Finite Group Databasebeta

← #14916699

Subgroups — #14916699

Order 2816.

2630 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66982C211yesmaximal, characteristic
2#13071760C214yesmaximal, complemented
3#13071608C214yesmaximal, complemented
4#13071494C212yesmaximal, complemented
5#13071468C212yesmaximal, complemented
6#13071467C212yesmaximal, complemented
7#13071432C212yesmaximal
8#13071406C214yesmaximal, complemented
9#13071282C214yesmaximal, complemented
10#13071233C211yesmaximal, characteristic, complemented
11#13071229C211yesmaximal, characteristic, complemented
12#13071218C211yesmaximal, characteristic, complemented
13#13071213C211yesmaximal, characteristic, complemented
14C2×#10622825C211yesmaximal, characteristic, complemented
15C11×#2280C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C2×C11×#117C2212yescomplemented
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C2×#66982C4116yescomplemented
22C2×#66982C2212yes—
23C2×#66982C2212yes—
24C2×#66982C2212yes—
25C2×#66982C2212yes—
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×C4⋊Dic11C2212yescomplemented
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C2×(C22⋊D11)⋊C4C2214yes—
32C2×C22⋊C4×D11C2212yes—
33C2×#66930C2212yes—
34C11×#381C2212yescomplemented
35C11×#380C2211yescharacteristic
36C11×#380C2211yescharacteristic
37C11×#380C2212yescomplemented
38C11×#379C2212yes—
39C4×C11×C22⋊C4C2212yes—
40C4×C11×C22⋊C4C2212yescomplemented
41#10622825C2212yes—
42#10622825C2211yescharacteristic
43#10622825C2211yescharacteristic
44#10622825C2212yescomplemented
45#10622825C2212yescomplemented
46C2×C11⋊#95C2212yescomplemented
47#10622603C2214yescomplemented
48#10622602C2214yescomplemented
49#10622591C2214yescomplemented
50#10622585C2214yescomplemented
51#10622571C2214yes—
52#10622570C2214yes—
53#10622569C2214yes—
54#10622568C2212yes—
55#10622559C2214yescomplemented
56#10622558C2214yescomplemented
57#10622557C2214yescomplemented
58#10622556C2212yes—
59#10622555C2212yes—
60#10622555C2212yes—
61C22⋊C4×Dic11C2212yes—
62C22⋊C4×Dic11C2212yes—
63C22⋊C4×Dic11C2214yescomplemented
64#10622553C2214yescomplemented
65C4×(C2×D11)⋊C4C2214yescomplemented
66#10622546C2214yescomplemented
67C4×Dic11⋊C4C2214yescomplemented
68#10622283C2214yescomplemented
69#10622283C2214yescomplemented
70#10622281C2214yescomplemented
71#10622281C2214yescomplemented
72#10622268C2214yescomplemented
73#10622268C2214yescomplemented
74#10622260C2214yescomplemented
75#10622260C2214yescomplemented
76C25×C11C2311yescharacteristic
77C24×D11C2311yescharacteristic
78C23×C4×C11—44no—
79C23×C4×C11C2×C418yescomplemented
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—44no—
87C22×C22⋊D11C2×C418yes—
88C22×C22⋊D11C2312yes—
89C22×C22⋊D11C2312yes—
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2314yes—
