Finite Group Databasebeta

← #14676316

Subgroups — #14676316

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×D44C211yesmaximal, characteristic
2C2×#10622277C211yesmaximal, characteristic, complemented
3C2×#10622279C211yesmaximal, characteristic, complemented
4#13066864C212yesmaximal, complemented
5#13066856C212yesmaximal
6#13066852C212yesmaximal, complemented
7#13066850C212yesmaximal, complemented
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)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4×Dic11C2212yes—
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#10622279—24no—
39#10622277—24no—
40C24×D11C2311yescharacteristic
41C24×D11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2312yes—
50C23×Dic11C2311yescharacteristic
51C22×D44—22no—
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—22no—
55C22×D44—22no—
56C22×D44—22no—
57C22×D44C2×C414yes—
58C22×C4×D11—22no—
59C22×C4×D11—22no—
60C22×C4×D11—42no—
61C22×C4×D11—42no—
62C22×C4×D11—42no—
63C22×C4×D11—42no—
64C22×C4×D11C2×C414yes—
65C22×C4×D11C2×C414yes—
66C22×C4×D11D414yes—
67C22×C4×D11D414yes—
68C2×C42×C11—22no—
69C2×C42×C11—22no—
70C2×C42×C11C2×C414yes—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—24no—
83C2×(C2×D11)⋊C4—42no—
84C2×(C2×D11)⋊C4—42no—
85C2×(C2×D11)⋊C4—42no—
86C2×(C2×D11)⋊C4—42no—
87C2×(C2×D11)⋊C4C2×C414yes—
88C2×(C2×D11)⋊C4C2×C414yes—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11C2×C414yes—
92C2×C4×Dic11—24no—
93C2×C4×Dic11—42no—
94C2×C4×Dic11—42no—
95C4×D44—232no—
96C11×#95—22no—
97C11×#95—22no—
98C11×#95—24no—
99C11×#95—24no—
100C11⋊#95—22no—
101C11⋊#95—22no—
102C11⋊#95—24no—
103C11⋊#95—24no—
104C11⋊#95—24no—
105C11⋊#95—42no—
106C11⋊#95—42no—
107#13940—111nomaximal, Sylow
108C24×C11C2411yescharacteristic
109C23×D11—21no—
110C23×D11—21no—
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—21no—
116C23×D11—21no—
117C23×D11—21no—
118C23×D11—21no—
119C23×D11—21no—
120C23×D11—21no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11C22×C412yes—
126C23×D11C22×C412yes—
127C23×D11C2×D412yes—
128C23×D11C2×D412yes—
129C23×D11#4112yes—
130C23×D11#4112yes—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
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×C4×C11#4112yes—
161C22×C4×C11#4112yes—
162C22×Dic11—22no—
163C22×Dic11—21no—
164C22×Dic11—21no—
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×Dic11—22no—
181C22×Dic11C22×C412yes—
182C22×Dic11C22×C412yes—
183C22×Dic11C2×D412yes—
184C22×Dic11C2×D412yes—
185C22×Dic11#4114yes—
186C2×D44—28no—
187C2×D44—28no—
188C2×D44—28no—
189C2×D44—28no—
190C2×D44—28no—
191C2×D44—28no—
192C2×D44—28no—
193C2×C4×D11—28no—
194C2×C4×D11—44no—
195C2×C4×D11—44no—
196C2×C4×D11—44no—
197C2×C4×D11—44no—
198C2×C4×D11—48no—
199C2×C4×D11—48no—
200C2×C4×D11—48no—
201C2×C4×D11—48no—
202C2×C4×D11C22⋊C4116yescomplemented
203C42×C11—28no—
204(C2×D11)⋊C4—216no—
205(C2×D11)⋊C4—28no—
206(C2×D11)⋊C4—28no—
207(C2×D11)⋊C4—48no—
208(C2×D11)⋊C4—48no—
209(C2×D11)⋊C4—48no—
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#1434D1111yescharacteristic, complemented
221C22⋊#95—111no—
