Finite Group Databasebeta

← #14680976

Subgroups — #14680976

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×C22⋊D11C211yesmaximal, characteristic
2C2×#10622277C211yesmaximal, characteristic, complemented
3C2×#10622280C211yesmaximal, characteristic, complemented
4#13066867C212yesmaximal, complemented
5#13066864C212yesmaximal, complemented
6#13066859C212yesmaximal, complemented
7#13066855C212yesmaximal
8#13066840C211yesmaximal, characteristic, complemented
9#13066840C211yesmaximal, characteristic, complemented
10#13066839C211yesmaximal, characteristic, complemented
11C11×C22⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C22⋊Dic11C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C2×C4×C22⋊D11—24no—
19C2×C4×C22⋊D11—24no—
20C2×C4×C22⋊D11C418yescomplemented
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C22×C4×Dic11C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622280—24no—
39#10622277—24no—
40C25×C11C2311yescharacteristic
41C24×D11C2311yescharacteristic
42C23×C4×C11—22no—
43C23×C4×C11—22no—
44C23×C4×C11—42no—
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⋊D11—24no—
55C22×C22⋊D11C2×C414yes—
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C22×C4×D11—42no—
62C22×C4×D11—42no—
63C22×C4×D11C2×C414yes—
64C22×C4×D11D414yes—
65C22×C4×D11D414yes—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—42no—
68C2×C11×C22⋊C4—42no—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—42no—
73C2×C22⋊Dic11—42no—
74C2×C22⋊Dic11C2×C414yes—
75C4×C22⋊D11—232no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—42no—
81C2×(C2×D11)⋊C4—42no—
82C2×(C2×D11)⋊C4—42no—
83C2×(C2×D11)⋊C4—42no—
84C2×(C2×D11)⋊C4C2×C414yes—
85C2×Dic11⋊C4—22no—
86C2×Dic11⋊C4—22no—
87C2×Dic11⋊C4—24no—
88C2×Dic11⋊C4—42no—
89C2×Dic11⋊C4—42no—
90C2×Dic11⋊C4C2×C414yes—
91C2×C4×Dic11—22no—
92C2×C4×Dic11—22no—
93C2×C4×Dic11C2×C414yes—
94C11×#95—22no—
95C11×#95—22no—
96C11×#95—42no—
97C11⋊#95—22no—
98C11⋊#95—22no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95—42no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105#14344—111nomaximal, Sylow
106C24×C11—21no—
107C24×C11—21no—
108C24×C11—22no—
109C24×C11—21no—
110C24×C11—22no—
111C24×C11—21no—
112C24×C11—22no—
113C24×C11—21no—
114C24×C11—21no—
115C24×C11C22×C412yes—
116C24×C11#4114yes—
117C24×C11C2411yescharacteristic
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—21no—
121C23×D11—21no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—21no—
125C23×D11—21no—
126C23×D11C22×C412yes—
127C23×D11C2×D412yes—
128C23×D11C2×D412yes—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—28no—
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—22no—
150C22×C4×C11—44no—
151C22×C4×C11—44no—
152C22×C4×C11—48no—
153C22×C4×C11—48no—
154C22×C4×C11C22×C412yes—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C2×C22⋊D11—216no—
159C2×C22⋊D11—216no—
160C2×C22⋊D11—28no—
161C2×C22⋊D11—28no—
162C2×C22⋊D11—28no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
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—21no—
177C22×Dic11—21no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—22no—
188C22×Dic11C22×C412yes—
189C22×Dic11C22×C412yes—
190C22×Dic11C22×C412yes—
191C22×Dic11C2×D412yes—
192C22×Dic11C2×D412yes—
193C22×Dic11#4114yes—
194C2×C4×D11—44no—
195C2×C4×D11—44no—
196C2×C4×D11—48no—
197C2×C4×D11—48no—
198C2×C4×D11C22⋊C4116yescomplemented
199C11×C22⋊C4—48no—
200C22⋊Dic11—28no—
201C22⋊Dic11—48no—
202(C2×D11)⋊C4—28no—
203(C2×D11)⋊C4—48no—
204(C2×D11)⋊C4—48no—
205Dic11⋊C4—28no—
206Dic11⋊C4—48no—
207C4×Dic11—28no—
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#1434—111no—
217C22⋊#95—111no—
218C22⋊#95D1111yescharacteristic, complemented
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—24no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11#11714yes—
242C23×C11C23×C411yescharacteristic
243C23×C11C22×D411yescharacteristic
244C23×C11C22×D411yescharacteristic
245C23×C11C2×#4112yes—
246C23×C11C2×#4112yes—
247C23×C11H(5,𝔽2)12yes—
248C23×C11H(5,𝔽2)12yes—
249C23×C11H(5,𝔽2)11yescharacteristic
250C23×C11H(5,𝔽2)11yescharacteristic
251C23×C112−1+411yescharacteristic
