Finite Group Databasebeta

← #30622132

Subgroups — #30622132

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×#16840792C211yesmaximal, characteristic, complemented
2C2×#16840792C211yesmaximal, characteristic, complemented
3C2×#16840790C211yesmaximal, characteristic, complemented
4C2×D61⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
5#21461945C211yesmaximal, characteristic, complemented
6#21461921C211yesmaximal, characteristic, complemented
7#21461894C211yesmaximal, characteristic, complemented
8#21461891C211yesmaximal, characteristic, complemented
9#21461795C211yesmaximal, characteristic, complemented
10#21461795C211yesmaximal, characteristic, complemented
11#21461765C211yesmaximal, characteristic, complemented
12#21461764C211yesmaximal, characteristic, complemented
13#21461619C211yesmaximal, characteristic, complemented
14#21461546C211yesmaximal, characteristic, complemented
15#21448327C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C22×D61⋊C8C2211yescharacteristic
19C22×D61⋊C8C2211yescharacteristic
20#16840792—24no—
21#16840792—24no—
22#16840790—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×#14519834C2211yescharacteristic
33C2×#14519834C2211yescharacteristic
34C2×#14519834C2211yescharacteristic
35C2×#14519834C2211yescharacteristic
36C2×#14519834C2211yescharacteristic
37C2×#14519834C2211yescharacteristic
38C2×#14519832C2211yescharacteristic
39C2×#14519832C2211yescharacteristic
40C2×#14519832C2211yescharacteristic
41C2×C4×#92420C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46#16840628C2211yescharacteristic
47#16840628C2211yescharacteristic
48C2×#14519752C411yescharacteristic
49C2×#14519739C2211yescharacteristic
50C2×#14519739C2211yescharacteristic
51C2×#14519739C2211yescharacteristic
52C2×C42×D61C2211yescharacteristic
53#16839664C411yescharacteristic
54#16839652C411yescharacteristic
55#16839652C411yescharacteristic
56#16839640C411yescharacteristic
57#16839640C411yescharacteristic
58#16839619C411yescharacteristic
59C4⋊C4×Dic61C2211yescharacteristic
60#16839609C2211yescharacteristic
61#16839609C2211yescharacteristic
62C61×#389C411yescharacteristic
63C2×#11758213—22no—
64C2×#11758213—22no—
65C2×#11758213—41no—
66C2×D61⋊C8—22no—
67C2×D61⋊C8—22no—
68C2×D61⋊C8—22no—
69C2×D61⋊C8—22no—
70C2×D61⋊C8—22no—
71C2×D61⋊C8—22no—
72C2×D61⋊C8—41no—
73C2×D61⋊C8—41no—
74C2×D61⋊C8—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#14519834—22no—
91#14519834—22no—
92#14519834—22no—
93#14519834—22no—
94#14519834—41no—
95#14519834—41no—
96#14519834D414yescomplemented
97#14519832—22no—
98#14519832—22no—
99#14519832—22no—
100C4×#92420—22no—
101C22×D244C2×C411yescharacteristic
102C22×D244C2×C411yescharacteristic
103C22×D244C2×C411yescharacteristic
104C22×C4×D61C2×C411yescharacteristic
105C22×C4×D61C2×C411yescharacteristic
106C22×C4×D61C2311yescharacteristic
107C22×C4×D61C2311yescharacteristic
108C22×C4×D61C2311yescharacteristic
109#14519752—24no—
110#14519739—22no—
111#14519739—22no—
112#14519739—22no—
113#14519739—22no—
114#14519739—22no—
115#14519739—22no—
116C2×C4⋊Dic61C2×C411yescharacteristic
117C2×#11758198C2×C411yescharacteristic
118C2×#11758198C2×C411yescharacteristic
119C2×#11758198C2×C411yescharacteristic
120C2×#11758198C2×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×C4⋊C4×C61C2×C411yescharacteristic
140C2×C4⋊C4×C61C2×C411yescharacteristic
141C2×C4⋊C4×C61C2×C411yescharacteristic
142C2×C42×C61C2×C411yescharacteristic
143#95×C61C2×C411yescharacteristic
144#95×C61C2×C411yescharacteristic
