Finite Group Databasebeta

← #14801922

Subgroups — #14801922

Order 2816.

1024 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622580C211yesmaximal, characteristic, complemented
2C2×#10622651C211yesmaximal, characteristic
3#13071630C211yesmaximal, characteristic, complemented
4#13070088C211yesmaximal, characteristic, complemented
5#13070020C211yesmaximal, characteristic, complemented
6#13070004C211yesmaximal, characteristic, complemented
7#13069926C211yesmaximal, characteristic, complemented
8#13069372C211yesmaximal, characteristic, complemented
9#13069233C211yesmaximal, characteristic, complemented
10#13068967C211yesmaximal, characteristic, complemented
11#13068934C211yesmaximal, characteristic, complemented
12#13068796C211yesmaximal, characteristic, complemented
13#13068613C211yesmaximal, characteristic, complemented
14C2×#10622167C211yesmaximal, characteristic, complemented
15C11×#2501C211yesmaximal, characteristic, complemented
16C2×C11×#123—21no—
17C2×C11×#123—21no—
18C2×C11×#121C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C23×C11⋊C8C2211yescharacteristic
24C2×(C22⋊D11)⋊C4—21no—
25C2×C4×D44C2211yescharacteristic
26C11×#399—21no—
27C11×#399—21no—
28C11×#390C2211yescharacteristic
29C11×#390C2211yescharacteristic
30C11×#384C2211yescharacteristic
31C11×#384C2211yescharacteristic
32C4×C11×C22⋊C4C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37#10622651—24no—
38#10622580—24no—
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622571—21no—
46#10622552C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622283—21no—
52#10622281—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11—21no—
66C23×Dic11—21no—
67C22×D44C2311yescharacteristic
68C22×C4×D11—21no—
69C11×#123—44no—
70C11×#123—44no—
71C11×#121—22no—
72C11×#121—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4D411yescharacteristic
89C2×C11×C22⋊C4D411yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×#4323—22no—
93C2×#4323—22no—
94C2×#4323—41no—
95#66983—22no—
96#66983D414yes—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11—41no—
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×Dic11⋊C4—21no—
108C2×C4×Dic11—21no—
109C22×C11⋊C8—22no—
110C22×C11⋊C8—22no—
111C22×C11⋊C8—41no—
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116(C22⋊D11)⋊C4—44no—
117C4×D44—22no—
118C4×D44—41no—
119C11×#95D411yescharacteristic
120C11×#95D411yescharacteristic
121#66896—22no—
122#66896—22no—
123#66896—41no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C22⋊(C11⋊C8)—22no—
127#66873—22no—
128#66873—22no—
129#66873—22no—
130#66871—22no—
131#66871—22no—
132#66871—22no—
133C4⋊(C11⋊C8)—22no—
134C4⋊(C11⋊C8)—41no—
135#25200—111nomaximal, Sylow
136C24×C11—21no—
137C24×C11C2×D411yescharacteristic
138C23×D11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—42no—
146C2×D4×C11—42no—
147C2×D4×C11—42no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11#4112yes—
165C22×C4×C11C2411yescharacteristic
166C2×C22⋊D11—24no—
167C2×C22⋊D11—42no—
168C2×C22⋊D11—42no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—42no—
173C22×Dic11—42no—
174C22×Dic11—81no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44C2×D412yes—
181C2×C4×D11—42no—
182C2×C4×D11—42no—
