Finite Group Databasebeta

← #14681927

Subgroups — #14681927

Order 2816.

2982 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66927C211yesmaximal, characteristic
2C2×#10622278C212yesmaximal, complemented
3C2×#10622278C212yesmaximal, complemented
4C2×#10622278C212yesmaximal, complemented
5#13066856C212yesmaximal, complemented
6#13066856C212yesmaximal, complemented
7#13066856C212yesmaximal, complemented
8#13066843C211yesmaximal, characteristic, complemented
9C11×#1434C211yesmaximal, characteristic, complemented
10C23×D44C2212yes—
11C23×D44C2212yes—
12C23×D44C2211yescharacteristic
13C23×D44C2211yescharacteristic
14C23×C4×D11C2212yes—
15C22×C42×C11C2211yescharacteristic
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C2×#66927—28no—
24C2×#66927C418yescomplemented
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2212yes—
27C2×C11×#95C2212yes—
28C2×C11×#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33#10622278—28no—
34#10622278—28no—
35#10622278—28no—
36C24×D11C2312yes—
37C24×D11C2312yes—
38C23×C4×C11C2312yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11C2312yes—
44C23×Dic11C2312yes—
45C22×D44—24no—
46C22×D44—24no—
47C22×D44—24no—
48C22×D44—24no—
49C22×D44—24no—
50C22×D44—24no—
51C22×D44—24no—
52C22×D44—24no—
53C22×D44—24no—
54C22×D44—41no—
55C22×D44—42no—
56C22×D44—41no—
57C22×D44—42no—
58C22×D44—42no—
59C22×D44—42no—
60C22×D44—42no—
61C22×D44—42no—
62C22×D44—41no—
63C22×D44—41no—
64C22×D44C2×C414yes—
65C22×D44C2×C418yescomplemented
66C22×D44C2×C418yescomplemented
67C22×D44C2×C414yescomplemented
68C22×D44D418yes—
69C22×C4×D11—24no—
70C22×C4×D11—24no—
71C22×C4×D11—24no—
72C22×C4×D11—42no—
73C22×C4×D11—42no—
74C22×C4×D11—42no—
75C22×C4×D11—42no—
76C2×C42×C11—24no—
77C2×C42×C11C2×C414yescomplemented
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—24no—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—24no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—42no—
88C2×(C2×D11)⋊C4—42no—
89C2×(C2×D11)⋊C4—42no—
90C2×(C2×D11)⋊C4—42no—
91C2×(C2×D11)⋊C4—42no—
92C2×(C2×D11)⋊C4—42no—
93C2×(C2×D11)⋊C4—42no—
94C2×(C2×D11)⋊C4—42no—
95C2×(C2×D11)⋊C4—42no—
96C2×(C2×D11)⋊C4—42no—
97C2×(C2×D11)⋊C4—42no—
98C2×(C2×D11)⋊C4—42no—
99#66927—232no—
100C11×#95—24no—
101C11×#95—24no—
102C11×#95—22no—
103C11×#95D414yescomplemented
104C11⋊#95—24no—
105C11⋊#95—24no—
106C11⋊#95—22no—
107C11⋊#95D414yescomplemented
108#14419—111nomaximal, Sylow
109C24×C11C2411yescharacteristic
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—22no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—22no—
126C23×D11—22no—
127C23×D11—22no—
128C23×D11—22no—
129C23×D11—22no—
130C23×D11—22no—
131C23×D11—22no—
132C23×D11—22no—
133C23×D11—22no—
134C23×D11—22no—
135C23×D11—22no—
136C23×D11C22×C414yes—
137C23×D11C22×C414yes—
138C23×D11C2×D414yes—
139C23×D11C2×D414yes—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
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×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11C22×C412yes—
161C22×C4×C11C22×C412yes—
162C22×C4×C11C22×C412yes—
