Finite Group Databasebeta

← #14788622

Subgroups — #14788622

Order 2816.

1138 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622667C211yesmaximal, characteristic, complemented
2C2×C4×#4324C211yesmaximal, characteristic, complemented
3#13073982C211yesmaximal, characteristic, complemented
4#13069852C211yesmaximal, characteristic, complemented
5#13069847C211yesmaximal, characteristic
6#13069710C211yesmaximal, characteristic, complemented
7#13069704C211yesmaximal, characteristic
8#13069553C211yesmaximal, characteristic, complemented
9#13069428C211yesmaximal, characteristic, complemented
10#13068957C211yesmaximal, characteristic, complemented
11#13068950C211yesmaximal, characteristic, complemented
12#13068884C211yesmaximal, characteristic, complemented
13#13068877C211yesmaximal, characteristic, complemented
14#13068626C211yesmaximal, characteristic, complemented
15C2×C11×#559C211yesmaximal, characteristic
16C11×#559—24no—
17C11×#559—24no—
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
29C22×#4326C2211yescharacteristic
30C22×#4324C2211yescharacteristic
31C22×#4324C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33#10622842—21no—
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43#10622667—24no—
44C4×#4324—24no—
45#10622595—21no—
46#10622591—21no—
47#10622591—21no—
48C2×#66874C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50#10622549C2211yescharacteristic
51#10622542C2211yescharacteristic
52#10622542C2211yescharacteristic
53#10622541C2211yescharacteristic
54#10622541C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4×C11⋊C8C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×Q8×C11D411yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11—21no—
66C22×D4×C11—21no—
67C22×D4×C11C2311yescharacteristic
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11—21no—
71C22×Dic22C2311yescharacteristic
72C11×#127—22no—
73C11×#127—22no—
74C11×#124—28no—
75C11×#124—22no—
76C11×#124—22no—
77C11×#124—22no—
78C11×#124D414yes—
79C11×#123—28no—
80C11×#123—28no—
81C4×Q8×C11—22no—
82C4×Q8×C11—22no—
83C4×Q8×C11—22no—
84C4×Q8×C11—22no—
85C4×D4×C11—28no—
86C4×D4×C11—22no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11D414yes—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4D411yescharacteristic
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C42×C11—21no—
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×#4326—22no—
106C2×#4326—22no—
107C2×#4326—41no—
108C2×#4324—22no—
109C2×#4324—22no—
110C2×#4324—22no—
111C2×#4324—22no—
112C2×#4324—22no—
113C2×#4324—41no—
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2311yescharacteristic
117C2×Dic11⋊C4—21no—
118C2×Dic11⋊C4—21no—
119C2×Dic11⋊C4—21no—
120C2×C4×Dic11—21no—
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C4×Dic22—22no—
126C4×Dic22—22no—
127#66899—22no—
128#66899—22no—
129#66899—41no—
130#66896—22no—
131#66896—22no—
132#66896—22no—
133#66896—41no—
134#66896—41no—
135#66896—41no—
136C11⋊#95—21no—
137C11⋊#95—21no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144#66874—22no—
145#66872—22no—
146C4⋊(C11⋊C8)—22no—
147C4×C11⋊C8—22no—
148#24194—111nomaximal, Sylow
149C24×C11—21no—
150C24×C11—21no—
151C2×Q8×C11—22no—
152C2×Q8×C11—22no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—41no—
159C2×Q8×C11C2×D412yes—
