Finite Group Databasebeta

← #29646001

Subgroups — #29646001

Order 15616.

1446 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840272C211yesmaximal, characteristic
2#407×D61C211yesmaximal, characteristic, complemented
3C2×C22⋊C8×D61C211yesmaximal, characteristic, complemented
4#21444184C211yesmaximal, characteristic, complemented
5#21444182C211yesmaximal, characteristic, complemented
6#21444179C211yesmaximal, characteristic, complemented
7#21444164C214yesmaximal, complemented
8#21444134C214yesmaximal, complemented
9C61×#1471C211yesmaximal, characteristic, complemented
10C22×#11758224C411yescharacteristic
11C23×C4×D61C2211yescharacteristic
12C2×M16×D61—21no—
13C22×C8×D61—21no—
14#16840272—21no—
15#16840272—21no—
16#16840272—21no—
17#16840272—21no—
18#16840272—21no—
19#16840272—21no—
20#16840272—21no—
21#16840272—21no—
22C2×#14519759C2212yes—
23C2×#14519757C411yescharacteristic
24C2×#14519756C2211yescharacteristic
25C2×#14519748C411yescharacteristic
26C2×#14519745C412yes—
27C2×D4×Dic61C412yes—
28C2×#14519737C2212yes—
29C2×#14519735C411yescharacteristic
30#16839726C2211yescharacteristic
31#16839725—21no—
32#16839724—21no—
33#16839724C2212yes—
34C2×C22⋊#92418C2211yescharacteristic
35C2×#14519689—21no—
36C22⋊C8×D61—21no—
37C22⋊C8×D61—21no—
38C22⋊C8×D61—21no—
39C22⋊C8×D61C2212yes—
40C22⋊C8×D61C2212yes—
41C22⋊C8×D61C2212yes—
42#16839487C2214yescomplemented
43#16839487C2214yescomplemented
44#16839486C2214yescomplemented
45C2×#121×C61C2211yescharacteristic
46C61×#407C2211yescharacteristic
47C2×C22⋊C8×C61C2211yescharacteristic
48C61×#323C2214yescomplemented
49C24×D61C2×C411yescharacteristic
50C2×#11758224—21no—
51C2×#11758224—21no—
52C2×#11758224—21no—
53C2×#11758224—21no—
54C2×#11758224—44no—
55C22×Dic122C2×C411yescharacteristic
56C22×C22⋊D61C2×C412yes—
57C22×C22⋊D61C2×C412yes—
58C23×Dic61C2×C412yes—
59C23×Dic61C2×C411yescharacteristic
60C22×C4×D61—44no—
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61C2311yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C2×#11758194—21no—
74C2×#11758189—22no—
75M16×D61—44no—
76C22×#92418—21no—
77C2×C8×D61—22no—
78C2×C8×D61—22no—
79C2×C8×D61—22no—
80C2×C8×D61—44no—
81#14519759—22no—
82#14519759—22no—
83#14519759—22no—
84#14519759—22no—
85#14519757—21no—
86#14519757—21no—
87#14519757—21no—
88#14519757—21no—
89#14519756—21no—
90#14519756—21no—
91#14519756—21no—
92#14519756—21no—
93#14519748—21no—
94#14519748—21no—
95#14519748—21no—
96#14519748—21no—
97#14519745—22no—
98#14519745—22no—
99#14519745—22no—
100#14519745—22no—
101D4×Dic61—22no—
102D4×Dic61—22no—
103D4×Dic61—22no—
104D4×Dic61—22no—
105#14519737—22no—
106#14519737—22no—
107#14519737—22no—
108#14519737—22no—
109#14519735—21no—
110#14519735—21no—
111#14519735—21no—
112#14519735—21no—
113C2×C4⋊Dic61C2×C411yescharacteristic
114C2×C4⋊Dic61C2×C412yes—
115C2×#11758196C2312yes—
116C2×C22⋊Dic61C2×C412yes—
117C2×C22⋊Dic61C2×C412yes—
118C2×#11758198C2×C412yes—
119C2×#11758198C2×C412yes—
120C2×C4×Dic61C2×C412yes—
121C22⋊#92418—21no—
122C22⋊#92418—21no—
123C22⋊#92418C2312yes—
124C22⋊#92418C2312yes—
125#14519689—22no—
126#14519689—22no—
127#14519689—22no—
128#14519689—22no—
