Finite Group Databasebeta

← #14916501

Subgroups — #14916501

Order 2816.

4134 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67006C211yesmaximal, characteristic
2#13071755C214yesmaximal, complemented
3#13071595C214yesmaximal, complemented
4#13071467C212yesmaximal, complemented
5#13071461C212yesmaximal, complemented
6C22⋊C4×C22⋊D11C212yesmaximal, complemented
7#13071432C212yesmaximal, complemented
8#13071274C214yesmaximal, complemented
9#13071271C214yesmaximal, complemented
10#13071212C211yesmaximal, characteristic, complemented
11#13071212C211yesmaximal, characteristic, complemented
12#13071197C211yesmaximal, characteristic, complemented
13#13071192C211yesmaximal, characteristic, complemented
14C2×#10622860C211yesmaximal, characteristic, complemented
15C2×C11×#379C211yesmaximal, characteristic, complemented
16C26×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C11×C22⋊C4C2212yescomplemented
22C22×C11×C22⋊C4C2212yescomplemented
23C2×#67006C4116yescomplemented
24C2×#67006C2212yes—
25C2×#67006C2212yes—
26C2×#67006C2212yes—
27C2×#67006C2212yes—
28C22×C22⋊Dic11C2212yes—
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2212yescomplemented
33C22×C22⋊Dic11C2212yescomplemented
34C2×C4×C22⋊D11C2214yescomplemented
35C2×(C22⋊D11)⋊C4C2214yescomplemented
36C2×C22⋊C4×D11C2212yescomplemented
37C2×#66930C2212yescomplemented
38C11×#379C2212yes—
39C11×#379C2211yescharacteristic
40C11×#379C2211yescharacteristic
41C11×#379C2212yescomplemented
42C11×#379C2212yescomplemented
43#10622860C2212yes—
44#10622860C2211yescharacteristic
45#10622860C2211yescharacteristic
46#10622860C2212yescomplemented
47#10622860C2212yescomplemented
48#10622826C2214yescomplemented
49#10622823C2214yescomplemented
50C4×C22⋊Dic11C2214yescomplemented
51#10622571C2214yescomplemented
52#10622570C2214yescomplemented
53#10622570C2214yescomplemented
54#10622570C2214yescomplemented
55#10622570C2214yescomplemented
56#10622569C2214yescomplemented
57#10622569C2214yescomplemented
58#10622569C2214yescomplemented
59#10622569C2214yescomplemented
60#10622568C2212yescomplemented
61#10622559C2214yescomplemented
62#10622558C2214yescomplemented
63#10622558C2214yescomplemented
64#10622558C2214yescomplemented
65#10622558C2214yescomplemented
66#10622557C2214yescomplemented
67#10622557C2214yescomplemented
68#10622557C2214yescomplemented
69#10622557C2214yescomplemented
70#10622556C2212yescomplemented
71#10622555C2212yescomplemented
72#10622555C2212yescomplemented
73C22⋊C4×Dic11C2212yescomplemented
74C22⋊C4×Dic11C2212yescomplemented
75C22⋊C4×Dic11C2214yescomplemented
76C25×C11—44no—
77C25×C11—44no—
78C25×C11—44no—
79C25×C11C2×C418yescomplemented
80C25×C11C2311yescharacteristic
81C25×C11C2311yescharacteristic
82C25×C11C2311yescharacteristic
83C25×C11C2311yescharacteristic
84C25×C11C2311yescharacteristic
85C25×C11C2311yescharacteristic
86C25×C11C2311yescharacteristic
87C24×D11C2311yescharacteristic
88C23×C4×C11C2314yes—
