Finite Group Databasebeta

← #30619314

Subgroups — #30619314

Order 15616.

994 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840793C211yesmaximal, characteristic, complemented
2C2×#16840791C211yesmaximal, characteristic, complemented
3#21461942C211yesmaximal, characteristic, complemented
4#21461940C211yesmaximal, characteristic, complemented
5#21461798C211yesmaximal, characteristic, complemented
6#21461797C211yesmaximal, characteristic, complemented
7#21461797C211yesmaximal, characteristic, complemented
8#21461796C211yesmaximal, characteristic, complemented
9#21461794C211yesmaximal, characteristic, complemented
10#21461792C211yesmaximal, characteristic, complemented
11#21461792C211yesmaximal, characteristic, complemented
12#21461792C211yesmaximal, characteristic, complemented
13#21461737C211yesmaximal, characteristic, complemented
14#21461538C211yesmaximal, characteristic, complemented
15#21449097C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic
17C22×#11758217C2211yescharacteristic
18C23×#92420C2211yescharacteristic
19C23×#92420C2211yescharacteristic
20#16840793—24no—
21#16840791—24no—
22C2×#14519844C2211yescharacteristic
23C2×C4⋊#92420C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25C2×#14519834C2211yescharacteristic
26C2×#14519834C2211yescharacteristic
27C2×C22⋊#92420C2211yescharacteristic
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×C4×#92420C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46C2×D4×Dic61C2211yescharacteristic
47C2×D4×Dic61C2211yescharacteristic
48C2×D4×Dic61C2211yescharacteristic
49C2×#14519737C2211yescharacteristic
50C2×#14519737C2211yescharacteristic
51C2×#14519737C2211yescharacteristic
52#16839699C411yescharacteristic
53#16839698C411yescharacteristic
54#16839698C411yescharacteristic
55#16839698C411yescharacteristic
56#16839670C411yescharacteristic
57#16839670C411yescharacteristic
58#16839670C411yescharacteristic
59#16839607C2211yescharacteristic
60C61×#392C411yescharacteristic
61C2×#11758213—22no—
62C2×#11758213—41no—
63C2×#11758213—41no—
64C2×#11758217—22no—
65C2×#11758217—41no—
66C2×#11758217—41no—
67C22×#92420—22no—
68C22×#92420—22no—
69C22×#92420—41no—
70C22×#92420—41no—
71C22×#92420—41no—
72C22×#92420—41no—
73C22×#92420C2311yescharacteristic
74C22×#92420C2311yescharacteristic
75C22×#92420C2311yescharacteristic
76C22×#92420C2311yescharacteristic
77C22×#92420C2311yescharacteristic
78C22×#92420C2311yescharacteristic
79C22×#92420C2311yescharacteristic
80C22×#92420C2311yescharacteristic
81#14519844—22no—
82C4⋊#92420—22no—
83#14519834—22no—
84#14519834—41no—
85#14519834—41no—
86C22⋊#92420—22no—
87C22⋊#92420—22no—
88C22⋊#92420—22no—
89C22⋊#92420—41no—
90C22⋊#92420—41no—
91C22⋊#92420—41no—
92C22⋊#92420—41no—
93C22⋊#92420—41no—
94C22⋊#92420—41no—
95#14519832D414yescomplemented
96C4×#92420—22no—
97C22×C22⋊D61C2×C411yescharacteristic
98C22×C22⋊D61C2×C411yescharacteristic
99C22×C22⋊D61C2×C411yescharacteristic
100C23×Dic61C2311yescharacteristic
101C23×Dic61C2311yescharacteristic
102C23×Dic61C2311yescharacteristic
103C22×C4×D61C2311yescharacteristic
104D4×Dic61—22no—
105D4×Dic61—22no—
106D4×Dic61—41no—
107D4×Dic61—41no—
108D4×Dic61—41no—
109D4×Dic61—41no—
110#14519737—22no—
111#14519737—22no—
112#14519737—41no—
113#14519737—41no—
114#14519737—41no—
115#14519737—41no—
116C2×C4⋊Dic61C2×C411yescharacteristic
117C2×C4⋊Dic61C2×C411yescharacteristic
118C2×C4⋊Dic61C2×C411yescharacteristic
119C2×#11758196C2×C411yescharacteristic
120C2×#11758196C2×C411yescharacteristic
121C2×#11758196C2×C411yescharacteristic
122C2×C22⋊Dic61C2×C411yescharacteristic
123C2×C22⋊Dic61C2×C411yescharacteristic
124C2×C22⋊Dic61C2×C411yescharacteristic
125C2×C22⋊Dic61C2×C411yescharacteristic
126C2×C22⋊Dic61C2×C411yescharacteristic
127C2×C22⋊Dic61C2×C411yescharacteristic
