Finite Group Databasebeta

← #29733116

Subgroups — #29733116

Order 15616.

1178 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840452C211yesmaximal, characteristic, complemented
2C2×#16840083C211yesmaximal, characteristic, complemented
3C2×#16840006C211yesmaximal, characteristic, complemented
4#21447157C211yesmaximal, characteristic, complemented
5#21447015C211yesmaximal, characteristic, complemented
6#21446965C211yesmaximal, characteristic, complemented
7#21446822C211yesmaximal, characteristic, complemented
8#21446177C211yesmaximal, characteristic, complemented
9#21446137C211yesmaximal, characteristic, complemented
10#21446126C211yesmaximal, characteristic, complemented
11#21446117C211yesmaximal, characteristic, complemented
12#21446072C211yesmaximal, characteristic, complemented
13#21446006C211yesmaximal, characteristic, complemented
14#21445538C211yesmaximal, characteristic, complemented
15C61×#2416C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18#16840452—24no—
19#16840452—24no—
20C2×#14519770—21no—
21C2×#14519769C2211yescharacteristic
22C2×#14519767—21no—
23C2×#14519758—21no—
24C2×#14519756C2211yescharacteristic
25C2×#14519756C2211yescharacteristic
26C2×C4×Dic122C2211yescharacteristic
27C2×#14519736C2211yescharacteristic
28C2×#14519733—21no—
29C22×C4⋊Dic61C2211yescharacteristic
30#16840083—24no—
31#16840006—24no—
32C2×#14519710C2211yescharacteristic
33C2×#14519710C2211yescharacteristic
34C2×#14519708C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43C2×C22⋊#92418C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C2×#121×C61—21no—
53C2×#121×C61C2211yescharacteristic
54C2×#121×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C22×C4⋊C4×C61C2211yescharacteristic
57C61×#396—21no—
58C61×#394—21no—
59C61×#390C2211yescharacteristic
60C61×#389C2211yescharacteristic
61C61×#386—21no—
62C61×#380C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C23×Dic61—21no—
65C2×#11758200—22no—
66C2×#11758200—22no—
67C2×#11758200—41no—
68C2×#11758194—22no—
69C2×#11758194—22no—
70C2×#11758194—41no—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519770—28no—
76#14519769—22no—
77#14519769—22no—
78#14519767—28no—
79#14519758—28no—
80#14519756—22no—
81#14519756—22no—
82#14519756—22no—
83#14519756D414yescomplemented
84C4×Dic122—22no—
85C4×Dic122—22no—
86#14519736—22no—
87#14519736D414yescomplemented
88#14519733—28no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61—22no—
91C2×C4⋊Dic61—22no—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×C22⋊Dic61—21no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105#14519710—22no—
106#14519710—22no—
107#14519708—22no—
108#14519700—22no—
109#14519700—22no—
110#14519700—41no—
111#14519698—22no—
112#14519698—22no—
113#14519698—22no—
114C22⋊#92418—22no—
115C22⋊#92418—22no—
116C22⋊#92418—41no—
117C22×D4×C61—21no—
118C22×D4×C61—21no—
119C22×D4×C61D411yescharacteristic
120C22×D4×C61C2311yescharacteristic
121C23×C4×C61—21no—
122C23×C4×C61C2311yescharacteristic
123C23×C4×C61C2311yescharacteristic
124#121×C61—22no—
125#121×C61—22no—
126#121×C61—22no—
127#121×C61—41no—
128#121×C61—44no—
129C4×D4×C61—22no—
130C4×D4×C61—22no—
131C2×C4⋊C4×C61—22no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—41no—
135C2×C4⋊C4×C61D411yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61D411yescharacteristic
145C2×C22⋊C4×C61D411yescharacteristic