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2×D414yes—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11#4112yes—
168C22×C4×C11#4112yes—
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×Dic11—22no—
182C22×Dic11C2×D414yes—
183C2×D44—216no—
184C2×D44—216no—
185C2×D44—28no—
186C2×D44—216no—
187C2×D44—216no—
188C2×D44—44no—
189C2×D44—44no—
190C2×D44—48no—
191C2×D44—48no—
192C2×D44—44no—
193C2×D44—44no—
194C2×D44—48no—
195C2×D44—48no—
196C2×D44—48no—
197C2×D44—48no—
198C2×D44—48no—
199C2×D44—48no—
200C2×D44—48no—
201C2×D44—48no—
202C2×D44—48no—
203C2×D44—48no—
204C2×D44—48no—
205C2×D44—48no—
206C2×D44C22⋊C4116yescomplemented
207C2×C4×D11—48no—
208C2×C4×D11—48no—
209C2×C4×D11—48no—
210C2×C4×D11—48no—
211C2×C4×D11—48no—
212C2×C4×D11—48no—
213C2×C4×D11—48no—
214C42×C11—28no—
215(C2×D11)⋊C4—48no—
216(C2×D11)⋊C4—48no—
217(C2×D11)⋊C4—48no—
218(C2×D11)⋊C4—48no—
219(C2×D11)⋊C4—48no—
220(C2×D11)⋊C4—48no—
221(C2×D11)⋊C4—48no—
222C22×#127—111no—
223C2×#386—112no—
224C2×#386—112no—
225C2×#386—112no—
226#1438—112no—
227#1438—112no—
228#1438—112no—
229#1434—111no—
230#1434D1111yescharacteristic, complemented
231C23×C11C23×C411yescharacteristic
232C23×C11C22×D411yescharacteristic
233C23×C11C22×D412yes—
234C23×C11C22×D411yescharacteristic
235C23×C11C2×#4111yescharacteristic
236C23×C11C2×#4111yescharacteristic
237C23×C11H(5,𝔽2)12yes—
238C23×C11H(5,𝔽2)11yescharacteristic
239C23×C11H(5,𝔽2)11yescharacteristic
240C23×C11H(5,𝔽2)12yes—
241C23×C11H(5,𝔽2)12yes—
242C22×D11—24no—
243C22×D11—24no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—24no—
247C22×D11—24no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—24no—
251C22×D11—24no—
252C22×D11—24no—
253C22×D11—24no—
254C22×D11—24no—
255C22×D11—24no—
256C22×D11—24no—
257C22×D11—24no—
258C22×D11—24no—
259C22×D11—24no—
260C22×D11—24no—
261C22×D11—24no—
262C22×D11—24no—
263C22×D11—24no—
264C22×D11—24no—
265C22×D11—24no—
266C22×D11—24no—
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×D11—42no—
279C22×D11—42no—
280C22×D11—42no—
281C22×D11—42no—
282C22×D11—42no—
283C22×D11—42no—
284C22×D11—42no—
285C22×D11—42no—
286C22×D11—42no—
287C22×D11—42no—
288C22×D11—42no—
289C22×D11—42no—
290C22×D11—42no—
291C22×D11—42no—
292C22×D11—42no—
293C22×D11—42no—
294C22×D11—42no—
295C22×D11—42no—
296C22×D11—42no—
297C22×D11—42no—
298C22×D11—42no—
299C22×D11—42no—
300C22×D11—42no—
301C22×D11—42no—
302C22×D11—42no—
303C22×D11—42no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11—42no—
308C22×D11—42no—
309C22×D11—42no—
310C22×D11—42no—
311C22×D11C2×C22⋊C418yes—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—24no—
319C2×C4×C11—24no—
320C2×C4×C11—24no—
321C2×C4×C11—24no—
322C2×C4×C11—24no—
323C2×C4×C11—24no—
324C2×C4×C11—24no—
325C2×C4×C11—24no—
326C2×C4×C11—24no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11—42no—
337C2×C4×C11—42no—
338C2×C4×C11C2×C22⋊C414yes—
339C2×C4×C11C4×D414yes—
340C2×C4×C11C4×D414yes—
341C2×Dic11—24no—
342C2×Dic11—24no—
343C2×Dic11—24no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355D44—416no—
