Finite Group Databasebeta

← #14675906

Subgroups — #14675906

Order 2816.

2546 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622833C212yesmaximal
2C2×#10622824C211yesmaximal, characteristic, complemented
3C22×C11⋊#95C211yesmaximal, characteristic, complemented
4#13066884C212yesmaximal, complemented
5#13066865C212yesmaximal, complemented
6#13066843C211yesmaximal, characteristic, complemented
7#13066843C211yesmaximal, characteristic, complemented
8#13066839C211yesmaximal, characteristic, complemented
9#13066839C211yesmaximal, characteristic, complemented
10#13066838C212yesmaximal, complemented
11C22×C4×D4×C11C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C24×Dic11C2212yes—
16C2×C4×D4×C11—28no—
17C2×C4×D4×C11C418yescomplemented
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25#10622833—28no—
26#10622824—24no—
27C2×C11⋊#95—24no—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40C25×C11C2311yescharacteristic
41C25×C11C2311yescharacteristic
42C22×D4×C11—22no—
43C22×D4×C11—24no—
44C22×D4×C11—22no—
45C22×D4×C11C2×C414yes—
46C22×D4×C11D418yes—
47C23×C4×C11—24no—
48C23×C4×C11—24no—
49C23×C4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11—22no—
52C23×C4×C11—22no—
53C23×C4×C11—42no—
54C23×C4×C11—42no—
55C23×C4×C11C2×C414yes—
56C23×C4×C11C2×C414yescomplemented
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—24no—
63C23×Dic11—24no—
64C23×Dic11—24no—
65C23×Dic11—24no—
66C23×Dic11—24no—
67C23×Dic11—42no—
68C23×Dic11—42no—
69C23×Dic11C2312yes—
70C23×Dic11C2312yes—
71C23×Dic11C2312yes—
72C23×Dic11C2312yes—
73C4×D4×C11—232no—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4C2×C414yescomplemented
76C2×C11×C22⋊C4—24no—
77C2×C11×C22⋊C4—24no—
78C2×C11×C22⋊C4C2×C414yes—
79C2×C11×C22⋊C4C2×C414yescomplemented
80C2×C42×C11—24no—
81C2×C42×C11C2×C414yescomplemented
82C2×C22⋊Dic11—24no—
83C2×C22⋊Dic11—24no—
84C2×C22⋊Dic11—24no—
85C2×C22⋊Dic11—24no—
86C2×C22⋊Dic11—24no—
87C2×C22⋊Dic11—24no—
88C2×C22⋊Dic11—24no—
89C2×C22⋊Dic11—42no—
90C2×C22⋊Dic11—42no—
91C11⋊#95—22no—
92C11⋊#95—22no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—22no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95—42no—
100C11⋊#95—42no—
101C11⋊#95—42no—
102C11⋊#95D414yescomplemented
103#13894—111nomaximal, Sylow
104C24×C11—21no—
105C24×C11—22no—
106C24×C11—21no—
107C24×C11—21no—
108C24×C11—22no—
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—22no—
112C24×C11—21no—
113C24×C11—22no—
114C24×C11—21no—
115C24×C11—21no—
116C24×C11—21no—
117C24×C11—22no—
118C24×C11—21no—
119C24×C11C22×C412yes—
120C24×C11C22×C412yes—
121C24×C11C2×D414yes—
122C24×C11C2×D414yes—
123C24×C11#4112yes—
124C24×C11#4114yes—
125C24×C11#4112yes—
126C24×C11C2411yescharacteristic
127C2×D4×C11—28no—
128C2×D4×C11—28no—
129C2×D4×C11—216no—
130C2×D4×C11—216no—
131C2×D4×C11C22⋊C4116yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—28no—
138C22×C4×C11—28no—
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—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—28no—
152C22×C4×C11—28no—
153C22×C4×C11—44no—
154C22×C4×C11—44no—
155C22×C4×C11—48no—
156C22×C4×C11—48no—
157C22×C4×C11—48no—
158C22×C4×C11—48no—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C22×C412yes—
161C22×C4×C11C22×C412yes—
162C22×C4×C11C22×C412yes—
163C22×C4×C11C22×C412yes—
164C22×C4×C11C2×D414yes—
165C22×C4×C11C2×D412yes—
166C22×C4×C11#4112yes—
167C22×Dic11—216no—
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×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—48no—
195C22×Dic11—48no—
196C22×Dic11—48no—
