Finite Group Databasebeta

← #14684792

Subgroups — #14684792

Order 2816.

1898 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C211yesmaximal, characteristic
2C2×#10622280C211yesmaximal, characteristic, complemented
3C2×#10622600C211yesmaximal, characteristic, complemented
4#13066869C211yesmaximal, characteristic, complemented
5#13066867C212yesmaximal, complemented
6#13066864C212yesmaximal, complemented
7#13066862C211yesmaximal, characteristic, complemented
8#13066860C212yesmaximal, complemented
9#13066858C211yesmaximal, characteristic, complemented
10#13066856C212yesmaximal
11C11×#1441C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×(C2×D11)⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C2×#66947—24no—
27C2×#66947—24no—
28C2×#66947C418yescomplemented
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2212yes—
31C2×C11×#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622600—24no—
39#10622280—24no—
40C24×D11C2311yescharacteristic
41C24×D11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C22×D44—22no—
52C22×D44—22no—
53C22×D44—42no—
54C22×D44—42no—
55C22×D44C2×C414yes—
56C22×C4×D11—42no—
57C22×C4×D11—42no—
58C22×C4×D11C2×C414yes—
59C22×C4×D11D414yes—
60C22×C4×D11D414yes—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—42no—
65C2×C11×C4⋊C4C2×C414yes—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—42no—
75C2×(C2×D11)⋊C4—42no—
76C2×(C2×D11)⋊C4—42no—
77C2×(C2×D11)⋊C4—42no—
78C2×(C2×D11)⋊C4—42no—
79C2×(C2×D11)⋊C4—42no—
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×(C2×D11)⋊C4C2×C414yes—
86C2×(C2×D11)⋊C4C2×C414yes—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—42no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4—24no—
92C2×Dic11⋊C4—42no—
93C2×Dic11⋊C4—42no—
94C2×Dic11⋊C4C2×C414yes—
95#66947—232no—
96C11×#95—22no—
97C11×#95—42no—
98C11×#95—42no—
99C11⋊#95—22no—
100C11⋊#95—24no—
101C11⋊#95—42no—
102C11⋊#95—42no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105#14658—111nomaximal, Sylow
106C24×C11C2411yescharacteristic
107C23×D11—21no—
108C23×D11—21no—
109C23×D11—22no—
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—21no—
113C23×D11—22no—
114C23×D11—21no—
115C23×D11—21no—
116C23×D11—21no—
117C23×D11—21no—
118C23×D11—21no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—21no—
123C23×D11—22no—
124C23×D11—21no—
125C23×D11C22×C412yes—
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—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
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×C11—22no—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C22×C412yes—
157C22×C4×C11C22×C412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D412yes—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
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×Dic11C22×C412yes—
181C22×Dic11C22×C412yes—
182C22×Dic11C2×D412yes—
183C22×Dic11C2×D412yes—
184C2×D44—28no—
185C2×D44—48no—
186C2×D44—44no—
187C2×D44—48no—
188C2×D44—44no—
189C2×C4×D11—48no—
190C2×C4×D11—44no—
191C2×C4×D11—44no—
192C2×C4×D11—48no—
193C2×C4×D11C22⋊C4116yescomplemented
194C11×C4⋊C4—28no—
195C11×C4⋊C4—44no—
196(C2×D11)⋊C4—28no—
197(C2×D11)⋊C4—28no—
198(C2×D11)⋊C4—28no—
199(C2×D11)⋊C4—48no—
200(C2×D11)⋊C4—48no—
201(C2×D11)⋊C4—48no—
202(C2×D11)⋊C4—48no—
203C4⋊Dic11—44no—
204Dic11⋊C4—28no—
