Finite Group Databasebeta

← #14675907

Subgroups — #14675907

Order 2816.

2546 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×C22⋊D11C211yesmaximal, characteristic
2C2×#10622571C212yesmaximal
3C2×#10622277C211yesmaximal, characteristic, complemented
4C22×C11⋊#95C211yesmaximal, characteristic, complemented
5#13066882C212yesmaximal, complemented
6#13066864C212yesmaximal, complemented
7#13066842C211yesmaximal, characteristic, complemented
8#13066841C211yesmaximal, characteristic, complemented
9#13066838C212yesmaximal, complemented
10(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
11C11×C22⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2212yes—
15C23×C4×D11C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C2×C4×C22⋊D11—28no—
19C2×C4×C22⋊D11C418yescomplemented
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11⋊#95—24no—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38#10622571—28no—
39#10622277—24no—
40C25×C11C2311yescharacteristic
41C24×D11C2311yescharacteristic
42C23×C4×C11—24no—
43C23×C4×C11—22no—
44C23×C4×C11—22no—
45C23×C4×C11—42no—
46C23×C4×C11C2×C414yes—
47C23×C4×C11C2312yes—
48C23×C4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—24no—
52C22×C22⋊D11—22no—
53C22×C22⋊D11—22no—
54C22×C22⋊D11C2×C414yes—
55C22×C22⋊D11D418yes—
56C23×Dic11—24no—
57C23×Dic11—24no—
58C23×Dic11—24no—
59C23×Dic11—24no—
60C23×Dic11—24no—
61C23×Dic11—42no—
62C23×Dic11—42no—
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2312yes—
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C22×C4×D11—24no—
69C22×C4×D11—22no—
70C22×C4×D11—22no—
71C22×C4×D11—42no—
72C22×C4×D11C2×C414yescomplemented
73C2×C11×C22⋊C4—24no—
74C2×C11×C22⋊C4—24no—
75C2×C11×C22⋊C4—24no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11C2×C414yes—
78C4×C22⋊D11—232no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—24no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—42no—
85C2×(C2×D11)⋊C4—42no—
86C2×(C2×D11)⋊C4C2×C414yescomplemented
87C2×Dic11⋊C4—24no—
88C2×Dic11⋊C4C2×C414yescomplemented
89C2×C4×Dic11—24no—
90C2×C4×Dic11C2×C414yescomplemented
91C11×#95—22no—
92C11×#95—22no—
93C11×#95—42no—
94C11⋊#95—22no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95—42no—
101C11⋊#95—42no—
102C11⋊#95D414yescomplemented
103#13894—111nomaximal, Sylow
104C24×C11—21no—
105C24×C11—22no—
106C24×C11—21no—
107C24×C11—21no—
108C24×C11—22no—
109C24×C11—21no—
110C24×C11C22×C412yes—
111C24×C11C2×D414yes—
112C24×C11#4114yes—
113C24×C11#4112yes—
114C24×C11#4112yes—
115C24×C11C2411yescharacteristic
116C23×D11—21no—
117C23×D11—22no—
118C23×D11—21no—
119C23×D11—22no—
120C23×D11—21no—
121C23×D11—21no—
122C23×D11—21no—
123C23×D11—22no—
124C23×D11—21no—
125C23×D11C22×C412yes—
126C23×D11C2×D414yes—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—28no—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—28no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
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—44no—
150C22×C4×C11—48no—
151C22×C4×C11—48no—
152C22×C4×C11C22×C412yes—
153C22×C4×C11C22×C412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11#4112yes—
156C2×C22⋊D11—28no—
157C2×C22⋊D11—28no—
158C2×C22⋊D11—216no—
159C2×C22⋊D11—216no—
160C2×C22⋊D11C22⋊C4116yes—
161C22×Dic11—216no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—22no—
172C22×Dic11—21no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—21no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—21no—
185C22×Dic11—48no—
186C22×Dic11—48no—
187C22×Dic11—48no—
188C22×Dic11—48no—
189C22×Dic11—48no—
190C22×Dic11—48no—
191C22×Dic11C22×C412yes—
192C22×Dic11C22×C412yes—
