Finite Group Databasebeta

← #30622134

Subgroups — #30622134

Order 15616.

1050 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×#16840797C211yesmaximal, characteristic, complemented
2C2×#16840793C211yesmaximal, characteristic, complemented
3C2×#16840793C211yesmaximal, characteristic, complemented
4C2×#16840765C211yesmaximal, characteristic, complemented
5#21461943C211yesmaximal, characteristic, complemented
6#21461921C211yesmaximal, characteristic, complemented
7#21461893C211yesmaximal, characteristic, complemented
8#21461888C211yesmaximal, characteristic, complemented
9#21461796C211yesmaximal, characteristic, complemented
10#21461796C211yesmaximal, characteristic, complemented
11#21461766C211yesmaximal, characteristic, complemented
12#21461762C211yesmaximal, characteristic, complemented
13#21461619C211yesmaximal, characteristic, complemented
14#21461545C211yesmaximal, characteristic, complemented
15#121×Dic61C211yesmaximal, characteristic
16C22×#11758217C2211yescharacteristic
17C22×#11758217C2211yescharacteristic
18C22×#11758217C2211yescharacteristic
19C23×#92420C2211yescharacteristic
20#16840797—24no—
21#16840793—24no—
22#16840793—24no—
23#16840765—24no—
24C2×#14519844C2211yescharacteristic
25C2×#14519844C2211yescharacteristic
26C2×#14519844C2211yescharacteristic
27C2×C4⋊#92420C2211yescharacteristic
28C2×C4⋊#92420C2211yescharacteristic
29C2×C4⋊#92420C2211yescharacteristic
30C2×C22⋊#92420C2211yescharacteristic
31C2×C22⋊#92420C2211yescharacteristic
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×D4×Dic61C2211yescharacteristic
49C2×D4×Dic61C2211yescharacteristic
50C2×D4×Dic61C2211yescharacteristic
51C22×C4×Dic61C2211yescharacteristic
52#16839665C411yescharacteristic
53#16839661C411yescharacteristic
54#16839655C411yescharacteristic
55#16839655C411yescharacteristic
56#16839642C411yescharacteristic
57#16839642C411yescharacteristic
58#16839622C411yescharacteristic
59C4⋊C4×Dic61C2211yescharacteristic
60C22⋊C4×Dic61C2211yescharacteristic
61C22⋊C4×Dic61C2211yescharacteristic
62C2×#121×C61C411yescharacteristic
63C2×#11758217—22no—
64C2×#11758217—22no—
65C2×#11758217—22no—
66C2×#11758217—22no—
67C2×#11758217—22no—
68C2×#11758217—22no—
69C2×#11758217—41no—
70C2×#11758217—41no—
71C2×#11758217—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—
89C22⋊#92420—22no—
90C22⋊#92420—22no—
91C22⋊#92420—22no—
92C22⋊#92420—22no—
93C22⋊#92420—22no—
94C22⋊#92420—41no—
95C22⋊#92420—41no—
96C22⋊#92420D414yescomplemented
97#14519832—22no—
98#14519832—22no—
99#14519832—22no—
100C4×#92420—22no—
101C23×Dic61C2×C411yescharacteristic
102C23×Dic61C2311yescharacteristic
103C23×Dic61C2311yescharacteristic
104C23×Dic61C2311yescharacteristic
105D4×Dic61—22no—
106D4×Dic61—22no—
107D4×Dic61—22no—
108D4×Dic61—22no—
109D4×Dic61—22no—
110D4×Dic61—22no—
111C2×C4⋊Dic61C2×C411yescharacteristic
112C2×C4⋊Dic61C2×C411yescharacteristic
113C2×C4⋊Dic61C2×C411yescharacteristic
114C2×C4⋊Dic61C2×C411yescharacteristic
115C2×C22⋊Dic61C2×C411yescharacteristic
116C2×C22⋊Dic61C2×C411yescharacteristic
117C2×C22⋊Dic61C2×C411yescharacteristic
118C2×C22⋊Dic61C2×C411yescharacteristic
119C2×C22⋊Dic61C2×C411yescharacteristic
120C2×C22⋊Dic61C2×C411yescharacteristic
121C2×C22⋊Dic61C2×C411yescharacteristic
122C2×C22⋊Dic61C2×C411yescharacteristic
123C2×C4×Dic61—22no—
124C2×C4×Dic61—22no—
125C2×C4×Dic61C2×C411yescharacteristic
126C2×C4×Dic61C2×C411yescharacteristic
127C2×C4×Dic61C2311yescharacteristic
128C2×C4×Dic61C2311yescharacteristic
129C2×C4×Dic61C2311yescharacteristic
130C2×C4×Dic61C2311yescharacteristic
131#14519684C2×C411yescharacteristic
132#14519684C2×C411yescharacteristic
133#14519684C2×C411yescharacteristic
134#14519684C2×C411yescharacteristic
135#14519684C2×C411yescharacteristic
136#14519684C2×C411yescharacteristic
137C22×D4×C61C2×C411yescharacteristic
138C22×D4×C61C2×C411yescharacteristic
139C22×D4×C61C2×C411yescharacteristic
140C23×C4×C61C2×C411yescharacteristic
141#121×C61—24no—
142C2×C4⋊C4×C61C2×C411yescharacteristic
143C2×C22⋊C4×C61C2×C411yescharacteristic
144C2×C22⋊C4×C61C2×C411yescharacteristic
145C24×C61C22×C411yescharacteristic
146C24×C61C22×C411yescharacteristic
147C24×C61C22×C411yescharacteristic
148C2×D4×C61—22no—
149C2×D4×C61—22no—
150C2×D4×C61—22no—
