Finite Group Databasebeta

← #29696852

Subgroups — #29696852

Order 15616.

1366 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840432C211yesmaximal, characteristic
2C2×#16839891C211yesmaximal, characteristic, complemented
3#21448777C211yesmaximal, characteristic, complemented
4#21446744C211yesmaximal, characteristic, complemented
5#21446744C211yesmaximal, characteristic, complemented
6#21446644C211yesmaximal, characteristic, complemented
7#21446641C211yesmaximal, characteristic, complemented
8#21446623C211yesmaximal, characteristic, complemented
9#21445830C211yesmaximal, characteristic, complemented
10#21445827C211yesmaximal, characteristic, complemented
11#21445817C211yesmaximal, characteristic, complemented
12#21445647C211yesmaximal, characteristic, complemented
13#21445646C211yesmaximal, characteristic, complemented
14#102×Dic61C211yesmaximal, characteristic, complemented
15C61×#1982C211yesmaximal, characteristic, complemented
16C22×#11758224—21no—
17#16840432—24no—
18#16840432C418yescomplemented
19C2×#14519773C2211yescharacteristic
20C2×#14519773C2211yescharacteristic
21C2×#14519749—21no—
22C2×#14519749—21no—
23C2×#14519748—21no—
24C2×C4×Dic122C2211yescharacteristic
25C2×C4×D244C2211yescharacteristic
26C2×D4×Dic61C2211yescharacteristic
27C2×D4×Dic61C2211yescharacteristic
28#16839891—24no—
29C2×#14519706C2211yescharacteristic
30C2×#14519706C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519688C2211yescharacteristic
40C2×#14519687C2211yescharacteristic
41C2×C8×Dic61C2211yescharacteristic
42#16839666—21no—
43#16839646—21no—
44#16839645—21no—
45#16839631C2211yescharacteristic
46#16839628C2211yescharacteristic
47#16839627C2211yescharacteristic
48C4⋊C4×Dic61C2211yescharacteristic
49C4⋊C4×Dic61C2211yescharacteristic
50C4×#11758196—21no—
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C2×#127×C61C2211yescharacteristic
56C2×C4⋊C8×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C4×C4⋊C4×C61C2211yescharacteristic
62C2×#11758224—28no—
63C2×#11758224—44no—
64C2×#11758224—44no—
65C22×Dic122D411yescharacteristic
66C22×D244C2311yescharacteristic
67C22×C22⋊D61—21no—
68C22×C22⋊D61—21no—
69C22×C22⋊D61—21no—
70C22×C22⋊D61—21no—
71C23×Dic61—21no—
72C23×Dic61—21no—
73C22×C4×D61—21no—
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76#14519773—22no—
77#14519773—22no—
78#14519773C2×C414yes—
79#14519773C2×C414yes—
80#14519749—28no—
81#14519749—28no—
82#14519748—28no—
83C4×Dic122C2×C414yes—
84C4×Dic122D414yes—
85C4×D244—22no—
86C4×D244C2×C414yes—
87D4×Dic61—22no—
88D4×Dic61—22no—
89D4×Dic61C2×C414yes—
90D4×Dic61C2×C414yes—
91C2×C4⋊Dic61D411yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196D411yescharacteristic
98C2×#11758196D411yescharacteristic
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61—21no—
101C2×#11758198—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61C2311yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106#14519706—22no—
107#14519706—22no—
108#14519699—41no—
109#14519699—41no—
110#14519698—22no—
111#14519698—22no—
112#14519698—41no—
113#14519698—41no—
114#14519697—22no—
115#14519697—22no—
116#14519688—22no—
117#14519687—22no—
118C8×Dic61—22no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125C22×D4×C61—21no—
126C22×D4×C61—21no—
127C22×D4×C61C2311yescharacteristic
128C22×D4×C61C2311yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131#127×C61—22no—
132#127×C61C2×C414yes—
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C42×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61—22no—
138#102×C61—22no—
139#102×C61—22no—
140#102×C61—41no—
141#102×C61—41no—
142#95×C61—21no—
143C24×C61—21no—
144C24×C61—21no—
145C23×D61—21no—
146C2×D4×C61—24no—
147C2×D4×C61—24no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—42no—
159C2×D4×C61—42no—
