Finite Group Databasebeta

← #30620472

Subgroups — #30620472

Order 15616.

1108 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840814C211yesmaximal, characteristic, complemented
2C2×#16840812C211yesmaximal, characteristic, complemented
3#21461944C211yesmaximal, characteristic, complemented
4#21461944C211yesmaximal, characteristic, complemented
5#21461944C211yesmaximal, characteristic, complemented
6#21461943C211yesmaximal, characteristic, complemented
7#21461942C211yesmaximal, characteristic, complemented
8#21461940C211yesmaximal, characteristic, complemented
9#21461678C211yesmaximal, characteristic, complemented
10#21461677C211yesmaximal, characteristic, complemented
11#21461673C211yesmaximal, characteristic, complemented
12#21461549C211yesmaximal, characteristic, complemented
13#21461548C211yesmaximal, characteristic, complemented
14#21461545C211yesmaximal, characteristic, complemented
15C2×#16840289C211yesmaximal, characteristic
16#16840814—24no—
17#16840812—24no—
18C2×#14519844C2211yescharacteristic
19C2×#14519844C2211yescharacteristic
20C2×C4⋊#92420C2211yescharacteristic
21C2×C4⋊#92420C2211yescharacteristic
22C2×C4⋊#92420C2211yescharacteristic
23C2×C4⋊#92420C2211yescharacteristic
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×C22⋊#92420C2211yescharacteristic
35C2×C22⋊#92420C2211yescharacteristic
36C2×#14519832C2211yescharacteristic
37C2×#14519832C2211yescharacteristic
38C2×#14519832C2211yescharacteristic
39C2×#14519832C2211yescharacteristic
40C2×C4×#92420C2211yescharacteristic
41C2×C4×#92420C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46#16840289—24no—
47#16840289—24no—
48C2×#14519772C411yescharacteristic
49C2×#14519770C411yescharacteristic
50C2×#14519767C411yescharacteristic
51C2×#14519763C411yescharacteristic
52C2×#14519760C411yescharacteristic
53C2×#14519754C411yescharacteristic
54C2×#14519749C411yescharacteristic
55C2×#14519742C2211yescharacteristic
56C2×D4×Dic61C2211yescharacteristic
57C2×#14519737C2211yescharacteristic
58C2×#14519737C2211yescharacteristic
59C2×#14519735C2211yescharacteristic
60C2×#14519733C2211yescharacteristic
61C22×C4×Dic61C2211yescharacteristic
62C2×#123×C61C411yescharacteristic
63C22×#92420C2311yescharacteristic
64C22×#92420C2311yescharacteristic
65C22×#92420C2311yescharacteristic
66C22×#92420C2311yescharacteristic
67C22×#92420C2311yescharacteristic
68C22×#92420C2311yescharacteristic
69C22×#92420C2311yescharacteristic
70C22×#92420C2311yescharacteristic
71#14519844—22no—
72#14519844—22no—
73C4⋊#92420—22no—
74C4⋊#92420—22no—
75C4⋊#92420—22no—
76C4⋊#92420—22no—
77#14519834—22no—
78#14519834—22no—
79#14519834—41no—
80#14519834—41no—
81C22⋊#92420—22no—
82C22⋊#92420—22no—
83C22⋊#92420—22no—
84C22⋊#92420—22no—
85C22⋊#92420—41no—
86C22⋊#92420—41no—
87C22⋊#92420—41no—
88C22⋊#92420—41no—
89#14519832—22no—
90#14519832—22no—
91#14519832—22no—
92#14519832—22no—
93C4×#92420—22no—
94C4×#92420—22no—
95C22×Dic122C2×C411yescharacteristic
96C22×C22⋊D61C2×C411yescharacteristic
97C22×C22⋊D61C2×C411yescharacteristic
98C23×Dic61C2×C411yescharacteristic
