Finite Group Databasebeta

← #29647370

Subgroups — #29647370

Order 15616.

1470 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840275C211yesmaximal, characteristic
2C2×C22⋊C8×D61C211yesmaximal, characteristic, complemented
3#21448201C211yesmaximal, characteristic, complemented
4#21444391C211yesmaximal, characteristic, complemented
5#21444388C211yesmaximal, characteristic, complemented
6#21444386C211yesmaximal, characteristic, complemented
7#21444374C214yesmaximal, complemented
8#21444309C214yesmaximal, complemented
9C61×#1520C211yesmaximal, characteristic, complemented
10C22×#11758226C411yescharacteristic, complemented
11C23×C4×D61C2211yescharacteristic
12C22×C8×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×#14519735—21no—
29C2×#14519735C411yescharacteristic, complemented
30C2×C22⋊#92418C2211yescharacteristic
31C2×#14519689—21no—
32C22⋊C8×D61—21no—
33C22⋊C8×D61—21no—
34C22⋊C8×D61C2212yescomplemented
35C22⋊C8×D61C2212yescomplemented
36#16839624C2212yescomplemented
37#16839622C2211yescharacteristic
38#16839619—21no—
39#16839617—21no—
40C22⋊C4×Dic61—21no—
41#16839609C2212yescomplemented
42#16839499C2214yescomplemented
43#16839497C2214yescomplemented
44#16839495C2214yescomplemented
45C2×C22⋊Q8×C61C2211yescharacteristic
46C2×C22⋊C8×C61C2211yescharacteristic
47C61×#380C2211yescharacteristic
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
74C22×#92418—21no—
75C2×C8×D61—22no—
76C2×C8×D61—22no—
77C2×C8×D61—44no—
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#14519735—44no—
109#14519735C2×C412yes—
110#14519735C2×C412yes—
111C2×C4⋊Dic61—21no—
112C2×C4⋊Dic61C2×C411yescharacteristic
113C2×#11758196—21no—
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—22no—
128#14519684C2312yes—
129C22×Q8×C61C2×C411yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C22×C8×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×C61—21no—
138C2×C4⋊C4×C61C2×C411yescharacteristic
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C22⋊C8×C61—21no—
142C22⋊C8×C61C2312yes—
143#95×C61C2312yes—
144C24×C61C2×D411yescharacteristic
145C23×D61—22no—
146C23×D61—22no—
147C23×D61—21no—
148C23×D61—42no—
149C23×D61—42no—
150C23×D61C22⋊C411yescharacteristic
151C23×D61C22⋊C411yescharacteristic
152C23×D61C22⋊C411yescharacteristic
153C23×D61C22⋊C411yescharacteristic
154C23×D61C2×D411yescharacteristic
155C23×D61C2×D411yescharacteristic
156C2×Q8×C61—21no—
157C2×Q8×C61—42no—
158C2×Q8×C61C22×C412yes—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—22no—
162C22×C4×C61—42no—
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2411yescharacteristic
169C2×C22⋊D61—22no—
170C2×C22⋊D61—22no—
171C2×C22⋊D61—42no—
172C2×C22⋊D61—42no—
173C22×Dic61—21no—
174C22×Dic61—22no—
175C22×Dic61—42no—
176C22×Dic61C22⋊C411yescharacteristic
177C22×Dic61C22⋊C411yescharacteristic
178C22×Dic61C22⋊C411yescharacteristic
179C22×Dic61C22⋊C411yescharacteristic
180C22×Dic61C2×D411yescharacteristic
181C22×Dic61C2×D411yescharacteristic
