Finite Group Databasebeta

← #29647291

Subgroups — #29647291

Order 15616.

1438 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840275C211yesmaximal, characteristic
2#407×D61C211yesmaximal, characteristic, complemented
3#21448199C211yesmaximal, characteristic, complemented
4#21444361C214yesmaximal, complemented
5#21444352C211yesmaximal, characteristic, complemented
6#21444349C211yesmaximal, characteristic, complemented
7#21444347C211yesmaximal, characteristic, complemented
8#21444309C214yesmaximal, complemented
9C61×#1511C211yesmaximal, characteristic, complemented
10C22×#11758226C411yescharacteristic, complemented
11C23×C4×D61C2211yescharacteristic
12C2×M16×D61—21no—
13#16840275—21no—
14#16840275—21no—
15#16840275—21no—
16#16840275—21no—
17#16840275C412yescomplemented
18#16840275C412yescomplemented
19#16840275C2212yes—
20#16840275C2212yes—
21C2×#14519762—21no—
22C2×#14519753C411yescharacteristic, complemented
23C2×#14519752C411yescharacteristic, complemented
24C2×#14519751C2211yescharacteristic
25C2×#14519747—21no—
26C2×#14519739—21no—
27C2×#14519737—21no—
28C2×#14519735C411yescharacteristic, complemented
29C2×#14519733—21no—
30#16839726C2211yescharacteristic
31#16839725—21no—
32#16839724—21no—
33#16839724C2212yescomplemented
34C22⋊C8×D61—21no—
35C22⋊C8×D61C2212yescomplemented
36#16839625C2211yescharacteristic
37#16839621—21no—
38#16839621C2212yescomplemented
39#16839617—21no—
40#16839609—21no—
41#16839609C2212yescomplemented
42#16839499C2214yescomplemented
43#16839497C2214yescomplemented
44#16839495C2214yescomplemented
45C2×C22⋊Q8×C61C2211yescharacteristic
46C61×#407C2211yescharacteristic
47C61×#381C2211yescharacteristic
48C61×#328C2214yescomplemented
49C24×D61D411yescharacteristic
50C2×#11758226—21no—
51C2×#11758226—21no—
52C2×#11758226—44no—
53C2×#11758226C2×C412yes—
54C2×#11758226C2×C412yes—
55C22×D244—21no—
56C22×D244—21no—
57C22×D244C2×C411yescharacteristic
58C22×C22⋊D61—21no—
59C23×Dic61D411yescharacteristic
60C22×C4×D61—21no—
61C22×C4×D61—44no—
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C22×C4×D61C2311yescharacteristic
74C2×#11758194—21no—
75C2×#11758189—22no—
76M16×D61—44no—
77C2×C8×D61—22no—
78#14519762—22no—
79#14519762—22no—
80#14519762—22no—
81#14519762—22no—
82#14519753—21no—
83#14519753—21no—
84#14519753C2×C412yes—
85#14519753C2×C412yes—
86#14519752—21no—
87#14519752—21no—
88#14519752C2×C412yes—
89#14519752C2×C412yes—
90#14519751—21no—
91#14519751—21no—
92#14519751C2×C412yes—
93#14519751C2312yes—
94#14519747—22no—
95#14519747—22no—
96#14519747—22no—
97#14519747—22no—
98#14519739—22no—
99#14519739—22no—
100#14519739—22no—
101#14519739—22no—
102#14519737—22no—
103#14519737—22no—
104#14519737—22no—
105#14519737—22no—
106#14519735—21no—
107#14519735—21no—
108#14519735C2×C412yes—
109#14519735C2×C412yes—
110#14519733—44no—
111C2×C4⋊Dic61C2×C411yescharacteristic
112C2×#11758196—21no—
113C2×#11758196—22no—
114C2×C22⋊Dic61—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—22no—
120C2×#11758198—22no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61—22no—
123C22⋊#92418—21no—
124C22⋊#92418C2312yes—
125#14519689—22no—
126#14519689—22no—
127#14519684—21no—
128#14519684C2312yes—
