Finite Group Databasebeta

← #30622404

Subgroups — #30622404

Order 15616.

978 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840793C211yesmaximal, characteristic, complemented
2C2×#16840779C211yesmaximal, characteristic, complemented
3#21461943C211yesmaximal, characteristic, complemented
4#21461943C211yesmaximal, characteristic, complemented
5#21461940C211yesmaximal, characteristic, complemented
6#21461921C211yesmaximal, characteristic, complemented
7#21461889C211yesmaximal, characteristic, complemented
8#21461888C211yesmaximal, characteristic, complemented
9#21461796C211yesmaximal, characteristic, complemented
10#21461792C211yesmaximal, characteristic, complemented
11#21461619C211yesmaximal, characteristic, complemented
12#21461561C211yesmaximal, characteristic, complemented
13C22⋊C4×#92420C211yesmaximal, characteristic, complemented
14#21461545C211yesmaximal, characteristic, complemented
15#121×Dic61C211yesmaximal, characteristic
16C22×#11758217C2211yescharacteristic
17C23×#92420C2211yescharacteristic
18#16840793—24no—
19#16840779—24no—
20C2×#14519844C2211yescharacteristic
21C2×#14519844C2211yescharacteristic
22C2×#14519844C2211yescharacteristic
23C2×C4⋊#92420C2211yescharacteristic
24C2×C22⋊#92420C2211yescharacteristic
25C2×C22⋊#92420C2211yescharacteristic
26C2×C22⋊#92420C2211yescharacteristic
27C2×C22⋊#92420C2211yescharacteristic
28C2×C22⋊#92420C2211yescharacteristic
29C2×C22⋊#92420C2211yescharacteristic
30C2×C22⋊#92420C2211yescharacteristic
31C2×C22⋊#92420C2211yescharacteristic
32C2×C22⋊#92420C2211yescharacteristic
33C2×C22⋊#92420C2211yescharacteristic
34C2×#14519832C2211yescharacteristic
35C2×#14519832C2211yescharacteristic
36C2×#14519832C2211yescharacteristic
37C2×C4×#92420C2211yescharacteristic
38C2×C4×#92420C2211yescharacteristic
39C2×C4×#92420C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46C2×D4×Dic61C2211yescharacteristic
47C2×D4×Dic61C2211yescharacteristic
48C2×D4×Dic61C2211yescharacteristic
49C22×C4×Dic61C2211yescharacteristic
50#16839665C411yescharacteristic
51#16839661C411yescharacteristic
52#16839655C411yescharacteristic
53#16839655C411yescharacteristic
54#16839642C411yescharacteristic
55#16839642C411yescharacteristic
56#16839622C411yescharacteristic
57C4⋊C4×Dic61C2211yescharacteristic
58C22⋊C4×Dic61C2211yescharacteristic
59C22⋊C4×Dic61C2211yescharacteristic
60C2×#121×C61C411yescharacteristic
61C2×#11758217—22no—
62C2×#11758217—22no—
63C2×#11758217—41no—
64C22×#92420—22no—
65C22×#92420—22no—
66C22×#92420—41no—
67C22×#92420C2311yescharacteristic
68C22×#92420C2311yescharacteristic
69C22×#92420C2311yescharacteristic
70C22×#92420C2311yescharacteristic
71C22×#92420C2311yescharacteristic
72C22×#92420C2311yescharacteristic
73C22×#92420C2311yescharacteristic
74C22×#92420C2311yescharacteristic
75#14519844—22no—
76#14519844—41no—
77#14519844D414yescomplemented
78C4⋊#92420—41no—
79C22⋊#92420—22no—
80C22⋊#92420—22no—
81C22⋊#92420—22no—
82C22⋊#92420—22no—
83C22⋊#92420—22no—
84C22⋊#92420—22no—
85C22⋊#92420—22no—
86C22⋊#92420—22no—
87C22⋊#92420—41no—
88C22⋊#92420—41no—
89#14519832—22no—
90#14519832—22no—
91#14519832—41no—
92C4×#92420—22no—
93C4×#92420—22no—
94C4×#92420—41no—
95C23×Dic61C2×C411yescharacteristic
96C23×Dic61C2311yescharacteristic
97C23×Dic61C2311yescharacteristic
98C23×Dic61C2311yescharacteristic
99D4×Dic61—22no—
100D4×Dic61—22no—
101D4×Dic61—41no—
102D4×Dic61—41no—
103D4×Dic61—41no—
104D4×Dic61—41no—
105C2×C4⋊Dic61C2×C411yescharacteristic
106C2×C4⋊Dic61C2×C411yescharacteristic
107C2×C4⋊Dic61C2×C411yescharacteristic