193C22×Dic11C22×C412yes—
194C22×Dic11C2×D414yes—
195C22×Dic11C2×D414yes—
196C22×Dic11#4114yes—
197C2×C4×D11—28no—
198C2×C4×D11—28no—
199C2×C4×D11—44no—
200C2×C4×D11—48no—
201C2×C4×D11—48no—
202C11×C22⋊C4—48no—
203C22⋊Dic11—28no—
204(C2×D11)⋊C4—28no—
205(C2×D11)⋊C4—48no—
206(C2×D11)⋊C4—48no—
207Dic11⋊C4—28no—
208C4×Dic11—28no—
209C22×C4×D4—111no—
210C2×#386—112no—
211C2×#381—111no—
212C22×#95—111no—
213#1445—112no—
214#1440—112no—
215#1434—111no—
216#1434—111no—
217C22⋊#95—111no—
218C22⋊#95—112no—
219C22⋊#95D1111yescharacteristic, complemented
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—24no—
229C23×C11—22no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11—24no—
233C23×C11—22no—
234C23×C11—24no—
235C23×C11—22no—
236C23×C11—24no—
237C23×C11—22no—
238C23×C11C2×C22⋊C414yes—
239C23×C11#11714yes—
240C23×C11#11714yes—
241C23×C11#12318yes—
242C23×C11#12318yes—
243C23×C11C23×C411yescharacteristic
244C23×C11C22×D412yes—
245C23×C11C22×D411yescharacteristic
246C23×C11C2×#4112yes—
247C23×C11C2×#4111yescharacteristic
248C23×C11C2×#4111yescharacteristic
249C23×C11C2×#4111yescharacteristic
250C23×C11C2×#4112yes—
251C23×C11H(5,𝔽2)12yes—
252C23×C11H(5,𝔽2)11yescharacteristic
253C23×C112−1+411yescharacteristic
254C22×D11—22no—
255C22×D11—22no—
256C22×D11—22no—
257C22×D11—22no—
258C22×D11—22no—
259C22×D11—22no—
260C22×D11—24no—
261C22×D11—24no—
262C22×D11—24no—
263C22×D11—24no—
264C22×D11—24no—
265C22×D11—24no—
266C22×D11—42no—
267C22×D11—42no—
268C22×D11—42no—
269C22×D11—42no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—42no—
273C22×D11—41no—
274C22×D11—42no—
275C22×D11—41no—
276C22×D11C2×C22⋊C414yes—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—24no—
280C2×C4×C11—24no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—416no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11—42no—
289C2×C4×C11—42no—
290C2×C4×C11—42no—
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×C11C4×D414yes—
302C22⋊D11—232no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—24no—
306C2×Dic11—24no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—24no—
314C2×Dic11—24no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11—432no—
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×Dic11C2×C22⋊C414yes—
333C4×D11—416no—
334C23×D4—111no—
335C24×C4—111no—
336C24×C4—112no—
337C24×C4C2×D1111yescharacteristic
338C2×C4×D4—118no—
339C2×C4×D4—228no—
340C22×C4⋊C4—111no—
341C22×C22⋊C4—111no—
342C22×C22⋊C4—111no—
343C22×C22⋊C4—112no—
344C22×C22⋊C4—112no—
345C22×C22⋊C4C2×D1112yes—
346C22×C42—111no—
347#386—228no—
348#381—224no—
349C2×#95—111no—
350C2×#95—112no—
351C2×#95—111no—
352C2×#95—112no—
353C2×#95—112no—
354C2×#95—112no—
355C2×#95—112no—
356C2×#95—112no—
357C2×#95—112no—
358C2×#95—224no—
359C2×#95C2×D1111yescharacteristic
360C2×#95C2×D1111yescharacteristic
361C2×#95C2×D1112yes—
362C22×C11—24no—
363C22×C11—24no—
364C22×C11—24no—
365C22×C11—24no—
366C22×C11—24no—
367C22×C11—28no—
368C22×C11—28no—
369C22×C11—28no—
370C22×C11—28no—
371C22×C11—24no—
372C22×C11#38118yescomplemented
373C22×C11C22×C22⋊C411yescharacteristic
374C22×C11C2×#11711yescharacteristic
375C22×C11C2×#11711yescharacteristic
376C22×C11C2×C4×D411yescharacteristic
377C22×C11C4×#4111yescharacteristic
378C22×C11#51811yescharacteristic
379C22×C11#52011yescharacteristic
380C22×C11C2×#12312yes—
381C22×C11C2×#12312yes—
382C22×C11#52512yes—
383C22×C11#52912yes—
384C22×C11#53812yes—
385C22×C11#53912yes—
386C22×C11D4212yes—
387C22×C11#54612yes—
388C22×C11#54611yescharacteristic
389C22×C11#54612yes—
390C22×C11#54712yes—
391C22×C11#54811yescharacteristic