89C22×C22⋊D11—44no—
90C22×C22⋊D11—44no—
91C22×C22⋊D11—44no—
92C22×C22⋊D11C2×C418yescomplemented
93C22×C22⋊D11C2×C418yescomplemented
94C22×C22⋊D11C2×C418yescomplemented
95C22×C22⋊D11C2312yes—
96C22×C22⋊D11C2312yes—
97C22×C22⋊D11C2312yes—
98C22×C22⋊D11C2312yes—
99C22×C22⋊D11C2312yes—
100C22×C22⋊D11C2312yes—
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2314yes—
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C22×C4×D11C2314yescomplemented
106C2×C11×C22⋊C4—44no—
107C2×C11×C22⋊C4—44no—
108C2×C11×C22⋊C4—44no—
109C2×C11×C22⋊C4C2312yes—
110C2×C11×C22⋊C4C2312yes—
111C2×C11×C22⋊C4C2314yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2312yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C11×C22⋊C4C2314yes—
116C2×C11×C22⋊C4C2312yes—
117C2×C11×C22⋊C4C2312yes—
118#67006C2×C4116yescomplemented
119#67006C2×C4116yescomplemented
120#67006C2×C4116yescomplemented
121#67006C2×C4116yescomplemented
122C2×C22⋊Dic11—44no—
123C2×C22⋊Dic11—44no—
124C2×C22⋊Dic11—44no—
125C2×C22⋊Dic11C2×C418yescomplemented
126C2×C22⋊Dic11C2×C418yescomplemented
127C2×C22⋊Dic11C2×C418yescomplemented
128C2×C22⋊Dic11C2312yes—
129C2×C22⋊Dic11C2312yes—
130C2×C22⋊Dic11C2314yes—
131C2×C22⋊Dic11C2312yes—
132C2×C22⋊Dic11C2312yes—
133C2×C22⋊Dic11C2314yes—
134C2×C22⋊Dic11C2314yes—
135C2×C22⋊Dic11C2312yes—
136C2×C22⋊Dic11C2312yes—
137C2×C22⋊Dic11C2312yes—
138C2×C22⋊Dic11C2312yes—
139C2×C22⋊Dic11C2312yes—
140C2×C22⋊Dic11C2312yes—
141C2×C22⋊Dic11C2312yes—
142C2×C22⋊Dic11C2312yes—
143C4×C22⋊D11—48no—
144C2×(C2×D11)⋊C4C2314yescomplemented
145C2×(C2×D11)⋊C4C2314yescomplemented
146C2×(C2×D11)⋊C4C2314yescomplemented
147C2×Dic11⋊C4C2314yescomplemented
148C2×Dic11⋊C4C2314yescomplemented
149C2×Dic11⋊C4C2314yescomplemented
150C2×C4×Dic11C2314yescomplemented
151C2×C4×Dic11C2314yescomplemented
152C2×C4×Dic11C2314yescomplemented
153(C22⋊D11)⋊C4—48no—
154C22⋊C4×D11—44no—
155#66930—44no—
156C11⋊#95C2314yescomplemented
157C11⋊#95C2314yescomplemented
158C11⋊#95C2314yescomplemented
159C11⋊#95C2314yescomplemented
160C11⋊#95C2314yescomplemented
161C11⋊#95C2314yescomplemented
162#34356—111nomaximal, Sylow
163C24×C11—24no—
164C24×C11—24no—
165C24×C11—24no—
166C24×C11—24no—
167C24×C11—24no—
168C24×C11—24no—
169C24×C11—24no—
170C24×C11—24no—
171C24×C11—24no—
172C24×C11—416no—
173C24×C11—416no—
174C24×C11—416no—
175C24×C11—42no—
176C24×C11—42no—
177C24×C11—42no—
178C24×C11—42no—
179C24×C11—42no—
180C24×C11—42no—
181C24×C11—42no—
182C24×C11—42no—
183C24×C11—42no—
184C24×C11—42no—
185C24×C11—42no—
186C24×C11—42no—
187C24×C11—464no—
188C24×C11C22×C414yes—
189C24×C11C22×C414yes—
190C24×C11C22×C414yes—
191C24×C11C22×C414yes—
192C24×C11C22×C414yes—
193C24×C11C22×C414yes—
194C24×C11C22×C414yes—
195C24×C11C2411yescharacteristic
196C24×C11C2411yescharacteristic
197C24×C11C2411yescharacteristic
198C24×C11C2411yescharacteristic
199C24×C11C2411yescharacteristic
200C24×C11C2411yescharacteristic
201C24×C11C2411yescharacteristic