222C22⋊#95—111no—
223C23×C11C23×C411yescharacteristic
224C23×C11C22×D411yescharacteristic
225C23×C11C22×D411yescharacteristic
226C23×C11C2×#4112yes—
227C23×C11C2×#4111yescharacteristic
228C23×C11C2×#4111yescharacteristic
229C23×C11C2×#4111yescharacteristic
230C23×C11C2×#4111yescharacteristic
231C23×C11C2×#4112yes—
232C23×C11H(5,𝔽2)12yes—
233C23×C11H(5,𝔽2)12yes—
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—22no—
243C22×D11—22no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—24no—
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—22no—
251C22×D11—22no—
252C22×D11—22no—
253C22×D11—22no—
254C22×D11—22no—
255C22×D11—24no—
256C22×D11—24no—
257C22×D11—24no—
258C22×D11—24no—
259C22×D11—24no—
260C22×D11—24no—
261C22×D11—24no—
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×D11—42no—
275C22×D11—42no—
276C22×D11—42no—
277C22×D11—42no—
278C22×D11C2×C22⋊C414yes—
279C22×D11#11714yes—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—24no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
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×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11C2×C22⋊C414yes—
310C2×C4×C11#11714yes—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—24no—
314C2×Dic11—24no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—24no—
319C2×Dic11—24no—
320C2×Dic11—24no—
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×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11C2×C22⋊C414yes—
335D44—232no—
336C4×D11—416no—
337C4×D11—416no—
338C23×D4—111no—
339C24×C4—111no—
340C24×C4—111no—
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⋊C4—112no—
351C22×C42—112no—
352C22×C42C2×D1111yescharacteristic
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×#95C2×D1111yescharacteristic
363C2×#95C2×D1111yescharacteristic
364C2×#95C2×D1112yes—
365C2×#95C2×D1112yes—
366C22×C11C22×C22⋊C411yescharacteristic
367C22×C11C2×#11711yescharacteristic
368C22×C11C2×#11711yescharacteristic
369C22×C11C4×#4111yescharacteristic
370C22×C11C4×#4111yescharacteristic
371C22×C11#51811yescharacteristic
372C22×C11#51811yescharacteristic
373C22×C11#52512yes—
374C22×C11#52511yescharacteristic
375C22×C11#52511yescharacteristic
376C22×C11#52511yescharacteristic
377C22×C11#52511yescharacteristic
378C22×C11#53212yes—
379C22×C11#53412yes—
380C22×C11#53412yes—
381C22×C11#55112yes—
382C22×C11#55112yes—
383C22×C11#55312yes—
384C22×C11#55312yes—
385C22×C11#55312yes—
386C22×C11#55312yes—
387C22×C11#55912yes—
388C22×C11#55912yes—
389C2×D11—24no—
390C2×D11—24no—
391C2×D11—24no—
392C2×D11—24no—
393C2×D11—24no—
394C2×D11—24no—
395C2×D11—42no—
396C2×D11—44no—
397C2×D11—44no—
398C2×D11—44no—
399C2×D11—44no—
400C2×D11—44no—
401C2×D11—44no—
402C2×D11—44no—
403C2×D11—44no—
404C2×D11—42no—
405C2×D11—42no—
406C2×D11—42no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—42no—
411C4×C11—24no—
412C4×C11—24no—
413C4×C11—44no—
414C4×C11—42no—
415C4×C11—82no—
416Dic11—24no—
417Dic11—42no—
418Dic11—44no—
419Dic11—82no—
420C25—111no—
421C25—111no—
422C22×D4—114no—
423C22×D4—222no—
424C22×D4—222no—