145C23×D61C22×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
154C22×C4×C61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C22×C411yescharacteristic
157C22×Dic61C22×C411yescharacteristic
158C22×Dic61C22×C411yescharacteristic
159C22×Dic61C2411yescharacteristic
160C2×D244—22no—
161C2×D244—22no—
162C2×D244—22no—
163C2×D244—22no—
164C2×D244—22no—
165C2×D244—22no—
166C2×D244—22no—
167C2×D244—41no—
168C2×D244M1614yescomplemented
169C2×C4×D61—22no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
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—21no—
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—21no—
212C2×#92420—21no—
213C2×#92420C2×D412yes—
214C2×#92420C2×D412yes—
215C2×#92420C2×D412yes—
216C2×#92420C2×D412yes—
217#11758213—44no—
218D61⋊C8—44no—
219D61⋊C8—44no—
220D61⋊C8—44no—
221C4⋊C4×C61—22no—
222C4⋊C4×C61—22no—
223C4⋊C4×C61—22no—
224C4⋊C4×C61—22no—
225C42×C61—22no—
226#11758198—22no—
227#11758198—22no—
228#11758198—22no—
229#11758198—22no—
230#11758198—22no—
231#11758198—22no—
232#11758198—22no—
233#11758198—22no—
234#11758198—22no—
235#11758198—22no—
236C4⋊Dic61—41no—
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×C61C23×C411yescharacteristic
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
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×D61C4×D412yes—
265C22×D61C2×M1612yes—
266C22×D61C2×M1612yes—
267C22×D61#13112yes—
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×C61—21no—
285C2×C4×C61C4×D412yes—
286C2×C4×C61C4×D412yes—
287C2×C4×C61C2×M1612yes—
288C2×C4×C61#13112yes—
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×Dic61C4×D412yes—
301C2×Dic61C22×D411yescharacteristic
302C2×Dic61C22×D411yescharacteristic
303C2×Dic61C2×#4111yescharacteristic
304C2×Dic61C2×#4111yescharacteristic
305C2×Dic61H(5,𝔽2)11yescharacteristic
306C2×Dic612−1+411yescharacteristic
307D244—28no—
308D244—44no—
309D244—44no—
310C4×D61—28no—
311C4×D61—22no—
312C4×D61—22no—
313C4×D61—22no—
314C4×D61—22no—
315C4×D61—44no—
316C4×D61—41no—
317C4×D61—41no—
318C4×D61—41no—
319C4×D61—41no—
320C4×D61—41no—
321C4×D61—41no—
322C4×D61—41no—
323C4×D61—41no—
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×C61C2×C4×D411yescharacteristic
334C22×C61C2×C4×D411yescharacteristic
335C22×C61#52011yescharacteristic
336C22×C61C22×M1611yescharacteristic
337C22×C61C2×#13111yescharacteristic
338C22×C61C2×#13111yescharacteristic
339C22×C61#56811yescharacteristic
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—22no—
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—41no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—41no—
354C2×D61—41no—
355C2×D61—41no—
356C2×D61—41no—
357C2×D61—41no—
358C2×D61—41no—
359C2×D61—41no—
360C2×D61#43514yescomplemented
361C4×C61—22no—
362C4×C61—22no—
363C4×C61—22no—
364C4×C61—22no—
365C4×C61—41no—
366C4×C61—41no—
367C4×C61—41no—
368Dic61—22no—
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#236111yescharacteristic
392C2×C61C2×#43511yescharacteristic
393C2×C61#292911yescharacteristic
394C2×C61D4×M1611yescharacteristic
395C2×C61#293511yescharacteristic
396C2×C61#299011yescharacteristic
397C2×C61#299211yescharacteristic
398D61—24no—
399D61—42no—
400D61—81no—
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—611no—
433#389#692311yescharacteristic
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×D4—611no—
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⋊C4C2×#692311yescharacteristic
486C2×C4⋊C4C2×#692311yescharacteristic
487C2×C4⋊C4C2×#692311yescharacteristic
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⋊C4—611no—