356D44—432no—
357D44—432no—
358D44—416no—
359C4×D11—432no—
360C23×D4—111no—
361C23×D4—112no—
362C23×D4—112no—
363C23×D4—111no—
364C24×C4—112no—
365C2×#127—118no—
366C2×#127—228no—
367C22×C22⋊C4—112no—
368C22×C22⋊C4—112no—
369C22×C22⋊C4—112no—
370C22×C22⋊C4—112no—
371C22×C22⋊C4—112no—
372C22×C22⋊C4—112no—
373C22×C22⋊C4—112no—
374C22×C42C2×D1111yescharacteristic
375#386—228no—
376#386—228no—
377#386—228no—
378C2×#95—111no—
379C2×#95—111no—
380C2×#95—112no—
381C2×#95—112no—
382C2×#95C2×D1111yescharacteristic
383C2×#95C2×D1112yes—
384C2×#95C2×D1112yes—
385C2×#95C2×D1111yescharacteristic
386C22×C11C22×C22⋊C411yescharacteristic
387C22×C11C2×C4×D411yescharacteristic
388C22×C11C2×C4×D411yescharacteristic
389C22×C11#51811yescharacteristic
390C22×C11#51811yescharacteristic
391C22×C11#51811yescharacteristic
392C22×C11#51811yescharacteristic
393C22×C11#53412yes—
394C22×C11#53412yes—
395C22×C11#53512yes—
396C22×C11#53512yes—
397C22×C11#54012yes—
398C22×C11#54012yes—
399C22×C11D4212yes—
400C22×C11D4211yescharacteristic
401C22×C11D4212yes—
402C22×C11#54612yes—
403C22×C11#54612yes—
404C22×C11#55011yescharacteristic
405C22×C11#55011yescharacteristic
406C22×C11#55911yescharacteristic
407C22×C11#56012yes—
408C22×C11#56012yes—
409C2×D11—28no—
410C2×D11—28no—
411C2×D11—28no—
412C2×D11—44no—
413C2×D11—44no—
414C2×D11—44no—
415C2×D11—44no—
416C2×D11—44no—
417C2×D11—44no—
418C2×D11—44no—
419C2×D11—44no—
420C2×D11—44no—
421C2×D11—44no—
422C2×D11—44no—
423C2×D11—44no—
424C2×D11—44no—
425C2×D11—44no—
426C2×D11—44no—
427C2×D11—44no—
428C2×D11—44no—
429C2×D11—44no—
430C2×D11—44no—
431C2×D11—82no—
432C2×D11—82no—
433C2×D11—82no—
434C2×D11—82no—
435C2×D11—82no—
436C2×D11—82no—
437C2×D11—82no—
438C2×D11—82no—
439C4×C11—24no—
440C4×C11—24no—
441C4×C11—24no—
442C4×C11—44no—
443C4×C11—82no—
444Dic11—44no—
445Dic11—82no—
446C25—112no—
447C25—112no—
448C22×D4—114no—
449C22×D4—118no—
450C22×D4—118no—
451C22×D4—114no—
452C22×D4—118no—
453C22×D4—224no—
454C22×D4—224no—
455C22×D4—224no—
456C22×D4—224no—
457C22×D4—224no—
458C22×D4—224no—
459C22×D4—224no—
460C22×D4—224no—
461C22×D4—224no—
462C22×D4—441no—
463C22×D4—442no—
464C22×D4—441no—
465C22×D4—442no—
466C22×D4—442no—
467C22×D4—442no—
468C22×D4—442no—
469C22×D4—441no—
470C22×D4—441no—
471C22×D4—442no—
472C23×C4—112no—
473C23×C4—112no—
474C23×C4—224no—
475C23×C4—224no—
476C23×C4—224no—
477C23×C4—442no—
478C23×C4—442no—
479C23×C4—442no—
480C23×C4—442no—
481C23×C4C22×D1112yes—
482C23×C4C22×D1112yes—
483C23×C4C22×D1111yescharacteristic
484C23×C4C22×D1111yescharacteristic
485C23×C4C22×D1111yescharacteristic
486#127—2232no—
487C2×C22⋊C4—224no—
488C2×C22⋊C4—224no—
489C2×C22⋊C4—224no—
490C2×C22⋊C4—224no—
491C2×C22⋊C4—224no—
492C2×C22⋊C4—224no—
493C2×C22⋊C4—224no—
494C2×C22⋊C4—224no—
495C2×C22⋊C4—224no—
496C2×C22⋊C4—442no—
497C2×C22⋊C4—442no—
498C2×C22⋊C4—442no—
499C2×C22⋊C4—442no—
500C2×C22⋊C4—442no—
501C2×C22⋊C4—442no—
502C2×C22⋊C4—442no—
503C2×C22⋊C4—442no—
504C2×C22⋊C4—442no—
505C2×C22⋊C4—442no—
506C2×C22⋊C4—442no—
507C2×C22⋊C4—442no—
