Finite Group Databasebeta

← #14680667

Subgroups — #14680667

Order 2816.

2198 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622836C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic, complemented
3C2×#10622569C212yesmaximal, complemented
4C2×#10622279C211yesmaximal, characteristic, complemented
5#13066872C211yesmaximal, characteristic, complemented
6#13066863C212yesmaximal, complemented
7#13066862C211yesmaximal, characteristic, complemented
8#13066855C212yesmaximal, complemented
9#13066853C212yesmaximal, complemented
10#13066841C211yesmaximal, characteristic, complemented
11C11×#1438C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C23×C22⋊D11C2212yes—
14C23×C4×D11C2211yescharacteristic
15C22×C11×C22⋊C4C2212yes—
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28#10622836C418yescomplemented
29#10622834—24no—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622569—28no—
38#10622279—24no—
39C25×C11C2312yes—
40C24×D11C2311yescharacteristic
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—42no—
44C22×D4×C11—42no—
45C22×D4×C11C2×C414yescomplemented
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C22×C22⋊D11—24no—
51C22×C22⋊D11—24no—
52C22×C22⋊D11—42no—
53C22×C22⋊D11—42no—
54C22×C22⋊D11—42no—
55C22×C22⋊D11—42no—
56C22×C22⋊D11C2×C418yes—
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2312yes—
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C22×C4×D11—22no—
63C22×C4×D11—22no—
64C22×C4×D11—42no—
65C22×C4×D11—42no—
66C22×C4×D11D414yescomplemented
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4—42no—
70C2×C11×C22⋊C4—42no—
71C2×C11×C22⋊C4—42no—
72C2×C11×C22⋊C4—42no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—24no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11—42no—
78C2×C22⋊Dic11—42no—
79C2×C22⋊Dic11—42no—
80C2×C22⋊Dic11—42no—
81C2×C22⋊Dic11C2×C418yescomplemented
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—42no—
89C2×(C2×D11)⋊C4—42no—
90C2×(C2×D11)⋊C4C2×C414yes—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—42no—
93C2×C4×Dic11—22no—
94C2×C4×Dic11—42no—
95C2×C4×Dic11—42no—
96C2×C4×Dic11D414yescomplemented
97C11×#95—22no—
98C11×#95—22no—
99C11⋊#95—24no—
100C11⋊#95—22no—
101C11⋊#95—24no—
102C11⋊#95—42no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105C11⋊#95C2×C414yescomplemented
106#14311—111nomaximal, Sylow
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11C22×C414yes—
122C24×C11C2411yescharacteristic
123C23×D11—21no—
124C23×D11—21no—
125C23×D11—21no—
126C23×D11—21no—
127C23×D11—22no—
128C23×D11—22no—
129C23×D11—22no—
130C23×D11—22no—
131C23×D11C22×C412yes—
132C23×D11C2×D412yes—
133C23×D11#4112yes—
134C2×D4×C11—28no—
135C2×D4×C11—48no—
136C2×D4×C11—44no—
137C2×D4×C11—44no—
138C2×D4×C11—48no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
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×C11C22×C412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11#4112yes—
160C22×C4×C11#4112yes—
161C2×C22⋊D11—216no—
162C2×C22⋊D11—48no—
163C2×C22⋊D11—48no—
164C2×C22⋊D11—48no—
165C2×C22⋊D11—48no—
166C2×C22⋊D11—48no—
167C2×C22⋊D11—48no—
168C22×Dic11—22no—
169C22×Dic11—21no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—21no—
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×Dic11—22no—
191C22×Dic11C22×C414yes—
192C22×Dic11C22×C412yes—
193C22×Dic11C2×D412yes—
194C22×Dic11C2×D412yes—
195C22×Dic11C2×D412yes—
196C22×Dic11#4112yes—
197C2×C4×D11—28no—
