Finite Group Databasebeta

← #14677194

Subgroups — #14677194

Order 2816.

2178 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622833C211yesmaximal, characteristic
2C2×#10622833C211yesmaximal, characteristic
3C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
4C22×C11⋊#95C211yesmaximal, characteristic, complemented
5#13066878C212yesmaximal, complemented
6#13066865C212yesmaximal, complemented
7#13066853C212yesmaximal, complemented
8#13066841C212yesmaximal, complemented
9#13066839C211yesmaximal, characteristic, complemented
10#13066838C211yesmaximal, characteristic, complemented
11C2×C11×#386C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C4×Dic11C2212yes—
24C11×#386C418yescomplemented
25C2×C11×#95C2212yes—
26#10622833—24no—
27#10622833—24no—
28C2×C11⋊#95—24no—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C22⋊C4×Dic11—24no—
40C25×C11C2311yescharacteristic
41C25×C11C2311yescharacteristic
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11C2×C414yes—
49C23×C4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11—42no—
52C23×C4×C11—42no—
53C23×C4×C11C2×C414yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×Dic11—22no—
58C23×Dic11—22no—
59C23×Dic11—22no—
60C23×Dic11—24no—
61C23×Dic11—24no—
62C23×Dic11—22no—
63C23×Dic11—22no—
64C23×Dic11—42no—
65C23×Dic11—42no—
66C23×Dic11D414yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2312yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2312yes—
72C23×Dic11C2311yescharacteristic
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—42no—
76C2×C11×C22⋊C4—42no—
77C2×C11×C22⋊C4C2×C414yes—
78C2×C11×C22⋊C4C2×C418yescomplemented
79C2×C22⋊Dic11—22no—
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—22no—
82C2×C22⋊Dic11—22no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—24no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—24no—
88C2×C22⋊Dic11—24no—
89C2×C22⋊Dic11—42no—
90C2×C22⋊Dic11—42no—
91C2×C22⋊Dic11D414yes—
92C2×C4×Dic11—24no—
93C2×C4×Dic11—24no—
94C2×C4×Dic11—42no—
95C11×#95C2×C418yescomplemented
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95—22no—
101C11⋊#95—22no—
102C11⋊#95—24no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105C11⋊#95—42no—
106#14020—111nomaximal, Sylow
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—21no—
112C24×C11—21no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—21no—
116C24×C11—21no—
117C24×C11—21no—
118C24×C11—21no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11C22×C412yes—
122C24×C11C22×C412yes—
123C24×C11C2×D412yes—
124C24×C11C2×D412yes—
125C24×C11#4112yes—
126C24×C11#4112yes—
127C24×C11#4112yes—
128C24×C11#4112yes—
129C24×C11C2411yescharacteristic
130C2×D4×C11—28no—
131C2×D4×C11—28no—
132C2×D4×C11—28no—
133C2×D4×C11—44no—
134C2×D4×C11—44no—
135C2×D4×C11—44no—
136C2×D4×C11—44no—
137C22×C4×C11—28no—
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—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
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—48no—
157C22×C4×C11—44no—
158C22×C4×C11—44no—
159C22×C4×C11—48no—
160C22×C4×C11C22×C412yes—
161C22×C4×C11C22×C414yes—
162C22×C4×C11C22×C414yes—
163C22×Dic11—28no—
164C22×Dic11—28no—
165C22×Dic11—28no—
166C22×Dic11—21no—
167C22×Dic11—22no—
168C22×Dic11—21no—
169C22×Dic11—22no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—21no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
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—44no—
196C22×Dic11—48no—
