Finite Group Databasebeta

← #29647198

Subgroups — #29647198

Order 15616.

1194 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459113C211yesmaximal, characteristic
2#21454449C211yesmaximal, characteristic, complemented
3C4×C4⋊C4×D61C211yesmaximal, characteristic, complemented
4#21444345C211yesmaximal, characteristic, complemented
5#21444344C211yesmaximal, characteristic, complemented
6#21444342C211yesmaximal, characteristic, complemented
7#21444322C212yesmaximal, complemented
8#21444320C212yesmaximal, complemented
9#21444316C212yesmaximal, complemented
10#21444312C212yesmaximal, complemented
11C61×#1509C211yesmaximal, characteristic, complemented
12#16840318C411yescharacteristic, complemented
13#16840316C411yescharacteristic, complemented
14#16840314C2211yescharacteristic
15#16840311C411yescharacteristic, complemented
16#16840309C411yescharacteristic, complemented
17#16840307C2211yescharacteristic
18#16840297C411yescharacteristic, complemented
19#16840296C2211yescharacteristic
20#16840295—21no—
21#16840295—21no—
22#16840291C411yescharacteristic, complemented
23#16840290—21no—
24#16840289—21no—
25#16840275C2211yescharacteristic
26#16840272C2211yescharacteristic
27#16840271—21no—
28#16840270—21no—
29C4×#11758226C411yescharacteristic, complemented
30#16840230—21no—
31C4×#11758224—21no—
32C4×#11758224C411yescharacteristic, complemented
33C2×C4⋊C4×D61—21no—
34C2×C42×D61—21no—
35C2×C42×D61C2211yescharacteristic
36#16839819C2211yescharacteristic
37#16839817—21no—
38#16839814—21no—
39#16839812C2212yes—
40#16839784—21no—
41#16839724C2212yes—
42#16839714—21no—
43C4⋊C4×Dic61—21no—
44C4×#11758196—21no—
45C4×C4⋊Dic61C2211yescharacteristic
46#16839613C2212yes—
47#95×D61C2212yes—
48#16839500C2212yes—
49#16839499C2212yes—
50#16839498C2212yes—
51#16839497C2212yes—
52#16839496C2212yes—
53#16839495C2212yes—
54C61×#529C2211yescharacteristic
55C61×#432C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C61×#328C2212yes—
58C61×#327C2212yes—
59C2×#11758226C2×C411yescharacteristic
60C2×#11758222—21no—
61C2×#11758224—21no—
62C2×#11758224C2×C411yescharacteristic
63C22×C4×D61—22no—
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61C2311yescharacteristic
67C2×#11758189—22no—
68#14519776C2×C411yescharacteristic, complemented
69#14519776C2×C411yescharacteristic, complemented
70#14519775C2×C411yescharacteristic, complemented
71#14519773C2×C411yescharacteristic, complemented
72#14519772—21no—
73#14519771—21no—
74#14519770—21no—
75#14519769C2×C411yescharacteristic, complemented
76#14519767—21no—
77#14519767—21no—
78#14519765C2×C411yescharacteristic, complemented
79#14519763—21no—
80#14519763—21no—
81#14519762—21no—
82#14519762—21no—
83#14519760—21no—
84#14519759—21no—
85#14519759—21no—
86#14519757C2×C411yescharacteristic
87#14519756C2311yescharacteristic
88#14519755—21no—
89#14519755—21no—
90#14519755—21no—
91#14519754—21no—
92#14519753C2×C411yescharacteristic
93#14519752C2×C411yescharacteristic
94#14519751C2311yescharacteristic
95#14519750—21no—
96#14519750—21no—
97#14519750—21no—
98#14519749—21no—
99#14519748C2×C411yescharacteristic
100#14519747—21no—
101#14519745—21no—
102Q8×Dic61C2×C411yescharacteristic, complemented
103C4×Dic122—21no—
104C4×Dic122C2×C411yescharacteristic, complemented
