Finite Group Databasebeta

← #30622128

Subgroups — #30622128

Order 15616.

1098 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840794C211yesmaximal, characteristic, complemented
2C2×#16840793C211yesmaximal, characteristic, complemented
3C2×#16840789C211yesmaximal, characteristic, complemented
4C2×D61⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
5#21461943C211yesmaximal, characteristic, complemented
6#21461921C211yesmaximal, characteristic, complemented
7#21461893C211yesmaximal, characteristic, complemented
8#21461888C211yesmaximal, characteristic, complemented
9#21461793C211yesmaximal, characteristic, complemented
10#21461793C211yesmaximal, characteristic, complemented
11#21461766C211yesmaximal, characteristic, complemented
12#21461762C211yesmaximal, characteristic, complemented
13#21461619C211yesmaximal, characteristic, complemented
14#21461546C211yesmaximal, characteristic, complemented
15#21448335C211yesmaximal, characteristic
16C22×#11758217C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C22×D61⋊C8C2211yescharacteristic
19C23×#92420C2211yescharacteristic
20#16840794—24no—
21#16840793—24no—
22#16840789—24no—
23C2×#14519844C2211yescharacteristic
24C2×#14519844C2211yescharacteristic
25C2×#14519844C2211yescharacteristic
26D61⋊(C4⋊C8)—24no—
27C2×C4⋊#92420C2211yescharacteristic
28C2×C4⋊#92420C2211yescharacteristic
29C2×C4⋊#92420C2211yescharacteristic
30C2×#14519834C2211yescharacteristic
31C2×#14519834C2211yescharacteristic
32C2×C22⋊#92420C2211yescharacteristic
33C2×C22⋊#92420C2211yescharacteristic
34C2×C22⋊#92420C2211yescharacteristic
35C2×C22⋊#92420C2211yescharacteristic
36C2×C22⋊#92420C2211yescharacteristic
37C2×C22⋊#92420C2211yescharacteristic
38C2×#14519832C2211yescharacteristic
39C2×#14519832C2211yescharacteristic
40C2×#14519832C2211yescharacteristic
41C2×C4×#92420C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46#16840628C2211yescharacteristic
47#16840628C2211yescharacteristic
48C2×#14519748C411yescharacteristic
49C2×D4×Dic61C2211yescharacteristic
50C2×#14519737C2211yescharacteristic
51C2×#14519737C2211yescharacteristic
52C2×C42×D61C2211yescharacteristic
53#16839660C411yescharacteristic
54#16839656C411yescharacteristic
55#16839656C411yescharacteristic
56#16839638C411yescharacteristic
57#16839638C411yescharacteristic
58#16839619C411yescharacteristic
59C4⋊C4×Dic61C2211yescharacteristic
60C22⋊C4×Dic61C2211yescharacteristic
61C22⋊C4×Dic61C2211yescharacteristic
62C61×#390C411yescharacteristic
63C2×#11758217—22no—
64C2×#11758217—22no—
65C2×#11758217—41no—
66C2×D61⋊C8—22no—
67C2×D61⋊C8—22no—
68C2×D61⋊C8—22no—
69C2×D61⋊C8—22no—
70C2×D61⋊C8—41no—
71C2×D61⋊C8—41no—
72C22×#92420—22no—
73C22×#92420—22no—
74C22×#92420—41no—
75C22×#92420C2311yescharacteristic
76C22×#92420C2311yescharacteristic
77C22×#92420C2311yescharacteristic
78C22×#92420C2311yescharacteristic
79C22×#92420C2311yescharacteristic
80C22×#92420C2311yescharacteristic
81C22×#92420C2311yescharacteristic
82C22×#92420C2311yescharacteristic
83#14519844—22no—
84#14519844—22no—
85#14519844D414yescomplemented
86C4⋊#92420—22no—
87C4⋊#92420—22no—
88C4⋊#92420—22no—
89#14519834—22no—
90#14519834D414yescomplemented
91C22⋊#92420—22no—
92C22⋊#92420—22no—
93C22⋊#92420—22no—
94C22⋊#92420—22no—
95C22⋊#92420—41no—
96C22⋊#92420—41no—
97#14519832—22no—
98#14519832—22no—
99#14519832—22no—
100C4×#92420—22no—
101C22×C22⋊D61C2×C411yescharacteristic
102C22×C22⋊D61C2×C411yescharacteristic
103C23×Dic61C2311yescharacteristic
104C23×Dic61C2311yescharacteristic
105C22×C4×D61C2×C411yescharacteristic
106C22×C4×D61C2×C411yescharacteristic
107C22×C4×D61C2311yescharacteristic
108#14519748—24no—
109D4×Dic61—22no—
110D4×Dic61—22no—
111#14519737—22no—