99C23×Dic61C2311yescharacteristic
100C23×Dic61C2311yescharacteristic
101C22×C4×D61C2311yescharacteristic
102#14519772—24no—
103#14519770—24no—
104#14519767—24no—
105#14519763—24no—
106#14519760—24no—
107#14519754—24no—
108#14519749—24no—
109#14519742D414yes—
110#14519742D414yes—
111D4×Dic61—22no—
112D4×Dic61—22no—
113#14519737—22no—
114#14519737—22no—
115#14519737—22no—
116#14519737—22no—
117#14519735—22no—
118#14519735—22no—
119#14519733—22no—
120#14519733—22no—
121C2×C4⋊Dic61C2×C411yescharacteristic
122C2×C4⋊Dic61C2×C411yescharacteristic
123C2×#11758196C2×C411yescharacteristic
124C2×#11758196C2×C411yescharacteristic
125C2×#11758196C2×C411yescharacteristic
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2×C411yescharacteristic
128C2×#11758196C2×C411yescharacteristic
129C2×C22⋊Dic61C2×C411yescharacteristic
130C2×C22⋊Dic61C2×C411yescharacteristic
131C2×C22⋊Dic61C2×C411yescharacteristic
132C2×#11758198C2×C411yescharacteristic
133C2×#11758198C2×C411yescharacteristic
134C2×#11758198C2×C411yescharacteristic
135C2×#11758198C2×C411yescharacteristic
136C2×C4×Dic61—22no—
137C2×C4×Dic61—22no—
138C2×C4×Dic61C2×C411yescharacteristic
139C2×C4×Dic61C2×C411yescharacteristic
140C2×C4×Dic61C2311yescharacteristic
141C2×C4×Dic61C2311yescharacteristic
142C2×C4×Dic61C2311yescharacteristic
143C2×C4×Dic61C2311yescharacteristic
144C22×D4×C61C2×C411yescharacteristic
145C23×C4×C61C2×C411yescharacteristic
146#123×C61—24no—
147C2×C4⋊C4×C61C2×C411yescharacteristic
148C2×C4⋊C4×C61C2×C411yescharacteristic
149C2×C22⋊C4×C61C2×C411yescharacteristic
150C2×C22⋊C4×C61C2×C411yescharacteristic
151C2×C22⋊C4×C61C2×C411yescharacteristic
152C24×C61C22×C411yescharacteristic
153C24×C61C22×C411yescharacteristic
154C23×D61C22×C411yescharacteristic
155C2×D4×C61—22no—
156C2×D4×C61—22no—
157C2×D4×C61—41no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—41no—
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C411yescharacteristic
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—22no—
169C2×C22⋊D61—41no—
170C2×C22⋊D61—41no—
171C2×C22⋊D61—41no—
172C22×Dic61—22no—
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—21no—
184C22×Dic61—21no—
185C22×Dic61—41no—
186C22×Dic61—41no—
187C22×Dic61C22×C411yescharacteristic
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C22×C411yescharacteristic
191C22×Dic61C22×C411yescharacteristic
192C22×Dic61C22×C411yescharacteristic
193C22×Dic61C2411yescharacteristic
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×Dic122—41no—
201C2×Dic122—41no—
202C2×Dic122C22⋊C414yes—
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—21no—
217C2×#92420—21no—
218C2×#92420—21no—
219C2×#92420—21no—
220C2×#92420—21no—
221C2×#92420—21no—
222C2×#92420—21no—
223C2×#92420—21no—
224C2×#92420—21no—
225C2×#92420#4112yes—
226C2×#92420#4112yes—
227C4⋊C4×C61—22no—
228C4⋊C4×C61C22⋊C414yes—
229C22⋊C4×C61—22no—
230C22⋊C4×C61—22no—
231C22⋊C4×C61—22no—
232C22⋊Dic61—22no—
233C22⋊Dic61—22no—
234C22⋊Dic61—22no—
235#11758198—22no—
236#11758198—22no—
237#11758198—22no—
238#11758198—22no—
239C4⋊Dic61—22no—
240C4⋊Dic61—22no—
241#11758196—22no—