182#11758226—44no—
183#11758226—44no—
184#11758226—44no—
185#11758226—44no—
186C2×D244—22no—
187C2×D244—22no—
188C2×D244—22no—
189C2×D244—22no—
190C2×D244—21no—
191C2×D244—44no—
192C2×D244—44no—
193C2×D244—42no—
194C2×D244C22×C412yes—
195C2×C4×D61—24no—
196C2×C4×D61—24no—
197C2×C4×D61—24no—
198C2×C4×D61—22no—
199C2×C4×D61—22no—
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—42no—
208C2×C4×D61—42no—
209C2×C4×D61—44no—
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×D61C22×C411yescharacteristic
221C2×C4×D61C22×C411yescharacteristic
222C2×C4×D61C2×D411yescharacteristic
223C2×C4×D61C2×D411yescharacteristic
224C2×C4×D61C2×D411yescharacteristic
225C2×C4×D61C2×D411yescharacteristic
226C2×C8×C61—22no—
227C2×C8×C61—42no—
228C4⋊C4×C61—22no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—22no—
231C4⋊C4×C61—42no—
232C4⋊C4×C61C22×C412yes—
233C22⋊C4×C61—22no—
234C22⋊C4×C61—22no—
235C22⋊C4×C61—42no—
236C22⋊Dic61—42no—
237#11758198—22no—
238#11758198—22no—
239#11758198—22no—
240#11758198—22no—
241#11758198—22no—
242#11758198—22no—
243#11758198—22no—
244#11758198—22no—
245#11758198—44no—
246#11758198—44no—
247C4⋊Dic61—21no—
248C4⋊Dic61—42no—
249C4⋊Dic61C22×C412yes—
250#11758196—22no—
251#11758196—22no—
252C4×Dic61—22no—
253C4×Dic61—22no—
254C4×Dic61—44no—
255C2×#92418—22no—
256C2×#92418—42no—
257C8×D61—44no—
258C8×D61—44no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61C2×C22⋊C411yescharacteristic
262C23×C61C2×C22⋊C411yescharacteristic
263C23×C61#13512yes—
264C23×C61#13512yes—
265C23×C61C22×D411yescharacteristic
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—22no—
274C22×D61—22no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—41no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—48no—
288C22×D61—48no—
289C22×D61—42no—
290C22×D61—42no—
291C22×D61—42no—
292C22×D61C2×C22⋊C411yescharacteristic
293C22×D61C2×C22⋊C411yescharacteristic
294C22×D61C2×C22⋊C411yescharacteristic
295C22×D61C2×C22⋊C411yescharacteristic
296Q8×C61—42no—
297Q8×C61—42no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61C2×C22⋊C411yescharacteristic
312C2×C4×C61C2×C22⋊C411yescharacteristic
313C2×C4×C61C23×C411yescharacteristic
314C2×C4×C61C22×D411yescharacteristic
315C22⋊D61—42no—
316C22⋊D61—42no—
317C22⋊D61—44no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61C2×C22⋊C411yescharacteristic
330C2×Dic61C2×C22⋊C411yescharacteristic
331C2×Dic61C2×C22⋊C411yescharacteristic
332C2×Dic61C2×C22⋊C411yescharacteristic
333D244—42no—
334D244—44no—
335D244—44no—
336D244—44no—
337D244—44no—
338D244—42no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—22no—
347C4×D61—22no—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61—41no—
351C4×D61—41no—
352C4×D61—41no—
353C4×D61—41no—
354C4×D61—44no—
355C4×D61—44no—
356C4×D61#9914yes—
357C8×C61—42no—
358#92418—42no—
359#17572—611nomaximal, Sylow
360C22×C61—21no—
361C22×C61—21no—
362C22×C61—21no—
363C22×C61—21no—
364C22×C61—21no—
365C22×C61—21no—
