Finite Group Databasebeta

← #14917765

Subgroups — #14917765

Order 2816.

2758 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623056C211yesmaximal, characteristic
2#13071771C212yesmaximal, complemented
3#13071756C212yesmaximal, complemented
4#13071685C211yesmaximal, characteristic, complemented
5#13071685C211yesmaximal, characteristic, complemented
6#13071680C211yesmaximal, characteristic, complemented
7#13071680C211yesmaximal, characteristic, complemented
8#13071662C212yesmaximal, complemented
9#13071594C212yesmaximal, complemented
10#13071456C211yesmaximal, characteristic, complemented
11#13071447C211yesmaximal, characteristic, complemented
12C22⋊C4×D44C211yesmaximal, characteristic, complemented
13C22⋊C4×D44C211yesmaximal, characteristic, complemented
14#13071380C212yesmaximal, complemented
15#13071341C211yesmaximal, characteristic, complemented
16#13071327C211yesmaximal, characteristic, complemented
17#13071315C212yesmaximal, complemented
18#13071278C212yesmaximal, complemented
19#13071269C212yesmaximal, complemented
20#13071225C211yesmaximal, characteristic, complemented
21C4×#66927C211yesmaximal, characteristic, complemented
22C4×#66928C211yesmaximal, characteristic, complemented
23C11×#2298C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic
25C23×D44C2211yescharacteristic
26C2×C11×#117C2211yescharacteristic
27#10623056C4116yescomplemented
28C2×#66948C2212yes—
29C2×#66948C2212yes—
30C2×#66946C2212yescomplemented
31C2×#66946C2212yescomplemented
32C2×#66935C2212yes—
33C2×#66935C2212yes—
34C2×C22⋊C4×D11C2212yes—
35C2×C22⋊C4×D11C2212yes—
36C2×#66928C2211yescharacteristic
37C2×#66928C2211yescharacteristic
38C2×#66927C2211yescharacteristic
39C2×#66927C2211yescharacteristic
40C2×C4×D44C2211yescharacteristic
41C2×C4×D44C2211yescharacteristic
42C2×C4×D44C2211yescharacteristic
43C2×C4×D44C2211yescharacteristic
44C2×C4×D44C2212yescomplemented
45C2×C4×D44C2211yescharacteristic, complemented
46C2×C4×D44C2211yescharacteristic, complemented
47C2×C4×D44C2212yescomplemented
48C2×C4×Dic22C2211yescharacteristic, complemented
49C2×C4×Dic22C2211yescharacteristic, complemented
50C11×#388C2211yescharacteristic
51C11×#388C2211yescharacteristic
52C11×#388C2211yescharacteristic
53C11×#388C2211yescharacteristic
54C11×#387C2211yescharacteristic, complemented
55C11×#387C2211yescharacteristic, complemented
56C11×#387C2211yescharacteristic, complemented
57C11×#387C2211yescharacteristic, complemented
58C4×C11×C4⋊C4C2211yescharacteristic, complemented
59C4×C11×C4⋊C4C2211yescharacteristic, complemented
60C4×C11×C22⋊C4C2211yescharacteristic
61C4×C11×C22⋊C4C2211yescharacteristic
62C11×#376C2211yescharacteristic, complemented
63C43×C11C2211yescharacteristic, complemented
64#10622825C2211yescharacteristic
65#10622825C2211yescharacteristic
66#10622603C2212yescomplemented
67#10622603C2212yescomplemented
68#10622602C2212yescomplemented
69#10622602C2212yescomplemented
70#10622601C2212yescomplemented
71#10622601C2212yescomplemented
72#10622594C2212yescomplemented
73#10622594C2212yescomplemented
74#10622570C2212yes—
75#10622570C2212yes—
76#10622569C2212yes—
77#10622569C2212yes—
78#10622568C2212yes—
79#10622568C2212yes—
80#10622564C2212yes—
81#10622564C2212yes—
82#10622553C2212yescomplemented
83#10622553C2212yescomplemented
84#10622552C2211yescharacteristic
85#10622552C2211yescharacteristic
86#10622552C2211yescharacteristic
87#10622552C2211yescharacteristic
88#10622552C2212yescomplemented
