Finite Group Databasebeta

← #30616938

Subgroups — #30616938

Order 15616.

1110 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×#16840792C211yesmaximal, characteristic, complemented
2C2×#16840791C211yesmaximal, characteristic, complemented
3C2×#16840789C211yesmaximal, characteristic, complemented
4C2×C4×#11758213C211yesmaximal, characteristic, complemented
5#21461942C211yesmaximal, characteristic, complemented
6#21461918C211yesmaximal, characteristic, complemented
7#21461894C211yesmaximal, characteristic, complemented
8#21461892C211yesmaximal, characteristic, complemented
9#21461799C211yesmaximal, characteristic, complemented
10#21461797C211yesmaximal, characteristic, complemented
11#21461676C211yesmaximal, characteristic, complemented
12#21461614C211yesmaximal, characteristic, complemented
13#21461557C211yesmaximal, characteristic, complemented
14#21461556C211yesmaximal, characteristic, complemented
15#21448331C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic
17C22×#11758213C2211yescharacteristic
18C22×D61⋊C8C2211yescharacteristic
19C23×#92420C2211yescharacteristic
20#16840792—24no—
21#16840791—24no—
22#16840789—24no—
23C2×#14519844C2211yescharacteristic
24C2×#14519844C2211yescharacteristic
25C2×#14519844C2211yescharacteristic
26C2×C4⋊#92420C2211yescharacteristic
27C2×#14519834C2211yescharacteristic
28C2×#14519834C2211yescharacteristic
29C2×#14519834C2211yescharacteristic
30C2×#14519834C2211yescharacteristic
31C2×#14519834C2211yescharacteristic
32C2×C22⋊#92420C2211yescharacteristic
33C2×C22⋊#92420C2211yescharacteristic
34C2×C22⋊#92420C2211yescharacteristic
35C4×#11758213—24no—
36C2×#14519832C2211yescharacteristic
37C2×#14519832C2211yescharacteristic
38C2×#14519832C2211yescharacteristic
39C2×#14519832C2211yescharacteristic
40C2×C4×#92420C2211yescharacteristic
41C2×C4×#92420C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46#16840628C2211yescharacteristic
47#16840628C2211yescharacteristic
48C2×#14519750C411yescharacteristic
49C2×#14519739C2211yescharacteristic
50C2×#14519737C2211yescharacteristic
51C2×#14519737C2211yescharacteristic
52C2×C42×D61C2211yescharacteristic
53#16839662C411yescharacteristic
54#16839657C411yescharacteristic
55#16839653C411yescharacteristic
56#16839640C411yescharacteristic
57#16839638C411yescharacteristic
58#16839621C411yescharacteristic
59#16839613C2211yescharacteristic
60C22⋊C4×Dic61C2211yescharacteristic
61#16839609C2211yescharacteristic
62C61×#388C411yescharacteristic
63C2×#11758213—22no—
64C2×#11758213—22no—
65C2×#11758213—22no—
66C2×#11758213—22no—
67C2×#11758213—22no—
68C2×#11758213D414yescomplemented
69C2×D61⋊C8—22no—
70C2×D61⋊C8—22no—
71C2×D61⋊C8—22no—
72C22×#92420—22no—
73C22×#92420—22no—
74C22×#92420—22no—
75C22×#92420C2311yescharacteristic
76C22×#92420C2311yescharacteristic
77C22×#92420C2311yescharacteristic
78C22×#92420C2311yescharacteristic
79C22×#92420C2311yescharacteristic
80C22×#92420C2311yescharacteristic
81C22×#92420C2311yescharacteristic
82C22×#92420C2311yescharacteristic
83#14519844—22no—
84#14519844—22no—
85#14519844—22no—
86C4⋊#92420—22no—
87#14519834—22no—
88#14519834—22no—
89#14519834—22no—
90#14519834—22no—
91#14519834—22no—
92C22⋊#92420—22no—
93C22⋊#92420—22no—
94C22⋊#92420—22no—
95#14519832—22no—
96#14519832—22no—
97#14519832—22no—
98#14519832—22no—
99C4×#92420—22no—
100C4×#92420D414yescomplemented
101C22×D244C2×C411yescharacteristic
102C22×C22⋊D61C2×C411yescharacteristic
103C22×C22⋊D61C2×C411yescharacteristic
104C23×Dic61C2311yescharacteristic
105C22×C4×D61C2×C411yescharacteristic
106C22×C4×D61C2×C411yescharacteristic
107C22×C4×D61C2311yescharacteristic