242#11758196—22no—
243#11758196—22no—
244#11758196—22no—
245#11758196C22⋊C414yes—
246#11758196C22⋊C414yes—
247C4×Dic61—22no—
248C4×Dic61—22no—
249C4×Dic61—21no—
250C4×Dic61—21no—
251C4×Dic61C2×D412yes—
252C4×Dic61C2×D412yes—
253C4×Dic61C2×D412yes—
254C4×Dic61C2×D412yes—
255C4×Dic61C2×D412yes—
256C4×Dic61C2×D412yes—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61#13112yes—
271C23×C61C23×C411yescharacteristic
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279D4×C61—44no—
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—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—44no—
293C2×C4×C61C2×C22⋊C412yes—
294C2×C4×C61C2×C22⋊C412yes—
295C2×C4×C61C2×C22⋊C412yes—
296C22⋊D61—44no—
297C22⋊D61—44no—
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×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—44no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61C2×C22⋊C412yes—
323C2×Dic61C2×C22⋊C412yes—
324C2×Dic61C2×C22⋊C412yes—
325C2×Dic61C22×D411yescharacteristic
326C2×Dic61C22×D411yescharacteristic
327C2×Dic61C2×#4111yescharacteristic
328C2×Dic61C2×#4111yescharacteristic
329C2×Dic61H(5,𝔽2)11yescharacteristic
330C2×Dic612−1+411yescharacteristic
331C4×D61—41no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—41no—
335Dic122—44no—
336#92420—22no—
337#92420—22no—
338#92420—41no—
339#92420—41no—
340#92420—41no—
341#92420—41no—
342#92420—41no—
343#92420—41no—
344#22533—611nomaximal, Sylow
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—22no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61C22×C22⋊C411yescharacteristic
360C22×C61C4×#4111yescharacteristic
361C22×C61#52011yescharacteristic
362C22×C61C2×#13111yescharacteristic
363C22×C61#56811yescharacteristic
364C22×C61#56811yescharacteristic
365C22×C61#56811yescharacteristic
366C2×D61—41no—
367C2×D61—41no—
368C2×D61—41no—
369C2×D61—41no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—41no—
373C4×C61—22no—
374C4×C61—22no—
375C4×C61—22no—
376C4×C61—41no—
377C4×C61—41no—
378Dic61—22no—
379Dic61—22no—
380Dic61—22no—
381Dic61—41no—
382Dic61—41no—
383Dic61—41no—
384Dic61#54811yescharacteristic
385Dic61#54811yescharacteristic
386Dic61#55011yescharacteristic
387Dic61#55011yescharacteristic
388C2×#529—611no—
389C2×#446—611no—
390C2×#446—611no—
391#1955—611no—
392#1955—611no—
393#1955—611no—
394#1955—611no—
395#1954—611no—
396#1954—611no—
397#1798—611no—
398#1798—611no—
399#1797—611no—
400#1750—611no—
401#1750—611no—
402#1749—611no—
403C2×C61—42no—
404C2×C61—81no—
405C2×C61#234111yescharacteristic
406C2×C61#287911yescharacteristic
407C2×C61#288011yescharacteristic
408C2×C61#296711yescharacteristic
409C2×C61#296811yescharacteristic
410C2×C61#299211yescharacteristic
411C2×C61#299511yescharacteristic
412D61—81no—
413#529—1224no—
414#529—1224no—
415C2×#126—611no—
416C2×#126—611no—
417C2×#125—611no—
418C2×#124—611no—
419C2×#123—611no—
420C2×#123#692311yescharacteristic
421C2×C22⋊Q8—611no—
422C2×#121—611no—
423C2×C4×Q8—611no—
424C2×C4×D4—611no—
425C2×C4×D4—611no—
426C2×C4×D4—611no—
427C2×#117—611no—
428C2×#117—611no—
429C22×C42—611no—
