Finite Group Databasebeta

← #14658276

Subgroups — #14658276

Order 2816.

374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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#13076888C211yesmaximal, characteristic
2#13068784C211yesmaximal, characteristic
3#13068750C211yesmaximal, characteristic
4#13068749C211yesmaximal, characteristic
5#13066498C211yesmaximal, characteristic
6#13066498C211yesmaximal, characteristic
7C11×#1295C211yesmaximal, characteristic
8C2×C11×#97C2211yescharacteristic
9C2×C11×#97C2211yescharacteristic
10C11×#382C2211yescharacteristic
11C2×#66882—21no—
12C2×#66881—21no—
13#10622599—21no—
14#10622592—21no—
15#10622549C2211yescharacteristic
16#10622549C2211yescharacteristic
17#10622548C2211yescharacteristic
18C2×#66867C2211yescharacteristic
19#10622273—21no—
20#10622273—21no—
21#10622269—21no—
22#10622269—21no—
23#10622189—21no—
24#10622189—21no—
25#10622167—21no—
26#10622167—21no—
27C22×Dic22—21no—
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C42×C11C2311yescharacteristic
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11D411yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×C4⋊Dic11D411yescharacteristic
40C2×C4⋊Dic11D411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C22×C11⋊C8—21no—
44C11×#97—21no—
45C11×#97—21no—
46C11×#97Q812yescomplemented
47C11×#97Q812yescomplemented
48C11×#95—21no—
49C11×#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58#66882—42no—
59#66881—42no—
60#66867—21no—
61#66867Q812yescomplemented
62#10584—111nomaximal, Sylow
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×Dic11—21no—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—41no—
73C2×Dic22—81no—
74C2×Dic22—81no—
75C2×Dic22—81no—
76C2×C8×C11—22no—
77C2×C8×C11—22no—
78C2×C8×C11—22no—
79C2×C8×C11—22no—
80C2×C8×C11—41no—
81C2×C8×C11—41no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C42×C11C2×Q811yescharacteristic
85C42×C11C2×Q811yescharacteristic
86C42×C11C2×Q811yescharacteristic
87C42×C11#4111yescharacteristic
88C4⋊Dic11—41no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11—42no—
95C4⋊Dic11—42no—
96C4⋊Dic11—81no—
97Dic11⋊C4—81no—
98Dic11⋊C4—81no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—41no—
101C2×C11⋊C8—41no—
102#2844—111no—
103#1847—111no—
104#1836—111no—
105#1836—111no—
106#1295—111no—
107#1295—111no—
108#1295D1111yescharacteristic
109C23×C11#12011yescharacteristic
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11C22⋊Q811yescharacteristic
123C2×C4×C11C22⋊Q811yescharacteristic
124C2×C4×C11C22⋊Q811yescharacteristic
125C2×C4×C11C4⋊Q811yescharacteristic
126C2×C4×C11C4⋊Q811yescharacteristic
127C2×C4×C11C4⋊Q811yescharacteristic
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—81no—
141C2×Dic11—81no—
142C2×Dic11—81no—
143Dic22—84no—
144C8×C11—24no—
145C8×C11—42no—
146C11⋊C8—42no—
147C2×#107—221no—
148C2×#106—221no—
149C2×#97—111no—
150C2×#97C2×D1111yescharacteristic
151C2×#97C2×D1111yescharacteristic
152#400—221no—
153#400—221no—
154#400—221no—
155#395—221no—
156#395—221no—
157#395—221no—
158#384—111no—
159#382—111no—
160#382—111no—
161#382C2×D1111yescharacteristic
162#340—221no—
163#340—221no—
164#340—221no—
165#340—221no—
166C22×C11#39511yescharacteristic
167C22×C11#45311yescharacteristic
168C22×C11#45411yescharacteristic
169C22×C11#45411yescharacteristic
170C22×C11#45511yescharacteristic
171C22×C11#45511yescharacteristic
172C22×C11#45611yescharacteristic