151C2×D4×C61—22no—
152C2×D4×C61—22no—
153C2×D4×C61—22no—
154C2×D4×C61—41no—
155C2×D4×C61—41no—
156C2×D4×C61—41no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—41no—
160C22×C4×C61C22×C411yescharacteristic
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—22no—
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×Dic61—41no—
182C22×Dic61—41no—
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C22×Dic61C22×C411yescharacteristic
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C2×D412yes—
191C22×Dic61#4112yes—
192C22×Dic61C2411yescharacteristic
193#11758217—44no—
194#11758217—44no—
195#11758217—44no—
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—21no—
215C2×#92420—21no—
216C2×#92420—44no—
217C2×#92420C2×D412yes—
218C2×#92420C2×D412yes—
219C2×#92420C2×D412yes—
220C2×#92420C2×D412yes—
221C4⋊C4×C61—22no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61M1614yescomplemented
224C22⋊Dic61—22no—
225C22⋊Dic61—22no—
226C22⋊Dic61—22no—
227C22⋊Dic61—22no—
228C22⋊Dic61—22no—
229C22⋊Dic61—22no—
230C22⋊Dic61—41no—
231C22⋊Dic61—41no—
232C4⋊Dic61—22no—
233C4⋊Dic61—22no—
234C4⋊Dic61—22no—
235C4⋊Dic61—41no—
236C4×Dic61—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×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61C4×D412yes—
266C23×C61C2×M1612yes—
267C23×C61C23×C411yescharacteristic
268D4×C61—44no—
269D4×C61—44no—
270D4×C61—44no—
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—44no—
281C2×C4×C61C4×D412yes—
282C2×C4×C61C2×M1612yes—
283C2×C4×C61C2×M1612yes—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—22no—
289C2×Dic61—22no—
290C2×Dic61—22no—
291C2×Dic61—22no—
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—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—44no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61C4×D412yes—
317C2×Dic61C4×D412yes—
318C2×Dic61C22×D411yescharacteristic
319C2×Dic61C22×D411yescharacteristic
320C2×Dic61C2×#4111yescharacteristic
321C2×Dic61C2×#4111yescharacteristic
322C2×Dic61H(5,𝔽2)11yescharacteristic
323C2×Dic612−1+411yescharacteristic
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#22988—611nomaximal, Sylow
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—22no—
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×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61C2×C4×D411yescharacteristic
355C22×C61C2×C4×D411yescharacteristic
356C22×C61#52011yescharacteristic
357C22×C61C22×M1611yescharacteristic
358C22×C61#56811yescharacteristic
359C22×C61#56811yescharacteristic
360C22×C61#56811yescharacteristic
361C4×C61—22no—
362C4×C61—22no—
363C4×C61—22no—
364C4×C61—41no—
365Dic61—22no—
366Dic61—22no—
367Dic61—41no—
368Dic61—41no—
369Dic61—41no—
370Dic61—41no—
371Dic61—41no—
372Dic61D4211yescharacteristic
373Dic61#54711yescharacteristic
374Dic61#54811yescharacteristic
375Dic61#55311yescharacteristic
376C2×#436—611no—
377C2×#435—611no—
378C2×#435—611no—
379C2×#423—611no—
380C4×#121—611no—
381#1955—611no—
382#1940—611no—
383#1924—611no—
384#1923—611no—
385#1870—611no—
386#1870—611no—
387#1851—611no—
388#1850—611no—
389#1771—611no—
390#1749—611no—
391C2×C61—42no—
392C2×C61—42no—
393C2×C61—81no—
394C2×C61#236111yescharacteristic
395C2×C61#293011yescharacteristic
396C2×C61#293211yescharacteristic
397C2×C61D4×M1611yescharacteristic
398C2×C61D4×M1611yescharacteristic
399C2×C61#298911yescharacteristic
400C2×C61#299511yescharacteristic
401C22×M16—611no—
402C22×M16—611no—
403C22×M16—611no—
404C23×C8—611no—
405C2×#121#692311yescharacteristic
406C2×C4×D4—611no—
407C2×C4×D4—611no—
408C2×C4×D4—611no—
409C22×C42—611no—
410#436—1224no—
411#435—1224no—
412#435—1224no—
413#423—1224no—
414C2×C4⋊C8—611no—
415C2×C4⋊C8—611no—
416C2×C4⋊C8—611no—
417C2×C4⋊C8—611no—
418C2×C4⋊C8—611no—
419C2×C4⋊C8—611no—
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—611no—
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#2298811yescharacteristic, complemented, Sylow
449C22×D4C2×#692311yescharacteristic
450C22×D4C2×#692311yescharacteristic
451C22×D4C2×#692311yescharacteristic
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4C2×#692311yescharacteristic
457C2×M16—1222no—
458C2×M16—1222no—
459C2×M16—1222no—
460C2×M16—1222no—
461C2×M16—1222no—
462C2×M16—1222no—
463C2×M16—2441no—