160C2×D4×C61—81no—
161C2×D4×C61—81no—
162C2×D4×C61C22×C412yes—
163C2×D4×C61C22×C412yes—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2411yescharacteristic
169C2×C22⋊D61—24no—
170C2×C22⋊D61—24no—
171C2×C22⋊D61—24no—
172C2×C22⋊D61—24no—
173C2×C22⋊D61—42no—
174C2×C22⋊D61—42no—
175C2×C22⋊D61—42no—
176C2×C22⋊D61—42no—
177C2×C22⋊D61—81no—
178C2×C22⋊D61—81no—
179C2×C22⋊D61—81no—
180C2×C22⋊D61—81no—
181C22×Dic61—21no—
182C22×Dic61—24no—
183C22×Dic61—24no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—42no—
187C22×Dic61—42no—
188C22×Dic61—42no—
189C22×Dic61—42no—
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192C22×Dic61C2×D411yescharacteristic
193C22×Dic61C2×D411yescharacteristic
194#11758224—432no—
195C2×D244—21no—
196C2×D244—21no—
197C2×D244—21no—
198C2×D244—21no—
199C2×D244—21no—
200C2×D244C22×C412yes—
201C2×C4×D61—24no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×Dic122—22no—
205C2×Dic122—22no—
206C2×Dic122C22⋊C414yes—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—21no—
216C4⋊C4×C61#4112yescomplemented
217C42×C61—81no—
218C42×C61C22×C412yes—
219C42×C61C2×D412yes—
220C22⋊Dic61—24no—
221C22⋊Dic61—24no—
222#11758198—24no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61C22⋊C414yes—
229C4⋊Dic61C22×C412yes—
230#11758196—42no—
231#11758196—81no—
232#11758196C22⋊C414yes—
233#11758196C22⋊C414yes—
234C4×Dic61—42no—
235C4×Dic61—81no—
236C4×Dic61C22×C412yes—
237C4×Dic61C22×C412yes—
238C4×Dic61C2×D412yes—
239C4×Dic61C2×D412yes—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418#4112yescomplemented
246C23×C61—22no—
247C23×C61—22no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61C22×D411yescharacteristic
261C22×D61—22no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—41no—
267C22×D61—41no—
268D4×C61—22no—
269D4×C61—22no—
270D4×C61—22no—
271D4×C61—22no—
272D4×C61—48no—
273D4×C61—41no—
274D4×C61—41no—
275D4×C61—41no—
276D4×C61—41no—
277D4×C61—84no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—22no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61C2×C22⋊C412yes—
289C2×C4×C61C2×C22⋊C412yes—
290C2×C4×C61C23×C411yescharacteristic
291C2×C4×C61C22×D411yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61C2×#4111yescharacteristic
294C2×C4×C61H(5,𝔽2)11yescharacteristic
295C2×C4×C612−1+411yescharacteristic
296C22⋊D61—48no—
297C22⋊D61—48no—
298C22⋊D61—84no—
299C22⋊D61—84no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—22no—
307C2×Dic61—48no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—48no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61C2×C22⋊C412yes—
318C2×Dic61C2×C22⋊C412yes—
319C2×Dic61C2×C22⋊C412yes—
320C2×Dic61C2×C22⋊C412yes—
321C2×Dic61AGL(1,ℤ/8)12yes—
322C2×Dic61AGL(1,ℤ/8)12yes—
323D244—22no—
324D244—22no—
325D244—41no—
326D244—41no—
327C4×D61—48no—
328Dic122—28no—
329C8×C61—41no—
330C8×C61—41no—
331#92418—22no—
332#92418—41no—
333#22545—611nomaximal, Sylow
334C22×C61—42no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—42no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—81no—
341C22×C61—81no—
342C22×C61—81no—
343C22×C61—81no—
344C22×C61—81no—
345C22×C61—81no—
346C22×C61—81no—
347C22×C61—81no—
348C22×C61C22×C22⋊C411yescharacteristic
349C22×C61#54811yescharacteristic
350C22×C61#55011yescharacteristic
351C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
352C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C61#57611yescharacteristic
354C22×C61#57711yescharacteristic
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—81no—
359C2×D61—81no—
360C2×D61—81no—
361C2×D61—81no—
362C4×C61—22no—
363C4×C61—22no—
364C4×C61—42no—
365C4×C61—81no—
366C4×C61C4×#4111yescharacteristic
367C4×C61#52011yescharacteristic
368C4×C61#54811yescharacteristic
369C4×C61#55011yescharacteristic
370Dic61—22no—
