Finite Group Databasebeta

← #30619310

Subgroups — #30619310

Order 15616.

1030 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840793C211yesmaximal, characteristic, complemented
2C2×#16840792C211yesmaximal, characteristic, complemented
3#21461945C211yesmaximal, characteristic, complemented
4#21461943C211yesmaximal, characteristic, complemented
5#21461798C211yesmaximal, characteristic, complemented
6#21461798C211yesmaximal, characteristic, complemented
7#21461797C211yesmaximal, characteristic, complemented
8#21461797C211yesmaximal, characteristic, complemented
9#21461794C211yesmaximal, characteristic, complemented
10#21461794C211yesmaximal, characteristic, complemented
11#21461793C211yesmaximal, characteristic, complemented
12#21461793C211yesmaximal, characteristic, complemented
13#21461735C211yesmaximal, characteristic, complemented
14#21461536C211yesmaximal, characteristic, complemented
15#21448383C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic
17C22×#11758217C2211yescharacteristic
18C22×D61⋊C8C2211yescharacteristic
19C23×#92420C2211yescharacteristic
20#16840793—24no—
21#16840792—24no—
22C2×#14519844C2211yescharacteristic
23C2×#14519844C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25C2×#14519834C2211yescharacteristic
26C2×#14519834C2211yescharacteristic
27C2×#14519834C2211yescharacteristic
28C2×#14519834C2211yescharacteristic
29C2×#14519834C2211yescharacteristic
30C2×C22⋊#92420C2211yescharacteristic
31C2×C22⋊#92420C2211yescharacteristic
32C2×C22⋊#92420C2211yescharacteristic
33C2×C22⋊#92420C2211yescharacteristic
34C2×C22⋊#92420C2211yescharacteristic
35C2×C22⋊#92420C2211yescharacteristic
36C2×#14519832C2211yescharacteristic
37C2×#14519832C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46C2×#14519773C411yescharacteristic
47C2×D4×Dic61C2211yescharacteristic
48C2×#14519739C2211yescharacteristic
49C2×#14519737C2211yescharacteristic
50C2×#14519737C2211yescharacteristic
51C2×#14519737C2211yescharacteristic
52C2×#14519737C2211yescharacteristic
53#16839664C411yescharacteristic
54#16839662C411yescharacteristic
55#16839662C411yescharacteristic
56#16839662C411yescharacteristic
57#16839662C411yescharacteristic
58#16839631C411yescharacteristic
59C42×Dic61C2211yescharacteristic
60C61×#390C411yescharacteristic
61C2×#11758213—22no—
62C2×#11758213—41no—
63C2×#11758213—41no—
64C2×#11758217—22no—
65C2×#11758217—41no—
66C2×#11758217—41no—
67C2×D61⋊C8—22no—
68C2×D61⋊C8—41no—
69C2×D61⋊C8—41no—
70C22×#92420—22no—
71C22×#92420—41no—
72C22×#92420—41no—
73C22×#92420C2311yescharacteristic
74C22×#92420C2311yescharacteristic
75C22×#92420C2311yescharacteristic
76C22×#92420C2311yescharacteristic
77C22×#92420C2311yescharacteristic
78C22×#92420C2311yescharacteristic
79C22×#92420C2311yescharacteristic
80C22×#92420C2311yescharacteristic
81#14519844—22no—
82#14519844—22no—
83#14519834—22no—
84#14519834—22no—
85#14519834—41no—
86#14519834—41no—
87#14519834—41no—
88#14519834—41no—
89C22⋊#92420—22no—
90C22⋊#92420—22no—
91C22⋊#92420—41no—
92C22⋊#92420—41no—
93C22⋊#92420—41no—
94C22⋊#92420—41no—
95#14519832—22no—
96#14519832D414yescomplemented
97C22×D244C2×C411yescharacteristic
