Finite Group Databasebeta

← #30620549

Subgroups — #30620549

Order 15616.

1018 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840781C211yesmaximal, characteristic, complemented
2C2×#16840735C211yesmaximal, characteristic
3#21461893C211yesmaximal, characteristic, complemented
4#21461889C211yesmaximal, characteristic, complemented
5#21461888C211yesmaximal, characteristic, complemented
6#21461888C211yesmaximal, characteristic, complemented
7#21461766C211yesmaximal, characteristic, complemented
8#21461762C211yesmaximal, characteristic, complemented
9#21461711C211yesmaximal, characteristic, complemented
10#21461678C211yesmaximal, characteristic, complemented
11#21461643C211yesmaximal, characteristic
12#21461561C211yesmaximal, characteristic, complemented
13C22⋊C4×#92420C211yesmaximal, characteristic, complemented
14#21461548C211yesmaximal, characteristic, complemented
15#21448306C211yesmaximal, characteristic
16C22×#11758217C2211yescharacteristic
17C23×#92420C2211yescharacteristic
18#16840781—24no—
19C2×#14519844C2211yescharacteristic
20C2×C4⋊#92420C2211yescharacteristic
21C2×C4⋊#92420C2211yescharacteristic
22C2×C4⋊#92420C2211yescharacteristic
23#16840735—24no—
24C2×#14519834C2211yescharacteristic
25C2×#14519834C2211yescharacteristic
26C2×#14519834C2211yescharacteristic
27C2×#14519834C2211yescharacteristic
28C2×C22⋊#92420C2211yescharacteristic
29C2×C22⋊#92420C2211yescharacteristic
30C2×C22⋊#92420C2211yescharacteristic
31C2×C22⋊#92420C2211yescharacteristic
32C2×C22⋊#92420C2211yescharacteristic
33C2×C22⋊#92420C2211yescharacteristic
34C2×#14519832C2211yescharacteristic
35C2×C4×#92420C2211yescharacteristic
36C2×C4×#92420C2211yescharacteristic
37C2×C4×#92420C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46C22×#11758224C2211yescharacteristic
47C2×#14519735C2211yescharacteristic
48C2×C42×D61C2211yescharacteristic
49#16839668C411yescharacteristic
50#16839667C411yescharacteristic
51#16839665C411yescharacteristic
52#16839638C411yescharacteristic
53#16839638C411yescharacteristic
54#16839638C411yescharacteristic
55#16839638C411yescharacteristic
56C22⋊C4×Dic61C2211yescharacteristic
57C22⋊C4×Dic61C2211yescharacteristic
58C22⋊C4×Dic61C2211yescharacteristic
59C22⋊C4×Dic61C2211yescharacteristic
60C61×#390C411yescharacteristic
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—41no—
76C4⋊#92420—22no—
77C4⋊#92420—22no—
78C4⋊#92420—41no—
79#14519834—22no—
80#14519834—22no—
81#14519834—22no—
82#14519834D414yes—
83C22⋊#92420—22no—
84C22⋊#92420—22no—
85C22⋊#92420—22no—
86C22⋊#92420—22no—
87C22⋊#92420—41no—
88C22⋊#92420—41no—
89#14519832—41no—
90C4×#92420—22no—
91C4×#92420—22no—
92C4×#92420—41no—
93C2×#11758224—22no—
94C2×#11758224—22no—
95C2×#11758224—22no—
96C2×#11758224—22no—
97C2×#11758224—41no—
98C2×#11758224—41no—
99C22×Dic122C2×C411yescharacteristic
100C22×C22⋊D61C2×C411yescharacteristic
101C22×C22⋊D61C2×C411yescharacteristic
102C23×Dic61C2311yescharacteristic
103C23×Dic61C2311yescharacteristic
104C22×C4×D61C2×C411yescharacteristic
105C22×C4×D61C2×C411yescharacteristic
106C22×C4×D61C2311yescharacteristic
107#14519735—41no—
108#14519735—41no—
109C2×C4⋊Dic61C2×C411yescharacteristic
110C2×C22⋊Dic61C2×C411yescharacteristic
111C2×C22⋊Dic61C2×C411yescharacteristic
112C2×C22⋊Dic61C2×C411yescharacteristic
113C2×C22⋊Dic61C2×C411yescharacteristic
114C2×#11758198C2×C411yescharacteristic
115C2×#11758198C2×C411yescharacteristic
116C2×C4×Dic61C2×C411yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118C2×C4×Dic61C2311yescharacteristic
