Finite Group Databasebeta

← #30620564

Subgroups — #30620564

Order 15616.

1100 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840786C211yesmaximal, characteristic, complemented
2C2×D61⋊(C22⋊C8)C211yesmaximal, characteristic
3#21461894C211yesmaximal, characteristic, complemented
4#21461894C211yesmaximal, characteristic, complemented
5#21461890C211yesmaximal, characteristic, complemented
6#21461890C211yesmaximal, characteristic, complemented
7#21461764C211yesmaximal, characteristic, complemented
8#21461764C211yesmaximal, characteristic, complemented
9#21461712C211yesmaximal, characteristic, complemented
10#21461677C211yesmaximal, characteristic, complemented
11#21461642C211yesmaximal, characteristic
12#21461557C211yesmaximal, characteristic, complemented
13#21461553C211yesmaximal, characteristic, complemented
14#21461549C211yesmaximal, characteristic, complemented
15#21448199C211yesmaximal, characteristic
16C22×D61⋊C8C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18#16840786—24no—
19C2×#14519844C2211yescharacteristic, complemented
20C2×#14519844C2211yescharacteristic, complemented
21C2×C4⋊#92420C2211yescharacteristic, complemented
22C2×C4⋊#92420C2211yescharacteristic, complemented
23C2×#14519834C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25C2×#14519834C2211yescharacteristic
26C2×#14519834C2211yescharacteristic
27C2×#14519834C2211yescharacteristic
28C2×#14519834C2211yescharacteristic
29D61⋊(C22⋊C8)—24no—
30C2×C22⋊#92420C2211yescharacteristic
31C2×C22⋊#92420C2211yescharacteristic
32C2×C22⋊#92420C2211yescharacteristic
33C2×C22⋊#92420C2211yescharacteristic
34C2×#14519832C2211yescharacteristic, complemented
35C2×#14519832C2211yescharacteristic, complemented
36C2×C4×#92420C2211yescharacteristic, complemented
37C2×C4×#92420C2211yescharacteristic, complemented
38#16840628C2211yescharacteristic, complemented
39#16840628C2211yescharacteristic, complemented
40#16840628C2211yescharacteristic, complemented
41#16840628C2211yescharacteristic, complemented
42#16840628C2211yescharacteristic, complemented
43#16840628C2211yescharacteristic, complemented
44#16840628C2211yescharacteristic, complemented
45#16840628C2211yescharacteristic, complemented
46C23×C4×D61C2211yescharacteristic
47C2×#14519733C2211yescharacteristic
48C2×#14519733C2211yescharacteristic
49#16839625C411yescharacteristic
50#16839621C411yescharacteristic
51#16839621C411yescharacteristic
52#16839621C411yescharacteristic
53#16839621C411yescharacteristic
54#16839617C411yescharacteristic
55#16839617C411yescharacteristic
56#16839609C2211yescharacteristic
57#16839609C2211yescharacteristic
58#16839609C2211yescharacteristic
59#16839609C2211yescharacteristic
60C61×#381C411yescharacteristic
61C2×D61⋊C8—22no—
62C2×D61⋊C8—22no—
63C2×D61⋊C8—22no—
64C2×D61⋊C8—22no—
65C2×D61⋊C8—41no—
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—
77C4⋊#92420—22no—
78C4⋊#92420—41no—
79#14519834—22no—
80#14519834—22no—
81#14519834—22no—
82#14519834—22no—
83#14519834—41no—
84#14519834—41no—
85C22⋊#92420—22no—
86C22⋊#92420—22no—
87C22⋊#92420—22no—
88C22⋊#92420D414yes—
89#14519832—22no—
90#14519832—41no—
91C4×#92420—22no—
92C4×#92420—41no—
93C24×D61C2×C411yescharacteristic
94C23×Dic61C2311yescharacteristic
95C22×C4×D61—22no—
96C22×C4×D61—22no—
97C22×C4×D61—22no—
98C22×C4×D61—22no—
99C22×C4×D61—41no—
100C22×C4×D61—41no—
101C22×C4×D61C2×C411yescharacteristic
102C22×C4×D61C2×C411yescharacteristic
103C22×C4×D61C2311yescharacteristic
104C22×C4×D61C2311yescharacteristic
105#14519733—22no—
106#14519733—22no—
107#14519733—41no—
108#14519733—41no—
109C2×#11758196C2×C411yescharacteristic
110C2×#11758196C2×C411yescharacteristic
111C2×#11758196C2×C411yescharacteristic
112C2×#11758196C2×C411yescharacteristic
113C2×C22⋊Dic61C2×C411yescharacteristic
114C2×C22⋊Dic61C2×C411yescharacteristic