146C2×C42×C61C2311yescharacteristic
147#95×C61—21no—
148#95×C61—21no—
149C24×C61—21no—
150C24×C61C2×D411yescharacteristic
151C24×C61C2×D411yescharacteristic
152C2×D4×C61—22no—
153C2×D4×C61—22no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—41no—
161C2×D4×C61—42no—
162C2×D4×C61—42no—
163C2×D4×C61—42no—
164C2×D4×C61—42no—
165C2×D4×C61—42no—
166C2×D4×C61—81no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—42no—
181C22×C4×C61—42no—
182C22×C4×C61—81no—
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D412yes—
188C22×C4×C61C2×D412yes—
189C22×C4×C61C2411yescharacteristic
190C22×Dic61—24no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—42no—
196C22×Dic61—42no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122—21no—
202C2×Dic122C2×D412yes—
203C4⋊C4×C61—22no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—42no—
210C4⋊C4×C61—42no—
211C4⋊C4×C61#4112yes—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—22no—
214C22⋊C4×C61—42no—
215C22⋊C4×C61—42no—
216C22⋊C4×C61—42no—
217C22⋊C4×C61—42no—
218C22⋊C4×C61—81no—
219C42×C61—21no—
220C42×C61—21no—
221C22⋊Dic61—24no—
222C22⋊Dic61—24no—
223C22⋊Dic61—24no—
224#11758200—44no—
225C4⋊Dic61—24no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61C2×D412yes—
230C4⋊Dic61C2×D412yes—
231C4⋊Dic61C2×D412yes—
232#11758196—24no—
233#11758196—24no—
234#11758196—24no—
235#11758196—24no—
236#11758196—24no—
237C4×Dic61—24no—
238C4×Dic61—24no—
239#11758194—44no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418#4112yes—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61#12012yes—
272C23×C61AGL(1,ℤ/8)12yes—
273C23×C61C22×D411yescharacteristic
274D4×C61—44no—
275D4×C61—41no—
276D4×C61—41no—
277D4×C61—41no—
278D4×C61—41no—
279D4×C61—84no—
280D4×C61—84no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—22no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—41no—
308C2×C4×C61—41no—
309C2×C4×C61—84no—
310C2×C4×C61#12012yes—
311C2×C4×C61C22×D411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C2×#4111yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61H(5,𝔽2)11yescharacteristic
316C2×C4×C612−1+411yescharacteristic
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—48no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330Dic122—22no—
331Dic122—22no—
332Dic122—41no—
333Dic122—41no—
334#92418—22no—
335#92418—41no—
336#92418—41no—
337#92418—41no—
338#25560—611nomaximal, Sylow
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61—81no—
356C22×C61—81no—
357C22×C61—81no—
358C22×C61—81no—
359C22×C61—81no—
360C22×C61C2×#12011yescharacteristic
361C22×C61#54611yescharacteristic
362C22×C61#54711yescharacteristic
363C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
364C22×C61#57511yescharacteristic
365C22×C61#57711yescharacteristic
366C22×C61#57811yescharacteristic
367C4×C61—22no—
368C4×C61—41no—
369C4×C61—41no—
370C4×C61—41no—
371C4×C61—42no—
372C4×C61—81no—
373C4×C61—81no—
374C4×C61#53211yescharacteristic
375C4×C61#53711yescharacteristic
376C4×C61#54611yescharacteristic
377C4×C61#54711yescharacteristic
378Dic61—42no—
379Dic61—42no—
380Dic61—42no—
381Dic61—42no—
382C2×#552—611no—
383C2×#482—611no—
384C2×#468—611no—
385#2416D6111yescharacteristic
386#2059—611no—
387#2035—611no—
388#2025—611no—
389#2000—611no—
390#1880—611no—
391#1874—611no—
392#1872—611no—
393#1870—611no—
394#1863—611no—
395#1852—611no—