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C22×C4×D11C2314yes—
95C11×#117—44no—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C22⋊C4C2312yes—
99C2×C11×C22⋊C4C2314yes—
100C2×C11×C22⋊C4C2312yes—
101C2×C11×C22⋊C4C2314yes—
102C2×C42×C11C2314yes—
103C2×C22⋊Dic11—44no—
104C2×C22⋊Dic11C2×C418yescomplemented
105C2×C22⋊Dic11C2312yes—
106C2×C22⋊Dic11C2312yes—
107C2×C22⋊Dic11C2314yes—
108C2×C22⋊Dic11C2312yes—
109C2×C22⋊Dic11C2312yes—
110#66982C2×C4116yescomplemented
111#66982C2×C4116yescomplemented
112#66982C2×C4116yescomplemented
113#66982C2×C4116yescomplemented
114C2×(C2×D11)⋊C4C2×C418yescomplemented
115C2×(C2×D11)⋊C4C2×C418yescomplemented
116C2×(C2×D11)⋊C4C2314yes—
117C2×(C2×D11)⋊C4C2314yes—
118C2×(C2×D11)⋊C4C2314yes—
119C2×(C2×D11)⋊C4C2312yes—
120C2×(C2×D11)⋊C4C2312yes—
121C2×(C2×D11)⋊C4C2312yes—
122C2×(C2×D11)⋊C4C2312yes—
123C2×C4⋊Dic11—44no—
124C2×C4⋊Dic11C2312yes—
125C2×C4⋊Dic11C2314yes—
126C2×C4⋊Dic11C2312yes—
127C2×Dic11⋊C4C2×C418yescomplemented
128C2×Dic11⋊C4C2×C418yescomplemented
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2314yes—
131C2×Dic11⋊C4C2314yes—
132C2×Dic11⋊C4C2312yes—
133C2×Dic11⋊C4C2312yes—
134C2×Dic11⋊C4C2312yes—
135C2×Dic11⋊C4C2312yes—
136C2×C4×Dic11C2314yes—
137C2×C4×Dic11C2314yes—
138C2×C4×Dic11C2314yes—
139(C22⋊D11)⋊C4—48no—
140C22⋊C4×D11—44no—
141#66930—44no—
142C11×#95C2312yes—
143C11×#95C2314yes—
144C11×#95C2312yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2312yes—
153C11⋊#95C2312yes—
154#34376—111nomaximal, Sylow
155C24×C11—22no—
156C24×C11—24no—
157C24×C11—22no—
158C24×C11—42no—
159C24×C11C22×C414yes—
160C24×C11C2411yescharacteristic
161C24×C11C2411yescharacteristic
162C24×C11C2411yescharacteristic
163C23×D11—22no—
164C23×D11—22no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11C22×C414yes—
168C23×D11C2412yes—
169C22×C4×C11—24no—
170C22×C4×C11—24no—
171C22×C4×C11—416no—
172C22×C4×C11—42no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11C22×C414yes—
177C22×C4×C11C22×C414yes—
178C22×C4×C11C22×C414yes—
179C22×C4×C11C22×C414yes—
180C22×C4×C11C22×C414yes—
181C22×C4×C11C22×C414yes—
182C22×C4×C11C2414yes—
183C22×C4×C11C2414yes—
184C22×C4×C11C2411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C22×C4×C11C2411yescharacteristic
187C22×C4×C11C2411yescharacteristic
188C2×C22⋊D11—28no—
189C2×C22⋊D11—44no—
190C2×C22⋊D11—416no—
191C2×C22⋊D11C22×C418yes—
192C2×C22⋊D11C22×C418yes—
193C22×Dic11—22no—
194C22×Dic11—28no—
195C22×Dic11—22no—
196C22×Dic11—42no—
197C22×Dic11—42no—
198C22×Dic11—44no—
199C22×Dic11—44no—
200C22×Dic11C22×C414yes—
201C22×Dic11C22×C414yes—
202C22×Dic11C22×C414yes—
203C22×Dic11C2414yes—
204C22×Dic11C2414yes—
205C22×Dic11C2412yes—
206C22×Dic11C2412yes—
207C22×Dic11C2412yes—
208C2×C4×D11—44no—
209C2×C4×D11—44no—
210C2×C4×D11—44no—
211C11×C4⋊C4—42no—
212C11×C4⋊C4—42no—
213C11×C22⋊C4—24no—
214C11×C22⋊C4—28no—