128C2×#11758198C2×C411yescharacteristic
129C2×#11758198C2×C411yescharacteristic
130C2×#11758198C2×C411yescharacteristic
131C2×C4×Dic61C2311yescharacteristic
132C2×C4×Dic61C2311yescharacteristic
133C2×C4×Dic61C2311yescharacteristic
134#14519684C2×C411yescharacteristic
135#14519684C2×C411yescharacteristic
136#14519684C2×C411yescharacteristic
137C22×D4×C61C2×C411yescharacteristic
138C22×D4×C61C2×C411yescharacteristic
139C22×D4×C61C2×C411yescharacteristic
140C2×C22⋊C4×C61C2×C411yescharacteristic
141C2×C22⋊C4×C61C2×C411yescharacteristic
142C2×C22⋊C4×C61C2×C411yescharacteristic
143#95×C61C2×C411yescharacteristic
144C24×C61C22×C411yescharacteristic
145C24×C61C22×C411yescharacteristic
146C24×C61C22×C411yescharacteristic
147C23×D61C22×C411yescharacteristic
148C2×D4×C61—22no—
149C2×D4×C61—22no—
150C2×D4×C61—22no—
151C2×D4×C61—22no—
152C2×D4×C61—22no—
153C2×D4×C61—41no—
154C2×D4×C61—41no—
155C2×D4×C61—41no—
156C2×D4×C61—41no—
157C22×C4×C61C22×C411yescharacteristic
158C22×C4×C61C22×C411yescharacteristic
159C22×C4×C61C22×C411yescharacteristic
160C22×C4×C61C22×C411yescharacteristic
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—22no—
164C2×C22⋊D61—41no—
165C2×C22⋊D61—41no—
166C2×C22⋊D61—41no—
167C2×C22⋊D61—41no—
168C2×C22⋊D61—41no—
169C2×C22⋊D61—41no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—21no—
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—21no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61C22×C411yescharacteristic
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C22×C411yescharacteristic
191C22×Dic61C22×C411yescharacteristic
192C22×Dic61C22×C411yescharacteristic
193C22×Dic61C22×C411yescharacteristic
194C22×Dic61C2411yescharacteristic
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201#11758217—44no—
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×#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—44no—
225C2×#92420—44no—
226C2×#92420C2×D412yes—
227C2×#92420C2×D412yes—
228#11758213—44no—
229C22⋊C4×C61—22no—
230C22⋊C4×C61—41no—
231C22⋊C4×C61—41no—
232C22⋊Dic61—22no—
233C22⋊Dic61—22no—
234C22⋊Dic61—41no—
235C22⋊Dic61—41no—
236C22⋊Dic61—41no—
237C22⋊Dic61—41no—
238#11758198—22no—
239#11758198—41no—
240#11758198—41no—
241C4⋊Dic61—22no—
242C4⋊Dic61—41no—
243C4⋊Dic61—41no—
244#11758196—22no—
245#11758196—41no—
246#11758196—41no—
247C4×Dic61—21no—
248C4×Dic61—21no—
249C4×Dic61—21no—
250C4×Dic61—21no—
251C4×Dic61C2×D412yes—
252C4×Dic61#4112yes—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
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—21no—
271C23×C61—21no—
272C23×C61#13112yes—
273C23×C61#13112yes—
274C23×C61C23×C411yescharacteristic
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—21no—
281C22×D61—21no—
282D4×C61—44no—
283D4×C61—44no—
284D4×C61—44no—
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—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61C4×D412yes—
297C22⋊D61—44no—
298C22⋊D61—44no—
299C22⋊D61—44no—
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—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61C4×D412yes—
330C2×Dic61C22×D411yescharacteristic
331C2×Dic61C2×#4111yescharacteristic
332C2×Dic61H(5,𝔽2)11yescharacteristic
333C2×Dic61H(5,𝔽2)11yescharacteristic
334C2×Dic61H(5,𝔽2)11yescharacteristic
335C2×Dic61H(5,𝔽2)11yescharacteristic
336C4×D61—41no—
337C4×D61—41no—
338C4×D61—41no—
339C4×D61—41no—
340#92420—22no—
341#92420—22no—
342#92420—41no—
343#92420—41no—
344#92420—41no—
345#92420—41no—
346#92420—41no—
347#92420—41no—
348#22267—611nomaximal, Sylow
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—22no—
352C22×C61—22no—
353C22×C61—22no—
354C22×C61—22no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61C2×C4×D411yescharacteristic
371C22×C61#51811yescharacteristic
372C22×C61#51811yescharacteristic
