476—611no—
418#1476—611no—
419#1476D6111yescharacteristic, complemented
420C2×C61—22no—
421C2×C61—81no—
422C2×C61C2×#40811yescharacteristic
423C2×C61#289611yescharacteristic
424C2×C61C22×#10411yescharacteristic
425D61—22no—
426D61—41no—
427D61—81no—
428C22×M16—1221no—
429#533—611no—
430#533—611no—
431#533—611no—
432#532—611no—
433#532—611no—
434#532—611no—
435#529—611no—
436#529—611no—
437#529—611no—
438#529—611no—
439#529—1221no—
440#529—1221no—
441#529—1221no—
442#529—1221no—
443#525—611no—
444#525—611no—
445#525—1221no—
446#525—1221no—
447C4×#41—611no—
448C4×#41—1221no—
449C4×#41—1221no—
450C4×#41C2×D6111yescharacteristic
451C22×C42—611no—
452#431—611no—
453#431—612no—
454#431—1221no—
455#431—1221no—
456#431C2×D6111yescharacteristic
457C2×C4⋊C8—612no—
458C2×C22⋊C8—1221no—
459C4×M16—612no—
460C4×M16—612no—
461C4×M16—1221no—
462C4×M16—1221no—
463C2×#97—1221no—
464C2×C4×C8—611no—
465C2×C4×C8—1221no—
466C2×C4×C8C2×D6111yescharacteristic
467Q8⋊C8—612no—
468Q8⋊C8—612no—
469Q8⋊C8—612no—
470Q8⋊C8C2×D6112yescomplemented
471D4⋊C8—612no—
472D4⋊C8—612no—
473D4⋊C8—612no—
474D4⋊C8C2×D6112yescomplemented
475C61#1746211yescharacteristic, complemented, Sylow
476C2×#41—611no—
477C2×#41—1221no—
478C2×#41—1221no—
479C2×#41C4×D6111yescharacteristic
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—611no—
483C2×M16—1222no—
484C2×M16—1222no—
485C2×M16—1228no—
486C22×C8—21no—
487C22×C8—1222no—
488C22×C8—1221no—
489C4⋊Q8—611no—
490C4⋊Q8—611no—
491C4⋊Q8—611no—
492#127—611no—
493#126—1221no—
494#126—1221no—
495#126—1221no—
496#126—1221no—
497#125—611no—
498#125—611no—
499#125—1221no—
500#125—1221no—
501#124—611no—
502#124—611no—
503#124—1221no—
504#124—1221no—
505#123—1221no—
506#123—1221no—
507#123—1221no—
508#123—1221no—
509#123—1221no—
510#123—1221no—
511C22⋊Q8—611no—
512C22⋊Q8—611no—
513C22⋊Q8—611no—
514C22⋊Q8—611no—
515C22⋊Q8—1221no—
516C22⋊Q8—1221no—
517C22⋊Q8—1221no—
518C22⋊Q8—1221no—
519#121—611no—
520#121—611no—
521#121—611no—
522#121—611no—
523#121—1221no—
524#121—1221no—
525#121—1221no—
526#121—1221no—
527#120—1221no—
528#120—1221no—
529C4×Q8—611no—
530C4×Q8—611no—
531C4×Q8—1221no—
532C4×Q8—1221no—
533C4×Q8—1221no—
534C4×Q8—1221no—
535C4×Q8C4×D6111yescharacteristic
536C4×Q8C22×D6111yescharacteristic
537C4×D4—21no—
538C4×D4—21no—
539C4×D4—611no—
540C4×D4—611no—
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×D4—1221no—
555C4×D4C4×D6111yescharacteristic
556C4×D4C22×D6111yescharacteristic
557#117—21no—
558#117—611no—
559#117—1221no—
560#117—1221no—
561#117—1221no—
562#117—1221no—
563#117—1221no—
564#117—1221no—
565#117—1221no—
566#117C4×D6111yescharacteristic
567C2×C42—21no—
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—611no—
579C2×C42—1221no—
580C2×C42C22×D6111yescharacteristic
581C4⋊C8—612no—
582C4⋊C8—1222no—
583C4⋊C8C22×D6112yes—
584C22⋊C8—21no—
585C22⋊C8—1222no—
586C22⋊C8—1221no—
587#97—1222no—
588#97—1222no—
589C4×C8—21no—
590C4×C8—21no—
591C4×C8—612no—
592C4×C8—1222no—
593C4×C8—1221no—
594C4×C8—1221no—
595C4×C8C22×D6112yes—
596C24—611no—
597#41—22no—
598#41—22no—
599#41—1222no—
600#41—1222no—
601#41—2444no—
602#41—2444no—
603C2×Q8—611no—
604C2×Q8—1221no—
605C2×Q8—1221no—
606C2×Q8C2×C4×D6111yescharacteristic
607C2×D4—21no—
608C2×D4—611no—
609C2×D4—1221no—
610C2×D4—1221no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4—1221no—
614C2×D4—1221no—
615C2×D4—1221no—
616C2×D4C2×C4×D6111yescharacteristic
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
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—611no—
635C22×C4—1224no—
636C22×C4—1222no—
637C22×C4—1222no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—2442no—
642C22×C4C2×C4×D6111yescharacteristic
643C22×C4D4×D6111yescharacteristic
644C22×C4D4×D6111yescharacteristic
645M16—1228no—
646M16—1228no—
