Finite Group Databasebeta

← #29646015

Subgroups — #29646015

Order 15616.

1020 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840295C211yesmaximal, characteristic
2#21454449C211yesmaximal, characteristic, complemented
3#431×D61C211yesmaximal, characteristic, complemented
4#21444189C211yesmaximal, characteristic, complemented
5#21444188C211yesmaximal, characteristic, complemented
6#21444186C211yesmaximal, characteristic, complemented
7#21444166C212yesmaximal, complemented
8#21444164C212yesmaximal, complemented
9#21444141C212yesmaximal, complemented
10#21444138C212yesmaximal, complemented
11C61×#1473C211yesmaximal, characteristic, complemented
12#16840295—21no—
13#16840295—21no—
14#16840295—21no—
15#16840295—21no—
16#16840295—21no—
17#16840295—21no—
18#16840295—21no—
19#16840295—21no—
20C2×#14519771C2211yescharacteristic
21C2×#14519767C411yescharacteristic
22C2×#14519763C411yescharacteristic
23C2×#14519762C2211yescharacteristic
24C2×#14519759C2211yescharacteristic
25C2×#14519755C411yescharacteristic
26C2×#14519750C411yescharacteristic
27C2×#14519742C2211yescharacteristic
28C2×#14519739C411yescharacteristic
29C2×#14519737C411yescharacteristic
30C2×#14519737C2211yescharacteristic
31C2×#14519735C411yescharacteristic
32C2×#14519733C411yescharacteristic
33C2×C42×D61C2211yescharacteristic
34#16839819C2211yescharacteristic
35#16839817—21no—
36#16839815C2211yescharacteristic
37#16839814—21no—
38#16839814—21no—
39#16839813—21no—
40#16839812C2212yes—
41#16839812C2212yes—
42#16839784—21no—
43C4⋊C8×D61—21no—
44#16839724C2212yes—
45C22⋊C8×D61C2212yes—
46#16839714—21no—
47C4×C8×D61—21no—
48#16839488C2212yes—
49#16839487C2212yes—
50#16839487C2212yes—
51#16839486C2212yes—
52#16839485C2212yes—
53#16839485C2212yes—
54C2×#126×C61C2211yescharacteristic
55C61×#432C2211yescharacteristic
56C61×#431C2211yescharacteristic
57C61×#324C2212yes—
58C61×#323C2212yes—
59C22×Dic122C2×C411yescharacteristic
60C22×D244C2×C411yescharacteristic
61C22×C22⋊D61C2×C411yescharacteristic
62C22×C22⋊D61C2×C411yescharacteristic
63C23×Dic61C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61C2311yescharacteristic
68C2×#11758189—22no—
69C2×C8×D61—22no—
70#14519771—21no—
71#14519771—21no—
72#14519771—21no—
73#14519771—21no—
74#14519767—21no—
75#14519767—21no—
76#14519767—21no—
77#14519767—21no—
78#14519763—21no—
79#14519763—21no—
80#14519763—21no—
81#14519763—21no—
82#14519762—21no—
83#14519762—21no—
84#14519762—21no—
85#14519762—21no—
86#14519759—21no—
87#14519759—21no—
88#14519759—21no—
89#14519759—21no—
90#14519755—21no—
91#14519755—21no—
92#14519755—21no—
93#14519755—21no—
94#14519750—21no—
95#14519750—21no—
96#14519750—21no—
97#14519750—21no—
98#14519742—21no—
99#14519742—21no—
100#14519742—21no—
101#14519742—21no—
102#14519739—21no—
103#14519739—21no—
104#14519739—21no—
105#14519739—21no—
106#14519737—21no—
107#14519737—21no—
108#14519737—21no—
109#14519737—21no—
110#14519737—21no—
111#14519737—21no—
112#14519737—21no—
113#14519737—21no—
114#14519735—21no—
115#14519735—21no—
116#14519735—21no—
117#14519735—21no—
118#14519733—21no—
119#14519733—21no—
120#14519733—21no—
121#14519733—21no—
122C2×C4⋊Dic61C2×C411yescharacteristic
123C2×#11758196C2×C411yescharacteristic
124C2×#11758196C2×C411yescharacteristic
125C2×#11758196C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2×C411yescharacteristic
128C2×#11758196C2311yescharacteristic
129C2×C22⋊Dic61C2×C411yescharacteristic
130C2×#11758198C2×C411yescharacteristic