129C22×Q8×C61C2×C411yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C2×M16×C61—21no—
132C22⋊Q8×C61—21no—
133C22⋊Q8×C61—21no—
134C22⋊Q8×C61C2×C412yes—
135C22⋊Q8×C61C2312yes—
136C2×C4⋊C4×C61—21no—
137C2×C4⋊C4×C61C2×C411yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C22⋊C8×C61—21no—
141C22⋊C8×C61C2312yes—
142#95×C61—21no—
143#95×C61C2312yes—
144C24×C61C2×D411yescharacteristic
145C23×D61—21no—
146C23×D61—42no—
147C23×D61—42no—
148C23×D61—42no—
149C23×D61C22⋊C411yescharacteristic
150C23×D61C22⋊C411yescharacteristic
151C23×D61C22⋊C411yescharacteristic
152C23×D61C22⋊C411yescharacteristic
153C23×D61C2×D411yescharacteristic
154C23×D61C2×D411yescharacteristic
155C2×Q8×C61—21no—
156C2×Q8×C61—42no—
157C2×Q8×C61C22×C412yes—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—22no—
161C22×C4×C61—42no—
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2411yescharacteristic
168C2×C22⋊D61—22no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—44no—
171C22×Dic61—24no—
172C22×Dic61—21no—
173C22×Dic61—22no—
174C22×Dic61C22⋊C411yescharacteristic
175C22×Dic61C22⋊C411yescharacteristic
176C22×Dic61C22⋊C411yescharacteristic
177C22×Dic61C22⋊C411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180#11758226—44no—
181#11758226—44no—
182#11758226—44no—
183#11758226—44no—
184C2×D244—22no—
185C2×D244—22no—
186C2×D244—22no—
187C2×D244—22no—
188C2×D244—21no—
189C2×D244—42no—
190C2×D244—44no—
191C2×D244—44no—
192C2×D244C22×C412yes—
193C2×C4×D61—24no—
194C2×C4×D61—24no—
195C2×C4×D61—22no—
196C2×C4×D61—22no—
197C2×C4×D61—42no—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×C4×D61—42no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61—44no—
208C2×C4×D61C22⋊C411yescharacteristic
209C2×C4×D61C22⋊C411yescharacteristic
210C2×C4×D61C22⋊C411yescharacteristic
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×D61C22×C411yescharacteristic
220C2×C4×D61C2×D411yescharacteristic
221C2×C4×D61C2×D411yescharacteristic
222C2×C4×D61C2×D411yescharacteristic
223C2×C4×D61C2×D411yescharacteristic
224M16×C61—42no—
225C2×C8×C61—22no—
226C4⋊C4×C61—22no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—22no—
229C4⋊C4×C61C22×C412yes—
230C22⋊C4×C61—22no—
231C22⋊C4×C61—22no—
232C22⋊C4×C61—42no—
233C22⋊Dic61—42no—
234#11758198—22no—
235#11758198—22no—
236#11758198—22no—
237#11758198—22no—
238#11758198—22no—
239#11758198—22no—
240#11758198—22no—
241#11758198—22no—
242#11758198—44no—
243#11758198—44no—
244C4⋊Dic61—21no—
245C4⋊Dic61C22×C412yes—
246#11758196—22no—
247#11758196—22no—
248#11758196—44no—
249C4×Dic61—22no—
250C4×Dic61—22no—
251C4×Dic61—44no—
252#11758194—42no—
253C2×#92418—22no—
254#11758189—44no—
255C8×D61—44no—
256C23×C61—22no—
257C23×C61—22no—
258C23×C61—41no—
259C23×C61C2×C22⋊C411yescharacteristic
260C23×C61C2×C22⋊C411yescharacteristic
261C23×C61C22×D411yescharacteristic
262C22×D61—22no—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—22no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—41no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—416no—
282C22×D61—42no—
283C22×D61—42no—
284C22×D61—42no—
285C22×D61C2×C22⋊C411yescharacteristic
286C22×D61C2×C22⋊C411yescharacteristic
287C22×D61C2×C22⋊C411yescharacteristic