396#1736—611no—
397C2×C61—42no—
398C2×C61—42no—
399C2×C61—161no—
400C2×C61#243011yescharacteristic
401C2×C61#300611yescharacteristic
402C2×C61#301311yescharacteristic
403C2×C61#331011yescharacteristic
404C2×C61#332711yescharacteristic
405C2×C61#334311yescharacteristic
406C2×C61#335111yescharacteristic
407C22×SD16—611no—
408C22×M16—611no—
409#552—1224no—
410#552—1224no—
411C2×#126—1221no—
412C2×#125—611no—
413C2×#125—1221no—
414C2×#123—1221no—
415C2×C22⋊Q8—611no—
416C2×C22⋊Q8—611no—
417C2×#121—21no—
418C2×#121C2×D6111yescharacteristic
419C2×#121C2×D6111yescharacteristic
420C2×C4×Q8—611no—
421C2×C4×D4C2×D6111yescharacteristic
422C2×#117—611no—
423C2×#117—1221no—
424C22×C4⋊C4—611no—
425C22×C4⋊C4C2×D6111yescharacteristic
426#482—1224no—
427#468—1224no—
428C2×#107—611no—
429C2×#107—611no—
430C2×#106—611no—
431C2×#103—611no—
432C2×#103—611no—
433C2×#103—611no—
434C2×#102—611no—
435C2×#102—611no—
436C2×#102—611no—
437C2×C22⋊C8—611no—
438C2×C22⋊C8—611no—
439C2×C22⋊C8—611no—
440#396—21no—
441#394—21no—
442#390C2×D6111yescharacteristic
443#389C2×D6111yescharacteristic
444#386—21no—
445#380C2×D6111yescharacteristic
446#340—611no—
447#340—611no—
448#340—611no—
449#340—611no—
450#340—611no—
451#340—611no—
452#336—611no—
453#336—611no—
454C61#2556011yescharacteristic, complemented, Sylow
455C22×Q8—611no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4C22⋊D6111yescharacteristic
459C22×D4C22×D6111yescharacteristic
460C23×C4—21no—
461C23×C4—1221no—
462C23×C4C22×D6111yescharacteristic
463C23×C4C22×D6111yescharacteristic
464C2×SD16—1222no—
465C2×SD16—1222no—
466C2×SD16—2441no—
467C2×M16—1222no—
468C2×M16—1222no—
469C2×M16—2441no—
470C22×C8—611no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8—611no—
474#126—1228no—
475#125—1222no—
476#125—1222no—
477#125—1228no—
478#123—1228no—
479C22⋊Q8—614no—
480C22⋊Q8—1222no—
481C22⋊Q8—1222no—
482C22⋊Q8—1222no—
483#121—22no—
484#121—22no—
485#121—22no—
486#121—41no—
487#121—44no—
488C4×Q8—1222no—
489C4×Q8—1222no—
490C4×D4—22no—
491C4×D4—22no—
492#117—614no—
493#117—1228no—
494#117—1222no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—41no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—1222no—
503C2×C4⋊C4—1222no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4C22⋊D6111yescharacteristic
511C2×C4⋊C4C22×D6111yescharacteristic
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C4⋊C4C22×D6111yescharacteristic
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—1221no—
520C2×C22⋊C4—1221no—
521C2×C22⋊C4—1221no—
522C2×C22⋊C4C22⋊D6111yescharacteristic
523C2×C22⋊C4C22⋊D6111yescharacteristic
524C2×C42—1221no—
525C2×C42—1221no—
526C2×C42C22×D6111yescharacteristic
527#107—1222no—
528#107—1222no—
529#106—1222no—
530#103—1222no—
531#103—1222no—
532#103—2441no—
533#102—1222no—
534#102—1222no—
535#102—1222no—
536C22⋊C8—1222no—
537C22⋊C8—1222no—
538C22⋊C8—2441no—
539#95—21no—
540#95—21no—
541C24—21no—
542C24C2×C22⋊D6111yescharacteristic
543C24C2×C22⋊D6111yescharacteristic
544C2×Q8—612no—
545C2×Q8—1221no—
546C2×Q8—1221no—
547C2×Q8—1221no—
548C2×Q8—1221no—
549C2×Q8—1221no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—41no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—81no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—81no—
581C22×C4—1224no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—2442no—
587C22×C4—2442no—
