Finite Group Databasebeta

← #14786254

Subgroups — #14786254

Order 2816.

1466 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1466 conjugacy classes of subgroups — too many to draw. Only its 191 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074332C212yesmaximal, complemented
2#13071196C211yesmaximal, characteristic, complemented
3#13069779C212yesmaximal, complemented
4#13069740C212yesmaximal, complemented
5#13069075C212yesmaximal, complemented
6#13069024C214yesmaximal, complemented
7#13068693C211yesmaximal, characteristic, complemented
8C11×#3491C211yesmaximal, characteristic, complemented
9C23×D44C2211yescharacteristic
10C11×#552—24no—
11C11×#551—24no—
12C11×#543C2211yescharacteristic
13C11×#539—22no—
14C11×#534C2211yescharacteristic
15C11×#529—22no—
16C2×C11×#123C2212yes—
17C11×#518C2212yes—
18C2×C11×#117C2211yescharacteristic
19C2×#66990C2214yes—
20C2×#66979C2211yescharacteristic
21C2×#66898C2214yes—
22#10622824C2212yes—
23#10622604—24no—
24#10622601—22no—
25#10622573—24no—
26#10622568C2212yes—
27#10622568C2212yes—
28#10622568C2214yes—
29#10622552—22no—
30#10622164C2214yes—
31#10622164C2212yes—
32#10622164C2212yes—
33C24×D11C2312yes—
34C22×D4×C11C2312yes—
35C23×C4×C11C2311yescharacteristic
36C22×C22⋊D11—24no—
37C22×D44—24no—
38C22×D44—21no—
39C22×D44—21no—
40C22×D44—24no—
41C22×D44—42no—
42C11×#126—24no—
43C11×#126—24no—
44C11×#125—22no—
45C11×#125—24no—
46C11×#124—22no—
47C11×#123—24no—
48C11×#123—22no—
49C11×#123—22no—
50C11×#123—24no—
51C11×#123—22no—
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—24no—
55C11×#121—22no—
56C11×#120—22no—
57C4×Q8×C11—22no—
58C4×D4×C11—22no—
59C4×D4×C11—24no—
60C4×D4×C11—24no—
61C11×#117—24no—
62C11×#117—24no—
63C11×#117—22no—
64C2×C11×C4⋊C4D412yescomplemented
65C2×C11×C4⋊C4D414yescomplemented
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4D414yescomplemented
68C2×C11×C22⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4C2312yes—
71C2×C42×C11D412yescomplemented
72C2×C22⋊Dic11C2312yes—
73C2×C22⋊Dic11C2314yes—
74#66990—28no—
75#66990—44no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—28no—
80#66979—42no—
81C2×C4⋊Dic11—21no—
82C2×C4×Dic11—21no—
83#66898—44no—
84C11⋊#95—24no—
85#23988—111nomaximal, Sylow
86C24×C11C2×D412yes—
87C24×C11C2411yescharacteristic
88C23×D11—22no—
89C23×D11—24no—
90C23×D11—22no—
91C23×D11—24no—
92C23×D11—84no—
93C23×D11#4114yes—
94C2×Q8×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—24no—
98C2×D4×C11—24no—
99C2×D4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—24no—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D414yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D414yes—
110C2×C22⋊D11—48no—
111C2×C22⋊D11—88no—
112C22×Dic11—24no—
113C22×Dic11—22no—
114C2×D44—24no—
115C2×D44—24no—
116C2×D44—416no—
117C2×D44—42no—
118C2×D44—42no—
119C2×D44—42no—
120C2×D44—42no—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—24no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—24no—
128C11×C22⋊C4—24no—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—22no—
131C11×C22⋊C4—22no—
132C11×C22⋊C4—22no—
133C11×C22⋊C4—22no—
134C11×C22⋊C4—24no—
135C11×C22⋊C4—24no—
136C42×C11—24no—
137C42×C11—22no—
138C42×C11—22no—
139C22⋊Dic11—24no—
140C22⋊Dic11—24no—
141C22⋊Dic11—24no—
142(C2×D11)⋊C4—48no—
