Finite Group Databasebeta

← #14680978

Subgroups — #14680978

Order 2816.

2150 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D44C211yesmaximal, characteristic
2C2×#10622277C211yesmaximal, characteristic, complemented
3C2×#10622280C211yesmaximal, characteristic, complemented
4#13066868C212yesmaximal, complemented
5#13066864C212yesmaximal, complemented
6#13066860C212yesmaximal, complemented
7#13066856C212yesmaximal
8#13066843C211yesmaximal, characteristic, complemented
9(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
11C11×#1434C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×(C2×D11)⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C2×C4×D44—24no—
25C2×C4×D44—24no—
26C2×C4×D44C418yescomplemented
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2212yes—
30C2×C11×#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622280—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—24no—
54C22×D44—24no—
55C22×D44C2×C414yes—
56C22×C4×D11—22no—
57C22×C4×D11—22no—
58C22×C4×D11—42no—
59C22×C4×D11—42no—
60C22×C4×D11—42no—
61C22×C4×D11—42no—
62C22×C4×D11C2×C414yes—
63C22×C4×D11C2×C414yes—
64C22×C4×D11D414yes—
65C22×C4×D11D414yes—
66C2×C42×C11—22no—
67C2×C42×C11—22no—
68C2×C42×C11C2×C414yes—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—42no—
78C2×(C2×D11)⋊C4—42no—
79C2×(C2×D11)⋊C4—42no—
80C2×(C2×D11)⋊C4—42no—
81C2×(C2×D11)⋊C4—42no—
82C2×(C2×D11)⋊C4—42no—
83C2×(C2×D11)⋊C4—42no—
84C2×(C2×D11)⋊C4—42no—
85C2×(C2×D11)⋊C4C2×C414yes—
86C2×(C2×D11)⋊C4C2×C414yes—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11C2×C414yes—
90C2×Dic11⋊C4—24no—
91C2×Dic11⋊C4—42no—
92C2×Dic11⋊C4—42no—
93C4×D44—232no—
94C11×#95—22no—
95C11×#95—22no—
96C11×#95—24no—
97C11×#95—42no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95—42no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105#14344—111nomaximal, Sylow
106C24×C11C2411yescharacteristic
107C23×D11—21no—
108C23×D11—21no—
109C23×D11—22no—
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—21no—
113C23×D11—21no—
114C23×D11—21no—
115C23×D11—21no—
116C23×D11—22no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—21no—
121C23×D11—21no—
122C23×D11—21no—
123C23×D11—21no—
124C23×D11C22×C412yes—
125C23×D11C22×C412yes—
126C23×D11C2×D412yes—
127C23×D11C2×D412yes—
128C23×D11#4114yes—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
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×C11C22×C412yes—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C22×C412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11#4114yes—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—22no—
163C22×Dic11—22no—
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×Dic11C22×C412yes—
181C22×Dic11C22×C412yes—
182C22×Dic11C2×D412yes—
183C22×Dic11C2×D412yes—
184C2×D44—216no—
185C2×D44—216no—
186C2×D44—28no—
187C2×D44—28no—
188C2×D44—28no—
189C2×C4×D11—28no—
190C2×C4×D11—44no—
191C2×C4×D11—44no—
192C2×C4×D11—44no—
193C2×C4×D11—44no—
194C2×C4×D11—48no—
195C2×C4×D11—48no—
196C2×C4×D11—48no—
197C2×C4×D11—48no—
198C2×C4×D11C22⋊C4116yescomplemented
199C42×C11—28no—
200(C2×D11)⋊C4—28no—
201(C2×D11)⋊C4—28no—
202(C2×D11)⋊C4—48no—
203(C2×D11)⋊C4—48no—
204(C2×D11)⋊C4—48no—
205(C2×D11)⋊C4—48no—
206C4⋊Dic11—28no—
207Dic11⋊C4—48no—
208C22×C4×D4—111no—
209C2×#381—111no—
210C2×#380—111no—
211#1441—112no—
