Finite Group Databasebeta

← #14770659

Subgroups — #14770659

Order 2816.

1118 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622637C211yesmaximal, characteristic, complemented
2#13071573C211yesmaximal, characteristic, complemented
3#13069549C211yesmaximal, characteristic, complemented
4#13069549C211yesmaximal, characteristic, complemented
5#13069544C211yesmaximal, characteristic
6#13069441C211yesmaximal, characteristic
7#13069433C211yesmaximal, characteristic, complemented
8#13069428C211yesmaximal, characteristic, complemented
9#13068631C211yesmaximal, characteristic, complemented
10#13068626C211yesmaximal, characteristic, complemented
11#13068616C211yesmaximal, characteristic, complemented
12#13068446C211yesmaximal, characteristic, complemented
13#13068441C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C2×C11×#559C211yesmaximal, characteristic
16C11×#559—24no—
17C11×#559C418yescomplemented
18C2×C11×#127C2211yescharacteristic
19C2×C11×#124—21no—
20C2×C11×#124C2211yescharacteristic
21C2×C11×#124C2211yescharacteristic
22C2×C11×#123—21no—
23C2×C11×#123—21no—
24C2×C4×Q8×C11C2211yescharacteristic
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×D4×C11—21no—
27C2×C4×D4×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29#10622843—21no—
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42#10622637—24no—
43#10622594—21no—
44#10622594—21no—
45C4⋊C4×Dic11—21no—
46#10622549C2211yescharacteristic
47#10622549C2211yescharacteristic
48#10622548C2211yescharacteristic
49C4×C4⋊Dic11C2211yescharacteristic
50C4×C4⋊Dic11C2211yescharacteristic
51C4×C4⋊Dic11C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55C2×#66867C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57C2×C4×C11⋊C8C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11D411yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11C2311yescharacteristic
67C22×D4×C11C2311yescharacteristic
68C23×C4×C11—21no—
69C23×C4×C11—21no—
70C11×#127—22no—
71C11×#127C2×C414yes—
72C11×#124—28no—
73C11×#124—22no—
74C11×#124—22no—
75C11×#124C2×C414yes—
76C11×#124C2×C414yes—
77C11×#123—28no—
78C11×#123—28no—
79C4×Q8×C11—22no—
80C4×Q8×C11C2×C414yes—
81C4×Q8×C11C2×C414yes—
82C4×Q8×C11D414yes—
83C4×D4×C11—28no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11C2×C414yes—
87C4×D4×C11C2×C414yes—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4D411yescharacteristic
91C2×C11×C4⋊C4D411yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C42×C11—21no—
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2311yescharacteristic
102C2×C42×C11C2311yescharacteristic
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116#66899—22no—
117#66899—22no—
118#66899—41no—
119#66899—41no—
120#66896—22no—
121#66896—22no—
122#66896—22no—
123#66896—22no—
124#66896—41no—
125#66896—41no—
126#66896—41no—
127#66896—41no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C11⋊#95—21no—
134C11⋊#95—21no—
135C4⋊(C11⋊C8)—22no—
136C4⋊(C11⋊C8)—22no—
137C4⋊(C11⋊C8)—22no—
138#66867—22no—
139#66867—22no—
140C4×C11⋊C8—22no—
141#22549—111nomaximal, Sylow
142C24×C11—21no—
143C24×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—41no—
150C2×Q8×C11—41no—
151C2×Q8×C11C22⋊C414yes—
152C2×Q8×C11C22×C412yes—
153C2×D4×C11—24no—