105#14519742—21no—
106#14519742—21no—
107#14519742—21no—
108#14519742C2×C411yescharacteristic, complemented
109C4×D244—21no—
110C4×D244C2×C411yescharacteristic, complemented
111D4×Dic61—21no—
112D4×Dic61C2×C411yescharacteristic, complemented
113#14519739—21no—
114#14519739—21no—
115#14519739—21no—
116#14519739C2×C411yescharacteristic, complemented
117C4×C22⋊D61—21no—
118C4×C22⋊D61—21no—
119C4×C22⋊D61—21no—
120#14519737—21no—
121#14519737—21no—
122#14519737—21no—
123#14519737—21no—
124#14519737—21no—
125#14519737—21no—
126#14519737—21no—
127#14519735—21no—
128#14519735—21no—
129#14519735C2×C411yescharacteristic
130#14519735C2×C411yescharacteristic
131#14519734—21no—
132#14519734—21no—
133#14519733—21no—
134#14519733—21no—
135#14519733—21no—
136C2×C4⋊Dic61—21no—
137C2×#11758196—22no—
138C4⋊C4×D61—28no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61—22no—
142C2×C4×Dic61D411yescharacteristic
143C2×C4×Dic61D411yescharacteristic
144C2×C4×Dic61C2311yescharacteristic
145C42×D61—21no—
146C42×D61—44no—
147C42×D61C2×C411yescharacteristic
148C42×D61C2×C411yescharacteristic
149C42×D61C2×C411yescharacteristic
150C42×D61C2×C411yescharacteristic
151C42×D61D411yescharacteristic
152C42×D61D411yescharacteristic
153C42×D61D411yescharacteristic
154C42×D61D411yescharacteristic
155C4⋊#92418—21no—
156#14519706—22no—
157C22⋊#92418C2312yes—
158#14519689—22no—
159#14519688—21no—
160C8×Dic61—22no—
161#14519684—22no—
162#14519684C2312yes—
163#126×C61—21no—
164#125×C61C2×C411yescharacteristic, complemented
165#124×C61C2×C411yescharacteristic, complemented
166#123×C61—21no—
167C22⋊Q8×C61C2311yescharacteristic
168#121×C61C2311yescharacteristic
169C4×Q8×C61C2×C411yescharacteristic, complemented
170C4×D4×C61—21no—
171C4×D4×C61C2×C411yescharacteristic, complemented
172#117×C61—21no—
173C2×C4⋊C4×C61—21no—
174C2×C42×C61—21no—
175C2×C42×C61C2311yescharacteristic
176C4⋊C8×C61—21no—
177C22⋊C8×C61C2312yes—
178#97×C61—21no—
179#95×C61C2312yes—
180C23×D61C2×D411yescharacteristic
181C2×Q8×C61C22×C411yescharacteristic
182C2×D4×C61—21no—
183C2×D4×C61C22×C411yescharacteristic
184C22×C4×C61—22no—
185C22×C4×C61—21no—
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2411yescharacteristic
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C2×C22⋊D61—21no—
192C2×C22⋊D61—21no—
193C2×C22⋊D61—21no—
194C22×Dic61—22no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61C2×D411yescharacteristic
198C22×Dic61C2×D411yescharacteristic
199C22×Dic61C2×D411yescharacteristic
200#11758226—42no—
201#11758224—42no—
202#11758224—42no—
203#11758224—42no—
204#11758222—44no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244C22×C411yescharacteristic
208C2×C4×D61—22no—
209C2×C4×D61—22no—
210C2×C4×D61—24no—
211C2×C4×D61—28no—
212C2×C4×D61—21no—
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61—42no—
216C2×C4×D61—44no—
217C2×C4×D61—44no—
218C2×C4×D61C22⋊C411yescharacteristic
219C2×C4×D61C22⋊C411yescharacteristic
220C2×C4×D61C22⋊C411yescharacteristic
221C2×C4×D61C22⋊C411yescharacteristic
222C2×C4×D61C22⋊C411yescharacteristic
223C2×C4×D61C22⋊C411yescharacteristic
224C2×C4×D61C22⋊C411yescharacteristic
225C2×C4×D61C22⋊C411yescharacteristic
226C2×C4×D61C22×C411yescharacteristic
227C2×C4×D61C22×C411yescharacteristic
228C2×C4×D61C2×D411yescharacteristic
