Finite Group Databasebeta

← #14667292

Subgroups — #14667292

Order 2816.

322 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 67 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#13081620C211yesmaximal, characteristic, complemented
2#13070653C211yesmaximal, characteristic
3#13067973C211yesmaximal, characteristic
4#13066665C211yesmaximal, characteristic, complemented
5#13066596C211yesmaximal, characteristic, complemented
6#13066581C211yesmaximal, characteristic, complemented
7C11×#2248C211yesmaximal, characteristic
8#10623252—21no—
9C2×C11×SD32—22no—
10C11×#494C2211yescharacteristic
11C11×#493C2211yescharacteristic
12Q16×Dic11—21no—
13#10622795—22no—
14#10622794—21no—
15C2×#66891—21no—
16#10622703—21no—
17#10622688—21no—
18C4×Dic44C2211yescharacteristic
19C8×Dic22C2211yescharacteristic
20C4×C11×C16C2211yescharacteristic
21#10622200—21no—
22#10622182—21no—
23C4⋊(C11⋊C16)C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16—21no—
26C2×C11×Q16D412yes—
27C2×C11×D8—21no—
28C2×C11×D8—21no—
29C11×C4⋊Q8—21no—
30C11×#127—21no—
31Q8×Dic11—22no—
32#66997—22no—
33C2×#4326—22no—
34C2×#4324—41no—
35C2×Dic44D411yescharacteristic
36#66943—41no—
37#66942—42no—
38#66940—41no—
39C4×Dic22—21no—
40C4×Dic22D411yescharacteristic
41C11×SD32—44no—
42C2×C11×C16—21no—
43C4×C8×C11C2311yescharacteristic
44#66899—22no—
45#66896—41no—
46#66891—42no—
47#66882D411yescharacteristic
48#66880—21no—
49Dic11⋊C8—21no—
50C8×Dic11—21no—
51C2×C11⋊C16—21no—
52C4⋊(C11⋊C8)—21no—
53C4⋊(C11⋊C8)D411yescharacteristic
54#12330—111nomaximal, Sylow
55C2×Q8×C11—22no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×D4×C11—41no—
59C2×Dic22—21no—
60C2×Dic22D811yescharacteristic
61C11×Q16—41no—
62C11×Q16—41no—
63C11×Q16—42no—
64C11×D8—42no—
65C11×D8—41no—
66C11×D8—41no—
67C2×C8×C11C2×D411yescharacteristic
68C2×C8×C11C2×D411yescharacteristic
69C11×C4⋊C4—41no—
70C11×C4⋊C4—41no—
71C42×C11C2×D411yescharacteristic
72#4326—82no—
73#4324—82no—
74C4⋊Dic11—21no—
75C4⋊Dic11—42no—
76C4⋊Dic11D811yescharacteristic
77Dic11⋊C4—21no—
78Dic11⋊C4—42no—
79Dic11⋊C4—42no—
80Dic11⋊C4—41no—
81C4×Dic11—21no—
82C4×Dic11—42no—
83C4×Dic11—41no—
84C2×C11⋊C8—21no—
85C2×C11⋊C8—41no—
86Dic44—21no—
87Dic44—21no—
88C11×C16—22no—
89C11⋊C16—41no—
90#3395—111no—
91#2248D1111yescharacteristic
92#2207—111no—
93#1668—111no—
94#1362—111no—
95Q8⋊C16—111no—
96#1332—111no—
97C23×C11—81no—
98Q8×C11—42no—
99Q8×C11—42no—
100D4×C11—81no—
101D4×C11—81no—
102D4×C11—81no—
103D4×C11—81no—
104D4×C11—161no—
105C2×C4×C11—42no—
106C2×C4×C11#12011yescharacteristic
107C2×C4×C11C2×D811yescharacteristic
108C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
109C2×Dic11—21no—
110C2×Dic11—21no—
111C2×Dic11—41no—
112C2×Dic11—41no—
113Dic22—21no—
114Dic22—41no—
115Dic22—41no—
116Dic22SD3212yescomplemented
117C8×C11—21no—
118C8×C11#13511yescharacteristic
119C8×C11AGL(1,ℤ/8)11yescharacteristic
120C11⋊C8—41no—
121C11⋊C8—81no—
122#557—221no—
123C2×SD32—22no—
124C2×SD32—221no—
125#494—221no—
126#494C2×D1111yescharacteristic
127#493C2×D1111yescharacteristic
128#462—221no—
129#462—222no—