202C23×D11—24no—
203C23×D11—42no—
204C23×D11—42no—
205C23×D11C22×C414yes—
206C23×D11C2412yes—
207C22×C4×C11—28no—
208C22×C4×C11—44no—
209C22×C4×C11—44no—
210C22×C4×C11C2414yes—
211C22×C4×C11C2414yes—
212C2×C22⋊D11—28no—
213C2×C22⋊D11—28no—
214C2×C22⋊D11—416no—
215C2×C22⋊D11—42no—
216C2×C22⋊D11—42no—
217C2×C22⋊D11—44no—
218C2×C22⋊D11—44no—
219C2×C22⋊D11—42no—
220C2×C22⋊D11—42no—
221C2×C22⋊D11—416no—
222C2×C22⋊D11—416no—
223C2×C22⋊D11C22×C418yes—
224C2×C22⋊D11C22×C418yes—
225C2×C22⋊D11C22×C418yes—
226C2×C22⋊D11C22×C418yes—
227C2×C22⋊D11C22×C418yes—
228C2×C22⋊D11C22×C418yes—
229C22×Dic11—24no—
230C22×Dic11—28no—
231C22×Dic11—42no—
232C22×Dic11—42no—
233C22×Dic11—44no—
234C22×Dic11—44no—
235C22×Dic11C22×C414yes—
236C22×Dic11C22×C414yes—
237C22×Dic11C22×C414yes—
238C22×Dic11C2414yes—
239C22×Dic11C2414yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C2×C4×D11—44no—
244C2×C4×D11—44no—
245C2×C4×D11—44no—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—28no—
249C11×C22⋊C4—44no—
250C11×C22⋊C4—42no—
251C11×C22⋊C4—42no—
252C11×C22⋊C4—44no—
253C11×C22⋊C4—42no—
254C11×C22⋊C4—42no—
255C22⋊Dic11—24no—
256C22⋊Dic11—24no—
257C22⋊Dic11—28no—
258C22⋊Dic11—44no—
259C22⋊Dic11—42no—
260C22⋊Dic11—42no—
261C22⋊Dic11—44no—
262C22⋊Dic11—42no—
263C22⋊Dic11—42no—
264C22⋊Dic11C22×C418yes—
265C22⋊Dic11C22×C418yes—
266C22⋊Dic11C22×C418yes—
267C22⋊Dic11C22×C418yes—
268C22⋊Dic11C22×C418yes—
269C22⋊Dic11C22×C418yes—
270(C2×D11)⋊C4—44no—
271(C2×D11)⋊C4—44no—
272(C2×D11)⋊C4—44no—
273Dic11⋊C4—44no—
274Dic11⋊C4—44no—
275Dic11⋊C4—44no—
276C4×Dic11—44no—
277C4×Dic11—44no—
278C4×Dic11—44no—
279C22×#120—111no—
280#2375—114no—
281#2358—114no—
282#2342—112no—
283#2342—112no—
284D4×C22⋊C4—112no—
285D4×C22⋊C4—112no—
286#2321—114no—
287#2321—114no—
288#2312—111no—
289#2312—111no—
290#2309—111no—
291#2308—111no—
292C2×#379—111no—
293C2×#379D1111yescharacteristic, complemented
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—28no—
301C23×C11—28no—
302C23×C11—28no—
303C23×C11—28no—
304C23×C11—28no—
305C23×C11—28no—
306C23×C11—28no—
307C23×C11—28no—
308C23×C11—28no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—22no—
314C23×C11—22no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—44no—
322C23×C11—44no—
323C23×C11—44no—
324C23×C11—44no—
325C23×C11—44no—
326C23×C11—44no—
327C23×C11—44no—
328C23×C11—44no—
329C23×C11—44no—
330C23×C11—44no—
331C23×C11—44no—
332C23×C11—44no—
333C23×C11—416no—
334C23×C11—416no—
335C23×C11—416no—
336C23×C11—416no—
337C23×C11—416no—
338C23×C11—416no—
339C23×C11—4128no—
340C23×C11—416no—
341C23×C11C23×C412yes—
342C23×C11C23×C412yes—
343C23×C11C23×C412yes—
344C23×C11C23×C412yes—
345C23×C11C23×C412yes—
346C23×C11C23×C412yes—
347C23×C11C23×C412yes—
348C23×C11H(5,𝔽2)14yes—
349C23×C11H(5,𝔽2)14yes—
350C23×C11H(5,𝔽2)14yes—
351C23×C11C2511yescharacteristic
352C22×D11—22no—
353C22×D11—24no—
354C22×D11—24no—
355C22×D11—22no—
356C22×D11—28no—
357C22×D11—44no—