108C22×C4×D61C2311yescharacteristic
109#14519750—24no—
110#14519739—22no—
111#14519739—22no—
112#14519737—22no—
113#14519737—22no—
114#14519737—22no—
115#14519737—22no—
116C2×#11758196C2×C411yescharacteristic
117C2×#11758196C2×C411yescharacteristic
118C2×#11758196C2×C411yescharacteristic
119C2×#11758196C2×C411yescharacteristic
120C2×C22⋊Dic61C2×C411yescharacteristic
121C2×#11758198C2×C411yescharacteristic
122C2×#11758198C2×C411yescharacteristic
123C2×#11758198C2×C411yescharacteristic
124C2×#11758198C2×C411yescharacteristic
125C2×#11758198C2×C411yescharacteristic
126C2×#11758198C2×C411yescharacteristic
127C2×C4×Dic61C2×C411yescharacteristic
128C2×C4×Dic61C2311yescharacteristic
129C2×C4×Dic61C2311yescharacteristic
130C2×C4×Dic61C2311yescharacteristic
131C2×C4×Dic61C2311yescharacteristic
132C42×D61—22no—
133C42×D61—22no—
134#14519684C2×C411yescharacteristic
135#14519684C2×C411yescharacteristic
136#14519684C2×C411yescharacteristic
137#14519684C2×C411yescharacteristic
138C2×C4⋊C4×C61C2×C411yescharacteristic
139C2×C22⋊C4×C61C2×C411yescharacteristic
140C2×C22⋊C4×C61C2×C411yescharacteristic
141C2×C22⋊C4×C61C2×C411yescharacteristic
142C2×C42×C61C2×C411yescharacteristic
143#95×C61C2×C411yescharacteristic
144#95×C61C2×C411yescharacteristic
145C24×C61C22×C411yescharacteristic
146C23×D61C22×C411yescharacteristic
147C23×D61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C2×C22⋊D61—22no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—41no—
159C2×C22⋊D61M1614yescomplemented
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C2411yescharacteristic
172C2×D244—22no—
173C2×D244—22no—
174C2×D244—41no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—22no—
180C2×C4×D61—22no—
181C2×C4×D61—22no—
182C2×C4×D61—22no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—21no—
188C2×C4×D61—21no—
189C2×C4×D61—41no—
190C2×C4×D61—41no—
191C2×C4×D61C2×D412yes—
192C2×C4×D61#4112yes—
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—44no—
212C2×#92420C2×D412yes—
213C2×#92420C2×D412yes—
214C2×#92420C2×D412yes—
215C2×#92420C2×D412yes—
216C2×#92420#4112yes—
217C2×#92420#4112yes—
218#11758213—28no—
219#11758213—28no—
220D61⋊C8—44no—
221C4⋊C4×C61—22no—
222C22⋊C4×C61—22no—
223C22⋊C4×C61—22no—
224C22⋊C4×C61—22no—
225C42×C61—22no—
226C22⋊Dic61—41no—
227#11758198—22no—
228#11758198—22no—
229#11758198—22no—
230#11758198—22no—
231#11758198—22no—
232#11758198—41no—
233#11758196—22no—
234#11758196—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×C61C2×M1612yes—
253C23×C61C23×C411yescharacteristic
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61C4×D412yes—
267C22×D61C2×M1612yes—
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—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61C4×D412yes—
285C2×C4×C61C4×D412yes—
286C22⋊D61—28no—
287C22⋊D61—44no—
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—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61C4×D412yes—
305C2×Dic61C2×M1612yes—
306C2×Dic61#13112yes—
307C2×Dic61C22×D411yescharacteristic
308C2×Dic61C22×D411yescharacteristic
309C2×Dic61C2×#4111yescharacteristic
310C2×Dic61C2×#4111yescharacteristic
311C2×Dic61C2×#4111yescharacteristic
312C2×Dic61C2×#4111yescharacteristic
313D244—44no—
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—44no—
319C4×D61—41no—
320C4×D61—41no—
321C4×D61—41no—
322C4×D61—41no—
323C4×D61—44no—
324#92420—22no—
325#92420—22no—
326#92420—22no—
327#92420—41no—
328#92420—41no—
329#92420—41no—
330#92420—41no—
331#92420#12114yescomplemented
332#21486—611nomaximal, Sylow
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—41no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61C2×C4×D411yescharacteristic
