Finite Group Databasebeta

← #14926323

Subgroups — #14926323

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
2C22×C22⋊C4×D11C211yesmaximal, characteristic
3#13076904C211yesmaximal, characteristic, complemented
4#13076902C212yesmaximal, complemented
5#13076900C211yesmaximal, characteristic, complemented
6#13074425C212yesmaximal, complemented
7#13074421C211yesmaximal, characteristic, complemented
8#13072283C214yesmaximal, complemented
9#13072278C214yesmaximal, complemented
10#13072278C214yesmaximal, complemented
11#13072276C214yesmaximal, complemented
12#13071229C211yesmaximal, characteristic, complemented
13#13071227C212yesmaximal, complemented
14D11×#379C212yesmaximal
15C11×#2626C211yesmaximal, characteristic, complemented
16C25×D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic, complemented
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C2×#66999C2212yescomplemented
23C2×#66999C2212yescomplemented
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C2×#66977C2211yescharacteristic, complemented
27#10623165—28no—
28C2×#66950C2212yescomplemented
29C2×#66950C2212yescomplemented
30C2×#66949C2212yescomplemented
31C2×#66949C2212yescomplemented
32C2×#66949C2214yescomplemented
33C2×C22⋊C4×D11—28no—
34C2×C22⋊C4×D11C2212yes—
35C2×C22⋊C4×D11C2212yes—
36C2×C22⋊C4×D11C2214yes—
37C2×C22⋊C4×D11C2214yes—
38C2×C22⋊C4×D11C2214yes—
39C2×C22⋊C4×D11C2214yes—
40C2×#66931C2212yescomplemented
41C11×#399C2212yescomplemented
42C11×#396C2214yescomplemented
43C11×#393C2212yescomplemented
44C11×#385C2212yescomplemented
45C11×#380C2211yescharacteristic, complemented
46C11×#379C2212yes—
47#10622860C2212yes—
48#10622825C2211yescharacteristic, complemented
49#10622823C2212yescomplemented
50#10622602C2214yescomplemented
51#10622602C2214yescomplemented
52#10622602C2214yescomplemented
53#10622602C2214yescomplemented
54#10622600C2214yescomplemented
55#10622600C2212yescomplemented
56#10622600C2212yescomplemented
57#10622568C2214yes—
58#10622568C2214yes—
59#10622568C2212yes—
60#10622568C2212yes—
61#10622563C2212yescomplemented
62#10622562C2214yescomplemented
63#10622562C2212yescomplemented
64#10622561C2214yescomplemented
65#10622561C2214yescomplemented
66#10622561C2214yescomplemented
67#10622560C2212yescomplemented
68#10622560C2214yescomplemented
69#10622559C2212yescomplemented
70#10622555C2212yescomplemented
71#10622281C2214yescomplemented
72#10622281C2214yescomplemented
73#10622281C2214yescomplemented
74#10622281C2214yescomplemented
75#10622280C2214yescomplemented
76#10622280C2214yescomplemented
77C25×C11C2311yescharacteristic
78C24×D11—24no—
79C24×D11—24no—
80C24×D11—44no—
81C24×D11—44no—
82C24×D11Q818yescomplemented
83C24×D11C2311yescharacteristic
84C24×D11C2314yes—
85C24×D11C2311yescharacteristic
86C22×Q8×C11C2311yescharacteristic, complemented
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C22×C4×D11—24no—
92C22×C4×D11—24no—
93C22×C4×D11—44no—
94C22×C4×D11—44no—
95C22×C4×D11C2314yes—
96C22×C4×D11C2312yes—
97C22×C4×D11C2312yes—