183C2×C4×D11—81no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—42no—
191C11×C4⋊C4—42no—
192C11×C4⋊C4—42no—
193C11×C4⋊C4—42no—
194C11×C4⋊C4—42no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—42no—
197C11×C22⋊C4—42no—
198C11×C22⋊C4—42no—
199C11×C22⋊C4—42no—
200C11×C22⋊C4—42no—
201C11×C22⋊C4D814yescomplemented
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206#4323—44no—
207(C2×D11)⋊C4—24no—
208(C2×D11)⋊C4—42no—
209(C2×D11)⋊C4—42no—
210(C2×D11)⋊C4—81no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—42no—
216C4⋊Dic11C2×D412yes—
217C4⋊Dic11#4112yes—
218Dic11⋊C4—42no—
219C4×Dic11—42no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
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—44no—
232C2×C11⋊C8#4112yes—
233C2×#480—111no—
234C2×#466—111no—
235#2501D1111yescharacteristic, complemented
236#2361—111no—
237#2083—111no—
238#2071—111no—
239#2067—111no—
240#2054—111no—
241#1947—111no—
242#1925—111no—
243#1879—111no—
244#1874—111no—
245#1850—111no—
246#1802—111no—
247C2×#340—111no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11#12112yes—
260C23×C11C2×D812yes—
261C23×C11AGL(1,ℤ/8)12yes—
262C23×C11C22×D411yescharacteristic
263C22×D11—22no—
264C22×D11—41no—
265C22×D11—41no—
266C22×D11—41no—
267C22×D11—41no—
268C22×D11—41no—
269C22×D11—41no—
270D4×C11—41no—
271D4×C11—41no—
272D4×C11—41no—
273D4×C11—41no—
274D4×C11—84no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
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—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—84no—
301C2×C4×C11#12112yes—
302C2×C4×C11C2×D812yes—
303C2×C4×C11C2×D812yes—
304C2×C4×C11C22×D411yescharacteristic
305C2×C4×C11C2×#4111yescharacteristic
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11H(5,𝔽2)11yescharacteristic
309C2×C4×C112−1+411yescharacteristic
310C22⋊D11—48no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—84no—
321D44—22no—
322D44—22no—
323D44—41no—
324D44—41no—
325C4×D11—84no—
326C11⋊C8—22no—
327C11⋊C8—41no—
328C11⋊C8—41no—
329C11⋊C8—41no—
330C22×D8—111no—
331C23×C8—111no—
332C2×#123—21no—
333C2×#123—21no—
334C2×#121—111no—
335C2×#121C2×D1111yescharacteristic
336C2×C4×D4—111no—
337C2×C4×D4—221no—
338C22×C4⋊C4—111no—
339C22×C4⋊C4C2×D1111yescharacteristic
340#480—224no—
341#466—224no—
342C2×#107—111no—
343C2×#107—111no—
344C2×#107—111no—
345C2×C4⋊C8—111no—
346C2×C4⋊C8—111no—
347C2×#102—111no—
348C2×#102—111no—
349C2×#102—111no—
350C2×#102—111no—
351C2×#102—111no—
352C2×#102—111no—
353C2×C22⋊C8—111no—
354#399—21no—
355#399—21no—
356#390—111no—
357#390C2×D1111yescharacteristic
358#390C2×D1111yescharacteristic
359#389—111no—
360#388—221no—
361#386—221no—
362#385—221no—
363#384C2×D1111yescharacteristic
364#384C2×D1111yescharacteristic
365C4×C4⋊C4—111no—
366C4×C22⋊C4C2×D1111yescharacteristic
367#340—111no—
368#340—111no—
369#340—111no—
370#340—111no—
371#340—111no—
372#340—111no—
373#336—111no—
374#336—111no—
375C22×C11—22no—
376C22×C11—22no—
377C22×C11—22no—
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—22no—
381C22×C11—81no—
382C22×C11—81no—
383C22×C11—81no—
384C22×C11—81no—
385C22×C11—81no—
386C22×C11—81no—
387C22×C11—81no—
388C22×C11#45914yes—
389C22×C11C2×#12111yescharacteristic
390C22×C11#54611yescharacteristic
391C22×C11#54711yescharacteristic