143(C2×D11)⋊C4—84no—
144(C2×D11)⋊C4—84no—
145(C2×D11)⋊C4—88no—
146C4⋊Dic11—42no—
147C4×Dic11—42no—
148#3491D1111yescharacteristic, complemented
149#2613—112no—
150#2309—111no—
151#2029—112no—
152#2021—112no—
153#1899—112no—
154#1889—114no—
155#1820—111no—
156C23×C11—22no—
157C23×C11—24no—
158C23×C11—42no—
159C23×C11—44no—
160C23×C11C22×D411yescharacteristic
161C23×C11C22×D412yes—
162C23×C11C2×#4112yes—
163C23×C11H(5,𝔽2)12yes—
164C22×D11—24no—
165C22×D11—28no—
166C22×D11—44no—
167C22×D11—44no—
168C22×D11—48no—
169C22×D11—48no—
170C22×D11—42no—
171C22×D11—42no—
172C22×D11—44no—
173C22×D11—84no—
174C22×D11—84no—
175C22×D11—88no—
176Q8×C11—82no—
177D4×C11—42no—
178D4×C11—42no—
179D4×C11—44no—
180D4×C11—82no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—28no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—24no—
190C2×C4×C11—24no—
191C2×C4×C11—42no—
192C2×C4×C11—44no—
193C2×C4×C11—42no—
194C2×C4×C11—84no—
195C2×C4×C11#12012yes—
196C2×C4×C11#12012yes—
197C22⋊D11—816no—
198C2×Dic11—44no—
199C2×Dic11—48no—
200C2×Dic11—42no—
201C2×Dic11—44no—
202D44—48no—
203D44—48no—
204C23×D4—111no—
205#552—24no—
206#551—24no—
207#543C2×D1111yescharacteristic
208#539—22no—
209#534C2×D1111yescharacteristic
210#529—22no—
211C2×#123C2×D1112yes—
212C2×#120—114no—
213#518C2×D1112yes—
214C2×#117—111no—
215C2×#117C2×D1111yescharacteristic
216C2×#99—114no—
217#394—224no—
218#392—224no—
219#390—222no—
220#390—222no—
221#381—112no—
222#379—112no—
223#379—112no—
224#379—114no—
225#342—112no—
226#342—112no—
227#342—114no—
228C22×C11—22no—
229C22×C11—24no—
230C22×C11—42no—
231C22×C11—42no—
232C22×C11—42no—
233C22×C11—44no—
234C22×C11—84no—
235C22×C11C2×#12011yescharacteristic
236C22×C11#52511yescharacteristic
237C22×C11#53511yescharacteristic
238C22×C11#54614yes—
239C2×D11—48no—
240C2×D11—44no—
241C2×D11—44no—
242C2×D11—48no—
243C2×D11—44no—
244C2×D11—84no—
245C2×D11—88no—
246C2×D11—84no—
247C4×C11—22no—
248C4×C11—22no—
249C4×C11—42no—
250C4×C11—42no—
251C4×C11—44no—
252C4×C11—42no—
253Dic11—82no—
254Dic11—84no—
255C25—112no—
256C22×D4—224no—
257C22×D4—224no—
258C22×D4—221no—
259C22×D4—221no—
260C22×D4—224no—
261C22×D4—442no—
262C22×D4C22×D1112yes—
263C23×C4C22×D1111yescharacteristic
264#126—24no—
265#126—24no—
266#125—22no—
267#125—24no—
268#124—22no—
269#123—24no—
270#123—22no—
271#123—22no—
272#123—24no—
273#123—22no—
274C22⋊Q8—24no—
275C22⋊Q8—22no—
276C22⋊Q8—24no—
277#121—22no—
278#120—22no—
279#120—228no—
280#120—444no—
281C4×Q8—22no—
282C4×D4—22no—
283C4×D4—24no—
284C4×D4—24no—
285#117—24no—
286#117—24no—
287#117—22no—
288#117—442no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4C22⋊D1112yescomplemented
291C2×C4⋊C4C22⋊D1114yescomplemented
292C2×C22⋊C4—22no—
293C2×C22⋊C4—112no—
294C2×C22⋊C4—114no—
295C2×C22⋊C4—224no—
296C2×C22⋊C4—224no—
297C2×C22⋊C4—224no—
298C2×C22⋊C4—228no—
299C2×C22⋊C4C22⋊D1114yescomplemented
300C2×C22⋊C4C22×D1111yescharacteristic
301C2×C22⋊C4C22×D1111yescharacteristic
302C2×C22⋊C4C22×D1112yes—
303C2×C42—221no—
304C2×C42C22⋊D1112yescomplemented
305#99—444no—
306#95—224no—
307C2×C11—21no—
308C2×C11—24no—
309C2×C11—21no—
310C2×C11—82no—
311C2×C11#240411yescharacteristic
312C2×C11#302712yes—
313D11—84no—
314C24—114no—
315C24—222no—
316C24—224no—
317C24—222no—
318C24—224no—
319C24—884no—
320C24C2×C22⋊D1112yes—