112#14519737—22no—
113#14519737—22no—
114#14519737—22no—
115C2×C4⋊Dic61C2×C411yescharacteristic
116C2×C4⋊Dic61C2×C411yescharacteristic
117C2×#11758196C2×C411yescharacteristic
118C2×#11758196C2×C411yescharacteristic
119C2×C22⋊Dic61C2×C411yescharacteristic
120C2×C22⋊Dic61C2×C411yescharacteristic
121C2×C22⋊Dic61C2×C411yescharacteristic
122C2×C22⋊Dic61C2×C411yescharacteristic
123C2×#11758198C2×C411yescharacteristic
124C2×#11758198C2×C411yescharacteristic
125C2×C4×Dic61C2×C411yescharacteristic
126C2×C4×Dic61C2311yescharacteristic
127C2×C4×Dic61C2311yescharacteristic
128C2×C4×Dic61C2311yescharacteristic
129C2×C4×Dic61C2311yescharacteristic
130C42×D61—22no—
131C42×D61—22no—
132#14519684C2×C411yescharacteristic
133#14519684C2×C411yescharacteristic
134#14519684C2×C411yescharacteristic
135#14519684C2×C411yescharacteristic
136#14519684C2×C411yescharacteristic
137#14519684C2×C411yescharacteristic
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
148C2×D4×C61—22no—
149C2×D4×C61—22no—
150C2×D4×C61—41no—
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61M1614yescomplemented
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×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C2411yescharacteristic
181C2×C4×D61—22no—
182C2×C4×D61—22no—
183C2×C4×D61—22no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—22no—
189C2×C4×D61—22no—
190C2×C4×D61—41no—
191C2×C4×D61C2×D412yes—
192C2×C4×D61#4112yes—
193#11758217—44no—
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—21no—
211C2×#92420—21no—
212C2×#92420—21no—
213C2×#92420—21no—
214C2×#92420—44no—
215C2×#92420C2×D412yes—
216C2×#92420C2×D412yes—
217C2×#92420C2×D412yes—
218C2×#92420C2×D412yes—
219D61⋊C8—44no—
220D61⋊C8—44no—
221C4⋊C4×C61—41no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61—22no—
224C22⋊C4×C61—22no—
225C22⋊C4×C61—22no—
226C42×C61—22no—
227C22⋊Dic61—22no—
228C22⋊Dic61—22no—
229C22⋊Dic61—22no—
230C22⋊Dic61—22no—
231#11758198—22no—
232#11758198—22no—
233C4⋊Dic61—22no—
234C4⋊Dic61—22no—
235#11758196—22no—
236#11758196—22no—
237C4×Dic61—22no—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—21no—
241C4×Dic61—21no—
242C4×Dic61—21no—
243C4×Dic61—21no—
244C4×Dic61C2×D412yes—
245C4×Dic61#4112yes—
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×C61C2×M1612yes—
260C23×C61C23×C411yescharacteristic
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61C4×D412yes—
266C22×D61C2×M1612yes—
267C22×D61#13112yes—
268D4×C61—44no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61C4×D412yes—
282C2×C4×C61C4×D412yes—
283C2×C4×C61#13112yes—
284C22⋊D61—28no—
285C22⋊D61—44no—
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—21no—
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×Dic61C2×M1612yes—
312C2×Dic61C22×D411yescharacteristic
313C2×Dic61C22×D411yescharacteristic
314C2×Dic61C2×#4111yescharacteristic
315C2×Dic61C2×#4111yescharacteristic
316C2×Dic61H(5,𝔽2)11yescharacteristic
317C2×Dic612−1+411yescharacteristic
318C4×D61—28no—
319C4×D61—22no—
320C4×D61—22no—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—44no—
324#92420—22no—
325#92420—22no—
326#92420—22no—
327#92420—22no—
328#92420—41no—
329#92420—41no—
330#92420—41no—
331#92420—41no—
332#22987—611nomaximal, Sylow
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
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×C61C2×C4×D411yescharacteristic
348C22×C61C2×C4×D411yescharacteristic
349C22×C61#52011yescharacteristic
350C22×C61C22×M1611yescharacteristic
351C22×C61C2×#13111yescharacteristic
352C22×C61C2×#13111yescharacteristic
353C22×C61#56811yescharacteristic
354C2×D61—22no—
355C2×D61—22no—
356C2×D61—22no—
357C2×D61—22no—
358C2×D61—22no—
359C2×D61—22no—
360C2×D61#43514yescomplemented