425C22×D4—222no—
426C22×D4—222no—
427C22×D4—222no—
428C22×D4—222no—
429C23×C4—111no—
430C23×C4—114no—
431C23×C4—114no—
432C23×C4—114no—
433C23×C4—112no—
434C23×C4—111no—
435C23×C4—114no—
436C23×C4—112no—
437C23×C4—222no—
438C23×C4—222no—
439C23×C4—442no—
440C23×C4—442no—
441C23×C4—442no—
442C23×C4—442no—
443C23×C4C22×D1112yes—
444C23×C4C22×D1111yescharacteristic
445C23×C4C22×D1112yes—
446C23×C4C22×D1111yescharacteristic
447C23×C4C22×D1111yescharacteristic
448C4×D4—2232no—
449C2×C4⋊C4—114no—
450C2×C4⋊C4—222no—
451C2×C4⋊C4—222no—
452C2×C22⋊C4—114no—
453C2×C22⋊C4—114no—
454C2×C22⋊C4—222no—
455C2×C22⋊C4—222no—
456C2×C22⋊C4—224no—
457C2×C22⋊C4—222no—
458C2×C22⋊C4—222no—
459C2×C22⋊C4—224no—
460C2×C22⋊C4—224no—
461C2×C22⋊C4—224no—
462C2×C22⋊C4—224no—
463C2×C22⋊C4—224no—
464C2×C22⋊C4—224no—
465C2×C22⋊C4—224no—
466C2×C22⋊C4—442no—
467C2×C22⋊C4—442no—
468C2×C22⋊C4—442no—
469C2×C22⋊C4—442no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42—224no—
473C2×C42—442no—
474C2×C42—442no—
475C2×C42C4×D1114yes—
476#95—24no—
477#95—22no—
478#95—22no—
479#95—24no—
480#95—224no—
481#95—224no—
482#95—222no—
483#95—222no—
484#95—224no—
485#95—442no—
486#95—442no—
487C2×C11#228011yescharacteristic
488C2×C11#229711yescharacteristic
489C2×C11#230811yescharacteristic
490C2×C11#235311yescharacteristic
491C2×C11#235311yescharacteristic
492C2×C11#235711yescharacteristic
493C2×C11#235711yescharacteristic
494C2×C11#260012yes—
495C2×C11#260012yes—
496C2×C11#260212yes—
497C2×C11#260212yes—
498D11—44no—
499D11—44no—
500C24—112no—
501C24—112no—
502C24—112no—
503C24—112no—
504C24—112no—
505C24—112no—
506C24—222no—
507C24—222no—
508C24—221no—
509C24—221no—
510C24—221no—
511C24—221no—
512C24—221no—
513C24—221no—
514C24—222no—
515C24—222no—
516C24—221no—
517C24—221no—
518C24—222no—
519C24—222no—
520C24—222no—
521C24—222no—
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—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—112no—
554C22×C4—112no—
555C22×C4—112no—
556C22×C4—1116no—
557C22×C4—112no—
558C22×C4—114no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
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—228no—
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—444no—
582C22×C4—444no—
583C22×C4—448no—
584C22×C4—448no—
585C22×C4—448no—
586C22×C4—448no—
587C22×C4C2×C4×D1112yes—
588C22×C4C2×C4×D1112yes—
589C22×C4C2×C4×D1112yes—
590C22×C4#433914yes—
591C22×C4D4×D1112yes—
592C22×C4D4×D1112yes—
593C22×C4#434112yes—
594C22×C4#434312yes—
595C4⋊C4—228no—
596C22⋊C4—228no—
597C22⋊C4—228no—
598C22⋊C4—2216no—
599C22⋊C4—448no—
600C22⋊C4—448no—
601C22⋊C4—448no—
602C42—28no—
603C42—448no—
604C11#1394011yescharacteristic, complemented, Sylow
605C23—114no—
606C23—114no—
607C23—224no—
608C23—224no—
609C23—222no—
610C23—222no—
611C23—222no—
612C23—222no—
613C23—222no—
614C23—222no—
615C23—222no—
616C23—222no—
617C23—222no—
618C23—222no—
619C23—222no—
620C23—222no—
621C23—224no—
622C23—224no—
623C23—224no—
624C23—224no—
625C23—222no—
626C23—222no—
627C23—222no—
628C23—222no—
629C23—222no—
630C23—222no—
631C23—222no—
632C23—222no—
633C23—224no—