321C24C23×D1111yescharacteristic
322C2×Q8—22no—
323C2×D4—24no—
324C2×D4—24no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—224no—
329C2×D4—224no—
330C2×D4—4416no—
331C2×D4—442no—
332C2×D4—442no—
333C2×D4—448no—
334C2×D4—442no—
335C2×D4—442no—
336C2×D4—888no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—24no—
340C22×C4—224no—
341C22×C4—222no—
342C22×C4C2×C22⋊D1112yes—
343C22×C4C2×C22⋊D1114yes—
344C22×C4C2×C22⋊D1111yescharacteristic
345C22×C4C2×C22⋊D1111yescharacteristic
346C22×C4C2×C22⋊D1112yes—
347C22×C4C2×C22⋊D1112yes—
348C22×C4C2×C22⋊D1114yes—
349C4⋊C4—24no—
350C4⋊C4—24no—
351C4⋊C4—22no—
352C4⋊C4—22no—
353C4⋊C4—24no—
354C4⋊C4—24no—
355C4⋊C4—24no—
356C4⋊C4—442no—
357C22⋊C4—24no—
358C22⋊C4—24no—
359C22⋊C4—22no—
360C22⋊C4—22no—
361C22⋊C4—22no—
362C22⋊C4—22no—
363C22⋊C4—24no—
364C22⋊C4—24no—
365C22⋊C4—224no—
366C22⋊C4—224no—
367C22⋊C4—224no—
368C22⋊C4—448no—
369C22⋊C4—884no—
370C22⋊C4—884no—
371C22⋊C4—888no—
372C42—24no—
373C42—22no—
374C42—22no—
375C42—442no—
376C11#2398811yescharacteristic, complemented, Sylow
377C23—22no—
378C23—24no—
379C23—42no—
380C23—44no—
381C23—224no—
382C23—228no—
383C23—444no—
384C23—444no—
385C23—448no—
386C23—448no—
387C23—444no—
388C23—442no—
389C23—442no—
390C23—884no—
391C23—884no—
392C23—888no—
393C23#41×D1112yes—
394C23#6704212yes—
395C23C22×C22⋊D1111yescharacteristic
396C23C22×C22⋊D1112yes—
397Q8—82no—
398D4—42no—
399D4—44no—
400D4—42no—
401D4—82no—
402D4—448no—
403D4—448no—
404D4—8816no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—28no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—24no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—42no—
416C2×C4—44no—
417C2×C4—42no—
418C2×C4—84no—
419C2×C4—444no—
420C2×C4—448no—
421C2×C4—444no—
422C2×C4—442no—
423C2×C4#6700612yes—
424C2×C4#6700612yes—
425C22—22no—
426C22—24no—
427C22—42no—
428C22—42no—
429C22—44no—
430C22—42no—
431C22—84no—
432C22—448no—
433C22—448no—
434C22—444no—
435C22—444no—
436C22—444no—
437C22—884no—
438C22—888no—
439C22—884no—
440C22#1062335911yescharacteristic
441C22#1062336014yes—
442C22#1062336111yescharacteristic
443C22C2×#6700611yescharacteristic
444C4—22no—
445C4—22no—
446C4—42no—
447C4—44no—
448C4—42no—
449C4—42no—
450C4—884no—
451C4—882no—
452C2—21no—
453C2—24no—
454C2—21no—
455C2—82no—
456C2—884no—
457C2#1307193111yescharacteristic
458C2#1307801812yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC11×#3491C2
socleC22×C11C2×#120
hypercenter#3491D11
hypocenterC11#23988
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3491

Complements

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

NH ≅ G/Ntype
1. #13074332C2semidirect
2. #13071196C2semidirect
3. #13069779C2semidirect
4. #13069740C2semidirect
5. #13069075C2semidirect
6. #13069024C2semidirect
7. #13068693C2semidirect
8. C11×#3491C2semidirect
64. C2×C11×C4⋊C4D4semidirect
65. C2×C11×C4⋊C4D4semidirect
67. C2×C11×C22⋊C4D4semidirect
71. C2×C42×C11D4semidirect
148. #3491D11semidirect
290. C2×C4⋊C4C22⋊D11semidirect
291. C2×C4⋊C4C22⋊D11semidirect
299. C2×C22⋊C4C22⋊D11semidirect
304. C2×C42C22⋊D11semidirect
376. C11#23988semidirect

Maximal subgroups

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

subgroupindex
#130743322
#130711962
#130697792
#130697402
#130690752
#130690242
#130686932
C11×#34912
#2398811