Finite Group Databasebeta

← #14680979

Subgroups — #14680979

Order 2816.

2150 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66946C211yesmaximal, characteristic
2C2×#10622277C211yesmaximal, characteristic, complemented
3C2×#10622600C211yesmaximal, characteristic, complemented
4#13066869C211yesmaximal, characteristic, complemented
5#13066864C212yesmaximal, complemented
6#13066862C211yesmaximal, characteristic, complemented
7#13066858C211yesmaximal, characteristic, complemented
8#13066856C212yesmaximal
9#13066841C212yesmaximal, complemented
10(C2×D11)⋊#95C212yesmaximal, complemented
11C11×#1441C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C2×#66946—24no—
26C2×#66946—24no—
27C2×#66946C418yescomplemented
28C2×C11×#95C2212yes—
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622600—24no—
39#10622277—24no—
40C24×D11C2311yescharacteristic
41C24×D11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C22×D44—22no—
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—22no—
55C22×D44—22no—
56C22×D44—22no—
57C22×D44C2×C414yes—
58C22×C4×D11—22no—
59C22×C4×D11—22no—
60C22×C4×D11—42no—
61C22×C4×D11—42no—
62C22×C4×D11—42no—
63C22×C4×D11—42no—
64C22×C4×D11C2×C414yes—
65C22×C4×D11C2×C414yes—
66C22×C4×D11D414yes—
67C22×C4×D11D414yes—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—42no—
72C2×C11×C4⋊C4C2×C414yes—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—42no—
82C2×(C2×D11)⋊C4—42no—
83C2×(C2×D11)⋊C4—42no—
84C2×(C2×D11)⋊C4—42no—
85C2×(C2×D11)⋊C4—42no—
86C2×(C2×D11)⋊C4—42no—
87C2×(C2×D11)⋊C4—42no—
88C2×(C2×D11)⋊C4—42no—
89C2×(C2×D11)⋊C4C2×C414yes—
90C2×(C2×D11)⋊C4C2×C414yes—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—42no—
93C2×C4×Dic11—22no—
94C2×C4×Dic11—22no—
95C2×C4×Dic11C2×C414yes—
96#66946—232no—
97C11×#95—22no—
98C11×#95—24no—
99C11×#95—42no—
100C11⋊#95—22no—
101C11⋊#95—24no—
102C11⋊#95—24no—
103C11⋊#95—24no—
104C11⋊#95—42no—
105C11⋊#95—42no—
106C11⋊#95—42no—
107#14344—111nomaximal, Sylow
108C24×C11C2411yescharacteristic
109C23×D11—21no—
110C23×D11—21no—
111C23×D11—21no—
112C23×D11—21no—
113C23×D11—21no—
114C23×D11—21no—
115C23×D11—21no—
116C23×D11—21no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11C22×C412yes—
126C23×D11C22×C412yes—
127C23×D11C2×D412yes—
128C23×D11C2×D412yes—
129C23×D11#4112yes—
130C23×D11#4112yes—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C22×C412yes—
157C22×C4×C11C22×C412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11#4112yes—
161C22×C4×C11#4112yes—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11C22×C412yes—
183C22×Dic11C22×C412yes—
184C22×Dic11C2×D412yes—
185C22×Dic11C2×D412yes—
186C2×D44—28no—
187C2×D44—28no—
188C2×D44—28no—
189C2×D44—28no—
190C2×D44—28no—
191C2×D44—28no—
192C2×D44—28no—
193C2×C4×D11—28no—
194C2×C4×D11—48no—
195C2×C4×D11—48no—
196C2×C4×D11—44no—
197C2×C4×D11—44no—
198C2×C4×D11—48no—
199C2×C4×D11—44no—
200C2×C4×D11—48no—
201C2×C4×D11—44no—
202C2×C4×D11C22⋊C4116yescomplemented
203C11×C4⋊C4—28no—
204C11×C4⋊C4—44no—
205(C2×D11)⋊C4—28no—
206(C2×D11)⋊C4—28no—
207(C2×D11)⋊C4—48no—
208(C2×D11)⋊C4—48no—
209(C2×D11)⋊C4—48no—
210(C2×D11)⋊C4—48no—
211C4⋊Dic11—44no—
212C4×Dic11—28no—
213C22×C4×D4—111no—
214C2×#381—111no—
215C2×#380—111no—
216#1441—111no—
217#1441D1111yescharacteristic, complemented
218#1440—112no—