392C22×C11#55112yes—
393C22×C11#55211yescharacteristic
394C22×C11#55312yes—
395C22×C11#55311yescharacteristic
396C2×D11—24no—
397C2×D11—24no—
398C2×D11—24no—
399C2×D11—42no—
400C2×D11—42no—
401C2×D11—42no—
402C2×D11—44no—
403C2×D11—44no—
404C2×D11—44no—
405C2×D11—44no—
406C2×D11—42no—
407C4×C11—24no—
408C4×C11—42no—
409C4×C11—82no—
410C4×C11—82no—
411Dic11—24no—
412Dic11—42no—
413Dic11—42no—
414Dic11—44no—
415Dic11—44no—
416C25—111no—
417C25C22×D1111yescharacteristic
418C22×D4—114no—
419C22×D4—118no—
420C22×D4—224no—
421C22×D4—222no—
422C22×D4—222no—
423C23×C4—24no—
424C23×C4—22no—
425C23×C4—22no—
426C23×C4—42no—
427C23×C4—111no—
428C23×C4—111no—
429C23×C4—111no—
430C23×C4—112no—
431C23×C4—112no—
432C23×C4—114no—
433C23×C4—224no—
434C23×C4—224no—
435C23×C4—224no—
436C23×C4—224no—
437C23×C4—222no—
438C23×C4—222no—
439C23×C4—224no—
440C23×C4—224no—
441C23×C4—442no—
442C23×C4—442no—
443C23×C4—442no—
444C23×C4C4×D1114yes—
445C23×C4C22×D1112yes—
446C23×C4C22×D1112yes—
447C23×C4C22×D1111yescharacteristic
448C23×C4C22×D1111yescharacteristic
449C4×D4—2232no—
450C2×C4⋊C4—114no—
451C2×C4⋊C4—224no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—114no—
456C2×C22⋊C4—114no—
457C2×C22⋊C4—224no—
458C2×C22⋊C4—224no—
459C2×C22⋊C4—224no—
460C2×C22⋊C4—224no—
461C2×C22⋊C4—224no—
462C2×C22⋊C4—224no—
463C2×C22⋊C4—442no—
464C2×C22⋊C4—442no—
465C2×C42—114no—
466C2×C42—224no—
467#95—22no—
468#95—22no—
469#95—42no—
470#95—114no—
471#95—224no—
472#95—224no—
473#95—224no—
474#95—224no—
475#95—224no—
476#95—222no—
477#95—442no—
478#95—442no—
479C2×C11—28no—
480C2×C11C2×#38111yescharacteristic
481C2×C11#229011yescharacteristic
482C2×C11#231811yescharacteristic
483C2×C11D4×C22⋊C411yescharacteristic
484C2×C11#233911yescharacteristic
485C2×C11#235211yescharacteristic
486C2×C11#235311yescharacteristic
487C2×C11#241812yes—
488C2×C11#241912yes—
489C2×C11#244312yes—
490C2×C11#244412yes—
491D11—44no—
492C24—21no—
493C24—21no—
494C24—22no—
495C24—22no—
496C24—21no—
497C24—21no—
498C24—112no—
499C24—114no—
500C24—222no—
501C24—221no—
502C24—221no—
503C24—221no—
504C24—222no—
505C24—221no—
506C24—222no—
507C24—221no—
508C24—221no—
509C24C2×C4×D1112yes—
510C24#433914yes—
511C24D4×D1114yes—
512C24#434112yes—
513C24#434312yes—
514C24C23×D1111yescharacteristic
515C2×D4—1116no—
516C2×D4—228no—
517C2×D4—2216no—
518C2×D4—228no—
519C2×D4—2216no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—28no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—28no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
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—44no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—112no—
546C22×C4—114no—
547C22×C4—112no—
548C22×C4—112no—
549C22×C4—114no—
550C22×C4—114no—
551C22×C4—228no—
552C22×C4—222no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—2216no—
556C22×C4—222no—
557C22×C4—222no—
558C22×C4—221no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—222no—
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—221no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—221no—
576C22×C4—228no—
577C22×C4—444no—
578C22×C4—448no—
579C22×C4—448no—
580C22×C4—448no—
581C22×C4—448no—
582C22×C4—448no—
583C22×C4—448no—
584C22×C4—448no—
585C22×C4—448no—
586C22×C4C2×C4×D1112yes—
587C22×C4C2×C4×D1112yes—
588C22×C4D4×D1112yes—
589C22×C4#434112yes—
590C4⋊C4—228no—
591C22⋊C4—48no—
592C22⋊C4—228no—
593C22⋊C4—228no—
594C22⋊C4—448no—
595C22⋊C4—448no—
596C42—228no—
597C11#1389411yescharacteristic, complemented, Sylow
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—22no—
609C23—24no—
610C23—22no—
611C23—22no—
612C23—24no—
