Finite Group Databasebeta

← #30620580

Subgroups — #30620580

Order 15616.

1010 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×#16840786C211yesmaximal, characteristic, complemented
2C2×#16840736C211yesmaximal, characteristic
3#21461892C211yesmaximal, characteristic, complemented
4#21461889C211yesmaximal, characteristic, complemented
5#21461889C211yesmaximal, characteristic, complemented
6#21461888C211yesmaximal, characteristic, complemented
7#21461767C211yesmaximal, characteristic, complemented
8#21461764C211yesmaximal, characteristic, complemented
9#21461712C211yesmaximal, characteristic, complemented
10#21461675C211yesmaximal, characteristic, complemented
11#21461643C211yesmaximal, characteristic
12#21461560C211yesmaximal, characteristic, complemented
13#21461553C211yesmaximal, characteristic, complemented
14C4×C22⋊#92420C211yesmaximal, characteristic, complemented
15#21448304C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18#16840786—24no—
19C2×#14519844C2211yescharacteristic
20C2×#14519844C2211yescharacteristic
21C2×#14519844C2211yescharacteristic
22C2×C4⋊#92420C2211yescharacteristic
23#16840736—24no—
24C2×#14519834C2211yescharacteristic
25C2×#14519834C2211yescharacteristic
26C2×C22⋊#92420C2211yescharacteristic
27C2×C22⋊#92420C2211yescharacteristic
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×#14519733C2211yescharacteristic
48C22×C4×Dic61C2211yescharacteristic
49#16839666C411yescharacteristic
50#16839666C411yescharacteristic
51#16839662C411yescharacteristic
52#16839662C411yescharacteristic
53#16839642C411yescharacteristic
54#16839641C411yescharacteristic
55#16839639C411yescharacteristic
56C22⋊C4×Dic61C2211yescharacteristic
57C22⋊C4×Dic61C2211yescharacteristic
58#16839609C2211yescharacteristic
59#16839609C2211yescharacteristic
60C61×#386C411yescharacteristic
61C2×#11758213—22no—
62C2×#11758213—22no—
63C2×#11758213—41no—
64C2×D61⋊C8—22no—
65C2×D61⋊C8—22no—
66C2×D61⋊C8—41no—
67C22×#92420C2311yescharacteristic
68C22×#92420C2311yescharacteristic
69C22×#92420C2311yescharacteristic
70C22×#92420C2311yescharacteristic
71C22×#92420C2311yescharacteristic
72C22×#92420C2311yescharacteristic
73C22×#92420C2311yescharacteristic
74C22×#92420C2311yescharacteristic
75#14519844—22no—
76#14519844—41no—
77#14519844—41no—
78C4⋊#92420—22no—
79#14519834—22no—
80#14519834—22no—
81C22⋊#92420—22no—
82C22⋊#92420—22no—
83C22⋊#92420—22no—
84C22⋊#92420—22no—
85C22⋊#92420—22no—
86C22⋊#92420—41no—
87C22⋊#92420—41no—
88C22⋊#92420D414yes—
89#14519832—22no—
90C4×#92420—22no—
91C4×#92420—41no—
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×Dic61C2×C411yescharacteristic
103C23×Dic61C2311yescharacteristic
104C23×Dic61C2311yescharacteristic
105C22×C4×D61C2311yescharacteristic
106#14519733—22no—
107#14519733—22no—
108C2×#11758196C2×C411yescharacteristic
109C2×#11758196C2×C411yescharacteristic
110C2×C22⋊Dic61C2×C411yescharacteristic
111C2×C22⋊Dic61C2×C411yescharacteristic
112C2×C22⋊Dic61C2×C411yescharacteristic
113C2×#11758198C2×C411yescharacteristic
114C2×#11758198C2×C411yescharacteristic
115C2×#11758198C2×C411yescharacteristic
116C2×#11758198C2×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
132C23×C4×C61C2×C411yescharacteristic
133C2×C22⋊C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136#95×C61C2×C411yescharacteristic
137#95×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×C61—22no—
145C22×C4×C61—41no—
146C22×C4×C61—41no—
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C2×C22⋊D61—22no—
153C2×C22⋊D61—22no—
154C2×C22⋊D61—22no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—41no—
157C2×C22⋊D61—41no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—22no—
163C22×Dic61—22no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—41no—
171C22×Dic61C22×C411yescharacteristic
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C2×D412yes—
178C22×Dic61#4112yes—
179C22×Dic61C2411yescharacteristic
180#11758224—44no—
181#11758224—44no—
182#11758224—44no—
183#11758224—44no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61#4112yes—
189C2×C4×D61#4112yes—
190C2×Dic122—22no—
191C2×Dic122—22no—
192C2×Dic122—41no—
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—21no—
211C2×#92420—21no—
212C2×#92420—21no—
213C2×#92420—21no—
214C2×#92420—21no—
215C2×#92420C2×D412yes—
216C2×#92420C2×D412yes—
217#11758213—44no—
218D61⋊C8—44no—
219C22⋊C4×C61—22no—
220C22⋊C4×C61—22no—
221C22⋊C4×C61—41no—
222C22⋊Dic61—22no—
223C22⋊Dic61—22no—
224C22⋊Dic61—22no—
225#11758198—22no—
226#11758198—22no—
227#11758198—22no—
228#11758198—41no—
229#11758196—22no—
230#11758196—22no—
231C4×Dic61—21no—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—41no—
240C4×Dic61—41no—
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×C61C4×D412yes—
255C23×C61C23×C411yescharacteristic
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61#11712yes—
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×C61—21no—
277C2×C4×C61—44no—
278C2×C4×C61#11712yes—
279C2×C4×C61#13112yes—
280C22⋊D61—44no—
281C22⋊D61—44no—
282C2×Dic61—21no—