373C22×C61C2×#13111yescharacteristic
374C22×C61C2×#13111yescharacteristic
375C22×C61#56811yescharacteristic
376C22×C61#56811yescharacteristic
377C2×D61—41no—
378C2×D61—41no—
379C2×D61—41no—
380C2×D61—41no—
381C2×D61—41no—
382C2×D61—41no—
383C2×D61—41no—
384C4×C61—22no—
385C4×C61—41no—
386C4×C61—41no—
387C4×C61—41no—
388Dic61—22no—
389Dic61—41no—
390Dic61—41no—
391Dic61—41no—
392Dic61—41no—
393Dic61—41no—
394Dic61#53511yescharacteristic
395Dic61#53511yescharacteristic
396Dic61#54011yescharacteristic
397Dic61#54011yescharacteristic
398C2×#435—611no—
399C2×#435—611no—
400#2397—611no—
401#1954—611no—
402#1954—611no—
403#1870—611no—
404#1870—611no—
405#1870—611no—
406#1870—611no—
407#1869—611no—
408#1869—611no—
409#1869—611no—
410#1869—611no—
411#1832—611no—
412#1746—611no—
413C2×C61—42no—
414C2×C61—42no—
415C2×C61—81no—
416C2×C61#232811yescharacteristic
417C2×C61#293311yescharacteristic
418C2×C61#293311yescharacteristic
419C2×C61#297611yescharacteristic
420C2×C61#297611yescharacteristic
421C2×C61#297711yescharacteristic
422C2×C61#297811yescharacteristic
423D61—81no—
424C22×M16—611no—
425C22×M16—611no—
426C23×C8—611no—
427C23×C8—611no—
428C2×C4×D4—611no—
429C2×C4×D4—611no—
430C2×C4×D4—611no—
431C2×C4×D4—611no—
432C2×C4×D4—611no—
433C2×C4×D4—611no—
434#435—1224no—
435#435—1224no—
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×C4×C8—611no—
452#399—611no—
453#399—611no—
454#399—611no—
455#399—611no—
456#392—611no—
457#392—611no—
458#392—611no—
459#392#692311yescharacteristic
460#376—611no—
461#336—611no—
462#336—611no—
463#336—611no—
464#336—611no—
465#336—611no—
466#336—611no—
467#336—611no—
468#336—611no—
469C61#2226711yescharacteristic, complemented, Sylow
470C22×D4—611no—
471C22×D4—611no—
472C22×D4—611no—
473C22×D4C2×#692311yescharacteristic
474C22×D4C2×#692311yescharacteristic
475C22×D4C2×#692311yescharacteristic
476C23×C4—611no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—611no—
480C2×M16—1222no—
481C2×M16—1222no—
482C2×M16—2441no—
483C2×M16—2441no—
484C2×M16—2441no—
485C2×M16—2441no—
486C22×C8—611no—
487C22×C8—611no—
488C22×C8—611no—
489C22×C8—611no—
490C22×C8—611no—
491C22×C8—611no—
492C22×C8—611no—
493C22×C8—611no—
494C22×C8—1222no—
495C22×C8—1222no—
496C22×C8—2441no—
497C22×C8—2441no—
498C22×C8—2441no—
499C22×C8—2441no—
500C4×D4—1222no—
501C4×D4—1222no—
502C4×D4—1222no—
503C4×D4—1222no—
504C4×D4—2441no—
505C4×D4—2441no—
506C4×D4—2441no—
507C4×D4—2441no—
508C4×D4—2441no—
509C4×D4—2441no—
510C4×D4—2441no—
511C4×D4—2441no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—611no—
515C2×C4⋊C4—611no—
516C2×C4⋊C4—611no—
517C2×C4⋊C4—611no—
518C2×C22⋊C4—611no—
519C2×C22⋊C4—611no—
520C2×C22⋊C4—611no—
521C2×C22⋊C4—611no—
522C2×C22⋊C4—611no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—611no—
527C2×C22⋊C4C2×#692311yescharacteristic
528C2×C22⋊C4C2×#692311yescharacteristic
529C2×C22⋊C4C2×#692311yescharacteristic
530C2×C42—611no—
531C2×C42—611no—
532C2×C42—611no—
533C4⋊C8—1222no—
534C4⋊C8—1222no—
535C22⋊C8—1222no—
536C22⋊C8—1222no—
537C22⋊C8—1222no—
538C22⋊C8—1222no—
539C22⋊C8—2441no—
540C22⋊C8—2441no—
541C22⋊C8—2441no—
542C22⋊C8—2441no—
543C22⋊C8—2441no—
544C22⋊C8—2441no—
545C22⋊C8—2441no—
546C22⋊C8—2441no—
547#97—614no—
548C4×C8—1222no—
549#95—611no—
550#95—611no—
551#95—611no—
552#95C2×#692311yescharacteristic
553C24—611no—
554C24C22×#692311yescharacteristic
555C24C22×#692311yescharacteristic
556C24C22×#692311yescharacteristic
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—1222no—
567C2×D4—1222no—
568C2×D4—1222no—
569C2×D4—2441no—
570C2×D4—2441no—
571C2×D4—2441no—
572C2×D4—2441no—
573C2×D4—2441no—
574C2×D4—2441no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—611no—
578C22×C4—611no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1221no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
