Finite Group Databasebeta

← #14681177

Subgroups — #14681177

Order 2816.

2854 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622564C212yesmaximal, complemented
2C2×#10622860C212yesmaximal
3#13066865C212yesmaximal, complemented
4#13066861C211yesmaximal, characteristic, complemented
5#13066861C212yesmaximal, complemented
6#13066861C211yesmaximal, characteristic, complemented
7#13066853C212yesmaximal, complemented
8#13066853C212yesmaximal, complemented
9C2×C11×#379C211yesmaximal, characteristic
10C26×C11C2211yescharacteristic
11C22×C11×C22⋊C4C2212yes—
12C22×C11×C22⋊C4C2211yescharacteristic
13C22×C11×C22⋊C4C2212yes—
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C22⋊Dic11C2212yes—
16C22×C22⋊Dic11C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21C22×C4⋊Dic11C2211yescharacteristic, complemented
22C22×C4⋊Dic11C2211yescharacteristic, complemented
23C22×C4×Dic11C2212yescomplemented
24C11×#379C418yescomplemented
25#10622860—28no—
26C2×C11⋊#95C2212yescomplemented
27C2×C11⋊#95C2212yescomplemented
28C2×C11⋊#95C2211yescharacteristic, complemented
29C2×C11⋊#95C2212yescomplemented
30C2×C11⋊#95C2212yescomplemented
31C2×C11⋊#95C2212yescomplemented
32C2×C11⋊#95C2211yescharacteristic, complemented
33#10622564—28no—
34C25×C11—24no—
35C25×C11—22no—
36C25×C11—22no—
37C25×C11—24no—
38C25×C11—42no—
39C25×C11—42no—
40C25×C11—41no—
41C25×C11—41no—
42C25×C11—41no—
43C25×C11—41no—
44C25×C11C2×C414yes—
45C25×C11C2312yes—
46C25×C11C2311yescharacteristic
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×Dic11C2312yes—
51C23×Dic11C2312yes—
52C23×Dic11C2312yes—
53C23×Dic11C2312yes—
54C2×C11×C22⋊C4—24no—
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4—41no—
57C2×C11×C22⋊C4—41no—
58C2×C11×C22⋊C4—42no—
59C2×C11×C22⋊C4—42no—
60C2×C11×C22⋊C4—41no—
61C2×C11×C22⋊C4—41no—
62C2×C11×C22⋊C4C2×C418yes—
63C2×C11×C22⋊C4C2×C414yes—
64C2×C11×C22⋊C4C2×C414yes—
65C2×C11×C22⋊C4C2×C418yes—
66C2×C22⋊Dic11—24no—
67C2×C22⋊Dic11—24no—
68C2×C22⋊Dic11—24no—
69C2×C22⋊Dic11—24no—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—42no—
76C2×C22⋊Dic11—42no—
77C2×C22⋊Dic11—42no—
78C2×C22⋊Dic11—42no—
79C2×C22⋊Dic11—42no—
80C2×C22⋊Dic11—42no—
81C2×C22⋊Dic11—42no—
82C2×C22⋊Dic11—42no—
83C2×C22⋊Dic11D418yes—
84C2×C4⋊Dic11—24no—
85C2×C4⋊Dic11—41no—
86C2×C4⋊Dic11—42no—
87C2×C4⋊Dic11—41no—
88C2×C4×Dic11—24no—
89C2×C4×Dic11—42no—
90C2×C4×Dic11—42no—
91C11⋊#95—24no—
92C11⋊#95—24no—
93C11⋊#95—41no—
94C11⋊#95—42no—
95C11⋊#95—42no—
96C11⋊#95—42no—
97C11⋊#95—41no—
98#14366—111nomaximal, Sylow
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—21no—
114C24×C11—21no—
115C24×C11—21no—
116C24×C11—21no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—28no—
120C24×C11—216no—
121C24×C11—44no—
122C24×C11—48no—
123C24×C11—44no—
124C24×C11—44no—
125C24×C11—48no—
126C24×C11—48no—
127C24×C11—48no—
128C24×C11—48no—
129C24×C11—48no—
130C24×C11—44no—
131C24×C11—48no—
132C24×C11—48no—
133C24×C11—44no—
134C24×C11—44no—
135C24×C11—44no—
136C24×C11—44no—
137C24×C11—48no—
138C24×C11—48no—
139C24×C11—44no—
140C24×C11—48no—
141C24×C11—44no—
142C24×C11C22×C412yes—
143C24×C11C22×C414yes—
144C24×C11C2×D414yes—
145C24×C11#4112yes—
146C24×C11#4112yes—
147C24×C11#4114yes—
148C24×C11C2411yescharacteristic
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—21no—
156C22×C4×C11—22no—
157C22×C4×C11—21no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—21no—