215C11×C22⋊C4—24no—
216C11×C22⋊C4—44no—
217C42×C11—44no—
218C22⋊Dic11—24no—
219C22⋊Dic11—24no—
220C22⋊Dic11—44no—
221C22⋊Dic11C22×C418yes—
222C22⋊Dic11C22×C418yes—
223(C2×D11)⋊C4—44no—
224(C2×D11)⋊C4—44no—
225(C2×D11)⋊C4—44no—
226(C2×D11)⋊C4C22×C418yes—
227(C2×D11)⋊C4C22×C418yes—
228(C2×D11)⋊C4C22×C418yes—
229(C2×D11)⋊C4C22×C418yes—
230C4⋊Dic11—42no—
231C4⋊Dic11—44no—
232C4⋊Dic11—42no—
233Dic11⋊C4—44no—
234Dic11⋊C4—44no—
235Dic11⋊C4—44no—
236Dic11⋊C4C22×C418yes—
237Dic11⋊C4C22×C418yes—
238Dic11⋊C4C22×C418yes—
239Dic11⋊C4C22×C418yes—
240C4×Dic11—44no—
241C4×Dic11—44no—
242C4×Dic11—44no—
243C22×#123—111no—
244#2376—114no—
245#2359—114no—
246#2345—112no—
247#2342—112no—
248#2342—112no—
249D4×C22⋊C4—112no—
250#2335—114no—
251#2322—114no—
252#2316—111no—
253#2315—111no—
254#2313—111no—
255#2312—111no—
256#2280D1111yescharacteristic, complemented
257C2×#380—111no—
258C23×C11—21no—
259C23×C11—22no—
260C23×C11—21no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—28no—
264C23×C11—28no—
265C23×C11—21no—
266C23×C11—22no—
267C23×C11—21no—
268C23×C11—22no—
269C23×C11—44no—
270C23×C11—48no—
271C23×C11—48no—
272C23×C11C23×C412yes—
273C23×C11C23×C412yes—
274C23×C11C23×C412yes—
275C23×C11H(5,𝔽2)14yes—
276C23×C11H(5,𝔽2)12yes—
277C23×C112−1+412yes—
278C23×C11C2511yescharacteristic
279C22×D11—22no—
280C22×D11—24no—
281C22×D11—22no—
282C22×D11—24no—
283C22×D11—28no—
284C22×D11—44no—
285C22×D11—44no—
286C22×D11—84no—
287C22×D11—84no—
288C22×D11C23×C414yes—
289C2×C4×C11—28no—
290C2×C4×C11—28no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—24no—
296C2×C4×C11—24no—
297C2×C4×C11—24no—
298C2×C4×C11—24no—
299C2×C4×C11—24no—
300C2×C4×C11—24no—
301C2×C4×C11—44no—
302C2×C4×C11—44no—
303C2×C4×C11—44no—
304C2×C4×C11—44no—
305C2×C4×C11C23×C412yes—
306C2×C4×C11C23×C412yes—
307C2×C4×C11C23×C412yes—
308C2×C4×C11C23×C412yes—
309C22⋊D11—216no—
310C22⋊D11—48no—
311C2×Dic11—28no—
312C2×Dic11—22no—
313C2×Dic11—24no—
314C2×Dic11—22no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11—24no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—44no—
323C2×Dic11—44no—
324C2×Dic11—88no—
325C2×Dic11C23×C414yes—
326C2×Dic11C23×C414yes—
327C2×Dic11C23×C414yes—
328C4×D11—88no—
329C23×D4—111no—
330C24×C4C2×D1111yescharacteristic
331C2×#123—112no—
332C2×#123—112no—
333C2×#123—112no—
334C2×#123—112no—
335C2×#123—1116no—
336C2×C4×D4—114no—
337C2×#117—112no—
338C2×#117C2×D1112yescomplemented
339C22×C4⋊C4—111no—
340C22×C4⋊C4—111no—
341C22×C4⋊C4—112no—
342C22×C22⋊C4—111no—
343C22×C22⋊C4—111no—
344C22×C22⋊C4—111no—
345C22×C22⋊C4—112no—
346C22×C22⋊C4—112no—
347#390—114no—
348#389—114no—
349#389—114no—
350#389—114no—
351#388—114no—
352#388—114no—
353#388—114no—
354#388—114no—
355#388—114no—
356#388—114no—
357#387—114no—
358#387—114no—
359#387—114no—
360#387—114no—
361#386—114no—
362#386—114no—
363#385—114no—