205Dic11⋊C4—48no—
206C22×#123—111no—
207C2×#380—111no—
208C2×#380—111no—
209#1441—112no—
210#1441—111no—
211#1441D1111yescharacteristic, complemented
212#1440—112no—
213#1439—112no—
214#1439—111no—
215#1439—111no—
216#1438—112no—
217C23×C11C23×C411yescharacteristic
218C23×C11C22×D411yescharacteristic
219C23×C11C22×D411yescharacteristic
220C23×C11H(5,𝔽2)12yes—
221C23×C11H(5,𝔽2)11yescharacteristic
222C23×C11H(5,𝔽2)12yes—
223C23×C11H(5,𝔽2)11yescharacteristic
224C23×C11H(5,𝔽2)12yes—
225C23×C112−1+412yes—
226C23×C112−1+411yescharacteristic
227C23×C112−1+411yescharacteristic
228C22×D11—24no—
229C22×D11—22no—
230C22×D11—22no—
231C22×D11—24no—
232C22×D11—22no—
233C22×D11—24no—
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—24no—
242C22×D11—22no—
243C22×D11—24no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—24no—
247C22×D11—42no—
248C22×D11—42no—
249C22×D11—42no—
250C22×D11—42no—
251C22×D11—42no—
252C22×D11—42no—
253C22×D11—42no—
254C22×D11—42no—
255C22×D11—41no—
256C22×D11—42no—
257C22×D11—41no—
258C22×D11—41no—
259C22×D11—41no—
260C22×D11—41no—
261C22×D11—41no—
262C22×D11—41no—
263C22×D11—41no—
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×D11C2×C22⋊C414yes—
274C2×C4×C11—24no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—24no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—24no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—41no—
284C2×C4×C11—42no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
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×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11C2×C22⋊C414yes—
305C2×Dic11—24no—
306C2×Dic11—24no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—24no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—42no—
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×Dic11C2×C22⋊C414yes—
329D44—416no—
330C4×D11—416no—
331C23×D4—111no—
332C24×C4—111no—
333C2×#123—118no—
334C2×#123—224no—
335C2×#123—224no—
336C22×C4⋊C4—111no—
337C22×C4⋊C4—112no—
338C22×C4⋊C4—111no—
339C22×C4⋊C4C2×D1111yescharacteristic
340C22×C4⋊C4C2×D1111yescharacteristic
341C22×C22⋊C4—111no—
342C22×C22⋊C4—111no—
343C22×C22⋊C4—111no—
344C22×C22⋊C4—112no—
345C22×C22⋊C4—112no—
346C22×C22⋊C4—112no—
347C22×C22⋊C4—112no—
348#380—224no—
349#380—224no—
350C2×#95—112no—
351C2×#95—111no—
352C2×#95—112no—
353C2×#95—112no—
354C2×#95—112no—
355C2×#95—112no—
356C2×#95C2×D1111yescharacteristic
357C2×#95C2×D1112yes—
358C2×#95C2×D1112yes—
359C22×C11C22×C22⋊C411yescharacteristic
360C22×C11#51812yes—
361C22×C11#52011yescharacteristic
362C22×C11#52011yescharacteristic
363C22×C11#52012yes—
364C22×C11#53411yescharacteristic
365C22×C11#53412yes—
366C22×C11#53411yescharacteristic
367C22×C11#53511yescharacteristic
368C22×C11#53511yescharacteristic
369C22×C11#53611yescharacteristic
370C22×C11#53611yescharacteristic
371C22×C11#53711yescharacteristic
372C22×C11#53711yescharacteristic
373C22×C11#53712yes—
374C22×C11#56012yes—
375C22×C11#56012yes—
376C22×C11#56212yes—
377C22×C11#56212yes—
378C22×C11#56212yes—
379C22×C11#56212yes—
380C22×C11#56312yes—
381C22×C11#56312yes—
382C2×D11—24no—
383C2×D11—24no—
384C2×D11—24no—
385C2×D11—44no—
386C2×D11—44no—
387C2×D11—42no—
388C2×D11—42no—
389C2×D11—44no—
390C2×D11—42no—
391C2×D11—42no—
392C2×D11—44no—
393C2×D11—42no—
394C2×D11—42no—
