Finite Group Databasebeta

← #14676314

Subgroups — #14676314

Order 2816.

2230 conjugacy classes of subgroups.

The subgroup lattice has 788 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×#10622279C211yesmaximal, characteristic, complemented
4#13066864C212yesmaximal, complemented
5#13066855C212yesmaximal
6#13066853C212yesmaximal, complemented
7#13066847C212yesmaximal, complemented
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⋊Dic11C2212yes—
17C22×C22⋊Dic11C2211yescharacteristic
18C2×C4×C22⋊D11—24no—
19C2×C4×C22⋊D11—24no—
20C2×C4×C22⋊D11C418yescomplemented
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2212yes—
24C22×Dic11⋊C4C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2212yes—
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#10622279—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×C11C2311yescharacteristic
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—22no—
52C22×C22⋊D11—22no—
53C22×C22⋊D11—22no—
54C22×C22⋊D11—22no—
55C22×C22⋊D11—22no—
56C22×C22⋊D11—22no—
57C22×C22⋊D11C2×C414yes—
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2312yes—
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C22×C4×D11—42no—
64C22×C4×D11—42no—
65C22×C4×D11C2×C414yes—
66C22×C4×D11D414yes—
67C22×C4×D11D414yes—
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4—24no—
70C2×C11×C22⋊C4—42no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—42no—
76C2×C22⋊Dic11C2×C414yes—
77C4×C22⋊D11—232no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—22no—
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×C414yes—
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4C2×C414yes—
90C2×C4×Dic11—22no—
91C2×C4×Dic11—22no—
92C2×C4×Dic11—24no—
93C2×C4×Dic11—42no—
94C2×C4×Dic11—42no—
95C2×C4×Dic11C2×C414yes—
96C11×#95—22no—
97C11×#95—22no—
98C11×#95—42no—
99C11⋊#95—22no—
100C11⋊#95—22no—
101C11⋊#95—24no—
102C11⋊#95—24no—
103C11⋊#95—24no—
104C11⋊#95—24no—
105C11⋊#95—24no—
106C11⋊#95—42no—
107#13940—111nomaximal, Sylow
108C24×C11—21no—
109C24×C11—21no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—21no—
113C24×C11—21no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11C22×C412yes—
117C24×C11#4112yes—
118C24×C11#4112yes—
119C24×C11C2411yescharacteristic
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—21no—
123C23×D11—21no—
124C23×D11—21no—
125C23×D11—21no—
126C23×D11—22no—
127C23×D11—22no—
128C23×D11C22×C412yes—
129C23×D11C2×D412yes—
130C23×D11C2×D412yes—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
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—28no—
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—44no—
152C22×C4×C11—44no—
153C22×C4×C11—48no—
154C22×C4×C11—48no—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C22×C412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11#4114yes—
160C2×C22⋊D11—28no—
161C2×C22⋊D11—28no—
162C2×C22⋊D11—28no—
163C2×C22⋊D11—28no—
164C2×C22⋊D11—28no—
165C2×C22⋊D11—28no—
166C2×C22⋊D11—28no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—22no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—22no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11C22×C412yes—
191C22×Dic11C22×C412yes—
192C22×Dic11C22×C412yes—
193C22×Dic11C2×D412yes—
194C22×Dic11C2×D412yes—
195C22×Dic11#4114yes—
196C22×Dic11#4112yes—
197C22×Dic11#4112yes—
198C2×C4×D11—44no—
199C2×C4×D11—44no—
200C2×C4×D11—48no—
201C2×C4×D11—48no—
202C2×C4×D11C22⋊C4116yescomplemented
203C11×C22⋊C4—48no—
204C22⋊Dic11—28no—
205C22⋊Dic11—48no—
206(C2×D11)⋊C4—216no—
207(C2×D11)⋊C4—28no—
208(C2×D11)⋊C4—48no—
209Dic11⋊C4—28no—
210C4×Dic11—28no—
211C4×Dic11—48no—
212C22×C4×D4—111no—
213C2×#381—111no—
214C2×C4×C22⋊C4—111no—
215#1440—112no—
216#1438—112no—
217#1437—112no—
218#1436—112no—
219#1434—111no—
220#1434—111no—
221C22⋊#95—111no—
222C22⋊#95D1111yescharacteristic, complemented
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11#11714yes—
246C23×C11C23×C411yescharacteristic
247C23×C11C22×D411yescharacteristic
248C23×C11C22×D411yescharacteristic
249C23×C11C2×#4112yes—
250C23×C11C2×#4111yescharacteristic
251C23×C11C2×#4111yescharacteristic
252C23×C11C2×#4111yescharacteristic
253C23×C11C2×#4111yescharacteristic
254C23×C11C2×#4112yes—
255C23×C11H(5,𝔽2)12yes—
256C23×C11H(5,𝔽2)12yes—
257C22×D11—22no—
258C22×D11—22no—
