Finite Group Databasebeta

← #29714005

Subgroups — #29714005

Order 15616.

1152 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840452C211yesmaximal, characteristic, complemented
2C2×#16840062C211yesmaximal, characteristic, complemented
3C2×C4×#11758200C211yesmaximal, characteristic, complemented
4#21447022C211yesmaximal, characteristic, complemented
5#21447015C211yesmaximal, characteristic, complemented
6#21446822C211yesmaximal, characteristic, complemented
7#21446822C211yesmaximal, characteristic, complemented
8#21446783C211yesmaximal, characteristic, complemented
9#21446614C211yesmaximal, characteristic, complemented
10#21446142C211yesmaximal, characteristic, complemented
11#21446137C211yesmaximal, characteristic, complemented
12#21446016C211yesmaximal, characteristic, complemented
13#21446011C211yesmaximal, characteristic, complemented
14#21445831C211yesmaximal, characteristic, complemented
15C61×#2535C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17#16840452—24no—
18#16840452—24no—
19C2×#14519770—21no—
20C2×#14519769C2211yescharacteristic
21C2×#14519767—21no—
22C2×#14519758—21no—
23C2×#14519756C2211yescharacteristic
24C2×#14519756C2211yescharacteristic
25C2×C4×Dic122C2211yescharacteristic
26C2×#14519736C2211yescharacteristic
27C2×#14519733—21no—
28C22×C4⋊Dic61C2211yescharacteristic
29#16840062—24no—
30C4×#11758200—24no—
31C2×#14519710C2211yescharacteristic
32C2×#14519708C2211yescharacteristic
33C2×#14519708C2211yescharacteristic
34C2×C4⋊#92418C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×C22⋊#92418C2211yescharacteristic
42C2×C22⋊#92418C2211yescharacteristic
43C2×C22⋊#92418C2211yescharacteristic
44C2×C22⋊#92418C2211yescharacteristic
45C2×C4×#92418C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52C2×#121×C61C2211yescharacteristic
53C2×#121×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C2×C4×D4×C61C2211yescharacteristic
56C61×#397—21no—
57C61×#392—21no—
58C61×#386—21no—
59C61×#386—21no—
60C61×#382C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C61×#380C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C23×Dic61—21no—
65C2×#11758200—22no—
66C2×#11758200—22no—
67C2×#11758200—22no—
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72#14519770—28no—
73#14519769—22no—
74#14519769D414yescomplemented
75#14519767—28no—
76#14519758—28no—
77#14519756—22no—
78#14519756—22no—
79#14519756—22no—
80#14519756—22no—
81C4×Dic122—22no—
82C4×Dic122D414yescomplemented
83#14519736—22no—
84#14519736—22no—
85#14519733—28no—
86C2×C4⋊Dic61—21no—
87C2×C4⋊Dic61—22no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×C4⋊Dic61C2311yescharacteristic
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×#11758196—21no—
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×C22⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61—21no—
102#14519710—22no—
103#14519708—22no—
104#14519708—22no—
105C4⋊#92418—22no—
106#14519700—22no—
107#14519700—41no—
108#14519700—41no—
109#14519698—22no—
110#14519698—22no—
111#14519698—22no—
112C22⋊#92418—22no—
113C22⋊#92418—22no—
114C22⋊#92418—41no—
115C22⋊#92418—41no—
116C4×#92418—22no—
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—41no—
127#121×C61—41no—
128C4×D4×C61—22no—
129C4×D4×C61—22no—
130C4×D4×C61—22no—
131C4×D4×C61—22no—
132C2×C4⋊C4×C61D411yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61D411yescharacteristic
142C2×C22⋊C4×C61D411yescharacteristic
