Finite Group Databasebeta

← #14926325

Subgroups — #14926325

Order 2816.

4046 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623165C211yesmaximal, characteristic, complemented
2C23×(C2×D11)⋊C4C211yesmaximal, characteristic
3#13076903C211yesmaximal, characteristic, complemented
4#13076901C212yesmaximal, complemented
5#13074427C212yesmaximal, complemented
6#13074424C211yesmaximal, characteristic, complemented
7#13074423C211yesmaximal, characteristic, complemented
8#13072284C214yesmaximal, complemented
9#13072281C214yesmaximal, complemented
10#13072280C214yesmaximal, complemented
11#13072279C214yesmaximal, complemented
12#13071229C211yesmaximal, characteristic, complemented
13#13071227C212yesmaximal, complemented
14D11×#379C212yesmaximal
15C11×#2848C211yesmaximal, characteristic, complemented
16C25×D11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic, complemented
20C2×C11×C22⋊Q8C2212yescomplemented
21C2×#66999C2212yescomplemented
22C22×(C2×D11)⋊C4—28no—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2214yes—
25C22×(C2×D11)⋊C4C2214yes—
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C2×#66977C2211yescharacteristic, complemented
30C2×#66977C2212yescomplemented
31#10623165—28no—
32C2×#66950C2212yescomplemented
33C2×#66949C2212yescomplemented
34C2×#66949C2212yescomplemented
35C2×C22⋊C4×D11C2212yes—
36C2×C22⋊C4×D11C2212yes—
37C2×C22⋊C4×D11C2214yes—
38C2×C22⋊C4×D11C2214yes—
39C2×#66931C2212yescomplemented
40C2×#66931C2214yescomplemented
41C11×#385C2212yescomplemented
42C11×#385C2214yescomplemented
43C11×#380C2211yescharacteristic, complemented
44C11×#380C2212yescomplemented
45C11×#379C2212yes—
46#10622860C2212yes—
47#10622844C2212yescomplemented
48#10622825C2211yescharacteristic, complemented
49#10622825C2212yescomplemented
50#10622823C2212yescomplemented
51#10622823C2214yescomplemented
52#10622607C2214yescomplemented
53#10622607C2214yescomplemented
54#10622607C2214yescomplemented
55#10622605C2214yescomplemented
56#10622605C2212yescomplemented
57#10622602C2214yescomplemented
58#10622602C2214yescomplemented
59#10622600C2214yescomplemented
60#10622568C2214yes—
61#10622568C2214yes—
62#10622568C2212yes—
63#10622568C2212yes—
64#10622563C2212yescomplemented
65#10622563C2214yescomplemented
66#10622559C2212yescomplemented
67#10622559C2214yescomplemented
68#10622555C2212yescomplemented
69#10622555C2214yescomplemented
70#10622290C2212yescomplemented
71#10622289C2214yescomplemented
72#10622286C2214yescomplemented
73#10622286C2212yescomplemented
74#10622281C2214yescomplemented
75#10622281C2214yescomplemented
76#10622280C2214yescomplemented
77C25×C11C2311yescharacteristic
78C24×D11—24no—
79C24×D11—24no—
80C24×D11—44no—
81C24×D11—44no—
82C24×D11Q818yescomplemented
83C24×D11C2314yes—
84C24×D11C2311yescharacteristic
85C24×D11C2311yescharacteristic
86C22×Q8×C11C2311yescharacteristic, complemented
