Finite Group Databasebeta

← #30622521

Subgroups — #30622521

Order 15616.

994 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840797C211yesmaximal, characteristic, complemented
2C2×#16840793C211yesmaximal, characteristic, complemented
3#21461889C211yesmaximal, characteristic, complemented
4#21461888C211yesmaximal, characteristic, complemented
5#21461876C211yesmaximal, characteristic, complemented
6#21461875C211yesmaximal, characteristic, complemented
7#21461796C211yesmaximal, characteristic, complemented
8#21461796C211yesmaximal, characteristic, complemented
9#21461796C211yesmaximal, characteristic, complemented
10#21461792C211yesmaximal, characteristic, complemented
11#21461561C211yesmaximal, characteristic, complemented
12C22⋊C4×#92420C211yesmaximal, characteristic, complemented
13C4×C22⋊#92420C211yesmaximal, characteristic, complemented
14#21461482C211yesmaximal, characteristic, complemented
15#121×Dic61C211yesmaximal, characteristic
16C22×#11758217C2211yescharacteristic
17C22×#11758217C2211yescharacteristic
18C22×#11758217C2211yescharacteristic
19C23×#92420C2211yescharacteristic
20#16840797—24no—
21#16840793—24no—
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×#14519832C2211yescharacteristic
33C2×C4×#92420C2211yescharacteristic
34C2×C4×#92420C2211yescharacteristic
35C2×C4×#92420C2211yescharacteristic
36#16840628C2211yescharacteristic
37#16840628C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
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—22no—
64C2×#11758217—22no—
65C2×#11758217—22no—
66C2×#11758217—22no—
67C2×#11758217—41no—
68C2×#11758217—41no—
69C2×#11758217—41no—
70C22×#92420—22no—
71C22×#92420—22no—
72C22×#92420—41no—
73C22×#92420C2311yescharacteristic
74C22×#92420C2311yescharacteristic
75C22×#92420C2311yescharacteristic
76C22×#92420C2311yescharacteristic
77C22×#92420C2311yescharacteristic
78C22×#92420C2311yescharacteristic
79C22×#92420C2311yescharacteristic
80C22×#92420C2311yescharacteristic
81#14519844—22no—
82C4⋊#92420—22no—
83C22⋊#92420—22no—
84C22⋊#92420—22no—
85C22⋊#92420—22no—
86C22⋊#92420—22no—
87C22⋊#92420—22no—
88C22⋊#92420—41no—
89C22⋊#92420—41no—
90C22⋊#92420D414yescomplemented
91#14519832—22no—
92C4×#92420—22no—
93C4×#92420—41no—
94C4×#92420—41no—
95C23×Dic61C2×C411yescharacteristic
96C23×Dic61C2311yescharacteristic
97C23×Dic61C2311yescharacteristic
98C23×Dic61C2311yescharacteristic
99D4×Dic61—22no—
100D4×Dic61—22no—
101D4×Dic61—22no—
102D4×Dic61—22no—
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—41no—
118C2×C4×Dic61—41no—
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—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—22no—
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—41no—
176C22×Dic61—41no—
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C22×C411yescharacteristic
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C2×D412yes—
185C22×Dic61#4112yes—
186C22×Dic61C2411yescharacteristic
187#11758217—44no—
188#11758217—44no—
189#11758217—44no—
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—21no—
209C2×#92420—21no—
210C2×#92420—44no—
211C2×#92420C2×D412yes—
212C2×#92420C2×D412yes—
213C2×#92420#4112yes—
214C2×#92420#4112yes—
215C4⋊C4×C61—22no—
216C22⋊C4×C61—22no—
217C22⋊C4×C61M1614yescomplemented
218C22⋊Dic61—22no—
219C22⋊Dic61—22no—
220C22⋊Dic61—22no—
221C22⋊Dic61—22no—
222C22⋊Dic61—22no—
223C22⋊Dic61—22no—
224C22⋊Dic61—41no—
225C22⋊Dic61—41no—
226C4⋊Dic61—22no—
227C4⋊Dic61—22no—
228C4⋊Dic61—22no—
229C4⋊Dic61—41no—
230C4×Dic61—21no—
231C4×Dic61—21no—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C4×Dic61—41no—
239C4×Dic61—41no—
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×C61—21no—
258C23×C61—21no—
259C23×C61C4×D412yes—
260C23×C61C2×M1612yes—
261C23×C61C23×C411yescharacteristic
262D4×C61—44no—
263D4×C61—44no—
264D4×C61—44no—
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—21no—
273C2×C4×C61—21no—
274C2×C4×C61—44no—
275C2×C4×C61C2×M1612yes—
276C2×C4×C61C2×M1612yes—