212#1440—112no—
213#1439—112no—
214#1438—112no—
215#1434—111no—
216#1434D1111yescharacteristic, complemented
217C22⋊#95—111no—
218C22⋊#95—111no—
219C23×C11C23×C411yescharacteristic
220C23×C11C22×D411yescharacteristic
221C23×C11C22×D411yescharacteristic
222C23×C11C2×#4112yes—
223C23×C11C2×#4112yes—
224C23×C11H(5,𝔽2)11yescharacteristic
225C23×C11H(5,𝔽2)12yes—
226C23×C11H(5,𝔽2)12yes—
227C23×C11H(5,𝔽2)11yescharacteristic
228C23×C112−1+411yescharacteristic
229C23×C112−1+411yescharacteristic
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—22no—
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—24no—
243C22×D11—24no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—24no—
247C22×D11—24no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—22no—
251C22×D11—22no—
252C22×D11—24no—
253C22×D11—24no—
254C22×D11—24no—
255C22×D11—24no—
256C22×D11—42no—
257C22×D11—42no—
258C22×D11—41no—
259C22×D11—41no—
260C22×D11—41no—
261C22×D11—41no—
262C22×D11—42no—
263C22×D11—42no—
264C22×D11—42no—
265C22×D11—42no—
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×D11C2×C22⋊C414yes—
275C22×D11#11714yes—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—24no—
281C2×C4×C11—24no—
282C2×C4×C11—24no—
283C2×C4×C11—24no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11—42no—
295C2×C4×C11—42no—
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×C11C2×C22⋊C414yes—
306C2×C4×C11#11714yes—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—24no—
310C2×Dic11—24no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—42no—
315C2×Dic11—42no—
316C2×Dic11—42no—
317C2×Dic11—42no—
318C2×Dic11—42no—
319C2×Dic11—42no—
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×Dic11C2×C22⋊C414yes—
331D44—232no—
332C4×D11—416no—
333C4×D11—416no—
334C23×D4—111no—
335C24×C4—111no—
336C24×C4—111no—
337C2×C4×D4—118no—
338C2×C4×D4—224no—
339C2×C4×D4—224no—
340C22×C4⋊C4—111no—
341C22×C4⋊C4—112no—
342C22×C22⋊C4—111no—
343C22×C22⋊C4—111no—
344C22×C22⋊C4—112no—
345C22×C22⋊C4—112no—
346C22×C22⋊C4—112no—
347C22×C22⋊C4—112no—
348C22×C42C2×D1111yescharacteristic
349#381—224no—
350#380—224no—
351C2×#95—111no—
352C2×#95—111no—
353C2×#95—112no—
354C2×#95—112no—
355C2×#95—112no—
356C2×#95—112no—
357C2×#95—112no—
358C2×#95C2×D1111yescharacteristic
359C2×#95C2×D1111yescharacteristic
360C2×#95C2×D1112yes—
361C2×#95C2×D1112yes—
362C22×C11C22×C22⋊C411yescharacteristic
363C22×C11C2×#11711yescharacteristic
364C22×C11C2×#11711yescharacteristic
365C22×C11#51811yescharacteristic
366C22×C11#51811yescharacteristic
367C22×C11#52011yescharacteristic
368C22×C11#52011yescharacteristic
369C22×C11#52512yes—
370C22×C11#52512yes—
371C22×C11#53412yes—
372C22×C11#53412yes—
373C22×C11#53511yescharacteristic
374C22×C11#53611yescharacteristic
375C22×C11#53711yescharacteristic
376C22×C11#53711yescharacteristic
377C22×C11#53812yes—
378C22×C11#53812yes—
379C22×C11#53912yes—
380C22×C11#53912yes—
381C22×C11#54012yes—
382C22×C11#54012yes—
383C22×C11#54212yes—
384C22×C11#54212yes—
385C2×D11—24no—
386C2×D11—24no—
387C2×D11—24no—
388C2×D11—24no—
389C2×D11—24no—
390C2×D11—24no—
391C2×D11—42no—
392C2×D11—42no—
393C2×D11—42no—
394C2×D11—42no—
395C2×D11—42no—
396C2×D11—42no—
397C2×D11—42no—
398C2×D11—42no—
399C2×D11—44no—
400C2×D11—44no—
401C2×D11—44no—
402C2×D11—44no—
403C2×D11—44no—
404C2×D11—44no—
405C2×D11—44no—