98C22×C22⋊D61C2×C411yescharacteristic
99C22×C22⋊D61C2×C411yescharacteristic
100C22×C22⋊D61C2×C411yescharacteristic
101C22×C22⋊D61C2×C411yescharacteristic
102C23×Dic61C2311yescharacteristic
103C23×Dic61C2311yescharacteristic
104C22×C4×D61C2311yescharacteristic
105C22×C4×D61C2311yescharacteristic
106#14519773—24no—
107D4×Dic61—22no—
108D4×Dic61—22no—
109#14519739—22no—
110#14519739—22no—
111#14519737—41no—
112#14519737—41no—
113#14519737—41no—
114#14519737—41no—
115#14519737—41no—
116#14519737—41no—
117#14519737—41no—
118#14519737—41no—
119C2×C4⋊Dic61C2×C411yescharacteristic
120C2×#11758196C2×C411yescharacteristic
121C2×#11758196C2×C411yescharacteristic
122C2×#11758196C2×C411yescharacteristic
123C2×#11758196C2×C411yescharacteristic
124C2×C22⋊Dic61C2×C411yescharacteristic
125C2×C22⋊Dic61C2×C411yescharacteristic
126C2×#11758198C2×C411yescharacteristic
127C2×#11758198C2×C411yescharacteristic
128C2×#11758198C2×C411yescharacteristic
129C2×#11758198C2×C411yescharacteristic
130C2×#11758198C2×C411yescharacteristic
131C2×#11758198C2×C411yescharacteristic
132C2×C4×Dic61C2×C411yescharacteristic
133C2×C4×Dic61C2×C411yescharacteristic
134C2×C4×Dic61C2×C411yescharacteristic
135C2×C4×Dic61C2311yescharacteristic
136C2×C4×Dic61C2311yescharacteristic
137C2×C4×Dic61C2311yescharacteristic
138C22×D4×C61C2×C411yescharacteristic
139C2×C4⋊C4×C61C2×C411yescharacteristic
140C2×C22⋊C4×C61C2×C411yescharacteristic
141C2×C22⋊C4×C61C2×C411yescharacteristic
142C2×C22⋊C4×C61C2×C411yescharacteristic
143C2×C22⋊C4×C61C2×C411yescharacteristic
144C2×C42×C61C2×C411yescharacteristic
145C24×C61C22×C411yescharacteristic
146C24×C61C22×C411yescharacteristic
147C23×D61C22×C411yescharacteristic
148C23×D61C22×C411yescharacteristic
149C2×D4×C61—22no—
150C2×D4×C61—22no—
151C2×D4×C61—41no—
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—41no—
163C2×C22⋊D61—41no—
164C2×C22⋊D61—41no—
165C2×C22⋊D61—41no—
166C2×C22⋊D61—41no—
167C2×C22⋊D61—41no—
168C2×C22⋊D61M1614yescomplemented
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×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61C22×C411yescharacteristic
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C22×Dic61C22×C411yescharacteristic
186C22×Dic61C2411yescharacteristic
187C2×D244—22no—
188C2×D244—22no—
189C2×D244—41no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202#11758217—44no—
203C2×#92420—21no—
204C2×#92420—21no—
205C2×#92420—21no—
206C2×#92420—21no—
207C2×#92420—21no—
208C2×#92420—21no—
209C2×#92420—21no—
210C2×#92420—21no—
211C2×#92420—21no—
212C2×#92420—21no—
213C2×#92420—21no—
214C2×#92420—21no—
215C2×#92420—21no—
216C2×#92420—21no—
217C2×#92420—21no—
218C2×#92420—21no—
219C2×#92420—21no—
220C2×#92420—21no—
221C2×#92420—21no—
222C2×#92420—21no—
223C2×#92420—21no—
224C2×#92420—21no—
225C2×#92420—44no—
226C2×#92420C2×D412yes—
227C2×#92420C2×D412yes—
228#11758213—44no—
229D61⋊C8—44no—
230C4⋊C4×C61—22no—
231C22⋊C4×C61—41no—
232C22⋊C4×C61—41no—
233C22⋊C4×C61—41no—
234C22⋊C4×C61—41no—
235C42×C61—41no—
236C22⋊Dic61—22no—
237C22⋊Dic61—22no—
238#11758198—22no—
239#11758198—22no—
240#11758198—41no—
241#11758198—41no—
242#11758198—41no—
243#11758198—41no—
244C4⋊Dic61—22no—