366C22×C61—42no—
367C22×C61—42no—
368C22×C61#41612yes—
369C22×C61#41612yes—
370C22×C61C22×C22⋊C411yescharacteristic
371C22×C61C2×#13511yescharacteristic
372C22×C61C2×#13511yescharacteristic
373C2×D61—28no—
374C2×D61—21no—
375C2×D61—21no—
376C2×D61—21no—
377C2×D61—21no—
378C2×D61—21no—
379C2×D61—21no—
380C2×D61—21no—
381C2×D61—21no—
382C2×D61—21no—
383C2×D61—21no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—44no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—44no—
390C2×D61—44no—
391C2×D61—42no—
392C2×D61—42no—
393C2×D61—42no—
394C2×D61—84no—
395C2×D61C2×#9912yes—
396C2×D61#42112yes—
397C4×C61—21no—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—42no—
401C4×C61—42no—
402C4×C61—82no—
403C4×C61C2×#9912yes—
404Dic61—21no—
405Dic61—21no—
406Dic61—21no—
407Dic61—42no—
408Dic61—82no—
409Dic61C2×#9912yes—
410C2×#525—611no—
411C22×C22⋊C8—611no—
412#2280—611no—
413#1520—611no—
414#1520D6111yescharacteristic, complemented
415#1519—611no—
416#1519—611no—
417#1516—614no—
418#1501—614no—
419C2×C61—21no—
420C2×C61—21no—
421C2×C61—22no—
422C2×C61—22no—
423C2×C61C22×#9911yescharacteristic
424C2×C61C2×#41611yescharacteristic
425C2×C61C2×#42111yescharacteristic
426D61—22no—
427D61—22no—
428D61—41no—
429D61—41no—
430D61—82no—
431C22×#41—611no—
432C24×C4—611no—
433C23×C8—1221no—
434#525—612no—
435#525—612no—
436#525—612no—
437#525—612no—
438#525—1221no—
439#525—1221no—
440#525—1221no—
441#525—1221no—
442C2×#123—1221no—
443C2×C22⋊Q8—611no—
444C2×C22⋊Q8C2×D6111yescharacteristic
445C2×#121—611no—
446C2×#121—611no—
447C2×#120—1221no—
448C2×C4×D4—1221no—
449C2×C4×D4—1221no—
450C2×#117—611no—
451C2×#117—1221no—
452C2×C22⋊C8—611no—
453C2×C22⋊C8—612no—
454C2×C22⋊C8—612no—
455C2×C22⋊C8—1221no—
456C2×C22⋊C8—1221no—
457C2×C22⋊C8—1221no—
458C2×C22⋊C8C2×D6111yescharacteristic
459#381—612no—
460#380—611no—
461#380—1221no—
462#380C2×D6111yescharacteristic
463#379—1221no—
464C4×C22⋊C4—612no—
465C4×C22⋊C4—1221no—
466#328—614no—
467#328C2×D6114yescomplemented
468#327—614no—
469#327—614no—
470C61#1757211yescharacteristic, complemented, Sylow
471C25—611no—
472C2×#41—612no—
473C2×#41—612no—
474C2×#41—1221no—
475C2×#41—1221no—
476C2×#41—2444no—
477C22×Q8C4×D6111yescharacteristic
478C22×D4—611no—
479C22×D4—1221no—
480C22×D4—1221no—
481C22×D4—1221no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—611no—
493C23×C4—611no—
494C23×C4—611no—
495C23×C4—1221no—
496C23×C4—2444no—
497C23×C4C22×D6111yescharacteristic
498C22×C8—21no—
499C22×C8—1222no—
500C22×C8—1222no—
501C22×C8—1221no—
502C22×C8—2444no—
503#123—1222no—
504#123—1222no—
505#123—1222no—
506#123—1222no—
507C22⋊Q8—21no—
508C22⋊Q8—21no—
509C22⋊Q8—612no—
510C22⋊Q8—612no—
511C22⋊Q8—1221no—
512C22⋊Q8—1221no—
513C22⋊Q8C4×D6112yes—
514C22⋊Q8C22×D6112yes—
515#121—612no—
516#121—612no—
517#121—612no—
518#121—612no—
519#121—1221no—
520#121—1221no—
521#121—1221no—
522#121—1221no—
523#120—1222no—
524#120—1222no—
525#120—1222no—
526#120—1222no—
527C4×D4—1222no—