634C23—224no—
635C23—442no—
636C23—442no—
637C23—442no—
638C23—442no—
639C23—442no—
640C23—442no—
641C23—442no—
642C23—442no—
643C23—442no—
644C23—442no—
645C23—442no—
646C23—442no—
647C23—442no—
648C23—442no—
649C23—442no—
650C23—442no—
651C23C22×C4×D1111yescharacteristic
652C23C2×#433912yes—
653C23C2×D4×D1111yescharacteristic
654C23C2×D4×D1111yescharacteristic
655C23C2×#434111yescharacteristic
656C23C2×#434311yescharacteristic
657C23#41×D1111yescharacteristic
658C23#41×D1112yes—
659C23#41×D1111yescharacteristic
660C23#6704212yes—
661C23#6704212yes—
662D4—2232no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
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—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—114no—
693C2×C4—222no—
694C2×C4—222no—
695C2×C4—224no—
696C2×C4—224no—
697C2×C4—224no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—224no—
702C2×C4—224no—
703C2×C4—4416no—
704C2×C4—4416no—
705C2×C4—442no—
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×C4C22⋊C4×D1114yes—
719C2×C4#6694514yes—
720C22—224no—
721C22—224no—
722C22—224no—
723C22—224no—
724C22—224no—
725C22—224no—
726C22—444no—
727C22—444no—
728C22—444no—
729C22—444no—
730C22—444no—
731C22—444no—
732C22—444no—
733C22—444no—
734C22—442no—
735C22—442no—
736C22—442no—
737C22—442no—
738C22—442no—
739C22—442no—
740C22—442no—
741C22—442no—
742C22C4×#433911yescharacteristic
743C22C2×C22⋊C4×D1111yescharacteristic
744C22C2×#6694511yescharacteristic
745C22D11×#11711yescharacteristic
746C22#1062305211yescharacteristic
747C22#1062305211yescharacteristic
748C22#1062305311yescharacteristic
749C22#1062305812yes—
750C22#1062306112yes—
751C22#1062307812yes—
752C22#1062307912yes—
753C22#1062309612yes—
754C22#1062311612yes—
755C22#1062313711yescharacteristic
756C22#1062313711yescharacteristic
757C22#1062315811yescharacteristic
758C22#1062315811yescharacteristic
759C22#1062318412yes—
760C22#1062318412yes—
761C22#1062321212yes—
762C22#1062322612yes—
763C22#1062323612yes—
764C22#1062324012yes—
765C4—24no—
766C4—24no—
767C4—44no—
768C4—42no—
769C4—82no—
770C4—224no—
771C4—444no—
772C4—442no—
773C4—882no—
774C2—444no—
775C2—444no—
776C2#1307099811yescharacteristic
777C2#1307110211yescharacteristic
778C2#1307119311yescharacteristic
779C2#1307154911yescharacteristic
780C2#1307155711yescharacteristic
781C2#1307158711yescharacteristic
782C2#1307159111yescharacteristic
783C2#1307420112yes—
784C2#1307420512yes—
785C2#1307422612yes—
786C2#1307423412yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1434D11
hypocenterC11#13940
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×#10622279C2semidirect
4. #13066864C2semidirect
6. #13066852C2semidirect
7. #13066850C2semidirect
8. #13066843C2semidirect
9. (C2×D11)⋊#95C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C11×#1434C2semidirect
26. C2×C4×D44C4semidirect
202. C2×C4×D11C22⋊C4semidirect
220. #1434D11semidirect
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×D442
C2×#106222772
C2×#106222792
#130668642
#130668562
#130668522
#130668502
#130668432
(C2×D11)⋊#952
C11×#14342
#1394011