115C2×#11758198C2×C411yescharacteristic
116C2×#11758198C2×C411yescharacteristic
117C2×#11758198C2×C411yescharacteristic
118C2×#11758198C2×C411yescharacteristic
119C2×#11758198C2×C411yescharacteristic
120C2×#11758198C2×C411yescharacteristic
121C2×#11758198C2×C411yescharacteristic
122C2×#11758198C2×C411yescharacteristic
123C2×C4×Dic61C2311yescharacteristic
124C2×C4×Dic61C2311yescharacteristic
125C2×C4×Dic61C2311yescharacteristic
126C2×C4×Dic61C2311yescharacteristic
127#14519684C2×C411yescharacteristic
128#14519684C2×C411yescharacteristic
129#14519684C2×C411yescharacteristic
130#14519684C2×C411yescharacteristic
131C23×C4×C61C2×C411yescharacteristic
132C2×C22⋊C4×C61C2×C411yescharacteristic
133C2×C22⋊C4×C61C2×C411yescharacteristic
134#95×C61C2×C411yescharacteristic
135#95×C61C2×C411yescharacteristic
136#95×C61C2×C411yescharacteristic
137#95×C61C2×C411yescharacteristic
138C24×C61C22×C411yescharacteristic
139C23×D61—22no—
140C23×D61—22no—
141C23×D61—22no—
142C23×D61—22no—
143C23×D61—22no—
144C23×D61—41no—
145C23×D61—41no—
146C23×D61C22×C411yescharacteristic
147C23×D61C22×C411yescharacteristic
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—41no—
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C22×C411yescharacteristic
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C2×D412yes—
167C22×Dic61#4112yes—
168C22×Dic61C2411yescharacteristic
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—44no—
184C2×C4×D61—44no—
185C2×C4×D61—44no—
186C2×C4×D61—44no—
187C2×C4×D61—41no—
188C2×C4×D61—41no—
189C2×C4×D61#4112yes—
190C2×C4×D61#4112yes—
191C2×#92420—21no—
192C2×#92420—21no—
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—
215D61⋊C8—44no—
216D61⋊C8—44no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—41no—
219C22⋊Dic61—22no—
220C22⋊Dic61—41no—
221#11758198—22no—
222#11758198—22no—
223#11758198—22no—
224#11758198—22no—
225#11758198—22no—
226#11758198—22no—
227#11758198—41no—
228#11758198—41no—
229#11758196—22no—
230#11758196—22no—
231#11758196—41no—
232#11758196—41no—
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×C61C4×D412yes—
248C23×C61C23×C411yescharacteristic
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—28no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—44no—
261C22×D61—44no—
262C22×D61—44no—
263C22×D61—44no—
264C22×D61—44no—
265C22×D61—44no—
266C22×D61#11712yes—
267C22×D61#13112yes—
268C22×D61#13112yes—
269C22×D61#13112yes—
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×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—44no—
288C2×C4×C61#11712yes—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—22no—
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×Dic61C4×D412yes—
308C2×Dic61C22×D411yescharacteristic
309C2×Dic61C2×#4111yescharacteristic
310C2×Dic61C2×#4111yescharacteristic
311C2×Dic61C2×#4111yescharacteristic
312C2×Dic61H(5,𝔽2)11yescharacteristic
313C2×Dic61H(5,𝔽2)11yescharacteristic
314C4×D61—22no—
315C4×D61—22no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—44no—
319C4×D61—44no—
320C4×D61—41no—
321C4×D61—41no—
322C4×D61—41no—
323C4×D61—41no—
324#92420—22no—
325#92420—22no—
326#92420—41no—
327#92420—41no—
328#92420—41no—
329#92420—41no—
330#92420—41no—
331#92420—41no—
332#22558—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×#11711yescharacteristic
341C22×C61C2×C4×D411yescharacteristic
342C22×C61#51811yescharacteristic
343C22×C61C2×#13111yescharacteristic
344C22×C61C2×#13111yescharacteristic
345C22×C61C2×#13111yescharacteristic
346C22×C61#56811yescharacteristic
347C2×D61—22no—
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—22no—
352C2×D61—22no—
353C2×D61—22no—
354C2×D61—22no—
355C2×D61—22no—
356C2×D61—416no—
357C2×D61—41no—
358C2×D61—41no—
359C2×D61—41no—
360C2×D61—41no—
361C2×D61#43314yescomplemented
362C4×C61—22no—
363C4×C61—41no—
364C4×C61—41no—