98C22×C4×D11C2312yes—
99C22×C4×D11C2312yes—
100C22×C4×D11C2314yes—
101C22×Dic22C2312yescomplemented
102C22×Dic22C2311yescharacteristic, complemented
103C11×C22⋊Q8—24no—
104C2×C11×C4⋊C4C2311yescharacteristic, complemented
105C2×C11×C4⋊C4C2312yescomplemented
106C2×C11×C4⋊C4C2314yescomplemented
107C2×C11×C4⋊C4C2312yescomplemented
108C2×C11×C22⋊C4—24no—
109C2×C11×C22⋊C4C2312yes—
110C2×C11×C22⋊C4C2312yes—
111C2×C11×C22⋊C4C2312yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2314yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C22⋊Dic11—24no—
116C2×C22⋊Dic11C2312yes—
117C2×C22⋊Dic11C2314yes—
118C2×C22⋊Dic11C2312yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2314yes—
121#66999—28no—
122#66999—44no—
123C2×(C2×D11)⋊C4—24no—
124C2×(C2×D11)⋊C4D418yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2312yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2312yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2312yes—
134C2×(C2×D11)⋊C4C2312yes—
135C2×C4⋊Dic11C2312yescomplemented
136C2×C4⋊Dic11C2311yescharacteristic, complemented
137C2×C4⋊Dic11C2314yescomplemented
138C2×C4⋊Dic11C2312yescomplemented
139#66977—24no—
140C2×Dic11⋊C4C2312yescomplemented
141C2×Dic11⋊C4C2312yescomplemented
142C2×Dic11⋊C4C2312yescomplemented
143C2×Dic11⋊C4C2314yescomplemented
144C2×Dic11⋊C4C2314yescomplemented
145C2×Dic11⋊C4C2314yescomplemented
146#66950—28no—
147#66950—44no—
148#66949—28no—
149#66949—28no—
150#66949—48no—
151C22⋊C4×D11—28no—
152C22⋊C4×D11—28no—
153C22⋊C4×D11—216no—
154C22⋊C4×D11—216no—
155C22⋊C4×D11—48no—
156C22⋊C4×D11—48no—
157#66931—28no—
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—42no—
169C24×C11—42no—
170C24×C11C2×Q814yes—
171C24×C11C2412yes—
172C24×C11C2411yescharacteristic
173C23×D11—22no—
174C23×D11—22no—
175C23×D11—24no—
176C23×D11—24no—
177C23×D11—232no—
178C23×D11—28no—
179C23×D11—28no—
180C23×D11—28no—
181C23×D11—28no—
182C23×D11—432no—
183C23×D11—42no—
184C23×D11—42no—
185C23×D11—44no—
186C23×D11—44no—
187C23×D11—416no—
188C23×D11—416no—
189C23×D11—432no—
190C23×D11C2×D414yes—
191C23×D11C2×Q814yes—
192C23×D11C2×Q8116yes—
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—42no—
201C22×C4×C11—42no—
202C22×C4×C11C2×D414yes—
203C22×C4×C11C2412yes—
204C22×C4×C11C2414yes—
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2411yescharacteristic
208C22×C4×C11C2411yescharacteristic
209C22×Dic11—22no—
210C22×Dic11—42no—
211C22×Dic11—42no—
212C22×Dic11C2×D414yes—
213C22×Dic11C2414yes—
214C22×Dic11C2412yes—
215C22×Dic11C2412yes—
216C22×Dic11C2412yes—
217C22×Dic11C2412yes—
218C2×C4×D11—28no—
219C2×C4×D11—24no—
220C2×C4×D11—24no—
221C2×C4×D11—28no—
222C2×C4×D11—28no—
223C2×C4×D11—24no—
224C2×C4×D11—24no—
225C2×C4×D11—24no—
226C2×C4×D11—24no—
227C2×C4×D11—42no—
228C2×C4×D11—42no—
229C2×C4×D11—44no—
230C2×C4×D11—44no—
231C2×C4×D11—44no—
232C2×C4×D11—44no—
233C2×C4×D11—44no—
234C2×C4×D11—416no—
235C2×C4×D11—416no—
236C2×Dic22—24no—
237C2×Dic22—22no—
238C2×Dic22—44no—
239C2×Dic22—42no—
240C11×C4⋊C4—22no—
241C11×C4⋊C4—24no—