361C4×C61—22no—
362C4×C61—22no—
363C4×C61—22no—
364C4×C61—41no—
365C4×C61—41no—
366Dic61—22no—
367Dic61—22no—
368Dic61—41no—
369Dic61—41no—
370Dic61—41no—
371Dic61—41no—
372Dic61D4211yescharacteristic
373Dic61#54711yescharacteristic
374Dic61#54811yescharacteristic
375Dic61#55311yescharacteristic
376C2×#435—611no—
377C2×#435—611no—
378C2×C8×D4—611no—
379C22×C4⋊C8—611no—
380C4×#121—611no—
381#1955—611no—
382#1940—611no—
383#1924—611no—
384#1923—611no—
385#1869—611no—
386#1869—611no—
387#1851—611no—
388#1850—611no—
389#1771—611no—
390#1749—611no—
391C2×C61—42no—
392C2×C61—81no—
393C2×C61#236111yescharacteristic
394C2×C61C2×#43511yescharacteristic
395C2×C61#292911yescharacteristic
396C2×C61D4×M1611yescharacteristic
397C2×C61#293511yescharacteristic
398C2×C61#299011yescharacteristic
399C2×C61#299211yescharacteristic
400D61—24no—
401C22×M16—611no—
402C23×C8—611no—
403C23×C8—611no—
404C23×C8—611no—
405C2×#121—611no—
406C2×C4×D4—611no—
407C2×C4×D4—611no—
408C2×C4×D4—611no—
409C22×C42—611no—
410#435—1224no—
411#435—1224no—
412C8×D4—1224no—
413C2×C4⋊C8—611no—
414C2×C4⋊C8—611no—
415C2×C4⋊C8—611no—
416C2×C4⋊C8—611no—
417C2×C4⋊C8—611no—
418C2×C4⋊C8—611no—
419C2×C4⋊C8—1224no—
420C2×C22⋊C8—611no—
421C2×C22⋊C8—611no—
422C2×C22⋊C8—611no—
423C2×C22⋊C8—611no—
424C2×C22⋊C8—611no—
425C2×C22⋊C8—611no—
426C2×C22⋊C8—611no—
427C2×C22⋊C8—611no—
428C2×#97—611no—
429C2×#97—611no—
430C2×#97—611no—
431C2×C4×C8—611no—
432#390#692311yescharacteristic
433#389—611no—
434#388—611no—
435#388—611no—
436#386—611no—
437#386—611no—
438#380—611no—
439C4×C4⋊C4—611no—
440C4×C22⋊C4—611no—
441C4×C22⋊C4—611no—
442#336—611no—
443#336—611no—
444#336—611no—
445#336—611no—
446#336—611no—
447#336—611no—
448C61#2298711yescharacteristic, complemented, Sylow
449C22×D4—611no—
450C22×D4—611no—
451C22×D4C2×#692311yescharacteristic
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C2×M16—1222no—
458C2×M16—1222no—
459C2×M16—2441no—
460C22×C8—611no—
461C22×C8—611no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8—611no—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8—611no—
468C22×C8—1222no—
469C22×C8—1222no—
470C22×C8—1222no—
471C22×C8—1222no—
472C22×C8—1222no—
473C22×C8—1222no—
474C22×C8—2441no—
475C22×C8—2441no—
476C22×C8—2441no—
477#121—1224no—
478C4×D4—1222no—
479C4×D4—1222no—
480C4×D4—1222no—
481C4×D4—1222no—
482C4×D4—1222no—
483C4×D4—1222no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4C2×#692311yescharacteristic
489C2×C22⋊C4—611no—
490C2×C22⋊C4—611no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—611no—
493C2×C22⋊C4—611no—
494C2×C22⋊C4—611no—
495C2×C22⋊C4C2×#692311yescharacteristic
496C2×C22⋊C4C2×#692311yescharacteristic
497C2×C22⋊C4C2×#692311yescharacteristic
498C2×C22⋊C4C2×#692311yescharacteristic
499C2×C42—611no—
500C2×C42—611no—
501C2×C42—611no—
502C2×C42—611no—
503C2×C42—611no—
504C2×C42—1222no—
505C2×C42—1222no—
506C2×C42C2×#692311yescharacteristic
507C4⋊C8—614no—
508C4⋊C8—1222no—
509C4⋊C8—1222no—
510C4⋊C8—1222no—
511C4⋊C8—1222no—
512C4⋊C8—1222no—
513C22⋊C8—614no—
514C22⋊C8—1222no—
515C22⋊C8—1222no—
516C22⋊C8—1222no—
517C22⋊C8—1222no—
518C22⋊C8—1222no—
519C22⋊C8—2441no—
520C22⋊C8—2441no—
521#97—1222no—
522#97—1222no—
523#97—1222no—
524C4×C8—1222no—
525#95—611no—
526#95—611no—
527#95—611no—
528#95—611no—
529#95—611no—
530#95—611no—
531C24—611no—
532C24C22×#692311yescharacteristic
533C24C22×#692311yescharacteristic
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—41no—
537C2×D4—614no—
538C2×D4—1222no—
539C2×D4—1222no—
540C2×D4—1222no—
541C2×D4—1222no—
542C2×D4—1222no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—612no—