129C22×D4×C61C2×C412yes—
130C22×D4×C61C2×C411yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C2×M16×C61—21no—
133C22×C8×C61—21no—
134#121×C61—21no—
135#121×C61—21no—
136#121×C61—21no—
137#121×C61—21no—
138C2×C4⋊C4×C61C2×C411yescharacteristic
139C2×C22⋊C4×C61C2312yes—
140C22⋊C8×C61—21no—
141C22⋊C8×C61—21no—
142C22⋊C8×C61C2312yes—
143C22⋊C8×C61C2312yes—
144C24×C61C22×C411yescharacteristic
145C24×C61C22×C412yes—
146C23×D61—24no—
147C23×D61—42no—
148C23×D61—42no—
149C23×D61C22⋊C411yescharacteristic
150C23×D61C22⋊C411yescharacteristic
151C23×D61C22⋊C411yescharacteristic
152C23×D61C22⋊C411yescharacteristic
153C23×D61C22×C411yescharacteristic
154C23×D61C22×C411yescharacteristic
155C2×D4×C61—22no—
156C2×D4×C61—22no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—42no—
160C2×D4×C61—44no—
161C22×C4×C61—42no—
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C412yes—
164C22×C4×C61C2×D411yescharacteristic
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—22no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61—28no—
174C2×C22⋊D61—44no—
175C22×Dic61—22no—
176C22×Dic61—22no—
177C22×Dic61—42no—
178C22×Dic61—44no—
179C22×Dic61C22⋊C411yescharacteristic
180C22×Dic61C22⋊C411yescharacteristic
181C22×Dic61C22⋊C411yescharacteristic
182C22×Dic61C22⋊C411yescharacteristic
183C22×Dic61C22×C412yes—
184C22×Dic61C22×C411yescharacteristic
185C22×Dic61C22×C412yes—
186C22×Dic61C22×C411yescharacteristic
187#11758224—44no—
188#11758224—44no—
189#11758224—44no—
190#11758224—44no—
191C2×C4×D61—24no—
192C2×C4×D61—24no—
193C2×C4×D61—24no—
194C2×C4×D61—42no—
195C2×C4×D61—42no—
196C2×C4×D61—42no—
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×D61C22⋊C411yescharacteristic
204C2×C4×D61C22⋊C411yescharacteristic
205C2×C4×D61C22⋊C411yescharacteristic
206C2×C4×D61C22⋊C411yescharacteristic
207C2×C4×D61C22⋊C411yescharacteristic
208C2×C4×D61C22⋊C411yescharacteristic
209C2×C4×D61C22⋊C411yescharacteristic
210C2×C4×D61C22⋊C411yescharacteristic
211C2×C4×D61C2×D411yescharacteristic
212C2×C4×D61C2×D411yescharacteristic
213C2×C4×D61C2×D411yescharacteristic
214C2×C4×D61C2×D411yescharacteristic
215C2×C4×D61C2×D411yescharacteristic
216C2×C4×D61C2×D411yescharacteristic
217C2×C4×D61C2×D411yescharacteristic
218C2×C4×D61C2×D411yescharacteristic
219C2×Dic122—21no—
220C2×Dic122—21no—
221C2×Dic122—42no—
222M16×C61—42no—
223C2×C8×C61—22no—
224C2×C8×C61—22no—
225C2×C8×C61—42no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C22⋊C4×C61—22no—
229C22⋊C4×C61—22no—
230C22⋊Dic61—22no—
231C22⋊Dic61—22no—
232C22⋊Dic61—22no—
233C22⋊Dic61—22no—
234#11758198—22no—
235#11758198—22no—
236#11758198—22no—
237#11758198—22no—
238C4⋊Dic61—21no—
239C4⋊Dic61—21no—
240C4⋊Dic61—22no—
241C4⋊Dic61—22no—
242#11758196—22no—
243#11758196—22no—
244C4×Dic61—22no—
245C4×Dic61—22no—
246#11758194—42no—
247C2×#92418—22no—
248C2×#92418—22no—
249C2×#92418—42no—
250#11758189—44no—
251C8×D61—44no—
252C8×D61—44no—
253C8×D61—44no—
254C23×C61—22no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—24no—
258C23×C61—41no—
259C23×C61—42no—
260C23×C61—42no—
261C23×C61C2×C22⋊C411yescharacteristic
262C23×C61C2×C22⋊C411yescharacteristic