197C22×Dic11—48no—
198C22×Dic11—48no—
199C22×Dic11—48no—
200C22×Dic11—44no—
201C22×Dic11—44no—
202C22×Dic11C2×D412yes—
203C22×Dic11C2×D414yes—
204C22×Dic11C2×D412yes—
205C22×Dic11#4114yes—
206C22×Dic11#4114yes—
207C11×C22⋊C4—28no—
208C11×C22⋊C4—48no—
209C22⋊Dic11—28no—
210C22⋊Dic11—48no—
211C22⋊Dic11—44no—
212C22⋊Dic11—44no—
213C22⋊Dic11—44no—
214C4×Dic11—48no—
215C2×#386—111no—
216C2×#386—111no—
217C2×#386D1111yescharacteristic
218C2×C4×C22⋊C4—111no—
219C22×#95—111no—
220#1443—112no—
221#1440—112no—
222#1437—112no—
223#1434—112no—
224C22⋊#95—111no—
225C22⋊#95—111no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—24no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—24no—
238C23×C11—24no—
239C23×C11—24no—
240C23×C11—24no—
241C23×C11—24no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—24no—
246C23×C11—24no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—42no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—42no—
257C23×C11—42no—
258C23×C11—42no—
259C23×C11—42no—
260C23×C11—42no—
261C23×C11—42no—
262C23×C11—42no—
263C23×C11—42no—
264C23×C11—42no—
265C23×C11#11714yes—
266C23×C11C4×D414yes—
267C23×C11C4×D414yes—
268C23×C11#12114yes—
269C23×C11#12314yes—
270C23×C11#12414yes—
271C23×C11#12614yes—
272C23×C11C23×C411yescharacteristic
273C23×C11C22×D411yescharacteristic
274C23×C11C22×D411yescharacteristic
275C23×C11C2×#4111yescharacteristic
276C23×C11C2×#4111yescharacteristic
277C23×C11C2×#4111yescharacteristic
278C23×C11C2×#4111yescharacteristic
279C23×C11C2×#4112yes—
280C23×C11C2×#4112yes—
281C23×C11H(5,𝔽2)12yes—
282C23×C11H(5,𝔽2)12yes—
283D4×C11—416no—
284C2×C4×C11—22no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—24no—
290C2×C4×C11—24no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—416no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
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×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—24no—
309C2×Dic11—24no—
310C2×Dic11—22no—
311C2×Dic11—24no—
312C2×Dic11—22no—
313C2×Dic11—24no—
314C2×Dic11—22no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11—416no—
320C2×Dic11—416no—
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—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11#12314yes—
342C23×D4C2×D1111yescharacteristic
343C24×C4—111no—
344C24×C4—111no—
345C24×C4C2×D1111yescharacteristic
346C22×C22⋊C4—111no—
347C22×C22⋊C4—111no—
348C22×C22⋊C4—111no—
349C22×C22⋊C4—112no—
350C22×C22⋊C4—111no—
351C22×C22⋊C4C2×D1111yescharacteristic
352C22×C22⋊C4C2×D1112yes—
353C22×C42—112no—
354#386—224no—
355#386—224no—
356#386Dic1118yescomplemented
357C4×C22⋊C4—224no—
358C2×#95—112no—
359C2×#95—111no—
360C2×#95—112no—
361C2×#95—112no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95—111no—
365C2×#95—112no—
366C2×#95—112no—
367C2×#95—112no—
368C2×#95—224no—
369C2×#95C2×D1112yes—
370C22×C11—24no—
371C22×C11—24no—
372C22×C11—28no—
373C22×C11—28no—
374C22×C11—24no—
375C22×C11—24no—
376C22×C11—28no—
377C22×C11—24no—
378C22×C11—28no—
379C22×C11—24no—
380C22×C11—42no—
381C22×C11—44no—
382C22×C11—44no—
383C22×C11—42no—
384C22×C11—42no—
385C22×C11—81no—
386C22×C11—81no—
387C22×C11—81no—
388C22×C11—82no—
389C22×C11—81no—
390C22×C11—82no—
391C22×C11#38818yes—
392C22×C11C2×#11711yescharacteristic
393C22×C11C2×C4×D411yescharacteristic
394C22×C11C2×C4×D411yescharacteristic
395C22×C11C4×#4112yes—
396C22×C11#51812yes—
397C22×C11C2×#12111yescharacteristic
398C22×C11C2×#12311yescharacteristic