283C2×Dic61—21no—
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—44no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61C4×D412yes—
307C2×Dic61#13112yes—
308C2×Dic61#13112yes—
309C2×Dic61C22×D411yescharacteristic
310C2×Dic61C2×#4111yescharacteristic
311C2×Dic61C2×#4111yescharacteristic
312C2×Dic61C2×#4111yescharacteristic
313C2×Dic61H(5,𝔽2)11yescharacteristic
314C2×Dic61H(5,𝔽2)11yescharacteristic
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—22no—
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#22560—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—41no—
360C4×C61—41no—
361C4×C61—41no—
362Dic61—22no—
363Dic61—22no—
364Dic61—22no—
365Dic61—41no—
366Dic61—41no—
367Dic61—41no—
368Dic61#54611yescharacteristic
369Dic61#54611yescharacteristic
370Dic61#55111yescharacteristic
371Dic61#55111yescharacteristic
372C2×#433—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#1818—611no—
382#1797—611no—
383#1780—611no—
384#1753—611no—
385C8×C22⋊C4—611no—
386C4×C22⋊C8—611no—
387C2×C61—42no—
388C2×C61—81no—
389C2×C61#234211yescharacteristic
390C2×C61#292211yescharacteristic
391C2×C61#292511yescharacteristic
392C2×C61#293111yescharacteristic
393C2×C61#293511yescharacteristic
394C2×C61#297611yescharacteristic
395C2×C61#297711yescharacteristic
396D61—42no—
397C22×#41—611no—
398C22×M16—611no—
399C23×C8—611no—
400C2×#117—611no—
401C22×C42—611no—
402#433—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—611no—
426#386—611no—
427#386—611no—
428#386—611no—
429#386#692311yescharacteristic
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#2256011yescharacteristic, 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×C4C2×#692311yescharacteristic
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—1222no—
473#117—1222no—
474C2×C4⋊C4—611no—
475C2×C4⋊C4—611no—
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⋊C4—611no—
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—611no—
492C2×C42—2441no—
493C2×C42—2441no—
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—1222no—
509C4×C8—1222no—
510C4×C8—2441no—
511C4×C8—2441no—
512#95—611no—
513#95—611no—
514#95—611no—
515#95—611no—
516#95—611no—
517#95—611no—
518#95C2×#692311yescharacteristic
519#95C2×#692311yescharacteristic
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—22no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—611no—
543C22×C4—612no—
544C22×C4—612no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—612no—
549C22×C4—612no—
550C22×C4—611no—
551C22×C4—611no—
552C22×C4—611no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
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—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—1222no—
602C4⋊C4—1222no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—41no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—1222no—
609C22⋊C4—1222no—
610C22⋊C4—1222no—
611C22⋊C4—1222no—
612C22⋊C4—2441no—
613C42—1221no—
614C42—1221no—
615C42—1221no—
616C42—1221no—
617C42—1221no—
618C42—1221no—
619C42—1221no—
620C42—1221no—
621C42—2441no—
622C42—2441no—
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—
643C23D4×#692312yes—
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—21no—
662C2×C4—44no—
663C2×C4—611no—
664C2×C4—611no—
665C2×C4—611no—
666C2×C4—611no—
667C2×C4—611no—
668C2×C4—611no—
669C2×C4—612no—
670C2×C4—612no—
671C2×C4—612no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—1222no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—1222no—
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—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4—2444no—
700C2×C4#1451985612yes—
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
735C22D61⋊#13111yescharacteristic
736C22D61⋊#13111yescharacteristic
737C22#1684084011yescharacteristic
738C4—22no—
739C4—22no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—611no—
744C4—611no—
745C4—611no—
746C4—611no—
747C4—1222no—
748C4—1222no—
749C4—1222no—
750C4—2441no—
751C4—2441no—
752C4—2441no—
753C2—42no—
754C2—81no—
755C2—2442no—
756C2#2146232511yescharacteristic
757C2#2146250311yescharacteristic
758C2#2146251611yescharacteristic
759C2#2146254211yescharacteristic
760C2#2146256311yescharacteristic
761C2#2146268511yescharacteristic
762C2#2146269311yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#386C4
prime radicalC22×#11758224C22
cosocleC22×Dic61C24
hypercenter#386#6923
hypocenterC61#22560
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#16840786C2semidirect
3. #21461892C2semidirect
4. #21461889C2semidirect
5. #21461889C2semidirect
6. #21461888C2semidirect
7. #21461767C2semidirect
8. #21461764C2semidirect
9. #21461712C2semidirect
10. #21461675C2semidirect
12. #21461560C2semidirect
13. #21461553C2semidirect
14. C4×C22⋊#92420C2semidirect
442. C61#22560semidirect

Maximal subgroups

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

subgroupindex
C2×#168407862
C2×#168407362
#214618922
#214618892
#214618882
#214617672
#214617642
#214617122
#214616752
#214616432
#214615602
#214615532
C4×C22⋊#924202
#214483042
#2256061