131C2×#11758198C2×C411yescharacteristic
132C2×#11758198C2×C411yescharacteristic
133C2×#11758198C2×C411yescharacteristic
134C2×#11758198C2×C411yescharacteristic
135C2×#11758198C2311yescharacteristic
136C2×C4×Dic61C2×C411yescharacteristic
137C2×C4×Dic61C2×C411yescharacteristic
138C2×C4×Dic61C2×C411yescharacteristic
139C2×C4×Dic61C2×C411yescharacteristic
140C2×C4×Dic61C2311yescharacteristic
141C42×D61D411yescharacteristic
142C42×D61D411yescharacteristic
143C42×D61D411yescharacteristic
144C42×D61D411yescharacteristic
145C42×D61D411yescharacteristic
146C42×D61D411yescharacteristic
147C42×D61D411yescharacteristic
148C42×D61D411yescharacteristic
149C4⋊#92418—21no—
150C4⋊#92418—21no—
151#14519706—22no—
152#14519706—22no—
153C22⋊#92418C2312yes—
154C22⋊#92418C2312yes—
155#14519689—22no—
156#14519689—22no—
157#14519688—21no—
158C4×#92418—21no—
159C8×Dic61—22no—
160C8×Dic61—22no—
161#126×C61—21no—
162#126×C61—21no—
163#126×C61—21no—
164#126×C61—21no—
165C2×C4⋊C4×C61C2×C411yescharacteristic
166C2×C4⋊C4×C61C2×C411yescharacteristic
167C2×C4⋊C4×C61C2311yescharacteristic
168C2×C22⋊C4×C61C2×C411yescharacteristic
169C2×C22⋊C4×C61C2×C411yescharacteristic
170C2×C22⋊C4×C61C2311yescharacteristic
171C2×C42×C61C2311yescharacteristic
172C4⋊C8×C61—21no—
173C4⋊C8×C61—21no—
174C22⋊C8×C61C2312yes—
175C22⋊C8×C61C2312yes—
176#97×C61—21no—
177C4×C8×C61—21no—
178C24×C61C22×C411yescharacteristic
179C23×D61C22×C411yescharacteristic
180C23×D61C22×C411yescharacteristic
181C22×C4×C61C22×C411yescharacteristic
182C22×C4×C61C22×C411yescharacteristic
183C22×C4×C61C22×C411yescharacteristic
184C22×C4×C61C22×C411yescharacteristic
185C22×C4×C61C22×C411yescharacteristic
186C22×C4×C61C2411yescharacteristic
187C2×C22⋊D61—21no—
188C2×C22⋊D61—21no—
189C2×C22⋊D61—21no—
190C2×C22⋊D61—21no—
191C2×C22⋊D61—24no—
192C2×C22⋊D61—42no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—42no—
196C22×Dic61C22×C411yescharacteristic
197C22×Dic61C22×C411yescharacteristic
198C22×Dic61C22×C411yescharacteristic
199C22×Dic61C22×C411yescharacteristic
200C22×Dic61C22×C411yescharacteristic
201C22×Dic61C22×C411yescharacteristic
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—42no—
205C2×C4×D61—24no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—42no—
209C2×C4×D61—42no—
210C2×C4×D61—42no—
211C2×C4×D61C22⋊C411yescharacteristic
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×D61C2×D411yescharacteristic
220C2×C4×D61C2×D411yescharacteristic
221C2×C4×D61C2×D411yescharacteristic
222C2×C4×D61C2×D411yescharacteristic
223C2×Dic122—21no—
224C2×Dic122—21no—
225C2×Dic122—24no—
226C2×C8×C61—22no—
227C2×C8×C61—22no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C22⋊C4×C61—21no—
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C22⋊C4×C61—21no—
238C22⋊C4×C61—21no—
239C22⋊C4×C61—21no—
240C42×C61C2×D411yescharacteristic
241C42×C61C2×D411yescharacteristic
242C42×C61C2×D411yescharacteristic
243C42×C61C2×D411yescharacteristic
244C22⋊Dic61—21no—
245C22⋊Dic61—21no—
246#11758198—21no—
247#11758198—21no—
248#11758198—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—
258C4⋊Dic61—21no—
259C4⋊Dic61—21no—
260#11758196—21no—
261#11758196—21no—
262#11758196—21no—
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—
272C4×Dic61—21no—
273C4×Dic61—21no—
274C4×Dic61—21no—
275C4×Dic61—21no—
276C4×Dic61C22⋊C411yescharacteristic
277C4×Dic61C22⋊C411yescharacteristic
278C4×Dic61C22⋊C411yescharacteristic
279C4×Dic61C22⋊C411yescharacteristic