277C2×C4×C61#13112yes—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—22no—
283C2×Dic61—22no—
284C2×Dic61—22no—
285C2×Dic61—22no—
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—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—44no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61C4×D412yes—
311C2×Dic61#13112yes—
312C2×Dic61C22×D411yescharacteristic
313C2×Dic61C2×#4111yescharacteristic
314C2×Dic61C2×#4111yescharacteristic
315C2×Dic61C2×#4111yescharacteristic
316C2×Dic61H(5,𝔽2)11yescharacteristic
317C2×Dic61H(5,𝔽2)11yescharacteristic
318#92420—22no—
319#92420—22no—
320#92420—22no—
321#92420—22no—
322#92420—41no—
323#92420—41no—
324#92420—41no—
325#92420—41no—
326#23118—611nomaximal, Sylow
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—22no—
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×C61—41no—
347C22×C61—41no—
348C22×C61C2×C4×D411yescharacteristic
349C22×C61C4×#4111yescharacteristic
350C22×C61#51811yescharacteristic
351C22×C61C22×M1611yescharacteristic
352C22×C61C2×#13111yescharacteristic
353C22×C61C2×#13111yescharacteristic
354C22×C61#56811yescharacteristic
355C4×C61—22no—
356C4×C61—22no—
357C4×C61—22no—
358C4×C61—41no—
359Dic61—22no—
360Dic61—22no—
361Dic61—41no—
362Dic61—41no—
363Dic61—41no—
364Dic61—41no—
365Dic61—41no—
366Dic61#54611yescharacteristic
367Dic61#54611yescharacteristic
368Dic61#55311yescharacteristic
369Dic61#55311yescharacteristic
370C2×#436—611no—
371C2×#435—611no—
372C4×#121—611no—
373#1923—611no—
374#1923—611no—
375#1917—611no—
376#1916—611no—
377#1870—611no—
378#1870—611no—
379#1870—611no—
380#1869—611no—
381#1753—611no—
382C8×C22⋊C4—611no—
383C4×C22⋊C8—611no—
384#1728—611no—
385C2×C61—42no—
386C2×C61—42no—
387C2×C61—81no—
388C2×C61#236411yescharacteristic
389C2×C61#293111yescharacteristic
390C2×C61D4×M1611yescharacteristic
391C2×C61#296511yescharacteristic
392C2×C61#296911yescharacteristic
393C2×C61#297411yescharacteristic
394C2×C61#297611yescharacteristic
395C22×M16—611no—
396C22×M16—611no—
397C22×M16—611no—
398C23×C8—611no—
399C2×#121#692311yescharacteristic
400C2×C4×D4—611no—
401C2×C4×D4—611no—
402C2×C4×D4—611no—
403C22×C42—611no—
404#436—1224no—
405#435—1224no—
406C2×C4⋊C8—611no—
407C2×C4⋊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×C4×C8—611no—
418C2×C4×C8—611no—
419C2×C4×C8—611no—
420#390—611no—
421#389—611no—
422#388—611no—
423#388—611no—
424#386—611no—
425#386—611no—
426#380—611no—
427C4×C4⋊C4—611no—
428C4×C22⋊C4—611no—
429C4×C22⋊C4—611no—
430#336—611no—
431#336—611no—
432#336—611no—
433#336—611no—
434#336—611no—
435#336—611no—
436#336—611no—
437#336—611no—
438#336—611no—
439#336—611no—
440C61#2311811yescharacteristic, complemented, Sylow
441C22×D4C2×#692311yescharacteristic
442C22×D4C2×#692311yescharacteristic
443C22×D4C2×#692311yescharacteristic
444C23×C4—611no—
445C23×C4—611no—
446C23×C4—611no—
447C23×C4—611no—
448C23×C4C2×#692311yescharacteristic
449C2×M16—1222no—
450C2×M16—1222no—
451C2×M16—1222no—
452C2×M16—1222no—
453C2×M16—1222no—
454C2×M16—1222no—
455C2×M16—2441no—
456C2×M16—2441no—
457C2×M16—2441no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—611no—
461C22×C8—611no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8—611no—
465C22×C8—611no—
466C22×C8—1222no—
467C22×C8—1222no—
468C22×C8—2441no—
469#121—24no—
470C4×D4—1222no—
471C4×D4—1222no—
472C4×D4—1222no—
473C4×D4—1222no—
474C4×D4—2441no—
475C4×D4—2441no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4C2×#692311yescharacteristic
481C2×C22⋊C4—611no—
482C2×C22⋊C4—611no—
483C2×C22⋊C4—611no—
484C2×C22⋊C4—611no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—611no—
487C2×C22⋊C4—611no—
488C2×C22⋊C4—611no—
489C2×C22⋊C4C2×#692311yescharacteristic
490C2×C22⋊C4C2×#692311yescharacteristic
491C2×C42—611no—
492C2×C42—611no—
493C2×C42—611no—
494C2×C42—611no—
495C2×C42—611no—
496C2×C42—611no—
497C2×C42—2441no—
498C2×C42—2441no—
499C4⋊C8—1222no—
500C4⋊C8—1222no—
501C22⋊C8—614no—
502C22⋊C8—1222no—
503C22⋊C8—1222no—
504C22⋊C8—1222no—
505C22⋊C8—1222no—