245#11758196—41no—
246#11758196—41no—
247#11758196—41no—
248#11758196—41no—
249C4×Dic61—22no—
250C4×Dic61—22no—
251C4×Dic61—21no—
252C4×Dic61—21no—
253C4×Dic61—21no—
254C4×Dic61—21no—
255C4×Dic61—41no—
256C4×Dic61C2×D412yes—
257C4×Dic61#4112yes—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61C2×M1612yes—
272C23×C61C23×C411yescharacteristic
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282C22×D61—21no—
283C22×D61—21no—
284C22×D61—21no—
285C22×D61—21no—
286C22×D61C2×M1612yes—
287D4×C61—44no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61C4×D412yes—
303C22⋊D61—44no—
304C22⋊D61—44no—
305C22⋊D61—44no—
306C22⋊D61—44no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61C4×D412yes—
328C2×Dic61C2×M1612yes—
329C2×Dic61#13112yes—
330C2×Dic61C22×D411yescharacteristic
331C2×Dic61C2×#4111yescharacteristic
332C2×Dic61H(5,𝔽2)11yescharacteristic
333C2×Dic61H(5,𝔽2)11yescharacteristic
334C2×Dic61H(5,𝔽2)11yescharacteristic
335C2×Dic61H(5,𝔽2)11yescharacteristic
336D244—44no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—41no—
340C4×D61—41no—
341C4×D61—41no—
342C4×D61—41no—
343C4×D61—41no—
344C4×D61—41no—
345#92420—22no—
346#92420—22no—
347#92420—41no—
348#92420—41no—
349#92420—41no—
350#92420—41no—
351#92420—41no—
352#92420—41no—
353#22266—611nomaximal, Sylow
354C22×C61—22no—
355C22×C61—22no—
356C22×C61—22no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61C2×C4×D411yescharacteristic
369C22×C61#51811yescharacteristic
370C22×C61#51811yescharacteristic
371C22×C61C22×M1611yescharacteristic
372C22×C61C2×#13111yescharacteristic
373C22×C61#56811yescharacteristic
374C22×C61#56811yescharacteristic
375C2×D61—22no—
376C2×D61—22no—
377C2×D61—22no—
378C2×D61—41no—
379C2×D61—41no—
380C2×D61—41no—
381C2×D61—41no—
382C2×D61—41no—
383C2×D61—41no—
384C2×D61—41no—
385C2×D61—41no—
386C2×D61—41no—
387C2×D61—41no—
388C2×D61—41no—
389C4×C61—22no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61—41no—
393C4×C61—41no—
394Dic61—22no—
395Dic61—22no—
396Dic61—22no—
397Dic61—41no—
398Dic61—41no—
399Dic61#53511yescharacteristic
400Dic61#53511yescharacteristic
401Dic61#54011yescharacteristic
402Dic61#54011yescharacteristic
403C2×#435—611no—
404C2×#435—611no—
405C4×#127—611no—
406#1955—611no—
407#1955—611no—
408#1870—611no—
409#1870—611no—
410#1870—611no—
411#1870—611no—
412#1869—611no—
413#1869—611no—
414#1869—611no—
415#1869—611no—
416#1831—611no—
417#1745—611no—
418C2×C61—42no—
419C2×C61—81no—
420C2×C61#232811yescharacteristic
421C2×C61D4×M1611yescharacteristic
422C2×C61#293511yescharacteristic
423C2×C61#297311yescharacteristic
424C2×C61#297411yescharacteristic
425C2×C61#298011yescharacteristic
426C2×C61#298111yescharacteristic
427D61—42no—
428D61—81no—
429C22×M16—611no—
430C22×M16—611no—
431C23×C8—611no—
432C23×C8—611no—
433C2×#127—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×C4×D4—611no—
437C2×C4×D4—611no—
438C2×C4×D4—611no—
439C2×C4×D4—611no—
440#435—1224no—
441#435—1224no—
442C2×C4⋊C8—611no—
443C2×C4⋊C8—611no—
444C2×C22⋊C8—611no—
445C2×C22⋊C8—611no—
446C2×C22⋊C8—611no—
447C2×C22⋊C8—611no—
448C2×C22⋊C8—611no—
449C2×C22⋊C8—611no—
450C2×C22⋊C8—611no—
451C2×C22⋊C8—611no—
