Finite Group Databasebeta

← #14680437

Subgroups — #14680437

Order 2816.

2302 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C211yesmaximal, characteristic
2C2×#10622556C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
4#13066882C212yesmaximal, complemented
5#13066857C211yesmaximal, characteristic, complemented
6#13066855C212yesmaximal, complemented
7#13066855C211yesmaximal, characteristic, complemented
8#13066855C211yesmaximal, characteristic, complemented
9#13066853C212yesmaximal, complemented
10#13066852C212yesmaximal, complemented
11C11×#1438C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2211yescharacteristic
23C2×#66992—24no—
24C2×#66992—24no—
25C2×#66992C418yescomplemented
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×Dic11⋊C4C2211yescharacteristic
30C22×C4×Dic11C2212yes—
31C2×C11×#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622556—24no—
39C22⋊C4×Dic11—24no—
40C25×C11C2311yescharacteristic
41C25×C11C2311yescharacteristic
42C24×D11C2311yescharacteristic
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—42no—
46C22×D4×C11—42no—
47C22×D4×C11C2×C414yes—
48C23×C4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C22×C22⋊D11—22no—
52C22×C22⋊D11—22no—
53C22×C22⋊D11—22no—
54C22×C22⋊D11—22no—
55C22×C22⋊D11—42no—
56C22×C22⋊D11—42no—
57C22×C22⋊D11—42no—
58C22×C22⋊D11—42no—
59C22×C22⋊D11C2×C414yes—
60C22×C22⋊D11C2×C414yes—
61C23×Dic11—42no—
62C23×Dic11—42no—
63C23×Dic11C2×C414yes—
64C23×Dic11D414yes—
65C23×Dic11D414yes—
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2312yes—
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4—24no—
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—24no—
75C2×C11×C22⋊C4—42no—
76C2×C11×C22⋊C4—42no—
77C2×C11×C22⋊C4—42no—
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11—22no—
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—24no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—24no—
84C2×C22⋊Dic11—42no—
85C2×C22⋊Dic11—42no—
86C2×C22⋊Dic11—42no—
87C2×C22⋊Dic11C2×C414yes—
88#66992—232no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—42no—
94C2×(C2×D11)⋊C4—42no—
95C2×(C2×D11)⋊C4—42no—
96C2×(C2×D11)⋊C4—42no—
97C2×(C2×D11)⋊C4C2×C414yes—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4C2×C414yes—
101C2×C4×Dic11—24no—
102C2×C4×Dic11—42no—
103C2×C4×Dic11—42no—
104C11×#95—42no—
105C11⋊#95—24no—
106C11⋊#95—24no—
107C11⋊#95—24no—
108C11⋊#95—42no—
109C11⋊#95—42no—
110C11⋊#95—42no—
111#14290—111nomaximal, Sylow
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—21no—
119C24×C11—21no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—22no—
124C24×C11—22no—
125C24×C11—22no—
126C24×C11C22×C412yes—
127C24×C11C22×C412yes—
128C24×C11C2×D412yes—
129C24×C11C2×D412yes—
130C24×C11C2411yescharacteristic
131C23×D11—21no—
132C23×D11—21no—
133C23×D11—22no—
134C23×D11—22no—
135C23×D11—22no—
136C23×D11—22no—
137C23×D11—22no—
138C23×D11—22no—
139C23×D11C22×C412yes—
140C2×D4×C11—28no—
141C2×D4×C11—44no—
142C2×D4×C11—44no—
143C2×D4×C11—48no—
144C2×D4×C11—48no—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
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×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11C22×C412yes—
163C22×C4×C11#4114yes—
164C2×C22⋊D11—28no—
165C2×C22⋊D11—28no—
166C2×C22⋊D11—44no—
167C2×C22⋊D11—44no—
168C2×C22⋊D11—48no—
169C2×C22⋊D11—48no—
170C2×C22⋊D11—48no—
171C2×C22⋊D11—44no—
172C2×C22⋊D11—48no—
173C2×C22⋊D11—44no—
174C22×Dic11—22no—
175C22×Dic11—21no—