280C4×Dic61C22⋊C411yescharacteristic
281C4×Dic61C22⋊C411yescharacteristic
282C4×Dic61C22⋊C411yescharacteristic
283C4×Dic61C22⋊C411yescharacteristic
284C4×Dic61C2×D411yescharacteristic
285C4×Dic61C2×D411yescharacteristic
286C4×Dic61C2×D411yescharacteristic
287C4×Dic61C2×D411yescharacteristic
288C2×#92418—22no—
289C2×#92418—22no—
290#11758189—44no—
291C8×D61—44no—
292C23×C61—21no—
293C23×C61—22no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61C23×C411yescharacteristic
297C22×D61—22no—
298C22×D61—22no—
299C22×D61—21no—
300C22×D61—22no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61C2×C22⋊C411yescharacteristic
305C22×D61C2×C22⋊C411yescharacteristic
306C2×C4×C61—22no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—22no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61C2×C22⋊C411yescharacteristic
316C2×C4×C61C2×C22⋊C411yescharacteristic
317C2×C4×C61C2×C22⋊C411yescharacteristic
318C2×C4×C61C2×C22⋊C411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C22×D411yescharacteristic
321C22⋊D61—42no—
322C22⋊D61—42no—
323C22⋊D61—42no—
324C22⋊D61—42no—
325C2×Dic61—22no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—21no—
329C2×Dic61—22no—
330C2×Dic61—41no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—41no—
334C2×Dic61—41no—
335C2×Dic61C2×C22⋊C411yescharacteristic
336C2×Dic61C2×C22⋊C411yescharacteristic
337C2×Dic61C2×C22⋊C411yescharacteristic
338C2×Dic61C2×C22⋊C411yescharacteristic
339C2×Dic61C2×C22⋊C411yescharacteristic
340C2×Dic61C2×C22⋊C411yescharacteristic
341C2×Dic61#13114yes—
342D244—42no—
343D244—42no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—22no—
349C4×D61—22no—
350C4×D61—22no—
351C4×D61—22no—
352C4×D61—41no—
353C4×D61—41no—
354C4×D61—41no—
355C4×D61—41no—
356C4×D61—42no—
357C4×D61—42no—
358Dic122—42no—
359Dic122—42no—
360C8×C61—42no—
361C8×C61—42no—
362#92418—42no—
363#92418—42no—
364#17383—611nomaximal, Sylow
365C22×C61—21no—
366C22×C61—21no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—82no—
371C22×C61C22×C22⋊C411yescharacteristic
372C22×C61C2×#13112yes—
373C2×D61—21no—
374C2×D61—21no—
375C2×D61—21no—
376C2×D61—21no—
377C2×D61—21no—
378C2×D61—44no—
379C2×D61—41no—
380C2×D61—41no—
381C2×D61—41no—
382C2×D61—82no—
383C2×D61#41012yes—
384C4×C61—21no—
385C4×C61—21no—
386C4×C61—21no—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—21no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61—41no—
393Dic61—21no—
394Dic61—21no—
395Dic61—21no—
396Dic61—41no—
397Dic61—41no—
398Dic61—41no—
399Dic61#40812yes—
400Dic61#40812yes—
401Dic61#41312yes—
402C2×#529—611no—
403#2920—611no—
404C2×#431—611no—
405#1473—611no—
406#1473—611no—
407#1473—611no—
408#1473D6111yescharacteristic, complemented
409#1468—612no—
410#1468—612no—
411#1461—612no—
412#1460—612no—
413C2×C61—22no—
414C2×C61—81no—
415C2×C61C2×#40811yescharacteristic
416C2×C61C2×#41011yescharacteristic
417C2×C61C2×#41311yescharacteristic
418D61—22no—
419D61—41no—
420D61—81no—
421#529—1221no—
422#529—1221no—
423#529—1221no—
424#529—1221no—
425#529—1221no—
426#529—1221no—
427#529—1221no—
428#529—1221no—
429C2×#126—611no—
430C2×#126C2×D6111yescharacteristic
431C2×#125—611no—
432C2×#124—611no—
433C2×#123—611no—
434C2×#123—611no—
435C2×C22⋊Q8—611no—
436C2×#121—611no—
437C2×C4×Q8—611no—
438C2×C4×D4—611no—
439C2×C4×D4—611no—
440C2×C4×D4—611no—
441C2×#117—611no—
442C2×#117—611no—
443C22×C42—611no—
444#432—611no—
445#432—1221no—
446#432C2×D6111yescharacteristic
447#431—611no—