263C23×C61C23×C411yescharacteristic
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
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×D61C2×C22⋊C411yescharacteristic
283C22×D61C2×C22⋊C411yescharacteristic
284C22×D61C2×C22⋊C411yescharacteristic
285C22×D61C2×C22⋊C411yescharacteristic
286C22×D61#13114yes—
287D4×C61—42no—
288D4×C61—44no—
289D4×C61—44no—
290D4×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—42no—
299C2×C4×C61C2×C22⋊C411yescharacteristic
300C2×C4×C61C2×C22⋊C411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C22⋊D61—44no—
304C22⋊D61—44no—
305C22⋊D61—44no—
306C22⋊D61—44no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—24no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—44no—
317C2×Dic61—44no—
318C2×Dic61—42no—
319C2×Dic61C2×C22⋊C411yescharacteristic
320C2×Dic61C2×C22⋊C411yescharacteristic
321C2×Dic61C2×C22⋊C411yescharacteristic
322C2×Dic61C2×C22⋊C411yescharacteristic
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—22no—
328C4×D61—22no—
329C4×D61—22no—
330C4×D61—22no—
331C4×D61—22no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
336C4×D61—41no—
337C4×D61—41no—
338C4×D61#9914yes—
339Dic122—42no—
340Dic122—42no—
341C8×C61—42no—
342C8×C61—42no—
343#92418—42no—
344#92418—42no—
345#17381—611nomaximal, Sylow
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—21no—
351C22×C61—21no—
352C22×C61—21no—
353C22×C61—44no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—84no—
358C22×C61#41312yes—
359C22×C61C22×C22⋊C411yescharacteristic
360C22×C61C2×#13112yes—
361C2×D61—28no—
362C2×D61—21no—
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—44no—
372C2×D61—44no—
373C2×D61—44no—
374C2×D61—44no—
375C2×D61—44no—
376C2×D61#40812yes—
377C2×D61#40812yes—
378C2×D61C2×#9912yes—
379C4×C61—21no—
380C4×C61—21no—
381C4×C61—21no—
382C4×C61—42no—
383C4×C61C2×#9912yes—
384Dic61—21no—
385Dic61—21no—
386Dic61—21no—
387Dic61—42no—
388Dic61—42no—
389Dic61C2×#9912yes—
390C2×#525—611no—
391C2×#407—611no—
392C22×C22⋊C8—611no—
393#1472—611no—
394#1472—611no—
395#1471—611no—
396#1471D6111yescharacteristic, complemented
397#1468—614no—
398#1459—614no—
399C2×C61—22no—
400C2×C61—22no—
401C2×C61—41no—
402C2×C61—82no—
403C2×C61C2×#40811yescharacteristic
404C2×C61C22×#9911yescharacteristic
405C2×C61C2×#41311yescharacteristic
406D61—22no—
407D61—22no—
408D61—22no—
409D61—41no—
410C22×#41—611no—
411C24×C4—611no—
412C22×M16—1221no—
413C23×C8—1221no—
414#525—1221no—
415#525—1221no—
416#525—1221no—
417#525—1221no—
418#525—1221no—
419#525—1221no—
420#525—1221no—
421#525—1221no—
422C2×#123—612no—
423C2×C22⋊Q8—611no—
424C2×C22⋊Q8—611no—
425C2×#121—611no—
426C2×#121C2×D6111yescharacteristic
427C2×#120—612no—
428C2×C4×D4—612no—
429C2×C4×D4—612no—
430C2×#117—611no—
431#407—611no—
432#407—612no—
433#407—1221no—
434#407—1221no—
435#407C2×D6111yescharacteristic
436C2×C22⋊C8—611no—
437C2×C22⋊C8—612no—
438C2×C22⋊C8—612no—
439C2×C22⋊C8—612no—
440C2×C22⋊C8—1221no—
441C2×C22⋊C8—1221no—
442C2×C22⋊C8—1221no—
443C2×C22⋊C8—1221no—
444C2×C22⋊C8C2×D6111yescharacteristic
445#324—614no—
446#324—614no—
447#323—614no—
448#323C2×D6114yescomplemented
449C61#1738111yescharacteristic, complemented, Sylow