395C2×D11—42no—
396C2×D11—44no—
397C2×D11—44no—
398C2×D11—81no—
399C2×D11—81no—
400C2×D11—82no—
401C2×D11—81no—
402C2×D11—81no—
403C2×D11—82no—
404C4×C11—24no—
405C4×C11—42no—
406C4×C11—42no—
407C4×C11—82no—
408C4×C11—82no—
409Dic11—24no—
410Dic11—42no—
411Dic11—82no—
412Dic11—82no—
413C25—111no—
414C25—111no—
415C22×D4—114no—
416C22×D4—222no—
417C22×D4—222no—
418C22×D4—442no—
419C22×D4—442no—
420C23×C4—111no—
421C23×C4—114no—
422C23×C4—114no—
423C23×C4—114no—
424C23×C4—111no—
425C23×C4—112no—
426C23×C4—112no—
427C23×C4—442no—
428C23×C4—442no—
429C23×C4C22×D1112yes—
430C23×C4C22×D1112yes—
431C23×C4C22×D1111yescharacteristic
432C23×C4C22×D1111yescharacteristic
433C23×C4C22×D1111yescharacteristic
434#123—2232no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—42no—
439C2×C4⋊C4—114no—
440C2×C4⋊C4—222no—
441C2×C4⋊C4—222no—
442C2×C4⋊C4—224no—
443C2×C4⋊C4—222no—
444C2×C4⋊C4—442no—
445C2×C4⋊C4—442no—
446C2×C4⋊C4—442no—
447C2×C4⋊C4C4×D1114yes—
448C2×C22⋊C4—114no—
449C2×C22⋊C4—114no—
450C2×C22⋊C4—114no—
451C2×C22⋊C4—222no—
452C2×C22⋊C4—222no—
453C2×C22⋊C4—222no—
454C2×C22⋊C4—222no—
455C2×C22⋊C4—222no—
456C2×C22⋊C4—222no—
457C2×C22⋊C4—224no—
458C2×C22⋊C4—224no—
459C2×C22⋊C4—442no—
460C2×C22⋊C4—442no—
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×C22⋊C4—442no—
468C2×C22⋊C4—442no—
469#95—22no—
470#95—42no—
471#95—42no—
472#95—224no—
473#95—222no—
474#95—442no—
475#95—442no—
476#95—442no—
477#95—442no—
478C2×C11#230811yescharacteristic
479C2×C11#231111yescharacteristic
480C2×C11#231111yescharacteristic
481C2×C11#237612yes—
482C2×C11#237612yes—
483C2×C11#281311yescharacteristic
484C2×C11#281311yescharacteristic
485C2×C11#281312yes—
486C2×C11#281411yescharacteristic
487C2×C11#281411yescharacteristic
488C2×C11#281412yes—
489D11—44no—
490D11—82no—
491C24—112no—
492C24—112no—
493C24—112no—
494C24—112no—
495C24—221no—
496C24—222no—
497C24—222no—
498C24—221no—
499C24—221no—
500C24—222no—
501C24—222no—
502C24—221no—
503C24—221no—
504C24—221no—
505C24—221no—
506C24—222no—
507C24—221no—
508C24—222no—
509C24—221no—
510C24—222no—
511C24—222no—
512C24—221no—
513C24C23×D1111yescharacteristic
514C2×D4—228no—
515C2×D4—448no—
516C2×D4—444no—
517C2×D4—448no—
518C2×D4—444no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—21no—
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—22no—
544C22×C4—22no—
545C22×C4—112no—
546C22×C4—112no—
547C22×C4—112no—
548C22×C4—1116no—
549C22×C4—112no—
550C22×C4—222no—
551C22×C4—222no—
552C22×C4—221no—
553C22×C4—221no—
554C22×C4—222no—
555C22×C4—222no—
556C22×C4—222no—
557C22×C4—222no—
558C22×C4—222no—
559C22×C4—222no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
570C22×C4—448no—
571C22×C4—444no—
572C22×C4—448no—
573C22×C4—444no—
574C22×C4C2×C4×D1112yes—
575C22×C4C2×C4×D1112yes—
576C22×C4C2×C4×D1112yes—
577C22×C4D4×D1112yes—
578C22×C4D4×D1112yes—
579C4⋊C4—28no—
580C4⋊C4—44no—
581C4⋊C4—228no—
582C4⋊C4—444no—
583C4⋊C4—448no—
584C22⋊C4—228no—
585C22⋊C4—228no—
586C22⋊C4—228no—
587C22⋊C4—448no—
588C22⋊C4—448no—
589C22⋊C4—448no—
590C22⋊C4—448no—
591C11#1465811yescharacteristic, complemented, Sylow
592C23—114no—
593C23—222no—
594C23—222no—
595C23—222no—
596C23—224no—
597C23—224no—
598C23—222no—
599C23—224no—
600C23—222no—
601C23—222no—
602C23—222no—
603C23—222no—
604C23—224no—
605C23—222no—