358C22×D11—44no—
359C22×D11—88no—
360C22×D11C23×C414yes—
361C2×C4×C11—24no—
362C2×C4×C11—24no—
363C2×C4×C11—24no—
364C2×C4×C11—24no—
365C2×C4×C11—24no—
366C2×C4×C11—24no—
367C2×C4×C11—88no—
368C22⋊D11—216no—
369C22⋊D11—216no—
370C22⋊D11—48no—
371C22⋊D11—48no—
372C22⋊D11—48no—
373C22⋊D11—48no—
374C2×Dic11—28no—
375C2×Dic11—22no—
376C2×Dic11—24no—
377C2×Dic11—24no—
378C2×Dic11—22no—
379C2×Dic11—24no—
380C2×Dic11—24no—
381C2×Dic11—24no—
382C2×Dic11—24no—
383C2×Dic11—24no—
384C2×Dic11—24no—
385C2×Dic11—44no—
386C2×Dic11—44no—
387C2×Dic11—88no—
388C2×Dic11C23×C414yes—
389C2×Dic11C23×C414yes—
390C2×Dic11C23×C414yes—
391C4×D11—88no—
392C26C2×D1111yescharacteristic
393C23×D4—111no—
394C23×D4—111no—
395C23×D4—111no—
396C2×#120—112no—
397C2×#120—112no—
398C2×#120—112no—
399C2×#120—112no—
400C2×#120—1116no—
401C2×C4×D4—114no—
402C2×C4×D4—114no—
403C2×#117—112no—
404C22×C22⋊C4—111no—
405C22×C22⋊C4—111no—
406C22×C22⋊C4—111no—
407C22×C22⋊C4—112no—
408C22×C22⋊C4—112no—
409C22×C22⋊C4—112no—
410C22×C22⋊C4—112no—
411C22×C22⋊C4C2×D1112yes—
412C22×C22⋊C4C2×D1112yescomplemented
413C22×C22⋊C4C2×D1112yescomplemented
414#390—114no—
415#390—114no—
416#390—114no—
417#390—114no—
418#388—114no—
419#388—114no—
420#388—114no—
421#388—114no—
422#388—114no—
423#388—114no—
424#388—114no—
425#388—114no—
426#386—114no—
427#386—114no—
428#386—114no—
429#386—114no—
430#386—114no—
431#386—114no—
432#385—114no—
433#385—114no—
434#381—112no—
435#380—112no—
436#380—112no—
437#379—111no—
438#379—111no—
439#379—112no—
440#379—112no—
441#379—112no—
442#379—112no—
443#379C2×D1111yescharacteristic
444#379C2×D1111yescharacteristic
445#379C2×D1112yes—
446#379C2×D1112yescomplemented
447#379C2×D1112yescomplemented
448C4×C22⋊C4—114no—
449C4×C22⋊C4—112no—
450C4×C22⋊C4—112no—
451C4×C22⋊C4—114no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—22no—
455C22×C11—22no—
456C22×C11—22no—
457C22×C11—22no—
458C22×C11—28no—
459C22×C11—28no—
460C22×C11—28no—
461C22×C11—22no—
462C22×C11—22no—
463C22×C11—22no—
464C22×C11—22no—
465C22×C11—22no—
466C22×C11—22no—
467C22×C11—22no—
468C22×C11—22no—
469C22×C11—22no—
470C22×C11—22no—
471C22×C11—22no—
472C22×C11—22no—
473C22×C11—416no—
474C22×C11—416no—
475C22×C11—416no—
476C22×C11—416no—
477C22×C11—416no—
478C22×C11—416no—
479C22×C11—416no—
480C22×C11—44no—
481C22×C11—44no—
482C22×C11—44no—
483C22×C11—44no—
484C22×C11#51814yes—
485C22×C11#51814yes—
486C22×C11#51814yes—
487C22×C11C24×C411yescharacteristic
488C22×C11C2×H(5,𝔽2)12yes—
489C22×C11C2×H(5,𝔽2)12yes—
490C22×C11C2×H(5,𝔽2)12yes—
491C2×D11—24no—
492C2×D11—24no—
493C2×D11—24no—
494C2×D11—44no—
495C2×D11—44no—
496C2×D11—88no—
497C4×C11—44no—
498C4×C11—44no—
499Dic11—24no—
500Dic11—24no—
501Dic11—24no—
502Dic11—44no—
503Dic11—44no—
504C25—44no—
505C25—44no—
506C25—44no—
507C25—111no—
508C25C4×D1118yescomplemented
509C25C22×D1111yescharacteristic
510C25C22×D1111yescharacteristic
511C25C22×D1111yescharacteristic