259C22×D11—22no—
260C22×D11—22no—
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—24no—
264C22×D11—22no—
265C22×D11—22no—
266C22×D11—22no—
267C22×D11—22no—
268C22×D11—24no—
269C22×D11—24no—
270C22×D11—24no—
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—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—24no—
283C2×C4×C11—24no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—24no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—416no—
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×C11C2×C22⋊C414yes—
305C22⋊D11—232no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—24no—
315C2×Dic11—24no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—24no—
320C2×Dic11—24no—
321C2×Dic11—24no—
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—
336C2×Dic11#11714yes—
337C4×D11—416no—
338C23×D4—111no—
339C24×C4—111no—
340C24×C4C2×D1111yescharacteristic
341C2×C4×D4—118no—
342C2×C4×D4—224no—
343C2×C4×D4—224no—
344C22×C4⋊C4—111no—
345C22×C22⋊C4—111no—
346C22×C22⋊C4—111no—
347C22×C22⋊C4—112no—
348C22×C22⋊C4—112no—
349C22×C22⋊C4—112no—
350C22×C22⋊C4C2×D1112yes—
351C22×C42—111no—
352C22×C42—112no—
353#381—224no—
354C4×C22⋊C4—224no—
355C2×#95—111no—
356C2×#95—111no—
357C2×#95—112no—
358C2×#95—112no—
359C2×#95—112no—
360C2×#95—112no—
361C2×#95—112no—
362C2×#95—112no—
363C2×#95C2×D1111yescharacteristic
364C2×#95C2×D1111yescharacteristic
365C2×#95C2×D1112yes—
366C22×C11—24no—
367C22×C11—24no—
368C22×C11—24no—
369C22×C11—42no—
370C22×C11—44no—
371C22×C11—44no—
372C22×C11—44no—
373C22×C11—44no—
374C22×C11—42no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11C22×C22⋊C411yescharacteristic
378C22×C11C2×#11711yescharacteristic
379C22×C11C2×#11711yescharacteristic
380C22×C11C4×#4111yescharacteristic
381C22×C11C4×#4111yescharacteristic
382C22×C11#51811yescharacteristic
383C22×C11#51811yescharacteristic
384C22×C11#52512yes—
385C22×C11#52511yescharacteristic
386C22×C11#52511yescharacteristic
387C22×C11#52511yescharacteristic
388C22×C11#52511yescharacteristic
389C22×C11#53212yes—
390C22×C11#53412yes—
391C22×C11#53412yes—
392C22×C11#55112yes—
393C22×C11#55112yes—
394C22×C11#55312yes—
395C22×C11#55312yes—
396C22×C11#55312yes—
397C22×C11#55312yes—
398C22×C11#55912yes—
399C22×C11#55912yes—
400C2×D11—24no—
401C2×D11—24no—
402C2×D11—24no—
403C2×D11—44no—
404C2×D11—44no—
405C2×D11—44no—
406C2×D11—44no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—42no—
411C4×C11—24no—
412C4×C11—42no—
413C4×C11—44no—
414C4×C11—82no—
415Dic11—24no—
416Dic11—24no—
417Dic11—44no—
418Dic11—42no—
419Dic11—82no—
420C25—111no—
421C25C22×D1111yescharacteristic
422C22×D4—114no—
423C22×D4—222no—
424C22×D4—222no—
425C22×D4—222no—
426C22×D4—222no—
427C22×D4—222no—
428C22×D4—222no—
429C23×C4—22no—
430C23×C4—22no—
431C23×C4—42no—
432C23×C4—42no—
433C23×C4—111no—
434C23×C4—111no—
435C23×C4—114no—
436C23×C4—114no—
437C23×C4—114no—
438C23×C4—111no—
439C23×C4—112no—
440C23×C4—112no—
441C23×C4—442no—
442C23×C4—442no—
443C23×C4C4×D1114yes—
444C23×C4C22×D1112yes—
445C23×C4C22×D1111yescharacteristic
446C23×C4C22×D1112yes—
447C23×C4C22×D1111yescharacteristic
448C4×D4—2232no—
449C2×C4⋊C4—114no—
450C2×C4⋊C4—222no—
451C2×C4⋊C4—222no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—42no—
455C2×C22⋊C4—114no—
456C2×C22⋊C4—114no—
457C2×C22⋊C4—224no—
458C2×C22⋊C4—222no—
459C2×C22⋊C4—222no—
460C2×C22⋊C4—224no—
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×C42—114no—
471C2×C42—222no—
472C2×C42—222no—
473C2×C42—224no—
474C2×C42—442no—
475C2×C42—442no—
476#95—22no—
477#95—22no—
478#95—42no—
479#95—224no—
480#95—224no—
481#95—224no—
482#95—224no—
483#95—224no—
484#95—222no—
485#95—222no—
486#95—442no—
487C2×C11—44no—
488C2×C11#228011yescharacteristic
489C2×C11#229711yescharacteristic
490C2×C11#230811yescharacteristic
491C2×C11#235311yescharacteristic
492C2×C11#235311yescharacteristic
493C2×C11#235711yescharacteristic
494C2×C11#235711yescharacteristic
495C2×C11#260012yes—
496C2×C11#260012yes—
497C2×C11#260212yes—
498C2×C11#260212yes—
499D11—44no—
500C24—22no—
501C24—21no—
502C24—21no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—21no—
507C24—21no—
508C24—112no—
509C24—112no—
510C24—112no—
511C24—222no—
512C24—221no—
513C24—222no—
514C24—222no—
515C24—221no—
516C24—222no—
517C24—221no—
518C24—221no—