450C25—611no—
451C2×#41—1221no—
452C2×#41—1221no—
453C2×#41—1221no—
454C2×#41—1221no—
455C2×#41—2444no—
456C22×Q8—611no—
457C22×D4—612no—
458C22×D4—612no—
459C22×D4C4×D6112yes—
460C22×D4C4×D6111yescharacteristic
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—611no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—611no—
473C23×C4—611no—
474C23×C4—612no—
475C23×C4—2444no—
476C23×C4C22×D6111yescharacteristic
477C2×M16—21no—
478C2×M16—1222no—
479C2×M16—1221no—
480C2×M16—2444no—
481C22×C8—21no—
482C22×C8—1222no—
483C22×C8—1222no—
484C22×C8—1222no—
485C22×C8—1221no—
486C22×C8—2444no—
487#123—1222no—
488#123—1222no—
489#123—1222no—
490#123—1222no—
491C22⋊Q8—1221no—
492C22⋊Q8—1221no—
493C22⋊Q8—1221no—
494C22⋊Q8—1221no—
495C22⋊Q8—1221no—
496C22⋊Q8—1221no—
497C22⋊Q8—1221no—
498C22⋊Q8—1221no—
499#121—21no—
500#121—21no—
501#121—21no—
502#121—21no—
503#121—1221no—
504#121—1221no—
505#121—1221no—
506#121—1221no—
507#120—1222no—
508#120—1222no—
509#120—1222no—
510#120—1222no—
511C4×D4—1222no—
512C4×D4—1222no—
513C4×D4—1222no—
514C4×D4—1222no—
515C4×D4—1222no—
516C4×D4—1222no—
517C4×D4—1222no—
518C4×D4—1222no—
519#117—1221no—
520#117—1221no—
521#117—1221no—
522#117—1221no—
523C2×C4⋊C4—611no—
524C2×C4⋊C4—612no—
525C2×C4⋊C4—612no—
526C2×C4⋊C4C4×D6111yescharacteristic
527C2×C22⋊C4—612no—
528C2×C22⋊C4—612no—
529C2×C22⋊C4—612no—
530C2×C22⋊C4—612no—
531C2×C22⋊C4C22×D6112yes—
532C2×C42—612no—
533C22⋊C8—21no—
534C22⋊C8—21no—
535C22⋊C8—612no—
536C22⋊C8—612no—
537C22⋊C8—1222no—
538C22⋊C8—1222no—
539C22⋊C8—1222no—
540C22⋊C8—1222no—
541C22⋊C8—1221no—
542C22⋊C8—1221no—
543C22⋊C8C22×D6112yes—
544C22⋊C8C22×D6112yes—
545C24—611no—
546C24—611no—
547C24—611no—
548C24—611no—
549C24—611no—
550C24—611no—
551C24—1224no—
552C24—2442no—
553C24—2442no—
554C24C2×C4×D6111yescharacteristic
555C24C2×C4×D6112yes—
556#41—2444no—
557#41—2444no—
558#41—2444no—
559#41—2444no—
560C2×Q8—1221no—
561C2×Q8—1221no—
562C2×Q8—2442no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—42no—
568C2×D4—44no—
569C2×D4—1222no—
570C2×D4—1222no—
571C2×D4—1222no—
572C2×D4—1222no—
573C2×D4—1228no—
574C2×D4—2444no—
575C22×C4—42no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
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—612no—
599C22×C4—612no—
600C22×C4—1224no—
601C22×C4—1224no—
602C22×C4—1224no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—2442no—
606C22×C4—2442no—
607C22×C4—2442no—
608C22×C4—2442no—
609C22×C4—2442no—
610C22×C4—2442no—
611C22×C4—2442no—
612C22×C4—2442no—
613C22×C4—2442no—
614C22×C4—2442no—
615C22×C4—2444no—
616C22×C4C2×C4×D6111yescharacteristic
617C22×C4C2×C4×D6112yes—
618C22×C4D4×D6111yescharacteristic
619C22×C4D4×D6111yescharacteristic
620C22×C4D4×D6111yescharacteristic
621C22×C4D4×D6111yescharacteristic
622C22×C4C23×D6111yescharacteristic
623M16—42no—
624M16—2444no—
625M16—2442no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—42no—
629C2×C8—1222no—
630C2×C8—1222no—
631C2×C8—2444no—
632C2×C8—2444no—
633C2×C8—2444no—
634C2×C8—2442no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—1222no—
638C4⋊C4—1222no—
639C4⋊C4—1222no—
640C4⋊C4—1222no—
641C4⋊C4—1221no—