364#385—114no—
365#385—114no—
366#385—114no—
367#381—112no—
368#381C2×D1112yescomplemented
369#380—111no—
370#380—111no—
371#380—112no—
372#380—112no—
373#380—112no—
374#380—112no—
375#380—112no—
376#380C2×D1111yescharacteristic
377#380C2×D1111yescharacteristic
378#380C2×D1112yescomplemented
379#379—112no—
380#379C2×D1112yes—
381C4×C4⋊C4—114no—
382C4×C22⋊C4—112no—
383C4×C22⋊C4—112no—
384C4×C22⋊C4—114no—
385C4×C22⋊C4—114no—
386C4×C22⋊C4C2×D1112yes—
387C4×C22⋊C4C2×D1112yescomplemented
388C2×#95—112no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—24no—
394C22×C11—24no—
395C22×C11—24no—
396C22×C11—24no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—416no—
401C22×C11—42no—
402C22×C11—42no—
403C22×C11#51814yes—
404C22×C11#52014yes—
405C22×C11C24×C411yescharacteristic
406C22×C11C2×H(5,𝔽2)12yes—
407C22×C11C2×H(5,𝔽2)11yescharacteristic
408C22×C11C2×2−1+411yescharacteristic
409C22×C11#58512yes—
410C2×D11—24no—
411C2×D11—24no—
412C2×D11—24no—
413C2×D11—44no—
414C2×D11—44no—
415C2×D11—88no—
416C4×C11—22no—
417C4×C11—22no—
418C4×C11—22no—
419C4×C11—22no—
420C4×C11—44no—
421C4×C11—44no—
422Dic11—24no—
423Dic11—24no—
424Dic11—24no—
425Dic11—44no—
426Dic11—44no—
427C25—111no—
428C25C22×D1111yescharacteristic
429C22×D4—112no—
430C22×D4—118no—
431C22×D4—112no—
432C22×D4—444no—
433C23×C4—44no—
434C23×C4—111no—
435C23×C4—111no—
436C23×C4—111no—
437C23×C4—114no—
438C23×C4—114no—
439C23×C4C4×D1118yescomplemented
440C23×C4C22×D1111yescharacteristic
441C23×C4C22×D1111yescharacteristic
442C23×C4C22×D1111yescharacteristic
443C23×C4C22×D1111yescharacteristic
444C23×C4C22×D1111yescharacteristic
445C23×C4C22×D1111yescharacteristic
446#123—1116no—
447#123—1116no—
448#123—1116no—
449#123—1116no—
450C4×D4—448no—
451#117—44no—
452#117—444no—
453C2×C4⋊C4—118no—
454C2×C4⋊C4—118no—
455C2×C4⋊C4—112no—
456C2×C4⋊C4—112no—
457C2×C4⋊C4—112no—
458C2×C4⋊C4—112no—
459C2×C4⋊C4—112no—
460C2×C4⋊C4—114no—
461C2×C4⋊C4—112no—
462C2×C4⋊C4—114no—
463C2×C4⋊C4—114no—
464C2×C4⋊C4—114no—
465C2×C4⋊C4—444no—
466C2×C4⋊C4C22×D1112yes—
467C2×C4⋊C4C22×D1112yes—
468C2×C22⋊C4—118no—
469C2×C22⋊C4—112no—
470C2×C22⋊C4—112no—
471C2×C22⋊C4—118no—
472C2×C22⋊C4—118no—
473C2×C22⋊C4—112no—
474C2×C22⋊C4—112no—
475C2×C22⋊C4—112no—
476C2×C22⋊C4—112no—
477C2×C22⋊C4—112no—
478C2×C22⋊C4—112no—
479C2×C22⋊C4—114no—
480C2×C22⋊C4—114no—
481C2×C22⋊C4—114no—
482C2×C22⋊C4—114no—
483C2×C22⋊C4—444no—
484C2×C22⋊C4—444no—
485C2×C22⋊C4C22×D1112yes—
486C2×C22⋊C4C22×D1114yes—
487C2×C22⋊C4C22×D1112yes—
488C2×C22⋊C4C22×D1114yes—
489C2×C42—114no—
490C2×C42—114no—
491C2×C42—114no—
492C2×C42C22×D1114yes—
493#95—114no—
494#95—112no—
495#95—112no—
496#95—114no—
497#95—114no—
498#95—114no—
499#95—114no—
500#95—114no—
501#95—114no—
502#95C22×D1114yes—
503#95C22×D1112yes—
504#95C22×D1112yes—
505C2×C11—24no—
506C2×C11—24no—
507C2×C11—42no—