89#10622552C2211yescharacteristic, complemented
90#10622552C2211yescharacteristic, complemented
91#10622552C2212yescomplemented
92C4×(C2×D11)⋊C4C2212yescomplemented
93C4×(C2×D11)⋊C4C2212yescomplemented
94#10622549C2211yescharacteristic, complemented
95#10622548C2211yescharacteristic, complemented
96C4×C4⋊Dic11C2211yescharacteristic, complemented
97C4×C4⋊Dic11C2211yescharacteristic, complemented
98#10622542C2211yescharacteristic, complemented
99#10622542C2211yescharacteristic, complemented
100#10622283C2212yescomplemented
101#10622283C2212yescomplemented
102#10622282C2212yescomplemented
103#10622282C2212yescomplemented
104#10622281C2212yescomplemented
105#10622281C2212yescomplemented
106#10622280C2212yescomplemented
107#10622279C2212yescomplemented
108#10622279C2212yescomplemented
109#10622279C2212yescomplemented
110#10622278C2212yes—
111#10622278C2212yes—
112#10622278C2212yes—
113#10622278C2212yes—
114#10622278C2212yescomplemented
115#10622278C2212yescomplemented
116#10622278C2212yescomplemented
117#10622278C2212yescomplemented
118#10622278C2212yescomplemented
119#10622278C2212yescomplemented
120#10622278C2212yescomplemented
121#10622278C2212yescomplemented
122#10622277C2212yescomplemented
123D11×#95C2212yescomplemented
124C24×D11C2312yes—
125C23×C4×C11C2311yescharacteristic
126C22×C22⋊D11C2312yes—
127C2×#4339—42no—
128C2×#4339—42no—
129C2×#4339C2×C418yescomplemented
130C22×D44—42no—
131C22×D44—42no—
132C22×D44C2×C418yescomplemented
133C22×D44C2311yescharacteristic
134C22×D44C2311yescharacteristic
135C22×D44C2311yescharacteristic
136C22×D44C2312yes—
137C22×D44C2312yes—
138C22×D44C2312yes—
139C22×D44C2312yes—
140C22×D44C2312yes—
141C22×C4×D11C2312yes—
142C22×C4×D11C2312yes—
143C22×C4×D11C2312yes—
144C22×C4×D11C2312yes—
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2312yes—
148C22×Dic22C2311yescharacteristic
149C11×#117C2×C418yescomplemented
150C2×C11×C4⋊C4C2311yescharacteristic
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C22⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4C2311yescharacteristic
158C2×C11×C22⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C42×C11C2311yescharacteristic
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C42×C11C2311yescharacteristic
169C2×C42×C11C2311yescharacteristic
170C2×C42×C11C2311yescharacteristic
171C2×C42×C11C2311yescharacteristic
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×(C2×D11)⋊C4C2312yes—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2312yes—
177C2×(C2×D11)⋊C4C2312yes—
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×C4⋊Dic11C2311yescharacteristic
197C2×C4⋊Dic11C2311yescharacteristic
198C2×C4⋊Dic11C2311yescharacteristic
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2312yes—
201C2×C4⋊Dic11C2312yes—
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×C4×Dic11C2312yes—
205C2×C4×Dic11C2312yes—
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2312yes—
208#66948C2×C4116yescomplemented
209#66948C2×C4116yescomplemented
210#66946—44no—
211#66946—44no—
212#66935C2×C4116yescomplemented
213#66935C2×C4116yescomplemented
214C22⋊C4×D11—44no—
215C22⋊C4×D11—44no—
216#66928C2×C418yescomplemented
217#66928C2×C418yescomplemented
218#66927C2×C418yescomplemented
219#66927C2×C418yescomplemented
220C4×D44—42no—
221C4×D44—42no—
222C4×D44—42no—
223C4×D44—42no—
224C4×D44—42no—
225C4×D44—42no—
226C4×D44—44no—
227C4×D44—44no—
228C4×Dic22—42no—
229C4×Dic22—42no—
230C11×#95C2311yescharacteristic
231C11×#95C2311yescharacteristic