508C2×C42—24no—
509C2×C42C4×D1114yescomplemented
510#95—22no—
511#95—24no—
512#95—24no—
513#95—114no—
514#95—224no—
515#95—224no—
516#95—222no—
517#95D4414yescomplemented
518C2×C11#230811yescharacteristic
519C2×C11#232811yescharacteristic
520C2×C11#232811yescharacteristic
521C2×C11D4×C22⋊C411yescharacteristic
522C2×C11D4×C22⋊C411yescharacteristic
523C2×C11#236611yescharacteristic
524C2×C11#238011yescharacteristic
525C2×C11#266912yes—
526C2×C11#267312yes—
527C2×C11#267312yes—
528C2×C11#270912yes—
529D11—48no—
530D11—84no—
531C24—114no—
532C24—114no—
533C24—114no—
534C24—114no—
535C24—222no—
536C24—222no—
537C24—222no—
538C24—222no—
539C24—222no—
540C24—222no—
541C24—222no—
542C24—222no—
543C24—222no—
544C24—222no—
545C24—222no—
546C24—222no—
547C24—222no—
548C24—222no—
549C24—222no—
550C24—222no—
551C24—222no—
552C24—222no—
553C24—222no—
554C24—222no—
555C24—222no—
556C24—222no—
557C24—222no—
558C24—222no—
559C24—222no—
560C24—222no—
561C24C23×D1111yescharacteristic
562C2×D4—1116no—
563C2×D4—2216no—
564C2×D4—2216no—
565C2×D4—2216no—
566C2×D4—228no—
567C2×D4—2216no—
568C2×D4—444no—
569C2×D4—444no—
570C2×D4—448no—
571C2×D4—448no—
572C2×D4—444no—
573C2×D4—444no—
574C2×D4—448no—
575C2×D4—448no—
576C2×D4—448no—
577C2×D4—448no—
578C2×D4—448no—
579C2×D4—448no—
580C2×D4—448no—
581C2×D4—448no—
582C2×D4—448no—
583C2×D4—448no—
584C2×D4—448no—
585C2×D4—448no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—114no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—222no—
620C22×C4—448no—
621C22×C4—448no—
622C22×C4—448no—
623C22×C4—448no—
624C22×C4—448no—
625C22×C4—448no—
626C22×C4—448no—
627C22×C4C2×C4×D1112yes—
628C22×C4C2×C4×D1112yes—
629C22×C4C2×C4×D1112yes—
630C22×C4C2×D4414yes—
631C22×C4C2×D4412yes—
632C22×C4#433912yes—
633C22×C4D4×D1114yes—
634C22×C4D4×D1112yes—
635C22×C4#434312yes—
636C22⋊C4—448no—
637C22⋊C4—448no—
638C22⋊C4—448no—
639C22⋊C4—448no—
640C22⋊C4—448no—
641C22⋊C4—448no—
642C22⋊C4—448no—
643C42—28no—
644C11#1441911yescharacteristic, complemented, Sylow
645C23—118no—
646C23—224no—
647C23—224no—
648C23—224no—
649C23—224no—
650C23—224no—
651C23—224no—
652C23—224no—
653C23—224no—
654C23—224no—
655C23—224no—
656C23—224no—
657C23—224no—
658C23—224no—
659C23—224no—
660C23—224no—
661C23—224no—
662C23—224no—
663C23—224no—
664C23—224no—
665C23—224no—
666C23—224no—
667C23—224no—
668C23—224no—
669C23—224no—
670C23—224no—
671C23—442no—
672C23—442no—
673C23—442no—
674C23—442no—
675C23—442no—
676C23—442no—
677C23—442no—
678C23—442no—
679C23—442no—
680C23—442no—
681C23—442no—
682C23—442no—
683C23—442no—
684C23—442no—
685C23—442no—
686C23—442no—
687C23—442no—
688C23—442no—
689C23—442no—
690C23—442no—
691C23—442no—
692C23—442no—
693C23—442no—
694C23—442no—
695C23—442no—
696C23—442no—
697C23—442no—
698C23—442no—
699C23—442no—
700C23—442no—
701C23—442no—
702C23—442no—
703C23—442no—
704C23—442no—
705C23—442no—
706C23—442no—
707C23—442no—
708C23—442no—
709C23—442no—
710C23—442no—
711C23—442no—
712C23—442no—
713C23—442no—
714C23—442no—
715C23C22×C4×D1111yescharacteristic