154C2×D4×C11—24no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11—81no—
168C2×D4×C11—81no—
169C2×D4×C11C22×C412yes—
170C2×D4×C11C22×C412yes—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—24no—
174C22×C4×C11—24no—
175C22×C4×C11—81no—
176C22×C4×C11—81no—
177C22×C4×C11—81no—
178C22×C4×C11—81no—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4C22⋊C414yes—
193C11×C4⋊C4C22⋊C414yes—
194C11×C4⋊C4C22⋊C414yes—
195C11×C4⋊C4C22×C412yes—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—24no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—24no—
200C11×C22⋊C4—24no—
201C11×C22⋊C4—24no—
202C42×C11—24no—
203C42×C11C22×C412yes—
204C42×C11C22×C412yes—
205C42×C11C22×C412yes—
206C42×C11C2×D412yes—
207C42×C11C2×D412yes—
208C42×C11C2×D412yes—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—42no—
217C4⋊Dic11—81no—
218C4⋊Dic11#4112yes—
219C4×Dic11—42no—
220C4×Dic11—81no—
221C4×Dic11—81no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8#4112yes—
234C2×#559D1111yescharacteristic
235C2×#446—111no—
236#2355—111no—
237#1983—111no—
238#1983—111no—
239#1982—111no—
240#1961—111no—
241#1959—111no—
242#1958—111no—
243#1805—111no—
244#1804—111no—
245#1802—111no—
246#1763—111no—
247#1762—111no—
248C4×#102—111no—
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11C22×D411yescharacteristic
264Q8×C11—22no—
265Q8×C11—22no—
266Q8×C11—44no—
267Q8×C11—41no—
268Q8×C11—41no—
269D4×C11—22no—
270D4×C11—22no—
271D4×C11—22no—
272D4×C11—22no—
273D4×C11—48no—
274D4×C11—41no—
275D4×C11—41no—
276D4×C11—41no—
277D4×C11—41no—
278D4×C11—84no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—84no—
298C2×C4×C11—84no—
299C2×C4×C11C2×C22⋊C412yes—
300C2×C4×C11C2×C22⋊C412yes—
301C2×C4×C11C2×C22⋊C412yes—
302C2×C4×C11C2×C22⋊C412yes—
303C2×C4×C11C2×C22⋊C412yes—
304C2×C4×C11C2×C22⋊C412yes—
305C2×C4×C11C23×C411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11H(5,𝔽2)11yescharacteristic
310C2×C4×C112−1+411yescharacteristic
311C2×Dic11—22no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C11⋊C8—22no—
324C11⋊C8—41no—
325C11⋊C8—41no—
326C11⋊C8—41no—
327#559—24no—
328#559Dic1118yescomplemented
329C2×#127C2×D1111yescharacteristic
330C2×#124—21no—
331C2×#124C2×D1111yescharacteristic
332C2×#124C2×D1111yescharacteristic
333C2×#123—21no—
334C2×#123—21no—
335C2×C4×Q8C2×D1111yescharacteristic
336C2×C4×Q8C2×D1111yescharacteristic
337C2×C4×D4—21no—
338C2×C4×D4C2×D1111yescharacteristic
339C2×C4×D4C2×D1111yescharacteristic
340#446—224no—
341C2×C4⋊C8—111no—
342C2×C4⋊C8—111no—
343C2×C4⋊C8—111no—
344C2×#103—111no—
345C2×#103—111no—
346C2×#103—111no—
347C2×#103—111no—
348C2×#102—111no—
349C2×#102—111no—
350C2×#102—111no—
351C2×#102—111no—
352C2×#102—111no—
353C2×#102—111no—
354C2×#102—111no—
355C2×#102—111no—
356C2×#97—111no—
357C2×#97—111no—
358C2×C4×C8—111no—
359#391—221no—
360#387—221no—
361#387—221no—
362#384—111no—
363#382—111no—
364#382—111no—
365C4×C4⋊C4—111no—
366C4×C4⋊C4—111no—
367C4×C4⋊C4—111no—
368C4×C4⋊C4—221no—
369#340—111no—
370#340—111no—
371#340—111no—
372#340—111no—
373C22×C11—42no—
374C22×C11—42no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—42no—
378C22×C11—42no—
379C22×C11—81no—
380C22×C11—81no—
381C22×C11—81no—
382C22×C11—81no—
383C22×C11—81no—
384C22×C11—81no—