430#446—1224no—
431#446—1224no—
432C2×C4⋊C8—611no—
433C2×C4⋊C8—611no—
434C2×C4⋊C8—611no—
435C2×C4⋊C8—611no—
436C2×C4⋊C8—611no—
437C2×C4⋊C8—611no—
438C2×C22⋊C8—611no—
439C2×C22⋊C8—611no—
440C2×C22⋊C8—611no—
441C2×C22⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C22⋊C8—611no—
444C2×C22⋊C8—611no—
445C2×C22⋊C8—611no—
446C2×C22⋊C8—611no—
447C2×C22⋊C8—611no—
448C2×C22⋊C8—611no—
449C2×C22⋊C8—611no—
450C2×#97—611no—
451C2×#97—611no—
452C2×#97—611no—
453C2×#97—611no—
454C2×C4×C8—611no—
455C2×C4×C8—611no—
456#336—611no—
457#336—611no—
458#336—611no—
459#336—611no—
460C61#2253311yescharacteristic, complemented, Sylow
461C22×Q8—611no—
462C22×D4—611no—
463C22×D4—611no—
464C22×D4C2×#692311yescharacteristic
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4C2×#692311yescharacteristic
470C22×C8—611no—
471C22×C8—611no—
472C22×C8—611no—
473C22×C8—611no—
474C22×C8—611no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8—611no—
478#126—1224no—
479#126—1224no—
480#125—1224no—
481#124—1224no—
482#123—24no—
483#123—1224no—
484C22⋊Q8—1224no—
485#121—1224no—
486C4×Q8—614no—
487C4×Q8—614no—
488C4×D4—1222no—
489C4×D4—1222no—
490C4×D4—1222no—
491C4×D4—1222no—
492C4×D4—1222no—
493C4×D4—1222no—
494#117—1222no—
495#117—1222no—
496#117—1222no—
497#117—1222no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—611no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4C2×#692311yescharacteristic
507C2×C4⋊C4C2×#692311yescharacteristic
508C2×C22⋊C4—611no—
509C2×C22⋊C4—611no—
510C2×C22⋊C4—611no—
511C2×C22⋊C4—611no—
512C2×C22⋊C4—611no—
513C2×C22⋊C4—611no—
514C2×C22⋊C4—611no—
515C2×C22⋊C4C2×#692311yescharacteristic
516C2×C22⋊C4C2×#692311yescharacteristic
517C2×C22⋊C4C2×#692311yescharacteristic
518C2×C42—611no—
519C2×C42—611no—
520C2×C42—611no—
521C2×C42—611no—
522C2×C42—611no—
523C2×C42—611no—
524C2×C42—1222no—
525C2×C42—1222no—
526C4⋊C8—1222no—
527C4⋊C8—1222no—
528C4⋊C8—1222no—
529C4⋊C8—1222no—
530C4⋊C8—1222no—
531C4⋊C8—1222no—
532C22⋊C8—1222no—
533C22⋊C8—1222no—
534C22⋊C8—1222no—
535C22⋊C8—1222no—
536C22⋊C8—1222no—
537C22⋊C8—1222no—
538C22⋊C8—2441no—
539C22⋊C8—2441no—
540C22⋊C8—2441no—
541C22⋊C8—2441no—
542C22⋊C8—2441no—
543C22⋊C8—2441no—
544#97—1222no—
545#97—1222no—
546#97—1222no—
547#97—1222no—
548C4×C8—1222no—
549C4×C8—1222no—
550C24—611no—
551C24C22×#692311yescharacteristic
552C24C22×#692311yescharacteristic
553C2×Q8—614no—
554C2×Q8—2441no—
555C2×Q8—2441no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—41no—
559C2×D4—1222no—
560C2×D4—1222no—
561C2×D4—1222no—
562C2×D4—2441no—
563C2×D4—2441no—
564C2×D4—2441no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—41no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—611no—
572C22×C4—611no—
573C22×C4—611no—
574C22×C4—611no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1222no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—2441no—
595C22×C4—2441no—
596C22×C4C22×#692311yescharacteristic
597C22×C4C22×#692311yescharacteristic
598C22×C4C22×#692311yescharacteristic
599C22×C4C22×#692311yescharacteristic
600C22×C4C22×#692311yescharacteristic
601C2×C8—612no—