716C23C22×D4411yescharacteristic
717C23C2×#433911yescharacteristic
718C23C2×D4×D1112yes—
719C23C2×D4×D1111yescharacteristic
720C23C2×#434311yescharacteristic
721C23#6704212yes—
722C23#6704212yes—
723C23#6704211yescharacteristic
724C23#6704211yescharacteristic
725C23#6704212yes—
726D4—4416no—
727D4—4432no—
728D4—4432no—
729D4—4416no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—224no—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—4432no—
760C2×C4—442no—
761C2×C4—442no—
762C2×C4—442no—
763C2×C4—442no—
764C2×C4—442no—
765C2×C4—442no—
766C2×C4—442no—
767C2×C4—442no—
768C2×C4—442no—
769C2×C4—442no—
770C2×C4—442no—
771C2×C4C4×D4414yes—
772C2×C4C22⋊C4×D1114yes—
773C2×C4#6694614yes—
774C22—228no—
775C22—228no—
776C22—228no—
777C22—444no—
778C22—444no—
779C22—444no—
780C22—444no—
781C22—444no—
782C22—444no—
783C22—444no—
784C22—444no—
785C22—444no—
786C22—444no—
787C22—444no—
788C22—444no—
789C22—444no—
790C22—444no—
791C22—444no—
792C22—444no—
793C22—444no—
794C22—444no—
795C22—444no—
796C22—882no—
797C22—882no—
798C22—882no—
799C22—882no—
800C22—882no—
801C22—882no—
802C22—882no—
803C22—882no—
804C22C2×C4×D4411yescharacteristic
805C22C2×C22⋊C4×D1111yescharacteristic
806C22C2×#6694611yescharacteristic
807C22#1062305211yescharacteristic
808C22#1062305211yescharacteristic
809C22#1062305211yescharacteristic
810C22#1062305211yescharacteristic
811C22#1062305612yes—
812C22#1062306612yes—
813C22D4×D4411yescharacteristic
814C22D4×D4412yes—
815C22#1062308112yes—
816C22#1062308411yescharacteristic
817C22#1062310811yescharacteristic
818C22#1062311611yescharacteristic
819C22#1062314012yes—
820C22#1062316112yes—
821C22#1062318412yes—
822C22#1062318412yes—
823C22#1062320512yes—
824C22#1062322912yes—
825C22#1062324212yes—
826C22#1062324212yes—
827C4—24no—
828C4—24no—
829C4—24no—
830C4—44no—
831C4—82no—
832C4—444no—
833C4—882no—
834C2—448no—
835C2—884no—
836C2#1307119311yescharacteristic
837C2#1307133911yescharacteristic
838C2#1307134111yescharacteristic
839C2#1307143611yescharacteristic
840C2C22⋊C4×D4411yescharacteristic
841C2#1307168011yescharacteristic
842C2#1307179211yescharacteristic
843C2#1307483112yes—
844C2#1307488312yes—
845C2#1307488512yes—
846C2#1307534812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC22×#66927C2
hypercenter#1434D11
hypocenterC11#14419
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#10622278C2semidirect
3. C2×#10622278C2semidirect
4. C2×#10622278C2semidirect
5. #13066856C2semidirect
6. #13066856C2semidirect
7. #13066856C2semidirect
8. #13066843C2semidirect
9. C11×#1434C2semidirect
24. C2×#66927C4semidirect
65. C22×D44C2×C4semidirect
66. C22×D44C2×C4semidirect
67. C22×D44C2×C4semidirect
77. C2×C42×C11C2×C4semidirect
103. C11×#95D4semidirect
107. C11⋊#95D4semidirect
206. C2×D44C22⋊C4semidirect
230. #1434D11semidirect
509. C2×C42C4×D11semidirect
517. #95D44semidirect
644. C11#14419semidirect

Maximal subgroups

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

subgroupindex
C22×#669272
C2×#106222782
#130668562
#130668432
C11×#14342
#1441911