Finite Group Databasebeta

← #14675900

Subgroups — #14675900

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×#10622826C212yesmaximal
3C2×#10622277C211yesmaximal, characteristic, complemented
4#13066882C212yesmaximal, complemented
5#13066864C212yesmaximal, complemented
6#13066842C211yesmaximal, characteristic, complemented
7#13066841C211yesmaximal, characteristic, complemented
8#13066839C211yesmaximal, characteristic, complemented
9#13066839C212yesmaximal, complemented
10(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
11C22×C11×#95C211yesmaximal, characteristic, complemented
12C24×C4×C11C2212yes—
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C22×C22⋊Dic11C2212yes—
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×#95—24no—
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11×#95C2211yescharacteristic
29#10622826—28no—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39#10622277—24no—
40C25×C11C2311yescharacteristic
41C24×D11C2311yescharacteristic
42C23×C4×C11—24no—
43C23×C4×C11—24no—
44C23×C4×C11—24no—
45C23×C4×C11—22no—
46C23×C4×C11—24no—
47C23×C4×C11—22no—
48C23×C4×C11—24no—
49C23×C4×C11—24no—
50C23×C4×C11—42no—
51C23×C4×C11—42no—
52C23×C4×C11—42no—
53C23×C4×C11C2×C414yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2312yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—24no—
59C22×C22⋊D11—22no—
60C22×C22⋊D11—22no—
61C22×C22⋊D11C2×C414yes—
62C22×C22⋊D11D418yes—
63C23×Dic11C2312yes—
64C23×Dic11C2312yes—
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C22×C4×D11—24no—
69C22×C4×D11—22no—
70C22×C4×D11—22no—
71C22×C4×D11—42no—
72C22×C4×D11C2×C414yescomplemented
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—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—24no—
92C11×#95—22no—
93C11×#95D414yescomplemented
94C11⋊#95—24no—
95C11⋊#95—22no—
96C11⋊#95—24no—
97C11⋊#95—22no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95—42no—
101C11⋊#95—42no—
102C11⋊#95—42no—
103#13894—111nomaximal, Sylow
104C24×C11—21no—
105C24×C11—21no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—21no—
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—216no—
130C22×C4×C11—28no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
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—28no—
148C22×C4×C11—44no—
149C22×C4×C11—48no—
150C22×C4×C11—48no—
151C22×C4×C11—48no—
152C22×C4×C11—48no—
153C22×C4×C11—48no—
154C22×C4×C11—48no—
155C22×C4×C11—48no—
156C22×C4×C11—48no—
157C22×C4×C11C22×C412yes—
158C22×C4×C11C22×C412yes—
159C22×C4×C11C2×D414yes—
160C22×C4×C11C2×D412yes—
161C22×C4×C11#4114yes—
162C22×C4×C11#4112yes—
163C2×C22⋊D11—28no—
164C2×C22⋊D11—28no—
165C2×C22⋊D11—216no—
166C2×C22⋊D11—216no—
167C2×C22⋊D11C22⋊C4116yes—
168C22×Dic11—21no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—22no—
178C22×Dic11—21no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—21no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—21no—
192C22×Dic11—22no—
193C22×Dic11C22×C412yes—
194C22×Dic11C22×C412yes—
195C22×Dic11C22×C412yes—
196C22×Dic11C2×D414yes—
197C2×C4×D11—28no—
198C2×C4×D11—28no—
199C2×C4×D11—44no—
200C2×C4×D11—48no—
201C2×C4×D11—48no—
202C22⋊Dic11—28no—
203C22⋊Dic11—48no—
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×#95D1111yescharacteristic, complemented
213#1445—112no—
214#1440—112no—
215#1434—111no—
216#1434—111no—
217C22⋊#95—111no—
218C22⋊#95—112no—
219C22⋊#95—111no—
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—22no—
237C23×C11—24no—
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×#4112yes—
249C23×C11C2×#4111yescharacteristic
250C23×C11C2×#4111yescharacteristic