519C24C2×C4×D1112yes—
520C24#434112yes—
521C24#434312yes—
522C24C23×D1111yescharacteristic
523C2×D4—228no—
524C2×D4—228no—
525C2×D4—228no—
526C2×D4—228no—
527C2×D4—228no—
528C2×D4—228no—
529C2×D4—228no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—28no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—112no—
555C22×C4—112no—
556C22×C4—112no—
557C22×C4—112no—
558C22×C4—112no—
559C22×C4—112no—
560C22×C4—1116no—
561C22×C4—112no—
562C22×C4—114no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—221no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—444no—
587C22×C4—444no—
588C22×C4—448no—
589C22×C4—448no—
590C22×C4C2×C4×D1112yes—
591C22×C4C2×C4×D1112yes—
592C22×C4#433914yes—
593C22×C4D4×D1112yes—
594C22×C4D4×D1112yes—
595C4⋊C4—228no—
596C22⋊C4—48no—
597C22⋊C4—228no—
598C22⋊C4—2216no—
599C22⋊C4—228no—
600C22⋊C4—448no—
601C22⋊C4—448no—
602C42—228no—
603C42—448no—
604C11#1394011yescharacteristic, complemented, Sylow
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—22no—
613C23—24no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—24no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—114no—
628C23—222no—
629C23—222no—
630C23—222no—
631C23—222no—
632C23—222no—
633C23—222no—
634C23—224no—
635C23—224no—
636C23—224no—
637C23—224no—
638C23—222no—
639C23—222no—
640C23—222no—
641C23—222no—
642C23—442no—
643C23—442no—
644C23—442no—
645C23—442no—
646C23—442no—
647C23—442no—
648C23—442no—
649C23—442no—
650C23#6694514yes—
651C23C22×C4×D1111yescharacteristic
652C23C2×#433912yes—
653C23C2×D4×D1111yescharacteristic
654C23C2×D4×D1111yescharacteristic
655C23C2×#434111yescharacteristic
656C23#6703712yes—
657C23#6703712yes—
658C23C2×#434311yescharacteristic
659C23#41×D1111yescharacteristic
660C23#41×D1111yescharacteristic
661C23#41×D1112yes—
662D4—2232no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—416no—
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—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—114no—
688C2×C4—114no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—224no—
694C2×C4—224no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—224no—
703C2×C4—224no—
704C2×C4—224no—
705C2×C4—4416no—
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×C4C22⋊C4×D1114yes—
720C22—24no—
721C22—24no—
722C22—24no—
723C22—44no—
724C22—44no—
725C22—44no—
726C22—44no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—224no—
732C22—224no—
733C22—224no—
734C22—444no—
735C22—444no—
736C22—444no—
737C22—444no—
738C22—442no—
739C22—442no—
740C22—442no—
741C22—442no—
742C22C4×#433911yescharacteristic
743C22C2×C22⋊C4×D1111yescharacteristic
744C22#1062301711yescharacteristic
745C22#1062301711yescharacteristic
746C22#1062302612yes—
747C22C2×#6694511yescharacteristic
748C22#1062304512yes—
749C22D11×#11711yescharacteristic
750C22#1062305311yescharacteristic
751C22#1062307112yes—
752C22#1062307812yes—
753C22#1062307912yes—
754C22#1062309012yes—
755C22#1062312012yes—
756C22#1062312012yes—
757C22#1062313212yes—
758C22#1062313711yescharacteristic
759C22#1062313711yescharacteristic
760C22#1062315811yescharacteristic
761C22#1062315811yescharacteristic
762C22#1062316812yes—
763C22#1062319212yes—
764C22#1062319512yes—
765C4—24no—
766C4—44no—
767C4—42no—
768C4—82no—
769C4—224no—
770C4—224no—
771C4—444no—
772C4—442no—
773C4—882no—
774C2—44no—
775C2—444no—
776C2#1307099811yescharacteristic
777C2#1307110211yescharacteristic
778C2#1307119211yescharacteristic
779C2#1307155211yescharacteristic
780C2#1307155811yescharacteristic
781C2#1307158411yescharacteristic
782C2#1307159011yescharacteristic
783C2#1307420012yes—
784C2#1307420212yes—
785C2#1307422412yes—
786C2#1307423212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22⋊#95D11
hypocenterC11#13940
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×#10622279C2semidirect
4. #13066864C2semidirect
6. #13066853C2semidirect
7. #13066847C2semidirect
8. #13066840C2semidirect
9. #13066840C2semidirect
10. #13066839C2semidirect
11. C11×C22⋊#95C2semidirect
20. C2×C4×C22⋊D11C4semidirect
202. C2×C4×D11C22⋊C4semidirect
222. C22⋊#95D11semidirect
604. C11#13940semidirect

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×#106222792
#130668642
#130668552
#130668532
#130668472
#130668402
#130668392
C11×C22⋊#952
#1394011