647C2×C8—24no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—1224no—
651C2×C8—1222no—
652C2×C8—1222no—
653C2×C8—2444no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—611no—
657C4⋊C4—611no—
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⋊C4—1221no—
671C4⋊C4—1221no—
672C4⋊C4C2×C4×D6111yescharacteristic
673C4⋊C4C2×C4×D6111yescharacteristic
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
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—
691C22⋊C4—1221no—
692C42—21no—
693C42—21no—
694C42—21no—
695C42—611no—
696C42—611no—
697C42—611no—
698C42—611no—
699C42—611no—
700C42—611no—
701C42—611no—
702C42—611no—
703C42—611no—
704C42—611no—
705C42—611no—
706C42—611no—
707C42—1221no—
708C42—1221no—
709C42—1221no—
710C42C2×C4×D6111yescharacteristic
711C42D4×D6111yescharacteristic
712C42D4×D6111yescharacteristic
713C42C23×D6111yescharacteristic
714C23—21no—
715C23—611no—
716C23—611no—
717C23—1222no—
718C23—1222no—
719C23—1221no—
720C23—2441no—
721C23C22⋊C4×D6111yescharacteristic
722Q8—21no—
723Q8—21no—
724Q8—1221no—
725Q8—1221no—
726Q8—2442no—
727Q8—2442no—
728D4—21no—
729D4—21no—
730D4—42no—
731D4—1221no—
732D4—1221no—
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—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—611no—
749C2×C4—614no—
750C2×C4—611no—
751C2×C4—611no—
752C2×C4—611no—
753C2×C4—611no—
754C2×C4—611no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1221no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2442no—
775C2×C4—2442no—
776C2×C4—2442no—
777C2×C4C22⋊C4×D6111yescharacteristic
778C2×C4C22⋊C4×D6111yescharacteristic
779C2×C4C22⋊C4×D6111yescharacteristic
780C2×C4#1451978312yes—
781C2×C4#1451978512yes—
782C2×C4C22×C4×D6111yescharacteristic
783C2×C4C2×D4×D6111yescharacteristic
784C2×C4C2×D4×D6111yescharacteristic
785C8—24no—
786C8—42no—
787C8—1224no—
788C8—2442no—
789C22—21no—
790C22—21no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—612no—
795C22—1221no—
796C22—1221no—
797C22—1221no—
798C22—1221no—
799C22—1221no—
800C22—2444no—
801C22—2441no—
802C22—2441no—
803C22—2441no—
804C22#1683972712yes—
805C22C2×C22⋊C4×D6111yescharacteristic
806C4—21no—
807C4—21no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—612no—
812C4—1221no—
813C4—1221no—
814C4—1221no—
815C4—1221no—
816C4—1221no—
817C4—2441no—
818C4—2441no—
819C4—2441no—
820C4#1683972712yes—
821C4#104×D6112yes—
822C4C2×#1451978311yescharacteristic
823C4C2×#1451978511yescharacteristic
824C4#1684055912yes—
825C2—22no—
826C2—81no—
827C2—1222no—
828C2—4881no—
829C2—2441no—
830C2C2×#1683972711yescharacteristic
831C2#2145433411yescharacteristic
832C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC42D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1476C2
socleC22×C61C22×C22⋊C4
prime radical#21459112C2
cosocleC42×C61C24
hypercenter#1476D61
hypocenterC61#17462
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C42 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
2. #431×D61C2semidirect
3. C2×C4×#11758189C2semidirect
4. #21444238C2semidirect
5. #21444234C2semidirect
6. #21444231C2semidirect
7. #21444229C2semidirect
8. #21444202C2semidirect
9. #21444201C2semidirect
10. #21444199C2semidirect
11. C61×#1476C2semidirect
48. #16839494C22semidirect
49. Q8⋊#92418C22semidirect
50. #16839492C22semidirect
51. #16839491C22semidirect
52. D4⋊#92418C22semidirect
53. #16839489C22semidirect
57. C61×Q8⋊C8C22semidirect
58. C61×D4⋊C8C22semidirect
419. #1476D61semidirect
470. Q8⋊C8C2×D61semidirect
474. D4⋊C8C2×D61semidirect
475. C61#17462semidirect

Maximal subgroups

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

subgroupindex
#214591122
#431×D612
C2×C4×#117581892
#214442382
#214442342
#214442312
#214442292
#214442022
#214442012
#214441992
C61×#14762
#1746261