232C11×#95C2311yescharacteristic
233C11×#95C2311yescharacteristic
234C11×#95C2311yescharacteristic
235C11×#95C2311yescharacteristic
236C11×#95C2311yescharacteristic
237C11×#95C2311yescharacteristic
238C11×#95C2311yescharacteristic
239C11×#95C2311yescharacteristic
240C11×#95C2311yescharacteristic
241C11×#95C2311yescharacteristic
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252#34438—111nomaximal, Sylow
253C24×C11C2411yescharacteristic
254C23×D11—42no—
255C23×D11—42no—
256C23×D11—42no—
257C23×D11—42no—
258C23×D11—42no—
259C23×D11—42no—
260C23×D11C22×C418yes—
261C23×D11C2412yes—
262C23×D11C2412yes—
263C23×D11C2412yes—
264C22×C4×C11—22no—
265C22×C4×C11—22no—
266C22×C4×C11C22×C414yes—
267C22×C4×C11C2411yescharacteristic
268C22×C4×C11C2411yescharacteristic
269C22×C4×C11C2411yescharacteristic
270C22×C4×C11C2411yescharacteristic
271C22×C4×C11C2411yescharacteristic
272C22×C4×C11C2411yescharacteristic
273C22×C4×C11C2411yescharacteristic
274C22×C4×C11C2411yescharacteristic
275C22×C4×C11C2411yescharacteristic
276C22×C4×C11C2411yescharacteristic
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2411yescharacteristic
281C2×C22⋊D11—42no—
282C2×C22⋊D11—42no—
283C2×C22⋊D11C22×C418yes—
284C22×Dic11C2412yes—
285C22×Dic11C2412yes—
286C22×Dic11C2412yes—
287C22×Dic11C2412yes—
288C22×Dic11C2412yes—
289#4339—416no—
290C2×D44—22no—
291C2×D44—22no—
292C2×D44—22no—
293C2×D44—22no—
294C2×D44—22no—
295C2×D44—22no—
296C2×D44—42no—
297C2×D44—42no—
298C2×D44—42no—
299C2×D44—42no—
300C2×D44—42no—
301C2×D44—42no—
302C2×D44—42no—
303C2×D44—42no—
304C2×D44—42no—
305C2×D44—42no—
306C2×D44—416no—
307C2×D44C22×C414yes—
308C2×D44C22×C414yes—
309C2×D44C22×C414yes—
310C2×D44C22×C418yes—
311C2×D44C22×C418yes—
312C2×D44C22×C418yes—
313C2×D44C22×C418yes—
314C2×D44C22×C418yes—
315C2×C4×D11—24no—
316C2×C4×D11—24no—
317C2×C4×D11—24no—
318C2×C4×D11—42no—
319C2×C4×D11—42no—
320C2×C4×D11—42no—
321C2×C4×D11—42no—
322C2×C4×D11—42no—
323C2×C4×D11—42no—
324C2×C4×D11—42no—
325C2×C4×D11—42no—
326C2×C4×D11—42no—
327C2×C4×D11—42no—
328C2×C4×D11—42no—
329C2×C4×D11—42no—
330C2×C4×D11—42no—
331C2×C4×D11—42no—
332C2×C4×D11—42no—
333C2×C4×D11—42no—
334C2×C4×D11—42no—
335C2×C4×D11C22×C418yes—
336C2×Dic22—22no—
337C2×Dic22—22no—
338C2×Dic22C22×C414yes—
339C11×C4⋊C4—22no—
340C11×C4⋊C4—22no—
341C11×C4⋊C4—41no—
342C11×C4⋊C4—41no—
343C11×C4⋊C4C22×C414yes—
344C11×C4⋊C4C22×C414yes—
345C11×C22⋊C4—22no—
346C11×C22⋊C4—22no—
347C11×C22⋊C4—41no—
348C11×C22⋊C4—41no—
349C11×C22⋊C4C22×C414yes—
350C11×C22⋊C4C22×C414yes—
351C42×C11—22no—
352C42×C11—22no—
353C42×C11—22no—
354C42×C11—22no—
355C42×C11—22no—
356C42×C11—22no—
357C42×C11—41no—
358C42×C11—41no—
359C42×C11C22×C414yes—
360C42×C11C22×C414yes—
361C22⋊Dic11—42no—
362C22⋊Dic11—42no—
363(C2×D11)⋊C4—24no—
364(C2×D11)⋊C4—24no—
365(C2×D11)⋊C4—24no—
366(C2×D11)⋊C4—42no—
367(C2×D11)⋊C4—42no—
368(C2×D11)⋊C4—42no—
369(C2×D11)⋊C4—42no—
370(C2×D11)⋊C4—42no—
371(C2×D11)⋊C4—42no—
372(C2×D11)⋊C4—42no—
373(C2×D11)⋊C4—42no—
374(C2×D11)⋊C4—42no—
375(C2×D11)⋊C4—42no—
376(C2×D11)⋊C4—42no—
377(C2×D11)⋊C4—42no—
378(C2×D11)⋊C4—42no—
379(C2×D11)⋊C4—42no—
380(C2×D11)⋊C4—42no—
381(C2×D11)⋊C4C22×C418yes—
382(C2×D11)⋊C4C22×C418yes—
383(C2×D11)⋊C4C22×C418yes—
384(C2×D11)⋊C4C22×C418yes—
385C4⋊Dic11—22no—
386C4⋊Dic11—22no—
387C4⋊Dic11—22no—
388C4⋊Dic11—22no—
389C4⋊Dic11—42no—
390C4⋊Dic11—42no—
391Dic11⋊C4—42no—
392Dic11⋊C4—42no—
393C4×Dic11—42no—
394C4×Dic11—42no—
395C4×Dic11—42no—
396C4×Dic11—42no—