198C2×C4×D11—48no—
199C2×C4×D11—44no—
200C2×C4×D11—44no—
201C2×C4×D11—48no—
202C11×C22⋊C4—48no—
203C11×C22⋊C4—48no—
204C22⋊Dic11—48no—
205C22⋊Dic11—48no—
206C22⋊Dic11—48no—
207(C2×D11)⋊C4—28no—
208(C2×D11)⋊C4—28no—
209(C2×D11)⋊C4—48no—
210C4⋊Dic11—44no—
211C4×Dic11—44no—
212C4×Dic11—44no—
213C2×#392—111no—
214C2×#390—111no—
215C2×#386—112no—
216C2×C4×C22⋊C4—111no—
217#1442—111no—
218#1440—112no—
219#1439—111no—
220#1438—112no—
221#1438D1111yescharacteristic, complemented
222#1437—112no—
223#1434—111no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—24no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—42no—
232C23×C11—42no—
233C23×C11—42no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11—42no—
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—42no—
246C23×C11—42no—
247C23×C11—42no—
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—42no—
257C23×C11—42no—
258C23×C11—42no—
259C23×C11C23×C411yescharacteristic
260C23×C11C22×D411yescharacteristic
261C23×C11C22×D411yescharacteristic
262C23×C11C2×#4111yescharacteristic
263C23×C11C2×#4111yescharacteristic
264C23×C11C2×#4111yescharacteristic
265C23×C11C2×#4111yescharacteristic
266C23×C11H(5,𝔽2)12yes—
267C23×C11H(5,𝔽2)12yes—
268C23×C11H(5,𝔽2)12yes—
269C23×C11H(5,𝔽2)12yes—
270C22×D11—22no—
271C22×D11—22no—
272C22×D11—24no—
273C22×D11—24no—
274C22×D11—22no—
275C22×D11—22no—
276C22×D11—22no—
277C22×D11—22no—
278C22×D11—24no—
279C22×D11—24no—
280C22×D11—24no—
281C22×D11—24no—
282C22×D11—41no—
283C22×D11—41no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11—42no—
287C22×D11—42no—
288C22×D11—42no—
289C22×D11—42no—
290C22×D11—42no—
291C22×D11—42no—
292C22×D11C4×D414yes—
293D4×C11—416no—
294C2×C4×C11—24no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—24no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—24no—
301C2×C4×C11—24no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11C4×D414yes—
316C22⋊D11—432no—
317C2×Dic11—22no—
318C2×Dic11—24no—
319C2×Dic11—22no—
320C2×Dic11—24no—
321C2×Dic11—22no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—42no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11#12114yes—
346C4×D11—416no—
347C23×D4—112no—
348C23×D4C2×D1111yescharacteristic
349C24×C4—111no—
350C22×C4⋊C4—111no—
351C22×C22⋊C4—111no—
352C22×C22⋊C4—112no—
353C22×C22⋊C4—112no—
354C22×C22⋊C4—111no—
355C22×C22⋊C4—112no—
356C22×C22⋊C4—112no—
357C22×C22⋊C4C2×D1112yes—
358C22×C22⋊C4C2×D1112yes—
359C22×C42—111no—
360C22×C42—111no—
361#392—118no—
362#390—224no—
363#386—228no—
364C4×C22⋊C4—224no—
365C2×#95—111no—
366C2×#95—112no—
367C2×#95—111no—
368C2×#95—112no—
369C2×#95—112no—
370C2×#95—112no—
371C2×#95—112no—
372C2×#95C2×D1111yescharacteristic
373C2×#95C2×D1111yescharacteristic
374C22×C11—44no—
375C22×C11—44no—
376C22×C11—44no—
377C22×C11—44no—
378C22×C11—44no—
379C22×C11—44no—
380C22×C11—44no—
381C22×C11—82no—
382C22×C11—82no—
383C22×C11—82no—
384C22×C11—82no—
385C22×C11—82no—
386C22×C11—82no—
387C22×C11—82no—
388C22×C11—82no—
389C22×C11C2×C4×D411yescharacteristic
390C22×C11C2×C4×D411yescharacteristic
391C22×C11C4×#4111yescharacteristic
392C22×C11#51812yes—
393C22×C11#51812yes—
394C22×C11C2×#12111yescharacteristic
395C22×C11#52511yescharacteristic
396C22×C11#52911yescharacteristic
397C22×C11#53211yescharacteristic
398C22×C11#53411yescharacteristic
399C22×C11#53412yes—
400C22×C11#53511yescharacteristic
401C22×C11#53511yescharacteristic
402C22×C11#53512yes—