385C22×C11—81no—
386C22×C11—81no—
387C22×C11C22×C22⋊C411yescharacteristic
388C22×C11#54811yescharacteristic
389C22×C11#55011yescharacteristic
390C22×C11#57511yescharacteristic
391C22×C11#57511yescharacteristic
392C22×C11#57611yescharacteristic
393C22×C11#57711yescharacteristic
394C4×C11—22no—
395C4×C11—22no—
396C4×C11—22no—
397C4×C11—22no—
398C4×C11—22no—
399C4×C11—22no—
400C4×C11—42no—
401C4×C11—42no—
402C4×C11C4×#4111yescharacteristic
403C4×C11#52011yescharacteristic
404C4×C11#54811yescharacteristic
405C4×C11#55011yescharacteristic
406Dic11—42no—
407Dic11—81no—
408Dic11—81no—
409Dic11—81no—
410C22×Q8C22⋊D1111yescharacteristic
411C22×Q8C22×D1111yescharacteristic
412C22×D4—21no—
413C22×D4—21no—
414C22×D4C22×D1111yescharacteristic
415C22×D4C22×D1111yescharacteristic
416C23×C4—21no—
417C23×C4—21no—
418C22×C8—111no—
419C22×C8—111no—
420C22×C8—111no—
421C22×C8—111no—
422#127—22no—
423#127C2×Dic1114yes—
424#124—28no—
425#124—22no—
426#124—22no—
427#124C2×Dic1114yes—
428#124C2×Dic1114yes—
429#123—28no—
430#123—28no—
431C4×Q8—22no—
432C4×Q8C2×Dic1114yes—
433C4×Q8C2×Dic1114yes—
434C4×Q8C22⋊D1114yes—
435C4×D4—28no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4C2×Dic1114yes—
439C4×D4C2×Dic1114yes—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—111no—
442C2×C4⋊C4—111no—
443C2×C4⋊C4—111no—
444C2×C4⋊C4—111no—
445C2×C4⋊C4—221no—
446C2×C4⋊C4—221no—
447C2×C4⋊C4C22⋊D1111yescharacteristic
448C2×C4⋊C4C22⋊D1111yescharacteristic
449C2×C4⋊C4C22⋊D1111yescharacteristic
450C2×C4⋊C4C22×D1111yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C42—21no—
458C2×C42—221no—
459C2×C42—221no—
460C2×C42—221no—
461C2×C42C22×D1111yescharacteristic
462C2×C42C22×D1111yescharacteristic
463C2×C42C22×D1111yescharacteristic
464C4⋊C8—222no—
465C4⋊C8—222no—
466C4⋊C8—222no—
467#103—222no—
468#103—222no—
469#103—441no—
470#103—441no—
471#102—222no—
472#102—222no—
473#102—222no—
474#102—222no—
475#102—441no—
476#102—441no—
477#102—441no—
478#102—441no—
479#97—222no—
480#97—222no—
481C4×C8—222no—
482#95—221no—
483#95—221no—
484#95—221no—
485#95—221no—
486#95—221no—
487#95—221no—
488#95—221no—
489C2×C11—82no—
490C2×C11—82no—
491C2×C11#234111yescharacteristic
492C2×C11#289611yescharacteristic
493C2×C11#289711yescharacteristic
494C2×C11#337011yescharacteristic
495C2×C11#337111yescharacteristic
496C2×C11#340111yescharacteristic
497C2×C11#340311yescharacteristic
498C24—21no—
499C24—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—41no—
506C2×Q8—41no—
507C2×Q8C22⋊Dic1114yes—
508C2×Q8C22×Dic1112yes—
509C2×D4—24no—
510C2×D4—24no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—81no—
524C2×D4—81no—
525C2×D4C22×Dic1112yes—
526C2×D4C22×Dic1112yes—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4—221no—
536C22×C4—221no—
537C22×C4—221no—
538C22×C4—221no—
539C22×C4C2×C22⋊D1111yescharacteristic
540C22×C4C2×C22⋊D1111yescharacteristic
541C22×C4C2×C22⋊D1111yescharacteristic
542C22×C4C2×C22⋊D1111yescharacteristic
543C22×C4C2×C22⋊D1111yescharacteristic
544C22×C4C2×C22⋊D1111yescharacteristic
545C22×C4C23×D1111yescharacteristic
546C2×C8—112no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—221no—
553C2×C8—221no—
554C2×C8—221no—
555C2×C8—221no—
556C2×C8—221no—
557C2×C8—221no—