229C2×C4×D61C2×D411yescharacteristic
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122C22×C411yescharacteristic
233C2×C8×C61—22no—
234C4⋊C4×C61—24no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61C22×C411yescharacteristic
240C4⋊C4×C61C22×C411yescharacteristic
241C22⋊C4×C61—21no—
242C22⋊C4×C61—21no—
243C22⋊C4×C61—21no—
244C22⋊C4×C61—21no—
245C22⋊C4×C61—21no—
246C42×C61—21no—
247C42×C61—42no—
248C42×C61C22×C411yescharacteristic
249C42×C61C22×C411yescharacteristic
250C42×C61C2×D411yescharacteristic
251C42×C61C2×D411yescharacteristic
252C22⋊Dic61—21no—
253C22⋊Dic61—21no—
254C22⋊Dic61—21no—
255#11758198—21no—
256#11758198—21no—
257#11758198—21no—
258#11758198—21no—
259#11758198—21no—
260#11758198—21no—
261#11758198—21no—
262#11758198—21no—
263#11758198—21no—
264#11758198—21no—
265C4⋊Dic61—24no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61C22×C411yescharacteristic
269C4⋊Dic61C22×C411yescharacteristic
270#11758196—28no—
271#11758196—21no—
272#11758196—21no—
273#11758196—21no—
274#11758196—21no—
275#11758196—21no—
276#11758196—21no—
277#11758196—21no—
278#11758196—21no—
279#11758196—21no—
280#11758196—21no—
281C4×Dic61—21no—
282C4×Dic61—21no—
283C4×Dic61—21no—
284C4×Dic61—21no—
285C4×Dic61—21no—
286C4×Dic61—42no—
287C4×Dic61—44no—
288C4×Dic61C22⋊C411yescharacteristic
289C4×Dic61C22⋊C411yescharacteristic
290C4×Dic61C22⋊C411yescharacteristic
291C4×Dic61C22⋊C411yescharacteristic
292C4×Dic61C22⋊C411yescharacteristic
293C4×Dic61C22⋊C411yescharacteristic
294C4×Dic61C22⋊C411yescharacteristic
295C4×Dic61C22⋊C411yescharacteristic
296C4×Dic61C22×C411yescharacteristic
297C4×Dic61C22×C411yescharacteristic
298C4×Dic61C2×D411yescharacteristic
299C4×Dic61C2×D411yescharacteristic
300C2×#92418—22no—
301#11758189—44no—
302C23×C61—21no—
303C23×C61C22×D411yescharacteristic
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—21no—
309C22×D61C2×C22⋊C411yescharacteristic
310C22×D61C2×C22⋊C411yescharacteristic
311Q8×C61—41no—
312D4×C61—41no—
313D4×C61—41no—
314D4×C61—41no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—22no—
318C2×C4×C61—24no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—41no—
323C2×C4×C61—42no—
324C2×C4×C61—42no—
325C2×C4×C61—42no—
326C2×C4×C61C2×C22⋊C411yescharacteristic
327C2×C4×C61C2×C22⋊C411yescharacteristic
328C2×C4×C61C2×C22⋊C411yescharacteristic
329C2×C4×C61C2×C22⋊C411yescharacteristic
330C2×C4×C61C23×C411yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C22⋊D61—41no—
333C22⋊D61—41no—
334C22⋊D61—42no—
335C22⋊D61—42no—
336C22⋊D61—42no—
337C22⋊D61—42no—
338C2×Dic61—22no—
339C2×Dic61—24no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—41no—
344C2×Dic61—42no—
345C2×Dic61—42no—
346C2×Dic61—42no—
347C2×Dic61—42no—
348C2×Dic61C2×C22⋊C411yescharacteristic
349C2×Dic61C2×C22⋊C411yescharacteristic
350C2×Dic61C2×C22⋊C411yescharacteristic
351C2×Dic61C2×C22⋊C411yescharacteristic
352C2×Dic61C2×C22⋊C411yescharacteristic
353C2×Dic61C2×C22⋊C411yescharacteristic
354C2×Dic61AGL(1,ℤ/8)12yes—
355C2×Dic61#13712yes—
356D244—41no—
357D244—42no—
358D244—42no—
359C4×D61—22no—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—22no—
364C4×D61—22no—
365C4×D61—22no—
366C4×D61—22no—
367C4×D61—22no—
368C4×D61—41no—
369C4×D61—41no—
370C4×D61—42no—
371C4×D61—416no—