341C22×C61C2×C4×D411yescharacteristic
342C22×C61C4×#4111yescharacteristic
343C22×C61C22×M1611yescharacteristic
344C22×C61C2×#13111yescharacteristic
345C22×C61#56811yescharacteristic
346C22×C61#56811yescharacteristic
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—41no—
354C2×D61—41no—
355C2×D61—41no—
356C2×D61—41no—
357C2×D61—41no—
358C2×D61—41no—
359C2×D61—41no—
360C2×D61—41no—
361C4×C61—22no—
362C4×C61—22no—
363C4×C61—41no—
364C4×C61—41no—
365C4×C61—41no—
366C4×C61—41no—
367Dic61—41no—
368Dic61—41no—
369Dic61—41no—
370Dic61—41no—
371Dic61#43514yescomplemented
372Dic61C2×#12111yescharacteristic
373Dic61#52511yescharacteristic
374Dic61#52911yescharacteristic
375Dic61#53211yescharacteristic
376C2×#435—611no—
377C2×#435—611no—
378C2×C8×D4—611no—
379C2×C4×M16—611no—
380C4×#121—611no—
381#1954—611no—
382#1939—611no—
383#1924—611no—
384#1924—611no—
385#1870—611no—
386#1870—611no—
387#1797—611no—
388#1770—611no—
389#1752—611no—
390#1752—611no—
391C2×C61—42no—
392C2×C61C4×#12111yescharacteristic
393C2×C61C2×#43511yescharacteristic
394C2×C61#293011yescharacteristic
395C2×C61D4×M1611yescharacteristic
396C2×C61#293511yescharacteristic
397C2×C61#296911yescharacteristic
398C2×C61#297011yescharacteristic
399D61—42no—
400D61—42no—
401C22×M16—611no—
402C22×M16—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×C22⋊C8—611no—
418C2×C22⋊C8—611no—
419C2×C22⋊C8—611no—
420C2×C22⋊C8—611no—
421C2×C22⋊C8—611no—
422C2×C22⋊C8—611no—
423C2×C22⋊C8—611no—
424C2×C22⋊C8—611no—
425C4×M16—1224no—
426C2×#97—611no—
427C2×#97—611no—
428C2×#97—611no—
429C2×#97—611no—
430C2×C4×C8—611no—
431C2×C4×C8—611no—
432#390—611no—
433#389—611no—
434#388—611no—
435#388#692311yescharacteristic
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#2148611yescharacteristic, complemented, Sylow
449C22×D4—611no—
450C22×D4—611no—
451C22×D4—611no—
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—611no—
455C23×C4—611no—
456C23×C4—611no—
457C2×M16—614no—
458C2×M16—1222no—
459C2×M16—1222no—
460C2×M16—1222no—
461C2×M16—1222no—
462C2×M16—1222no—
463C22×C8—611no—
464C22×C8—611no—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8—611no—
468C22×C8—611no—
469C22×C8—611no—
470C22×C8—611no—
471C22×C8—1222no—
472C22×C8—1222no—
473C22×C8—1222no—
474C22×C8—1222no—
475C22×C8—1222no—
476C22×C8—1222no—
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⋊C4—611no—
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—1222no—
508C4⋊C8—1222no—
509C4⋊C8—1222no—
510C4⋊C8—1222no—
511C22⋊C8—1222no—
512C22⋊C8—1222no—
513C22⋊C8—1222no—
514C22⋊C8—1222no—
515C22⋊C8—1222no—
516C22⋊C8—1222no—
517C22⋊C8—1222no—
518C22⋊C8—1222no—
519#97—1222no—
520#97—1222no—
521#97—1222no—
522#97—1222no—
523C4×C8—614no—
524C4×C8—1222no—
525#95—611no—
526#95—611no—
527#95—611no—
528#95—611no—
529#95C2×#692311yescharacteristic
530#95C2×#692311yescharacteristic
531C24—611no—
532C24—611no—
533C24C22×#692311yescharacteristic
534C2×D4—614no—
535C2×D4—1222no—
536C2×D4—1222no—
537C2×D4—1222no—
538C2×D4—1222no—
539C2×D4—1222no—
540C2×D4—1222no—
541C2×D4—2441no—
542C2×D4—2441no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—612no—
546C22×C4—612no—
547C22×C4—611no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—611no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1222no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1222no—
562C22×C4—1221no—
563C22×C4—1222no—
564C22×C4—1221no—
565C22×C4—1221no—
566C22×C4—1221no—
567C22×C4—1221no—
568C22×C4—1221no—
569C22×C4—1221no—
570C22×C4—1222no—
571C22×C4—2441no—
572C22×C4—2441no—