197C22×Dic11—48no—
198C22×Dic11—48no—
199C22×Dic11—48no—
200C22×Dic11C2×D414yes—
201C22×Dic11#4114yes—
202C11×C4⋊C4—28no—
203C11×C22⋊C4—28no—
204C11×C22⋊C4—28no—
205C42×C11—28no—
206C22⋊Dic11—48no—
207C22⋊Dic11—48no—
208C22⋊Dic11—48no—
209C22×C4×D4D1111yescharacteristic
210C2×#386—112no—
211C2×#381—111no—
212C22×#95—111no—
213#1445—112no—
214#1440—112no—
215#1434—111no—
216#1434—111no—
217C22⋊#95—111no—
218C22⋊#95—111no—
219C22⋊#95—112no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—24no—
229C23×C11—22no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11—24no—
233C23×C11—22no—
234C23×C11—24no—
235C23×C11—22no—
236C23×C11—24no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—24no—
245C23×C11—24no—
246C23×C11—24no—
247C23×C11—24no—
248C23×C11—24no—
249C23×C11—24no—
250C23×C11—42no—
251C23×C11—42no—
252C23×C11—42no—
253C23×C11—42no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—42no—
257C23×C11—41no—
258C23×C11—42no—
259C23×C11—41no—
260C23×C11C2×C22⋊C414yes—
261C23×C11C2×C22⋊C414yes—
262C23×C11#11714yes—
263C23×C11#11714yes—
264C23×C11#12318yes—
265C23×C11#12318yes—
266C23×C11C23×C411yescharacteristic
267C23×C11C22×D411yescharacteristic
268C23×C11C22×D412yes—
269C23×C11C2×#4112yes—
270C23×C11C2×#4111yescharacteristic
271C23×C11C2×#4111yescharacteristic
272C23×C11C2×#4111yescharacteristic
273C23×C11C2×#4112yes—
274C23×C11H(5,𝔽2)12yes—
275C23×C11H(5,𝔽2)11yescharacteristic
276C23×C112−1+411yescharacteristic
277D4×C11—232no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—24no—
283C2×C4×C11—24no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—416no—
296C2×C4×C11—416no—
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×C11C2×C22⋊C414yes—
304C2×C4×C11C4×D414yes—
305C2×Dic11—24no—
306C2×Dic11—24no—
307C2×Dic11—24no—
308C2×Dic11—24no—
309C2×Dic11—24no—
310C2×Dic11—24no—
311C2×Dic11—432no—
312C2×Dic11—42no—
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×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C23×D4C2×D1111yescharacteristic
335C24×C4—112no—
336C24×C4C2×D1111yescharacteristic
337C24×C4C2×D1111yescharacteristic
338C2×C4×D4—28no—
339C2×C4×D4Dic1118yescomplemented
340C22×C4⋊C4C2×D1111yescharacteristic
341C22×C22⋊C4—112no—
342C22×C22⋊C4—112no—
343C22×C22⋊C4—112no—
344C22×C22⋊C4C2×D1111yescharacteristic
345C22×C22⋊C4C2×D1111yescharacteristic
346C22×C42C2×D1111yescharacteristic
347#386—228no—
348#381—224no—
349C2×#95—111no—
350C2×#95—111no—
351C2×#95—112no—
352C2×#95—111no—
353C2×#95—111no—
354C2×#95—112no—
355C2×#95—112no—
356C2×#95—112no—
357C2×#95—112no—
358C2×#95—112no—
359C2×#95—112no—
360C2×#95—112no—
361C2×#95—224no—
362C22×C11—24no—
363C22×C11—24no—
364C22×C11—24no—
365C22×C11—24no—
366C22×C11—24no—
367C22×C11—28no—
368C22×C11—28no—
369C22×C11—28no—
370C22×C11—28no—
371C22×C11—24no—
372C22×C11—24no—
373C22×C11—24no—
374C22×C11—24no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—42no—
378C22×C11—44no—
379C22×C11—44no—
380C22×C11—44no—
381C22×C11—44no—
382C22×C11—42no—
383C22×C11#38118yescomplemented
384C22×C11C22×C22⋊C411yescharacteristic
385C22×C11C2×#11711yescharacteristic
386C22×C11C2×#11711yescharacteristic
387C22×C11C2×C4×D411yescharacteristic
388C22×C11C4×#4111yescharacteristic
389C22×C11#51811yescharacteristic
390C22×C11#52011yescharacteristic
391C22×C11C2×#12312yes—
392C22×C11C2×#12312yes—
393C22×C11#52512yes—
394C22×C11#52912yes—
395C22×C11#53812yes—
396C22×C11#53912yes—
397C22×C11D4212yes—
398C22×C11#54611yescharacteristic
399C22×C11#54612yes—
400C22×C11#54612yes—
401C22×C11#54712yes—