108C2×C4⋊Dic61C2×C411yescharacteristic
109C2×C22⋊Dic61C2×C411yescharacteristic
110C2×C22⋊Dic61C2×C411yescharacteristic
111C2×C22⋊Dic61C2×C411yescharacteristic
112C2×C22⋊Dic61C2×C411yescharacteristic
113C2×C22⋊Dic61C2×C411yescharacteristic
114C2×C22⋊Dic61C2×C411yescharacteristic
115C2×C22⋊Dic61C2×C411yescharacteristic
116C2×C22⋊Dic61C2×C411yescharacteristic
117C2×C4×Dic61—22no—
118C2×C4×Dic61—22no—
119C2×C4×Dic61C2×C411yescharacteristic
120C2×C4×Dic61C2×C411yescharacteristic
121C2×C4×Dic61C2311yescharacteristic
122C2×C4×Dic61C2311yescharacteristic
123C2×C4×Dic61C2311yescharacteristic
124C2×C4×Dic61C2311yescharacteristic
125#14519684C2×C411yescharacteristic
126#14519684C2×C411yescharacteristic
127#14519684C2×C411yescharacteristic
128#14519684C2×C411yescharacteristic
129#14519684C2×C411yescharacteristic
130#14519684C2×C411yescharacteristic
131C22×D4×C61C2×C411yescharacteristic
132C22×D4×C61C2×C411yescharacteristic
133C22×D4×C61C2×C411yescharacteristic
134C23×C4×C61C2×C411yescharacteristic
135#121×C61—24no—
136C2×C4⋊C4×C61C2×C411yescharacteristic
137C2×C22⋊C4×C61C2×C411yescharacteristic
138C2×C22⋊C4×C61C2×C411yescharacteristic
139C24×C61C22×C411yescharacteristic
140C24×C61C22×C411yescharacteristic
141C24×C61C22×C411yescharacteristic
142C2×D4×C61—22no—
143C2×D4×C61—22no—
144C2×D4×C61—22no—
145C2×D4×C61—22no—
146C2×D4×C61—22no—
147C2×D4×C61—22no—
148C2×D4×C61—41no—
149C2×D4×C61—41no—
150C2×D4×C61—41no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—41no—
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C22×C411yescharacteristic
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C22×Dic61C22×C411yescharacteristic
186C22×Dic61C2411yescharacteristic
187#11758217—44no—
188C2×#92420—21no—
189C2×#92420—21no—
190C2×#92420—21no—
191C2×#92420—21no—
192C2×#92420—21no—
193C2×#92420—21no—
194C2×#92420—21no—
195C2×#92420—21no—
196C2×#92420—21no—
197C2×#92420—21no—
198C2×#92420—21no—
199C2×#92420—21no—
200C2×#92420—21no—
201C2×#92420—21no—
202C2×#92420—21no—
203C2×#92420—21no—
204C2×#92420—21no—
205C2×#92420—21no—
206C2×#92420—21no—
207C2×#92420—21no—
208C2×#92420—44no—
209C2×#92420C2×D412yes—
210C2×#92420C2×D412yes—
211C2×#92420#4112yes—
212C2×#92420#4112yes—
213C4⋊C4×C61—22no—
214C22⋊C4×C61—22no—
215C22⋊C4×C61M1614yescomplemented
216C22⋊Dic61—22no—
217C22⋊Dic61—22no—
218C22⋊Dic61—22no—
219C22⋊Dic61—22no—
220C22⋊Dic61—41no—
221C22⋊Dic61—41no—
222C22⋊Dic61—41no—
223C22⋊Dic61—41no—
224C4⋊Dic61—22no—
225C4⋊Dic61—41no—
226C4⋊Dic61—41no—
227C4⋊Dic61—41no—
228C4×Dic61—22no—
229C4×Dic61—22no—
230C4×Dic61—21no—
231C4×Dic61—21no—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61C2×D412yes—
237C4×Dic61#4112yes—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61C2×M1612yes—
258C23×C61#13112yes—
259C23×C61C23×C411yescharacteristic
260D4×C61—44no—
261D4×C61—44no—
262D4×C61—44no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—44no—
273C2×C4×C61C4×D412yes—
274C2×C4×C61C2×M1612yes—
275C2×C4×C61C2×M1612yes—
276C2×Dic61—28no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61C4×D412yes—
309C2×Dic61#13112yes—
310C2×Dic61C22×D411yescharacteristic
311C2×Dic61C2×#4111yescharacteristic
312C2×Dic61C2×#4111yescharacteristic
313C2×Dic61C2×#4111yescharacteristic
314C2×Dic61H(5,𝔽2)11yescharacteristic
315C2×Dic61H(5,𝔽2)11yescharacteristic
316#92420—22no—
317#92420—22no—
318#92420—22no—
319#92420—22no—
320#92420—41no—
321#92420—41no—
322#92420—41no—
323#92420—41no—
324#23085—611nomaximal, Sylow
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61C2×C4×D411yescharacteristic