160C2×D4×C11—24no—
161C2×D4×C11—24no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—42no—
173C2×D4×C11—42no—
174C2×D4×C11—81no—
175C2×D4×C11—81no—
176C2×D4×C11C2×D412yes—
177C2×D4×C11C2×D412yes—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—24no—
181C22×C4×C11—24no—
182C22×C4×C11—81no—
183C22×C4×C11—81no—
184C22×C4×C11—81no—
185C22×C4×C11—81no—
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2411yescharacteristic
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C2×Dic22—21no—
198C2×Dic22—21no—
199C2×Dic22—21no—
200C2×Dic22—21no—
201C2×Dic22—21no—
202C2×Dic22#4112yes—
203C11×C4⋊C4—24no—
204C11×C4⋊C4—22no—
205C11×C4⋊C4—22no—
206C11×C4⋊C4—22no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4C2×D412yes—
209C11×C22⋊C4—24no—
210C11×C22⋊C4—24no—
211C11×C22⋊C4—24no—
212C11×C22⋊C4—24no—
213C11×C22⋊C4—24no—
214C11×C22⋊C4—24no—
215C42×C11—24no—
216C42×C11—21no—
217C42×C11—21no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11C2×D412yes—
221C42×C11C2×D412yes—
222#4326—44no—
223#4324—28no—
224#4324—44no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231Dic11⋊C4—42no—
232Dic11⋊C4—42no—
233Dic11⋊C4—42no—
234C4×Dic11—42no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8#4112yes—
247C2×#559D1111yescharacteristic
248C2×#464—111no—
249C2×C4×SD16—111no—
250#2581—111no—
251#2042—111no—
252#2041—111no—
253#2015—111no—
254#2014—111no—
255#1984—111no—
256#1958—111no—
257#1878—111no—
258#1877—111no—
259#1865—111no—
260#1864—111no—
261#1804—111no—
262C23×C11—22no—
263C23×C11—22no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11C22×D411yescharacteristic
277Q8×C11—22no—
278Q8×C11—22no—
279Q8×C11—44no—
280Q8×C11—41no—
281Q8×C11—41no—
282D4×C11—22no—
283D4×C11—22no—
284D4×C11—22no—
285D4×C11—22no—
286D4×C11—48no—
287D4×C11—41no—
288D4×C11—41no—
289D4×C11—41no—
290D4×C11—41no—
291D4×C11—84no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—22no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—22no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—84no—
314C2×C4×C11—84no—
315C2×C4×C11#12012yes—
316C2×C4×C11#12012yes—
317C2×C4×C11#13512yes—
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C22×D411yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11C2×#4111yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C2×C4×C112−1+411yescharacteristic
324C2×Dic11—22no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336Dic22—22no—
337Dic22—22no—
338Dic22—41no—
339Dic22—41no—
340C11⋊C8—22no—
341C11⋊C8—41no—
342C11⋊C8—41no—
343C11⋊C8—41no—
344C22×Q16—111no—
345C22×SD16—111no—
346C22×SD16—111no—
347#559—24no—
348#559—24no—
349C2×#127C2×D1111yescharacteristic
350C2×#124—21no—
351C2×#124C2×D1111yescharacteristic
352C2×#124C2×D1111yescharacteristic
353C2×#123—21no—
354C2×#123—21no—
355C2×C4×Q8—111no—
356C2×C4×Q8C2×D1111yescharacteristic
357C2×C4×Q8C2×D1111yescharacteristic
358C2×C4×D4—21no—
359C2×C4×D4C2×D1111yescharacteristic
360C2×C4×D4C2×D1111yescharacteristic
361#464—224no—
362C4×SD16—224no—
363C2×#106—111no—
364C2×C4⋊C8—111no—
365C2×#103—111no—
366C2×#103—111no—
367C2×#103—111no—
368C2×#103—111no—
369C2×#102—111no—
370C2×#102—111no—
371C2×#102—111no—
372C2×#102—111no—
373C2×#102—111no—
374C2×#102—111no—
375C2×C4×C8—111no—
376#400—221no—
377#395—221no—
378#391—111no—