606C23—222no—
607C23—222no—
608C23—222no—
609C23—222no—
610C23—224no—
611C23—224no—
612C23—442no—
613C23—442no—
614C23—442no—
615C23—442no—
616C23—442no—
617C23—442no—
618C23—442no—
619C23—442no—
620C23—442no—
621C23—441no—
622C23—442no—
623C23—441no—
624C23—442no—
625C23—441no—
626C23—441no—
627C23—442no—
628C23—441no—
629C23—441no—
630C23—442no—
631C23—442no—
632C23—442no—
633C23—441no—
634C23—442no—
635C23—441no—
636C23—442no—
637C23—442no—
638C23C22×C4×D1111yescharacteristic
639C23C2×D4×D1111yescharacteristic
640C23C2×D4×D1111yescharacteristic
641C23#6703712yes—
642C23#6703711yescharacteristic
643C23#6704012yes—
644C23#6704011yescharacteristic
645C23#6704211yescharacteristic
646C23#6704212yes—
647C23#6704212yes—
648C23#6704311yescharacteristic
649D4—4416no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
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—224no—
682C2×C4—222no—
683C2×C4—224no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—224no—
687C2×C4—4416no—
688C2×C4—441no—
689C2×C4—442no—
690C2×C4—441no—
691C2×C4—442no—
692C2×C4—442no—
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×C4C22⋊C4×D1114yes—
706C22—224no—
707C22—224no—
708C22—224no—
709C22—442no—
710C22—442no—
711C22—444no—
712C22—444no—
713C22—444no—
714C22—442no—
715C22—442no—
716C22—444no—
717C22—442no—
718C22—442no—
719C22—442no—
720C22—444no—
721C22—444no—
722C22—881no—
723C22—881no—
724C22—882no—
725C22—881no—
726C22—881no—
727C22—882no—
728C22C2×C22⋊C4×D1111yescharacteristic
729C22#1062303511yescharacteristic
730C22#1062305411yescharacteristic
731C22#1062307612yes—
732C22#1062310512yes—
733C22#1062312011yescharacteristic
734C22#1062313612yes—
735C22#1062313811yescharacteristic
736C22#1062313911yescharacteristic
737C22#1062315112yes—
738C22#1062315911yescharacteristic
739C22#1062316011yescharacteristic
740C22#1062316012yes—
741C22#1062317812yes—
742C22#1062317812yes—
743C22#1062318411yescharacteristic
744C22#1062319812yes—
745C22#1062320511yescharacteristic
746C22#1062323012yes—
747C22#1062323112yes—
748C22#1062324212yes—
749C22#1062325511yescharacteristic
750C22#1062326612yes—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—82no—
755C4—82no—
756C4—224no—
757C4—442no—
758C4—882no—
759C4—882no—
760C2—444no—
761C2—882no—
762C2#1307119011yescharacteristic
763C2#1307120511yescharacteristic
764C2#1307120711yescharacteristic
765C2#1307176112yes—
766C2#1307176312yes—
767C2#1307661711yescharacteristic
768C2#1307662111yescharacteristic
769C2#1307662512yes—
770C2#1307662811yescharacteristic
771C2#1307663211yescharacteristic
772C2#1307663612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1441D11
hypocenterC11#14658
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C2×#10622280C2semidirect
3. C2×#10622600C2semidirect
4. #13066869C2semidirect
5. #13066867C2semidirect
6. #13066864C2semidirect
7. #13066862C2semidirect
8. #13066860C2semidirect
9. #13066858C2semidirect
11. C11×#1441C2semidirect
28. C2×#66947C4semidirect
193. C2×C4×D11C22⋊C4semidirect
211. #1441D11semidirect
591. C11#14658semidirect

Maximal subgroups

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

subgroupindex
C22×#669472
C2×#106222802
C2×#106226002
#130668692
#130668672
#130668642
#130668622
#130668602
#130668582
#130668562
C11×#14412
#1465811