Finite Group Databasebeta

← #30622183

Subgroups — #30622183

Order 15616.

992 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840796C211yesmaximal, characteristic, complemented
2C2×#16840795C211yesmaximal, characteristic, complemented
3C2×#16840794C211yesmaximal, characteristic, complemented
4C2×#16840769C211yesmaximal, characteristic, complemented
5#21461944C211yesmaximal, characteristic, complemented
6#21461916C211yesmaximal, characteristic, complemented
7#21461895C211yesmaximal, characteristic, complemented
8#21461888C211yesmaximal, characteristic, complemented
9#21461797C211yesmaximal, characteristic, complemented
10#21461795C211yesmaximal, characteristic, complemented
11#21461766C211yesmaximal, characteristic, complemented
12#21461765C211yesmaximal, characteristic, complemented
13#21461619C211yesmaximal, characteristic, complemented
14#21461548C211yesmaximal, characteristic, complemented
15#21449064C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic
17C22×#11758213C2211yescharacteristic
18C22×#11758217C2211yescharacteristic
19C22×D61⋊C8C2211yescharacteristic
20#16840796—24no—
21#16840795—24no—
22#16840794—24no—
23#16840769—24no—
24C2×#14519844C2211yescharacteristic
25C2×#14519844C2211yescharacteristic
26C2×C4⋊#92420C2211yescharacteristic
27C2×C4⋊#92420C2211yescharacteristic
28C2×C4⋊#92420C2211yescharacteristic
29C2×C4⋊#92420C2211yescharacteristic
30C2×#14519834C2211yescharacteristic
31C2×#14519834C2211yescharacteristic
32C2×#14519834C2211yescharacteristic
33C2×#14519834C2211yescharacteristic
34C2×#14519834C2211yescharacteristic
35C2×C22⋊#92420C2211yescharacteristic
36C2×C22⋊#92420C2211yescharacteristic
37C2×C22⋊#92420C2211yescharacteristic
38C2×#14519832C2211yescharacteristic
39C2×#14519832C2211yescharacteristic
40C2×C4×#92420C2211yescharacteristic
41C2×C4×#92420C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46#16840628C2211yescharacteristic
47#16840628C2211yescharacteristic
48C2×#14519739C2211yescharacteristic
49C2×#14519737C2211yescharacteristic
50C2×#14519737C2211yescharacteristic
51C2×#14519735C2211yescharacteristic
52#16839695C411yescharacteristic
53#16839691C411yescharacteristic
54#16839684C411yescharacteristic
55#16839679C411yescharacteristic
56#16839678C411yescharacteristic
57#16839678C411yescharacteristic
58#16839671C411yescharacteristic
59C4⋊C4×Dic61C2211yescharacteristic
60C22⋊C4×Dic61C2211yescharacteristic
61#16839609C2211yescharacteristic
62C61×#396C411yescharacteristic
63C2×#11758213—22no—
64C2×#11758213—22no—
65C2×#11758213—22no—
66C2×#11758213—22no—
67C2×#11758213—41no—
68C2×#11758213—41no—
69C2×#11758217—22no—
70C2×#11758217—22no—
71C2×#11758217—41no—
72C2×D61⋊C8—22no—
73C2×D61⋊C8—22no—
74C2×D61⋊C8—41no—
75C22×#92420C2311yescharacteristic
76C22×#92420C2311yescharacteristic
77C22×#92420C2311yescharacteristic
78C22×#92420C2311yescharacteristic
79C22×#92420C2311yescharacteristic
80C22×#92420C2311yescharacteristic
81C22×#92420C2311yescharacteristic
82C22×#92420C2311yescharacteristic
83#14519844—22no—
84#14519844D414yescomplemented
85C4⋊#92420—22no—
86C4⋊#92420—22no—
87C4⋊#92420—22no—
88C4⋊#92420—22no—
89#14519834—22no—
90#14519834—22no—
91#14519834—22no—
92#14519834—41no—
93#14519834D414yescomplemented
94C22⋊#92420—22no—
95C22⋊#92420—22no—
96C22⋊#92420—41no—
97#14519832—22no—
98#14519832—22no—
99C4×#92420—22no—
100C4×#92420—22no—
101C22×D244C2×C411yescharacteristic
102C22×C22⋊D61C2×C411yescharacteristic
103C22×C22⋊D61C2×C411yescharacteristic
104C23×Dic61C2311yescharacteristic
105C22×C4×D61C2311yescharacteristic