397C2×#535—111no—
398#2377—112no—
399#2375—112no—
400#2367—111no—
401#2367—111no—
402#2366—111no—
403#2366—111no—
404#2364—112no—
405#2358—112no—
406#2341—111no—
407#2339—111no—
408D4×C22⋊C4—111no—
409D4×C22⋊C4—111no—
410#2333—112no—
411#2328—111no—
412#2326—111no—
413#2325—112no—
414#2321—112no—
415#2321—112no—
416#2314—111no—
417C4×#127—111no—
418C4×#124—111no—
419#2298D1111yescharacteristic, complemented
420C23×C11—21no—
421C23×C11—21no—
422C23×C11—21no—
423C23×C11—21no—
424C23×C11—21no—
425C23×C11—21no—
426C23×C11C23×C412yes—
427C23×C11C2511yescharacteristic
428C22×D11—22no—
429C22×D11—22no—
430C22×D11—22no—
431C22×D11—22no—
432C22×D11—22no—
433C22×D11—22no—
434C22×D11—22no—
435C22×D11—22no—
436C22×D11—22no—
437C22×D11—22no—
438C22×D11—22no—
439C22×D11—22no—
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—48no—
447C22×D11—48no—
448C22×D11—48no—
449C22×D11—84no—
450C22×D11—84no—
451C22×D11—84no—
452C22×D11—84no—
453C22×D11C23×C414yes—
454C22×D11C23×C414yes—
455C22×D11C23×C414yes—
456C2×C4×C11—21no—
457C2×C4×C11—21no—
458C2×C4×C11—21no—
459C2×C4×C11—21no—
460C2×C4×C11—21no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—21no—
464C2×C4×C11—21no—
465C2×C4×C11—21no—
466C2×C4×C11—21no—
467C2×C4×C11—21no—
468C2×C4×C11—21no—
469C2×C4×C11—21no—
470C2×C4×C11—28no—
471C2×C4×C11—21no—
472C2×C4×C11—21no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—21no—
478C2×C4×C11—21no—
479C2×C4×C11—21no—
480C2×C4×C11—21no—
481C2×C4×C11—21no—
482C2×C4×C11—21no—
483C2×C4×C11—21no—
484C2×C4×C11—21no—
485C2×C4×C11—21no—
486C2×C4×C11—21no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11C23×C412yes—
490C2×C4×C11C23×C412yes—
491C2×C4×C11C23×C412yes—
492C2×C4×C11C23×C412yes—
493C2×C4×C11C23×C412yes—
494C2×C4×C11C23×C412yes—
495C2×C4×C11H(5,𝔽2)12yes—
496C2×C4×C11H(5,𝔽2)12yes—
497C2×C4×C11H(5,𝔽2)12yes—
498C2×C4×C11H(5,𝔽2)12yes—
499C22⋊D11—48no—
500C2×Dic11—22no—
501C2×Dic11—22no—
502C2×Dic11—22no—
503C2×Dic11—22no—
504C2×Dic11—22no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11C23×C414yes—
515D44—28no—
516D44—28no—
517D44—28no—
518D44—48no—
519D44—48no—
520D44—48no—
521D44—48no—
522D44—48no—
523C4×D11—48no—
524C4×D11—84no—
525C4×D11—84no—
526C4×D11—84no—
527C4×D11—84no—
528C4×D11—84no—
529C4×D11—84no—
530Dic22—28no—
531C22×#41—111no—
532C23×D4—111no—
533#535—1116no—
534C2×#127—111no—
535C2×#127—111no—
536C2×#124—111no—
537C2×#124—111no—
538C2×#121—112no—
539C2×#121—112no—
540C2×#120—112no—
541C2×#120—112no—
542C2×C4×Q8—111no—
543C2×C4×Q8—111no—
544C2×C4×D4—112no—
545C2×C4×D4—112no—
546C2×C4×D4—112no—
547C2×C4×D4—111no—
548C2×C4×D4—111no—
549C2×C4×D4—112no—
550C2×C4×D4—111no—
551C2×C4×D4—111no—
552C2×C4×D4—111no—
553C2×C4×D4—111no—
554C2×#117C2×D1111yescharacteristic
555C22×C22⋊C4—112no—
556C22×C22⋊C4—112no—
557#391—111no—
558#391—111no—
559#390—112no—
560#390—112no—
561#390—112no—
562#390—112no—
563#390—112no—
564#390—111no—
565#390—111no—
566#390—112no—
567#390—111no—
568#390—111no—
569#390—111no—
570#390—111no—
571#388—112no—
572#388—112no—
573#388—112no—
574#388—112no—
575#388—112no—
576#388—112no—
577#388—112no—
578#388—112no—
579#388—112no—
580#388—112no—
581#388C2×D1111yescharacteristic
582#388C2×D1111yescharacteristic
583#388C2×D1111yescharacteristic
584#388C2×D1111yescharacteristic
585#387—112no—
586#387—112no—
587#387C2×D1111yescharacteristic, complemented
588#387C2×D1111yescharacteristic, complemented
589#387C2×D1111yescharacteristic, complemented
590#387C2×D1111yescharacteristic, complemented