87C23×C4×C11—24no—
88C23×C4×C11—44no—
89C23×C4×C11C2312yes—
90C23×C4×C11C2312yes—
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×Dic11—24no—
94C23×Dic11—44no—
95C23×Dic11C2314yes—
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C22×C4×D11C2312yes—
99C22×C4×D11C2312yes—
100C22×C4×D11C2314yes—
101C22×Dic22C2312yescomplemented
102C22×Dic22C2311yescharacteristic, complemented
103C11×C22⋊Q8—24no—
104C11×C22⋊Q8—44no—
105C2×C11×C4⋊C4C2311yescharacteristic, complemented
106C2×C11×C4⋊C4C2312yescomplemented
107C2×C11×C4⋊C4C2314yescomplemented
108C2×C11×C4⋊C4C2312yescomplemented
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2312yes—
111C2×C11×C22⋊C4C2312yes—
112C2×C11×C22⋊C4C2314yes—
113C2×C22⋊Dic11C2312yes—
114C2×C22⋊Dic11C2314yes—
115C2×C22⋊Dic11C2314yes—
116C2×C22⋊Dic11C2312yes—
117#66999—28no—
118C2×(C2×D11)⋊C4—24no—
119C2×(C2×D11)⋊C4—24no—
120C2×(C2×D11)⋊C4—24no—
121C2×(C2×D11)⋊C4—216no—
122C2×(C2×D11)⋊C4—216no—
123C2×(C2×D11)⋊C4D418yes—
124C2×(C2×D11)⋊C4C2312yes—
125C2×(C2×D11)⋊C4C2312yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2312yes—
130C2×(C2×D11)⋊C4C2312yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2312yes—
136C2×(C2×D11)⋊C4C2312yes—
137C2×C4⋊Dic11C2312yescomplemented
138C2×C4⋊Dic11C2311yescharacteristic, complemented
139C2×C4⋊Dic11C2314yescomplemented
140C2×C4⋊Dic11C2312yescomplemented
141#66977—24no—
142#66977—44no—
143C2×Dic11⋊C4C2312yescomplemented
144C2×Dic11⋊C4C2312yescomplemented
145C2×Dic11⋊C4C2312yescomplemented
146C2×Dic11⋊C4C2314yescomplemented
147C2×Dic11⋊C4C2314yescomplemented
148C2×Dic11⋊C4C2314yescomplemented
149#66950—28no—
150#66949—28no—
151#66949—28no—
152C22⋊C4×D11—28no—
153C22⋊C4×D11—28no—
154C22⋊C4×D11—48no—
155C22⋊C4×D11—48no—
156#66931—28no—
157#66931—48no—
158C11×#95C2314yescomplemented
159C11×#95C2312yescomplemented
160C11⋊#95C2314yescomplemented
161C11⋊#95C2314yescomplemented
162C11⋊#95C2314yescomplemented
163C11⋊#95C2314yescomplemented
164C11⋊#95C2312yescomplemented
165#34982—111nomaximal, Sylow
166C24×C11—22no—
167C24×C11—22no—
168C24×C11—24no—
169C24×C11—24no—
170C24×C11C2×Q814yes—
171C24×C11C2411yescharacteristic
172C24×C11C2412yes—
173C23×D11—22no—
174C23×D11—22no—
175C23×D11—28no—
176C23×D11—28no—
177C23×D11—232no—
178C23×D11—28no—
179C23×D11—28no—
180C23×D11—432no—
181C23×D11—42no—
182C23×D11—42no—
183C23×D11—44no—
184C23×D11—44no—
185C23×D11—42no—
186C23×D11—42no—
187C23×D11—416no—
188C23×D11—416no—
189C23×D11—432no—
190C23×D11C2×D414yes—
191C23×D11C2×Q8116yes—
192C23×D11C2×Q814yes—
193C23×D11C2×Q814yes—
194C23×D11#4114yes—
195C23×D11C2412yes—
196C23×D11C2412yes—
197C2×Q8×C11—22no—
198C2×Q8×C11—42no—
199C22×C4×C11—22no—
200C22×C4×C11—24no—
201C22×C4×C11—24no—
202C22×C4×C11—24no—
203C22×C4×C11—24no—
204C22×C4×C11—42no—
205C22×C4×C11—42no—
206C22×C4×C11—42no—
207C22×C4×C11—42no—
208C22×C4×C11—416no—