547C22×C4—612no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—611no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1222no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1222no—
558C22×C4—1222no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—2441no—
574C22×C4C22×#692311yescharacteristic
575C22×C4C22×#692311yescharacteristic
576C22×C4C22×#692311yescharacteristic
577C22×C4C22×#692311yescharacteristic
578C22×C4C22×#692311yescharacteristic
579M16—2444no—
580C2×C8—612no—
581C2×C8—612no—
582C2×C8—612no—
583C2×C8—612no—
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—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—
603C2×C8—1221no—
604C2×C8—2444no—
605C2×C8—2444no—
606C2×C8—2444no—
607C4⋊C4—41no—
608C4⋊C4—1222no—
609C4⋊C4—1222no—
610C4⋊C4—1222no—
611C4⋊C4—1222no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—1222no—
617C22⋊C4—1222no—
618C22⋊C4—1222no—
619C22⋊C4—1222no—
620C22⋊C4—1222no—
621C22⋊C4—1222no—
622C42—22no—
623C42—612no—
624C42—612no—
625C42—1221no—
626C42—1221no—
627C42—1221no—
628C42—1221no—
629C42—1222no—
630C42—1221no—
631C42—1221no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—612no—
646C23—612no—
647C23—612no—
648C23—1221no—
649C23—1221no—
650C23—1221no—
651C23—1221no—
652C23D61⋊M1612yes—
653C23C23×#692311yescharacteristic
654D4—44no—
655D4—1228no—
656D4—2444no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—611no—
670C2×C4—611no—
671C2×C4—611no—
672C2×C4—611no—
673C2×C4—611no—
674C2×C4—611no—
675C2×C4—612no—
676C2×C4—612no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
680C2×C4—1222no—
681C2×C4—1228no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—1221no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—2444no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4D4×#692312yes—
708C2×C4D4×#692312yes—
709C2×C4#1451986412yes—
710C8—1222no—
711C8—1222no—
712C8—1222no—
713C8—1222no—
714C8—2441no—
715C8—2441no—
716C8—2441no—
717C8—2441no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—614no—
733C22—1222no—
734C22—1222no—
735C22—1222no—
736C22—1222no—
737C22—1222no—
738C22—1222no—
739C22C2×D4×#692311yescharacteristic
740C22C2×D4×#692311yescharacteristic
741C22#1684083111yescharacteristic
742C22C2×D61⋊M1611yescharacteristic
743C22C2×#1451986411yescharacteristic
744C22D61⋊#13111yescharacteristic
745C22#1684084011yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—41no—
751C4—611no—
752C4—611no—
753C4—611no—
754C4—611no—
755C4—1222no—
756C4—1222no—
757C4—2441no—
758C4—2441no—
759C4—2441no—
760C4—2441no—
761C2—42no—
762C2—81no—
763C2—1224no—
764C2#2146234411yescharacteristic
765C2D61⋊#43511yescharacteristic
766C2#2146253311yescharacteristic
767C2#2146255711yescharacteristic
768C2#2146256211yescharacteristic
769C2#2146274411yescharacteristic
770C2#2146275611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#390C4
prime radicalC2×#14519748C4
cosocleC22×Dic61C24
hypercenter#390#6923
hypocenterC61#22987
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#16840794C2semidirect
2. C2×#16840793C2semidirect
3. C2×#16840789C2semidirect
4. C2×D61⋊(C4⋊C8)C2semidirect
5. #21461943C2semidirect
6. #21461921C2semidirect
7. #21461893C2semidirect
8. #21461888C2semidirect
9. #21461793C2semidirect
10. #21461793C2semidirect
11. #21461766C2semidirect
12. #21461762C2semidirect
13. #21461619C2semidirect
14. #21461546C2semidirect
85. #14519844D4semidirect
90. #14519834D4semidirect
161. C2×C22⋊D61M16semidirect
360. C2×D61#435semidirect
448. C61#22987semidirect

Maximal subgroups

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

subgroupindex
C2×#168407942
C2×#168407932
C2×#168407892
C2×D61⋊(C4⋊C8)2
#214619432
#214619212
#214618932
#214618882
#214617932
#214617662
#214617622
#214616192
#214615462
#214483352
#2298761