591#386—112no—
592#386—112no—
593#386—112no—
594#386—112no—
595#386—112no—
596#386—112no—
597#386—112no—
598#386—112no—
599#386—112no—
600#386—112no—
601#386—112no—
602#386—112no—
603#386—112no—
604#386—112no—
605#385—112no—
606#385—112no—
607#385—112no—
608#385—112no—
609#384—111no—
610#382—111no—
611#381—112no—
612#380—111no—
613#380—111no—
614#380—112no—
615#379—112no—
616#379—112no—
617C4×C4⋊C4—111no—
618C4×C4⋊C4—111no—
619C4×C4⋊C4C2×D1111yescharacteristic, complemented
620C4×C4⋊C4C2×D1111yescharacteristic, complemented
621C4×C22⋊C4—112no—
622C4×C22⋊C4—112no—
623C4×C22⋊C4—112no—
624C4×C22⋊C4—112no—
625C4×C22⋊C4—112no—
626C4×C22⋊C4C2×D1111yescharacteristic
627C4×C22⋊C4C2×D1111yescharacteristic
628#376C2×D1111yescharacteristic, complemented
629C2×#95—112no—
630C43C2×D1111yescharacteristic, complemented
631C22×C11—22no—
632C22×C11—22no—
633C22×C11—22no—
634C22×C11—41no—
635C22×C11—41no—
636C22×C11—41no—
637C22×C11—41no—
638C22×C11C24×C411yescharacteristic
639C22×C11C2×H(5,𝔽2)11yescharacteristic
640C22×C11C2×H(5,𝔽2)11yescharacteristic
641C22×C11C2×H(5,𝔽2)11yescharacteristic
642C22×C11C2×H(5,𝔽2)11yescharacteristic
643C22×C11#58511yescharacteristic
644C22×C11#58511yescharacteristic
645C2×D11—24no—
646C2×D11—24no—
647C2×D11—24no—
648C2×D11—24no—
649C2×D11—24no—
650C2×D11—24no—
651C2×D11—24no—
652C2×D11—24no—
653C2×D11—24no—
654C2×D11—42no—
655C2×D11—42no—
656C2×D11—42no—
657C2×D11—42no—
658C2×D11—42no—
659C2×D11—42no—
660C2×D11—42no—
661C2×D11—42no—
662C2×D11—42no—
663C2×D11—42no—
664C2×D11—42no—
665C2×D11—42no—
666C2×D11—816no—
667C4×C11—22no—
668C4×C11—22no—
669C4×C11—22no—
670C4×C11—22no—
671C4×C11—22no—
672C4×C11—22no—
673C4×C11—22no—
674C4×C11—41no—
675C4×C11—41no—
676C4×C11—41no—
677C4×C11—41no—
678C4×C11—41no—
679C4×C11—41no—
680C4×C11#51814yes—
681Dic11—24no—
682Dic11—42no—
683Dic11—42no—
684Dic11—42no—
685Dic11—42no—
686C25—112no—
687C2×#41—118no—
688C2×#41—442no—
689C2×#41—442no—
690C22×Q8—111no—
691C22×D4—112no—
692C22×D4—118no—
693C22×D4—111no—
694C22×D4—111no—
695C22×D4—111no—
696C22×D4—112no—
697C22×D4—112no—
698C22×D4—112no—
699C22×D4—112no—
700C22×D4—112no—
701C22×D4—442no—
702C22×D4—442no—
703C23×C4—112no—
704C23×C4—112no—
705C23×C4—112no—
706C23×C4—112no—
707C23×C4—112no—
708C23×C4—112no—
709C23×C4—112no—
710C23×C4C22×D1111yescharacteristic
711#127—118no—
712#127—118no—
713#124—118no—
714#124—118no—
715#121—1116no—
716#121—1116no—
717#120—1116no—
718#120—1116no—
719C4×Q8—442no—
720C4×Q8—442no—
721C4×D4—444no—
722C4×D4—442no—
723C4×D4—442no—
724C4×D4—442no—
725C4×D4—442no—
726C4×D4—442no—
727C4×D4—442no—
728C4×D4—444no—
729C4×D4—444no—
730C4×D4—444no—
731#117C4×D1118yescomplemented
732C2×C4⋊C4—111no—
733C2×C4⋊C4—111no—
734C2×C4⋊C4—111no—
735C2×C4⋊C4—111no—
736C2×C4⋊C4—112no—
737C2×C4⋊C4—112no—
738C2×C4⋊C4—112no—
739C2×C4⋊C4—112no—
740C2×C4⋊C4C22×D1111yescharacteristic
741C2×C4⋊C4C22×D1111yescharacteristic
742C2×C4⋊C4C22×D1111yescharacteristic
743C2×C4⋊C4C22×D1111yescharacteristic
744C2×C4⋊C4C22×D1111yescharacteristic
745C2×C4⋊C4C22×D1111yescharacteristic
746C2×C22⋊C4—112no—
747C2×C22⋊C4—112no—
748C2×C22⋊C4—112no—
749C2×C22⋊C4—112no—
750C2×C22⋊C4—112no—
751C2×C22⋊C4—112no—
752C2×C22⋊C4—112no—
753C2×C22⋊C4—112no—
754C2×C22⋊C4—112no—
755C2×C22⋊C4—112no—
756C2×C22⋊C4—112no—
757C2×C22⋊C4—112no—
758C2×C22⋊C4—112no—
759C2×C22⋊C4—112no—
760C2×C22⋊C4—112no—
761C2×C22⋊C4—112no—
762C2×C22⋊C4—112no—
763C2×C22⋊C4—112no—
764C2×C22⋊C4—112no—
765C2×C22⋊C4—112no—