347C22×C61C4×#4111yescharacteristic
348C22×C61#51811yescharacteristic
349C22×C61C22×M1611yescharacteristic
350C22×C61C2×#13111yescharacteristic
351C22×C61C2×#13111yescharacteristic
352C22×C61#56811yescharacteristic
353C4×C61—22no—
354C4×C61—22no—
355C4×C61—22no—
356C4×C61—41no—
357Dic61—22no—
358Dic61—22no—
359Dic61—41no—
360Dic61—41no—
361Dic61—41no—
362Dic61—41no—
363Dic61—41no—
364Dic61#54611yescharacteristic
365Dic61#55011yescharacteristic
366Dic61#55311yescharacteristic
367Dic61#55511yescharacteristic
368C2×#435—611no—
369C2×#431—611no—
370C4×#121—611no—
371#1955—611no—
372#1955—611no—
373#1954—611no—
374#1940—611no—
375#1923—611no—
376#1923—611no—
377#1870—611no—
378#1869—611no—
379#1771—611no—
380#1753—611no—
381C8×C22⋊C4—611no—
382#1749—611no—
383C2×C61—42no—
384C2×C61—42no—
385C2×C61—81no—
386C2×C61#236311yescharacteristic
387C2×C61#292911yescharacteristic
388C2×C61D4×M1611yescharacteristic
389C2×C61#296511yescharacteristic
390C2×C61#296811yescharacteristic
391C2×C61#297411yescharacteristic
392C2×C61#298111yescharacteristic
393C22×M16—611no—
394C23×C8—611no—
395C2×#121#692311yescharacteristic
396C2×C4×D4—611no—
397C2×C4×D4—611no—
398C2×C4×D4—611no—
399C22×C42—611no—
400#435—1224no—
401#431—1224no—
402C2×C4⋊C8—611no—
403C2×C4⋊C8—611no—
404C2×C4⋊C8—611no—
405C2×C4⋊C8—611no—
406C2×C22⋊C8—611no—
407C2×C22⋊C8—611no—
408C2×C22⋊C8—611no—
409C2×C22⋊C8—611no—
410C2×C22⋊C8—611no—
411C2×C22⋊C8—611no—
412C2×C22⋊C8—611no—
413C2×C22⋊C8—611no—
414C2×C22⋊C8—611no—
415C2×C22⋊C8—611no—
416C2×#97—611no—
417C2×#97—611no—
418C2×#97—611no—
419C2×C4×C8—611no—
420C2×C4×C8—611no—
421C2×C4×C8—611no—
422#390—611no—
423#389—611no—
424#388—611no—
425#388—611no—
426#386—611no—
427#386—611no—
428#380—611no—
429C4×C4⋊C4—611no—
430C4×C22⋊C4—611no—
431C4×C22⋊C4—611no—
432#336—611no—
433#336—611no—
434#336—611no—
435#336—611no—
436#336—611no—
437#336—611no—
438C61#2308511yescharacteristic, complemented, Sylow
439C22×D4C2×#692311yescharacteristic
440C22×D4C2×#692311yescharacteristic
441C22×D4C2×#692311yescharacteristic
442C23×C4—611no—
443C23×C4—611no—
444C23×C4—611no—
445C23×C4—611no—
446C23×C4C2×#692311yescharacteristic
447C2×M16—1222no—
448C2×M16—1222no—
449C2×M16—2441no—
450C22×C8—611no—
451C22×C8—611no—
452C22×C8—611no—
453C22×C8—611no—
454C22×C8—611no—
455C22×C8—611no—
456C22×C8—611no—
457C22×C8—611no—
458C22×C8—1222no—
459C22×C8—1222no—
460C22×C8—2441no—
461#121—24no—
462C4×D4—1222no—
463C4×D4—1222no—
464C4×D4—2441no—
465C4×D4—2441no—
466C4×D4—2441no—
467C4×D4—2441no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4C2×#692311yescharacteristic
473C2×C22⋊C4—611no—
474C2×C22⋊C4—611no—
475C2×C22⋊C4—611no—
476C2×C22⋊C4—611no—
477C2×C22⋊C4—611no—
478C2×C22⋊C4—611no—
479C2×C22⋊C4—611no—
480C2×C22⋊C4—611no—
481C2×C22⋊C4C2×#692311yescharacteristic
482C2×C22⋊C4C2×#692311yescharacteristic
483C2×C42—611no—
484C2×C42—611no—
485C2×C42—611no—
486C2×C42—611no—
487C2×C42—611no—
488C2×C42—611no—
489C2×C42—1222no—
490C2×C42—1222no—
491C4⋊C8—614no—
492C4⋊C8—1222no—
493C4⋊C8—2441no—
494C4⋊C8—2441no—
495C22⋊C8—1222no—
496C22⋊C8—1222no—
497C22⋊C8—1222no—
498C22⋊C8—1222no—
499C22⋊C8—1222no—
500C22⋊C8—1222no—
501C22⋊C8—1222no—
502C22⋊C8—1222no—
503C22⋊C8—2441no—
504C22⋊C8—2441no—
505#97—1222no—
506#97—1222no—
507#97—2441no—
508C4×C8—1222no—
509C4×C8—1222no—
510C4×C8—2441no—
511#95—611no—
512#95—611no—
513#95—611no—
514#95—611no—
515#95—611no—
516#95—611no—
517C24C22×#692311yescharacteristic
518C24C22×#692311yescharacteristic
519C24C22×#692311yescharacteristic