392C22×C11C22×D811yescharacteristic
393C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
394C22×C11#57711yescharacteristic
395C22×C11#57811yescharacteristic
396C2×D11—42no—
397C2×D11—42no—
398C2×D11—42no—
399C2×D11—81no—
400C2×D11—81no—
401C2×D11—81no—
402C2×D11—81no—
403C4×C11—22no—
404C4×C11—22no—
405C4×C11—22no—
406C4×C11—41no—
407C4×C11—41no—
408C4×C11—81no—
409C4×C11—81no—
410C4×C11—81no—
411C4×C11#52911yescharacteristic
412C4×C11#53911yescharacteristic
413C4×C11#54611yescharacteristic
414C4×C11#54711yescharacteristic
415Dic11—42no—
416Dic11—42no—
417Dic11—81no—
418C22×D4—21no—
419C22×D4—111no—
420C22×D4—221no—
421C22×D4C22×D1111yescharacteristic
422C23×C4—21no—
423C23×C4—221no—
424C23×C4—221no—
425C23×C4C22×D1111yescharacteristic
426C2×D8—222no—
427C2×D8—222no—
428C2×D8—441no—
429C22×C8—111no—
430C22×C8—111no—
431C22×C8—111no—
432C22×C8—111no—
433C22×C8—222no—
434C22×C8—222no—
435C22×C8—441no—
436#123—44no—
437#123—44no—
438#121—22no—
439#121—22no—
440#121—114no—
441#121—222no—
442C4×D4—222no—
443C4×D4—441no—
444C4×D4—444no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—111no—
453C2×C4⋊C4—111no—
454C2×C4⋊C4—111no—
455C2×C4⋊C4—222no—
456C2×C4⋊C4—221no—
457C2×C4⋊C4—221no—
458C2×C4⋊C4—441no—
459C2×C4⋊C4C22×D1111yescharacteristic
460C2×C4⋊C4C22×D1111yescharacteristic
461C2×C4⋊C4C22×D1111yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—221no—
468C2×C22⋊C4—221no—
469C2×C22⋊C4—221no—
470C2×C22⋊C4—221no—
471C2×C22⋊C4C22⋊D1111yescharacteristic
472C2×C22⋊C4C22⋊D1111yescharacteristic
473C2×C42—221no—
474C2×C42C22×D1111yescharacteristic
475C2×C42C22×D1111yescharacteristic
476#107—222no—
477#107—222no—
478#107—222no—
479C4⋊C8—222no—
480C4⋊C8—441no—
481#102—222no—
482#102—222no—
483#102—222no—
484#102—222no—
485#102—222no—
486#102—441no—
487C22⋊C8—222no—
488#95—221no—
489#95—221no—
490#95C22⋊D1111yescharacteristic
491#95C22⋊D1111yescharacteristic
492C2×C11—24no—
493C2×C11—161no—
494C2×C11#242511yescharacteristic
495C2×C11C2×#45911yescharacteristic
496C2×C11#304611yescharacteristic
497C2×C11#329411yescharacteristic
498C2×C11#330811yescharacteristic
499C2×C11#333411yescharacteristic
500C2×C11#334511yescharacteristic
501D11—82no—
502C24—21no—
503C24—221no—
504C24C2×C22⋊D1111yescharacteristic
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—112no—
515C2×D4—224no—
516C2×D4—221no—
517C2×D4—221no—
518C2×D4—221no—
519C2×D4—221no—
520C2×D4—221no—
521C2×D4—442no—
522C2×D4—442no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—221no—
534C22×C4—221no—
535C22×C4—221no—
536C22×C4—442no—
537C22×C4—442no—
538C22×C4—442no—
539C22×C4—442no—
540C22×C4—881no—
541C22×C4—881no—
542C22×C4D4×D1112yes—
543C22×C4#434112yes—
544C22×C4C2×C22⋊D1111yescharacteristic
545C22×C4C2×C22⋊D1111yescharacteristic
546C22×C4C2×C22⋊D1111yescharacteristic
547C22×C4C2×C22⋊D1111yescharacteristic
548C22×C4C2×C22⋊D1111yescharacteristic
549C22×C4C23×D1111yescharacteristic
550D8—444no—
551C2×C8—112no—
552C2×C8—221no—
553C2×C8—221no—
554C2×C8—221no—
555C2×C8—221no—
556C2×C8—221no—
557C2×C8—221no—
558C2×C8—221no—
559C2×C8—221no—
560C2×C8—221no—
561C2×C8—221no—
562C2×C8—221no—
563C2×C8—444no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—112no—
576C4⋊C4—112no—
577C4⋊C4—221no—
578C4⋊C4—221no—
579C4⋊C4—221no—