288C22×D61C2×C22⋊C411yescharacteristic
289Q8×C61—42no—
290Q8×C61—42no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61C2×C22⋊C411yescharacteristic
305C2×C4×C61C2×C22⋊C411yescharacteristic
306C2×C4×C61C23×C411yescharacteristic
307C2×C4×C61C22×D411yescharacteristic
308C22⋊D61—44no—
309C22⋊D61—44no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—42no—
320C2×Dic61#9914yes—
321C2×Dic61C2×C22⋊C411yescharacteristic
322C2×Dic61C2×C22⋊C411yescharacteristic
323C2×Dic61C2×C22⋊C411yescharacteristic
324C2×Dic61C2×C22⋊C411yescharacteristic
325D244—42no—
326D244—42no—
327D244—44no—
328D244—44no—
329D244—44no—
330D244—44no—
331C4×D61—22no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—22no—
337C4×D61—22no—
338C4×D61—22no—
339C4×D61—41no—
340C4×D61—41no—
341C4×D61—41no—
342C4×D61—41no—
343C4×D61—41no—
344C4×D61—41no—
345C4×D61—41no—
346C4×D61—41no—
347C4×D61—44no—
348C4×D61—44no—
349C8×C61—42no—
350#92418—42no—
351#17559—611nomaximal, Sylow
352C22×C61—21no—
353C22×C61—21no—
354C22×C61—21no—
355C22×C61—21no—
356C22×C61—21no—
357C22×C61—21no—
358C22×C61—21no—
359C22×C61—44no—
360C22×C61C2×#9912yes—
361C22×C61C22×C22⋊C411yescharacteristic
362C22×C61#57512yes—
363C2×D61—21no—
364C2×D61—21no—
365C2×D61—21no—
366C2×D61—21no—
367C2×D61—21no—
368C2×D61—21no—
369C2×D61—21no—
370C2×D61—21no—
371C2×D61—21no—
372C2×D61—21no—
373C2×D61—21no—
374C2×D61—44no—
375C2×D61—44no—
376C2×D61—44no—
377C2×D61—44no—
378C2×D61—44no—
379C2×D61—44no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—84no—
384C2×D61#42112yes—
385C4×C61—21no—
386C4×C61—21no—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—42no—
390C4×C61—42no—
391C4×C61—82no—
392Dic61—21no—
393Dic61—21no—
394Dic61—42no—
395Dic61—82no—
396Dic61C2×#9912yes—
397Dic61C2×#9912yes—
398C2×#525—611no—
399C2×#407—611no—
400#2280—611no—
401#1513—614no—
402#1511—611no—
403#1511D6111yescharacteristic, complemented
404#1510—611no—
405#1510—611no—
406#1501—614no—
407C2×C61—22no—
408C2×C61—22no—
409C2×C61—41no—
410C2×C61C22×#9911yescharacteristic
411C2×C61#289611yescharacteristic
412C2×C61C2×#42111yescharacteristic
413D61—22no—
414D61—41no—
415D61—41no—
416D61—41no—
417D61—82no—
418C22×#41—611no—
419C24×C4—611no—
420C22×M16—1221no—
421#525—612no—
422#525—612no—
423#525—612no—
424#525—612no—
425#525—1221no—
426#525—1221no—
427#525—1221no—
428#525—1221no—
429C2×#123—1221no—
430C2×C22⋊Q8—611no—
431C2×C22⋊Q8C2×D6111yescharacteristic
432C2×#121—611no—
433C2×#121—611no—
434C2×#120—1221no—
435C2×C4×D4—1221no—
436C2×C4×D4—1221no—
437C2×#117—611no—
438C2×#117—1221no—
439#407—611no—
440#407—612no—
441#407—1221no—
442#407—1221no—
443#407C2×D6111yescharacteristic
444C2×C22⋊C8—612no—
445C2×C22⋊C8—1221no—
446#381—611no—
447#381C2×D6111yescharacteristic
448#380—612no—
449#380—1221no—
450#379—1221no—
451C4×C22⋊C4—612no—
452C4×C22⋊C4—1221no—
453#328—614no—
454#328C2×D6114yescomplemented
455#327—614no—
456#327—614no—
457C61#1755911yescharacteristic, complemented, Sylow
458C25—611no—
459C2×#41—612no—
460C2×#41—612no—
461C2×#41—1221no—
462C2×#41—1221no—
463C2×#41—2444no—
464C22×Q8C4×D6111yescharacteristic
465C22×D4—611no—
466C22×D4—1221no—
467C22×D4—1221no—
468C22×D4—1221no—