379#391—111no—
380#389—111no—
381#389—111no—
382#387—221no—
383#387—221no—
384#382—111no—
385#340—111no—
386#340—111no—
387#336—111no—
388#336—111no—
389#336—111no—
390#336—111no—
391C22×C11—42no—
392C22×C11—42no—
393C22×C11—42no—
394C22×C11—42no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11C2×#12011yescharacteristic
406C22×C11#54811yescharacteristic
407C22×C11#55011yescharacteristic
408C22×C11C2×#13511yescharacteristic
409C22×C11#57511yescharacteristic
410C22×C11#57711yescharacteristic
411C22×C11#57711yescharacteristic
412C4×C11—22no—
413C4×C11—22no—
414C4×C11—22no—
415C4×C11—42no—
416C4×C11—41no—
417C4×C11—41no—
418C4×C11—41no—
419C4×C11—42no—
420C4×C11#52511yescharacteristic
421C4×C11#53711yescharacteristic
422C4×C11#54611yescharacteristic
423C4×C11#54711yescharacteristic
424Dic11—42no—
425Dic11—81no—
426Dic11—81no—
427Dic11—81no—
428C22×Q8—111no—
429C22×Q8C22⋊D1111yescharacteristic
430C22×Q8C22×D1111yescharacteristic
431C22×D4—21no—
432C22×D4—21no—
433C22×D4C22×D1111yescharacteristic
434C22×D4C22×D1111yescharacteristic
435C23×C4—21no—
436C23×C4—21no—
437C2×Q16—222no—
438C2×Q16—222no—
439C2×Q16—441no—
440C2×SD16—222no—
441C2×SD16—222no—
442C2×SD16—222no—
443C2×SD16—222no—
444C2×SD16—222no—
445C2×SD16—441no—
446C22×C8—111no—
447C22×C8—111no—
448C22×C8—111no—
449C22×C8—111no—
450#127—22no—
451#127—22no—
452#124—28no—
453#124—22no—
454#124—22no—
455#124—22no—
456#124C22⋊D1114yes—
457#123—28no—
458#123—28no—
459C4×Q8—22no—
460C4×Q8—22no—
461C4×Q8—22no—
462C4×Q8—22no—
463C4×Q8—222no—
464C4×Q8—222no—
465C4×D4—28no—
466C4×D4—22no—
467C4×D4—22no—
468C4×D4—22no—
469C4×D4C22⋊D1114yes—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4—111no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4—221no—
475C2×C4⋊C4—221no—
476C2×C4⋊C4—221no—
477C2×C4⋊C4C22⋊D1111yescharacteristic
478C2×C4⋊C4C22⋊D1111yescharacteristic
479C2×C4⋊C4C22⋊D1111yescharacteristic
480C2×C4⋊C4C22×D1111yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C42—21no—
488C2×C42—221no—
489C2×C42C22×D1111yescharacteristic
490C2×C42C22×D1111yescharacteristic
491C2×C42C22×D1111yescharacteristic
492#106—222no—
493C4⋊C8—222no—
494#103—222no—
495#103—222no—
496#103—222no—
497#103—441no—
498#102—222no—
499#102—222no—
500#102—222no—
501#102—441no—
502#102—441no—
503#102—441no—
504C4×C8—222no—
505#95—221no—
506#95—221no—
507#95—221no—
508#95—221no—
509#95—221no—
510#95—221no—
511#95—221no—
512#95—221no—
513C2×C11—82no—
514C2×C11—82no—
515C2×C11#240711yescharacteristic
516C2×C11#300211yescharacteristic
517C2×C11#300911yescharacteristic
518C2×C11#336511yescharacteristic
519C2×C11#337111yescharacteristic
520C2×C11#339411yescharacteristic
521C2×C11#340111yescharacteristic
522C24—21no—
523C24—21no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—41no—
532C2×Q8—112no—
533C2×Q8—221no—
534C2×Q8—221no—
535C2×Q8—221no—
536C2×Q8—221no—
537C2×Q8—221no—
538C2×Q8C2×C22⋊D1112yes—
539C2×D4—24no—
540C2×D4—24no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—81no—
554C2×D4—81no—
555C2×D4C2×C22⋊D1112yes—
556C2×D4C2×C22⋊D1112yes—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—81no—
562C22×C4—81no—
563C22×C4—81no—
564C22×C4—81no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4C2×C22⋊D1111yescharacteristic
570C22×C4C2×C22⋊D1111yescharacteristic