209C22×C4×C11C2×D414yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2414yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2411yescharacteristic
215C22×C4×C11C2411yescharacteristic
216C22×Dic11—28no—
217C22×Dic11—22no—
218C22×Dic11—28no—
219C22×Dic11—42no—
220C22×Dic11—44no—
221C22×Dic11—42no—
222C22×Dic11—416no—
223C22×Dic11C2×D414yes—
224C22×Dic11C2414yes—
225C22×Dic11C2412yes—
226C22×Dic11C2412yes—
227C22×Dic11C2412yes—
228C22×Dic11C2412yes—
229C2×C4×D11—24no—
230C2×C4×D11—24no—
231C2×C4×D11—28no—
232C2×C4×D11—44no—
233C2×C4×D11—44no—
234C2×C4×D11—44no—
235C2×C4×D11—44no—
236C2×Dic22—24no—
237C2×Dic22—22no—
238C2×Dic22—44no—
239C2×Dic22—42no—
240C11×C4⋊C4—22no—
241C11×C4⋊C4—24no—
242C11×C4⋊C4—42no—
243C11×C4⋊C4—44no—
244C11×C22⋊C4—24no—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—28no—
247C11×C22⋊C4—28no—
248C22⋊Dic11—24no—
249C22⋊Dic11—24no—
250C22⋊Dic11—28no—
251C22⋊Dic11—28no—
252(C2×D11)⋊C4—28no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—24no—
255(C2×D11)⋊C4—28no—
256(C2×D11)⋊C4—28no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—44no—
260(C2×D11)⋊C4—44no—
261(C2×D11)⋊C4—44no—
262(C2×D11)⋊C4—44no—
263(C2×D11)⋊C4C2×D418yes—
264(C2×D11)⋊C4C2×D418yes—
265C4⋊Dic11—24no—
266C4⋊Dic11—22no—
267C4⋊Dic11—44no—
268C4⋊Dic11—42no—
269Dic11⋊C4—24no—
270Dic11⋊C4—24no—
271Dic11⋊C4—24no—
272Dic11⋊C4—44no—
273Dic11⋊C4—44no—
274Dic11⋊C4—44no—
275C2×#543—111no—
276C23×C22⋊C4—111no—
277#2848—112no—
278#2848—111no—
279#2848D1111yescharacteristic, complemented
280#2626—112no—
281#2626—111no—
282#2626—111no—
283#2437—114no—
284#2437—114no—
285#2437—114no—
286#2437—114no—
287#2315—112no—
288#2315—111no—
289C2×#379—112no—
290C23×C11—28no—
291C23×C11—28no—
292C23×C11—216no—
293C23×C11—28no—
294C23×C11—216no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11C22×D412yes—
302C23×C11C22×Q812yes—
303C23×C11C22×Q814yes—
304C23×C11C2×#4112yes—
305C23×C11H(5,𝔽2)14yes—
306C23×C11H(5,𝔽2)14yes—
307C23×C11C2511yescharacteristic
308C22×D11—24no—
309C22×D11—24no—
310C22×D11—28no—
311C22×D11—232no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—24no—
315C22×D11—24no—
316C22×D11—232no—
317C22×D11—44no—
318C22×D11—44no—
319C22×D11—48no—
320C22×D11—416no—
321C22×D11—48no—
322C22×D11—48no—
323C22×D11—416no—
324C22×D11—416no—
325C22×D11—416no—
326C22×D11—416no—
327C22×D11—4128no—
328C22×D11—44no—
329C22×D11—44no—
330C22×D11—48no—
331C22×D11C22⋊Q8116yescomplemented
332C22×D11C22×D414yes—
333C22×D11C22×Q814yes—
334C22×D11C22×Q814yes—
335C22×D11C2×#4114yes—
336Q8×C11—82no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—24no—
343C2×C4×C11—22no—
344C2×C4×C11—24no—
345C2×C4×C11—24no—
346C2×C4×C11—24no—
347C2×C4×C11—24no—
348C2×C4×C11—22no—
349C2×C4×C11—44no—
350C2×C4×C11—48no—
351C2×C4×C11—48no—
352C2×C4×C11—44no—
353C2×C4×C11C22×D412yes—
354C2×C4×C11C22×D412yes—