252C23×C112−1+411yescharacteristic
253C22×D11—22no—
254C22×D11—22no—
255C22×D11—22no—
256C22×D11—22no—
257C22×D11—22no—
258C22×D11—22no—
259C22×D11—24no—
260C22×D11—24no—
261C22×D11—24no—
262C22×D11—24no—
263C22×D11—22no—
264C22×D11—22no—
265C22×D11—22no—
266C22×D11—22no—
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×D11C2×C22⋊C414yes—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—416no—
284C2×C4×C11—42no—
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×C11C2×C22⋊C414yes—
301C22⋊D11—232no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—24no—
307C2×Dic11—24no—
308C2×Dic11—24no—
309C2×Dic11—24no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
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×Dic11C2×C22⋊C414yes—
332C2×Dic11#11714yes—
333C4×D11—416no—
334C23×D4—111no—
335C24×C4—111no—
336C24×C4C2×D1111yescharacteristic
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⋊C4C2×D1112yes—
348C22×C42—111no—
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×#95—112no—
359C2×#95C2×D1111yescharacteristic
360C2×#95C2×D1111yescharacteristic
361C2×#95C2×D1112yes—
362C22×C11—24no—
363C22×C11—24no—
364C22×C11—24no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11—42no—
369C22×C11—44no—
370C22×C11—44no—
371C22×C11—44no—
372C22×C11—44no—
373C22×C11C22×C22⋊C411yescharacteristic
374C22×C11C2×#11711yescharacteristic
375C22×C11C2×#11711yescharacteristic
376C22×C11#51811yescharacteristic
377C22×C11#51811yescharacteristic
378C22×C11#52011yescharacteristic
379C22×C11#52011yescharacteristic
380C22×C11#52512yes—
381C22×C11#52512yes—
382C22×C11#53412yes—
383C22×C11#53412yes—
384C22×C11#53511yescharacteristic
385C22×C11#53611yescharacteristic
386C22×C11#53711yescharacteristic
387C22×C11#53711yescharacteristic
388C22×C11#53812yes—
389C22×C11#53812yes—
390C22×C11#53912yes—
391C22×C11#53912yes—
392C22×C11#54012yes—
393C22×C11#54012yes—
394C22×C11#54212yes—
395C22×C11#54212yes—
396C2×D11—24no—
397C2×D11—24no—
398C2×D11—24no—
399C2×D11—42no—
400C2×D11—42no—
401C2×D11—42no—
402C2×D11—42no—
403C2×D11—44no—
404C2×D11—44no—
405C2×D11—44no—
406C2×D11—44no—
407C4×C11—24no—
408C4×C11—42no—
409C4×C11—82no—
410C4×C11—82no—
411Dic11—24no—
412Dic11—24no—
413Dic11—42no—
414Dic11—82no—
415Dic11—82no—
416C25—111no—
417C25C22×D1111yescharacteristic
418C22×D4—114no—
419C22×D4—224no—
420C22×D4—222no—
421C22×D4—222no—
422C22×D4—224no—
423C23×C4—22no—
424C23×C4—22no—
425C23×C4—42no—
426C23×C4—42no—
427C23×C4—111no—
428C23×C4—111no—
429C23×C4—114no—
430C23×C4—114no—
431C23×C4—114no—
432C23×C4—111no—
433C23×C4—112no—
434C23×C4—112no—
435C23×C4—442no—
436C23×C4—442no—
437C23×C4C4×D1114yes—
438C23×C4C22×D1112yes—
439C23×C4C22×D1112yes—
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—24no—
450C2×C22⋊C4—42no—
451C2×C22⋊C4—42no—
452C2×C22⋊C4—114no—
453C2×C22⋊C4—114no—
454C2×C22⋊C4—222no—
455C2×C22⋊C4—222no—
456C2×C22⋊C4—222no—
457C2×C22⋊C4—222no—
458C2×C22⋊C4—224no—
459C2×C22⋊C4—224no—
460C2×C22⋊C4—224no—
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—114no—
468C2×C42—222no—
469C2×C42—222no—
470#95—22no—
471#95—22no—
472#95—42no—
473#95—224no—
474#95—224no—
475#95—224no—
476#95—222no—
477#95—222no—
478#95—442no—
479#95—442no—
480#95—442no—
481C2×C11—44no—
482C2×C11#228011yescharacteristic
483C2×C11#230811yescharacteristic
484C2×C11#231111yescharacteristic
485C2×C11#231811yescharacteristic
486C2×C11#231811yescharacteristic
487C2×C11#231911yescharacteristic
488C2×C11#231911yescharacteristic
489C2×C11#263012yes—
490C2×C11#263012yes—
491C2×C11#263512yes—
492C2×C11#263812yes—
493D11—44no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—22no—
498C24—22no—
499C24—21no—
500C24—22no—
501C24—21no—
502C24—21no—
503C24—112no—
504C24—112no—
505C24—112no—
506C24—222no—
507C24—221no—
508C24—222no—
509C24—222no—
510C24—221no—
511C24—222no—
512C24—221no—
513C24—221no—
514C24C2×C4×D1112yes—
515C24#433914yes—
516C24C23×D1111yescharacteristic
517C2×D4—228no—
518C2×D4—228no—
519C2×D4—2216no—
520C2×D4—2216no—
521C2×D4—228no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—28no—
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—22no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—112no—