161C22×C4×C11—22no—
162C22×C4×C11—21no—
163C22×C4×C11C22×C412yes—
164C22×C4×C11C22×C414yes—
165C22×C4×C11C22×C412yes—
166C22×Dic11—22no—
167C22×Dic11—22no—
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×Dic11C2×D414yes—
193C22×Dic11C2×D414yes—
194C11×C22⋊C4—216no—
195C11×C22⋊C4—44no—
196C11×C22⋊C4—48no—
197C11×C22⋊C4—44no—
198C22⋊Dic11—48no—
199C22⋊Dic11—48no—
200C22⋊Dic11—48no—
201C22⋊Dic11—48no—
202C22⋊Dic11—48no—
203C22⋊Dic11—48no—
204C4⋊Dic11—44no—
205C4⋊Dic11—44no—
206C4×Dic11—48no—
207C2×#388—112no—
208C2×#379—112no—
209C2×#379D1111yescharacteristic
210#1440—112no—
211#1439—111no—
212#1439—111no—
213#1439—112no—
214#1437—112no—
215#1437—112no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—24no—
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—24no—
243C23×C11—24no—
244C23×C11—24no—
245C23×C11—24no—
246C23×C11—432no—
247C23×C11—416no—
248C23×C11—416no—
249C23×C11—432no—
250C23×C11—416no—
251C23×C11—416no—
252C23×C11—416no—
253C23×C11—432no—
254C23×C11—432no—
255C23×C11—416no—
256C23×C11—416no—
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—42no—
266C23×C11—42no—
267C23×C11—42no—
268C23×C11—42no—
269C23×C11—41no—
270C23×C11—42no—
271C23×C11—42no—
272C23×C11—42no—
273C23×C11—42no—
274C23×C11—42no—
275C23×C11—41no—
276C23×C11—42no—
277C23×C11—41no—
278C23×C11—42no—
279C23×C11—42no—
280C23×C11—42no—
281C23×C11—42no—
282C23×C11—41no—
283C23×C11#11714yes—
284C23×C11C4×D418yes—
285C23×C11C23×C411yescharacteristic
286C23×C11C22×D412yes—
287C23×C11C2×#4111yescharacteristic
288C23×C11C2×#4111yescharacteristic
289C23×C11C2×#4112yes—
290C23×C11H(5,𝔽2)11yescharacteristic
291C23×C11H(5,𝔽2)12yes—
292C23×C11H(5,𝔽2)11yescharacteristic
293C23×C11H(5,𝔽2)12yes—
294C23×C11H(5,𝔽2)11yescharacteristic
295C23×C11H(5,𝔽2)11yescharacteristic
296C2×C4×C11—24no—
297C2×C4×C11—24no—
298C2×C4×C11—24no—
299C2×C4×C11—24no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—24no—
303C2×C4×C11—42no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11—41no—
308C2×C4×C11—42no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—42no—
312C2×C4×C11—41no—
313C2×Dic11—24no—
314C2×Dic11—24no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—24no—
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—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C26C2×D1111yescharacteristic
342C22×C4⋊C4—111no—
343C22×C4⋊C4—111no—
344C22×C22⋊C4—112no—
345C22×C22⋊C4—112no—
346C22×C22⋊C4—112no—
347C22×C22⋊C4—112no—
348C22×C22⋊C4—112no—
349C22×C22⋊C4—112no—
350C22×C22⋊C4C2×D1112yes—
351C22×C22⋊C4C2×D1111yescharacteristic
352C22×C22⋊C4C2×D1112yes—
353C22×C22⋊C4C2×D1111yescharacteristic
354C22×C42—112no—
355#388—228no—
356#379—228no—
357#379Dic1118yescomplemented
358C2×#95—112no—
359C2×#95—112no—
360C2×#95—111no—
361C2×#95—112no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95—111no—
365C22×C11—24no—
366C22×C11—28no—
367C22×C11—28no—
368C22×C11—28no—
369C22×C11—28no—
370C22×C11—464no—
371C22×C11—44no—
372C22×C11—44no—
373C22×C11—44no—
374C22×C11—44no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—44no—
378C22×C11—44no—
379C22×C11—42no—
380C22×C11—44no—
381C22×C11—42no—
382C22×C11—44no—
383C22×C11—44no—
384C22×C11—44no—
385C22×C11—44no—
386C22×C11—44no—
387C22×C11—44no—
388C22×C11—42no—
389C22×C11—44no—
390C22×C11—42no—
391C22×C11—44no—
392C22×C11C2×#11711yescharacteristic
393C22×C11C2×C4×D412yes—