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—611no—
473C23×C4—611no—
474C23×C4—611no—
475C23×C4—611no—
476C23×C4—611no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—1221no—
483C23×C4—2444no—
484C23×C4C22×D6111yescharacteristic
485C2×M16—21no—
486C2×M16—1222no—
487C2×M16—1221no—
488C2×M16—2444no—
489C22×C8—1222no—
490#123—1222no—
491#123—1222no—
492#123—1222no—
493#123—1222no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—612no—
497C22⋊Q8—612no—
498C22⋊Q8—1221no—
499C22⋊Q8—1221no—
500C22⋊Q8C4×D6112yes—
501C22⋊Q8C22×D6112yes—
502#121—612no—
503#121—612no—
504#121—612no—
505#121—612no—
506#121—1221no—
507#121—1221no—
508#121—1221no—
509#121—1221no—
510#120—1222no—
511#120—1222no—
512#120—1222no—
513#120—1222no—
514C4×D4—1222no—
515C4×D4—1222no—
516C4×D4—1222no—
517C4×D4—1222no—
518C4×D4—1222no—
519C4×D4—1222no—
520C4×D4—1222no—
521C4×D4—1222no—
522#117—612no—
523#117—612no—
524#117—1221no—
525#117—1221no—
526#117—2444no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1222no—
531C2×C4⋊C4C4×D6111yescharacteristic
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—1221no—
535C2×C22⋊C4—1221no—
536C2×C22⋊C4—1221no—
537C2×C22⋊C4—1221no—
538C2×C22⋊C4—1222no—
539C2×C22⋊C4—1222no—
540C2×C22⋊C4—1221no—
541C2×C42—1221no—
542C2×C42—1222no—
543C22⋊C8—21no—
544C22⋊C8—612no—
545C22⋊C8—1222no—
546C22⋊C8—1222no—
547C22⋊C8—1221no—
548C22⋊C8C22×D6112yes—
549#95—21no—
550#95—612no—
551#95—1221no—
552#95C22×D6112yes—
553C24—611no—
554C24—611no—
555C24—611no—
556C24—611no—
557C24—611no—
558C24—611no—
559C24—1221no—
560C24—2442no—
561C24—2442no—
562C24—2442no—
563C24D4×D6111yescharacteristic
564#41—2444no—
565#41—2444no—
566#41—2444no—
567#41—2444no—
568C2×Q8—21no—
569C2×Q8—42no—
570C2×Q8C2×C4×D6112yes—
571C2×D4—612no—
572C2×D4—1222no—
573C2×D4—1222no—
574C2×D4—1222no—
575C2×D4—1222no—
576C2×D4—1222no—
577C2×D4—1222no—
578C2×D4—1221no—
579C2×D4—2442no—
580C2×D4—2444no—
581C2×D4—2444no—
582C2×D4—2444no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—42no—
587C22×C4—611no—
588C22×C4—611no—
589C22×C4—611no—
590C22×C4—611no—
591C22×C4—611no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—1224no—
610C22×C4—1224no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1224no—
614C22×C4—1221no—
615C22×C4—1222no—
616C22×C4—2442no—
617C22×C4—2442no—
618C22×C4—2444no—
619C22×C4—2442no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4—2442no—
623C22×C4—2442no—
624C22×C4—2442no—
625C22×C4—2442no—
626C22×C4—2442no—
627C22×C4C2×C4×D6111yescharacteristic
628C22×C4C2×C4×D6111yescharacteristic
629C22×C4D4×D6111yescharacteristic
630C22×C4D4×D6111yescharacteristic
631C22×C4D4×D6111yescharacteristic
632C22×C4C23×D6111yescharacteristic
633M16—42no—
634M16—2444no—
635M16—2442no—
636C2×C8—22no—
637C2×C8—1222no—
638C2×C8—2444no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—21no—
642C4⋊C4—612no—
643C4⋊C4—1222no—
644C4⋊C4—1222no—
645C4⋊C4—1221no—
646C4⋊C4—2444no—
647C4⋊C4C2×C4×D6112yes—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—42no—
651C22⋊C4—1222no—
652C22⋊C4—1222no—
653C22⋊C4—1222no—
654C22⋊C4—1222no—
655C22⋊C4—1222no—
656C22⋊C4—1222no—
657C22⋊C4—1222no—
658C22⋊C4—1222no—
659C22⋊C4—2444no—
660C22⋊C4—2444no—
661C22⋊C4—2442no—
