Finite Group Databasebeta

← #14656396

Subgroups — #14656396

Order 2816.

510 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C2×#10622704C212yesmaximal
2#13069552C211yesmaximal, characteristic
3C2×#10622184C212yesmaximal
4#13066451C211yesmaximal, characteristic
5C2×C11×#500C211yesmaximal, characteristic
6C2×C11×C4⋊Q8C2212yes—
7C2×C4×Dic22C2211yescharacteristic
8C11×#500—24no—
9C2×C11×#107—22no—
10C2×C4×C8×C11C2211yescharacteristic
11#10622704—24no—
12#10622704—24no—
13C2×#66874—22no—
14C2×#66871—22no—
15C2×C4⋊(C11⋊C8)C2211yescharacteristic
16C2×C4⋊(C11⋊C8)C2212yes—
17#10622188—22no—
18#10622184—24no—
19C22×Q8×C11—22no—
20C22×Dic22D411yescharacteristic
21C22×C8×C11D412yes—
22C11×C4⋊Q8—22no—
23C11×C4⋊Q8—22no—
24C11×C4⋊Q8—22no—
25C11×C4⋊Q8D414yes—
26C2×C11×C4⋊C4—22no—
27C2×C11×C4⋊C4—22no—
28C2×C42×C11C2311yescharacteristic
29C2×C4⋊Dic11D411yescharacteristic
30C2×Dic11⋊C4—21no—
31C2×C4×Dic11—21no—
32C22×C11⋊C8—22no—
33C22×C11⋊C8—21no—
34C4×Dic22—22no—
35C4×Dic22—22no—
36C11×#107—28no—
37C4×C8×C11—22no—
38#66874—28no—
39#66871—28no—
40C4⋊(C11⋊C8)—22no—
41C4⋊(C11⋊C8)—22no—
42C4⋊(C11⋊C8)D414yes—
43#10279—111nomaximal, Sylow
44C2×Q8×C11—24no—
45C2×Q8×C11—42no—
46C2×Q8×C11—84no—
47C22×C4×C11—42no—
48C22×C4×C11C2×D411yescharacteristic
49C22×C4×C11C2×D411yescharacteristic
50C22×C4×C11#4111yescharacteristic
51C22×Dic11—21no—
52C22×Dic11—21no—
53C2×Dic22—22no—
54C2×Dic22—21no—
55C2×Dic22—22no—
56C2×Dic22Q1612yes—
57C2×C8×C11—22no—
58C2×C8×C11—22no—
59C2×C8×C11Q1614yes—
60C11×C4⋊C4—24no—
61C11×C4⋊C4—24no—
62C11×C4⋊C4—42no—
63C11×C4⋊C4—42no—
64C42×C11C2×D412yes—
65C42×C11C2×D412yes—
66C4⋊Dic11—22no—
67Dic11⋊C4—42no—
68C4×Dic11—41no—
69C4×Dic11—41no—
70C2×C11⋊C8—24no—
71C2×C11⋊C8—41no—
72C2×C11⋊C8—42no—
73C2×C11⋊C8—42no—
74C2×C11⋊C8—42no—
75C2×#500D1111yescharacteristic
76C2×#477—112no—
77#1984—111no—
78C2×#333—112no—
79#1277—111no—
80C23×C11#12111yescharacteristic
81Q8×C11—84no—
82Q8×C11—84no—
83C2×C4×C11—22no—
84C2×C4×C11—44no—
85C2×C4×C11—84no—
86C2×C4×C11#12012yes—
87C2×C4×C11#12011yescharacteristic
88C2×C4×C11#12112yes—
89C2×C4×C11#12711yescharacteristic
90C2×C4×C11C2×Q1611yescharacteristic
91C2×C4×C11C2×Q1612yes—
92C2×C4×C11#13511yescharacteristic
93C2×C4×C11#13712yes—
94C2×C4×C11#13712yes—
95C2×Dic11—22no—
96C2×Dic11—41no—
97C2×Dic11—41no—
98C2×Dic11—41no—
99C2×Dic11—42no—
100Dic22—24no—
101Dic22—42no—
102C8×C11—24no—
103C11⋊C8—44no—
104C11⋊C8—81no—
105C2×C4⋊Q8C2×D1112yes—
106C2×C4×Q8—111no—
107#500—24no—
108#477—224no—
109#477—224no—
110C2×#107—22no—
111C2×#107—222no—
112C2×C4⋊C8—112no—
113C2×C4⋊C8—111no—
114C2×#103—222no—
115C2×C4×C8C2×D1111yescharacteristic
116#336—222no—
117#333—224no—
118C22×C11#39211yescharacteristic
119C22×C11#46212yes—
120C22×C11#46711yescharacteristic
121C22×C11#47011yescharacteristic
122C22×C11#47212yes—