365C4×C61—41no—
366C4×C61—41no—
367C4×C61—41no—
368Dic61—22no—
369Dic61—41no—
370Dic61—41no—
371Dic61—41no—
372Dic61—41no—
373Dic61#54611yescharacteristic
374Dic61#54611yescharacteristic
375Dic61#55111yescharacteristic
376Dic61#55111yescharacteristic
377C2×#433—611no—
378C22×C22⋊C8—611no—
379#2280—611no—
380#1924—611no—
381#1924—611no—
382#1923—611no—
383#1923—611no—
384#1850—611no—
385#1850—611no—
386#1818—611no—
387#1798—611no—
388#1779—611no—
389#1752—611no—
390C8×C22⋊C4—611no—
391#1750—611no—
392C2×C61—42no—
393C2×C61#234211yescharacteristic
394C2×C61C2×#43311yescharacteristic
395C2×C61#292411yescharacteristic
396C2×C61#292911yescharacteristic
397C2×C61#293311yescharacteristic
398C2×C61#297611yescharacteristic
399C2×C61#297711yescharacteristic
400D61—24no—
401D61—42no—
402C24×C4—611no—
403C23×C8—611no—
404C23×C8—611no—
405C2×#117—611no—
406C2×#117—611no—
407#433—1224no—
408C2×C4⋊C8—611no—
409C2×C4⋊C8—611no—
410C2×C4⋊C8—611no—
411C2×C4⋊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×C22⋊C8—611no—
419C2×C22⋊C8—611no—
420C2×C22⋊C8—611no—
421C2×C22⋊C8—611no—
422C2×C22⋊C8—1224no—
423C2×#97—611no—
424C2×#97—611no—
425C2×C4×C8—611no—
426C2×C4×C8—611no—
427#381—611no—
428#381#692311yescharacteristic
429#380—611no—
430#380—611no—
431#380—611no—
432#380—611no—
433#379—611no—
434#379—611no—
435C4×C22⋊C4—611no—
436C4×C22⋊C4—611no—
437C4×C22⋊C4—611no—
438C4×C22⋊C4—611no—
439#336—611no—
440#336—611no—
441#336—611no—
442#336—611no—
443#336—611no—
444#336—611no—
445#336—611no—
446#336—611no—
447C61#2255811yescharacteristic, complemented, Sylow
448C25—611no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—611no—
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—1222no—
455C23×C4—1222no—
456C23×C4—1222no—
457C23×C4—1222no—
458C23×C4—2441no—
459C23×C4—2441no—
460C23×C4C2×#692311yescharacteristic
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—1222no—
472C22×C8—1222no—
473C22×C8—2441no—
474C22×C8—2441no—
475#117—1222no—
476#117—1222no—
477#117—2441no—
478#117—2441no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C22⋊C4—611no—
484C2×C22⋊C4—611no—
485C2×C22⋊C4—611no—
486C2×C22⋊C4—611no—
487C2×C22⋊C4—611no—
488C2×C22⋊C4—611no—
489C2×C22⋊C4—611no—
490C2×C22⋊C4—611no—
491C2×C22⋊C4—611no—
492C2×C22⋊C4—611no—
493C2×C22⋊C4C2×#692311yescharacteristic
494C2×C22⋊C4C2×#692311yescharacteristic
495C2×C42—611no—
496C2×C42—611no—
497C2×C42—611no—
498C2×C42—611no—
499C4⋊C8—1222no—
500C4⋊C8—1222no—
501C4⋊C8—2441no—
502C4⋊C8—2441no—
503C22⋊C8—614no—
504C22⋊C8—1222no—
505C22⋊C8—1222no—
506C22⋊C8—1222no—
507C22⋊C8—1222no—
508C22⋊C8—1222no—
509C22⋊C8—1222no—
510C22⋊C8—1222no—
511C22⋊C8—2441no—
512C22⋊C8—2441no—
513#97—1222no—
514#97—2441no—
515C4×C8—1222no—
516C4×C8—2441no—
517#95—611no—
518#95—611no—
519#95—611no—
520#95—611no—
521#95C2×#692311yescharacteristic
522#95C2×#692311yescharacteristic
523#95C2×#692311yescharacteristic
524#95C2×#692311yescharacteristic
525C24—611no—
526C24—611no—
527C24—1222no—
528C24—1222no—
529C24—1222no—
530C24—1222no—
531C24—1222no—
532C24—2441no—
533C24—2441no—
534C24C22×#692311yescharacteristic
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—41no—
538C22×C4—611no—
539C22×C4—612no—
540C22×C4—612no—
541C22×C4—611no—
542C22×C4—612no—
543C22×C4—612no—
544C22×C4—611no—
545C22×C4—611no—
546C22×C4—611no—
547C22×C4—611no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1222no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4—1222no—
560C22×C4—1222no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—1221no—
564C22×C4—1221no—
565C22×C4—1222no—
566C22×C4—2441no—
567C22×C4—2441no—
568C22×C4—2444no—
569C22×C4—2444no—
570C22×C4—2444no—
571C22×C4—2444no—
572C22×C4C22×#692311yescharacteristic
573C22×C4C22×#692311yescharacteristic
574C22×C4C22×#692311yescharacteristic
575C22×C4C22×#692311yescharacteristic