399C22×C11C2×#12311yescharacteristic
400C22×C11#52511yescharacteristic
401C22×C11C2×#12411yescharacteristic
402C22×C11C2×#12611yescharacteristic
403C22×C11#52912yes—
404C22×C11#53411yescharacteristic
405C22×C11#53511yescharacteristic
406C22×C11#53812yes—
407C22×C11#54612yes—
408C22×C11#54612yes—
409C22×C11#55112yes—
410C22×C11#55112yes—
411C22×C11#55312yes—
412C22×C11#55312yes—
413C22×C11#55312yes—
414C22×C11#55312yes—
415C4×C11—44no—
416C4×C11—44no—
417C4×C11—42no—
418Dic11—24no—
419Dic11—44no—
420Dic11—42no—
421Dic11—44no—
422Dic11—81no—
423Dic11—81no—
424C25C22×D1111yescharacteristic
425C25C22×D1111yescharacteristic
426C22×D4—22no—
427C22×D4—22no—
428C22×D4—22no—
429C22×D4—22no—
430C22×D4—22no—
431C22×D4—22no—
432C22×D4C2×Dic1114yes—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—42no—
436C23×C4—42no—
437C23×C4—111no—
438C23×C4—112no—
439C23×C4—111no—
440C23×C4—112no—
441C23×C4—114no—
442C23×C4—111no—
443C23×C4—111no—
444C23×C4—224no—
445C23×C4—224no—
446C23×C4—222no—
447C23×C4—222no—
448C23×C4—222no—
449C23×C4—222no—
450C23×C4—222no—
451C23×C4—442no—
452C23×C4—442no—
453C23×C4C2×Dic1114yes—
454C23×C4C22×D1112yes—
455C23×C4C22×D1112yes—
456C23×C4C22×D1111yescharacteristic
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—42no—
461C2×C22⋊C4—114no—
462C2×C22⋊C4—222no—
463C2×C22⋊C4—222no—
464C2×C22⋊C4—222no—
465C2×C22⋊C4—224no—
466C2×C22⋊C4—222no—
467C2×C22⋊C4—224no—
468C2×C22⋊C4—224no—
469C2×C22⋊C4—222no—
470C2×C22⋊C4—222no—
471C2×C22⋊C4—222no—
472C2×C22⋊C4—442no—
473C2×C22⋊C4—442no—
474C2×C22⋊C4C2×Dic1114yes—
475C2×C22⋊C4C2×Dic1118yescomplemented
476C2×C42—224no—
477C2×C42—224no—
478C2×C42—442no—
479#95—224no—
480#95—224no—
481#95—224no—
482#95—224no—
483#95—222no—
484#95—222no—
485#95—224no—
486#95—442no—
487#95—442no—
488#95—442no—
489#95C2×Dic1118yescomplemented
490C2×C11—28no—
491C2×C11—82no—
492C2×C11C2×#38811yescharacteristic
493C2×C11C4×#12311yescharacteristic
494C2×C11#232111yescharacteristic
495C2×C11#235312yes—
496C2×C11#236412yes—
497C2×C11#241111yescharacteristic
498C2×C11#241211yescharacteristic
499C2×C11#244412yes—
500C2×C11#250411yescharacteristic
501C2×C11#251012yes—
502C2×C11#259111yescharacteristic
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24#433912yes—
518C24#433912yes—
519C24D4×D1112yes—
520C24D4×D1112yes—
521C24#434112yes—
522C24#434112yes—
523C24C22×Dic1112yes—
524C24C22×Dic1112yes—
525C24C23×D1111yescharacteristic
526C2×D4—28no—
527C2×D4—28no—
528C2×D4—28no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—44no—
533C22×C4—28no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
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—48no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—48no—
556C22×C4—112no—
557C22×C4—114no—
558C22×C4—112no—
559C22×C4—114no—
560C22×C4—114no—
561C22×C4—228no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—222no—
565C22×C4—228no—
566C22×C4—228no—
567C22×C4—222no—
568C22×C4—221no—
569C22×C4—222no—
570C22×C4—221no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—221no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—444no—
594C22×C4—448no—
595C22×C4—448no—
596C22×C4—448no—
597C22×C4—448no—
598C22×C4—444no—
599C22×C4—444no—
600C22×C4C22×Dic1112yes—
601C22×C4C22×Dic1114yes—
602C22×C4C22×Dic1114yes—
603C22⋊C4—28no—
604C22⋊C4—48no—
605C22⋊C4—228no—
606C22⋊C4—444no—
607C22⋊C4—448no—
608C22⋊C4—444no—
609C22⋊C4—444no—
610C42—448no—
611C11#1402011yescharacteristic, complemented, Sylow