106C22×C4×D61C2311yescharacteristic
107#14519739—22no—
108#14519739—22no—
109#14519737—22no—
110#14519737—22no—
111#14519737—22no—
112#14519737—22no—
113#14519735—22no—
114#14519735—22no—
115C2×C4⋊Dic61C2×C411yescharacteristic
116C2×C4⋊Dic61C2×C411yescharacteristic
117C2×#11758196C2×C411yescharacteristic
118C2×#11758196C2×C411yescharacteristic
119C2×C22⋊Dic61C2×C411yescharacteristic
120C2×#11758198C2×C411yescharacteristic
121C2×#11758198C2×C411yescharacteristic
122C2×#11758198C2×C411yescharacteristic
123C2×#11758198C2×C411yescharacteristic
124C2×#11758198C2×C411yescharacteristic
125C2×#11758198C2×C411yescharacteristic
126C2×#11758198C2×C411yescharacteristic
127C2×#11758198C2×C411yescharacteristic
128C2×C4×Dic61C2311yescharacteristic
129C2×C4×Dic61C2311yescharacteristic
130C2×C4×Dic61C2311yescharacteristic
131C2×C4×Dic61C2311yescharacteristic
132#14519684C2×C411yescharacteristic
133#14519684C2×C411yescharacteristic
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
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C2×C22⋊D61—22no—
154C2×C22⋊D61—22no—
155C2×C22⋊D61—41no—
156C2×C22⋊D61—41no—
157C2×C22⋊D61—41no—
158C2×C22⋊D61—41no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61C22×C411yescharacteristic
166C22×Dic61C22×C411yescharacteristic
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C2411yescharacteristic
171C2×D244—22no—
172C2×D244—22no—
173C2×D244—41no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
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—21no—
184C2×C4×D61C2×D412yes—
185C2×C4×D61#4112yes—
186#11758217—44no—
187C2×#92420—21no—
188C2×#92420—21no—
189C2×#92420—21no—
190C2×#92420—21no—
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×#92420C2×D412yes—
208C2×#92420C2×D412yes—
209C2×#92420C2×D412yes—
210C2×#92420C2×D412yes—
211#11758213—44no—
212#11758213—44no—
213D61⋊C8—44no—
214C4⋊C4×C61—22no—
215C4⋊C4×C61—22no—
216C4⋊C4×C61—22no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—22no—
219C22⋊C4×C61—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—
229C4⋊Dic61—22no—
230C4⋊Dic61—41no—
231#11758196—22no—
232#11758196—22no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61C2×D412yes—
240C4×Dic61#4112yes—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61C23×C411yescharacteristic
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×D61C4×D412yes—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
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×C61C4×D412yes—
279C2×C4×C61C4×D412yes—
280C2×C4×C61#13112yes—
281C22⋊D61—44no—
282C22⋊D61—44no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
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—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61C4×D412yes—
302C2×Dic61C22×D411yescharacteristic
303C2×Dic61C22×D411yescharacteristic
304C2×Dic61C2×#4111yescharacteristic
305C2×Dic61C2×#4111yescharacteristic
306C2×Dic61H(5,𝔽2)11yescharacteristic
307C2×Dic612−1+411yescharacteristic
308D244—44no—
309C4×D61—22no—
310C4×D61—22no—
311C4×D61—22no—
312C4×D61—22no—
313C4×D61—41no—
314C4×D61—41no—
315C4×D61—41no—
316C4×D61—41no—
317#92420—22no—
318#92420—22no—
319#92420—22no—
320#92420—22no—
321#92420—41no—
322#92420—41no—
323#92420—41no—
324#92420—41no—
325#22994—611nomaximal, Sylow
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61C2×C4×D411yescharacteristic
334C22×C61C2×C4×D411yescharacteristic
335C22×C61#52011yescharacteristic
336C22×C61C2×#13111yescharacteristic
337C22×C61#56811yescharacteristic
338C22×C61#56811yescharacteristic
339C22×C61#56811yescharacteristic