176C22×Dic11—21no—
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×Dic11—22no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—48no—
196C22×Dic11—44no—
197C22×Dic11—44no—
198C22×Dic11—48no—
199C22×Dic11C22⋊C4116yescomplemented
200C22×Dic11C22×C412yes—
201C22×Dic11C22×C412yes—
202C22×Dic11C22×C412yes—
203C22×Dic11C2×D412yes—
204C22×Dic11C2×D412yes—
205C22×Dic11C2×D412yes—
206C22×Dic11C2×D412yes—
207C22×Dic11#4114yes—
208C11×C22⋊C4—28no—
209C11×C22⋊C4—48no—
210C11×C22⋊C4—44no—
211C22⋊Dic11—28no—
212C22⋊Dic11—28no—
213C22⋊Dic11—44no—
214C22⋊Dic11—48no—
215(C2×D11)⋊C4—28no—
216(C2×D11)⋊C4—48no—
217(C2×D11)⋊C4—48no—
218Dic11⋊C4—28no—
219C4×Dic11—48no—
220C22×#121—111no—
221C2×#381—111no—
222C2×C4×C22⋊C4—111no—
223#1445—112no—
224#1438—111no—
225#1438—111no—
226#1438—112no—
227#1438—111no—
228#1438D1111yescharacteristic, complemented
229#1437—112no—
230#1437—112no—
231C23×C11—24no—
232C23×C11—24no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—24no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—24no—
241C23×C11—24no—
242C23×C11—24no—
243C23×C11—22no—
244C23×C11—24no—
245C23×C11—24no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11—42no—
251C23×C11—42no—
252C23×C11—42no—
253C23×C11—42no—
254C23×C11—42no—
255C23×C11—42no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—42no—
259C23×C11—41no—
260C23×C11—42no—
261C23×C11—41no—
262C23×C11—42no—
263C23×C11—42no—
264C23×C11—42no—
265C23×C11—42no—
266C23×C11—42no—
267C23×C11—42no—
268C23×C11—42no—
269C23×C11—42no—
270C23×C11—42no—
271C23×C11—42no—
272C23×C11C2×C22⋊C414yes—
273C23×C11C23×C411yescharacteristic
274C23×C11C22×D411yescharacteristic
275C23×C11C22×D411yescharacteristic
276C23×C11C2×#4112yes—
277C23×C11C2×#4112yes—
278C23×C11H(5,𝔽2)12yes—
279C23×C11H(5,𝔽2)12yes—
280C23×C11H(5,𝔽2)12yes—
281C23×C11H(5,𝔽2)12yes—
282C22×D11—22no—
283C22×D11—24no—
284C22×D11—22no—
285C22×D11—22no—
286C22×D11—24no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—42no—
290C22×D11—41no—
291C22×D11—42no—
292C22×D11—41no—
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—
303D4×C11—416no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—24no—
308C2×C4×C11—24no—
309C2×C4×C11—24no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C22⋊D11—416no—
324C22⋊D11—416no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—24no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—24no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—24no—
337C2×Dic11—24no—
338C2×Dic11—24no—
339C2×Dic11—416no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—42no—
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×Dic11C2×C22⋊C414yes—
354C2×Dic11C2×C22⋊C414yes—
355C23×D4—111no—
356C23×D4—111no—
357C23×D4C2×D1111yescharacteristic
358C24×C4—111no—
359C2×#121—118no—
360C2×#121—224no—
361C2×#121—224no—
362C22×C4⋊C4—111no—
363C22×C22⋊C4—111no—
364C22×C22⋊C4—111no—
365C22×C22⋊C4—111no—
366C22×C22⋊C4—112no—
367C22×C22⋊C4—111no—
368C22×C22⋊C4—112no—
369C22×C22⋊C4—112no—
370C22×C22⋊C4C2×D1111yescharacteristic
371C22×C22⋊C4C2×D1112yes—
372C22×C22⋊C4C2×D1111yescharacteristic
373C22×C42—112no—
374#381—224no—
375C4×C22⋊C4—224no—
376C2×#95—112no—
377C2×#95—112no—
378C2×#95—112no—
379C2×#95—112no—
380C2×#95—112no—
381C2×#95—112no—
382C2×#95C2×D1112yes—
383C22×C11—24no—
384C22×C11—24no—
385C22×C11—24no—
386C22×C11—44no—
387C22×C11—44no—
388C22×C11—44no—
389C22×C11—44no—
390C22×C11—44no—
391C22×C11—44no—
392C22×C11—42no—