448#431—612no—
449#431—612no—
450#431—1221no—
451#431—1221no—
452#431—1221no—
453#431C2×D6111yescharacteristic
454#423—1221no—
455C2×C4⋊C8—1221no—
456#407—612no—
457C2×C22⋊C8—612no—
458C4×M16—1221no—
459C2×C4×C8—1221no—
460#324—612no—
461#324—612no—
462#324—612no—
463#324C2×D6112yes—
464#323—612no—
465#323—612no—
466#323—612no—
467#323C2×D6112yes—
468C61#1738311yescharacteristic, complemented, Sylow
469C22×Q8—611no—
470C22×D4—611no—
471C22×D4—611no—
472C22×D4—611no—
473C23×C4—611no—
474C23×C4—611no—
475C23×C4—611no—
476C23×C4—611no—
477C23×C4—611no—
478C2×M16—1222no—
479C22×C8—1222no—
480#126—21no—
481#126—21no—
482#126—21no—
483#126—21no—
484#126—1221no—
485#126—1221no—
486#126—1221no—
487#126—1221no—
488#125—1221no—
489#125—1221no—
490#125—1221no—
491#125—1221no—
492#124—1221no—
493#124—1221no—
494#124—1221no—
495#124—1221no—
496#123—1221no—
497#123—1221no—
498#123—1221no—
499#123—1221no—
500#123—1221no—
501#123—1221no—
502#123—1221no—
503#123—1221no—
504C22⋊Q8—1221no—
505C22⋊Q8—1221no—
506C22⋊Q8—1221no—
507C22⋊Q8—1221no—
508#121—1221no—
509#121—1221no—
510#121—1221no—
511#121—1221no—
512C4×Q8—1221no—
513C4×Q8—1221no—
514C4×Q8—1221no—
515C4×Q8—1221no—
516C4×D4—1221no—
517C4×D4—1221no—
518C4×D4—1221no—
519C4×D4—1221no—
520C4×D4—1221no—
521C4×D4—1221no—
522C4×D4—1221no—
523C4×D4—1221no—
524C4×D4—1221no—
525C4×D4—1221no—
526C4×D4—1221no—
527C4×D4—1221no—
528#117—1221no—
529#117—1221no—
530#117—1221no—
531#117—1221no—
532#117—1221no—
533#117—1221no—
534#117—1221no—
535#117—1221no—
536C2×C4⋊C4—611no—
537C2×C4⋊C4—611no—
538C2×C4⋊C4—611no—
539C2×C4⋊C4—611no—
540C2×C4⋊C4—611no—
541C2×C4⋊C4—611no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4C4×D6111yescharacteristic
544C2×C4⋊C4C4×D6111yescharacteristic
545C2×C4⋊C4C22×D6111yescharacteristic
546C2×C22⋊C4—611no—
547C2×C22⋊C4—611no—
548C2×C22⋊C4—611no—
549C2×C22⋊C4—611no—
550C2×C22⋊C4—611no—
551C2×C22⋊C4—611no—
552C2×C22⋊C4—611no—
553C2×C22⋊C4C4×D6111yescharacteristic
554C2×C22⋊C4C4×D6111yescharacteristic
555C2×C22⋊C4C22×D6111yescharacteristic
556C2×C42—611no—
557C2×C42—611no—
558C2×C42—611no—
559C2×C42—611no—
560C2×C42—611no—
561C2×C42—611no—
562C2×C42—611no—
563C2×C42—611no—
564C2×C42—611no—
565C2×C42—611no—
566C2×C42—611no—
567C2×C42—611no—
568C2×C42—611no—
569C2×C42C22×D6111yescharacteristic
570C4⋊C8—21no—
571C4⋊C8—21no—
572C4⋊C8—1222no—
573C4⋊C8—1222no—
574C4⋊C8—1221no—
575C4⋊C8—1221no—
576C22⋊C8—612no—
577C22⋊C8—612no—
578C22⋊C8—1222no—
579C22⋊C8—1222no—
580C22⋊C8C22×D6112yes—
581C22⋊C8C22×D6112yes—
582#97—21no—
583#97—1221no—
584C4×C8—21no—
585C4×C8—1222no—
586C4×C8—1222no—
587C4×C8—1221no—
588C24—611no—
589C24—611no—
590C24C2×C4×D6111yescharacteristic
591C2×Q8—1221no—
592C2×Q8—1221no—
593C2×Q8—1224no—
594C2×D4—1221no—
595C2×D4—1221no—
596C2×D4—1221no—
597C2×D4—1221no—
598C2×D4—1224no—
599C2×D4—1221no—
600C2×D4—1221no—
601C2×D4—2442no—
602C2×D4—2442no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—611no—
616C22×C4—611no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—1224no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—2442no—
627C22×C4—2442no—
628C22×C4—2442no—
629C22×C4—2442no—
630C22×C4C2×C4×D6111yescharacteristic
631C22×C4C2×C4×D6111yescharacteristic
632C22×C4C2×C4×D6111yescharacteristic
633C22×C4C2×C4×D6111yescharacteristic
634C22×C4C2×C4×D6111yescharacteristic
635C22×C4C23×D6111yescharacteristic
636M16—2444no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—1222no—
640C2×C8—1222no—