143C2×C42×C61C2311yescharacteristic
144#95×C61—21no—
145#95×C61—21no—
146#95×C61—21no—
147#95×C61—21no—
148C24×C61—21no—
149C24×C61C2×D411yescharacteristic
150C24×C61C2×D411yescharacteristic
151C2×D4×C61—22no—
152C2×D4×C61—22no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—41no—
159C2×D4×C61—42no—
160C2×D4×C61—42no—
161C2×D4×C61—42no—
162C2×D4×C61—42no—
163C2×D4×C61—81no—
164C2×D4×C61—81no—
165C2×D4×C61#4112yes—
166C22×C4×C61—21no—
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—21no—
181C22×C4×C61—42no—
182C22×C4×C61—81no—
183C22×C4×C61—81no—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2411yescharacteristic
189C22×Dic61—24no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—42no—
195C22×Dic61—42no—
196C2×Dic122—21no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122C2×D412yes—
202C4⋊C4×C61—22no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C22⋊C4×C61—22no—
210C22⋊C4×C61—22no—
211C22⋊C4×C61—42no—
212C22⋊C4×C61—42no—
213C22⋊C4×C61—42no—
214C22⋊C4×C61—81no—
215C22⋊C4×C61—81no—
216C42×C61C2×D412yes—
217C42×C61C2×D412yes—
218C22⋊Dic61—24no—
219C22⋊Dic61—24no—
220C22⋊Dic61—24no—
221#11758200—28no—
222C4⋊Dic61—24no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61C2×D412yes—
227C4⋊Dic61C2×D412yes—
228C4⋊Dic61C2×D412yes—
229#11758196—24no—
230#11758196—24no—
231#11758196—24no—
232#11758196—24no—
233#11758196—24no—
234C4×Dic61—24no—
235C4×Dic61—24no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418#4112yes—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—22no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61#13512yes—
269C23×C61C22×D411yescharacteristic
270D4×C61—22no—
271D4×C61—22no—
272D4×C61—44no—
273D4×C61—41no—
274D4×C61—41no—
275D4×C61—84no—
276D4×C61—84no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
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—84no—
305C2×C4×C61#12012yes—
306C2×C4×C61#12012yes—
307C2×C4×C61C22×D411yescharacteristic
308C2×C4×C61C22×D411yescharacteristic
309C2×C4×C61C2×#4111yescharacteristic
310C2×C4×C61C2×#4111yescharacteristic
311C2×C4×C61H(5,𝔽2)11yescharacteristic
312C2×C4×C612−1+411yescharacteristic
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—48no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326Dic122—22no—
327Dic122—22no—
328Dic122—41no—
329Dic122—41no—
330#92418—22no—
331#92418—41no—
332#92418—41no—
333#92418—41no—
334#24125—611nomaximal, Sylow
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—42no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—42no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—42no—
352C22×C61—81no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61—81no—
356C22×C61C2×#12011yescharacteristic
357C22×C61#54611yescharacteristic
358C22×C61#54711yescharacteristic
359C22×C61C2×#13511yescharacteristic
360C22×C61#57511yescharacteristic
361C22×C61#57711yescharacteristic
362C22×C61#57711yescharacteristic
363C4×C61—22no—
364C4×C61—22no—
365C4×C61—41no—
366C4×C61—41no—
367C4×C61—81no—
368C4×C61—81no—
369C4×C61—81no—
370C4×C61#52511yescharacteristic
371C4×C61#53711yescharacteristic
372C4×C61#54811yescharacteristic
373C4×C61#55011yescharacteristic
374Dic61—42no—
375Dic61—42no—
376Dic61—42no—
377Dic61—42no—
378C2×#552—611no—
379C2×#478—611no—
380C2×C4×SD16—611no—
381#2535D6111yescharacteristic
382#2036—611no—
383#2035—611no—
384#2000—611no—
385#2000—611no—
386#1991—611no—
387#1954—611no—
388#1875—611no—