119C2×C4×Dic61C2311yescharacteristic
120C2×C4×Dic61C2311yescharacteristic
121C42×D61—22no—
122C42×D61—22no—
123#14519684C2×C411yescharacteristic
124#14519684C2×C411yescharacteristic
125#14519684C2×C411yescharacteristic
126#14519684C2×C411yescharacteristic
127#14519684C2×C411yescharacteristic
128#14519684C2×C411yescharacteristic
129#14519684C2×C411yescharacteristic
130#14519684C2×C411yescharacteristic
131C22×D4×C61C2×C411yescharacteristic
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C22⋊C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2×C411yescharacteristic
137C2×C42×C61C2×C411yescharacteristic
138C24×C61C22×C411yescharacteristic
139C24×C61C22×C411yescharacteristic
140C23×D61C22×C411yescharacteristic
141C2×D4×C61—22no—
142C2×D4×C61—22no—
143C2×D4×C61—41no—
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C2×C22⋊D61—22no—
150C2×C22⋊D61—22no—
151C2×C22⋊D61—22no—
152C2×C22⋊D61—22no—
153C2×C22⋊D61—41no—
154C2×C22⋊D61—41no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61#4112yes—
172C22×Dic61#4112yes—
173C22×Dic61C2411yescharacteristic
174#11758224—44no—
175#11758224—44no—
176#11758224—44no—
177#11758224—44no—
178C2×C4×D61—22no—
179C2×C4×D61—22no—
180C2×C4×D61—22no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—22no—
186C2×C4×D61—22no—
187C2×C4×D61—41no—
188C2×C4×D61C2×D412yes—
189C2×C4×D61#4112yes—
190C2×Dic122—22no—
191C2×Dic122—22no—
192C2×Dic122—41no—
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—21no—
215C2×#92420—21no—
216C2×#92420—44no—
217C2×#92420C2×D412yes—
218C2×#92420C2×D412yes—
219C4⋊C4×C61—41no—
220C22⋊C4×C61—22no—
221C22⋊C4×C61—22no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61—22no—
224C42×C61—22no—
225C22⋊Dic61—22no—
226C22⋊Dic61—22no—
227C22⋊Dic61—41no—
228C22⋊Dic61—41no—
229#11758198—41no—
230#11758198—41no—
231C4⋊Dic61—41no—
232C4×Dic61—22no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—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#11712yes—
255C23×C61C23×C411yescharacteristic
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61C4×D412yes—
263D4×C61—44no—
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—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61C4×D412yes—
277C2×C4×C61#13112yes—
278C2×C4×C61#13112yes—
279C22⋊D61—44no—
280C22⋊D61—44no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—22no—
286C2×Dic61—22no—
287C2×Dic61—22no—
288C2×Dic61—22no—
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—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61#11712yes—
306C2×Dic61#13112yes—
307C2×Dic61C22×D411yescharacteristic
308C2×Dic61C2×#4111yescharacteristic
309C2×Dic61C2×#4111yescharacteristic
310C2×Dic61C2×#4111yescharacteristic
311C2×Dic61H(5,𝔽2)11yescharacteristic
312C2×Dic61H(5,𝔽2)11yescharacteristic
313C4×D61—28no—
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—44no—
319Dic122—44no—
320#92420—22no—
321#92420—22no—
322#92420—41no—
323#92420—41no—
324#92420—41no—
325#92420—41no—
326#92420—41no—
327#92420—41no—
328#22556—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
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×C61C2×#11711yescharacteristic
344C22×C61C2×C4×D411yescharacteristic
345C22×C61#51811yescharacteristic
346C22×C61C2×#13111yescharacteristic
347C22×C61C2×#13111yescharacteristic
348C22×C61C2×#13111yescharacteristic
349C22×C61#56811yescharacteristic
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—41no—
354C2×D61—41no—
355C2×D61—41no—
356C2×D61—41no—
357C4×C61—22no—
358C4×C61—22no—
359C4×C61—22no—
360C4×C61—41no—