528C4×D4—1222no—
529C4×D4—1222no—
530C4×D4—1222no—
531C4×D4—1222no—
532C4×D4—1222no—
533C4×D4—1222no—
534C4×D4—1222no—
535#117—612no—
536#117—612no—
537#117—1221no—
538#117—1221no—
539#117—2444no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—611no—
543C2×C4⋊C4—1221no—
544C2×C4⋊C4—1221no—
545C2×C4⋊C4C4×D6111yescharacteristic
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—1221no—
549C2×C22⋊C4—1221no—
550C2×C22⋊C4—1221no—
551C2×C22⋊C4—1221no—
552C2×C22⋊C4—1222no—
553C2×C22⋊C4—1222no—
554C2×C22⋊C4—1221no—
555C2×C42—1221no—
556C2×C42—1222no—
557C22⋊C8—21no—
558C22⋊C8—612no—
559C22⋊C8—1222no—
560C22⋊C8—1222no—
561C22⋊C8—1221no—
562C22⋊C8C22×D6112yes—
563#95—612no—
564#95—1222no—
565#95C22×D6112yes—
566C24—611no—
567C24—611no—
568C24—611no—
569C24—611no—
570C24—611no—
571C24—611no—
572C24—1222no—
573C24—1222no—
574C24—1221no—
575C24—2442no—
576C24—2442no—
577C24D4×D6111yescharacteristic
578#41—2444no—
579#41—2444no—
580#41—2444no—
581#41—2444no—
582C2×Q8—21no—
583C2×Q8—42no—
584C2×Q8C2×C4×D6112yes—
585C2×D4—612no—
586C2×D4—1222no—
587C2×D4—1222no—
588C2×D4—1222no—
589C2×D4—1222no—
590C2×D4—1222no—
591C2×D4—1222no—
592C2×D4—1221no—
593C2×D4—2442no—
594C2×D4—2444no—
595C2×D4—2444no—
596C2×D4—2442no—
597C2×D4—2442no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—42no—
602C22×C4—611no—
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—611no—
622C22×C4—611no—
623C22×C4—611no—
624C22×C4—1224no—
625C22×C4—1224no—
626C22×C4—1224no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1221no—
630C22×C4—1222no—
631C22×C4—2442no—
632C22×C4—2442no—
633C22×C4—2442no—
634C22×C4—2442no—
635C22×C4—2442no—
636C22×C4—2442no—
637C22×C4—2442no—
638C22×C4—2442no—
639C22×C4—2442no—
640C22×C4—2444no—
641C22×C4—2442no—
642C22×C4C2×C4×D6111yescharacteristic
643C22×C4C2×C4×D6111yescharacteristic
644C22×C4D4×D6111yescharacteristic
645C22×C4D4×D6111yescharacteristic
646C22×C4D4×D6111yescharacteristic
647C22×C4C23×D6111yescharacteristic
648C2×C8—22no—
649C2×C8—42no—
650C2×C8—1222no—
651C2×C8—2444no—
652C2×C8—2444no—
653C2×C8—2442no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—42no—
658C4⋊C4—612no—
659C4⋊C4—1222no—
660C4⋊C4—1222no—
661C4⋊C4—1221no—
662C4⋊C4—2442no—
663C4⋊C4C2×C4×D6112yes—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—42no—
667C22⋊C4—1222no—
668C22⋊C4—1222no—
669C22⋊C4—1222no—
670C22⋊C4—1222no—
671C22⋊C4—1222no—
672C22⋊C4—1222no—
673C22⋊C4—1222no—
674C22⋊C4—1222no—
675C22⋊C4—2444no—
676C22⋊C4—2444no—
677C22⋊C4—2442no—
678C42—1222no—
679C42—1222no—
680C42—2444no—
681C23—41no—
682C23—41no—
683C23—611no—
684C23—611no—
685C23—611no—
686C23—611no—
687C23—1222no—
688C23—1222no—
689C23—1222no—
690C23—1222no—
691C23—1222no—
692C23—1222no—
693C23—1222no—
694C23—1222no—
695C23—1222no—
696C23—1222no—
697C23—1221no—
698C23—1221no—
699C23—1221no—
700C23—1221no—
701C23—1222no—
702C23—2441no—
703C23—2441no—
704C23—2441no—
705C23—2441no—
706C23—2441no—
707C23—2441no—
708C23—2442no—