512C25C22×D1111yescharacteristic
513C25C22×D1111yescharacteristic
514C25C22×D1111yescharacteristic
515C25C22×D1111yescharacteristic
516C22×D4—112no—
517C22×D4—112no—
518C22×D4—118no—
519C22×D4—118no—
520C22×D4—118no—
521C22×D4—112no—
522C22×D4—112no—
523C22×D4—112no—
524C22×D4—112no—
525C22×D4—444no—
526C22×D4—444no—
527C22×D4—444no—
528C23×C4—111no—
529C23×C4—111no—
530C23×C4—111no—
531C23×C4—114no—
532C23×C4—114no—
533C23×C4C22×D1114yes—
534#120—1116no—
535#120—1116no—
536#120—1116no—
537#120—1116no—
538C4×D4—448no—
539C4×D4—448no—
540#117—444no—
541C2×C4⋊C4—114no—
542C2×C4⋊C4—114no—
543C2×C4⋊C4—114no—
544C2×C22⋊C4—44no—
545C2×C22⋊C4—44no—
546C2×C22⋊C4—44no—
547C2×C22⋊C4—118no—
548C2×C22⋊C4—118no—
549C2×C22⋊C4—118no—
550C2×C22⋊C4—112no—
551C2×C22⋊C4—112no—
552C2×C22⋊C4—112no—
553C2×C22⋊C4—112no—
554C2×C22⋊C4—112no—
555C2×C22⋊C4—112no—
556C2×C22⋊C4—112no—
557C2×C22⋊C4—112no—
558C2×C22⋊C4—114no—
559C2×C22⋊C4—112no—
560C2×C22⋊C4—112no—
561C2×C22⋊C4—114no—
562C2×C22⋊C4—114no—
563C2×C22⋊C4—112no—
564C2×C22⋊C4—112no—
565C2×C22⋊C4—114no—
566C2×C22⋊C4—114no—
567C2×C22⋊C4—114no—
568C2×C22⋊C4—444no—
569C2×C22⋊C4—444no—
570C2×C22⋊C4—444no—
571C2×C22⋊C4—444no—
572C2×C22⋊C4C22×D1112yes—
573C2×C22⋊C4C22×D1112yes—
574C2×C22⋊C4C22×D1114yes—
575C2×C22⋊C4C22×D1114yes—
576C2×C22⋊C4C22×D1112yes—
577C2×C22⋊C4C22×D1112yes—
578C2×C22⋊C4C22×D1114yes—
579C2×C22⋊C4C22×D1112yes—
580C2×C22⋊C4C22×D1112yes—
581C2×C42—114no—
582C2×C42—114no—
583C2×C42—114no—
584#95—114no—
585#95—114no—
586#95—114no—
587#95—114no—
588#95—114no—
589#95—114no—
590C2×C11—24no—
591C2×C11—24no—
592C2×C11—24no—
593C2×C11—42no—
594C2×C11—42no—
595C2×C11—42no—
596C2×C11—42no—
597C2×C11C2×#51811yescharacteristic
598C2×C11C2×#51811yescharacteristic
599C2×C11C2×#51811yescharacteristic
600C2×C11#353214yes—
601D11—44no—
602C24—24no—
603C24—24no—
604C24—24no—
605C24—24no—
606C24—24no—
607C24—24no—
608C24—24no—
609C24—24no—
610C24—24no—
611C24—42no—
612C24—42no—
613C24—42no—
614C24—42no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—42no—
620C24—42no—
621C24—42no—
622C24—42no—
623C24—416no—
624C24—416no—
625C24—416no—
626C24—464no—
627C24—112no—
628C24—114no—
629C24—224no—
630C24—442no—
631C24—442no—
632C24C2×C4×D1114yes—
633C24C2×C4×D1114yes—
634C24C2×C4×D1114yes—
635C24C2×C4×D1114yes—
636C24C2×C4×D1114yes—
637C24C2×C4×D1114yes—
638C24C2×C4×D1114yes—
639C24C23×D1111yescharacteristic
640C24C23×D1111yescharacteristic
641C24C23×D1111yescharacteristic
642C24C23×D1111yescharacteristic
643C24C23×D1111yescharacteristic
644C24C23×D1111yescharacteristic
645C24C23×D1111yescharacteristic
646C2×D4—118no—
647C2×D4—118no—
648C2×D4—118no—
649C2×D4—118no—
650C2×D4—118no—
651C2×D4—118no—
652C2×D4—228no—
653C2×D4—228no—
654C2×D4—4416no—
655C2×D4—442no—
656C2×D4—442no—
657C2×D4—444no—
658C2×D4—444no—
659C2×D4—442no—
660C2×D4—442no—
661C2×D4—4416no—
662C2×D4—4416no—
663C22×C4—28no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—114no—