371Dic61—22no—
372Dic61—22no—
373Dic61—42no—
374Dic61—81no—
375Dic61—81no—
376Dic61#41814yes—
377C2×#550—611no—
378C2×#446—611no—
379#2355—611no—
380#1982—611no—
381#1982—611no—
382#1982D6111yescharacteristic, complemented
383#1961—611no—
384#1961—611no—
385#1957—611no—
386#1804—611no—
387#1804—611no—
388#1802—611no—
389#1762—611no—
390#1762—611no—
391C4×#102—611no—
392C2×C61—82no—
393C2×C61—82no—
394C2×C61#234111yescharacteristic
395C2×C61C2×#41811yescharacteristic
396C2×C61#289711yescharacteristic
397C2×C61#336611yescharacteristic
398C2×C61#336811yescharacteristic
399C2×C61#339711yescharacteristic
400C2×C61#339911yescharacteristic
401D61—82no—
402C22×#41—1221no—
403#550—618no—
404#550—1224no—
405C2×#127—611no—
406C2×#127—611no—
407C2×#127C2×D6111yescharacteristic
408C2×#121—1221no—
409C2×#121—1221no—
410C2×#121—1221no—
411C2×C4×Q8—611no—
412C2×C4×D4—611no—
413C2×C4×D4—611no—
414C2×C4×D4—611no—
415#446—1224no—
416C2×C4⋊C8—611no—
417C2×C4⋊C8—611no—
418C2×C4⋊C8C2×D6111yescharacteristic
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×#102—611no—
425C2×#102—611no—
426C2×#102—611no—
427C2×#102C2×D6111yescharacteristic
428C2×#102C2×D6111yescharacteristic
429C2×#102C2×D6111yescharacteristic
430C2×#102C2×D6111yescharacteristic
431C2×#97—611no—
432C2×#97—611no—
433C2×C4×C8—611no—
434#391—1221no—
435#387—1221no—
436#387—1221no—
437#384—611no—
438#382—611no—
439#382—611no—
440C4×C4⋊C4—611no—
441C4×C4⋊C4—611no—
442C4×C4⋊C4—1221no—
443C4×C4⋊C4C2×D6111yescharacteristic
444#340—611no—
445#340—611no—
446#340—611no—
447#340—611no—
448C61#2254511yescharacteristic, complemented, Sylow
449C2×#41—1228no—
450C2×#41—2444no—
451C2×#41—2444no—
452C22×Q8—611no—
453C22×D4—21no—
454C22×D4—21no—
455C22×D4—611no—
456C22×D4—1221no—
457C22×D4—1221no—
458C22×D4—1221no—
459C22×D4—1221no—
460C22×D4C22×D6111yescharacteristic
461C22×D4C22×D6111yescharacteristic
462C23×C4—1221no—
463C23×C4—1221no—
464C23×C4—1221no—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8C22×D6111yescharacteristic
468C22×C8C22×D6111yescharacteristic
469#127—22no—
470#127—614no—
471#127—614no—
472#127—1222no—
473#127—1222no—
474#127C4×D6114yes—
475#121—1228no—
476#121—1228no—
477#121—1228no—
478C4×Q8—614no—
479C4×Q8—614no—
480C4×D4—614no—
481C4×D4—614no—
482C4×D4—614no—
483C4×D4—1222no—
484C4×D4—1222no—
485C4×D4—1222no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4C22×D6111yescharacteristic
495C2×C4⋊C4C22×D6111yescharacteristic
496C2×C22⋊C4—1221no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1221no—
499C2×C42—21no—
500C2×C42—611no—
501C2×C42—611no—
502C2×C42—1221no—
503C2×C42—1221no—
504C2×C42C22×D6111yescharacteristic
505C4⋊C8—22no—
506C4⋊C8—1222no—
507C4⋊C8—1222no—
508#102—22no—
509#102—22no—
510#102—41no—
511#102—41no—
512#102—1222no—
513#102—1222no—
514#102—1222no—
515#102—1222no—
516#102—2441no—
517#102—2441no—
518#102—2441no—
519#102—2441no—
520#97—1222no—
521#97—1222no—
522C4×C8—1222no—
523#95—21no—
524#95—1221no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528#95—1221no—
529#95—1221no—
530C24—21no—
531C24—21no—
532C24—1221no—
533#41—24432no—
534C2×Q8—614no—
535C2×Q8—1222no—
536C2×Q8—1222no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—24no—
548C2×D4—24no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—81no—
552C2×D4—81no—
553C2×D4—612no—
554C2×D4—1224no—
555C2×D4—1224no—
556C2×D4—1224no—
557C2×D4—1224no—
558C2×D4—1221no—
559C2×D4—1221no—
560C2×D4—1221no—
561C2×D4—1221no—
562C2×D4—1221no—
563C2×D4—4881no—
564C2×D4—4881no—
565C2×D4—4881no—
566C2×D4—4881no—
567C2×D4—2442no—
568C2×D4—2442no—
569C2×D4—2442no—
570C2×D4—2442no—
571C2×D4C2×C4×D6112yes—
572C2×D4C2×C4×D6112yes—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—1224no—
580C22×C4—1224no—
581C22×C4—1221no—