641C2×C8—2444no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—1221no—
649C4⋊C4—1221no—
650C4⋊C4—1221no—
651C4⋊C4—1221no—
652C4⋊C4—1221no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1221no—
656C4⋊C4—1221no—
657C4⋊C4—1221no—
658C4⋊C4—1221no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—1221no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—1221no—
669C22⋊C4—1221no—
670C22⋊C4—1221no—
671C22⋊C4—1221no—
672C22⋊C4—1221no—
673C22⋊C4—1221no—
674C22⋊C4—1221no—
675C22⋊C4—1221no—
676C22⋊C4—1221no—
677C22⋊C4—1221no—
678C22⋊C4—1221no—
679C22⋊C4—1221no—
680C22⋊C4—1221no—
681C22⋊C4—1221no—
682C42—611no—
683C42—611no—
684C42—611no—
685C42—611no—
686C42—611no—
687C42—611no—
688C42—611no—
689C42—611no—
690C42—611no—
691C42—611no—
692C42—611no—
693C42—611no—
694C42—1221no—
695C42—1221no—
696C42—1221no—
697C42—1221no—
698C42D4×D6111yescharacteristic
699C42D4×D6111yescharacteristic
700C42D4×D6111yescharacteristic
701C42D4×D6111yescharacteristic
702C23—21no—
703C23—22no—
704C23—41no—
705C23—41no—
706C23—611no—
707C23—611no—
708C23—1222no—
709C23—1222no—
710C23—1222no—
711C23—1221no—
712C23—2441no—
713C23—2441no—
714C23—2441no—
715C23C22×C4×D6111yescharacteristic
716Q8—2442no—
717Q8—2442no—
718D4—2442no—
719D4—2442no—
720D4—2442no—
721D4—2442no—
722D4—2442no—
723D4—2442no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—611no—
734C2×C4—611no—
735C2×C4—611no—
736C2×C4—614no—
737C2×C4—611no—
738C2×C4—611no—
739C2×C4—611no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1221no—
750C2×C4—1221no—
751C2×C4—1221no—
752C2×C4—1222no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2441no—
761C2×C4—2442no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4C22⋊C4×D6111yescharacteristic
765C2×C4C22⋊C4×D6111yescharacteristic
766C2×C4C22⋊C4×D6111yescharacteristic
767C2×C4C22⋊C4×D6111yescharacteristic
768C2×C4C2×D4×D6111yescharacteristic
769C2×C4C2×D4×D6111yescharacteristic
770C8—42no—
771C8—42no—
772C8—2442no—
773C8—2442no—
774C22—21no—
775C22—21no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—82no—
780C22—612no—
781C22—1221no—
782C22—1221no—
783C22—1221no—
784C22—1221no—
785C22—1221no—
786C22—4882no—
787C22—2444no—
788C22—2441no—
789C22—2441no—
790C22—2441no—
791C22C2×C22⋊C4×D6111yescharacteristic
792C22#131×D6112yes—
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—612no—
803C4—612no—
804C4—612no—
805C4—1221no—
806C4—1221no—
807C4—1221no—
808C4—2441no—
809C4—2441no—
810C4—2441no—
811C2—22no—
812C2—81no—
813C2—1222no—
814C2—4881no—
815C2—2441no—
816C2#408×D6111yescharacteristic
817C2#410×D6111yescharacteristic
818C2#413×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1473C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519750C4
cosocleC22×C4×C61C24
hypercenter#1473D61
hypocenterC61#17383
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1473

Complements

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

NH ≅ G/Ntype
2. #21454449C2semidirect
3. #431×D61C2semidirect
4. #21444189C2semidirect
5. #21444188C2semidirect
6. #21444186C2semidirect
7. #21444166C2semidirect
8. #21444164C2semidirect
9. #21444141C2semidirect
10. #21444138C2semidirect
11. C61×#1473C2semidirect
408. #1473D61semidirect
468. C61#17383semidirect

Maximal subgroups

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

subgroupindex
C2×#168402952
#214544492
#431×D612
#214441892
#214441882
#214441862
#214441662
#214441642
#214441412
#214441382
C61×#14732
#1738361