Finite Group Databasebeta

← #14667514

Subgroups — #14667514

Order 2816.

294 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 65 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#13081585C211yesmaximal, characteristic, complemented
2#13070858C211yesmaximal, characteristic
3#13070657C211yesmaximal, characteristic
4#13068100C211yesmaximal, characteristic
5#13066667C211yesmaximal, characteristic, complemented
6#13066587C211yesmaximal, characteristic, complemented
7C11×#1338C211yesmaximal, characteristic, complemented
8#10623098—21no—
9C11×#446C2211yescharacteristic
10#10622640—21no—
11C2×#66864—21no—
12#10622463—21no—
13#10622442—21no—
14#10622442—21no—
15#10622329—21no—
16#10622315—21no—
17C4×Dic44C2211yescharacteristic
18#10622308C2211yescharacteristic
19#10622296C2211yescharacteristic
20C11×C4⋊C16C2211yescharacteristic
21C11×#346C2211yescharacteristic
22#10622147—21no—
23#10622147—21no—
24#10622147—21no—
25#10622123—21no—
26#10622095C2211yescharacteristic
27C4×Q8×C11D411yescharacteristic
28#66997—41no—
29C2×#4325—41no—
30C2×Dic44D411yescharacteristic
31C2×D88—21no—
32C2×D88—21no—
33#66942—41no—
34#66942—41no—
35#66940—41no—
36#66927—21no—
37#66923—21no—
38#66923—21no—
39#66922—21no—
40C4×Dic22—21no—
41C4×Dic22—21no—
42C4×Dic22—21no—
43C2×C11×C16—21no—
44C2×C11×C16—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8D411yescharacteristic
47C11×#97—21no—
48C4×C8×C11C2311yescharacteristic
49#66882—21no—
50#66882D411yescharacteristic
51#66882D411yescharacteristic
52#66882D411yescharacteristic
53#66881—21no—
54#66881—21no—
55#66880—21no—
56#66880—21no—
57#66880—21no—
58#66873—41no—
59C4⋊(C11⋊C8)—21no—
60#66864—42no—
61#12361—111nomaximal, Sylow
62C2×Q8×C11D811yescharacteristic
63C2×D44—41no—
64C2×D44—41no—
65C2×D44—41no—
66C2×Dic22—21no—
67C2×Dic22—41no—
68C2×C8×C11—21no—
69C2×C8×C11C2×D411yescharacteristic
70C2×C8×C11C2×D411yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4D811yescharacteristic
73C42×C11—21no—
74C42×C11C2×D411yescharacteristic
75#4325—82no—
76C4⋊Dic11—21no—
77C4⋊Dic11—21no—
78C4⋊Dic11—21no—
79C4⋊Dic11—41no—
80Dic11⋊C4—41no—
81Dic11⋊C4—41no—
82Dic11⋊C4—41no—
83Dic11⋊C4—41no—
84Dic11⋊C4—41no—
85Dic11⋊C4—41no—
86Dic11⋊C4—41no—
87C4×Dic11—41no—
88C4×Dic11—41no—
89C4×Dic11—41no—
90C2×C11⋊C8—41no—
91Dic44—21no—
92Dic44SD1612yescomplemented
93D88—42no—
94D88—41no—
95D88—41no—
96C11×C16—41no—
97C11×C16—41no—
98#3390—111no—
99#2244—111no—
100#2207—111no—
101#1688—111no—
102#1363—111no—
103#1338D1111yescharacteristic, complemented
104#1334—111no—
105C22×D11—81no—
106Q8×C11—41no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11#12011yescharacteristic
110C2×C4×C11C2×D811yescharacteristic
111C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
112C2×Dic11—41no—
113C2×Dic11—41no—
114C2×Dic11—41no—
115C2×Dic11—41no—
116D44—81no—
117D44—81no—
118D44—81no—
119D44—81no—
120D44—161no—
121Dic22—22no—
122Dic22—41no—
123Dic22—82no—
124C8×C11—21no—
125C8×C11—41no—
126C8×C11C2×SD1611yescharacteristic
127C8×C11#13711yescharacteristic
128C11⋊C8—81no—
129#557—221no—
130C2×SD32—221no—
131#501—221no—
132#499—111no—
133#493—111no—
134#479—221no—
135#479—221no—
136#477—221no—
137#460—221no—
138#446C2×D1111yescharacteristic
139#441—221no—
140C4×Q16—111no—