406C2×D11—44no—
407C4×C11—24no—
408C4×C11—24no—
409C4×C11—42no—
410C4×C11—82no—
411C4×C11—82no—
412Dic11—24no—
413Dic11—42no—
414Dic11—82no—
415Dic11—82no—
416C25—111no—
417C25—111no—
418C22×D4—114no—
419C22×D4—222no—
420C22×D4—222no—
421C22×D4—224no—
422C22×D4—224no—
423C23×C4—111no—
424C23×C4—114no—
425C23×C4—114no—
426C23×C4—114no—
427C23×C4—111no—
428C23×C4—114no—
429C23×C4—112no—
430C23×C4—112no—
431C23×C4—222no—
432C23×C4—222no—
433C23×C4—442no—
434C23×C4—442no—
435C23×C4—442no—
436C23×C4—442no—
437C23×C4C22×D1112yes—
438C23×C4C22×D1112yes—
439C23×C4C22×D1111yescharacteristic
440C23×C4C22×D1111yescharacteristic
441C23×C4C22×D1111yescharacteristic
442C4×D4—2232no—
443C2×C4⋊C4—114no—
444C2×C4⋊C4—222no—
445C2×C4⋊C4—222no—
446C2×C4⋊C4—224no—
447C2×C4⋊C4—442no—
448C2×C4⋊C4—442no—
449C2×C22⋊C4—114no—
450C2×C22⋊C4—114no—
451C2×C22⋊C4—222no—
452C2×C22⋊C4—222no—
453C2×C22⋊C4—222no—
454C2×C22⋊C4—222no—
455C2×C22⋊C4—224no—
456C2×C22⋊C4—224no—
457C2×C22⋊C4—224no—
458C2×C22⋊C4—224no—
459C2×C22⋊C4—442no—
460C2×C22⋊C4—442no—
461C2×C22⋊C4—442no—
462C2×C22⋊C4—442no—
463C2×C22⋊C4—442no—
464C2×C22⋊C4—442no—
465C2×C22⋊C4—442no—
466C2×C22⋊C4—442no—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42C4×D1114yes—
470#95—24no—
471#95—22no—
472#95—22no—
473#95—42no—
474#95—224no—
475#95—224no—
476#95—222no—
477#95—222no—
478#95—442no—
479#95—442no—
480#95—442no—
481C2×C11#228011yescharacteristic
482C2×C11#230811yescharacteristic
483C2×C11#231111yescharacteristic
484C2×C11#231811yescharacteristic
485C2×C11#231811yescharacteristic
486C2×C11#231911yescharacteristic
487C2×C11#231911yescharacteristic
488C2×C11#263012yes—
489C2×C11#263012yes—
490C2×C11#263512yes—
491C2×C11#263812yes—
492D11—44no—
493D11—44no—
494C24—112no—
495C24—112no—
496C24—112no—
497C24—112no—
498C24—114no—
499C24—222no—
500C24—222no—
501C24—221no—
502C24—221no—
503C24—221no—
504C24—221no—
505C24—221no—
506C24—221no—
507C24—222no—
508C24—221no—
509C24—221no—
510C24—222no—
511C24—222no—
512C24—222no—
513C24—222no—
514C24—221no—
515C24—221no—
516C24C23×D1111yescharacteristic
517C2×D4—228no—
518C2×D4—228no—
519C2×D4—2216no—
520C2×D4—2216no—
521C2×D4—228no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
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—112no—
548C22×C4—112no—
549C22×C4—112no—
550C22×C4—1116no—
551C22×C4—112no—
552C22×C4—222no—
553C22×C4—222no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—222no—
557C22×C4—222no—
558C22×C4—228no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—222no—
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—444no—
574C22×C4—444no—
575C22×C4—444no—
576C22×C4—444no—
577C22×C4—448no—
578C22×C4—448no—
579C22×C4—448no—
580C22×C4—448no—
581C22×C4C2×C4×D1112yes—
582C22×C4C2×C4×D1112yes—
583C22×C4C2×C4×D1112yes—
584C22×C4#433914yes—
585C22×C4D4×D1112yes—
586C22×C4D4×D1112yes—
587C4⋊C4—228no—
588C4⋊C4—448no—
589C22⋊C4—228no—
590C22⋊C4—228no—
591C22⋊C4—448no—
592C22⋊C4—448no—
593C22⋊C4—448no—
594C22⋊C4—448no—
595C42—28no—
596C11#1434411yescharacteristic, complemented, Sylow
597C23—114no—
598C23—114no—
599C23—224no—
600C23—224no—
601C23—222no—
602C23—222no—
603C23—222no—
604C23—222no—
605C23—222no—
606C23—222no—
607C23—222no—
608C23—222no—
609C23—222no—
610C23—222no—
611C23—222no—
612C23—222no—
613C23—224no—
614C23—224no—
615C23—224no—