602C2×C8—612no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C4⋊C4—22no—
626C4⋊C4—614no—
627C4⋊C4—614no—
628C4⋊C4—1222no—
629C4⋊C4—1222no—
630C4⋊C4—1222no—
631C4⋊C4—1222no—
632C4⋊C4—1222no—
633C4⋊C4—1222no—
634C4⋊C4C22⋊#692314yes—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—1222no—
639C22⋊C4—1222no—
640C22⋊C4—1222no—
641C22⋊C4—1222no—
642C22⋊C4—1222no—
643C22⋊C4—1222no—
644C22⋊C4—1222no—
645C42—612no—
646C42—612no—
647C42—612no—
648C42—612no—
649C42—612no—
650C42—612no—
651C42—1221no—
652C42—1221no—
653C42—1222no—
654C42—1222no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—1221no—
669C23—1221no—
670C23—1221no—
671C23—1221no—
672C23—1221no—
673C23—1221no—
674C23—1221no—
675C23#1451986412yes—
676C23C23×#692311yescharacteristic
677Q8—2444no—
678D4—44no—
679D4—2444no—
680D4—2444no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—44no—
694C2×C4—611no—
695C2×C4—611no—
696C2×C4—611no—
697C2×C4—611no—
698C2×C4—611no—
699C2×C4—611no—
700C2×C4—612no—
701C2×C4—612no—
702C2×C4—612no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1221no—
712C2×C4—1221no—
713C2×C4—1221no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2444no—
731C2×C4C2×C22⋊#692312yes—
732C2×C4C2×C22⋊#692312yes—
733C2×C4C2×C22⋊#692312yes—
734C8—1222no—
735C8—1222no—
736C8—2441no—
737C8—2441no—
738C8—2441no—
739C8—2441no—
740C8—2441no—
741C8—2441no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—2441no—
757C22—2441no—
758C22—2441no—
759C22—2441no—
760C22—2441no—
761C22—2441no—
762C22—2441no—
763C22C22×C22⋊#692311yescharacteristic
764C22#41×#692311yescharacteristic
765C22#1684083111yescharacteristic
766C22C2×#1451986411yescharacteristic
767C22#1684084011yescharacteristic
768C22#1684084111yescharacteristic
769C22#1684084111yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—41no—
774C4—41no—
775C4—611no—
776C4—611no—
777C4—611no—
778C4—611no—
779C4—1222no—
780C4—1222no—
781C4—1222no—
782C4—2441no—
783C4—2441no—
784C4—2441no—
785C2—42no—
786C2—81no—
787C2—4881no—
788C2#2146232411yescharacteristic
789C2#2146240411yescharacteristic
790C2#2146240711yescharacteristic
791C2#2146264111yescharacteristic
792C2#2146264611yescharacteristic
793C2#2146275411yescharacteristic
794C2#2146277311yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC2×#123×C61C4
prime radicalC2×#14519749C4
cosocleC22×Dic61C24
hypercenterC2×#123#6923
hypocenterC61#22533
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#16840814C2semidirect
2. C2×#16840812C2semidirect
3. #21461944C2semidirect
4. #21461944C2semidirect
5. #21461944C2semidirect
6. #21461943C2semidirect
7. #21461942C2semidirect
8. #21461940C2semidirect
9. #21461678C2semidirect
10. #21461677C2semidirect
11. #21461673C2semidirect
12. #21461549C2semidirect
13. #21461548C2semidirect
14. #21461545C2semidirect
460. C61#22533semidirect

Maximal subgroups

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

subgroupindex
C2×#168408142
C2×#168408122
#214619442
#214619432
#214619422
#214619402
#214616782
#214616772
#214616732
#214615492
#214615482
#214615452
C2×#168402892
#2253361