393C22×C11—42no—
394C22×C11—44no—
395C22×C11—44no—
396C22×C11—42no—
397C22×C11—82no—
398C22×C11—82no—
399C22×C11—82no—
400C22×C11—82no—
401C22×C11C22×C22⋊C411yescharacteristic
402C22×C11C4×#4112yes—
403C22×C11#51811yescharacteristic
404C22×C11#51811yescharacteristic
405C22×C11#51812yes—
406C22×C11#52511yescharacteristic
407C22×C11#52511yescharacteristic
408C22×C11#53212yes—
409C22×C11#53411yescharacteristic
410C22×C11#53412yes—
411C22×C11#53411yescharacteristic
412C22×C11#53512yes—
413C22×C11#53512yes—
414C22×C11#53812yes—
415C22×C11#53812yes—
416C22×C11#53812yes—
417C22×C11#53812yes—
418C22×C11#54012yes—
419C22×C11#54012yes—
420C22×C11#54012yes—
421C22×C11#54012yes—
422C2×D11—42no—
423C2×D11—42no—
424C2×D11—44no—
425C2×D11—44no—
426C2×D11—42no—
427C2×D11—82no—
428C2×D11—82no—
429C2×D11—82no—
430C2×D11—82no—
431C4×C11—42no—
432C4×C11—44no—
433C4×C11—82no—
434Dic11—24no—
435Dic11—24no—
436Dic11—42no—
437Dic11—44no—
438Dic11—82no—
439C25—111no—
440C25C22×D1111yescharacteristic
441C25C22×D1111yescharacteristic
442C22×D4—22no—
443C22×D4—22no—
444C22×D4—42no—
445C22×D4—42no—
446C22×D4—114no—
447C22×D4—114no—
448C22×D4—222no—
449C22×D4—222no—
450C22×D4—222no—
451C22×D4—222no—
452C22×D4—442no—
453C22×D4—442no—
454C22×D4—442no—
455C22×D4—442no—
456C22×D4C4×D1114yes—
457C23×C4—111no—
458C23×C4—111no—
459C23×C4—114no—
460C23×C4—114no—
461C23×C4—114no—
462C23×C4—112no—
463C23×C4—111no—
464C23×C4—112no—
465C23×C4—442no—
466C23×C4—442no—
467C23×C4C22×D1112yes—
468C23×C4C22×D1111yescharacteristic
469C23×C4C22×D1112yes—
470#121—2232no—
471C2×C4⋊C4—114no—
472C2×C4⋊C4—222no—
473C2×C4⋊C4—222no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—114no—
482C2×C22⋊C4—114no—
483C2×C22⋊C4—222no—
484C2×C22⋊C4—222no—
485C2×C22⋊C4—222no—
486C2×C22⋊C4—222no—
487C2×C22⋊C4—224no—
488C2×C22⋊C4—222no—
489C2×C22⋊C4—224no—
490C2×C22⋊C4—224no—
491C2×C22⋊C4—222no—
492C2×C22⋊C4—224no—
493C2×C22⋊C4—442no—
494C2×C22⋊C4—442no—
495C2×C22⋊C4—442no—
496C2×C22⋊C4—442no—
497C2×C22⋊C4—442no—
498C2×C22⋊C4—442no—
499C2×C22⋊C4—442no—
500C2×C42—224no—
501C2×C42—442no—
502C2×C42—442no—
503#95—42no—
504#95—224no—
505#95—224no—
506#95—224no—
507#95—442no—
508#95—442no—
509#95—442no—
510C2×C11—44no—
511C2×C11—82no—
512C2×C11#229711yescharacteristic
513C2×C11#230811yescharacteristic
514C2×C11#230911yescharacteristic
515C2×C11#233312yes—
516C2×C11#233312yes—
517C2×C11#263512yes—
518C2×C11#263512yes—
519C2×C11#266112yes—
520C2×C11#266112yes—
521D11—82no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—21no—
529C24—21no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—112no—
537C24—221no—
538C24—221no—
539C24—222no—
540C24—222no—
541C24—222no—
542C24—222no—
543C24—222no—
544C24—222no—
545C24C2×C4×D1112yes—
546C24C2×C4×D1112yes—
547C24D4×D1112yes—
548C24D4×D1112yes—
549C24C23×D1111yescharacteristic
550C2×D4—28no—
551C2×D4—44no—
552C2×D4—44no—
553C2×D4—48no—
554C2×D4—48no—
555C2×D4—228no—
556C2×D4—228no—
557C2×D4—448no—
558C2×D4—444no—
559C2×D4—444no—
560C2×D4—444no—
561C2×D4—448no—
562C2×D4—444no—
563C2×D4—448no—
564C2×D4—448no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—112no—
583C22×C4—112no—
584C22×C4—112no—
585C22×C4—112no—
586C22×C4—112no—
587C22×C4—112no—
588C22×C4—1116no—
589C22×C4—112no—
590C22×C4—114no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—448no—
613C22×C4—444no—
614C22×C4—448no—
615C22×C4—444no—
616C22×C4C2×C4×D1112yes—
617C22×C4#434114yes—
618C4⋊C4—228no—
619C22⋊C4—28no—