709C23—2442no—
710C23—2448no—
711C23—2448no—
712C23—2442no—
713C23C22⋊C4×D6111yescharacteristic
714C23C22⋊C4×D6111yescharacteristic
715C23#1451979812yes—
716C23#1451980012yes—
717C23C2×D4×D6111yescharacteristic
718Q8—42no—
719Q8—42no—
720D4—2442no—
721D4—2444no—
722D4—2444no—
723D4—2444no—
724D4—2444no—
725D4—2444no—
726D4—2442no—
727D4—2442no—
728D4—2442no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—611no—
743C2×C4—614no—
744C2×C4—611no—
745C2×C4—611no—
746C2×C4—611no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2441no—
765C2×C4—2441no—
766C2×C4—2444no—
767C2×C4—2444no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2442no—
772C2×C4—2442no—
773C2×C4—2442no—
774C2×C4—2442no—
775C2×C4C22⋊C4×D6111yescharacteristic
776C2×C4C22⋊C4×D6111yescharacteristic
777C2×C4C22×C4×D6111yescharacteristic
778C2×C4C2×D4×D6111yescharacteristic
779C8—42no—
780C8—2442no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—42no—
788C22—42no—
789C22—612no—
790C22—612no—
791C22—1228no—
792C22—1221no—
793C22—1221no—
794C22—1221no—
795C22—1221no—
796C22—1221no—
797C22—1221no—
798C22—1221no—
799C22—1221no—
800C22—1221no—
801C22—1221no—
802C22—4884no—
803C22—2442no—
804C22—2442no—
805C22—2442no—
806C22—2442no—
807C22—2444no—
808C22—2444no—
809C22—2444no—
810C22—2442no—
811C22—2442no—
812C22—2442no—
813C22#1683975712yes—
814C22#1683975712yes—
815C22C2×C22⋊C4×D6111yescharacteristic
816C22C2×#1451979811yescharacteristic
817C22C2×#1451980011yescharacteristic
818C4—21no—
819C4—21no—
820C4—21no—
821C4—42no—
822C4—42no—
823C4—82no—
824C4—612no—
825C4—1221no—
826C4—1221no—
827C4—1221no—
828C4—4882no—
829C4—2442no—
830C4#99×D6112yes—
831C2—21no—
832C2—21no—
833C2—22no—
834C2—22no—
835C2—1222no—
836C2—1222no—
837C2—4882no—
838C2—2441no—
839C2—2441no—
840C2C2×#99×D6111yescharacteristic
841C2C2×#1683975711yescharacteristic
842C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1520C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840275C2
cosocleC22×C4×C61C24
hypercenter#1520D61
hypocenterC61#17572
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C8×D61C2semidirect
3. #21448201C2semidirect
4. #21444391C2semidirect
5. #21444388C2semidirect
6. #21444386C2semidirect
7. #21444374C2semidirect
8. #21444309C2semidirect
9. C61×#1520C2semidirect
10. C22×#11758226C4semidirect
17. #16840275C4semidirect
18. #16840275C4semidirect
22. C2×#14519753C4semidirect
23. C2×#14519752C4semidirect
29. C2×#14519735C4semidirect
34. C22⋊C8×D61C22semidirect
35. C22⋊C8×D61C22semidirect
36. #16839624C22semidirect
41. #16839609C22semidirect
42. #16839499C22semidirect
43. #16839497C22semidirect
44. #16839495C22semidirect
48. C61×#328C22semidirect
414. #1520D61semidirect
467. #328C2×D61semidirect
470. C61#17572semidirect

Maximal subgroups

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

subgroupindex
C2×#168402752
C2×C22⋊C8×D612
#214482012
#214443912
#214443882
#214443862
#214443742
#214443092
C61×#15202
#1757261