506C22⋊C8—1222no—
507C22⋊C8—2441no—
508C22⋊C8—2441no—
509#97—1222no—
510C4×C8—1222no—
511C4×C8—2441no—
512C4×C8—2441no—
513#95—611no—
514#95—611no—
515#95—611no—
516#95—611no—
517#95—611no—
518#95—611no—
519C24C22×#692311yescharacteristic
520C24C22×#692311yescharacteristic
521C24C22×#692311yescharacteristic
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—41no—
529C2×D4—41no—
530C2×D4—41no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—41no—
534C22×C4—611no—
535C22×C4—612no—
536C22×C4—612no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—611no—
543C22×C4—611no—
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×C4—2441no—
562C22×C4—2441no—
563C22×C4C22×#692311yescharacteristic
564C22×C4C22×#692311yescharacteristic
565C22×C4C22×#692311yescharacteristic
566C22×C4C22×#692311yescharacteristic
567M16—2444no—
568M16—2444no—
569M16—2444no—
570C2×C8—612no—
571C2×C8—612no—
572C2×C8—612no—
573C2×C8—612no—
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—1221no—
591C2×C8—1221no—
592C2×C8—1221no—
593C2×C8—1221no—
594C2×C8—2444no—
595C4⋊C4—22no—
596C4⋊C4—1222no—
597C4⋊C4—1222no—
598C4⋊C4—1222no—
599C4⋊C4—2441no—
600C22⋊C4—22no—
601C22⋊C4—1222no—
602C22⋊C4—1222no—
603C22⋊C4—1222no—
604C22⋊C4—1222no—
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—2441no—
608C22⋊C4—2441no—
609C22⋊C4#1175821714yescomplemented
610C42—1221no—
611C42—1221no—
612C42—1221no—
613C42—1221no—
614C42—1221no—
615C42—1221no—
616C42—1221no—
617C42—1221no—
618C42—2441no—
619C42—2441no—
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—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23D4×#692312yes—
640C23C2×#1175821712yes—
641C23C23×#692311yescharacteristic
642D4—44no—
643D4—44no—
644D4—44no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—44no—
655C2×C4—611no—
656C2×C4—611no—
657C2×C4—611no—
658C2×C4—611no—
659C2×C4—611no—
660C2×C4—611no—
661C2×C4—612no—
662C2×C4—612no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—1222no—
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—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2444no—
695C2×C4C2×#1175821712yes—
696C2×C4C2×#1175821712yes—
697C2×C4#1451986412yes—
698C8—1222no—
699C8—1222no—
700C8—1222no—
701C8—1222no—
702C8—2441no—
703C8—2441no—
704C8—2441no—
705C8—2441no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22C2×D4×#692311yescharacteristic
728C22#41×#692311yescharacteristic
729C22#1684082911yescharacteristic
730C22C22×#1175821711yescharacteristic
731C22C2×#1451986411yescharacteristic
732C22D61⋊#13111yescharacteristic
733C22#1684084011yescharacteristic
734C4—22no—
735C4—22no—
736C4—22no—
737C4—41no—
738C4—611no—
739C4—611no—
740C4—611no—
741C4—611no—
742C4—1222no—
743C4—1222no—
744C4—2441no—
745C4—2441no—
746C4—2441no—
747C4—2441no—
748C4—2441no—
749C2—42no—
750C2—42no—
751C2—81no—
752C2#2146234711yescharacteristic
753C2#2146254211yescharacteristic
754C2D4×#1175821711yescharacteristic
755C2#2146262811yescharacteristic
756C2#2146265011yescharacteristic
757C2#2146267511yescharacteristic
758C2#2146268811yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
Fitting, prime radicalC2×#121×C61C4
cosocleC22×Dic61C24
hypercenterC2×#121#6923
hypocenterC61#23118
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16840797C2semidirect
2. C2×#16840793C2semidirect
3. #21461889C2semidirect
4. #21461888C2semidirect
5. #21461876C2semidirect
6. #21461875C2semidirect
7. #21461796C2semidirect
8. #21461796C2semidirect
9. #21461796C2semidirect
10. #21461792C2semidirect
11. #21461561C2semidirect
12. C22⋊C4×#92420C2semidirect
13. C4×C22⋊#92420C2semidirect
14. #21461482C2semidirect
90. C22⋊#92420D4semidirect
217. C22⋊C4×C61M16semidirect
440. C61#23118semidirect
609. C22⋊C4#11758217semidirect

Maximal subgroups

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

subgroupindex
C2×#168407972
C2×#168407932
#214618892
#214618882
#214618762
#214618752
#214617962
#214617922
#214615612
C22⋊C4×#924202
C4×C22⋊#924202
#214614822
#121×Dic612
#2311861