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—41no—
344C2×D61—41no—
345C2×D61—41no—
346C2×D61—41no—
347C2×D61—41no—
348C2×D61—41no—
349C2×D61—41no—
350C2×D61—41no—
351C2×D61—41no—
352C2×D61—41no—
353C2×D61—41no—
354C4×C61—22no—
355C4×C61—22no—
356C4×C61—22no—
357C4×C61—41no—
358C4×C61—41no—
359C4×C61—41no—
360Dic61—22no—
361Dic61—41no—
362Dic61—41no—
363Dic61—41no—
364Dic61—41no—
365Dic61D4211yescharacteristic
366Dic61#54711yescharacteristic
367Dic61#54811yescharacteristic
368Dic61#55311yescharacteristic
369C2×#436—611no—
370C2×#436—611no—
371C2×#435—611no—
372C2×#424—611no—
373#2392—611no—
374#1955—611no—
375#1939—611no—
376#1924—611no—
377#1923—611no—
378#1870—611no—
379#1869—611no—
380#1851—611no—
381#1851—611no—
382#1771—611no—
383#1750—611no—
384C2×C61—81no—
385C2×C61#236111yescharacteristic
386C2×C61#293011yescharacteristic
387C2×C61#293011yescharacteristic
388C2×C61#293311yescharacteristic
389C2×C61#293511yescharacteristic
390C2×C61#299311yescharacteristic
391C2×C61#299511yescharacteristic
392D61—42no—
393D61—81no—
394C22×M16—611no—
395C22×M16—611no—
396C22×M16—611no—
397C23×C8—611no—
398C2×C4×D4—611no—
399C2×C4×D4—611no—
400C2×C4×D4—611no—
401C2×#117—611no—
402#436—1224no—
403#436—1224no—
404#435—1224no—
405#424—1224no—
406C2×C4⋊C8—611no—
407C2×C4⋊C8—611no—
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×#97—611no—
421C2×#97—611no—
422C2×C4×C8—611no—
423C2×C4×C8—611no—
424#398—611no—
425#397—611no—
426#396—611no—
427#396#692311yescharacteristic
428#394—611no—
429#394—611no—
430#394—611no—
431#392—611no—
432C4×C4⋊C4—611no—
433C4×C22⋊C4—611no—
434C4×C22⋊C4—611no—
435#336—611no—
436#336—611no—
437#336—611no—
438#336—611no—
439#336—611no—
440#336—611no—
441C61#2299411yescharacteristic, complemented, Sylow
442C22×D4—611no—
443C22×D4—611no—
444C22×D4—611no—
445C23×C4—611no—
446C23×C4—611no—
447C23×C4—611no—
448C2×M16—1222no—
449C2×M16—1222no—
450C2×M16—1222no—
451C2×M16—1222no—
452C2×M16—1222no—
453C2×M16—1222no—
454C2×M16—2441no—
455C2×M16—2441no—
456C2×M16—2441no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—611no—
461C22×C8—611no—
462C22×C8—611no—
463C22×C8—611no—
464C22×C8—611no—
465C22×C8—1222no—
466C22×C8—1222no—
467C22×C8—2441no—
468C4×D4—1222no—
469C4×D4—1222no—
470C4×D4—1222no—
471C4×D4—1222no—
472C4×D4—1222no—
473C4×D4—1222no—
474#117—1222no—
475#117—1222no—
476C2×C4⋊C4—611no—
477C2×C4⋊C4—611no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4C2×#692311yescharacteristic
481C2×C4⋊C4C2×#692311yescharacteristic
482C2×C4⋊C4C2×#692311yescharacteristic
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⋊C4C2×#692311yescharacteristic
493C2×C22⋊C4C2×#692311yescharacteristic
494C2×C22⋊C4C2×#692311yescharacteristic
495C2×C42—611no—
496C2×C42—611no—
497C2×C42—611no—
498C2×C42—611no—
499C4⋊C8—614no—
500C4⋊C8—1222no—
501C4⋊C8—1222no—
502C4⋊C8—1222no—
503C4⋊C8—1222no—
504C4⋊C8—1222no—
505C22⋊C8—614no—
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—1222no—
515C4×C8—1222no—
516C4×C8—1222no—
517#95—611no—
518#95—611no—
519#95—611no—
520#95—611no—
521#95—611no—
522#95C2×#692311yescharacteristic
523C24—611no—
524C24—611no—
525C24C22×#692311yescharacteristic
526C2×D4—1222no—
527C2×D4—1222no—
528C2×D4—1222no—
529C2×D4—1222no—
530C2×D4—2441no—
531C2×D4—2441no—
532C2×D4—2441no—
533C2×D4—2441no—
534C2×D4—2441no—
535C22×C4—611no—
536C22×C4—611no—
537C22×C4—612no—
538C22×C4—612no—
539C22×C4—611no—
540C22×C4—611no—
541C22×C4—611no—
542C22×C4—611no—
543C22×C4—1221no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—1221no—
559C22×C4C22×#692311yescharacteristic