766C2×C22⋊C4—112no—
767C2×C22⋊C4—112no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—444no—
771C2×C22⋊C4—444no—
772C2×C22⋊C4C22×D1111yescharacteristic
773C2×C22⋊C4C22×D1111yescharacteristic
774C2×C22⋊C4C22×D1111yescharacteristic
775C2×C22⋊C4C22×D1111yescharacteristic
776C2×C22⋊C4C22×D1111yescharacteristic
777C2×C22⋊C4C22×D1111yescharacteristic
778C2×C42—112no—
779C2×C42—112no—
780C2×C42—112no—
781C2×C42—112no—
782C2×C42C22×D1111yescharacteristic
783C2×C42C22×D1111yescharacteristic
784C2×C42C22×D1111yescharacteristic
785C2×C42C22×D1111yescharacteristic
786C2×C42C22×D1111yescharacteristic
787C2×C42C22×D1111yescharacteristic
788C2×C42C22×D1111yescharacteristic
789C2×C42C22×D1111yescharacteristic
790C2×C42C22×D1111yescharacteristic
791C2×C42C22×D1111yescharacteristic
792#95—112no—
793#95—112no—
794#95—112no—
795#95—112no—
796#95—112no—
797#95—112no—
798#95—112no—
799#95—112no—
800#95—112no—
801#95—112no—
802#95C22×D1111yescharacteristic
803#95C22×D1111yescharacteristic
804#95C22×D1111yescharacteristic
805#95C22×D1111yescharacteristic
806#95C22×D1111yescharacteristic
807#95C22×D1111yescharacteristic
808#95C22×D1111yescharacteristic
809#95C22×D1111yescharacteristic
810#95C22×D1111yescharacteristic
811#95C22×D1111yescharacteristic
812#95C22×D1111yescharacteristic
813#95C22×D1111yescharacteristic
814C2×C11—42no—
815C2×C11C2×#51811yescharacteristic
816C2×C11C4×H(5,𝔽2)11yescharacteristic
817C2×C11C4×H(5,𝔽2)11yescharacteristic
818C2×C11#354311yescharacteristic
819C2×C11#354611yescharacteristic
820C2×C11#355811yescharacteristic
821C2×C11#356211yescharacteristic
822D11—44no—
823D11—44no—
824D11—44no—
825C24—112no—
826C24—112no—
827C24—112no—
828C24—118no—
829C24—442no—
830C24—442no—
831C24—442no—
832C24—442no—
833C24—442no—
834C24—442no—
835C24C23×D1111yescharacteristic
836#41—4416no—
837C2×Q8—114no—
838C2×Q8—222no—
839C2×Q8—222no—
840C2×D4—118no—
841C2×D4—114no—
842C2×D4—114no—
843C2×D4—114no—
844C2×D4—118no—
845C2×D4—118no—
846C2×D4—118no—
847C2×D4—118no—
848C2×D4—118no—
849C2×D4—222no—
850C2×D4—222no—
851C2×D4—222no—
852C2×D4—222no—
853C2×D4—222no—
854C2×D4—222no—
855C2×D4—4416no—
856C2×D4—442no—
857C2×D4—442no—
858C2×D4—442no—
859C2×D4—442no—
860C2×D4—442no—
861C2×D4—442no—
862C2×D4—442no—
863C2×D4—442no—
864C2×D4—442no—
865C2×D4—442no—
866C2×D4—442no—
867C2×D4—442no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—112no—
871C22×C4—118no—
872C22×C4—112no—
873C22×C4—112no—
874C22×C4—112no—
875C22×C4—112no—
876C22×C4—224no—
877C22×C4—224no—
878C22×C4—224no—
879C22×C4—442no—
880C22×C4—442no—
881C22×C4—442no—
882C22×C4—442no—
883C22×C4—442no—
884C22×C4—442no—
885C22×C4—442no—
886C22×C4—442no—
887C22×C4—442no—
888C22×C4—442no—
889C22×C4—442no—
890C22×C4—442no—
891C22×C4—442no—
892C22×C4—442no—
893C22×C4—442no—
894C22×C4—442no—
895C22×C4—442no—
896C22×C4C2×C4×D1114yes—
897C22×C4C23×D1111yescharacteristic
898C22×C4C23×D1111yescharacteristic
899C22×C4C23×D1111yescharacteristic
900C22×C4C23×D1111yescharacteristic
901C22×C4C23×D1111yescharacteristic
902C22×C4C23×D1111yescharacteristic
903C22×C4C23×D1111yescharacteristic
904C22×C4C23×D1111yescharacteristic
905C22×C4C23×D1111yescharacteristic
906C22×C4C23×D1111yescharacteristic
907C22×C4C23×D1111yescharacteristic
908C22×C4C23×D1111yescharacteristic
909C22×C4C23×D1111yescharacteristic
910C22×C4C23×D1111yescharacteristic
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—222no—
916C4⋊C4—222no—
917C4⋊C4—222no—
918C4⋊C4—222no—