242C11×C4⋊C4—44no—
243C11×C4⋊C4—42no—
244C11×C22⋊C4—24no—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—44no—
249C11×C22⋊C4—44no—
250C22⋊Dic11—28no—
251C22⋊Dic11—24no—
252C22⋊Dic11—24no—
253C22⋊Dic11—44no—
254C22⋊Dic11—44no—
255(C2×D11)⋊C4—28no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—28no—
259(C2×D11)⋊C4—28no—
260(C2×D11)⋊C4—28no—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—28no—
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#2848—111no—
280#2626—112no—
281#2626—111no—
282#2626D1111yescharacteristic, complemented
283#2437—114no—
284#2437—114no—
285#2437—114no—
286#2437—114no—
287#2315—112no—
288#2315—111no—
289C2×#379—112no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—28no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—24no—
296C23×C11—24no—
297C23×C11—48no—
298C23×C11—44no—
299C23×C11—44no—
300C23×C11—48no—
301C23×C11C22×D412yes—
302C23×C11C22×Q814yes—
303C23×C11C22×Q812yes—
304C23×C11C2×#4112yes—
305C23×C11C2511yescharacteristic
306C22×D11—28no—
307C22×D11—28no—
308C22×D11—216no—
309C22×D11—28no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—24no—
315C22×D11—24no—
316C22×D11—216no—
317C22×D11—232no—
318C22×D11—232no—
319C22×D11—44no—
320C22×D11—44no—
321C22×D11—48no—
322C22×D11—416no—
323C22×D11—48no—
324C22×D11—416no—
325C22×D11—416no—
326C22×D11—416no—
327C22×D11—416no—
328C22×D11—4128no—
329C22×D11C22⋊Q8116yescomplemented
330C22×D11C22×D414yes—
331C22×D11C22×Q814yes—
332C22×D11C22×Q814yes—
333C22×D11C2×#4114yes—
334C22×D11H(5,𝔽2)14yes—
335C22×D11H(5,𝔽2)14yes—
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—24no—
344C2×C4×C11—24no—
345C2×C4×C11—24no—
346C2×C4×C11—24no—
347C2×C4×C11—24no—
348C2×C4×C11—44no—
349C2×C4×C11—44no—
350C2×C4×C11C22×D412yes—
351C2×C4×C11C22×D412yes—
352C2×Dic11—24no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—24no—
357C2×Dic11—24no—
358C2×Dic11—22no—
359C2×Dic11—24no—
360C2×Dic11—24no—
361C2×Dic11—22no—
362C2×Dic11—24no—
363C2×Dic11—44no—
364C2×Dic11—44no—
365C2×Dic11C22×D414yes—
366C4×D11—416no—
367C4×D11—48no—
368C4×D11—48no—
369C4×D11—84no—
370C4×D11—84no—
371C4×D11—88no—
372Dic22—84no—
373Dic22—82no—
374C26—111no—
375C24×C4—111no—
376C24×C4—111no—
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—114no—
385C2×C22⋊Q8—112no—
386C2×C22⋊Q8—112no—
387C2×C22⋊Q8C2×D1111yescharacteristic, complemented
388C22×C22⋊C4—111no—
389C22×C22⋊C4—111no—
390C22×C22⋊C4—111no—
391C22×C22⋊C4—112no—
392C22×C22⋊C4—112no—
393C22×C22⋊C4—114no—
394C22×C22⋊C4—114no—
395C22×C22⋊C4—114no—
396C22×C22⋊C4—114no—
397C22×C22⋊C4—228no—
398C22×C22⋊C4C2×D1111yescharacteristic
399#399—114no—
400#399—112no—
401#399C2×D1112yescomplemented
402#396—114no—
403#396—114no—
404#396—114no—
405#396C2×D1114yescomplemented
406#393—114no—
407#393—112no—
408#393C2×D1112yescomplemented
409#385—112no—
410#385—114no—
411#385—114no—
412#385—114no—
413#385—114no—
414#385—112no—
415#385—112no—
416#385—114no—
417#385—114no—
418#385—114no—
419#385—114no—
420#385C2×D1112yescomplemented