642C4⋊C4—1221no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—1222no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—1222no—
651C22⋊C4—1222no—
652C22⋊C4—1222no—
653C42—1222no—
654C42—1222no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—24no—
659C23—41no—
660C23—42no—
661C23—42no—
662C23—611no—
663C23—611no—
664C23—611no—
665C23—614no—
666C23—611no—
667C23—1222no—
668C23—1222no—
669C23—1222no—
670C23—1222no—
671C23—1222no—
672C23—1222no—
673C23—1222no—
674C23—1222no—
675C23—1222no—
676C23—1222no—
677C23—2441no—
678C23—2441no—
679C23—2441no—
680C23—2441no—
681C23—2441no—
682C23—2441no—
683C23—2441no—
684C23—24416no—
685C23C22⋊C4×D6111yescharacteristic
686C23C22⋊C4×D6111yescharacteristic
687C23C22×C4×D6111yescharacteristic
688Q8—2442no—
689Q8—2442no—
690D4—42no—
691D4—44no—
692D4—44no—
693D4—42no—
694D4—2444no—
695D4—2444no—
696D4—2444no—
697D4—2444no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—611no—
707C2×C4—614no—
708C2×C4—611no—
709C2×C4—611no—
710C2×C4—611no—
711C2×C4—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1224no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4—2444no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2444no—
737C2×C4—2442no—
738C2×C4C22⋊C4×D6111yescharacteristic
739C2×C4C22⋊C4×D6111yescharacteristic
740C2×C4C2×D4×D6111yescharacteristic
741C2×C4C2×D4×D6111yescharacteristic
742C8—42no—
743C8—42no—
744C8—2442no—
745C8—2442no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—44no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—84no—
758C22—612no—
759C22—612no—
760C22—612no—
761C22—1228no—
762C22—1221no—
763C22—1221no—
764C22—1221no—
765C22—1221no—
766C22—1221no—
767C22—1221no—
768C22—1221no—
769C22—1221no—
770C22—1221no—
771C22—2444no—
772C22—2444no—
773C22—2444no—
774C22—2444no—
775C22—2444no—
776C22#1683974312yes—
777C22C2×C22⋊C4×D6111yescharacteristic
778C22#131×D6112yes—
779C4—21no—
780C4—21no—
781C4—21no—
782C4—42no—
783C4—612no—
784C4—1221no—
785C4—1221no—
786C4—1221no—
787C4—2442no—
788C4—2442no—
789C4#99×D6112yes—
790C2—22no—
791C2—22no—
792C2—41no—
793C2—82no—
794C2—1222no—
795C2—1222no—
796C2—1222no—
797C2—2441no—
798C2#408×D6111yescharacteristic
799C2C2×#99×D6111yescharacteristic
800C2C2×#1683974311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1471C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840272C2
cosocleC22×C4×C61C24
hypercenter#1471D61
hypocenterC61#17381
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1471

Complements

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

NH ≅ G/Ntype
2. #407×D61C2semidirect
3. C2×C22⋊C8×D61C2semidirect
4. #21444184C2semidirect
5. #21444182C2semidirect
6. #21444179C2semidirect
7. #21444164C2semidirect
8. #21444134C2semidirect
9. C61×#1471C2semidirect
42. #16839487C22semidirect
43. #16839487C22semidirect
44. #16839486C22semidirect
48. C61×#323C22semidirect
396. #1471D61semidirect
448. #323C2×D61semidirect
449. C61#17381semidirect

Maximal subgroups

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

subgroupindex
C2×#168402722
#407×D612
C2×C22⋊C8×D612
#214441842
#214441822
#214441792
#214441642
#214441342
C61×#14712
#1738161