508C2×C11C2×#51811yescharacteristic
509C2×C11C2×#52011yescharacteristic
510C2×C11#342811yescharacteristic
511C2×C11#353412yes—
512C2×C11#353512yes—
513D11—44no—
514C24—24no—
515C24—22no—
516C24—22no—
517C24—42no—
518C24—112no—
519C24—114no—
520C24—222no—
521C24—222no—
522C24—442no—
523C24—442no—
524C24C2×C4×D1114yes—
525C24C23×D1111yescharacteristic
526C24C23×D1111yescharacteristic
527C24C23×D1111yescharacteristic
528C2×D4—118no—
529C2×D4—118no—
530C2×D4—228no—
531C2×D4—444no—
532C2×D4—4416no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—416no—
540C22×C4—114no—
541C22×C4—112no—
542C22×C4—112no—
543C22×C4—112no—
544C22×C4—114no—
545C22×C4—114no—
546C22×C4—114no—
547C22×C4—114no—
548C22×C4—222no—
549C22×C4—222no—
550C22×C4—228no—
551C22×C4—444no—
552C22×C4—444no—
553C22×C4—444no—
554C22×C4—442no—
555C22×C4—442no—
556C22×C4—444no—
557C22×C4—444no—
558C22×C4C2×C4×D1114yes—
559C22×C4C2×C4×D1114yes—
560C22×C4C2×C4×D1114yes—
561C22×C4C2×C4×D1114yes—
562C22×C4C2×C4×D1114yes—
563C22×C4C2×C4×D1114yes—
564C22×C4C23×D1114yes—
565C22×C4C23×D1114yes—
566C22×C4C23×D1111yescharacteristic
567C22×C4C23×D1111yescharacteristic
568C22×C4C23×D1111yescharacteristic
569C22×C4C23×D1111yescharacteristic
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—118no—
573C4⋊C4—118no—
574C4⋊C4—118no—
575C4⋊C4—118no—
576C4⋊C4—442no—
577C4⋊C4—444no—
578C4⋊C4—442no—
579C4⋊C4—444no—
580C4⋊C4—444no—
581C4⋊C4—444no—
582C22⋊C4—28no—
583C22⋊C4—24no—
584C22⋊C4—24no—
585C22⋊C4—44no—
586C22⋊C4—118no—
587C22⋊C4—118no—
588C22⋊C4—118no—
589C22⋊C4—118no—
590C22⋊C4—118no—
591C22⋊C4—118no—
592C22⋊C4—224no—
593C22⋊C4—224no—
594C22⋊C4—444no—
595C22⋊C4—444no—
596C22⋊C4—444no—
597C22⋊C4—444no—
598C42—44no—
599C42—444no—
600C42—444no—
601C42—444no—
602C11#3437611yescharacteristic, complemented, Sylow
603C23—22no—
604C23—21no—
605C23—21no—
606C23—22no—
607C23—22no—
608C23—28no—
609C23—28no—
610C23—22no—
611C23—21no—
612C23—21no—
613C23—22no—
614C23—44no—
615C23—48no—
616C23—48no—
617C23—114no—
618C23—224no—
619C23—222no—
620C23—222no—
621C23—224no—
622C23—228no—
623C23—444no—
624C23—444no—
625C23—884no—
626C23—884no—
627C23C22×C4×D1112yes—
628C23C22×C4×D1112yes—
629C23C22×C4×D1112yes—
630C23#6703714yes—
631C23#6704212yes—
632C23#6704312yes—
633C23C24×D1111yescharacteristic
634D4—2216no—
635D4—448no—
636C2×C4—28no—
637C2×C4—28no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—44no—
652C2×C4—114no—
653C2×C4—114no—
654C2×C4—114no—
655C2×C4—228no—
656C2×C4—224no—
657C2×C4—222no—
658C2×C4—222no—
659C2×C4—224no—
660C2×C4—224no—
661C2×C4—224no—
662C2×C4—224no—
663C2×C4—224no—
664C2×C4—224no—
665C2×C4—224no—
666C2×C4—444no—
667C2×C4—444no—
668C2×C4—888no—
669C2×C4—888no—
670C2×C4C22×C4×D1112yes—
671C2×C4C22×C4×D1112yes—
672C2×C4C22×C4×D1112yes—
673C2×C4C22×C4×D1112yes—
674C22—24no—
675C22—24no—
676C22—24no—