421#380—111no—
422#380—114no—
423#380—112no—
424#380—112no—
425#380—112no—
426#380—114no—
427#380—114no—
428#380C2×D1111yescharacteristic, complemented
429#379—112no—
430#379—112no—
431#379—112no—
432#379—114no—
433#379—114no—
434#379C2×D1112yes—
435C22×C11—24no—
436C22×C11—22no—
437C22×C11—22no—
438C22×C11—24no—
439C22×C11—24no—
440C22×C11—28no—
441C22×C11—416no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11—44no—
445C22×C11C2×C22⋊Q814yes—
446C22×C11C23×D411yescharacteristic
447C22×C11C23×Q811yescharacteristic
448C22×C11C22×#4111yescharacteristic
449C22×C11C2×H(5,𝔽2)12yes—
450C22×C11C2×H(5,𝔽2)12yes—
451C2×D11—232no—
452C2×D11—24no—
453C2×D11—24no—
454C2×D11—28no—
455C2×D11—24no—
456C2×D11—24no—
457C2×D11—24no—
458C2×D11—24no—
459C2×D11—24no—
460C2×D11—24no—
461C2×D11—28no—
462C2×D11—416no—
463C2×D11—464no—
464C2×D11C2×C22⋊Q818yes—
465C2×D11#54318yescomplemented
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—111no—
479C25—114no—
480C25—118no—
481C25—224no—
482C25—224no—
483C25—444no—
484C25—444no—
485C25C22×D1111yescharacteristic
486C22×Q8—112no—
487C22×Q8—111no—
488C22×Q8C22×D1111yescharacteristic, complemented
489C23×C4—111no—
490C23×C4—111no—
491C23×C4—114no—
492C23×C4—112no—
493C23×C4—112no—
494C23×C4—112no—
495C23×C4—112no—
496C23×C4—114no—
497C23×C4—224no—
498C23×C4—224no—
499C23×C4—444no—
500C23×C4—444no—
501C23×C4C22×D1111yescharacteristic
502C23×C4C22×D1111yescharacteristic
503C22⋊Q8—24no—
504C22⋊Q8—228no—
505C22⋊Q8—228no—
506C22⋊Q8—228no—
507C22⋊Q8—228no—
508C22⋊Q8—228no—
509C22⋊Q8—224no—
510C22⋊Q8—448no—
511C22⋊Q8—444no—
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×D1112yescomplemented
526C2×C4⋊C4C22×D1114yescomplemented
527C2×C22⋊C4—24no—
528C2×C22⋊C4—118no—
529C2×C22⋊C4—112no—
530C2×C22⋊C4—112no—
531C2×C22⋊C4—114no—
532C2×C22⋊C4—112no—
533C2×C22⋊C4—112no—
534C2×C22⋊C4—114no—
535C2×C22⋊C4—112no—
536C2×C22⋊C4—112no—
537C2×C22⋊C4—114no—
538C2×C22⋊C4—114no—
539C2×C22⋊C4—114no—
540C2×C22⋊C4—114no—
541C2×C22⋊C4—114no—
542C2×C22⋊C4—114no—
543C2×C22⋊C4—114no—
544C2×C22⋊C4—2216no—
545C2×C22⋊C4—2216no—
546C2×C22⋊C4—228no—
547C2×C22⋊C4—228no—
548C2×C22⋊C4—224no—
549C2×C22⋊C4—224no—
550C2×C22⋊C4—448no—
551C2×C22⋊C4—448no—
552C2×C22⋊C4C22×D1112yes—
553C2×C22⋊C4C22×D1112yes—
554C2×C22⋊C4C22×D1112yes—
555C2×C22⋊C4C22×D1112yes—
556C2×C22⋊C4C22×D1114yes—
557C2×C22⋊C4C22×D1114yes—
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—44no—
567C2×C11C22×C22⋊Q811yescharacteristic
568C2×C11C2×#54312yes—
569C2×C11#348411yescharacteristic
570C2×C11#348411yescharacteristic
571C2×C11#349012yes—
572D11—28no—
573D11—28no—
574C24—22no—
575C24—22no—
576C24—42no—
577C24—42no—
578C24—112no—
579C24—112no—
580C24—114no—
581C24—114no—
582C24—114no—
583C24—114no—
584C24—1116no—
585C24—224no—
586C24—224no—
587C24—228no—
588C24—228no—
589C24—228no—
590C24—2232no—
591C24—228no—
592C24—222no—
593C24—222no—
594C24—442no—
595C24—442no—
596C24—444no—
597C24—444no—
598C24—4432no—
599C24—4416no—
600C24—4416no—
601C24—4432no—
602C24Q8×D1114yes—