558C4⋊C4—24no—
559C4⋊C4—21no—
560C4⋊C4—112no—
561C4⋊C4—221no—
562C4⋊C4—221no—
563C4⋊C4—221no—
564C4⋊C4—221no—
565C4⋊C4—221no—
566C4⋊C4—221no—
567C4⋊C4—221no—
568C4⋊C4—442no—
569C4⋊C4—881no—
570C4⋊C4C22⋊Dic1114yes—
571C4⋊C4C22⋊Dic1114yes—
572C4⋊C4C22⋊Dic1114yes—
573C4⋊C4C22×Dic1112yes—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C42—24no—
581C42—442no—
582C42—881no—
583C42—881no—
584C42C22×Dic1112yes—
585C42C22×Dic1112yes—
586C42C22×Dic1112yes—
587C42C2×C22⋊D1112yes—
588C42C2×C22⋊D1112yes—
589C42C2×C22⋊D1112yes—
590C11#2254911yescharacteristic, complemented, Sylow
591C23—22no—
592C23—22no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C22×C22⋊D1111yescharacteristic
606Q8—22no—
607Q8—22no—
608Q8—44no—
609Q8—41no—
610Q8—41no—
611D4—22no—
612D4—22no—
613D4—22no—
614D4—22no—
615D4—48no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—84no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—84no—
640C2×C4—84no—
641C2×C4—222no—
642C2×C4—441no—
643C2×C4—441no—
644C2×C4—441no—
645C2×C4—441no—
646C2×C4—441no—
647C2×C4—441no—
648C2×C4—441no—
649C2×C4—441no—
650C2×C4—441no—
651C2×C4—441no—
652C2×C4—441no—
653C2×C4C2×C22⋊Dic1112yes—
654C2×C4C2×C22⋊Dic1112yes—
655C2×C4C2×C22⋊Dic1112yes—
656C2×C4C2×C22⋊Dic1112yes—
657C2×C4C2×C22⋊Dic1112yes—
658C2×C4C2×C22⋊Dic1112yes—
659C2×C4#41×D1111yescharacteristic
660C2×C4#41×D1111yescharacteristic
661C2×C4#6704211yescharacteristic
662C2×C4#6704311yescharacteristic
663C2×C4C23×Dic1111yescharacteristic
664C2×C4C22×C22⋊D1111yescharacteristic
665C8—222no—
666C8—441no—
667C8—441no—
668C8—441no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22#1062335311yescharacteristic
684C22#1062335311yescharacteristic
685C22#1062336211yescharacteristic
686C22#1062336511yescharacteristic
687C22#1062336611yescharacteristic
688C22#1062336711yescharacteristic
689C22C22×C22⋊Dic1111yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—22no—
696C4—42no—
697C4—42no—
698C4—442no—
699C4—881no—
700C4—881no—
701C4—881no—
702C4#41×Dic1111yescharacteristic
703C4#1062335811yescharacteristic
704C4#1062336211yescharacteristic
705C4#1062336511yescharacteristic
706C2—82no—
707C2—82no—
708C2#1307145711yescharacteristic
709C2#1307713511yescharacteristic
710C2#1307714211yescharacteristic
711C2#1308136311yescharacteristic
712C2#1308137811yescharacteristic
713C2#1308167611yescharacteristic
714C2#1308170011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#559C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
cosocleC22×C4×C11C24
hypercenterC2×#559D11
hypocenterC11#22549
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#10622637C2semidirect
2. #13071573C2semidirect
3. #13069549C2semidirect
4. #13069549C2semidirect
7. #13069433C2semidirect
8. #13069428C2semidirect
9. #13068631C2semidirect
10. #13068626C2semidirect
11. #13068616C2semidirect
12. #13068446C2semidirect
13. #13068441C2semidirect
14. C4×#66896C2semidirect
17. C11×#559C4semidirect
328. #559Dic11semidirect
590. C11#22549semidirect

Maximal subgroups

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

subgroupindex
C2×#106226372
#130715732
#130695492
#130695442
#130694412
#130694332
#130694282
#130686312
#130686262
#130686162
#130684462
#130684412
C4×#668962
C2×C11×#5592
#2254911