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—22no—
619C23—22no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—24no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—41no—
642C23—41no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—41no—
650C23—41no—
651C23#6693214yes—
652C23#6693614yes—
653C23#6693714yes—
654C23#6693814yes—
655C23#6697914yes—
656C23D4×Dic1114yes—
657C23D4×Dic1114yes—
658C23C2×#433911yescharacteristic
659C23C2×#433911yescharacteristic
660C23C2×D4×D1111yescharacteristic
661C23C2×D4×D1111yescharacteristic
662C23C2×#434111yescharacteristic
663C23C2×#434111yescharacteristic
664C23#6703712yes—
665C23#6703712yes—
666C23#41×D1112yes—
667C23#41×D1112yes—
668C23C23×Dic1111yescharacteristic
669D4—416no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—416no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
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—224no—
695C2×C4—222no—
696C2×C4—224no—
697C2×C4—224no—
698C2×C4—222no—
699C2×C4—224no—
700C2×C4—222no—
701C2×C4—224no—
702C2×C4—224no—
703C2×C4—224no—
704C2×C4—222no—
705C2×C4—224no—
706C2×C4—4416no—
707C2×C4—4416no—
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×C4—441no—
719C2×C4—441no—
720C2×C4—442no—
721C2×C4—442no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—441no—
727C2×C4—441no—
728C22—28no—
729C22—24no—
730C22—28no—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—28no—
736C22—24no—
737C22—28no—
738C22—42no—
739C22—44no—
740C22—42no—
741C22—44no—
742C22—42no—
743C22—82no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—82no—
749C22#1062256418yes—
750C22C2×#6693211yescharacteristic
751C22C2×#6693611yescharacteristic
752C22C2×#6693711yescharacteristic
753C22C2×#6693811yescharacteristic
754C22#1062307112yes—
755C22#1062307112yes—
756C22#1062308712yes—
757C22#1062308712yes—
758C22#1062312011yescharacteristic
759C22#1062312311yescharacteristic
760C22#1062312412yes—
761C22#1062313212yes—
762C22#1062313212yes—
763C22#1062314112yes—
764C22#1062314112yes—
765C22#1062318012yes—
766C22D11×#12311yescharacteristic
767C22#1062318711yescharacteristic
768C22C2×#6697911yescharacteristic
769C22C2×D4×Dic1111yescharacteristic
770C22C2×D4×Dic1111yescharacteristic
771C22#1062332912yes—
772C22#41×Dic1112yes—
773C4—44no—
774C4—44no—
775C4—42no—
776C4—224no—
777C4—444no—
778C4—442no—
779C4—444no—
780C4—881no—
781C4—881no—
782C2—28no—
783C2—82no—
784C2C2×#1062256411yescharacteristic
785C2#123×Dic1111yescharacteristic
786C2#1307127711yescharacteristic
787C2#1307155612yes—
788C2#1307166812yes—
789C2#1307200411yescharacteristic
790C2#1307201511yescharacteristic
791C2#1307237212yes—
792C2#1307310611yescharacteristic
793C2#1307317412yes—
794C2#1307409511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11#14020
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×C22⋊C4×Dic11C2semidirect
4. C22×C11⋊#95C2semidirect
5. #13066878C2semidirect
6. #13066865C2semidirect
7. #13066853C2semidirect
8. #13066841C2semidirect
9. #13066839C2semidirect
10. #13066838C2semidirect
24. C11×#386C4semidirect
78. C2×C11×C22⋊C4C2×C4semidirect
95. C11×#95C2×C4semidirect
356. #386Dic11semidirect
475. C2×C22⋊C4C2×Dic11semidirect
489. #95C2×Dic11semidirect
611. C11#14020semidirect

Maximal subgroups

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

subgroupindex
C2×#106228332
C2×C22⋊C4×Dic112
C22×C11⋊#952
#130668782
#130668652
#130668532
#130668412
#130668392
#130668382
C2×C11×#3862
#1402011