355C2×Dic11—24no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—24no—
360C2×Dic11—24no—
361C2×Dic11—24no—
362C2×Dic11—24no—
363C2×Dic11—24no—
364C2×Dic11—24no—
365C2×Dic11—44no—
366C2×Dic11—416no—
367C2×Dic11—44no—
368C2×Dic11C22×D414yes—
369C4×D11—84no—
370C4×D11—84no—
371C4×D11—88no—
372Dic22—84no—
373Dic22—82no—
374C26—111no—
375C24×C4—111no—
376C24×C4C2×D1111yescharacteristic
377#543—228no—
378C2×C22⋊Q8—112no—
379C2×C22⋊Q8—111no—
380C2×C22⋊Q8—112no—
381C2×C22⋊Q8—112no—
382C2×C22⋊Q8—112no—
383C2×C22⋊Q8—112no—
384C2×C22⋊Q8—112no—
385C2×C22⋊Q8—114no—
386C2×C22⋊Q8C2×D1111yescharacteristic, complemented
387C2×C22⋊Q8C2×D1112yescomplemented
388C22×C22⋊C4—111no—
389C22×C22⋊C4—111no—
390C22×C22⋊C4—111no—
391C22×C22⋊C4—111no—
392C22×C22⋊C4—114no—
393C22×C22⋊C4—114no—
394C22×C22⋊C4—112no—
395C22×C22⋊C4—112no—
396C22×C22⋊C4—114no—
397C22×C22⋊C4—114no—
398C22×C22⋊C4—228no—
399#399—114no—
400#399—112no—
401#399—112no—
402#396—114no—
403#396—114no—
404#396—114no—
405#396—114no—
406#393—112no—
407#393—112no—
408#393—114no—
409#385—112no—
410#385—114no—
411#385—114no—
412#385—114no—
413#385—112no—
414#385—112no—
415#385—114no—
416#385—114no—
417#385—114no—
418#385—114no—
419#385C2×D1112yescomplemented
420#385C2×D1114yescomplemented
421#380—111no—
422#380—112no—
423#380—114no—
424#380—112no—
425#380—114no—
426#380—114no—
427#380C2×D1111yescharacteristic, complemented
428#380C2×D1112yescomplemented
429#379—112no—
430#379—112no—
431#379—112no—
432#379—114no—
433#379—114no—
434#379C2×D1112yes—
435C22×C11—232no—
436C22×C11—24no—
437C22×C11—24no—
438C22×C11—24no—
439C22×C11—22no—
440C22×C11—24no—
441C22×C11—22no—
442C22×C11—24no—
443C22×C11—24no—
444C22×C11—24no—
445C22×C11—24no—
446C22×C11C2×C22⋊Q814yes—
447C22×C11#54318yescomplemented
448C22×C11C23×D411yescharacteristic
449C22×C11C23×Q811yescharacteristic
450C22×C11C22×#4111yescharacteristic
451C22×C11C2×H(5,𝔽2)12yes—
452C22×C11C2×H(5,𝔽2)12yes—
453C2×D11—28no—
454C2×D11—24no—
455C2×D11—24no—
456C2×D11—28no—
457C2×D11—24no—
458C2×D11—28no—
459C2×D11—416no—
460C2×D11—464no—
461C2×D11—416no—
462C2×D11—42no—
463C2×D11—42no—
464C2×D11—44no—
465C2×D11C2×C22⋊Q818yes—
466C4×C11—22no—
467C4×C11—22no—
468C4×C11—42no—
469C4×C11—42no—
470C4×C11—42no—
471C4×C11—44no—
472Dic11—24no—
473Dic11—42no—
474Dic11—42no—
475Dic11—42no—
476Dic11—44no—
477C25—111no—
478C25—114no—
479C25—118no—
480C25—111no—
481C25—224no—
482C25—224no—
483C25—444no—
484C25—444no—
485C25C22×D1111yescharacteristic
486C22×Q8—112no—
487C22×Q8—111no—
488C22×Q8C22×D1111yescharacteristic, complemented
489C23×C4—24no—
490C23×C4—44no—
491C23×C4—111no—
492C23×C4—114no—
493C23×C4—111no—
494C23×C4—112no—
495C23×C4—112no—
496C23×C4—114no—
497C23×C4—224no—
498C23×C4—444no—
499C23×C4C22×D1112yes—
500C23×C4C22×D1112yes—
501C23×C4C22×D1111yescharacteristic
502C23×C4C22×D1111yescharacteristic
503C22⋊Q8—24no—
504C22⋊Q8—44no—