403C22×C11#53511yescharacteristic
404C22×C11#53812yes—
405C22×C11#53812yes—
406C22×C11#53812yes—
407C22×C11#53812yes—
408C22×C11#53812yes—
409C22×C11#54012yes—
410C22×C11#54012yes—
411C22×C11#54012yes—
412C2×D11—28no—
413C2×D11—24no—
414C2×D11—42no—
415C2×D11—42no—
416C2×D11—44no—
417C2×D11—42no—
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—44no—
422C2×D11—44no—
423C4×C11—24no—
424C4×C11—42no—
425C4×C11—42no—
426C4×C11—82no—
427Dic11—24no—
428Dic11—44no—
429Dic11—42no—
430Dic11—42no—
431Dic11—82no—
432C25—111no—
433C25C22×D1112yes—
434C22×D4—22no—
435C22×D4—22no—
436C22×D4—42no—
437C22×D4—42no—
438C22×D4—118no—
439C22×D4—224no—
440C22×D4—224no—
441C22×D4—442no—
442C22×D4—442no—
443C22×D4—442no—
444C22×D4—442no—
445C22×D4C4×D1114yescomplemented
446C23×C4—111no—
447C23×C4—111no—
448C23×C4—111no—
449C23×C4—112no—
450C23×C4—114no—
451C23×C4—112no—
452C23×C4—222no—
453C23×C4—222no—
454C23×C4—442no—
455C23×C4—442no—
456C23×C4C22×D1112yes—
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459C23×C4C22×D1111yescharacteristic
460C2×C4⋊C4—222no—
461C2×C4⋊C4—442no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—42no—
466C2×C22⋊C4—42no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4—114no—
469C2×C22⋊C4—118no—
470C2×C22⋊C4—222no—
471C2×C22⋊C4—222no—
472C2×C22⋊C4—222no—
473C2×C22⋊C4—222no—
474C2×C22⋊C4—222no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4—224no—
478C2×C22⋊C4—224no—
479C2×C22⋊C4—224no—
480C2×C22⋊C4—442no—
481C2×C22⋊C4—442no—
482C2×C22⋊C4—442no—
483C2×C22⋊C4—442no—
484C2×C22⋊C4—442no—
485C2×C22⋊C4—442no—
486C2×C42—114no—
487C2×C42—222no—
488C2×C42—442no—
489C2×C42—442no—
490#95—22no—
491#95—22no—
492#95—114no—
493#95—222no—
494#95—224no—
495#95—224no—
496#95—442no—
497#95—442no—
498#95—442no—
499C2×C11—84no—
500C2×C11C4×#12111yescharacteristic
501C2×C11#232111yescharacteristic
502C2×C11#232112yes—
503C2×C11#232811yescharacteristic
504C2×C11#233312yes—
505C2×C11#261711yescharacteristic
506C2×C11#261911yescharacteristic
507C2×C11#263111yescharacteristic
508C2×C11#263511yescharacteristic
509C2×C11#264812yes—
510C2×C11#266112yes—
511D11—44no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—112no—
527C24—112no—
528C24—112no—
529C24—221no—
530C24—221no—
531C24—221no—
532C24—222no—
533C24—222no—
534C24—222no—
535C24—221no—
536C24—222no—
537C24C2×C4×D1114yes—
538C24C23×D1111yescharacteristic
539C2×D4—28no—
540C2×D4—48no—
541C2×D4—44no—
542C2×D4—44no—
543C2×D4—48no—
544C2×D4—2216no—
545C2×D4—448no—
546C2×D4—448no—
547C2×D4—448no—
548C2×D4—448no—
549C2×D4—448no—
550C2×D4—448no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—112no—
569C22×C4—112no—
570C22×C4—112no—
571C22×C4—114no—
572C22×C4—112no—
573C22×C4—112no—
574C22×C4—228no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—221no—
579C22×C4—221no—
580C22×C4—221no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—221no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—448no—
599C22×C4—444no—
600C22×C4—444no—
601C22×C4—448no—
602C22×C4C2×C4×D1112yes—
603C22×C4D4×D1112yes—
604C22×C4D4×D1112yes—
605C22×C4#434112yes—
606C22×C4#434112yes—
607C4⋊C4—444no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—228no—
611C22⋊C4—228no—
612C22⋊C4—448no—
613C22⋊C4—448no—
614C22⋊C4—448no—
615C22⋊C4—448no—
616C42—444no—
617C42—444no—
618C11#1431111yescharacteristic, complemented, Sylow
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—114no—
655C23—222no—