919C4⋊C4—442no—
920C4⋊C4—442no—
921C4⋊C4—442no—
922C4⋊C4—442no—
923C4⋊C4C2×C4×D1114yes—
924C4⋊C4C2×C4×D1114yes—
925C22⋊C4—22no—
926C22⋊C4—22no—
927C22⋊C4—41no—
928C22⋊C4—41no—
929C22⋊C4—118no—
930C22⋊C4—118no—
931C22⋊C4—118no—
932C22⋊C4—118no—
933C22⋊C4—224no—
934C22⋊C4—224no—
935C22⋊C4—224no—
936C22⋊C4—442no—
937C22⋊C4—442no—
938C22⋊C4—442no—
939C22⋊C4—442no—
940C22⋊C4—442no—
941C22⋊C4—442no—
942C22⋊C4—442no—
943C22⋊C4—442no—
944C22⋊C4—442no—
945C22⋊C4—442no—
946C22⋊C4—442no—
947C22⋊C4—442no—
948C22⋊C4—442no—
949C22⋊C4—442no—
950C22⋊C4—442no—
951C22⋊C4—442no—
952C22⋊C4—442no—
953C22⋊C4C2×C4×D1114yes—
954C22⋊C4C2×C4×D1114yes—
955C42—22no—
956C42—22no—
957C42—22no—
958C42—22no—
959C42—22no—
960C42—22no—
961C42—41no—
962C42—41no—
963C42—442no—
964C42—442no—
965C42—442no—
966C42—442no—
967C42C2×C4×D1114yes—
968C42C2×C4×D1114yes—
969C11#3443811yescharacteristic, complemented, Sylow
970C23—21no—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—114no—
977C23—114no—
978C23—114no—
979C23—222no—
980C23—222no—
981C23—222no—
982C23—222no—
983C23—222no—
984C23—222no—
985C23—222no—
986C23—222no—
987C23—222no—
988C23—222no—
989C23—222no—
990C23—222no—
991C23—222no—
992C23—222no—
993C23—222no—
994C23—222no—
995C23—222no—
996C23—222no—
997C23—448no—
998C23—448no—
999C23—448no—
1000C23—884no—
1001C23—884no—
1002C23—884no—
1003C23—884no—
1004C23C22×C4×D1112yes—
1005C23C24×D1111yescharacteristic
1006Q8—228no—
1007D4—228no—
1008D4—228no—
1009D4—228no—
1010D4—448no—
1011D4—448no—
1012D4—448no—
1013D4—448no—
1014D4—448no—
1015D4—448no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—28no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—114no—
1050C2×C4—222no—
1051C2×C4—222no—
1052C2×C4—222no—
1053C2×C4—222no—
1054C2×C4—222no—
1055C2×C4—222no—
1056C2×C4—222no—
1057C2×C4—222no—
1058C2×C4—222no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—222no—
1063C2×C4—222no—
1064C2×C4—448no—
1065C2×C4—884no—
1066C2×C4—884no—
1067C2×C4—884no—
1068C2×C4—884no—
1069C2×C4—884no—
1070C2×C4—884no—
1071C2×C4C22×C4×D1112yes—
1072C2×C4C22×C4×D1112yes—
1073C2×C4C22×C4×D1112yes—
1074C2×C4C22×C4×D1112yes—
1075C2×C4C22×C4×D1112yes—
1076C2×C4C22×C4×D1112yes—
1077C2×C4#6704212yes—
1078C2×C4#6704212yes—
1079C2×C4#6704212yes—
1080C2×C4#6704212yes—
1081C22—22no—
1082C22—22no—
1083C22—22no—
1084C22—41no—
1085C22—41no—
1086C22—41no—
1087C22—41no—
1088C22—224no—
1089C22—224no—
1090C22—224no—
1091C22—224no—
1092C22—224no—
1093C22—224no—
1094C22—224no—
1095C22—224no—
1096C22—224no—
1097C22—442no—
1098C22—442no—
1099C22—442no—
1100C22—442no—
1101C22—442no—
1102C22—442no—
1103C22—442no—
1104C22—442no—
1105C22—442no—
1106C22—442no—
1107C22—442no—
1108C22—442no—
1109C22—8816no—
1110C22C23×C4×D1111yescharacteristic
1111C22C2×#6704211yescharacteristic
1112C22C2×#6704211yescharacteristic
1113C22C2×#6704211yescharacteristic
1114C22C2×#6704211yescharacteristic
1115C22#1062345311yescharacteristic
1116C22#1062345311yescharacteristic
1117C4—22no—
1118C4—22no—
1119C4—22no—
1120C4—22no—
1121C4—22no—
1122C4—22no—
1123C4—22no—
1124C4—41no—
1125C4—41no—
1126C4—41no—
1127C4—41no—
1128C4—41no—
1129C4—41no—
1130C4—224no—
1131C4—442no—
1132C4—442no—
1133C4—442no—
1134C4—442no—
1135C4#1062305214yes—
1136C2—42no—
1137C2—444no—
1138C2—444no—
1139C2—444no—
1140C2C2×#1062305211yescharacteristic
1141C2C4×#6704211yescharacteristic
1142C2C4×#6704211yescharacteristic
1143C2#1308294611yescharacteristic
1144C2#1308299011yescharacteristic