616C23—224no—
617C23—222no—
618C23—222no—
619C23—222no—
620C23—222no—
621C23—224no—
622C23—224no—
623C23—224no—
624C23—224no—
625C23—442no—
626C23—442no—
627C23—442no—
628C23—442no—
629C23—442no—
630C23—442no—
631C23—442no—
632C23—442no—
633C23—442no—
634C23—442no—
635C23—441no—
636C23—441no—
637C23—441no—
638C23—441no—
639C23—442no—
640C23—442no—
641C23—442no—
642C23—442no—
643C23C22×C4×D1111yescharacteristic
644C23C2×#433912yes—
645C23C2×D4×D1111yescharacteristic
646C23C2×D4×D1111yescharacteristic
647C23#6703711yescharacteristic
648C23#6704011yescharacteristic
649C23#41×D1112yes—
650C23#6704211yescharacteristic
651C23#6704212yes—
652C23#6704212yes—
653C23#6704311yescharacteristic
654D4—2232no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—114no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—224no—
688C2×C4—224no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—4416no—
693C2×C4—4416no—
694C2×C4—442no—
695C2×C4—442no—
696C2×C4—442no—
697C2×C4—442no—
698C2×C4—442no—
699C2×C4—442no—
700C2×C4—442no—
701C2×C4—442no—
702C2×C4—442no—
703C2×C4—442no—
704C2×C4—442no—
705C2×C4—442no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—442no—
709C2×C4—442no—
710C2×C4#6692514yes—
711C2×C4C22⋊C4×D1114yes—
712C22—224no—
713C22—224no—
714C22—224no—
715C22—224no—
716C22—224no—
717C22—224no—
718C22—444no—
719C22—444no—
720C22—444no—
721C22—444no—
722C22—444no—
723C22—444no—
724C22—442no—
725C22—442no—
726C22—444no—
727C22—444no—
728C22—442no—
729C22—442no—
730C22—442no—
731C22—442no—
732C22—442no—
733C22—442no—
734C22C2×#6692511yescharacteristic
735C22C2×C22⋊C4×D1111yescharacteristic
736C22#1062303511yescharacteristic
737C22D11×#11711yescharacteristic
738C22#1062305211yescharacteristic
739C22#1062305211yescharacteristic
740C22#1062305411yescharacteristic
741C22#1062306512yes—
742C22#1062306612yes—
743C22#1062307812yes—
744C22#1062307812yes—
745C22#1062309312yes—
746C22#1062311312yes—
747C22#1062313811yescharacteristic
748C22#1062313911yescharacteristic
749C22#1062315911yescharacteristic
750C22#1062316011yescharacteristic
751C22#1062318412yes—
752C22#1062318412yes—
753C22#1062320912yes—
754C22#1062322312yes—
755C22#1062323512yes—
756C22#1062323812yes—
757C4—24no—
758C4—24no—
759C4—42no—
760C4—82no—
761C4—82no—
762C4—224no—
763C4—442no—
764C4—882no—
765C4—882no—
766C2—444no—
767C2—444no—
768C2#1307099711yescharacteristic
769C2#1307119311yescharacteristic
770C2#1307120511yescharacteristic
771C2#1307124711yescharacteristic
772C2#1307125211yescharacteristic
773C2#1307125411yescharacteristic
774C2#1307126011yescharacteristic
775C2#1307446312yes—
776C2#1307446512yes—
777C2#1307450712yes—
778C2#1307454012yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1434D11
hypocenterC11#14344
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#10622277C2semidirect
3. C2×#10622280C2semidirect
4. #13066868C2semidirect
5. #13066864C2semidirect
6. #13066860C2semidirect
8. #13066843C2semidirect
9. (C2×D11)⋊#95C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C11×#1434C2semidirect
26. C2×C4×D44C4semidirect
198. C2×C4×D11C22⋊C4semidirect
216. #1434D11semidirect
596. C11#14344semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D442
C2×#106222772
C2×#106222802
#130668682
#130668642
#130668602
#130668562
#130668432
(C2×D11)⋊#952
C11×#14342
#1434411