402C22×C11#54811yescharacteristic
403C22×C11#55112yes—
404C22×C11#55211yescharacteristic
405C22×C11#55312yes—
406C22×C11#55311yescharacteristic
407C4×C11—24no—
408C4×C11—24no—
409C4×C11—42no—
410C4×C11—42no—
411C4×C11—42no—
412Dic11—44no—
413Dic11—44no—
414Dic11—82no—
415Dic11—82no—
416C25C22×D1111yescharacteristic
417C25C22×D1111yescharacteristic
418C22×D4—22no—
419C22×D4—24no—
420C22×D4—22no—
421C22×D4C2×Dic1114yes—
422C22×D4C22⋊D1118yes—
423C23×C4—24no—
424C23×C4—24no—
425C23×C4—22no—
426C23×C4—22no—
427C23×C4—22no—
428C23×C4—22no—
429C23×C4—42no—
430C23×C4—42no—
431C23×C4—112no—
432C23×C4—112no—
433C23×C4—112no—
434C23×C4—112no—
435C23×C4—224no—
436C23×C4—224no—
437C23×C4—224no—
438C23×C4—224no—
439C23×C4—224no—
440C23×C4—442no—
441C23×C4—442no—
442C23×C4C2×Dic1114yes—
443C23×C4C2×Dic1114yescomplemented
444C23×C4C22×D1111yescharacteristic
445C23×C4C22×D1111yescharacteristic
446C23×C4C22×D1111yescharacteristic
447C23×C4C22×D1111yescharacteristic
448C23×C4C22×D1111yescharacteristic
449C4×D4—232no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4C2×Dic1114yescomplemented
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—224no—
455C2×C22⋊C4—224no—
456C2×C22⋊C4—224no—
457C2×C22⋊C4—224no—
458C2×C22⋊C4—224no—
459C2×C22⋊C4—224no—
460C2×C22⋊C4—224no—
461C2×C22⋊C4—442no—
462C2×C22⋊C4—442no—
463C2×C22⋊C4C2×Dic1114yes—
464C2×C22⋊C4C2×Dic1114yescomplemented
465C2×C42—24no—
466C2×C42C2×Dic1114yescomplemented
467#95—114no—
468#95—224no—
469#95—224no—
470#95—224no—
471#95—222no—
472#95—222no—
473#95—222no—
474#95—224no—
475#95—224no—
476#95—442no—
477#95—442no—
478#95—442no—
479C2×C11—28no—
480C2×C11—44no—
481C2×C11C2×#38111yescharacteristic
482C2×C11#229011yescharacteristic
483C2×C11#231811yescharacteristic
484C2×C11D4×C22⋊C411yescharacteristic
485C2×C11#233911yescharacteristic
486C2×C11#235211yescharacteristic
487C2×C11#235311yescharacteristic
488C2×C11#241812yes—
489C2×C11#241912yes—
490C2×C11#244312yes—
491C2×C11#244412yes—
492C24—21no—
493C24—21no—
494C24—22no—
495C24—22no—
496C24—21no—
497C24—21no—
498C24—22no—
499C24—21no—
500C24—21no—
501C24—21no—
502C24—21no—
503C24—22no—
504C24—22no—
505C24—21no—
506C24—21no—
507C24#433912yes—
508C24#433914yes—
509C24#433912yes—
510C24C22×Dic1112yes—
511C24C22×Dic1112yes—
512C24C2×C22⋊D1114yes—
513C24C2×C22⋊D1114yes—
514C24C23×D1111yescharacteristic
515C2×D4—28no—
516C2×D4—28no—
517C2×D4—216no—
518C2×D4—216no—
519C2×D4C22⋊Dic11116yes—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—114no—
548C22×C4—114no—
549C22×C4—2216no—
550C22×C4—222no—
551C22×C4—222no—
552C22×C4—222no—
553C22×C4—222no—
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—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—448no—
577C22×C4—448no—
578C22×C4—448no—
579C22×C4—448no—
580C22×C4—448no—
581C22×C4—448no—
582C22×C4D4×D1112yes—
583C22×C4#434112yes—
584C22×C4C22×Dic1112yes—
585C22×C4C22×Dic1112yes—
586C22×C4C22×Dic1112yes—
587C22×C4C22×Dic1112yes—
588C22×C4C22×Dic1112yes—
589C22×C4C2×C22⋊D1114yes—
590C4⋊C4—28no—
591C22⋊C4—28no—
592C22⋊C4—28no—
593C22⋊C4—448no—
594C22⋊C4—448no—
595C22⋊C4—448no—
596C42—28no—
597C11#1389411yescharacteristic, complemented, Sylow
598C23—24no—
599C23—22no—
600C23—24no—
601C23—22no—
602C23—22no—
603C23—24no—
604C23—24no—
605C23—22no—
606C23—24no—
607C23—22no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—24no—
613C23—22no—
614C23—22no—
615C23—24no—
616C23—22no—
617C23—22no—
618C23—24no—
619C23—24no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—22no—
626C23—22no—
627C23—24no—