372C4×D61—42no—
373C4×D61—42no—
374C4×D61#10414yes—
375Dic122—42no—
376Dic122—42no—
377Dic122—41no—
378C8×C61—42no—
379#92418—42no—
380#17546—611nomaximal, Sylow
381C22×C61—21no—
382C22×C61—21no—
383C22×C61—41no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61C22×C22⋊C411yescharacteristic
387C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
388C22×C61C2×#13711yescharacteristic
389C2×D61—24no—
390C2×D61—24no—
391C2×D61—21no—
392C2×D61—21no—
393C2×D61—21no—
394C2×D61—21no—
395C2×D61—41no—
396C2×D61—41no—
397C2×D61—41no—
398C2×D61#41012yes—
399C2×D61C2×#10412yes—
400C4×C61—21no—
401C4×C61—21no—
402C4×C61—21no—
403C4×C61—21no—
404C4×C61—21no—
405C4×C61—44no—
406C4×C61—41no—
407C4×C61—41no—
408C4×C61—41no—
409C4×C61C2×#10412yes—
410Dic61—21no—
411Dic61—21no—
412Dic61—21no—
413Dic61—44no—
414Dic61—41no—
415Dic61—41no—
416Dic61—41no—
417Dic61#41712yes—
418Dic61#41712yes—
419Dic61C2×#10412yes—
420#3444—611no—
421#2920—611no—
422C2×C4×C4⋊C4—611no—
423#1509—611no—
424#1509—611no—
425#1509—611no—
426#1509D6111yescharacteristic, complemented
427#1504—612no—
428#1504—612no—
429#1503—612no—
430#1502—612no—
431C2×C61—21no—
432C2×C61—21no—
433C2×C61—81no—
434C2×C61C2×#41011yescharacteristic
435C2×C61C2×#41711yescharacteristic
436C2×C61C22×#10411yescharacteristic
437D61—22no—
438D61—22no—
439D61—81no—
440#533—611no—
441#533—611no—
442#533—611no—
443#532—611no—
444#532—611no—
445#532—611no—
446#529—611no—
447#529—611no—
448#529—611no—
449#529—1221no—
450#529—1221no—
451#529—1221no—
452#529—1221no—
453#529C2×D6111yescharacteristic
454#525—611no—
455#525—611no—
456#525—1221no—
457#525—1221no—
458C4×#41—611no—
459C4×#41—611no—
460C4×#41—1221no—
461C4×#41—1221no—
462C22×C4⋊C4—1221no—
463C22×C42—611no—
464C22×C42—1221no—
465#432—611no—
466#432—1221no—
467#432C2×D6111yescharacteristic
468#431—612no—
469#431—1221no—
470#423—1221no—
471#407—612no—
472C4×M16—1221no—
473C4×C4⋊C4—611no—
474C4×C4⋊C4—612no—
475C4×C4⋊C4—1221no—
476C4×C4⋊C4—1221no—
477C4×C4⋊C4C2×D6111yescharacteristic
478C2×#95—612no—
479#328—612no—
480#328—612no—
481#328—612no—
482#328C2×D6112yes—
483#327—612no—
484#327—612no—
485#327—612no—
486#327C2×D6112yes—
487C61#1754611yescharacteristic, complemented, Sylow
488C2×#41—611no—
489C2×#41—611no—
490C2×#41—1221no—
491C2×#41—1221no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—1222no—
496C2×M16—1222no—
497C4⋊Q8—611no—
498C4⋊Q8—611no—
499C4⋊Q8—611no—
500#127—611no—
501#126—21no—
502#126—1221no—
503#126—1221no—
504#126—1221no—
505#125—611no—
506#125—1221no—
507#125—1221no—
508#125C4×D6111yescharacteristic, complemented
509#124—611no—
510#124—1221no—
511#124—1221no—
512#124C4×D6111yescharacteristic, complemented
513#123—21no—
514#123—1221no—
515#123—1221no—
516#123—1221no—
517#123—1221no—
518#123—1221no—
519C22⋊Q8—611no—
520C22⋊Q8—611no—
521C22⋊Q8—611no—
522C22⋊Q8—1221no—
523C22⋊Q8—1221no—
524C22⋊Q8—1221no—
525C22⋊Q8—1221no—
526C22⋊Q8C22×D6111yescharacteristic
527#121—611no—
528#121—611no—
529#121—611no—
530#121—1221no—
531#121—1221no—
532#121—1221no—
533#121—1221no—
534#121C22×D6111yescharacteristic
535#120—1221no—
536#120—1221no—
537C4×Q8—611no—
538C4×Q8—611no—
539C4×Q8—611no—
540C4×Q8—1221no—
541C4×Q8—1221no—
542C4×Q8—1221no—
543C4×Q8—1221no—
544C4×Q8C4×D6111yescharacteristic, complemented