603C22×C4—1221no—
604C22×C4—1221no—
605C22×C4—1221no—
606C22×C4C22×#692311yescharacteristic
607C22×C4C22×#692311yescharacteristic
608C22×C4C22×#692311yescharacteristic
609C22×C4C22×#692311yescharacteristic
610M16—2444no—
611M16—2444no—
612C2×C8—612no—
613C2×C8—612no—
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—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—1221no—
631C2×C8—1221no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—2444no—
637C2×C8—2444no—
638C4⋊C4—1222no—
639C4⋊C4—1222no—
640C4⋊C4—2441no—
641C4⋊C4—2441no—
642C4⋊C4—2441no—
643C4⋊C4—2441no—
644C22⋊C4—22no—
645C22⋊C4—41no—
646C22⋊C4—41no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—2441no—
651C22⋊C4—2441no—
652C22⋊C4—2441no—
653C22⋊C4—2441no—
654C22⋊C4—2441no—
655C22⋊C4—2441no—
656C42—612no—
657C42—612no—
658C42—1221no—
659C42—1221no—
660C42—1221no—
661C42—1221no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—1221no—
682C23—1221no—
683C23—1221no—
684C23—1221no—
685C23—1221no—
686C23—1221no—
687C23—1221no—
688C23#1451986412yes—
689C23#1451986412yes—
690C23C23×#692311yescharacteristic
691D4—44no—
692D4—44no—
693D4—44no—
694D4—2444no—
695D4—2444no—
696D4—2444no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—611no—
709C2×C4—611no—
710C2×C4—611no—
711C2×C4—611no—
712C2×C4—611no—
713C2×C4—611no—
714C2×C4—612no—
715C2×C4—1221no—
716C2×C4—1221no—
717C2×C4—1221no—
718C2×C4—1221no—
719C2×C4—1221no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—1221no—
724C2×C4—1221no—
725C2×C4—1221no—
726C2×C4—1221no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—2441no—
733C2×C4—2441no—
734C2×C4—2441no—
735C2×C4—2441no—
736C2×C4—2441no—
737C2×C4—2441no—
738C2×C4—2441no—
739C2×C4—2441no—
740C2×C4—2441no—
741C2×C4—2441no—
742C2×C4—2441no—
743C2×C4—2441no—
744C2×C4—2441no—
745C2×C4—2441no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4D4×#692312yes—
749C8—1222no—
750C8—1222no—
751C8—2441no—
752C8—2441no—
753C8—2441no—
754C8—2441no—
755C8—2441no—
756C8—2441no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—2441no—
779C22—2441no—
780C22—2441no—
781C22—2441no—
782C22—2441no—
783C22—2441no—
784C22—2441no—
785C22C2×D4×#692311yescharacteristic
786C22#1684082911yescharacteristic
787C22#1684082911yescharacteristic
788C22C2×#1451986411yescharacteristic
789C22C2×#1451986411yescharacteristic
790C22#1684084011yescharacteristic
791C22#1684084111yescharacteristic
792C4—22no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—611no—
797C4—611no—
798C4—611no—
799C4—611no—
800C4—1222no—
801C4—2441no—
802C4—2441no—
803C4—2441no—
804C4—2441no—
805C4—2441no—
806C2—42no—
807C2—42no—
808C2—81no—
809C2—4881no—
810C2#2146231111yescharacteristic
811C2#2146254911yescharacteristic
812C2#2146255111yescharacteristic
813C2#2146268511yescharacteristic
814C2#2146268611yescharacteristic
815C2#2146269111yescharacteristic
816C2#2146269611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#392C4
prime radical#21449097C2
cosocleC22×Dic61C24
hypercenter#392#6923
hypocenterC61#22267
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#16840793C2semidirect
2. C2×#16840791C2semidirect
3. #21461942C2semidirect
4. #21461940C2semidirect
5. #21461798C2semidirect
6. #21461797C2semidirect
7. #21461797C2semidirect
8. #21461796C2semidirect
9. #21461794C2semidirect
10. #21461792C2semidirect
11. #21461792C2semidirect
12. #21461792C2semidirect
13. #21461737C2semidirect
14. #21461538C2semidirect
95. #14519832D4semidirect
469. C61#22267semidirect

Maximal subgroups

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

subgroupindex
C2×#168407932
C2×#168407912
#214619422
#214619402
#214617982
#214617972
#214617962
#214617942
#214617922
#214617372
#214615382
#214490972
#2226761