389#1874—611no—
390#1854—611no—
391#1853—611no—
392#1805—611no—
393C2×C61—42no—
394C2×C61—81no—
395C2×C61—82no—
396C2×C61#240711yescharacteristic
397C2×C61#300211yescharacteristic
398C2×C61#301011yescharacteristic
399C2×C61#329611yescharacteristic
400C2×C61#332311yescharacteristic
401C2×C61#333711yescharacteristic
402C2×C61#335111yescharacteristic
403C22×SD16—611no—
404#552—1224no—
405#552—1224no—
406C2×#126—1221no—
407C2×#125—611no—
408C2×#125—1221no—
409C2×#123—1221no—
410C2×C22⋊Q8—611no—
411C2×C22⋊Q8—611no—
412C2×#121C2×D6111yescharacteristic
413C2×#121C2×D6111yescharacteristic
414C2×C4×Q8—611no—
415C2×C4×D4C2×D6111yescharacteristic
416C2×C4×D4C2×D6111yescharacteristic
417C2×#117—611no—
418C2×#117—1221no—
419C22×C4⋊C4—611no—
420#478—1224no—
421C4×SD16—1224no—
422C2×#107—611no—
423C2×#106—611no—
424C2×#106—611no—
425C2×C4⋊C8—611no—
426C2×#103—611no—
427C2×#103—611no—
428C2×#103—611no—
429C2×#102—611no—
430C2×#102—611no—
431C2×#102—611no—
432C2×C22⋊C8—611no—
433C2×C22⋊C8—611no—
434C2×C22⋊C8—611no—
435C2×C22⋊C8—611no—
436C2×C4×C8—611no—
437#397—21no—
438#392—21no—
439#386—21no—
440#386—21no—
441#382C2×D6111yescharacteristic
442#380C2×D6111yescharacteristic
443#380C2×D6111yescharacteristic
444#340—611no—
445#340—611no—
446#340—611no—
447#340—611no—
448#340—611no—
449#340—611no—
450C61#2412511yescharacteristic, complemented, Sylow
451C22×Q8—611no—
452C22×D4—21no—
453C22×D4—21no—
454C22×D4C22⋊D6111yescharacteristic
455C22×D4C22×D6111yescharacteristic
456C23×C4—21no—
457C23×C4—1221no—
458C23×C4C22×D6111yescharacteristic
459C23×C4C22×D6111yescharacteristic
460C2×SD16—1222no—
461C2×SD16—1222no—
462C2×SD16—1222no—
463C22×C8—611no—
464C22×C8—611no—
465C22×C8—611no—
466C22×C8—611no—
467#126—1228no—
468#125—614no—
469#125—1228no—
470#125—1222no—
471#123—1228no—
472C22⋊Q8—1222no—
473C22⋊Q8—1222no—
474C22⋊Q8—1222no—
475C22⋊Q8—1222no—
476#121—22no—
477#121—22no—
478#121—41no—
479#121—41no—
480C4×Q8—614no—
481C4×Q8—1222no—
482C4×D4—22no—
483C4×D4—22no—
484C4×D4—22no—
485C4×D4—22no—
486#117—1228no—
487#117—1222no—
488#117—1222no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—1222no—
493C2×C4⋊C4—1222no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4—1221no—
497C2×C4⋊C4—1221no—
498C2×C4⋊C4—1221no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4C22⋊D6111yescharacteristic
501C2×C4⋊C4C22×D6111yescharacteristic
502C2×C4⋊C4C22×D6111yescharacteristic
503C2×C4⋊C4C22×D6111yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4C22⋊D6111yescharacteristic
513C2×C22⋊C4C22⋊D6111yescharacteristic
514C2×C42—1221no—
515C2×C42—1221no—
516C2×C42C22×D6111yescharacteristic
517#107—1222no—
518#106—1222no—
519#106—1222no—
520C4⋊C8—1222no—
521#103—1222no—
522#103—2441no—
523#103—2441no—
524#102—1222no—
525#102—1222no—
526#102—1222no—
527C22⋊C8—1222no—
528C22⋊C8—1222no—
529C22⋊C8—2441no—
530C22⋊C8—2441no—
531C4×C8—1222no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536C24—21no—
537C24C2×C22⋊D6111yescharacteristic
538C24C2×C22⋊D6111yescharacteristic
539C2×Q8—612no—
540C2×Q8—1221no—
541C2×Q8—1221no—
542C2×Q8—1221no—
543C2×Q8—1221no—
544C2×Q8—1221no—
545C2×D4—22no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—41no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—81no—
558C2×D4—81no—
559C2×D4#1175822412yes—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
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—42no—
576C22×C4—81no—
577C22×C4—81no—