545C4×D4—21no—
546C4×D4—611no—
547C4×D4—611no—
548C4×D4—611no—
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×D4—1221no—
562C4×D4—1221no—
563C4×D4—1221no—
564C4×D4C4×D6111yescharacteristic, complemented
565#117—21no—
566#117—611no—
567#117—611no—
568#117—1221no—
569#117—1221no—
570#117—1221no—
571#117—1221no—
572#117—1221no—
573#117—1221no—
574#117—1221no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—1228no—
577C2×C4⋊C4—1222no—
578C2×C4⋊C4—1221no—
579C2×C42—21no—
580C2×C42—611no—
581C2×C42—611no—
582C2×C42—611no—
583C2×C42—611no—
584C2×C42—611no—
585C2×C42—611no—
586C2×C42—611no—
587C2×C42—611no—
588C2×C42—611no—
589C2×C42—611no—
590C2×C42—611no—
591C2×C42—1221no—
592C2×C42—1221no—
593C2×C42—1222no—
594C2×C42—1221no—
595C2×C42—2444no—
596C2×C42C22×D6111yescharacteristic
597C4⋊C8—21no—
598C4⋊C8—1222no—
599C4⋊C8—1221no—
600C22⋊C8—612no—
601C22⋊C8—1222no—
602C22⋊C8C22×D6112yes—
603#97—21no—
604#97—1221no—
605C4×C8—1222no—
606#95—612no—
607#95—1222no—
608#95C22×D6112yes—
609C24—611no—
610#41—2444no—
611#41—2442no—
612#41—2442no—
613#41—2442no—
614#41—2442no—
615C2×Q8—611no—
616C2×Q8—1221no—
617C2×Q8—1221no—
618C2×Q8C2×C4×D6111yescharacteristic
619C2×D4—21no—
620C2×D4—611no—
621C2×D4—1221no—
622C2×D4—1221no—
623C2×D4—1221no—
624C2×D4—1221no—
625C2×D4—1221no—
626C2×D4—1221no—
627C2×D4—1221no—
628C2×D4C2×C4×D6111yescharacteristic
629C22×C4—22no—
630C22×C4—21no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—611no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—1222no—
647C22×C4—1224no—
648C22×C4—1222no—
649C22×C4—1221no—
650C22×C4—1221no—
651C22×C4—1228no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1222no—
655C22×C4—1221no—
656C22×C4—2442no—
657C22×C4—2444no—
658C22×C4—2444no—
659C22×C4D4×D6111yescharacteristic
660C22×C4D4×D6111yescharacteristic
661C22×C4C23×D6111yescharacteristic
662M16—2444no—
663C2×C8—22no—
664C2×C8—1222no—
665C4⋊C4—24no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—611no—
671C4⋊C4—611no—
672C4⋊C4—1221no—
673C4⋊C4—1221no—
674C4⋊C4—1221no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—1228no—
681C4⋊C4—1224no—
682C4⋊C4—1221no—
683C4⋊C4—1221no—
684C4⋊C4—1221no—
685C4⋊C4—1221no—
686C4⋊C4C2×C4×D6111yescharacteristic
687C4⋊C4C2×C4×D6111yescharacteristic
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—1221no—
694C22⋊C4—1221no—
695C22⋊C4—1221no—
696C22⋊C4—1221no—
697C22⋊C4—1221no—
698C22⋊C4—1221no—
699C22⋊C4—1221no—
700C22⋊C4—1221no—
701C22⋊C4—1221no—
702C22⋊C4—1221no—
703C22⋊C4—1221no—
704C22⋊C4—1221no—
705C22⋊C4—1221no—
706C42—21no—
707C42—42no—
708C42—611no—
709C42—611no—
710C42—611no—
711C42—611no—
712C42—611no—
713C42—611no—
714C42—611no—
715C42—611no—
716C42—611no—
717C42—611no—
718C42—611no—
719C42—611no—
720C42—1221no—
721C42—1221no—
722C42—1221no—
723C42—1221no—
724C42—1221no—
725C42—2442no—
726C42—2444no—
727C42C2×C4×D6111yescharacteristic
728C42C2×C4×D6111yescharacteristic
729C42D4×D6111yescharacteristic
730C42D4×D6111yescharacteristic
731C23—21no—
732C23—611no—
733C23—611no—
734C23—1222no—
735C23—1222no—
736C23—1221no—
737C23—1221no—
738C23—1221no—
739C23C2×D4×D6111yescharacteristic
740Q8—41no—
741Q8—2441no—
742Q8—2442no—
743Q8—2442no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—2441no—