219#1439—111no—
220#1439—111no—
221#1438—112no—
222#1434—112no—
223C22⋊#95—112no—
224C23×C11C23×C411yescharacteristic
225C23×C11C22×D411yescharacteristic
226C23×C11C22×D411yescharacteristic
227C23×C11C2×#4111yescharacteristic
228C23×C11C2×#4111yescharacteristic
229C23×C11C2×#4111yescharacteristic
230C23×C11C2×#4111yescharacteristic
231C23×C11H(5,𝔽2)12yes—
232C23×C11H(5,𝔽2)12yes—
233C23×C11H(5,𝔽2)12yes—
234C23×C112−1+412yes—
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—24no—
240C22×D11—24no—
241C22×D11—24no—
242C22×D11—24no—
243C22×D11—22no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—22no—
251C22×D11—24no—
252C22×D11—22no—
253C22×D11—22no—
254C22×D11—22no—
255C22×D11—22no—
256C22×D11—24no—
257C22×D11—24no—
258C22×D11—24no—
259C22×D11—24no—
260C22×D11—24no—
261C22×D11—41no—
262C22×D11—42no—
263C22×D11—41no—
264C22×D11—41no—
265C22×D11—41no—
266C22×D11—42no—
267C22×D11—42no—
268C22×D11—42no—
269C22×D11—42no—
270C22×D11—42no—
271C22×D11—42no—
272C22×D11—42no—
273C22×D11—42no—
274C22×D11—42no—
275C22×D11—42no—
276C22×D11—42no—
277C22×D11—42no—
278C22×D11—42no—
279C22×D11C2×C22⋊C414yes—
280C22×D11#11714yes—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—24no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—24no—
291C2×C4×C11—22no—
292C2×C4×C11—24no—
293C2×C4×C11—41no—
294C2×C4×C11—42no—
295C2×C4×C11—41no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11C2×C22⋊C414yes—
311C2×C4×C11#11714yes—
312C2×Dic11—24no—
313C2×Dic11—22no—
314C2×Dic11—24no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—24no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—42no—
321C2×Dic11—42no—
322C2×Dic11—42no—
323C2×Dic11—42no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11C2×C22⋊C414yes—
336D44—232no—
337C4×D11—416no—
338C4×D11—416no—
339C23×D4—111no—
340C24×C4—111no—
341C24×C4—111no—
342C2×C4×D4—118no—
343C2×C4×D4—224no—
344C2×C4×D4—224no—
345C22×C4⋊C4—111no—
346C22×C4⋊C4C2×D1111yescharacteristic
347C22×C4⋊C4C2×D1111yescharacteristic
348C22×C22⋊C4—111no—
349C22×C22⋊C4—111no—
350C22×C22⋊C4—112no—
351C22×C22⋊C4—112no—
352C22×C22⋊C4—112no—
353C22×C22⋊C4—112no—
354C22×C42—111no—
355#381—224no—
356#380—224no—
357C2×#95—112no—
358C2×#95—112no—
359C2×#95—112no—
360C2×#95—111no—
361C2×#95—112no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95C2×D1112yes—
365C2×#95C2×D1111yescharacteristic
366C2×#95C2×D1112yes—
367C22×C11C22×C22⋊C411yescharacteristic
368C22×C11C2×#11711yescharacteristic
369C22×C11C2×#11711yescharacteristic
370C22×C11#51812yes—
371C22×C11#52012yes—
372C22×C11#52511yescharacteristic
373C22×C11#52511yescharacteristic
374C22×C11#52511yescharacteristic
375C22×C11#52511yescharacteristic
376C22×C11#53411yescharacteristic
377C22×C11#53412yes—
378C22×C11#53411yescharacteristic
379C22×C11#53511yescharacteristic
380C22×C11#53611yescharacteristic
381C22×C11#53712yes—
382C22×C11#53812yes—
383C22×C11#53812yes—
384C22×C11#53912yes—
385C22×C11#53912yes—
386C22×C11#54012yes—
387C22×C11#54012yes—
388C22×C11#54212yes—
389C22×C11#54212yes—
390C2×D11—24no—
391C2×D11—24no—
392C2×D11—28no—
393C2×D11—24no—
394C2×D11—24no—
395C2×D11—42no—
396C2×D11—42no—
397C2×D11—44no—
398C2×D11—44no—
399C2×D11—44no—
400C2×D11—44no—
401C2×D11—44no—
402C2×D11—44no—
403C2×D11—44no—
404C2×D11—42no—