1145C2#1308313211yescharacteristic
1146C2#1308320411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2298C2
socle, cosocleC23×C11C25
prime radicalC2×#10623056C2
hypercenter#2298D11
hypocenterC11#34438
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2298

Complements

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

NH ≅ G/Ntype
2. #13071771C2semidirect
3. #13071756C2semidirect
4. #13071685C2semidirect
5. #13071685C2semidirect
6. #13071680C2semidirect
7. #13071680C2semidirect
8. #13071662C2semidirect
9. #13071594C2semidirect
10. #13071456C2semidirect
11. #13071447C2semidirect
12. C22⋊C4×D44C2semidirect
13. C22⋊C4×D44C2semidirect
14. #13071380C2semidirect
15. #13071341C2semidirect
16. #13071327C2semidirect
17. #13071315C2semidirect
18. #13071278C2semidirect
19. #13071269C2semidirect
20. #13071225C2semidirect
21. C4×#66927C2semidirect
22. C4×#66928C2semidirect
23. C11×#2298C2semidirect
27. #10623056C4semidirect
30. C2×#66946C22semidirect
31. C2×#66946C22semidirect
44. C2×C4×D44C22semidirect
45. C2×C4×D44C22semidirect
46. C2×C4×D44C22semidirect
47. C2×C4×D44C22semidirect
48. C2×C4×Dic22C22semidirect
49. C2×C4×Dic22C22semidirect
54. C11×#387C22semidirect
55. C11×#387C22semidirect
56. C11×#387C22semidirect
57. C11×#387C22semidirect
58. C4×C11×C4⋊C4C22semidirect
59. C4×C11×C4⋊C4C22semidirect
62. C11×#376C22semidirect
63. C43×C11C22semidirect
66. #10622603C22semidirect
67. #10622603C22semidirect
68. #10622602C22semidirect
69. #10622602C22semidirect
70. #10622601C22semidirect
71. #10622601C22semidirect
72. #10622594C22semidirect
73. #10622594C22semidirect
82. #10622553C22semidirect
83. #10622553C22semidirect
88. #10622552C22semidirect
89. #10622552C22semidirect
90. #10622552C22semidirect
91. #10622552C22semidirect
92. C4×(C2×D11)⋊C4C22semidirect
93. C4×(C2×D11)⋊C4C22semidirect
94. #10622549C22semidirect
95. #10622548C22semidirect
96. C4×C4⋊Dic11C22semidirect
97. C4×C4⋊Dic11C22semidirect
98. #10622542C22semidirect
99. #10622542C22semidirect
100. #10622283C22semidirect
101. #10622283C22semidirect
102. #10622282C22semidirect
103. #10622282C22semidirect
104. #10622281C22semidirect
105. #10622281C22semidirect
106. #10622280C22semidirect
107. #10622279C22semidirect
108. #10622279C22semidirect
109. #10622279C22semidirect
114. #10622278C22semidirect
115. #10622278C22semidirect
116. #10622278C22semidirect
117. #10622278C22semidirect
118. #10622278C22semidirect
119. #10622278C22semidirect
120. #10622278C22semidirect
121. #10622278C22semidirect
122. #10622277C22semidirect
123. D11×#95C22semidirect
129. C2×#4339C2×C4semidirect
132. C22×D44C2×C4semidirect
149. C11×#117C2×C4semidirect
208. #66948C2×C4semidirect
209. #66948C2×C4semidirect
212. #66935C2×C4semidirect
213. #66935C2×C4semidirect
216. #66928C2×C4semidirect
217. #66928C2×C4semidirect
218. #66927C2×C4semidirect
219. #66927C2×C4semidirect
419. #2298D11semidirect
587. #387C2×D11semidirect
588. #387C2×D11semidirect
589. #387C2×D11semidirect
590. #387C2×D11semidirect
619. C4×C4⋊C4C2×D11semidirect
620. C4×C4⋊C4C2×D11semidirect
628. #376C2×D11semidirect
630. C43C2×D11semidirect
731. #117C4×D11semidirect
969. C11#34438semidirect

Maximal subgroups

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

subgroupindex
C2×#106230562
#130717712
#130717562
#130716852
#130716802
#130716622
#130715942
#130714562
#130714472
C22⋊C4×D442
#130713802
#130713412
#130713272
#130713152
#130712782
#130712692
#130712252
C4×#669272
C4×#669282
C11×#22982
#3443811