548C22×C4—112no—
549C22×C4—112no—
550C22×C4—112no—
551C22×C4—114no—
552C22×C4—1116no—
553C22×C4—112no—
554C22×C4—222no—
555C22×C4—221no—
556C22×C4—221no—
557C22×C4—222no—
558C22×C4—222no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
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—444no—
580C22×C4—444no—
581C22×C4—448no—
582C22×C4—448no—
583C22×C4C2×C4×D1112yes—
584C22×C4C2×C4×D1112yes—
585C22×C4D4×D1112yes—
586C22×C4D4×D1112yes—
587C4⋊C4—228no—
588C4⋊C4—448no—
589C22⋊C4—48no—
590C22⋊C4—228no—
591C22⋊C4—228no—
592C22⋊C4—448no—
593C22⋊C4—448no—
594C22⋊C4—448no—
595C42—228no—
596C11#1434411yescharacteristic, complemented, Sylow
597C23—22no—
598C23—22no—
599C23—22no—
600C23—24no—
601C23—22no—
602C23—24no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—42no—
610C23—42no—
611C23—41no—
612C23—41no—
613C23—42no—
614C23—41no—
615C23—41no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—114no—
620C23—222no—
621C23—222no—
622C23—222no—
623C23—222no—
624C23—222no—
625C23—222no—
626C23—224no—
627C23—224no—
628C23—224no—
629C23—224no—
630C23—222no—
631C23—222no—
632C23—222no—
633C23—222no—
634C23—442no—
635C23—442no—
636C23—442no—
637C23—442no—
638C23—442no—
639C23—442no—
640C23—442no—
641C23—442no—
642C23#6692514yes—
643C23C22×C4×D1111yescharacteristic
644C23C2×#433912yes—
645C23C2×D4×D1111yescharacteristic
646C23C2×D4×D1111yescharacteristic
647C23#6703712yes—
648C23#6703712yes—
649C23#6703711yescharacteristic
650C23#6704011yescharacteristic
651C23#41×D1112yes—
652C23#6704211yescharacteristic
653C23#6704311yescharacteristic
654D4—2232no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—416no—
663C2×C4—42no—
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—114no—
680C2×C4—114no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—224no—
686C2×C4—224no—
687C2×C4—224no—
688C2×C4—224no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—4416no—
693C2×C4—441no—
694C2×C4—441no—
695C2×C4—441no—
696C2×C4—441no—
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×C4C22⋊C4×D1114yes—
712C22—24no—
713C22—24no—
714C22—24no—
715C22—44no—
716C22—44no—
717C22—44no—
718C22—42no—
719C22—42no—
720C22—44no—
721C22—42no—
722C22—42no—
723C22—224no—
724C22—224no—
725C22—224no—
726C22—444no—
727C22—444no—
728C22—444no—
729C22—444no—
730C22—442no—
731C22—442no—
732C22—442no—
733C22—442no—
734C22C2×#6692511yescharacteristic
735C22C2×C22⋊C4×D1111yescharacteristic
736C22#1062301711yescharacteristic
737C22#1062301711yescharacteristic
738C22#1062302512yes—
739C22#1062303511yescharacteristic
740C22#1062304612yes—
741C22D11×#11711yescharacteristic
742C22#1062305411yescharacteristic
743C22#1062307812yes—
744C22#1062307812yes—
745C22#1062309112yes—
746C22#1062309512yes—
747C22#1062312012yes—
748C22#1062312012yes—
749C22#1062313811yescharacteristic
750C22#1062313911yescharacteristic
751C22#1062314612yes—
752C22#1062315911yescharacteristic
753C22#1062316011yescharacteristic
754C22#1062317112yes—
755C22#1062319312yes—
756C22#1062319412yes—
757C4—24no—
758C4—42no—
759C4—82no—
760C4—82no—
761C4—224no—
762C4—224no—
763C4—442no—
764C4—882no—
765C4—882no—
766C2—44no—
767C2—444no—
768C2#1307099711yescharacteristic
769C2#1307119211yescharacteristic
770C2#1307120511yescharacteristic
771C2#1307124311yescharacteristic
772C2#1307125011yescharacteristic
773C2#1307125611yescharacteristic
774C2#1307125811yescharacteristic
775C2#1307445912yes—
776C2#1307446112yes—
777C2#1307450412yes—
778C2#1307453712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22⋊#95D11
hypocenterC11#14344
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622277C2semidirect
3. C2×#10622280C2semidirect
4. #13066867C2semidirect
5. #13066864C2semidirect
6. #13066859C2semidirect
8. #13066840C2semidirect
9. #13066840C2semidirect
10. #13066839C2semidirect
11. C11×C22⋊#95C2semidirect
20. C2×C4×C22⋊D11C4semidirect
198. C2×C4×D11C22⋊C4semidirect
218. C22⋊#95D11semidirect
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×C22⋊D112
C2×#106222772
C2×#106222802
#130668672
#130668642
#130668592
#130668552
#130668402
#130668392
C11×C22⋊#952
#1434411