361C4×C61—41no—
362Dic61—22no—
363Dic61—22no—
364Dic61—41no—
365Dic61—41no—
366Dic61—41no—
367Dic61—41no—
368Dic61#54611yescharacteristic
369Dic61#54611yescharacteristic
370Dic61#55111yescharacteristic
371Dic61#55111yescharacteristic
372C2×#431—611no—
373C2×#408—611no—
374#2297—611no—
375#1924—611no—
376#1923—611no—
377#1923—611no—
378#1923—611no—
379#1851—611no—
380#1850—611no—
381#1817—611no—
382#1798—611no—
383#1780—611no—
384#1753—611no—
385C8×C22⋊C4—611no—
386#1750—611no—
387C2×C61—42no—
388C2×C61—81no—
389C2×C61#234211yescharacteristic
390C2×C61#292211yescharacteristic
391C2×C61#292511yescharacteristic
392C2×C61#292911yescharacteristic
393C2×C61#293311yescharacteristic
394C2×C61#297911yescharacteristic
395C2×C61#298111yescharacteristic
396D61—42no—
397C22×#41—611no—
398C22×M16—611no—
399C23×C8—611no—
400C2×#117—611no—
401C22×C42—611no—
402#431—1224no—
403C2×C4⋊C8—611no—
404C2×C4⋊C8—611no—
405C2×C4⋊C8—611no—
406C2×C4⋊C8—611no—
407#408—1224no—
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×C22⋊C8—611no—
417C2×C22⋊C8—611no—
418C2×#97—611no—
419C2×C4×C8—611no—
420C2×C4×C8—611no—
421C2×C4×C8—611no—
422#391—611no—
423#391—611no—
424#390—611no—
425#390#692311yescharacteristic
426#386—611no—
427#386—611no—
428#386—611no—
429#386—611no—
430C4×C22⋊C4—611no—
431C4×C22⋊C4—611no—
432C4×C22⋊C4—611no—
433C4×C22⋊C4—611no—
434#336—611no—
435#336—611no—
436#336—611no—
437#336—611no—
438#336—611no—
439#336—611no—
440#336—611no—
441#336—611no—
442C61#2255611yescharacteristic, complemented, Sylow
443C2×#41—1222no—
444C2×#41—1222no—
445C2×#41—1222no—
446C2×#41—1222no—
447C2×#41—2441no—
448C2×#41—2441no—
449C22×Q8—611no—
450C22×D4—611no—
451C22×D4—611no—
452C22×D4C2×#692311yescharacteristic
453C23×C4—611no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C23×C4—611no—
458C2×M16—1222no—
459C2×M16—1222no—
460C2×M16—2441no—
461C22×C8—611no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8—611no—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8—611no—
468C22×C8—611no—
469C22×C8—1222no—
470C22×C8—1222no—
471C22×C8—2441no—
472#117—2441no—
473#117—2441no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4C2×#692311yescharacteristic
476C2×C22⋊C4—611no—
477C2×C22⋊C4—611no—
478C2×C22⋊C4—611no—
479C2×C22⋊C4—611no—
480C2×C22⋊C4—611no—
481C2×C22⋊C4—611no—
482C2×C22⋊C4C2×#692311yescharacteristic
483C2×C22⋊C4C2×#692311yescharacteristic
484C2×C22⋊C4C2×#692311yescharacteristic
485C2×C22⋊C4C2×#692311yescharacteristic
486C2×C42—611no—
487C2×C42—611no—
488C2×C42—611no—
489C2×C42—611no—
490C2×C42—611no—
491C2×C42—1222no—
492C2×C42—1222no—
493C2×C42C2×#692311yescharacteristic
494C4⋊C8—1222no—
495C4⋊C8—1222no—
496C4⋊C8—2441no—
497C4⋊C8—2441no—
498C22⋊C8—614no—
499C22⋊C8—1222no—
500C22⋊C8—1222no—
501C22⋊C8—1222no—
502C22⋊C8—1222no—
503C22⋊C8—1222no—
504C22⋊C8—1222no—
505C22⋊C8—1222no—
506C22⋊C8—2441no—
507C22⋊C8—2441no—
508#97—2441no—
509C4×C8—1222no—
510C4×C8—1222no—
511C4×C8—2441no—
512#95—611no—
513#95—611no—
514#95—611no—
515#95—611no—
516#95—611no—
517#95—611no—
518#95—611no—
519#95—611no—
520C24—611no—
521C24C22×#692311yescharacteristic
522C24C22×#692311yescharacteristic
523#41—2444no—
524#41—2444no—
525#41—2444no—
526#41—2444no—
527C2×Q8—1222no—
528C2×Q8—1222no—
529C2×Q8—2441no—
530C2×D4—22no—
531C2×D4—22no—
532C2×D4—41no—
533C2×D4—1222no—
534C2×D4—1222no—
535C2×D4—1222no—
536C2×D4—1222no—
537C2×D4—2441no—
538C2×D4—2441no—
539C22×C4—611no—
540C22×C4—612no—
541C22×C4—612no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—612no—