628C23—42no—
629C23—42no—
630C23—41no—
631C23—42no—
632C23—41no—
633C23—41no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—41no—
638C23#6697914yes—
639C23#6697914yes—
640C23#6698218yes—
641C23#6698218yes—
642C23C2×C22⋊Dic1114yes—
643C23C2×C22⋊Dic1114yes—
644C23C2×#433912yes—
645C23C2×#433911yescharacteristic
646C23C2×#433911yescharacteristic
647C23C2×D4×D1111yescharacteristic
648C23C2×#434111yescharacteristic
649C23#6703712yes—
650C23#41×D1112yes—
651C23#6704211yescharacteristic
652C23#6704311yescharacteristic
653C23C23×Dic1111yescharacteristic
654C23C22×C22⋊D1112yes—
655D4—232no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—416no—
674C2×C4—416no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—224no—
682C2×C4—224no—
683C2×C4—224no—
684C2×C4—224no—
685C2×C4—224no—
686C2×C4—224no—
687C2×C4—4432no—
688C2×C4—442no—
689C2×C4—442no—
690C2×C4—442no—
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×C4—442no—
706C2×C4—442no—
707C2×C4—442no—
708C2×C4—442no—
709C2×C4—442no—
710C2×C4D4×Dic1114yes—
711C2×C4C2×C22⋊Dic1114yes—
712C22—24no—
713C22—24no—
714C22—24no—
715C22—24no—
716C22—24no—
717C22—28no—
718C22—24no—
719C22—28no—
720C22—28no—
721C22—28no—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—44no—
729C22—42no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22#1062282418yescomplemented
734C22#1062306912yes—
735C22#1062307112yes—
736C22#1062307211yescharacteristic
737C22#1062307812yes—
738C22#1062308111yescharacteristic
739C22#1062308311yescharacteristic
740C22#1062308712yes—
741C22#1062309112yes—
742C22#1062309512yes—
743C22#1062309611yescharacteristic
744C22C2×#6697911yescharacteristic
745C22C2×#6697911yescharacteristic
746C22C2×#6698212yes—
747C22C2×#6698212yes—
748C22C2×D4×Dic1111yescharacteristic
749C22#1062332911yescharacteristic
750C22D4×C22⋊D1112yes—
751C22#1062333712yes—
752C22#1062335512yes—
753C22#41×Dic1111yescharacteristic
754C22#1062335811yescharacteristic
755C22#1062336012yes—
756C22C22×C22⋊Dic1111yescharacteristic
757C4—24no—
758C4—24no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—444no—
763C4—444no—
764C4—882no—
765C4—882no—
766C2—28no—
767C2—44no—
768C2C2×#1062282411yescharacteristic
769C2#1307106111yescharacteristic
770C2#1307124911yescharacteristic
771C2D4×C22⋊Dic1111yescharacteristic
772C2#1307144611yescharacteristic
773C2#1307154511yescharacteristic
774C2#1307155611yescharacteristic
775C2#1307207212yes—
776C2#1307208712yes—
777C2#1307234512yes—
778C2#1307236012yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C4×D4×C11C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×C4×D4D11
hypocenterC11#13894
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#10622824C2semidirect
3. C22×C11⋊#95C2semidirect
4. #13066884C2semidirect
5. #13066865C2semidirect
6. #13066843C2semidirect
7. #13066843C2semidirect
8. #13066839C2semidirect
9. #13066839C2semidirect
10. #13066838C2semidirect
17. C2×C4×D4×C11C4semidirect
56. C23×C4×C11C2×C4semidirect
75. C2×C11×C4⋊C4C2×C4semidirect
79. C2×C11×C22⋊C4C2×C4semidirect
81. C2×C42×C11C2×C4semidirect
102. C11⋊#95D4semidirect
339. C2×C4×D4Dic11semidirect
383. C22×C11#381semidirect
443. C23×C4C2×Dic11semidirect
451. C2×C4⋊C4C2×Dic11semidirect
464. C2×C22⋊C4C2×Dic11semidirect
466. C2×C42C2×Dic11semidirect
597. C11#13894semidirect
733. C22#10622824semidirect

Maximal subgroups

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

subgroupindex
C2×#106228332
C2×#106228242
C22×C11⋊#952
#130668842
#130668652
#130668432
#130668392
#130668382
C22×C4×D4×C112
#1389411