464C2×M16—2441no—
465C2×M16—2441no—
466C22×C8—611no—
467C22×C8—611no—
468C22×C8—611no—
469C22×C8—611no—
470C22×C8—611no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8—611no—
474C22×C8—1222no—
475C22×C8—1222no—
476C22×C8—2441no—
477#121—24no—
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⋊C4—611no—
496C2×C22⋊C4—611no—
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—611no—
505C2×C42—1222no—
506C2×C42—1222no—
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—
531C24C22×#692311yescharacteristic
532C24C22×#692311yescharacteristic
533C24C22×#692311yescharacteristic
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—41no—
541C2×D4—41no—
542C2×D4—41no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—41no—
546C22×C4—611no—
547C22×C4—612no—
548C22×C4—612no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—611no—
552C22×C4—611no—
553C22×C4—611no—
554C22×C4—611no—
555C22×C4—611no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1222no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—2441no—
574C22×C4—2441no—
575C22×C4C22×#692311yescharacteristic
576C22×C4C22×#692311yescharacteristic
577C22×C4C22×#692311yescharacteristic
578C22×C4C22×#692311yescharacteristic
579M16—2444no—
580M16—2444no—
581M16—2444no—
582C2×C8—612no—
583C2×C8—612no—
584C2×C8—612no—
585C2×C8—612no—
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—1221no—
605C2×C8—1221no—
606C2×C8—2444no—
607C4⋊C4—22no—
608C4⋊C4—1222no—
609C4⋊C4—1222no—
610C4⋊C4—1222no—
611C4⋊C4—2441no—
612C22⋊C4—22no—
613C22⋊C4—1222no—
614C22⋊C4—1222no—
615C22⋊C4—1222no—
616C22⋊C4—1222no—
617C22⋊C4—1222no—
618C22⋊C4—1222no—
619C22⋊C4—2441no—
620C22⋊C4—2441no—
621C22⋊C4#1175821714yescomplemented
622C42—612no—
623C42—612no—
624C42—1221no—
625C42—1221no—
626C42—1221no—
627C42—1221no—
628C42—1222no—
629C42—1221no—
630C42—1221no—
631C42—1222no—
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—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23D4×#692312yes—
652C23C2×#1175821712yes—
653C23C23×#692311yescharacteristic
654D4—44no—
655D4—44no—
656D4—44no—
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—44no—
667C2×C4—611no—
668C2×C4—611no—
669C2×C4—611no—
670C2×C4—611no—
671C2×C4—611no—
672C2×C4—611no—
673C2×C4—612no—
674C2×C4—612no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
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—2441no—
699C2×C4—2441no—
700C2×C4—2441no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2444no—
707C2×C4D4×#692312yes—
708C2×C4C2×#1175821712yes—
709C2×C4C2×#1175821712yes—
710C8—1222no—
711C8—1222no—
712C8—1222no—
713C8—1222no—
714C8—2441no—
715C8—2441no—
716C8—2441no—
717C8—2441no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22C2×D4×#692311yescharacteristic
740C22C2×D4×#692311yescharacteristic
741C22#1684083111yescharacteristic
742C22C22×#1175821711yescharacteristic
743C22#1684084011yescharacteristic
744C22#1684084011yescharacteristic
745C22#1684084111yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—611no—
751C4—611no—
752C4—611no—
753C4—611no—
754C4—1222no—
755C4—1222no—
756C4—2441no—
757C4—2441no—
758C4—2441no—
759C4—2441no—
760C4—2441no—
761C2—42no—
762C2—42no—
763C2—81no—
764C2#2146234411yescharacteristic
765C2#2146253711yescharacteristic
766C2#2146254711yescharacteristic
767C2D4×#1175821711yescharacteristic
768C2D4×#1175821711yescharacteristic
769C2#2146273811yescharacteristic
770C2#2146277211yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
Fitting, prime radicalC2×#121×C61C4
cosocleC22×Dic61C24
hypercenterC2×#121#6923
hypocenterC61#22988
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. C2×#16840793C2semidirect
4. C2×#16840765C2semidirect
5. #21461943C2semidirect
6. #21461921C2semidirect
7. #21461893C2semidirect
8. #21461888C2semidirect
9. #21461796C2semidirect
10. #21461796C2semidirect
11. #21461766C2semidirect
12. #21461762C2semidirect
13. #21461619C2semidirect
14. #21461545C2semidirect
85. #14519844D4semidirect
96. C22⋊#92420D4semidirect
223. C22⋊C4×C61M16semidirect
448. C61#22988semidirect
621. 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
C2×#168407652
#214619432
#214619212
#214618932
#214618882
#214617962
#214617662
#214617622
#214616192
#214615452
#121×Dic612
#2298861