452C2×C22⋊C8—611no—
453C2×C22⋊C8—611no—
454C2×C22⋊C8—611no—
455C2×C22⋊C8—611no—
456C2×#97—611no—
457C2×#97—611no—
458#390—611no—
459#390—611no—
460#390—611no—
461#390—611no—
462#390—611no—
463#390#692311yescharacteristic
464#384—611no—
465C43—611no—
466#336—611no—
467#336—611no—
468#336—611no—
469#336—611no—
470#336—611no—
471#336—611no—
472#336—611no—
473#336—611no—
474C61#2226611yescharacteristic, complemented, Sylow
475C22×D4—611no—
476C22×D4—611no—
477C22×D4—611no—
478C22×D4—611no—
479C22×D4—611no—
480C22×D4C2×#692311yescharacteristic
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—611no—
485C2×M16—1222no—
486C2×M16—1222no—
487C2×M16—2441no—
488C2×M16—2441no—
489C2×M16—2441no—
490C2×M16—2441no—
491C22×C8—611no—
492C22×C8—611no—
493C22×C8—611no—
494C22×C8—611no—
495C22×C8—611no—
496C22×C8—611no—
497C22×C8—611no—
498C22×C8—611no—
499C22×C8—1222no—
500C22×C8—1222no—
501C22×C8—2441no—
502C22×C8—2441no—
503C22×C8—2441no—
504C22×C8—2441no—
505#127—1224no—
506C4×D4—1222no—
507C4×D4—1222no—
508C4×D4—1222no—
509C4×D4—1222no—
510C4×D4—2441no—
511C4×D4—2441no—
512C4×D4—2441no—
513C4×D4—2441no—
514C4×D4—2441no—
515C4×D4—2441no—
516C4×D4—2441no—
517C4×D4—2441no—
518C2×C4⋊C4—611no—
519C2×C4⋊C4—611no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—611no—
523C2×C4⋊C4C2×#692311yescharacteristic
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—611no—
527C2×C22⋊C4—611no—
528C2×C22⋊C4—611no—
529C2×C22⋊C4—611no—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—611no—
532C2×C22⋊C4C2×#692311yescharacteristic
533C2×C22⋊C4C2×#692311yescharacteristic
534C2×C22⋊C4C2×#692311yescharacteristic
535C2×C22⋊C4C2×#692311yescharacteristic
536C2×C42—611no—
537C2×C42—611no—
538C2×C42—611no—
539C2×C42—611no—
540C2×C42—611no—
541C2×C42—611no—
542C2×C42C2×#692311yescharacteristic
543C4⋊C8—1222no—
544C4⋊C8—1222no—
545C22⋊C8—1222no—
546C22⋊C8—1222no—
547C22⋊C8—1222no—
548C22⋊C8—1222no—
549C22⋊C8—2441no—
550C22⋊C8—2441no—
551C22⋊C8—2441no—
552C22⋊C8—2441no—
553C22⋊C8—2441no—
554C22⋊C8—2441no—
555C22⋊C8—2441no—
556C22⋊C8—2441no—
557#97—614no—
558#97—1222no—
559C24—611no—
560C24—611no—
561C24C22×#692311yescharacteristic
562C24C22×#692311yescharacteristic
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—41no—
566C2×D4—614no—
567C2×D4—1222no—
568C2×D4—1222no—
569C2×D4—1222no—
570C2×D4—1222no—
571C2×D4—1222no—
572C2×D4—1222no—
573C2×D4—1222no—
574C2×D4—2441no—
575C2×D4—2441no—
576C2×D4—2441no—
577C2×D4—2441no—
578C2×D4—2441no—
579C2×D4—2441no—
580C2×D4—2441no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4—1221no—
607C22×C4—1221no—
608C22×C4—1221no—
609C22×C4—1221no—
610C22×C4—1221no—
611C22×C4C22×#692311yescharacteristic
612C22×C4C22×#692311yescharacteristic
613C22×C4C22×#692311yescharacteristic
614C22×C4C22×#692311yescharacteristic
615C22×C4C22×#692311yescharacteristic
616M16—2444no—
617M16—2444no—
618C2×C8—612no—
619C2×C8—612no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—1221no—
631C2×C8—1221no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—2444no—
643C2×C8—2444no—
644C4⋊C4—22no—
645C4⋊C4—1222no—
646C4⋊C4—2441no—
647C4⋊C4—2441no—
648C4⋊C4—2441no—
649C4⋊C4—2441no—