394C22×C11#51811yescharacteristic
395C22×C11#51811yescharacteristic
396C22×C11#51812yes—
397C22×C11#53412yes—
398C22×C11#53512yes—
399C22×C11#53811yescharacteristic
400C22×C11#53811yescharacteristic
401C22×C11#53811yescharacteristic
402C22×C11#53811yescharacteristic
403C22×C11#53812yes—
404C22×C11#53812yes—
405C22×C11D4211yescharacteristic
406C22×C11#54612yes—
407C22×C11#54612yes—
408C22×C11#54612yes—
409C22×C11#55112yes—
410C22×C11#55112yes—
411C22×C11#55111yescharacteristic
412C22×C11#56011yescharacteristic
413C22×C11#56012yes—
414C22×C11H(3,𝔽4)11yescharacteristic
415C4×C11—44no—
416C4×C11—42no—
417C4×C11—42no—
418Dic11—44no—
419Dic11—44no—
420Dic11—82no—
421Dic11—82no—
422C25—22no—
423C25—22no—
424C25—24no—
425C25—24no—
426C25—42no—
427C25—42no—
428C25—41no—
429C25—41no—
430C25—41no—
431C25—41no—
432C25C2×Dic1114yes—
433C25C22×D1111yescharacteristic
434C25C22×D1112yes—
435C23×C4—112no—
436C23×C4—112no—
437C23×C4—112no—
438C23×C4—112no—
439C23×C4C22×D1111yescharacteristic
440C23×C4C22×D1111yescharacteristic
441C23×C4C22×D1112yes—
442C2×C4⋊C4—224no—
443C2×C4⋊C4—441no—
444C2×C4⋊C4—442no—
445C2×C4⋊C4—441no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—41no—
449C2×C22⋊C4—41no—
450C2×C22⋊C4—42no—
451C2×C22⋊C4—42no—
452C2×C22⋊C4—41no—
453C2×C22⋊C4—41no—
454C2×C22⋊C4—118no—
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—224no—
462C2×C22⋊C4—224no—
463C2×C22⋊C4—224no—
464C2×C22⋊C4—442no—
465C2×C22⋊C4—442no—
466C2×C22⋊C4—442no—
467C2×C22⋊C4—442no—
468C2×C22⋊C4—442no—
469C2×C22⋊C4—442no—
470C2×C22⋊C4—442no—
471C2×C22⋊C4—442no—
472C2×C22⋊C4C2×Dic1118yes—
473C2×C22⋊C4C2×Dic1114yes—
474C2×C22⋊C4C2×Dic1114yes—
475C2×C22⋊C4C2×Dic1118yes—
476C2×C42—224no—
477C2×C42—442no—
478C2×C42—442no—
479#95—224no—
480#95—224no—
481#95—441no—
482#95—442no—
483#95—442no—
484#95—442no—
485#95—441no—
486C2×C11—44no—
487C2×C11—48no—
488C2×C11#231211yescharacteristic
489C2×C11#232112yes—
490C2×C11#234212yes—
491C2×C11#235811yescharacteristic
492C2×C11#237511yescharacteristic
493C2×C11#266811yescharacteristic
494C2×C11#267011yescharacteristic
495C2×C11#268512yes—
496C2×C11#269712yes—
497C2×C11#273511yescharacteristic
498C2×C11#273611yescharacteristic
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—28no—
520C24—216no—
521C24—48no—
522C24—44no—
523C24—44no—
524C24—48no—
525C24—48no—
526C24—48no—
527C24—48no—
528C24—44no—
529C24—44no—
530C24—48no—
531C24—44no—
532C24—44no—
533C24—44no—
534C24—44no—
535C24—48no—
536C24—48no—
537C24—48no—
538C24—48no—
539C24—44no—
540C24—48no—
541C24—44no—
542C24#433912yes—
543C24#433912yes—
544C24D4×D1114yes—
545C24#434114yes—
546C24C22×Dic1112yes—
547C24C22×Dic1114yes—
548C24C23×D1111yescharacteristic
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—114no—
564C22×C4—114no—
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—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4C22×Dic1112yes—
592C22×C4C22×Dic1114yes—
593C22×C4C22×Dic1112yes—
594C4⋊C4—444no—
595C4⋊C4—444no—
596C22⋊C4—216no—
597C22⋊C4—48no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—448no—
601C22⋊C4—448no—
602C22⋊C4—448no—
603C22⋊C4—448no—
604C22⋊C4—448no—
605C22⋊C4—448no—
606C42—448no—
607C11#1436611yescharacteristic, complemented, Sylow
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—22no—
625C23—22no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—432no—
639C23—416no—
640C23—416no—
641C23—432no—