498C2×C22⋊C4—611no—
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#95C2×#692311yescharacteristic
530#95C2×#692311yescharacteristic
531C24—611no—
532C24—611no—
533C24—611no—
534C2×D4—614no—
535C2×D4—1222no—
536C2×D4—1222no—
537C2×D4—1222no—
538C2×D4—1222no—
539C2×D4—1222no—
540C2×D4—1222no—
541C2×D4—1222no—
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—1221no—
551C22×C4—1221no—
552C22×C4—1222no—
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—1222no—
570C22×C4—1222no—
571C22×C4—2441no—
572C22×C4C22×#692311yescharacteristic
573C22×C4C22×#692311yescharacteristic
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—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—2441no—
612C22⋊C4—1222no—
613C22⋊C4—1222no—
614C22⋊C4—1222no—
615C22⋊C4—1222no—
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—612no—
633C23—612no—
634C23—612no—
635C23—612no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23—1221no—
641C23—1221no—
642C23—1221no—
643C23—1221no—
644C23—1221no—
645C23—1221no—
646C23—1221no—
647C23—1221no—
648C23—1221no—
649C23—1221no—
650C23—1221no—
651C23—1221no—
652C23—1221no—
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—21no—
674C2×C4—611no—
675C2×C4—611no—
676C2×C4—611no—
677C2×C4—611no—
678C2×C4—611no—
679C2×C4—611no—
680C2×C4—612no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1228no—
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—2444no—
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×C4D4×#692312yes—
707C2×C4D4×#692312yes—
708C2×C4D61⋊M1612yes—
709C2×C4#1451986512yes—
710C8—1222no—
711C8—1222no—
712C8—1222no—
713C8—1222no—
714C8—2441no—
715C8—2441no—
716C8—2441no—
717C8—2441no—
718C22—614no—
719C22—1222no—
720C22—1222no—
721C22—1222no—
722C22—1222no—
723C22—1222no—
724C22—1222no—
725C22—1222no—
726C22—1222no—
727C22—1222no—
728C22—2441no—
729C22—2441no—
730C22—2441no—
731C22—2441no—
732C22—2441no—
733C22—2441no—
734C22—2441no—
735C22—2441no—
736C22—2441no—
737C22—2441no—
738C22—2441no—
739C22C2×D4×#692311yescharacteristic
740C22C2×D4×#692311yescharacteristic
741C22#1684083111yescharacteristic
742C22C2×D61⋊M1611yescharacteristic
743C22D61⋊#13111yescharacteristic
744C22C2×#1451986511yescharacteristic
745C22#1684084211yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—611no—
754C4—611no—
755C4—611no—
756C4—611no—
757C4—1222no—
758C4—2441no—
759C4—2441no—
760C4—2441no—
761C2—1224no—
762C2—4881no—
763C2—2442no—
764C2#2146234411yescharacteristic
765C2D61⋊#43511yescharacteristic
766C2#2146253511yescharacteristic
767C2#2146255911yescharacteristic
768C2#2146256511yescharacteristic
769C2#2146274911yescharacteristic
770C2#2146275911yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#389C4
prime radicalC2×#14519752C4
cosocleC22×Dic61C24
hypercenter#389#6923
hypocenterC61#22987
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#16840792C2semidirect
2. C2×#16840792C2semidirect
3. C2×#16840790C2semidirect
4. C2×D61⋊(C4⋊C8)C2semidirect
5. #21461945C2semidirect
6. #21461921C2semidirect
7. #21461894C2semidirect
8. #21461891C2semidirect
9. #21461795C2semidirect
10. #21461795C2semidirect
11. #21461765C2semidirect
12. #21461764C2semidirect
13. #21461619C2semidirect
14. #21461546C2semidirect
85. #14519844D4semidirect
96. #14519834D4semidirect
168. C2×D244M16semidirect
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×#168407922
C2×#168407902
C2×D61⋊(C4⋊C8)2
#214619452
#214619212
#214618942
#214618912
#214617952
#214617652
#214617642
#214616192
#214615462
#214483272
#2298761