Finite Group Databasebeta

← #30619312

Subgroups — #30619312

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×#16840794C211yesmaximal, characteristic, complemented
2C2×#16840792C211yesmaximal, characteristic, complemented
3#21461942C211yesmaximal, characteristic, complemented
4#21461941C211yesmaximal, characteristic, complemented
5#21461799C211yesmaximal, characteristic, complemented
6#21461798C211yesmaximal, characteristic, complemented
7#21461798C211yesmaximal, characteristic, complemented
8#21461797C211yesmaximal, characteristic, complemented
9#21461795C211yesmaximal, characteristic, complemented
10#21461795C211yesmaximal, characteristic, complemented
11#21461795C211yesmaximal, characteristic, complemented
12#21461793C211yesmaximal, characteristic, complemented
13#21461737C211yesmaximal, characteristic, complemented
14#21461538C211yesmaximal, characteristic, complemented
15#21449099C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic
17C22×#11758217C2211yescharacteristic
18C22×D61⋊C8C2211yescharacteristic
19C22×D61⋊C8C2211yescharacteristic
20#16840794—24no—
21#16840792—24no—
22C2×#14519844C2211yescharacteristic
23C2×C4⋊#92420C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25C2×#14519834C2211yescharacteristic
26C2×#14519834C2211yescharacteristic
27C2×#14519834C2211yescharacteristic
28C2×#14519834C2211yescharacteristic
29C2×#14519834C2211yescharacteristic
30C2×#14519834C2211yescharacteristic
31C2×#14519834C2211yescharacteristic
32C2×#14519834C2211yescharacteristic
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×#14519739C2211yescharacteristic
47C2×#14519739C2211yescharacteristic
48C2×#14519739C2211yescharacteristic
49C2×#14519737C2211yescharacteristic
50C2×#14519737C2211yescharacteristic
51C2×#14519737C2211yescharacteristic
52#16839697C411yescharacteristic
53#16839697C411yescharacteristic
54#16839697C411yescharacteristic
55#16839672C411yescharacteristic
56#16839671C411yescharacteristic
57#16839671C411yescharacteristic
58#16839671C411yescharacteristic
59#16839607C2211yescharacteristic
60C61×#399C411yescharacteristic
61C2×#11758213—22no—
62C2×#11758213—41no—
63C2×#11758213—41no—
64C2×#11758217—22no—
65C2×#11758217—41no—
66C2×#11758217—41no—
67C2×D61⋊C8—22no—
68C2×D61⋊C8—22no—
69C2×D61⋊C8—41no—
70C2×D61⋊C8—41no—
71C2×D61⋊C8—41no—
72C2×D61⋊C8—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—22no—
85#14519834—22no—
86#14519834—41no—
87#14519834—41no—
88#14519834—41no—
89#14519834—41no—
90#14519834—41no—
91#14519834—41no—
92C22⋊#92420—22no—
93C22⋊#92420—41no—
94C22⋊#92420—41no—
95#14519832D414yescomplemented
96C4×#92420—22no—
97C22×D244C2×C411yescharacteristic
98C22×D244C2×C411yescharacteristic
99C22×D244C2×C411yescharacteristic
100C22×C22⋊D61C2×C411yescharacteristic
101C22×C22⋊D61C2×C411yescharacteristic
102C22×C22⋊D61C2×C411yescharacteristic
103C23×Dic61C2311yescharacteristic
104C22×C4×D61C2311yescharacteristic
105C22×C4×D61C2311yescharacteristic
106C22×C4×D61C2311yescharacteristic
107#14519739—22no—
108#14519739—22no—
109#14519739—41no—
110#14519739—41no—
111#14519739—41no—
112#14519739—41no—
113#14519737—22no—
114#14519737—22no—
115#14519737—41no—
116#14519737—41no—
117#14519737—41no—
118#14519737—41no—
119C2×#11758196C2×C411yescharacteristic
120C2×#11758196C2×C411yescharacteristic
121C2×#11758196C2×C411yescharacteristic
122C2×#11758198C2×C411yescharacteristic
123C2×#11758198C2×C411yescharacteristic
124C2×#11758198C2×C411yescharacteristic
125C2×#11758198C2×C411yescharacteristic
126C2×#11758198C2×C411yescharacteristic
127C2×#11758198C2×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
137C2×C4⋊C4×C61C2×C411yescharacteristic
138C2×C4⋊C4×C61C2×C411yescharacteristic
139C2×C4⋊C4×C61C2×C411yescharacteristic
140C2×C22⋊C4×C61C2×C411yescharacteristic
141C2×C22⋊C4×C61C2×C411yescharacteristic
142C2×C22⋊C4×C61C2×C411yescharacteristic
143#95×C61C2×C411yescharacteristic
144C24×C61C22×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
154C2×C22⋊D61—22no—
155C2×C22⋊D61—22no—
156C2×C22⋊D61—22no—
157C2×C22⋊D61—41no—
158C2×C22⋊D61—41no—
159C2×C22⋊D61—41no—
160C2×C22⋊D61—41no—
161C2×C22⋊D61—41no—
162C2×C22⋊D61—41no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C22×C411yescharacteristic
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C2411yescharacteristic
174C2×D244—22no—
175C2×D244—22no—
176C2×D244—22no—
177C2×D244—22no—
178C2×D244—22no—
179C2×D244—41no—
180C2×D244—41no—
181C2×D244—41no—
182C2×D244—41no—
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—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
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×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×#92420C2×D412yes—
225C2×#92420C2×D412yes—
226#11758213—44no—
227D61⋊C8—44no—
228D61⋊C8—44no—
229C4⋊C4×C61—22no—
230C4⋊C4×C61—41no—
231C4⋊C4×C61—41no—
232C22⋊C4×C61—22no—
233C22⋊C4×C61—41no—
234C22⋊C4×C61—41no—
235#11758198—22no—
236#11758198—22no—
237#11758198—22no—
238#11758198—41no—
239#11758198—41no—
240#11758198—41no—
241#11758198—41no—
242#11758198—41no—
243#11758198—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×C61C23×C411yescharacteristic
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61—21no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61#13112yes—