505C22⋊Q8—228no—
506C22⋊Q8—228no—
507C22⋊Q8—228no—
508C22⋊Q8—228no—
509C22⋊Q8—228no—
510C22⋊Q8—224no—
511C22⋊Q8—448no—
512C22⋊Q8—444no—
513C2×C4⋊C4—112no—
514C2×C4⋊C4—111no—
515C2×C4⋊C4—112no—
516C2×C4⋊C4—112no—
517C2×C4⋊C4—112no—
518C2×C4⋊C4—114no—
519C2×C4⋊C4—112no—
520C2×C4⋊C4—114no—
521C2×C4⋊C4—114no—
522C2×C4⋊C4—114no—
523C2×C4⋊C4C22×D1111yescharacteristic, complemented
524C2×C4⋊C4C22×D1112yescomplemented
525C2×C4⋊C4C22×D1114yescomplemented
526C2×C4⋊C4C22×D1112yescomplemented
527C2×C22⋊C4—118no—
528C2×C22⋊C4—112no—
529C2×C22⋊C4—112no—
530C2×C22⋊C4—112no—
531C2×C22⋊C4—114no—
532C2×C22⋊C4—114no—
533C2×C22⋊C4—112no—
534C2×C22⋊C4—114no—
535C2×C22⋊C4—114no—
536C2×C22⋊C4—112no—
537C2×C22⋊C4—112no—
538C2×C22⋊C4—112no—
539C2×C22⋊C4—112no—
540C2×C22⋊C4—114no—
541C2×C22⋊C4—114no—
542C2×C22⋊C4—114no—
543C2×C22⋊C4—114no—
544C2×C22⋊C4—114no—
545C2×C22⋊C4—228no—
546C2×C22⋊C4—228no—
547C2×C22⋊C4—2216no—
548C2×C22⋊C4—2216no—
549C2×C22⋊C4—224no—
550C2×C22⋊C4—224no—
551C2×C22⋊C4—224no—
552C2×C22⋊C4—448no—
553C2×C22⋊C4—448no—
554C2×C22⋊C4C22×D1112yes—
555C2×C22⋊C4C22×D1114yes—
556C2×C22⋊C4C22×D1114yes—
557C2×C22⋊C4C22×D1112yes—
558#95—114no—
559#95—114no—
560#95—114no—
561#95—114no—
562#95—112no—
563#95C22×D1114yescomplemented
564#95C22×D1112yescomplemented
565C2×C11—24no—
566C2×C11—28no—
567C2×C11C22×C22⋊Q811yescharacteristic
568C2×C11C2×#54312yes—
569C2×C11#348411yescharacteristic
570C2×C11#348411yescharacteristic
571C2×C11#349012yes—
572D11—28no—
573D11—44no—
574C24—22no—
575C24—24no—
576C24—22no—
577C24—24no—
578C24—112no—
579C24—114no—
580C24—114no—
581C24—114no—
582C24—112no—
583C24—1116no—
584C24—114no—
585C24—228no—
586C24—2232no—
587C24—228no—
588C24—222no—
589C24—228no—
590C24—222no—
591C24—228no—
592C24—4432no—
593C24—442no—
594C24—444no—
595C24—442no—
596C24—442no—
597C24—444no—
598C24—442no—
599C24—4416no—
600C24—4416no—
601C24—4432no—
602C24Q8×D1114yes—
603C24C23×D1111yescharacteristic
604C24C23×D1112yes—
605C2×Q8—22no—
606C2×Q8—42no—
607C2×Q8—224no—
608C2×Q8—222no—
609C2×Q8—442no—
610C2×Q8—444no—
611C22×C4—22no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—24no—
615C22×C4—24no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—416no—
621C22×C4—112no—
622C22×C4—114no—
623C22×C4—114no—
624C22×C4—112no—
625C22×C4—112no—
626C22×C4—112no—
627C22×C4—224no—
628C22×C4—224no—
629C22×C4—228no—
630C22×C4—228no—
631C22×C4—222no—
632C22×C4—228no—
633C22×C4—444no—
634C22×C4—444no—
635C22×C4—444no—
636C22×C4—444no—
637C22×C4—442no—
638C22×C4—444no—
639C22×C4—442no—
640C22×C4—4416no—
641C22×C4D4×D1114yes—
642C22×C4C23×D1112yes—
643C22×C4C23×D1114yes—
644C22×C4C23×D1112yes—
645C22×C4C23×D1112yes—
646C22×C4C23×D1111yescharacteristic
647C22×C4C23×D1111yescharacteristic
648C4⋊C4—22no—
649C4⋊C4—24no—
650C4⋊C4—42no—
651C4⋊C4—44no—
652C4⋊C4—224no—
653C4⋊C4—224no—
654C4⋊C4—224no—
655C4⋊C4—224no—