667C22×C4—112no—
668C22×C4—112no—
669C22×C4—112no—
670C22×C4—114no—
671C22×C4—114no—
672C22×C4—114no—
673C22×C4—114no—
674C22×C4—224no—
675C22×C4—228no—
676C22×C4—444no—
677C22×C4—444no—
678C22×C4—444no—
679C22×C4—442no—
680C22×C4—442no—
681C22×C4—444no—
682C22×C4—444no—
683C22×C4C23×D1114yes—
684C22×C4C23×D1114yes—
685C4⋊C4—444no—
686C4⋊C4—444no—
687C4⋊C4—444no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—28no—
691C22⋊C4—42no—
692C22⋊C4—44no—
693C22⋊C4—42no—
694C22⋊C4—44no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—118no—
698C22⋊C4—118no—
699C22⋊C4—118no—
700C22⋊C4—118no—
701C22⋊C4—118no—
702C22⋊C4—118no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—228no—
706C22⋊C4—444no—
707C22⋊C4—444no—
708C22⋊C4—444no—
709C22⋊C4—442no—
710C22⋊C4—444no—
711C22⋊C4—442no—
712C22⋊C4—444no—
713C22⋊C4—442no—
714C22⋊C4—442no—
715C42—444no—
716C42—444no—
717C42—444no—
718C11#3435611yescharacteristic, complemented, Sylow
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—28no—
726C23—28no—
727C23—28no—
728C23—28no—
729C23—28no—
730C23—28no—
731C23—28no—
732C23—28no—
733C23—28no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—416no—
762C23—416no—
763C23—416no—
764C23—4128no—
765C23—416no—
766C23—114no—
767C23—222no—
768C23—224no—
769C23—224no—
770C23—222no—
771C23—228no—
772C23—444no—
773C23—444no—
774C23—888no—
775C23C22×C4×D1112yes—
776C23C22×C4×D1112yes—
777C23C22×C4×D1112yes—
778C23C22×C4×D1112yes—
779C23C22×C4×D1112yes—
780C23C22×C4×D1112yes—
781C23C22×C4×D1112yes—
782C23#6703714yes—
783C23#6703714yes—
784C23#6703714yes—
785C23C24×D1111yescharacteristic
786D4—2216no—
787D4—2216no—
788D4—448no—
789D4—448no—
790D4—448no—
791D4—448no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—88no—
799C2×C4—114no—
800C2×C4—114no—
801C2×C4—114no—
802C2×C4—228no—
803C2×C4—222no—
804C2×C4—224no—
805C2×C4—224no—
806C2×C4—222no—
807C2×C4—224no—
808C2×C4—224no—
809C2×C4—224no—
810C2×C4—224no—
811C2×C4—224no—
812C2×C4—224no—
813C2×C4—444no—
814C2×C4—444no—
815C2×C4—888no—
816C2×C4—888no—
817C22—28no—
818C22—28no—
819C22—28no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—416no—
839C22—416no—
840C22—416no—
841C22—416no—
842C22—416no—
843C22—416no—
844C22—416no—
845C22—44no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—224no—
850C22—224no—
851C22—224no—
852C22—444no—
853C22—444no—
854C22—888no—
855C22#1062301714yes—
856C22#1062301714yes—
857C22#1062301714yes—
858C22C23×C4×D1111yescharacteristic
859C22C2×#6703712yes—
860C22C2×#6703712yes—
861C22C2×#6703712yes—
862C4—44no—
863C4—44no—
864C4—224no—
865C4—224no—
866C4—224no—
867C4—444no—
868C4—444no—
869C2—24no—
870C2—24no—
871C2—24no—
872C2—42no—
873C2—42no—
874C2—42no—
875C2—42no—
876C2—444no—
877C2C2×#1062301711yescharacteristic
878C2C2×#1062301711yescharacteristic
879C2C2×#1062301711yescharacteristic
880C2#1308277114yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#379C2