588C22×C4D4×D6112yes—
589C22×C4D4×D6112yes—
590C22×C4C2×C22⋊D6111yescharacteristic
591C22×C4C2×C22⋊D6111yescharacteristic
592C22×C4C2×C22⋊D6111yescharacteristic
593C22×C4C2×C22⋊D6111yescharacteristic
594C22×C4C23×D6111yescharacteristic
595SD16—2444no—
596M16—2444no—
597C2×C8—612no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C4⋊C4—21no—
610C4⋊C4—22no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—612no—
618C4⋊C4—612no—
619C4⋊C4—612no—
620C4⋊C4—1224no—
621C4⋊C4—1224no—
622C4⋊C4—1224no—
623C4⋊C4—1224no—
624C4⋊C4—1224no—
625C4⋊C4—1221no—
626C4⋊C4—1221no—
627C4⋊C4—1221no—
628C4⋊C4—1224no—
629C4⋊C4#1175822412yes—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—81no—
637C22⋊C4—1224no—
638C22⋊C4—1224no—
639C22⋊C4—1224no—
640C42—21no—
641C42—21no—
642C42—1224no—
643C42—1224no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23#1451974512yes—
664C23#1451980312yes—
665C23C22×C22⋊D6111yescharacteristic
666Q8—1222no—
667Q8—1222no—
668Q8—2441no—
669Q8—2441no—
670D4—44no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—84no—
676D4—84no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—84no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—2448no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4#1451974512yes—
720C2×C4C2×D4×D6111yescharacteristic
721C2×C4C2×D4×D6111yescharacteristic
722C2×C4#41×D6111yescharacteristic
723C2×C4C2×#1175822411yescharacteristic
724C2×C4#1451982211yescharacteristic
725C2×C4#1451982411yescharacteristic
726C8—1222no—
727C8—2441no—
728C8—2441no—
729C8—2441no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22C2×#1451974511yescharacteristic
752C22#1684040611yescharacteristic
753C22#1684041111yescharacteristic
754C22C2×#1451980311yescharacteristic
755C22#1684056011yescharacteristic
756C22#1684057311yescharacteristic
757C22#1684057711yescharacteristic
758C4—22no—
759C4—41no—
760C4—42no—
761C4—41no—
762C4—41no—
763C4—81no—
764C4—81no—
765C4—2442no—
766C4—2442no—
767C4—2442no—
768C4—2442no—
769C4#1684030711yescharacteristic
770C4#1684033911yescharacteristic
771C4#1684040111yescharacteristic
772C4#1684041211yescharacteristic
773C2—42no—
774C2—42no—
775C2—161no—
776C2#2144942511yescharacteristic
777C2#2145506911yescharacteristic
778C2#2145513111yescharacteristic
779C2#2145784011yescharacteristic
780C2#2145808711yescharacteristic
781C2#2145825311yescharacteristic
782C2#2145837311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#2416C2
socleC23×C61C22×D4
hypercenter#2416D61
hypocenterC61#25560
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2416

Complements

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

NH ≅ G/Ntype
1. C2×#16840452C2semidirect
2. C2×#16840083C2semidirect
3. C2×#16840006C2semidirect
4. #21447157C2semidirect
5. #21447015C2semidirect
6. #21446965C2semidirect
7. #21446822C2semidirect
8. #21446177C2semidirect
9. #21446137C2semidirect
10. #21446126C2semidirect
11. #21446117C2semidirect
12. #21446072C2semidirect
13. #21446006C2semidirect
14. #21445538C2semidirect
83. #14519756D4semidirect
87. #14519736D4semidirect
454. C61#25560semidirect

Maximal subgroups

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

subgroupindex
C2×#168404522
C2×#168400832
C2×#168400062
#214471572
#214470152
#214469652
#214468222
#214461772
#214461372
#214461262
#214461172
#214460722
#214460062
#214455382
C61×#24162
#2556061