281C22×D61#13112yes—
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—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61C4×D412yes—
300C22⋊D61—44no—
301C22⋊D61—44no—
302C22⋊D61—44no—
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—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61C4×D412yes—
319C2×Dic61C22×D411yescharacteristic
320C2×Dic61C2×#4111yescharacteristic
321C2×Dic61H(5,𝔽2)11yescharacteristic
322C2×Dic61H(5,𝔽2)11yescharacteristic
323C2×Dic61H(5,𝔽2)11yescharacteristic
324C2×Dic61H(5,𝔽2)11yescharacteristic
325D244—44no—
326D244—44no—
327D244—44no—
328C4×D61—41no—
329C4×D61—41no—
330C4×D61—41no—
331C4×D61—41no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—41no—
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—41no—
350C22×C61—41no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61C2×C4×D411yescharacteristic
357C22×C61#51811yescharacteristic
358C22×C61#51811yescharacteristic
359C22×C61C2×#13111yescharacteristic
360C22×C61C2×#13111yescharacteristic
361C22×C61#56811yescharacteristic
362C22×C61#56811yescharacteristic
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—22no—
369C2×D61—41no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61—41no—
376C2×D61—41no—
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—
388C4×C61—41no—
389C4×C61—41no—
390Dic61—22no—
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—81no—
414C2×C61#232811yescharacteristic
415C2×C61#293311yescharacteristic
416C2×C61#293311yescharacteristic
417C2×C61#297611yescharacteristic
418C2×C61#297611yescharacteristic
419C2×C61#297711yescharacteristic
420C2×C61#297811yescharacteristic
421D61—42no—
422D61—42no—
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#692311yescharacteristic
456#392—611no—
457#392—611no—
458#392—611no—
459#392—611no—
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×D4—611no—
474C22×D4—611no—
475C22×D4—611no—
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⋊C4C2×#692311yescharacteristic
516C2×C4⋊C4C2×#692311yescharacteristic
517C2×C4⋊C4C2×#692311yescharacteristic
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—
554C24—611no—
555C24—611no—
556C24C22×#692311yescharacteristic
557C2×D4—1222no—
558C2×D4—1222no—
559C2×D4—1222no—
560C2×D4—1222no—
561C2×D4—1222no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—1222no—
565C2×D4—2441no—
566C2×D4—2441no—
567C2×D4—2441no—
568C2×D4—2441no—
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—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—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×C4C22×#692311yescharacteristic
605C22×C4C22×#692311yescharacteristic
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—22no—
639C4⋊C4—41no—
640C4⋊C4—41no—
641C4⋊C4—1222no—
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—612no—
670C23—612no—
671C23—1221no—
672C23—1221no—
673C23—1221no—
674C23—1221no—
675C23—1221no—
676C23—1221no—
677C23—1221no—
678C23—1221no—
679C23—1221no—
680C23—1221no—
681C23—1221no—
682C23—1221no—
683C23—1221no—
684C23—1221no—
685C23—1221no—
686C23—1221no—
687C23—1221no—
688C23—1221no—
689C23—1221no—
690C23C23×#692311yescharacteristic
691D4—2444no—
692D4—2444no—
693D4—2444no—
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—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—611no—
715C2×C4—611no—
716C2×C4—611no—
717C2×C4—611no—
718C2×C4—611no—
719C2×C4—611no—
720C2×C4—612no—
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—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—1222no—
765C22—1222no—
766C22—1222no—
767C22—1222no—
768C22—1222no—
769C22—1222no—
770C22—2441no—
771C22—2441no—
772C22—2441no—
773C22—2441no—
774C22—2441no—
775C22—2441no—
776C22—2441no—
777C22—2441no—
778C22—2441no—
779C22—2441no—
780C22—2441no—
781C22—2441no—
782C22—2441no—
783C22—2441no—
784C22—2441no—
785C22C2×D4×#692311yescharacteristic
786C22#1684082911yescharacteristic
787C22#1684082911yescharacteristic
788C22D61⋊#13111yescharacteristic
789C22D61⋊#13111yescharacteristic
790C22#1684084111yescharacteristic
791C22#1684084211yescharacteristic
792C4—22no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—611no—
799C4—611no—
800C4—611no—
801C4—611no—
802C4—1222no—
803C4—2441no—
804C4—2441no—
805C4—2441no—
806C2—81no—
807C2—4881no—
808C2—2442no—
809C2—2442no—
810C2#2146231111yescharacteristic
811C2#2146255311yescharacteristic
812C2#2146255411yescharacteristic
813C2#2146268711yescharacteristic
814C2#2146269011yescharacteristic
815C2#2146269311yescharacteristic
816C2#2146269811yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#399C4
prime radical#21449099C2
cosocleC22×Dic61C24
hypercenter#399#6923
hypocenterC61#22267
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#16840794C2semidirect
2. C2×#16840792C2semidirect
3. #21461942C2semidirect
4. #21461941C2semidirect
5. #21461799C2semidirect
6. #21461798C2semidirect
7. #21461798C2semidirect
8. #21461797C2semidirect
9. #21461795C2semidirect
10. #21461795C2semidirect
11. #21461795C2semidirect
12. #21461793C2semidirect
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×#168407942
C2×#168407922
#214619422
#214619412
#214617992
#214617982
#214617972
#214617952
#214617932
#214617372
#214615382
#214490992
#2226761