405C2×D11—42no—
406C2×D11—42no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—42no—
411C2×D11—42no—
412C4×C11—24no—
413C4×C11—24no—
414C4×C11—42no—
415C4×C11—82no—
416C4×C11—82no—
417Dic11—24no—
418Dic11—42no—
419Dic11—82no—
420Dic11—82no—
421C25—111no—
422C25—111no—
423C22×D4—114no—
424C22×D4—222no—
425C22×D4—222no—
426C22×D4—222no—
427C22×D4—222no—
428C22×D4—222no—
429C22×D4—222no—
430C23×C4—111no—
431C23×C4—114no—
432C23×C4—114no—
433C23×C4—114no—
434C23×C4—111no—
435C23×C4—114no—
436C23×C4—112no—
437C23×C4—112no—
438C23×C4—222no—
439C23×C4—222no—
440C23×C4—442no—
441C23×C4—442no—
442C23×C4—442no—
443C23×C4—442no—
444C23×C4C22×D1112yes—
445C23×C4C22×D1112yes—
446C23×C4C22×D1111yescharacteristic
447C23×C4C22×D1111yescharacteristic
448C23×C4C22×D1111yescharacteristic
449C4×D4—2232no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—222no—
455C2×C4⋊C4—442no—
456C2×C4⋊C4C4×D1114yes—
457C2×C22⋊C4—114no—
458C2×C22⋊C4—114no—
459C2×C22⋊C4—222no—
460C2×C22⋊C4—222no—
461C2×C22⋊C4—222no—
462C2×C22⋊C4—222no—
463C2×C22⋊C4—224no—
464C2×C22⋊C4—224no—
465C2×C22⋊C4—224no—
466C2×C22⋊C4—224no—
467C2×C22⋊C4—442no—
468C2×C22⋊C4—442no—
469C2×C22⋊C4—442no—
470C2×C22⋊C4—442no—
471C2×C22⋊C4—442no—
472C2×C22⋊C4—442no—
473C2×C22⋊C4—442no—
474C2×C22⋊C4—442no—
475C2×C42—114no—
476C2×C42—222no—
477C2×C42—222no—
478#95—22no—
479#95—24no—
480#95—42no—
481#95—224no—
482#95—224no—
483#95—222no—
484#95—224no—
485#95—442no—
486#95—442no—
487#95—442no—
488C2×C11#228011yescharacteristic
489C2×C11#230811yescharacteristic
490C2×C11#231111yescharacteristic
491C2×C11#231812yes—
492C2×C11#231912yes—
493C2×C11#263012yes—
494C2×C11#263012yes—
495C2×C11#263511yescharacteristic
496C2×C11#263511yescharacteristic
497C2×C11#263811yescharacteristic
498C2×C11#263811yescharacteristic
499D11—44no—
500D11—44no—
501C24—112no—
502C24—112no—
503C24—112no—
504C24—112no—
505C24—112no—
506C24—112no—
507C24—221no—
508C24—221no—
509C24—221no—
510C24—221no—
511C24—222no—
512C24—222no—
513C24—221no—
514C24—221no—
515C24—222no—
516C24—222no—
517C24—221no—
518C24—221no—
519C24—222no—
520C24—222no—
521C24—222no—
522C24—222no—
523C24C23×D1111yescharacteristic
524C2×D4—228no—
525C2×D4—228no—
526C2×D4—228no—
527C2×D4—228no—
528C2×D4—228no—
529C2×D4—228no—
530C2×D4—228no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—112no—
556C22×C4—112no—
557C22×C4—112no—
558C22×C4—1116no—
559C22×C4—112no—
560C22×C4—228no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—448no—
582C22×C4—444no—
583C22×C4—448no—
584C22×C4—444no—
585C22×C4—448no—
586C22×C4—444no—
587C22×C4—448no—
588C22×C4—444no—
589C22×C4C2×C4×D1112yes—
590C22×C4C2×C4×D1112yes—
591C22×C4C2×C4×D1112yes—
592C22×C4D4×D1112yes—
593C22×C4D4×D1112yes—
594C22×C4#434112yes—
595C22×C4#434312yes—
596C4⋊C4—28no—
597C4⋊C4—44no—
598C4⋊C4—444no—
599C22⋊C4—228no—
600C22⋊C4—228no—
601C22⋊C4—448no—
602C22⋊C4—448no—
603C22⋊C4—448no—
604C22⋊C4—448no—
605C42—228no—
606C11#1434411yescharacteristic, complemented, Sylow
607C23—114no—
608C23—114no—
609C23—224no—
610C23—222no—
611C23—222no—
612C23—222no—
613C23—222no—
614C23—222no—
615C23—224no—
616C23—224no—
617C23—224no—
618C23—224no—
619C23—222no—
620C23—224no—
621C23—222no—
622C23—222no—
623C23—222no—
624C23—222no—
625C23—222no—
626C23—222no—
627C23—222no—
628C23—222no—