662C42—1222no—
663C42—1222no—
664C42—2444no—
665C23—22no—
666C23—22no—
667C23—41no—
668C23—611no—
669C23—611no—
670C23—611no—
671C23—611no—
672C23—1222no—
673C23—1222no—
674C23—1222no—
675C23—1222no—
676C23—1222no—
677C23—1222no—
678C23—1222no—
679C23—1222no—
680C23—2441no—
681C23—2441no—
682C23—2441no—
683C23—2441no—
684C23—2441no—
685C23—2441no—
686C23—2441no—
687C23—2441no—
688C23—2441no—
689C23—2441no—
690C23—2441no—
691C23—2442no—
692C23—2442no—
693C23—24416no—
694C23—2442no—
695C23C22⋊C4×D6111yescharacteristic
696C23C22⋊C4×D6111yescharacteristic
697C23C2×D4×D6111yescharacteristic
698Q8—42no—
699Q8—42no—
700D4—2442no—
701D4—2442no—
702D4—2444no—
703D4—2444no—
704D4—2444no—
705D4—2444no—
706D4—2444no—
707D4—2444no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—611no—
722C2×C4—611no—
723C2×C4—614no—
724C2×C4—611no—
725C2×C4—611no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2444no—
749C2×C4—2444no—
750C2×C4—2442no—
751C2×C4—2442no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4C22⋊C4×D6111yescharacteristic
755C2×C4C22⋊C4×D6111yescharacteristic
756C2×C4C22×C4×D6111yescharacteristic
757C2×C4C2×D4×D6111yescharacteristic
758C8—42no—
759C8—2442no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—44no—
768C22—612no—
769C22—1221no—
770C22—1221no—
771C22—1221no—
772C22—1221no—
773C22—1221no—
774C22—1221no—
775C22—1221no—
776C22—1221no—
777C22—1221no—
778C22—1221no—
779C22—1221no—
780C22—4884no—
781C22—2444no—
782C22—2444no—
783C22—2444no—
784C22—2444no—
785C22—2444no—
786C22—2444no—
787C22—2442no—
788C22—2442no—
789C22—2442no—
790C22#99×D6112yes—
791C22C2×C22⋊C4×D6111yescharacteristic
792C22#1684056112yes—
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—42no—
798C4—42no—
799C4—82no—
800C4—612no—
801C4—612no—
802C4—1221no—
803C4—1221no—
804C4—4882no—
805C4—2442no—
806C2—22no—
807C2—22no—
808C2—41no—
809C2—1222no—
810C2—4882no—
811C2—2441no—
812C2—2441no—
813C2—2441no—
814C2C2×#99×D6111yescharacteristic
815C2#2145433711yescharacteristic
816C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1511C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840275C2
cosocleC22×C4×C61C24
hypercenter#1511D61
hypocenterC61#17559
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1511

Complements

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

NH ≅ G/Ntype
2. #407×D61C2semidirect
3. #21448199C2semidirect
4. #21444361C2semidirect
5. #21444352C2semidirect
6. #21444349C2semidirect
7. #21444347C2semidirect
8. #21444309C2semidirect
9. C61×#1511C2semidirect
10. C22×#11758226C4semidirect
17. #16840275C4semidirect
18. #16840275C4semidirect
22. C2×#14519753C4semidirect
23. C2×#14519752C4semidirect
28. C2×#14519735C4semidirect
33. #16839724C22semidirect
35. C22⋊C8×D61C22semidirect
38. #16839621C22semidirect
41. #16839609C22semidirect
42. #16839499C22semidirect
43. #16839497C22semidirect
44. #16839495C22semidirect
48. C61×#328C22semidirect
403. #1511D61semidirect
454. #328C2×D61semidirect
457. C61#17559semidirect

Maximal subgroups

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

subgroupindex
C2×#168402752
#407×D612
#214481992
#214443612
#214443522
#214443492
#214443472
#214443092
C61×#15112
#1755961