603C24C23×D1112yes—
604C24C23×D1111yescharacteristic
605C2×Q8—22no—
606C2×Q8—42no—
607C2×Q8—224no—
608C2×Q8—222no—
609C2×Q8—442no—
610C2×Q8—444no—
611C22×C4—22no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—112no—
615C22×C4—114no—
616C22×C4—114no—
617C22×C4—112no—
618C22×C4—112no—
619C22×C4—112no—
620C22×C4—228no—
621C22×C4—224no—
622C22×C4—224no—
623C22×C4—228no—
624C22×C4—224no—
625C22×C4—224no—
626C22×C4—228no—
627C22×C4—222no—
628C22×C4—224no—
629C22×C4—224no—
630C22×C4—442no—
631C22×C4—442no—
632C22×C4—444no—
633C22×C4—444no—
634C22×C4—444no—
635C22×C4—444no—
636C22×C4—444no—
637C22×C4—4416no—
638C22×C4—4416no—
639C22×C4—442no—
640C22×C4—442no—
641C22×C4D4×D1114yes—
642C22×C4C23×D1114yes—
643C22×C4C23×D1112yes—
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—24no—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—118no—
669C22⋊C4—118no—
670C22⋊C4—228no—
671C22⋊C4—224no—
672C22⋊C4—224no—
673C22⋊C4—228no—
674C22⋊C4—228no—
675C22⋊C4—228no—
676C22⋊C4—228no—
677C22⋊C4—228no—
678C22⋊C4—228no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4—444no—
682C22⋊C4—444no—
683C11#3498211yescharacteristic, complemented, Sylow
684C23—22no—
685C23—22no—
686C23—28no—
687C23—22no—
688C23—22no—
689C23—24no—
690C23—24no—
691C23—48no—
692C23—44no—
693C23—44no—
694C23—48no—
695C23—114no—
696C23—114no—
697C23—114no—
698C23—114no—
699C23—114no—
700C23—114no—
701C23—1116no—
702C23—2216no—
703C23—2232no—
704C23—2232no—
705C23—228no—
706C23—228no—
707C23—2216no—
708C23—228no—
709C23—222no—
710C23—222no—
711C23—222no—
712C23—224no—
713C23—222no—
714C23—224no—
715C23—444no—
716C23—444no—
717C23—448no—
718C23—448no—
719C23—4416no—
720C23—4416no—
721C23—4416no—
722C23—4416no—
723C23—4416no—
724C23—44128no—
725C23C2×D4×D1112yes—
726C23C2×Q8×D1114yes—
727C23C2×Q8×D1112yes—
728C23#41×D1112yes—
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—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—114no—
747C2×C4—224no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—224no—
752C2×C4—224no—
753C2×C4—224no—
754C2×C4—224no—
755C2×C4—224no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—448no—
759C2×C4—448no—
760C2×C4—4416no—
761C2×C4—444no—
762C2×C4—444no—
763C2×C4—884no—
764C2×C4—884no—
765C2×C4—888no—
766C2×C4C2×D4×D1112yes—
767C2×C4C2×D4×D1112yes—
768C22—22no—
769C22—22no—
770C22—24no—
771C22—24no—
772C22—28no—
773C22—24no—
774C22—416no—
775C22—42no—
776C22—42no—
777C22—44no—
778C22—118no—
779C22—118no—
780C22—2232no—
781C22—224no—
782C22—224no—
783C22—224no—
784C22—224no—
785C22—224no—
786C22—228no—
787C22—228no—
788C22—224no—
789C22—224no—
790C22—224no—
791C22—4416no—
792C22—4464no—
793C22D11×C22⋊Q814yes—
794C22C22×D4×D1111yescharacteristic
795C22C22×Q8×D1111yescharacteristic
796C22C2×#41×D1111yescharacteristic
797C22D11×H(5,𝔽2)12yes—
798C22D11×H(5,𝔽2)12yes—
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—44no—
812C2—228no—
813C2—228no—
814C2C2×D11×C22⋊Q811yescharacteristic
815C2D11×#54312yes—
816C2#1308224811yescharacteristic