545C22×C4—612no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1222no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1222no—
556C22×C4—1222no—
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—1221no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—2441no—
570C22×C4C22×#692311yescharacteristic
571C22×C4C22×#692311yescharacteristic
572C22×C4C22×#692311yescharacteristic
573C22×C4C22×#692311yescharacteristic
574C22×C4C22×#692311yescharacteristic
575M16—2444no—
576C2×C8—612no—
577C2×C8—612no—
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—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—2444no—
601C4⋊C4—41no—
602C4⋊C4—2441no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—1222no—
608C22⋊C4—1222no—
609C22⋊C4—2441no—
610C22⋊C4—2441no—
611C22⋊C4—2441no—
612C22⋊C4—2441no—
613C42—22no—
614C42—1221no—
615C42—1221no—
616C42—1221no—
617C42—1221no—
618C42—1221no—
619C42—1221no—
620C42—1221no—
621C42—1221no—
622C42—1222no—
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—612no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23—1221no—
641C23—1221no—
642C23—1221no—
643C23#1451985612yes—
644C23C23×#692311yescharacteristic
645Q8—2444no—
646D4—44no—
647D4—2444no—
648D4—2444no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—611no—
662C2×C4—611no—
663C2×C4—611no—
664C2×C4—611no—
665C2×C4—611no—
666C2×C4—611no—
667C2×C4—612no—
668C2×C4—612no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1228no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
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—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—2444no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4D4×#692312yes—
700C2×C4#1451986412yes—
701C2×C4#1451986412yes—
702C8—1222no—
703C8—1222no—
704C8—2441no—
705C8—2441no—
706C8—2441no—
707C8—2441no—
708C8—2441no—
709C8—2441no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—1222no—
725C22—1222no—
726C22—1222no—
727C22—2441no—
728C22—2441no—
729C22—2441no—
730C22—2441no—
731C22C2×#1451985611yescharacteristic
732C22C2×D4×#692311yescharacteristic
733C22#1684082911yescharacteristic
734C22C2×#1451986411yescharacteristic
735C22C2×#1451986411yescharacteristic
736C22D61⋊#13111yescharacteristic
737C22#1684084111yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—41no—
742C4—41no—
743C4—611no—
744C4—611no—
745C4—611no—
746C4—611no—
747C4—1222no—
748C4—1222no—
749C4—2441no—
750C4—2441no—
751C4—2441no—
752C4—2441no—
753C2—42no—
754C2—81no—
755C2—2442no—
756C2#2146232511yescharacteristic
757C2#2146250211yescharacteristic
758C2#2146251411yescharacteristic
759C2#2146253311yescharacteristic
760C2#2146254911yescharacteristic
761C2#2146270011yescharacteristic
762C2#2146271011yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#390C4
prime radicalC22×#11758224C22
cosocleC22×Dic61C24
hypercenter#390#6923
hypocenterC61#22556
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#16840781C2semidirect
3. #21461893C2semidirect
4. #21461889C2semidirect
5. #21461888C2semidirect
6. #21461888C2semidirect
7. #21461766C2semidirect
8. #21461762C2semidirect
9. #21461711C2semidirect
10. #21461678C2semidirect
12. #21461561C2semidirect
13. C22⋊C4×#92420C2semidirect
14. #21461548C2semidirect
442. C61#22556semidirect

Maximal subgroups

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

subgroupindex
C2×#168407812
C2×#168407352
#214618932
#214618892
#214618882
#214617662
#214617622
#214617112
#214616782
#214616432
#214615612
C22⋊C4×#924202
#214615482
#214483062
#2255661