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—41no—
275C22×D11—42no—
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—24no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—24no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—416no—
291C2×C4×C11—432no—
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×C11C4×D414yes—
303C22⋊D11—232no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—24no—
307C2×Dic11—24no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—22no—
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×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11C2×C22⋊C414yes—
333C4×D11—416no—
334C23×D4—111no—
335C24×C4—111no—
336C24×C4C2×D1112yes—
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⋊C4—112no—
346C22×C42—111no—
347#386—228no—
348#381—224no—
349C2×#95—24no—
350C2×#95—111no—
351C2×#95—112no—
352C2×#95—111no—
353C2×#95—112no—
354C2×#95—112no—
355C2×#95—112no—
356C2×#95—112no—
357C2×#95—112no—
358C2×#95—112no—
359C2×#95C2×D1111yescharacteristic
360C2×#95C2×D1112yes—
361C2×#95C2×D1111yescharacteristic
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#54612yes—
389C22×C11#54611yescharacteristic
390C22×C11#54712yes—
391C22×C11#54811yescharacteristic
392C22×C11#55112yes—
393C22×C11#55211yescharacteristic
394C22×C11#55311yescharacteristic
395C22×C11#55312yes—
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—44no—
410C4×C11—44no—
411Dic11—24no—
412Dic11—42no—
413Dic11—42no—
414Dic11—82no—
415Dic11—82no—
416C25—111no—
417C25C22×D1111yescharacteristic
418C22×D4—114no—
419C22×D4—118no—
420C22×D4—224no—
421C22×D4—222no—
422C22×D4—222no—
423C23×C4—24no—
424C23×C4—24no—
425C23×C4—24no—
426C23×C4—22no—
427C23×C4—24no—
428C23×C4—22no—
429C23×C4—24no—
430C23×C4—24no—
431C23×C4—42no—
432C23×C4—42no—
433C23×C4—42no—
434C23×C4—111no—
435C23×C4—111no—
436C23×C4—111no—
437C23×C4—114no—
438C23×C4—112no—
439C23×C4—112no—
440C23×C4—224no—
441C23×C4—222no—
442C23×C4—222no—
443C23×C4—442no—
444C23×C4C4×D1114yes—
445C23×C4C22×D1111yescharacteristic
446C23×C4C22×D1112yes—
447C23×C4C22×D1112yes—
448C23×C4C22×D1111yescharacteristic
449C4×D4—2232no—
450C2×C4⋊C4—114no—
451C2×C4⋊C4—224no—
452C2×C22⋊C4—114no—
453C2×C22⋊C4—114no—
454C2×C22⋊C4—224no—
455C2×C22⋊C4—224no—
456C2×C22⋊C4—224no—
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—24no—
468#95—22no—
469#95—224no—
470#95—224no—
471#95—224no—
472#95—222no—
473#95—224no—
474#95—222no—
475#95—442no—
476#95—442no—
477#95—442no—
478#95C22⋊D1114yescomplemented
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—22no—
493C24—21no—
494C24—22no—
495C24—21no—
496C24—21no—
497C24—21no—
498C24—112no—
499C24—114no—
500C24—222no—
501C24—221no—
502C24—222no—
503C24—221no—
504C24—221no—
505C24—222no—
506C24—221no—
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—216no—
523C22×C4—28no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
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—21no—
539C22×C4—22no—
540C22×C4—28no—
541C22×C4—44no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—112no—
551C22×C4—114no—
552C22×C4—112no—
553C22×C4—112no—
554C22×C4—228no—
555C22×C4—222no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—222no—
559C22×C4—221no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—221no—
563C22×C4—222no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—228no—
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—444no—
582C22×C4—448no—
583C22×C4—448no—
584C22×C4C2×C4×D1112yes—
585C22×C4C2×C4×D1112yes—
586C22×C4#433914yes—
587C22×C4#433912yes—
588C22×C4C2×C22⋊D1114yes—
589C22×C4C2×C22⋊D1112yes—
590C4⋊C4—228no—
591C22⋊C4—228no—