748D4—2442no—
749D4—2442no—
750D4—2442no—
751D4—2442no—
752D4—2442no—
753D4—2442no—
754D4—2441no—
755D4—2441no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—611no—
768C2×C4—611no—
769C2×C4—611no—
770C2×C4—612no—
771C2×C4—612no—
772C2×C4—614no—
773C2×C4—611no—
774C2×C4—611no—
775C2×C4—611no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1222no—
781C2×C4—1222no—
782C2×C4—1222no—
783C2×C4—1222no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1224no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2442no—
793C2×C4—2442no—
794C2×C4—24416no—
795C2×C4—2442no—
796C2×C4—2441no—
797C2×C4—2442no—
798C2×C4—2442no—
799C2×C4—2442no—
800C2×C4—2442no—
801C2×C4C22⋊C4×D6111yescharacteristic
802C2×C4C22⋊C4×D6111yescharacteristic
803C2×C4C22⋊C4×D6111yescharacteristic
804C2×C4C22⋊C4×D6111yescharacteristic
805C2×C4C22×C4×D6111yescharacteristic
806C2×C4C2×D4×D6111yescharacteristic
807C8—42no—
808C8—2442no—
809C22—21no—
810C22—21no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—612no—
815C22—612no—
816C22—1224no—
817C22—1224no—
818C22—1221no—
819C22—1221no—
820C22—1221no—
821C22—1221no—
822C22—2441no—
823C22—2441no—
824C22—2441no—
825C22C2×C22⋊C4×D6111yescharacteristic
826C22AGL(1,ℤ/8)×D6111yescharacteristic
827C22#137×D6111yescharacteristic
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—44no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—612no—
838C4—612no—
839C4—612no—
840C4—1221no—
841C4—1221no—
842C4—1221no—
843C4—2444no—
844C4—2441no—
845C4—2441no—
846C4—2441no—
847C4#104×D6112yes—
848C2—21no—
849C2—21no—
850C2—81no—
851C2—1222no—
852C2—1222no—
853C2—4881no—
854C2#410×D6111yescharacteristic
855C2#417×D6111yescharacteristic
856C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1509C2
socleC22×C61C22×C22⋊C4
prime radical#21459113C2
cosocleC22×C4×C61C24
hypercenter#1509D61
hypocenterC61#17546
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1509

Complements

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

NH ≅ G/Ntype
2. #21454449C2semidirect
3. C4×C4⋊C4×D61C2semidirect
4. #21444345C2semidirect
5. #21444344C2semidirect
6. #21444342C2semidirect
7. #21444322C2semidirect
8. #21444320C2semidirect
9. #21444316C2semidirect
10. #21444312C2semidirect
11. C61×#1509C2semidirect
12. #16840318C4semidirect
13. #16840316C4semidirect
15. #16840311C4semidirect
16. #16840309C4semidirect
18. #16840297C4semidirect
22. #16840291C4semidirect
29. C4×#11758226C4semidirect
32. C4×#11758224C4semidirect
68. #14519776C2×C4semidirect
69. #14519776C2×C4semidirect
70. #14519775C2×C4semidirect
71. #14519773C2×C4semidirect
75. #14519769C2×C4semidirect
78. #14519765C2×C4semidirect
102. Q8×Dic61C2×C4semidirect
104. C4×Dic122C2×C4semidirect
108. #14519742C2×C4semidirect
110. C4×D244C2×C4semidirect
112. D4×Dic61C2×C4semidirect
116. #14519739C2×C4semidirect
164. #125×C61C2×C4semidirect
165. #124×C61C2×C4semidirect
169. C4×Q8×C61C2×C4semidirect
171. C4×D4×C61C2×C4semidirect
426. #1509D61semidirect
487. C61#17546semidirect
508. #125C4×D61semidirect
512. #124C4×D61semidirect
544. C4×Q8C4×D61semidirect
564. C4×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214591132
#214544492
C4×C4⋊C4×D612
#214443452
#214443442
#214443422
#214443222
#214443202
#214443162
#214443122
C61×#15092
#1754661