817C2#1308225011yescharacteristic
818C2#1308230212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2626C2
prime radicalC25×D11C22
hypercenter#2626D11
hypocenterC11#34982
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2626

Complements

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

NH ≅ G/Ntype
1. C2×#10623165C2semidirect
3. #13076904C2semidirect
4. #13076902C2semidirect
5. #13076900C2semidirect
6. #13074425C2semidirect
7. #13074421C2semidirect
8. #13072283C2semidirect
9. #13072278C2semidirect
10. #13072278C2semidirect
11. #13072276C2semidirect
12. #13071229C2semidirect
13. #13071227C2semidirect
15. C11×#2626C2semidirect
19. C2×C11×C22⋊Q8C22semidirect
22. C2×#66999C22semidirect
23. C2×#66999C22semidirect
26. C2×#66977C22semidirect
28. C2×#66950C22semidirect
29. C2×#66950C22semidirect
30. C2×#66949C22semidirect
31. C2×#66949C22semidirect
32. C2×#66949C22semidirect
40. C2×#66931C22semidirect
41. C11×#399C22semidirect
42. C11×#396C22semidirect
43. C11×#393C22semidirect
44. C11×#385C22semidirect
45. C11×#380C22semidirect
48. #10622825C22semidirect
49. #10622823C22semidirect
50. #10622602C22semidirect
51. #10622602C22semidirect
52. #10622602C22semidirect
53. #10622602C22semidirect
54. #10622600C22semidirect
55. #10622600C22semidirect
56. #10622600C22semidirect
61. #10622563C22semidirect
62. #10622562C22semidirect
63. #10622562C22semidirect
64. #10622561C22semidirect
65. #10622561C22semidirect
66. #10622561C22semidirect
67. #10622560C22semidirect
68. #10622560C22semidirect
69. #10622559C22semidirect
70. #10622555C22semidirect
71. #10622281C22semidirect
72. #10622281C22semidirect
73. #10622281C22semidirect
74. #10622281C22semidirect
75. #10622280C22semidirect
76. #10622280C22semidirect
82. C24×D11Q8semidirect
86. C22×Q8×C11C23semidirect
101. C22×Dic22C23semidirect
102. C22×Dic22C23semidirect
104. C2×C11×C4⋊C4C23semidirect
105. C2×C11×C4⋊C4C23semidirect
106. C2×C11×C4⋊C4C23semidirect
107. C2×C11×C4⋊C4C23semidirect
135. C2×C4⋊Dic11C23semidirect
136. C2×C4⋊Dic11C23semidirect
137. C2×C4⋊Dic11C23semidirect
138. C2×C4⋊Dic11C23semidirect
140. C2×Dic11⋊C4C23semidirect
141. C2×Dic11⋊C4C23semidirect
142. C2×Dic11⋊C4C23semidirect
143. C2×Dic11⋊C4C23semidirect
144. C2×Dic11⋊C4C23semidirect
145. C2×Dic11⋊C4C23semidirect
158. C11×#95C23semidirect
159. C11×#95C23semidirect
160. C11⋊#95C23semidirect
161. C11⋊#95C23semidirect
162. C11⋊#95C23semidirect
163. C11⋊#95C23semidirect
164. C11⋊#95C23semidirect
282. #2626D11semidirect
329. C22×D11C22⋊Q8semidirect
387. C2×C22⋊Q8C2×D11semidirect
401. #399C2×D11semidirect
405. #396C2×D11semidirect
408. #393C2×D11semidirect
420. #385C2×D11semidirect
428. #380C2×D11semidirect
465. C2×D11#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

Maximal subgroups

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

subgroupindex
C2×#106231652
C22×C22⋊C4×D112
#130769042
#130769022
#130769002
#130744252
#130744212
#130722832
#130722782
#130722762
#130712292
#130712272
D11×#3792
C11×#26262
#3498211