656C4⋊C4—222no—
657C4⋊C4—444no—
658C4⋊C4—444no—
659C4⋊C4—444no—
660C4⋊C4—442no—
661C4⋊C4—444no—
662C22⋊C4—24no—
663C22⋊C4—28no—
664C22⋊C4—24no—
665C22⋊C4—28no—
666C22⋊C4—118no—
667C22⋊C4—118no—
668C22⋊C4—228no—
669C22⋊C4—228no—
670C22⋊C4—224no—
671C22⋊C4—224no—
672C22⋊C4—228no—
673C22⋊C4—224no—
674C22⋊C4—228no—
675C22⋊C4—224no—
676C22⋊C4—228no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—444no—
680C22⋊C4—444no—
681C22⋊C4—444no—
682C22⋊C4—444no—
683C11#3498211yescharacteristic, complemented, Sylow
684C23—28no—
685C23—28no—
686C23—216no—
687C23—28no—
688C23—216no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—114no—
696C23—114no—
697C23—114no—
698C23—1116no—
699C23—114no—
700C23—2232no—
701C23—224no—
702C23—224no—
703C23—228no—
704C23—2232no—
705C23—222no—
706C23—224no—
707C23—222no—
708C23—224no—
709C23—444no—
710C23—444no—
711C23—448no—
712C23—4416no—
713C23—448no—
714C23—448no—
715C23—4416no—
716C23—4416no—
717C23—4416no—
718C23—4416no—
719C23—44128no—
720C23—444no—
721C23—444no—
722C23—448no—
723C23C2×D4×D1112yes—
724C23#6703714yes—
725C23C2×Q8×D1112yes—
726C23C2×Q8×D1114yes—
727C23#41×D1112yes—
728C23#6704214yes—
729C23C24×D1111yescharacteristic
730Q8—82no—
731Q8—882no—
732Q8—884no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—44no—
746C2×C4—48no—
747C2×C4—48no—
748C2×C4—44no—
749C2×C4—114no—
750C2×C4—224no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—224no—
755C2×C4—224no—
756C2×C4—224no—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—224no—
760C2×C4—444no—
761C2×C4—4416no—
762C2×C4—444no—
763C2×C4—884no—
764C2×C4—884no—
765C2×C4—888no—
766C2×C4C2×D4×D1112yes—
767C2×C4C2×D4×D1112yes—
768C22—232no—
769C22—22no—
770C22—24no—
771C22—22no—
772C22—24no—
773C22—24no—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—118no—
780C22—224no—
781C22—224no—
782C22—228no—
783C22—228no—
784C22—228no—
785C22—224no—
786C22—4416no—
787C22—4464no—
788C22—4416no—
789C22—442no—
790C22—442no—
791C22—444no—
792C22D11×C22⋊Q814yes—
793C22#1062316518yescomplemented
794C22C22×D4×D1111yescharacteristic
795C22C2×#6703712yes—
796C22C22×Q8×D1111yescharacteristic
797C22C2×#41×D1111yescharacteristic
798C22C2×#6704212yes—
799C4—22no—
800C4—22no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—44no—
805C4—224no—
806C4—442no—
807C4—442no—
808C4—442no—
809C4—444no—
810C2—24no—
811C2—28no—
812C2—228no—
813C2—444no—
814C2C2×D11×C22⋊Q811yescharacteristic
815C2C2×#1062316512yes—
816C2#1308224511yescharacteristic
817C2#1308224911yescharacteristic
818C2#1308229912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2848C2
prime radicalC25×D11C22
hypercenter#2848D11
hypocenterC11#34982
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2848

Complements

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

NH ≅ G/Ntype
1. C2×#10623165C2semidirect
3. #13076903C2semidirect
4. #13076901C2semidirect