578C22×C4—1224no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—2442no—
584C22×C4—2442no—
585C22×C4C2×C22⋊D6111yescharacteristic
586C22×C4C2×C22⋊D6111yescharacteristic
587C22×C4C2×C22⋊D6111yescharacteristic
588C22×C4C2×C22⋊D6111yescharacteristic
589C22×C4C23×D6111yescharacteristic
590SD16—1228no—
591C2×C8—612no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—1221no—
603C4⋊C4—22no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—612no—
611C4⋊C4—612no—
612C4⋊C4—612no—
613C4⋊C4—1224no—
614C4⋊C4—1224no—
615C4⋊C4—1224no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—1224no—
620C4⋊C4—1224no—
621C4⋊C4—1224no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—1224no—
630C22⋊C4—1224no—
631C22⋊C4—1224no—
632C42—1224no—
633C42—1224no—
634C42D4×D6112yes—
635C42D4×D6112yes—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23#1451979712yes—
657C23C22×C22⋊D6111yescharacteristic
658Q8—1222no—
659Q8—1222no—
660Q8—2441no—
661Q8—2441no—
662D4—22no—
663D4—22no—
664D4—44no—
665D4—41no—
666D4—41no—
667D4—84no—
668D4—84no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—84no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—2448no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4#1451974512yes—
711C2×C4#1451974512yes—
712C2×C4C2×D4×D6111yescharacteristic
713C2×C4C2×D4×D6111yescharacteristic
714C2×C4#41×D6111yescharacteristic
715C2×C4C2×#1175822411yescharacteristic
716C2×C4#1451982211yescharacteristic
717C2×C4#1451982411yescharacteristic
718C8—1222no—
719C8—2441no—
720C8—2441no—
721C8—2441no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—42no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—42no—
736C22—42no—
737C22—41no—
738C22—41no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22C2×#1451974511yescharacteristic
744C22#1684040611yescharacteristic
745C22#1684041111yescharacteristic
746C22C2×#1451979711yescharacteristic
747C22#1684056011yescharacteristic
748C22#1684057311yescharacteristic
749C22#1684057311yescharacteristic
750C4—22no—
751C4—22no—
752C4—41no—
753C4—41no—
754C4—81no—
755C4—81no—
756C4—81no—
757C4—2442no—
758C4—2442no—
759C4—2442no—
760C4—2442no—
761C4#1684027211yescharacteristic
762C4#1684034111yescharacteristic
763C4#1684041811yescharacteristic
764C4#1684043011yescharacteristic
765C2—42no—
766C2—81no—
767C2—82no—
768C2#2144916011yescharacteristic
769C2#2145503511yescharacteristic
770C2#2145510311yescharacteristic
771C2#2145765411yescharacteristic
772C2#2145803511yescharacteristic
773C2#2145819211yescharacteristic
774C2#2145837311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#2535C2
socleC23×C61C22×D4
hypercenter#2535D61
hypocenterC61#24125
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. C2×#16840452C2semidirect
2. C2×#16840062C2semidirect
3. C2×C4×#11758200C2semidirect
4. #21447022C2semidirect
5. #21447015C2semidirect
6. #21446822C2semidirect
7. #21446822C2semidirect
8. #21446783C2semidirect
9. #21446614C2semidirect
10. #21446142C2semidirect
11. #21446137C2semidirect
12. #21446016C2semidirect
13. #21446011C2semidirect
14. #21445831C2semidirect
74. #14519769D4semidirect
82. C4×Dic122D4semidirect
450. C61#24125semidirect

Maximal subgroups

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

subgroupindex
C2×#168404522
C2×#168400622
C2×C4×#117582002
#214470222
#214470152
#214468222
#214467832
#214466142
#214461422
#214461372
#214460162
#214460112
#214458312
C61×#25352
#2412561