571C22×C4C2×C22⋊D1111yescharacteristic
572C22×C4C2×C22⋊D1111yescharacteristic
573C22×C4C2×C22⋊D1111yescharacteristic
574C22×C4C2×C22⋊D1111yescharacteristic
575C22×C4C23×D1111yescharacteristic
576Q16—444no—
577SD16—228no—
578SD16—444no—
579C2×C8—112no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C2×C8—221no—
587C2×C8—221no—
588C2×C8—221no—
589C2×C8—221no—
590C2×C8—221no—
591C4⋊C4—24no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—221no—
600C4⋊C4—221no—
601C4⋊C4—221no—
602C4⋊C4—442no—
603C4⋊C4—442no—
604C4⋊C4—442no—
605C4⋊C4C2×C22⋊D1112yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C42—24no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—442no—
618C42C2×C22⋊D1112yes—
619C42C2×C22⋊D1112yes—
620C11#2419411yescharacteristic, complemented, Sylow
621C23—22no—
622C23—22no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23C22×C22⋊D1111yescharacteristic
636Q8—22no—
637Q8—22no—
638Q8—44no—
639Q8—41no—
640Q8—41no—
641Q8—222no—
642Q8—222no—
643Q8—441no—
644Q8—441no—
645D4—22no—
646D4—22no—
647D4—22no—
648D4—22no—
649D4—48no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—84no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—84no—
677C2×C4—84no—
678C2×C4—222no—
679C2×C4—441no—
680C2×C4—441no—
681C2×C4—441no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4#6700312yes—
691C2×C4#6700612yes—
692C2×C4#6700612yes—
693C2×C4#41×D1111yescharacteristic
694C2×C4#41×D1111yescharacteristic
695C2×C4#6704211yescharacteristic
696C2×C4#6704311yescharacteristic
697C2×C4C22×C22⋊D1111yescharacteristic
698C2×C4C22×C22⋊D1111yescharacteristic
699C8—222no—
700C8—441no—
701C8—441no—
702C8—441no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22C2×#6700311yescharacteristic
718C22#1062335311yescharacteristic
719C22#1062336211yescharacteristic
720C22#1062336511yescharacteristic
721C22#1062336711yescharacteristic
722C22#1062336711yescharacteristic
723C22C2×#6700611yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—41no—
728C4—42no—
729C4—41no—
730C4—41no—
731C4—42no—
732C4—442no—
733C4—881no—
734C4—881no—
735C4—881no—
736C4#1062335511yescharacteristic
737C4#1062335911yescharacteristic
738C4#1062336011yescharacteristic
739C4#1062336411yescharacteristic
740C2—82no—
741C2—82no—
742C2#1307195511yescharacteristic
743C2#1307783411yescharacteristic
744C2#1307789311yescharacteristic
745C2#1308130811yescharacteristic
746C2#1308137811yescharacteristic
747C2#1308160811yescharacteristic
748C2#1308167611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#559C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenterC2×#559D11
hypocenterC11#24194
LCSG ▷ C22×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×#10622667C2semidirect
2. C2×C4×#4324C2semidirect
3. #13073982C2semidirect
4. #13069852C2semidirect
6. #13069710C2semidirect
8. #13069553C2semidirect
9. #13069428C2semidirect
10. #13068957C2semidirect
11. #13068950C2semidirect
12. #13068884C2semidirect
13. #13068877C2semidirect
14. #13068626C2semidirect
620. C11#24194semidirect

Maximal subgroups

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

subgroupindex
C2×#106226672
C2×C4×#43242
#130739822
#130698522
#130698472
#130697102
#130697042
#130695532
#130694282
#130689572
#130689502
#130688842
#130688772
#130686262
C2×C11×#5592
#2419411