620C22⋊C4—48no—
621C22⋊C4—44no—
622C22⋊C4—228no—
623C22⋊C4—228no—
624C22⋊C4—228no—
625C22⋊C4—448no—
626C22⋊C4—448no—
627C22⋊C4—448no—
628C22⋊C4—444no—
629C42—448no—
630C11#1429011yescharacteristic, complemented, Sylow
631C23—22no—
632C23—22no—
633C23—24no—
634C23—24no—
635C23—22no—
636C23—22no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—24no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—41no—
658C23—41no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—41no—
669C23—41no—
670C23—42no—
671C23—42no—
672C23—222no—
673C23—222no—
674C23—222no—
675C23—224no—
676C23—224no—
677C23—442no—
678C23—441no—
679C23—441no—
680C23—442no—
681C23—442no—
682C23—442no—
683C23—442no—
684C23—442no—
685C23—442no—
686C23—442no—
687C23—442no—
688C23—442no—
689C23—441no—
690C23—441no—
691C23—442no—
692C23—442no—
693C23C22⋊C4×D1114yes—
694C23C22×C4×D1111yescharacteristic
695C23C2×D4×D1111yescharacteristic
696C23C2×D4×D1111yescharacteristic
697C23C2×#434112yes—
698C23#6703712yes—
699C23#6703712yes—
700C23#6703712yes—
701C23#41×D1112yes—
702C23#6704212yes—
703D4—416no—
704D4—4416no—
705D4—4416no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—114no—
726C2×C4—114no—
727C2×C4—224no—
728C2×C4—224no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—224no—
732C2×C4—224no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—224no—
739C2×C4—224no—
740C2×C4—224no—
741C2×C4—4416no—
742C2×C4—442no—
743C2×C4—442no—
744C2×C4—442no—
745C2×C4—442no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4—442no—
749C2×C4—442no—
750C2×C4—442no—
751C2×C4—442no—
752C2×C4—442no—
753C2×C4—442no—
754C2×C4—442no—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—444no—
774C22—444no—
775C22—442no—
776C22—442no—
777C22—442no—
778C22—882no—
779C22—882no—
780C22—882no—
781C22—882no—
782C22C2×C22⋊C4×D1111yescharacteristic
783C22#1062301711yescharacteristic
784C22#1062301711yescharacteristic
785C22C4×#434112yes—
786C22#1062307612yes—
787C22#1062311711yescharacteristic
788C22#1062312011yescharacteristic
789C22#1062312312yes—
790C22#1062312312yes—
791C22#1062312412yes—
792C22#1062312712yes—
793C22#1062313612yes—
794C22#1062314412yes—
795C22#1062314612yes—
796C22#1062314812yes—
797C22#1062315012yes—
798C22#1062318411yescharacteristic
799C22#1062318711yescharacteristic
800C22#1062319412yes—
801C22#1062320912yes—
802C22#1062325012yes—
803C4—44no—
804C4—42no—
805C4—82no—
806C4—224no—
807C4—224no—
808C4—444no—
809C4—442no—
810C4—882no—
811C2—44no—
812C2—82no—
813C2—882no—
814C2#1307110111yescharacteristic
815C2#1307119011yescharacteristic
816C2#1307119711yescharacteristic
817C2#1307137512yes—
818C2#1307138212yes—
819C2#1307449912yes—
820C2#1307450212yes—
821C2#1307474112yes—
822C2#1307474312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC22×#66992C2
hypercenter#1438D11
hypocenterC11#14290
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#10622556C2semidirect
3. C2×C22⋊C4×Dic11C2semidirect
4. #13066882C2semidirect
5. #13066857C2semidirect
6. #13066855C2semidirect
7. #13066855C2semidirect
8. #13066855C2semidirect
9. #13066853C2semidirect
10. #13066852C2semidirect
11. C11×#1438C2semidirect
25. C2×#66992C4semidirect
199. C22×Dic11C22⋊C4semidirect
228. #1438D11semidirect
630. C11#14290semidirect

Maximal subgroups

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

subgroupindex
C22×#669922
C2×#106225562
C2×C22⋊C4×Dic112
#130668822
#130668572
#130668552
#130668532
#130668522
C11×#14382
#1429011