656C23—222no—
657C23—224no—
658C23—222no—
659C23—224no—
660C23—224no—
661C23—222no—
662C23—222no—
663C23—224no—
664C23—224no—
665C23—224no—
666C23—222no—
667C23—441no—
668C23—441no—
669C23—441no—
670C23—442no—
671C23—442no—
672C23—442no—
673C23—442no—
674C23—442no—
675C23—442no—
676C23—441no—
677C23C22×C4×D1111yescharacteristic
678C23C2×D4×D1111yescharacteristic
679C23C2×D4×D1111yescharacteristic
680C23C2×#434111yescharacteristic
681C23C2×#434111yescharacteristic
682C23#6703712yes—
683C23#6703712yes—
684C23#6703712yes—
685C23#41×D1111yescharacteristic
686C23#41×D1111yescharacteristic
687C23#6704212yes—
688D4—416no—
689D4—4432no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—114no—
712C2×C4—222no—
713C2×C4—222no—
714C2×C4—224no—
715C2×C4—224no—
716C2×C4—222no—
717C2×C4—224no—
718C2×C4—224no—
719C2×C4—224no—
720C2×C4—224no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—4416no—
725C2×C4—441no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4—442no—
732C2×C4—442no—
733C2×C4—441no—
734C2×C4—442no—
735C2×C4—442no—
736C2×C4—442no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4(C22⋊D11)⋊C414yes—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—82no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22—224no—
758C22—228no—
759C22—444no—
760C22—442no—
761C22—444no—
762C22—442no—
763C22—442no—
764C22—444no—
765C22—442no—
766C22—442no—
767C22—442no—
768C22C2×(C22⋊D11)⋊C411yescharacteristic
769C22#1062301712yes—
770C22C4×#434111yescharacteristic
771C22C4×D4×D1111yescharacteristic
772C22#1062307612yes—
773C22#1062312012yes—
774C22#1062312011yescharacteristic
775C22#1062312311yescharacteristic
776C22#1062312412yes—
777C22#1062312412yes—
778C22D11×#12111yescharacteristic
779C22#1062313711yescharacteristic
780C22#1062313812yes—
781C22#1062314412yes—
782C22#1062314412yes—
783C22#1062315012yes—
784C22#1062315012yes—
785C22#1062318812yes—
786C22#1062319412yes—
787C22#1062320511yescharacteristic
788C22#1062321111yescharacteristic
789C22#1062324611yescharacteristic
790C22#1062324711yescharacteristic
791C4—24no—
792C4—42no—
793C4—42no—
794C4—82no—
795C4—224no—
796C4—442no—
797C4—444no—
798C4—442no—
799C4—882no—
800C2—84no—
801C2—444no—
802C2#1307113211yescharacteristic
803C2#1307127111yescharacteristic
804C2#1307127212yes—
805C2#1307134011yescharacteristic
806C2#1307138212yes—
807C2#1307434911yescharacteristic
808C2#1307436811yescharacteristic
809C2#1307447311yescharacteristic
810C2#1307450811yescharacteristic
811C2#1307460112yes—
812C2#1307474712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC2×#10622836C2
hypercenter#1438D11
hypocenterC11#14311
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#10622834C2semidirect
3. C2×#10622569C2semidirect
4. C2×#10622279C2semidirect
5. #13066872C2semidirect
6. #13066863C2semidirect
7. #13066862C2semidirect
8. #13066855C2semidirect
9. #13066853C2semidirect
10. #13066841C2semidirect
11. C11×#1438C2semidirect
28. #10622836C4semidirect
45. C22×D4×C11C2×C4semidirect
66. C22×C4×D11D4semidirect
81. C2×C22⋊Dic11C2×C4semidirect
96. C2×C4×Dic11D4semidirect
105. C11⋊#95C2×C4semidirect
221. #1438D11semidirect
445. C22×D4C4×D11semidirect
618. C11#14311semidirect

Maximal subgroups

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

subgroupindex
C2×#106228362
C2×#106228342
C2×#106225692
C2×#106222792
#130668722
#130668632
#130668622
#130668552
#130668532
#130668412
C11×#14382
#1431111