629C23—224no—
630C23—224no—
631C23—222no—
632C23—224no—
633C23—222no—
634C23—224no—
635C23—442no—
636C23—441no—
637C23—442no—
638C23—442no—
639C23—441no—
640C23—442no—
641C23—442no—
642C23—442no—
643C23—442no—
644C23—442no—
645C23—442no—
646C23—442no—
647C23—441no—
648C23—442no—
649C23—441no—
650C23—442no—
651C23—442no—
652C23—442no—
653C23C22×C4×D1111yescharacteristic
654C23C2×D4×D1111yescharacteristic
655C23C2×D4×D1111yescharacteristic
656C23C2×#434111yescharacteristic
657C23#6703712yes—
658C23C2×#434311yescharacteristic
659C23#6704012yes—
660C23#41×D1111yescharacteristic
661C23#41×D1111yescharacteristic
662C23#6704212yes—
663C23#6704212yes—
664D4—2232no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—114no—
695C2×C4—224no—
696C2×C4—222no—
697C2×C4—224no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—224no—
701C2×C4—4416no—
702C2×C4—4416no—
703C2×C4—441no—
704C2×C4—442no—
705C2×C4—441no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—442no—
709C2×C4—442no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4—442no—
713C2×C4—442no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4C22⋊C4×D1114yes—
721C2×C4#6694514yes—
722C22—224no—
723C22—224no—
724C22—228no—
725C22—224no—
726C22—224no—
727C22—444no—
728C22—444no—
729C22—444no—
730C22—444no—
731C22—442no—
732C22—442no—
733C22—442no—
734C22—442no—
735C22—442no—
736C22—442no—
737C22—442no—
738C22—442no—
739C22—442no—
740C22—442no—
741C22—444no—
742C22—444no—
743C22—444no—
744C22C2×C22⋊C4×D1111yescharacteristic
745C22C2×#6694511yescharacteristic
746C22D11×#11711yescharacteristic
747C22#1062307612yes—
748C22#1062310512yes—
749C22#1062312011yescharacteristic
750C22#1062313612yes—
751C22#1062313711yescharacteristic
752C22#1062313711yescharacteristic
753C22#1062315012yes—
754C22#1062315811yescharacteristic
755C22#1062315811yescharacteristic
756C22#1062316012yes—
757C22#1062316912yes—
758C22#1062317412yes—
759C22#1062318411yescharacteristic
760C22#1062318812yes—
761C22#1062320511yescharacteristic
762C22#1062322312yes—
763C22#1062322912yes—
764C22#1062323512yes—
765C22#1062325511yescharacteristic
766C22#1062326412yes—
767C4—24no—
768C4—24no—
769C4—42no—
770C4—82no—
771C4—82no—
772C4—224no—
773C4—442no—
774C4—882no—
775C4—882no—
776C2—444no—
777C2—444no—
778C2#1307099811yescharacteristic
779C2#1307119011yescharacteristic
780C2#1307120711yescharacteristic
781C2#1307124812yes—
782C2#1307125512yes—
783C2#1307446412yes—
784C2#1307446612yes—
785C2#1307450811yescharacteristic
786C2#1307450911yescharacteristic
787C2#1307454111yescharacteristic
788C2#1307454211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1441D11
hypocenterC11#14344
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C2×#10622277C2semidirect
3. C2×#10622600C2semidirect
4. #13066869C2semidirect
5. #13066864C2semidirect
6. #13066862C2semidirect
7. #13066858C2semidirect
9. #13066841C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C11×#1441C2semidirect
27. C2×#66946C4semidirect
202. C2×C4×D11C22⋊C4semidirect
217. #1441D11semidirect
606. C11#14344semidirect

Maximal subgroups

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

subgroupindex
C22×#669462
C2×#106222772
C2×#106226002
#130668692
#130668642
#130668622
#130668582
#130668562
#130668412
(C2×D11)⋊#952
C11×#14412
#1434411