613C23—22no—
614C23—24no—
615C23—24no—
616C23—114no—
617C23—222no—
618C23—222no—
619C23—222no—
620C23—224no—
621C23—222no—
622C23—224no—
623C23—222no—
624C23—222no—
625C23—224no—
626C23—224no—
627C23—224no—
628C23—224no—
629C23—442no—
630C23—442no—
631C23—442no—
632C23—442no—
633C23—441no—
634C23—442no—
635C23—441no—
636C23—441no—
637C23—442no—
638C23—441no—
639C23#6692514yes—
640C23C22⋊C4×D1114yes—
641C23#6693618yes—
642C23#6694514yes—
643C23#6694718yes—
644C23C22×C4×D1111yescharacteristic
645C23C2×#433912yes—
646C23C2×D4×D1112yes—
647C23C2×D4×D1111yescharacteristic
648C23C2×#434111yescharacteristic
649C23C2×#434111yescharacteristic
650C23#6703712yes—
651C23C2×#434311yescharacteristic
652C23#41×D1112yes—
653C23#6704211yescharacteristic
654C23#6704311yescharacteristic
655D4—2232no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—416no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
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—114no—
681C2×C4—222no—
682C2×C4—224no—
683C2×C4—222no—
684C2×C4—224no—
685C2×C4—222no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—224no—
692C2×C4—224no—
693C2×C4—224no—
694C2×C4—224no—
695C2×C4—224no—
696C2×C4—224no—
697C2×C4—4416no—
698C2×C4—4432no—
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—442no—
711C2×C4(C22⋊D11)⋊C414yes—
712C22—24no—
713C22—24no—
714C22—24no—
715C22—24no—
716C22—24no—
717C22—24no—
718C22—28no—
719C22—28no—
720C22—28no—
721C22—28no—
722C22—224no—
723C22—224no—
724C22—224no—
725C22—442no—
726C22—442no—
727C22—442no—
728C22—442no—
729C22—444no—
730C22—444no—
731C22—444no—
732C22—444no—
733C22#1062227718yescomplemented
734C22C2×#6692511yescharacteristic
735C22C2×C22⋊C4×D1111yescharacteristic
736C22C2×(C22⋊D11)⋊C411yescharacteristic
737C22#1062301711yescharacteristic
738C22C2×#6693612yes—
739C22C2×#6694511yescharacteristic
740C22C2×#6694712yes—
741C22#1062305311yescharacteristic
742C22#1062305411yescharacteristic
743C22#1062306912yes—
744C22#1062307812yes—
745C22#1062309112yes—
746C22#1062309512yes—
747C22#1062312112yes—
748C22#1062312212yes—
749C22#1062312911yescharacteristic
750C22#1062313212yes—
751C22#1062314911yescharacteristic
752C22#1062316111yescharacteristic
753C22#1062316812yes—
754C22#1062317311yescharacteristic
755C22#1062318512yes—
756C22#1062318612yes—
757C4—24no—
758C4—42no—
759C4—82no—
760C4—82no—
761C4—224no—
762C4—442no—
763C4—442no—
764C4—444no—
765C4—444no—
766C2—28no—
767C2—444no—
768C2C2×#1062227711yescharacteristic
769C2#1307105511yescharacteristic
770C2#1307124311yescharacteristic
771C2#1307143211yescharacteristic
772C2#1307144011yescharacteristic
773C2#1307154711yescharacteristic
774C2#1307155811yescharacteristic
775C2#1307208012yes—
776C2#1307209512yes—
777C2#1307235312yes—
778C2#1307236812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22⋊#95D11
hypocenterC11#13894
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#10622277C2semidirect
4. C22×C11⋊#95C2semidirect
5. #13066882C2semidirect
6. #13066864C2semidirect
7. #13066842C2semidirect
8. #13066841C2semidirect
9. #13066838C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C11×C22⋊#95C2semidirect
19. C2×C4×C22⋊D11C4semidirect
72. C22×C4×D11C2×C4semidirect
86. C2×(C2×D11)⋊C4C2×C4semidirect
88. C2×Dic11⋊C4C2×C4semidirect
90. C2×C4×Dic11C2×C4semidirect
102. C11⋊#95D4semidirect
219. C22⋊#95D11semidirect
372. C22×C11#381semidirect
597. C11#13894semidirect
733. C22#10622277semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106225712
C2×#106222772
C22×C11⋊#952
#130668822
#130668642
#130668422
#130668412
#130668382
(C2×D11)⋊#952
C11×C22⋊#952
#1389411