592C22⋊C4—228no—
593C22⋊C4—448no—
594C22⋊C4—448no—
595C22⋊C4—448no—
596C42—228no—
597C11#1389411yescharacteristic, complemented, Sylow
598C23—22no—
599C23—24no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—22no—
606C23—24no—
607C23—22no—
608C23—22no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—24no—
613C23—24no—
614C23—22no—
615C23—22no—
616C23—114no—
617C23—222no—
618C23—222no—
619C23—222no—
620C23—224no—
621C23—224no—
622C23—224no—
623C23—222no—
624C23—222no—
625C23—224no—
626C23—224no—
627C23—222no—
628C23—224no—
629C23—442no—
630C23—442no—
631C23—442no—
632C23—441no—
633C23—441no—
634C23—442no—
635C23—442no—
636C23—442no—
637C23—441no—
638C23—441no—
639C23#6692514yes—
640C23C22⋊C4×D1114yes—
641C23#6693618yes—
642C23#6694514yes—
643C23#6694718yes—
644C23C22×C4×D1111yescharacteristic
645C23C2×#433912yes—
646C23C2×#433912yes—
647C23C2×#433911yescharacteristic
648C23C2×D4×D1112yes—
649C23C2×#434111yescharacteristic
650C23#6703712yes—
651C23#6703711yescharacteristic
652C23C2×#434311yescharacteristic
653C23#6704011yescharacteristic
654C23C22×C22⋊D1111yescharacteristic
655D4—2232no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—416no—
670C2×C4—432no—
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—114no—
682C2×C4—222no—
683C2×C4—224no—
684C2×C4—222no—
685C2×C4—224no—
686C2×C4—222no—
687C2×C4—222no—
688C2×C4—222no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—4416no—
693C2×C4—442no—
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—442no—
711C2×C4C4×C22⋊D1114yes—
712C22—24no—
713C22—24no—
714C22—24no—
715C22—24no—
716C22—24no—
717C22—28no—
718C22—24no—
719C22—28no—
720C22—28no—
721C22—28no—
722C22—224no—
723C22—224no—
724C22—224no—
725C22—442no—
726C22—442no—
727C22—442no—
728C22—444no—
729C22—442no—
730C22—444no—
731C22—444no—
732C22—444no—
733C22#1062227718yescomplemented
734C22C2×#6692511yescharacteristic
735C22C4×#433911yescharacteristic
736C22#1062301012yes—
737C22C2×C22⋊C4×D1111yescharacteristic
738C22#1062301711yescharacteristic
739C22C2×#6693612yes—
740C22#1062302112yes—
741C22#1062302112yes—
742C22#1062302512yes—
743C22#1062302612yes—
744C22C2×#6694511yescharacteristic
745C22#1062303511yescharacteristic
746C22C2×#6694712yes—
747C22#1062303812yes—
748C22#1062304411yescharacteristic
749C22#1062304511yescharacteristic
750C22#1062304512yes—
751C22#1062304612yes—
752C22C2×C4×C22⋊D1111yescharacteristic
753C22#1062332212yes—
754C22D4×C22⋊D1112yes—
755C22#1062333711yescharacteristic
756C22#1062334811yescharacteristic
757C4—24no—
758C4—42no—
759C4—44no—
760C4—44no—
761C4—224no—
762C4—442no—
763C4—442no—
764C4—882no—
765C4—882no—
766C2—28no—
767C2—444no—
768C2C2×#1062227711yescharacteristic
769C2#1307105911yescharacteristic
770C2#1307125011yescharacteristic
771C2C22⋊C4×C22⋊D1111yescharacteristic
772C2#1307144311yescharacteristic
773C2#1307154111yescharacteristic
774C2#1307155211yescharacteristic
775C2#1307207812yes—
776C2#1307209312yes—
777C2#1307235112yes—
778C2#1307236612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#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. #13066882C2semidirect
5. #13066864C2semidirect
6. #13066842C2semidirect
7. #13066841C2semidirect
8. #13066839C2semidirect
9. #13066839C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C22×C11×#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
93. C11×#95D4semidirect
212. C22×#95D11semidirect
372. C22×C11#381semidirect
478. #95C22⋊D11semidirect
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×#106228262
C2×#106222772
#130668822
#130668642
#130668422
#130668412
#130668392
(C2×D11)⋊#952
C22×C11×#952
#1389411