650C22⋊C4—41no—
651C22⋊C4—41no—
652C22⋊C4—41no—
653C22⋊C4—41no—
654C22⋊C4—1222no—
655C22⋊C4—1222no—
656C22⋊C4—1222no—
657C22⋊C4—1222no—
658C22⋊C4—2441no—
659C22⋊C4—2441no—
660C22⋊C4—2441no—
661C22⋊C4—2441no—
662C42—41no—
663C42—612no—
664C42—612no—
665C42—1222no—
666C42—1221no—
667C42—1221no—
668C42—1221no—
669C42—1221no—
670C42—1222no—
671C42—2441no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—612no—
686C23—1221no—
687C23—1221no—
688C23—1221no—
689C23—1221no—
690C23—1221no—
691C23—1221no—
692C23—1221no—
693C23—1221no—
694C23—1221no—
695C23—1221no—
696C23—1221no—
697C23—1221no—
698C23—1221no—
699C23D61⋊M1612yes—
700C23C23×#692311yescharacteristic
701D4—44no—
702D4—2444no—
703D4—2444no—
704D4—2444no—
705D4—2444no—
706D4—2444no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—611no—
722C2×C4—611no—
723C2×C4—611no—
724C2×C4—611no—
725C2×C4—611no—
726C2×C4—611no—
727C2×C4—612no—
728C2×C4—612no—
729C2×C4—612no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—1221no—
734C2×C4—1221no—
735C2×C4—1221no—
736C2×C4—1221no—
737C2×C4—1221no—
738C2×C4—1221no—
739C2×C4—1221no—
740C2×C4—1221no—
741C2×C4—1221no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2441no—
758C2×C4D4×#692312yes—
759C8—1222no—
760C8—1222no—
761C8—2441no—
762C8—2441no—
763C8—2441no—
764C8—2441no—
765C8—2441no—
766C8—2441no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—1222no—
782C22—1222no—
783C22—1222no—
784C22—2441no—
785C22—2441no—
786C22—2441no—
787C22—2441no—
788C22—2441no—
789C22—2441no—
790C22—2441no—
791C22—2441no—
792C22—2441no—
793C22—2441no—
794C22—2441no—
795C22C2×D4×#692311yescharacteristic
796C22#1684082911yescharacteristic
797C22#1684082911yescharacteristic
798C22C2×D61⋊M1611yescharacteristic
799C22D61⋊#13111yescharacteristic
800C22#1684084011yescharacteristic
801C22#1684084111yescharacteristic
802C4—22no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—611no—
808C4—611no—
809C4—611no—
810C4—611no—
811C4—1222no—
812C4—1222no—
813C4—1222no—
814C4—2441no—
815C4—2441no—
816C2—42no—
817C2—81no—
818C2—4881no—
819C2—2442no—
820C2#2146231111yescharacteristic
821C2#2146255711yescharacteristic
822C2#2146256411yescharacteristic
823C2#2146267111yescharacteristic
824C2#2146267611yescharacteristic
825C2#2146270311yescharacteristic
826C2#2146270711yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#390C4
prime radicalC2×#14519773C4
cosocleC22×Dic61C24
hypercenter#390#6923
hypocenterC61#22266
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#16840793C2semidirect
2. C2×#16840792C2semidirect
3. #21461945C2semidirect
4. #21461943C2semidirect
5. #21461798C2semidirect
6. #21461798C2semidirect
7. #21461797C2semidirect
8. #21461797C2semidirect
9. #21461794C2semidirect
10. #21461794C2semidirect
11. #21461793C2semidirect
12. #21461793C2semidirect
13. #21461735C2semidirect
14. #21461536C2semidirect
96. #14519832D4semidirect
168. C2×C22⋊D61M16semidirect
474. C61#22266semidirect

Maximal subgroups

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

subgroupindex
C2×#168407932
C2×#168407922
#214619452
#214619432
#214617982
#214617972
#214617942
#214617932
#214617352
#214615362
#214483832
#2226661