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—81no—
180C4×C11—81no—
181Dic11—81no—
182Dic11—81no—
183Dic11—81no—
184Dic11—81no—
185Dic11—161no—
186C22×Q8—221no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—221no—
190C2×C4⋊C4—111no—
191C2×C4⋊C4—111no—
192C2×C4⋊C4—111no—
193C2×C4⋊C4—111no—
194C2×C4⋊C4—221no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—221no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4D4411yescharacteristic
201C2×C4⋊C4D4411yescharacteristic
202C2×C42C22×D1111yescharacteristic
203#107—442no—
204#106—442no—
205#97—21no—
206#97—21no—
207#97—112no—
208#97—221no—
209#97Dic2212yescomplemented
210#97Dic2212yescomplemented
211#95—21no—
212#95—21no—
213#95—221no—
214#95—221no—
215#95—221no—
216#95—221no—
217#95—221no—
218#95—221no—
219#95—221no—
220#95—221no—
221C2×C11#165711yescharacteristic
222C2×C11#165911yescharacteristic
223C2×C11#166411yescharacteristic
224C2×C11#166411yescharacteristic
225C2×C11#206011yescharacteristic
226C2×C11#206111yescharacteristic
227C2×C11#206111yescharacteristic
228C2×Q8—881no—
229C2×Q8—881no—
230C2×Q8—881no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—221no—
234C22×C4—221no—
235C22×C4—221no—
236C22×C4—221no—
237C22×C4—441no—
238C22×C4C2×D4411yescharacteristic
239C22×C4D4×D1111yescharacteristic
240C22×C4D4×D1111yescharacteristic
241C2×C8—22no—
242C2×C8—22no—
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—222no—
248C2×C8—441no—
249C2×C8—441no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—441no—
253C4⋊C4—441no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—442no—
259C4⋊C4—442no—
260C4⋊C4—881no—
261C4⋊C4—881no—
262C4⋊C4—881no—
263C42C2×Dic2211yescharacteristic
264C42C2×Dic2211yescharacteristic
265C42#434111yescharacteristic
266C42Q8×D1111yescharacteristic
267C11#1058411yescharacteristic, complemented, Sylow
268C23#6693511yescharacteristic
269Q8—884no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4—441no—
291C2×C4—441no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—881no—
295C2×C4—881no—
296C2×C4—881no—
297C2×C4#6692211yescharacteristic
298C2×C4#6693111yescharacteristic
299C2×C4#6693111yescharacteristic
300C2×C4#6694111yescharacteristic
301C2×C4#6694111yescharacteristic
302C2×C4#6695011yescharacteristic
303C8—24no—
304C8—42no—
305C8—442no—
306C22#1062226911yescharacteristic
307C22#1062235911yescharacteristic
308C22#1062236611yescharacteristic
309C22#1062243511yescharacteristic
310C22#1062243811yescharacteristic
311C22#1062243911yescharacteristic
312C22#1062244011yescharacteristic
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—81no—
320C4—81no—
321C4—881no—
322C4—881no—
323C4—881no—
324C4—881no—
325C4—1761no—
326C2#1306791611yescharacteristic
327C2#1306792411yescharacteristic
328C2#1306795111yescharacteristic
329C2#1306795311yescharacteristic
330C2#1306996011yescharacteristic
331C2#1306996511yescharacteristic
332C2#1306996711yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1295C2
socle, prime radicalC23×C11#120
hypercenter#1295D11
hypocenterC11#10584
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
46. C11×#97Q8semidirect
47. C11×#97Q8semidirect
61. #66867Q8semidirect
209. #97Dic22semidirect
210. #97Dic22semidirect
267. C11#10584semidirect

Maximal subgroups

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

subgroupindex
#130768882
#130687842
#130687502
#130687492
#130664982
C11×#12952
#1058411