580C4⋊C4—221no—
581C4⋊C4—442no—
582C4⋊C4—442no—
583C22⋊C4—22no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—224no—
590C22⋊C4—442no—
591C22⋊C4—442no—
592C22⋊C4—881no—
593C22⋊C4#432314yescomplemented
594C42—21no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—442no—
599C11#2520011yescharacteristic, complemented, Sylow
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—222no—
612C23—441no—
613C23—441no—
614C23—441no—
615C23—441no—
616C23—441no—
617C23—441no—
618C23C2×#432312yes—
619C23#6698512yes—
620C23#6699112yes—
621C23C22×C22⋊D1111yescharacteristic
622D4—41no—
623D4—41no—
624D4—41no—
625D4—41no—
626D4—84no—
627D4—222no—
628D4—222no—
629D4—448no—
630D4—441no—
631D4—441no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—84no—
658C2×C4—222no—
659C2×C4—222no—
660C2×C4—441no—
661C2×C4—441no—
662C2×C4—441no—
663C2×C4—441no—
664C2×C4—441no—
665C2×C4—441no—
666C2×C4—441no—
667C2×C4—884no—
668C2×C4—884no—
669C2×C4C2×#432312yes—
670C2×C4C2×#432312yes—
671C2×C4#6699112yes—
672C2×C4C2×D4×D1111yescharacteristic
673C2×C4C2×#434111yescharacteristic
674C2×C4#41×D1111yescharacteristic
675C2×C4#41×D1111yescharacteristic
676C2×C4#6704211yescharacteristic
677C2×C4#6704311yescharacteristic
678C8—222no—
679C8—441no—
680C8—441no—
681C8—441no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—442no—
696C22—442no—
697C22—442no—
698C22—881no—
699C22—881no—
700C22—881no—
701C22—881no—
702C22#1062268514yes—
703C22C22×#432311yescharacteristic
704C22C2×#6698511yescharacteristic
705C22C2×#6699111yescharacteristic
706C22#1062335511yescharacteristic
707C22#1062336011yescharacteristic
708C22#1062336811yescharacteristic
709C22#1062336911yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—41no—
714C4—41no—
715C4—81no—
716C4—81no—
717C4—81no—
718C4—442no—
719C4—442no—
720C4—881no—
721C4#1062318011yescharacteristic
722C4#1062318511yescharacteristic
723C4#1062318611yescharacteristic
724C4#1062319611yescharacteristic
725C2—24no—
726C2—161no—
727C2—882no—
728C2#1307216311yescharacteristic
729C2C2×#1062268511yescharacteristic
730C2#1307816211yescharacteristic
731C2#1308042311yescharacteristic
732C2#1308060111yescharacteristic
733C2#1308095911yescharacteristic
734C2#1308108611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2501C2
socleC23×C11C22×D4
prime radicalC2×#10622651C2
hypercenter#2501D11
hypocenterC11#25200
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2501

Complements

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

NH ≅ G/Ntype
1. C2×#10622580C2semidirect
3. #13071630C2semidirect
4. #13070088C2semidirect
5. #13070020C2semidirect
6. #13070004C2semidirect
7. #13069926C2semidirect
8. #13069372C2semidirect
9. #13069233C2semidirect
10. #13068967C2semidirect
11. #13068934C2semidirect
12. #13068796C2semidirect
13. #13068613C2semidirect
14. C2×#10622167C2semidirect
15. C11×#2501C2semidirect
201. C11×C22⋊C4D8semidirect
235. #2501D11semidirect
593. C22⋊C4#4323semidirect
599. C11#25200semidirect

Maximal subgroups

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

subgroupindex
C2×#106225802
C2×#106226512
#130716302
#130700882
#130700202
#130700042
#130699262
#130693722
#130692332
#130689672
#130689342
#130687962
#130686132
C2×#106221672
C11×#25012
#2520011