123C4×C11—22no—
124C4×C11—84no—
125C4×C11#45112yes—
126C4×C11#45112yes—
127C4×C11#45212yes—
128C4×C11#49411yescharacteristic
129C4×C11#49711yescharacteristic
130Dic11—42no—
131Dic11—81no—
132C22×Q8—22no—
133C22×Q8—111no—
134C22×C8—222no—
135C22×C8—221no—
136C22×C8C22⋊D1112yes—
137C4⋊Q8—22no—
138C4⋊Q8—22no—
139C4⋊Q8—22no—
140C4⋊Q8C22⋊D1114yes—
141C4×Q8—222no—
142C4×Q8—222no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—22no—
145C2×C4⋊C4—111no—
146C2×C4⋊C4—221no—
147C2×C42—221no—
148C2×C42C22×D1111yescharacteristic
149#107—28no—
150#107—228no—
151C4⋊C8—114no—
152C4⋊C8—222no—
153C4⋊C8—222no—
154#103—228no—
155C4×C8—22no—
156C2×C11#167612yes—
157C2×C11#169612yes—
158C2×C11#200111yescharacteristic
159C2×C11#201611yescharacteristic
160C2×C11#201811yescharacteristic
161C2×Q8—24no—
162C2×Q8—42no—
163C2×Q8—84no—
164C2×Q8—112no—
165C2×Q8—221no—
166C2×Q8—222no—
167C2×Q8—222no—
168C22×C4—42no—
169C22×C4—221no—
170C22×C4—221no—
171C22×C4D4×D1111yescharacteristic
172C22×C4#434111yescharacteristic
173C22×C4C2×C22⋊D1111yescharacteristic
174C2×C8—22no—
175C2×C8—22no—
176C2×C8—224no—
177C2×C8—442no—
178C2×C8—442no—
179C2×C8—441no—
180C2×C8—442no—
181C2×C8#432614yes—
182C4⋊C4—24no—
183C4⋊C4—24no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—222no—
187C4⋊C4—442no—
188C42—441no—
189C42—441no—
190C42D4×D1112yes—
191C42C2×C22⋊D1112yes—
192C11#1027911yescharacteristic, complemented, Sylow
193C23#6699111yescharacteristic
194Q8—84no—
195Q8—84no—
196Q8—224no—
197Q8—442no—
198C2×C4—22no—
199C2×C4—44no—
200C2×C4—84no—
201C2×C4—222no—
202C2×C4—441no—
203C2×C4—441no—
204C2×C4—442no—
205C2×C4—441no—
206C2×C4Q16×D1111yescharacteristic
207C2×C4#6697112yes—
208C2×C4#6697211yescharacteristic
209C2×C4#6699012yes—
210C2×C4#6699212yes—
211C2×C4#6699311yescharacteristic
212C2×C4#6699512yes—
213C2×C4C2×#432612yes—
214C2×C4#6700611yescharacteristic
215C8—24no—
216C8—444no—
217C8—881no—
218C22#1062270312yes—
219C22#1062277312yes—
220C22#1062280111yescharacteristic
221C22#1062280211yescharacteristic
222C22#1062283611yescharacteristic
223C4—22no—
224C4—84no—
225C4—442no—
226C4—881no—
227C4#1062269911yescharacteristic
228C4#1062270511yescharacteristic
229C4#1062279912yes—
230C4#1062280012yes—
231C4#1062284112yes—
232C2#1306801712yes—
233C2#1306814112yes—
234C2#1306962311yescharacteristic
235C2#1306971611yescharacteristic
236C2#1306972311yescharacteristic
subgroupG/H
centerC23#66991
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#500C2
socle, prime radicalC23×C11#121
hypercenterC2×#500D11
hypocenterC11#10279
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
192. C11#10279semidirect

Maximal subgroups

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

subgroupindex
C2×#106227042
#130695522
C2×#106221842
#130664512
C2×C11×#5002
#1027911