573C22×C4C22×#692311yescharacteristic
574C22×C4C22×#692311yescharacteristic
575C22×C4C22×#692311yescharacteristic
576C22×C4C22×#692311yescharacteristic
577C22×C4C22×#692311yescharacteristic
578C22×C4C22×#692311yescharacteristic
579M16—1228no—
580M16—1228no—
581C2×C8—612no—
582C2×C8—612no—
583C2×C8—612no—
584C2×C8—612no—
585C2×C8—612no—
586C2×C8—612no—
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—2444no—
606C2×C8—2444no—
607C4⋊C4—22no—
608C4⋊C4—1222no—
609C4⋊C4—1222no—
610C4⋊C4—1222no—
611C4⋊C4—1222no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—1222no—
616C22⋊C4—1222no—
617C22⋊C4—1222no—
618C22⋊C4—1222no—
619C22⋊C4—1222no—
620C22⋊C4—2441no—
621C22⋊C4—2441no—
622C42—22no—
623C42—612no—
624C42—612no—
625C42—1221no—
626C42—1221no—
627C42—1221no—
628C42—1222no—
629C42—1221no—
630C42—1221no—
631C42—1221no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—612no—
639C23—612no—
640C23—1221no—
641C23—1221no—
642C23—1221no—
643C23—1221no—
644C23—1221no—
645C23—1221no—
646C23—1221no—
647C23—1221no—
648C23—1221no—
649C23—1221no—
650C23—1221no—
651C23—1221no—
652C23D61⋊M1612yes—
653C23C23×#692311yescharacteristic
654D4—1228no—
655D4—2444no—
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—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—612no—
674C2×C4—611no—
675C2×C4—611no—
676C2×C4—611no—
677C2×C4—611no—
678C2×C4—611no—
679C2×C4—611no—
680C2×C4—612no—
681C2×C4—612no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
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—2444no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4D4×#692312yes—
709C2×C4D4×#692312yes—
710C8—614no—
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—1222no—
726C22—1222no—
727C22—1222no—
728C22—1222no—
729C22—1222no—
730C22—1222no—
731C22—2441no—
732C22—2441no—
733C22—2441no—
734C22—2441no—
735C22—2441no—
736C22—2441no—
737C22—2441no—
738C22—2441no—
739C22C2×D4×#692311yescharacteristic
740C22C2×D4×#692311yescharacteristic
741C22#41×#692311yescharacteristic
742C22C2×D61⋊M1611yescharacteristic
743C22D61⋊#13111yescharacteristic
744C22#1684084111yescharacteristic
745C22#1684084111yescharacteristic
746C4—22no—
747C4—22no—
748C4—41no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—611no—
753C4—611no—
754C4—611no—
755C4—611no—
756C4—614no—
757C4—2441no—
758C4—2441no—
759C4—2441no—
760C4—2441no—
761C2—42no—
762C2—2442no—
763C2—2442no—
764C2#121×#692311yescharacteristic
765C2D61⋊#43511yescharacteristic
766C2#2146254011yescharacteristic
767C2#2146255811yescharacteristic
768C2#2146256411yescharacteristic
769C2#2146265411yescharacteristic
770C2#2146265811yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#388C4
prime radicalC2×#14519750C4
cosocleC22×Dic61C24
hypercenter#388#6923
hypocenterC61#21486
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#16840792C2semidirect
2. C2×#16840791C2semidirect
3. C2×#16840789C2semidirect
4. C2×C4×#11758213C2semidirect
5. #21461942C2semidirect
6. #21461918C2semidirect
7. #21461894C2semidirect
8. #21461892C2semidirect
9. #21461799C2semidirect
10. #21461797C2semidirect
11. #21461676C2semidirect
12. #21461614C2semidirect
13. #21461557C2semidirect
14. #21461556C2semidirect
68. C2×#11758213D4semidirect
100. C4×#92420D4semidirect
159. C2×C22⋊D61M16semidirect
331. #92420#121semidirect
371. Dic61#435semidirect
448. C61#21486semidirect

Maximal subgroups

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

subgroupindex
C2×#168407922
C2×#168407912
C2×#168407892
C2×C4×#117582132
#214619422
#214619182
#214618942
#214618922
#214617992
#214617972
#214616762
#214616142
#214615572
#214615562
#214483312
#2148661