582C22×C4—1224no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—2442no—
586C22×C4—2442no—
587C22×C4—2442no—
588C22×C4—2442no—
589C22×C4—2442no—
590C22×C4—2442no—
591C22×C4D4×D6111yescharacteristic
592C22×C4D4×D6111yescharacteristic
593C22×C4C23×D6111yescharacteristic
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—612no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—614no—
610C4⋊C4—614no—
611C4⋊C4—614no—
612C4⋊C4—612no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—4881no—
619C4⋊C4—2442no—
620C4⋊C4#1175822412yescomplemented
621C22⋊C4—1224no—
622C22⋊C4—1224no—
623C22⋊C4—1224no—
624C42—81no—
625C42—612no—
626C42—612no—
627C42—612no—
628C42—612no—
629C42—4881no—
630C42—2442no—
631C42C2×C4×D6112yes—
632C42D4×D6112yes—
633C23—22no—
634C23—22no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—1222no—
648C23—2441no—
649C23—2441no—
650C23—2441no—
651C23—2441no—
652C23—2441no—
653C23—2441no—
654C23C2×D4×D6111yescharacteristic
655Q8—1228no—
656D4—22no—
657D4—22no—
658D4—22no—
659D4—22no—
660D4—48no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—84no—
666D4—1222no—
667D4—1222no—
668D4—4884no—
669D4—4884no—
670D4—2448no—
671D4—2448no—
672D4—2441no—
673D4—2441no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—612no—
685C2×C4—612no—
686C2×C4—612no—
687C2×C4—612no—
688C2×C4—612no—
689C2×C4—612no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1222no—
697C2×C4—2448no—
698C2×C4—2448no—
699C2×C4—2448no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4C22⋊C4×D6112yes—
709C2×C4C22⋊C4×D6112yes—
710C2×C4C22×C4×D6111yescharacteristic
711C2×C4C2×D4×D6111yescharacteristic
712C2×C4#41×D6111yescharacteristic
713C2×C4C2×#1175822411yescharacteristic
714C2×C4#1451982211yescharacteristic
715C2×C4#1451982411yescharacteristic
716C8—41no—
717C8—41no—
718C8—1222no—
719C8—2441no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22—81no—
734C22—4881no—
735C22—4881no—
736C22—4881no—
737C22—4881no—
738C22—2442no—
739C22—2442no—
740C22—2442no—
741C22C2×C22⋊C4×D6111yescharacteristic
742C22#1684041811yescharacteristic
743C22#1684043011yescharacteristic
744C22AGL(1,ℤ/8)×D6111yescharacteristic
745C22AGL(1,ℤ/8)×D6111yescharacteristic
746C22#1684056311yescharacteristic
747C22#1684056811yescharacteristic
748C4—22no—
749C4—22no—
750C4—42no—
751C4—81no—
752C4—614no—
753C4—1222no—
754C4—1222no—
755C4—1222no—
756C4—4881no—
757C4—4881no—
758C4—2442no—
759C4C4×#1175822411yescharacteristic
760C4#1684024111yescharacteristic
761C4#1684042011yescharacteristic
762C4#1684043211yescharacteristic
763C2—82no—
764C2—82no—
765C2—4882no—
766C2#2144865811yescharacteristic
767C2#418×D6111yescharacteristic
768C2#2145434011yescharacteristic
769C2#2145852111yescharacteristic
770C2#2145854311yescharacteristic
771C2#2145883411yescharacteristic
772C2#2145886411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1982C2
socleC23×C61C22×D4
prime radicalC2×#16840432C2
cosocleC22×C4×C61C24
hypercenter#1982D61
hypocenterC61#22545
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
2. C2×#16839891C2semidirect
3. #21448777C2semidirect
4. #21446744C2semidirect
5. #21446744C2semidirect
6. #21446644C2semidirect
7. #21446641C2semidirect
8. #21446623C2semidirect
9. #21445830C2semidirect
10. #21445827C2semidirect
11. #21445817C2semidirect
12. #21445647C2semidirect
13. #21445646C2semidirect
14. #102×Dic61C2semidirect
15. C61×#1982C2semidirect
18. #16840432C4semidirect
216. C4⋊C4×C61#41semidirect
245. C2×#92418#41semidirect
382. #1982D61semidirect
448. C61#22545semidirect
620. C4⋊C4#11758224semidirect

Maximal subgroups

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

subgroupindex
C2×#168404322
C2×#168398912
#214487772
#214467442
#214466442
#214466412
#214466232
#214458302
#214458272
#214458172
#214456472
#214456462
#102×Dic612
C61×#19822
#2254561