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—41no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—41no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—611no—
535C22×C4—611no—
536C22×C4—611no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—611no—
540C22×C4—1222no—
541C22×C4—1222no—
542C22×C4—1221no—
543C22×C4—1221no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1222no—
561C22×C4C22×#692311yescharacteristic
562C22×C4C22×#692311yescharacteristic
563C22×C4C22×#692311yescharacteristic
564C22×C4C22×#692311yescharacteristic
565M16—2444no—
566C2×C8—612no—
567C2×C8—612no—
568C2×C8—612no—
569C2×C8—612no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—2444no—
591C4⋊C4—22no—
592C4⋊C4—1222no—
593C4⋊C4—2441no—
594C4⋊C4—2441no—
595C4⋊C4—2441no—
596C22⋊C4—22no—
597C22⋊C4—1222no—
598C22⋊C4—1222no—
599C22⋊C4—1222no—
600C22⋊C4—1222no—
601C22⋊C4—2441no—
602C22⋊C4—2441no—
603C22⋊C4—2441no—
604C22⋊C4—2441no—
605C22⋊C4#1175821714yescomplemented
606C42—612no—
607C42—612no—
608C42—1221no—
609C42—1221no—
610C42—1221no—
611C42—1221no—
612C42—1221no—
613C42—1221no—
614C42—1222no—
615C42—1222no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23C2×#1175821712yes—
636C23#1451986412yes—
637C23C23×#692311yescharacteristic
638D4—44no—
639D4—44no—
640D4—44no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—44no—
651C2×C4—611no—
652C2×C4—611no—
653C2×C4—611no—
654C2×C4—611no—
655C2×C4—611no—
656C2×C4—611no—
657C2×C4—612no—
658C2×C4—612no—
659C2×C4—1228no—
660C2×C4—1221no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—1221no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4D4×#692312yes—
692C2×C4C2×#1175821712yes—
693C2×C4C2×#1175821712yes—
694C8—1222no—
695C8—1222no—
696C8—1222no—
697C8—1222no—
698C8—2441no—
699C8—2441no—
700C8—2441no—
701C8—2441no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22C2×D4×#692311yescharacteristic
724C22#41×#692311yescharacteristic
725C22#1684082911yescharacteristic
726C22C22×#1175821711yescharacteristic
727C22C2×#1451986411yescharacteristic
728C22D61⋊#13111yescharacteristic
729C22#1684084011yescharacteristic
730C4—22no—
731C4—22no—
732C4—22no—
733C4—41no—
734C4—611no—
735C4—611no—
736C4—611no—
737C4—611no—
738C4—1222no—
739C4—1222no—
740C4—2441no—
741C4—2441no—
742C4—2441no—
743C4—2441no—
744C4—2441no—
745C2—42no—
746C2—42no—
747C2—81no—
748C2#2146234611yescharacteristic
749C2#2146253311yescharacteristic
750C2D4×#1175821711yescharacteristic
751C2#2146262811yescharacteristic
752C2#2146264411yescharacteristic
753C2#2146267511yescharacteristic
754C2#2146270711yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
Fitting, prime radicalC2×#121×C61C4
cosocleC22×Dic61C24
hypercenterC2×#121#6923
hypocenterC61#23085
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16840793C2semidirect
2. C2×#16840779C2semidirect
3. #21461943C2semidirect
4. #21461943C2semidirect
5. #21461940C2semidirect
6. #21461921C2semidirect
7. #21461889C2semidirect
8. #21461888C2semidirect
9. #21461796C2semidirect
10. #21461792C2semidirect
11. #21461619C2semidirect
12. #21461561C2semidirect
13. C22⋊C4×#92420C2semidirect
14. #21461545C2semidirect
77. #14519844D4semidirect
215. C22⋊C4×C61M16semidirect
438. C61#23085semidirect
605. C22⋊C4#11758217semidirect

Maximal subgroups

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

subgroupindex
C2×#168407932
C2×#168407792
#214619432
#214619402
#214619212
#214618892
#214618882
#214617962
#214617922
#214616192
#214615612
C22⋊C4×#924202
#214615452
#121×Dic612
#2308561