576C22×C4C22×#692311yescharacteristic
577C22×C4C22×#692311yescharacteristic
578C2×C8—612no—
579C2×C8—612no—
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—1221no—
601C2×C8—1221no—
602C2×C8—2444no—
603C2×C8—2444no—
604C4⋊C4—1222no—
605C4⋊C4—1222no—
606C4⋊C4—2441no—
607C4⋊C4—2441no—
608C22⋊C4—22no—
609C22⋊C4—41no—
610C22⋊C4—1222no—
611C22⋊C4—1222no—
612C22⋊C4—1222no—
613C22⋊C4—1222no—
614C22⋊C4—1222no—
615C22⋊C4—1222no—
616C22⋊C4—1222no—
617C22⋊C4—2441no—
618C22⋊C4—2441no—
619C22⋊C4—2441no—
620C42—1221no—
621C42—1221no—
622C42—1221no—
623C42—1221no—
624C42—1221no—
625C42—1221no—
626C42—1221no—
627C42—1221no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—612no—
635C23—612no—
636C23—612no—
637C23—612no—
638C23—1228no—
639C23—1221no—
640C23—1221no—
641C23—1221no—
642C23—1221no—
643C23—1221no—
644C23—1221no—
645C23—1221no—
646C23—1221no—
647C23—1221no—
648C23—1221no—
649C23—2444no—
650C23—2444no—
651C23—2444no—
652C23—2444no—
653C23—2444no—
654C23—2444no—
655C23D4×#692312yes—
656C23C23×#692311yescharacteristic
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—44no—
675C2×C4—611no—
676C2×C4—611no—
677C2×C4—611no—
678C2×C4—611no—
679C2×C4—611no—
680C2×C4—611no—
681C2×C4—612no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
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—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—1221no—
704C2×C4—2444no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2444no—
710C2×C4#1451985612yes—
711C8—1222no—
712C8—1222no—
713C8—2441no—
714C8—2441no—
715C8—2441no—
716C8—2441no—
717C8—2441no—
718C8—2441no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—614no—
727C22—1222no—
728C22—1222no—
729C22—1222no—
730C22—1222no—
731C22—1222no—
732C22—1222no—
733C22—1222no—
734C22—1222no—
735C22—1222no—
736C22—24416no—
737C22—2441no—
738C22—2441no—
739C22—2441no—
740C22—2441no—
741C22C2×#1451985611yescharacteristic
742C22C2×D4×#692311yescharacteristic
743C22#1684082911yescharacteristic
744C22D61⋊#13111yescharacteristic
745C22D61⋊#13111yescharacteristic
746C22D61⋊#13111yescharacteristic
747C22#1684084111yescharacteristic
748C4—22no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—611no—
755C4—611no—
756C4—611no—
757C4—611no—
758C4—1222no—
759C4—2441no—
760C4—2441no—
761C4—2441no—
762C4—2441no—
763C2—42no—
764C2—1224no—
765C2—2442no—
766C2#2146232511yescharacteristic
767C2D61⋊#43311yescharacteristic
768C2#2146251211yescharacteristic
769C2#2146253611yescharacteristic
770C2#2146255311yescharacteristic
771C2#2146268711yescharacteristic
772C2#2146269311yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#381C4
prime radicalC24×D61C2×C4
cosocleC22×Dic61C24
hypercenter#381#6923
hypocenterC61#22558
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
1. C2×#16840786C2semidirect
3. #21461894C2semidirect
4. #21461894C2semidirect
5. #21461890C2semidirect
6. #21461890C2semidirect
7. #21461764C2semidirect
8. #21461764C2semidirect
9. #21461712C2semidirect
10. #21461677C2semidirect
12. #21461557C2semidirect
13. #21461553C2semidirect
14. #21461549C2semidirect
19. C2×#14519844C22semidirect
20. C2×#14519844C22semidirect
21. C2×C4⋊#92420C22semidirect
22. C2×C4⋊#92420C22semidirect
34. C2×#14519832C22semidirect
35. C2×#14519832C22semidirect
36. C2×C4×#92420C22semidirect
37. C2×C4×#92420C22semidirect
38. #16840628C22semidirect
39. #16840628C22semidirect
40. #16840628C22semidirect
41. #16840628C22semidirect
42. #16840628C22semidirect
43. #16840628C22semidirect
44. #16840628C22semidirect
45. #16840628C22semidirect
361. C2×D61#433semidirect
447. C61#22558semidirect

Maximal subgroups

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

subgroupindex
C2×#168407862
C2×D61⋊(C22⋊C8)2
#214618942
#214618902
#214617642
#214617122
#214616772
#214616422
#214615572
#214615532
#214615492
#214481992
#2255861