141C4⋊C16C2×D1111yescharacteristic
142#357—221no—
143#357—221no—
144#357—221no—
145#346C2×D1111yescharacteristic
146#334—111no—
147#331—221no—
148C22×C11#44711yescharacteristic
149C2×D11—161no—
150C2×D11—161no—
151C2×D11—161no—
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—41no—
155C4×C11—41no—
156C4×C11#44811yescharacteristic
157C4×C11#45411yescharacteristic
158Dic11—42no—
159Dic11—81no—
160Dic11—81no—
161Dic11—81no—
162C2×Q16—111no—
163C2×SD16—441no—
164C2×D8—221no—
165C2×D8—221no—
166C4⋊Q8—221no—
167C4⋊Q8—441no—
168#127—221no—
169#125—221no—
170#125—221no—
171#125—441no—
172#125—441no—
173C4×Q8—221no—
174C4×Q8—221no—
175C4×Q8—221no—
176C4×Q8—441no—
177C4×Q8D4411yescharacteristic
178SD32—442no—
179C2×C16—21no—
180C2×C16—21no—
181#107—111no—
182#107—111no—
183#107—111no—
184#107—221no—
185#106—221no—
186#106—221no—
187C4⋊C8—21no—
188C4⋊C8—221no—
189C4⋊C8D4411yescharacteristic
190#103—221no—
191#103—221no—
192#103—221no—
193#102—441no—
194#97—21no—
195C4×C8C22×D1111yescharacteristic
196C2×C11#162711yescharacteristic
197C2×C11#219011yescharacteristic
198C2×C11#219311yescharacteristic
199D11—321no—
200C2×Q8—221no—
201C2×Q8—441no—
202C2×Q8D8811yescharacteristic
203C2×D4—441no—
204C2×D4—441no—
205C2×D4—441no—
206Q16—112no—
207Q16—221no—
208SD16—882no—
209D8—442no—
210D8—441no—
211D8—441no—
212C2×C8—21no—
213C2×C8—441no—
214C2×C8D4×D1111yescharacteristic
215C2×C8D4×D1111yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—221no—
218C4⋊C4—221no—
219C4⋊C4—221no—
220C4⋊C4—441no—
221C4⋊C4—441no—
222C4⋊C4—441no—
223C4⋊C4—441no—
224C4⋊C4—441no—
225C4⋊C4—441no—
226C4⋊C4—441no—
227C4⋊C4—441no—
228C4⋊C4D8811yescharacteristic
229C42—21no—
230C42—441no—
231C42—441no—
232C42—441no—
233C42C2×D4411yescharacteristic
234C16—41no—
235C16—41no—
236C11#1236111yescharacteristic, complemented, Sylow
237C23—881no—
238Q8—41no—
239Q8—222no—
240Q8—441no—
241Q8—882no—
242D4—881no—
243D4—881no—
244D4—881no—
245D4—881no—
246D4—1761no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—441no—
250C2×C4—441no—
251C2×C4—441no—
252C2×C4—441no—
253C2×C4#6693511yescharacteristic
254C2×C4C2×D8811yescharacteristic
255C2×C4#6696111yescharacteristic
256C8—21no—
257C8—41no—
258C8—881no—
259C8SD16×D1111yescharacteristic
260C8#6697111yescharacteristic
261C22—1761no—
262C22—1761no—
263C22—1761no—
264C22#1062234511yescharacteristic
265C4—21no—
266C4—21no—
267C4—41no—
268C4—41no—
269C4—442no—
270C4—881no—
271C4—881no—
272C4—881no—
273C4#1062241911yescharacteristic
274C4#1062244011yescharacteristic
275C2—3521no—
276C2#1306772111yescharacteristic
277C2#1307056411yescharacteristic
278C2#1307058211yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1338C2
socleC22×C11#447
prime radical#10622308C22
hypercenter#1338D11
hypocenterC11#12361
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #446 ◁ #1338

Complements

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

NH ≅ G/Ntype
1. #13081585C2semidirect
5. #13066667C2semidirect
6. #13066587C2semidirect
7. C11×#1338C2semidirect
92. Dic44SD16semidirect
103. #1338D11semidirect
236. C11#12361semidirect

Maximal subgroups

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

subgroupindex
#130815852
#130708582
#130706572
#130681002
#130666672
#130665872
C11×#13382
#1236111