560C22×C4C22×#692311yescharacteristic
561C22×C4C22×#692311yescharacteristic
562C22×C4C22×#692311yescharacteristic
563C22×C4C22×#692311yescharacteristic
564C22×C4C22×#692311yescharacteristic
565M16—2444no—
566M16—2444no—
567M16—2444no—
568C2×C8—612no—
569C2×C8—612no—
570C2×C8—612no—
571C2×C8—612no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
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—2444no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—1222no—
597C4⋊C4—1222no—
598C4⋊C4—1222no—
599C4⋊C4—2441no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—1222no—
604C22⋊C4—1222no—
605C22⋊C4—1222no—
606C22⋊C4—1222no—
607C22⋊C4—1222no—
608C22⋊C4—1222no—
609C22⋊C4—2441no—
610C22⋊C4—2441no—
611C22⋊C4—2441no—
612C42—612no—
613C42—612no—
614C42—1221no—
615C42—1221no—
616C42—1221no—
617C42—1221no—
618C42—1221no—
619C42—1221no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—612no—
628C23—1221no—
629C23—1221no—
630C23—1221no—
631C23—1221no—
632C23—1221no—
633C23—1221no—
634C23—1221no—
635C23—1221no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23—1221no—
640C23—1221no—
641C23C23×#692311yescharacteristic
642D4—2444no—
643D4—2444no—
644D4—2444no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—611no—
661C2×C4—611no—
662C2×C4—611no—
663C2×C4—611no—
664C2×C4—611no—
665C2×C4—611no—
666C2×C4—612no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1221no—
677C2×C4—1221no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1221no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4D4×#692312yes—
694C2×C4D4×#692312yes—
695C2×C4#1451986412yes—
696C8—1222no—
697C8—1222no—
698C8—1222no—
699C8—1222no—
700C8—2441no—
701C8—2441no—
702C8—2441no—
703C8—2441no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—1222no—
712C22—1222no—
713C22—1222no—
714C22—2441no—
715C22—2441no—
716C22—2441no—
717C22—2441no—
718C22—2441no—
719C22—2441no—
720C22—2441no—
721C22—2441no—
722C22—2441no—
723C22—2441no—
724C22—2441no—
725C22C2×D4×#692311yescharacteristic
726C22C2×D4×#692311yescharacteristic
727C22#1684083111yescharacteristic
728C22C2×#1451986411yescharacteristic
729C22#1684084111yescharacteristic
730C22#1684084111yescharacteristic
731C22#1684084211yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—611no—
739C4—611no—
740C4—611no—
741C4—611no—
742C4—1222no—
743C4—2441no—
744C4—2441no—
745C4—2441no—
746C4—2441no—
747C2—81no—
748C2—4881no—
749C2—2442no—
750C2#2146234411yescharacteristic
751C2#2146253911yescharacteristic
752C2#2146253911yescharacteristic
753C2#2146254911yescharacteristic
754C2#2146256111yescharacteristic
755C2#2146276411yescharacteristic
756C2#2146277411yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#396C4
prime radical#16839671C4
cosocleC22×Dic61C24
hypercenter#396#6923
hypocenterC61#22994
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#16840796C2semidirect
2. C2×#16840795C2semidirect
3. C2×#16840794C2semidirect
4. C2×#16840769C2semidirect
5. #21461944C2semidirect
6. #21461916C2semidirect
7. #21461895C2semidirect
8. #21461888C2semidirect
9. #21461797C2semidirect
10. #21461795C2semidirect
11. #21461766C2semidirect
12. #21461765C2semidirect
13. #21461619C2semidirect
14. #21461548C2semidirect
84. #14519844D4semidirect
93. #14519834D4semidirect
441. C61#22994semidirect

Maximal subgroups

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

subgroupindex
C2×#168407962
C2×#168407952
C2×#168407942
C2×#168407692
#214619442
#214619162
#214618952
#214618882
#214617972
#214617952
#214617662
#214617652
#214616192
#214615482
#214490642
#2299461