socle, cosocleC23×C11C25
prime radicalC22×#67006C2
hypercenterC2×#379D11
hypocenterC11#34356
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
2. #13071755C2semidirect
3. #13071595C2semidirect
4. #13071467C2semidirect
5. #13071461C2semidirect
6. C22⋊C4×C22⋊D11C2semidirect
7. #13071432C2semidirect
8. #13071274C2semidirect
9. #13071271C2semidirect
10. #13071212C2semidirect
11. #13071212C2semidirect
12. #13071197C2semidirect
13. #13071192C2semidirect
14. C2×#10622860C2semidirect
15. C2×C11×#379C2semidirect
21. C22×C11×C22⋊C4C22semidirect
22. C22×C11×C22⋊C4C22semidirect
23. C2×#67006C4semidirect
32. C22×C22⋊Dic11C22semidirect
33. C22×C22⋊Dic11C22semidirect
34. C2×C4×C22⋊D11C22semidirect
35. C2×(C22⋊D11)⋊C4C22semidirect
36. C2×C22⋊C4×D11C22semidirect
37. C2×#66930C22semidirect
41. C11×#379C22semidirect
42. C11×#379C22semidirect
46. #10622860C22semidirect
47. #10622860C22semidirect
48. #10622826C22semidirect
49. #10622823C22semidirect
50. C4×C22⋊Dic11C22semidirect
51. #10622571C22semidirect
52. #10622570C22semidirect
53. #10622570C22semidirect
54. #10622570C22semidirect
55. #10622570C22semidirect
56. #10622569C22semidirect
57. #10622569C22semidirect
58. #10622569C22semidirect
59. #10622569C22semidirect
60. #10622568C22semidirect
61. #10622559C22semidirect
62. #10622558C22semidirect
63. #10622558C22semidirect
64. #10622558C22semidirect
65. #10622558C22semidirect
66. #10622557C22semidirect
67. #10622557C22semidirect
68. #10622557C22semidirect
69. #10622557C22semidirect
70. #10622556C22semidirect
71. #10622555C22semidirect
72. #10622555C22semidirect
73. C22⋊C4×Dic11C22semidirect
74. C22⋊C4×Dic11C22semidirect
75. C22⋊C4×Dic11C22semidirect
79. C25×C11C2×C4semidirect
92. C22×C22⋊D11C2×C4semidirect
93. C22×C22⋊D11C2×C4semidirect
94. C22×C22⋊D11C2×C4semidirect
105. C22×C4×D11C23semidirect
118. #67006C2×C4semidirect
119. #67006C2×C4semidirect
120. #67006C2×C4semidirect
121. #67006C2×C4semidirect
125. C2×C22⋊Dic11C2×C4semidirect
126. C2×C22⋊Dic11C2×C4semidirect
127. C2×C22⋊Dic11C2×C4semidirect
144. C2×(C2×D11)⋊C4C23semidirect
145. C2×(C2×D11)⋊C4C23semidirect
146. C2×(C2×D11)⋊C4C23semidirect
147. C2×Dic11⋊C4C23semidirect
148. C2×Dic11⋊C4C23semidirect
149. C2×Dic11⋊C4C23semidirect
150. C2×C4×Dic11C23semidirect
151. C2×C4×Dic11C23semidirect
152. C2×C4×Dic11C23semidirect
156. C11⋊#95C23semidirect
157. C11⋊#95C23semidirect
158. C11⋊#95C23semidirect
159. C11⋊#95C23semidirect
160. C11⋊#95C23semidirect
161. C11⋊#95C23semidirect
293. C2×#379D11semidirect
412. C22×C22⋊C4C2×D11semidirect
413. C22×C22⋊C4C2×D11semidirect
446. #379C2×D11semidirect
447. #379C2×D11semidirect
508. C25C4×D11semidirect
718. C11#34356semidirect

Maximal subgroups

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

subgroupindex
C22×#670062
#130717552
#130715952
#130714672
#130714612
C22⋊C4×C22⋊D112
#130714322
#130712742
#130712712
#130712122
#130711972
#130711922
C2×#106228602
C2×C11×#3792
#3435611