5. #13074427C2semidirect
6. #13074424C2semidirect
7. #13074423C2semidirect
8. #13072284C2semidirect
9. #13072281C2semidirect
10. #13072280C2semidirect
11. #13072279C2semidirect
12. #13071229C2semidirect
13. #13071227C2semidirect
15. C11×#2848C2semidirect
19. C2×C11×C22⋊Q8C22semidirect
20. C2×C11×C22⋊Q8C22semidirect
21. C2×#66999C22semidirect
29. C2×#66977C22semidirect
30. C2×#66977C22semidirect
32. C2×#66950C22semidirect
33. C2×#66949C22semidirect
34. C2×#66949C22semidirect
39. C2×#66931C22semidirect
40. C2×#66931C22semidirect
41. C11×#385C22semidirect
42. C11×#385C22semidirect
43. C11×#380C22semidirect
44. C11×#380C22semidirect
47. #10622844C22semidirect
48. #10622825C22semidirect
49. #10622825C22semidirect
50. #10622823C22semidirect
51. #10622823C22semidirect
52. #10622607C22semidirect
53. #10622607C22semidirect
54. #10622607C22semidirect
55. #10622605C22semidirect
56. #10622605C22semidirect
57. #10622602C22semidirect
58. #10622602C22semidirect
59. #10622600C22semidirect
64. #10622563C22semidirect
65. #10622563C22semidirect
66. #10622559C22semidirect
67. #10622559C22semidirect
68. #10622555C22semidirect
69. #10622555C22semidirect
70. #10622290C22semidirect
71. #10622289C22semidirect
72. #10622286C22semidirect
73. #10622286C22semidirect
74. #10622281C22semidirect
75. #10622281C22semidirect
76. #10622280C22semidirect
82. C24×D11Q8semidirect
86. C22×Q8×C11C23semidirect
101. C22×Dic22C23semidirect
102. C22×Dic22C23semidirect
105. C2×C11×C4⋊C4C23semidirect
106. C2×C11×C4⋊C4C23semidirect
107. C2×C11×C4⋊C4C23semidirect
108. C2×C11×C4⋊C4C23semidirect
137. C2×C4⋊Dic11C23semidirect
138. C2×C4⋊Dic11C23semidirect
139. C2×C4⋊Dic11C23semidirect
140. C2×C4⋊Dic11C23semidirect
143. C2×Dic11⋊C4C23semidirect
144. C2×Dic11⋊C4C23semidirect
145. C2×Dic11⋊C4C23semidirect
146. C2×Dic11⋊C4C23semidirect
147. C2×Dic11⋊C4C23semidirect
148. C2×Dic11⋊C4C23semidirect
158. C11×#95C23semidirect
159. C11×#95C23semidirect
160. C11⋊#95C23semidirect
161. C11⋊#95C23semidirect
162. C11⋊#95C23semidirect
163. C11⋊#95C23semidirect
164. C11⋊#95C23semidirect
279. #2848D11semidirect
331. C22×D11C22⋊Q8semidirect
386. C2×C22⋊Q8C2×D11semidirect
387. C2×C22⋊Q8C2×D11semidirect
419. #385C2×D11semidirect
420. #385C2×D11semidirect
427. #380C2×D11semidirect
428. #380C2×D11semidirect
447. C22×C11#543semidirect
488. C22×Q8C22×D11semidirect
523. C2×C4⋊C4C22×D11semidirect
524. C2×C4⋊C4C22×D11semidirect
525. C2×C4⋊C4C22×D11semidirect
526. C2×C4⋊C4C22×D11semidirect
563. #95C22×D11semidirect
564. #95C22×D11semidirect
683. C11#34982semidirect
793. C22#10623165semidirect

Maximal subgroups

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

subgroupindex
C2×#106231652
C23×(C2×D11)⋊C42
#130769032
#130769012
#130744272
#130744242
#130744232
#130722842
#130722812
#130722802
#130722792
#130712292
#130712272
D11×#3792
C11×#28482
#3498211