677C22—24no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—416no—
686C22—42no—
687C22—42no—
688C22—224no—
689C22—224no—
690C22—224no—
691C22—444no—
692C22—444no—
693C22—888no—
694C22#1062301714yes—
695C22#1062305414yes—
696C22C23×C4×D1111yescharacteristic
697C22C2×#6703712yes—
698C22C2×#6704211yescharacteristic
699C22C2×#6704311yescharacteristic
700C22#1062345312yes—
701C4—22no—
702C4—22no—
703C4—22no—
704C4—22no—
705C4—44no—
706C4—44no—
707C4—224no—
708C4—224no—
709C4—224no—
710C4—444no—
711C4—444no—
712C2—24no—
713C2—24no—
714C2—42no—
715C2—444no—
716C2C2×#1062301711yescharacteristic
717C2C2×#1062305411yescharacteristic
718C2#1308181711yescharacteristic
719C2#1308280012yes—
720C2#1308281912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2280C2
socle, cosocleC23×C11C25
prime radicalC23×C22⋊D11C22
hypercenter#2280D11
hypocenterC11#34376
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. #13071760C2semidirect
3. #13071608C2semidirect
4. #13071494C2semidirect
5. #13071468C2semidirect
6. #13071467C2semidirect
8. #13071406C2semidirect
9. #13071282C2semidirect
10. #13071233C2semidirect
11. #13071229C2semidirect
12. #13071218C2semidirect
13. #13071213C2semidirect
14. C2×#10622825C2semidirect
15. C11×#2280C2semidirect
18. C2×C11×#117C22semidirect
21. C2×#66982C4semidirect
28. C22×C4⋊Dic11C22semidirect
34. C11×#381C22semidirect
37. C11×#380C22semidirect
40. C4×C11×C22⋊C4C22semidirect
44. #10622825C22semidirect
45. #10622825C22semidirect
46. C2×C11⋊#95C22semidirect
47. #10622603C22semidirect
48. #10622602C22semidirect
49. #10622591C22semidirect
50. #10622585C22semidirect
55. #10622559C22semidirect
56. #10622558C22semidirect
57. #10622557C22semidirect
63. C22⋊C4×Dic11C22semidirect
64. #10622553C22semidirect
65. C4×(C2×D11)⋊C4C22semidirect
66. #10622546C22semidirect
67. C4×Dic11⋊C4C22semidirect
68. #10622283C22semidirect
69. #10622283C22semidirect
70. #10622281C22semidirect
71. #10622281C22semidirect
72. #10622268C22semidirect
73. #10622268C22semidirect
74. #10622260C22semidirect
75. #10622260C22semidirect
79. C23×C4×C11C2×C4semidirect
104. C2×C22⋊Dic11C2×C4semidirect
110. #66982C2×C4semidirect
111. #66982C2×C4semidirect
112. #66982C2×C4semidirect
113. #66982C2×C4semidirect
114. C2×(C2×D11)⋊C4C2×C4semidirect
115. C2×(C2×D11)⋊C4C2×C4semidirect
127. C2×Dic11⋊C4C2×C4semidirect
128. C2×Dic11⋊C4C2×C4semidirect
256. #2280D11semidirect
338. C2×#117C2×D11semidirect
368. #381C2×D11semidirect
378. #380C2×D11semidirect
387. C4×C22⋊C4C2×D11semidirect
439. C23×C4C4×D11semidirect
602. C11#34376semidirect

Maximal subgroups

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

subgroupindex
C22×#669822
#130717602
#130716082
#130714942
#130714682
#130714672
#130714322
#130714062
#130712822
#130712332
#130712292
#130712182
#130712132
C2×#106228252
C11×#22802
#3437611