642C23—432no—
643C23—416no—
644C23—416no—
645C23—416no—
646C23—416no—
647C23—416no—
648C23—432no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—41no—
658C23—42no—
659C23—42no—
660C23—41no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—41no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—41no—
674C23—42no—
675C23#6697914yes—
676C23D4×Dic1118yes—
677C23C2×#433911yescharacteristic
678C23C2×#433911yescharacteristic
679C23C2×D4×D1112yes—
680C23C2×#434112yes—
681C23#6703712yes—
682C23#6703712yes—
683C23#6703711yescharacteristic
684C23#6703711yescharacteristic
685C23#6703711yescharacteristic
686C23#6703711yescharacteristic
687C23C23×Dic1111yescharacteristic
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—224no—
706C2×C4—224no—
707C2×C4—224no—
708C2×C4—224no—
709C2×C4—224no—
710C2×C4—224no—
711C2×C4—442no—
712C2×C4—442no—
713C2×C4—442no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—442no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4—442no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4—442no—
732C2×C4—442no—
733C22—28no—
734C22—28no—
735C22—24no—
736C22—28no—
737C22—28no—
738C22—464no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—42no—
745C22—44no—
746C22—42no—
747C22—44no—
748C22—42no—
749C22—44no—
750C22—44no—
751C22—44no—
752C22—42no—
753C22—44no—
754C22—42no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—42no—
760C22#1062302112yes—
761C22#1062302112yes—
762C22#1062302511yescharacteristic
763C22#1062302511yescharacteristic
764C22#1062302511yescharacteristic
765C22#1062302511yescharacteristic
766C22#1062302612yes—
767C22#1062302612yes—
768C22#1062311811yescharacteristic
769C22#1062312012yes—
770C22#1062312111yescharacteristic
771C22#1062312212yes—
772C22#1062312312yes—
773C22#1062312412yes—
774C22#1062312412yes—
775C22#1062312511yescharacteristic
776C22#1062312612yes—
777C22#1062312611yescharacteristic
778C22C2×#6697911yescharacteristic
779C22C2×D4×Dic1112yes—
780C22#1062332912yes—
781C22#1062332911yescharacteristic
782C22#1062332911yescharacteristic
783C4—42no—
784C4—44no—
785C4—42no—
786C4—444no—
787C4—444no—
788C4—882no—
789C4—882no—
790C2—44no—
791C2—48no—
792C2#1307121411yescharacteristic
793C2#1307127712yes—
794C2#1307146512yes—
795C2#1307160011yescharacteristic
796C2#1307175711yescharacteristic
797C2#1307482411yescharacteristic
798C2#1307484211yescharacteristic
799C2#1307500712yes—
800C2#1307517912yes—
801C2#1307565711yescharacteristic
802C2#1307566211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#379C2
socle, cosocleC24×C11C24
prime radicalC26×C11C22
hypercenterC2×#379D11
hypocenterC11#14366
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C2×#10622564C2semidirect
3. #13066865C2semidirect
4. #13066861C2semidirect
5. #13066861C2semidirect
6. #13066861C2semidirect
7. #13066853C2semidirect
8. #13066853C2semidirect
21. C22×C4⋊Dic11C22semidirect
22. C22×C4⋊Dic11C22semidirect
23. C22×C4×Dic11C22semidirect
24. C11×#379C4semidirect
26. C2×C11⋊#95C22semidirect
27. C2×C11⋊#95C22semidirect
28. C2×C11⋊#95C22semidirect
29. C2×C11⋊#95C22semidirect
30. C2×C11⋊#95C22semidirect
31. C2×C11⋊#95C22semidirect
32. C2×C11⋊#95C22semidirect
357. #379Dic11semidirect
607. C11#14366semidirect

Maximal subgroups

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

subgroupindex
C2×#106225642
C2×#106228602
#130668652
#130668612
#130668532
C2×C11×#3792
#1436611