130#460—221no—
131C8×Q8—111no—
132C4×Q16—111no—
133C4×Q16—221no—
134C4⋊C16—111no—
135#357—221no—
136C4×C16C2×D1111yescharacteristic
137#335—111no—
138#331—221no—
139C22×C11—161no—
140C22×C11—161no—
141C22×C11—161no—
142C22×C11#44711yescharacteristic
143C4×C11—21no—
144C4×C11—82no—
145C4×C11#44911yescharacteristic
146C4×C11#45311yescharacteristic
147C4×C11C2×SD3211yescharacteristic
148C4×C11#51011yescharacteristic
149Dic11—22no—
150Dic11—41no—
151Dic11—81no—
152Dic11—81no—
153C2×Q16—21no—
154C2×Q16—111no—
155C2×Q16—222no—
156C2×Q16C22⋊D1112yes—
157C2×SD16—441no—
158C2×D8—21no—
159C2×D8—21no—
160C4⋊Q8—21no—
161C4⋊Q8—222no—
162#127—21no—
163#125—441no—
164#125—442no—
165C4×Q8—111no—
166C4×Q8—222no—
167C4×Q8—221no—
168C4×Q8—441no—
169SD32—44no—
170SD32—442no—
171C2×C16—21no—
172C2×C16—221no—
173#107—111no—
174C4⋊C8—111no—
175C4⋊C8—221no—
176C4⋊C8—221no—
177#103—222no—
178#103—221no—
179#102—441no—
180C4×C8—221no—
181C4×C8C22×D1111yescharacteristic
182C2×C11—321no—
183C2×C11#162111yescharacteristic
184C2×C11#218511yescharacteristic
185C2×C11#219311yescharacteristic
186C2×Q8—22no—
187C2×Q8—111no—
188C2×Q8—221no—
189C2×D4—41no—
190C2×D4—41no—
191C2×D4—41no—
192Q16—42no—
193Q16—41no—
194Q16—41no—
195Q16—221no—
196Q16—221no—
197Q16—882no—
198SD16—882no—
199D8—42no—
200D8—41no—
201D8—41no—
202C2×C8—221no—
203C2×C8—441no—
204C2×C8D4×D1111yescharacteristic
205C2×C8C2×C22⋊D1111yescharacteristic
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—111no—
209C4⋊C4—221no—
210C4⋊C4—221no—
211C4⋊C4—442no—
212C4⋊C4—442no—
213C4⋊C4—442no—
214C4⋊C4—441no—
215C42—221no—
216C42—442no—
217C42—441no—
218C42D4×D1111yescharacteristic
219C16—22no—
220C16—441no—
221C11#1233011yescharacteristic, complemented, Sylow
222C23—81no—
223Q8—42no—
224Q8—42no—
225Q8—112no—
226Q8—221no—
227Q8—441no—
228Q8—441no—
229D4—81no—
230D4—81no—
231D4—81no—
232D4—81no—
233D4—161no—
234C2×C4—42no—
235C2×C4—221no—
236C2×C4—221no—
237C2×C4—441no—
238C2×C4—441no—
239C2×C4D8×D1111yescharacteristic
240C2×C4#6696411yescharacteristic
241C2×C4#6699011yescharacteristic
242C8—21no—
243C8—441no—
244C8—881no—
245C8#6696411yescharacteristic
246C8#6696511yescharacteristic
247C22—161no—
248C22—161no—
249C22—161no—
250C22#1062276911yescharacteristic
251C4—21no—
252C4—82no—
253C4—222no—
254C4—441no—
255C4—881no—
256C4—881no—
257C4D11×SD3211yescharacteristic
258C4#1062252811yescharacteristic
259C4#1062269011yescharacteristic
260C4#1062277111yescharacteristic
261C2—321no—
262C2#1306767811yescharacteristic
263C2#1307053111yescharacteristic
264C2#1307057911yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2248C2
socleC22×C11#447
prime radicalC11×#493C22
hypercenter#2248D11
hypocenterC11#12330
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
1. #13081620C2semidirect
4. #13066665C2semidirect
5. #13066596C2semidirect
6. #13066581C2semidirect
116. Dic22SD32semidirect
221. C11#12330semidirect

Maximal subgroups

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

subgroupindex
#130816202
#130706532
#130679732
#130666652
#130665962
#130665812
C11×#22482
#1233011