Finite Group Databasebeta

← #14656398

Subgroups — #14656398

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×#10622295C211yesmaximal, characteristic
2C2×#10622634C212yesmaximal
3C2×#10622119C212yesmaximal
4#13066451C211yesmaximal, characteristic
5C11×#1984C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66922C2212yes—
8C2×C11×C4⋊C8C2211yescharacteristic
9C2×C4×C8×C11C2211yescharacteristic
10C2×#66899—22no—
11C2×#66882—22no—
12#10622634—24no—
13#10622634—24no—
14C2×#66871—22no—
15C2×C4⋊(C11⋊C8)C2212yes—
16#10622295—24no—
17C11×#336—22no—
18#10622119—24no—
19C22×Q8×C11D411yescharacteristic
20C22×Dic22—22no—
21C22×C8×C11—21no—
22C22×C8×C11D412yes—
23C4×Q8×C11—22no—
24C4×Q8×C11—22no—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C42×C11—21no—
28C2×C42×C11C2311yescharacteristic
29C2×C4⋊Dic11—22no—
30C2×C4⋊Dic11—22no—
31C22×C11⋊C8—22no—
32#66922—22no—
33#66922—22no—
34#66922—22no—
35#66922D414yes—
36C11×C4⋊C8—22no—
37C4×C8×C11—22no—
38#66899—28no—
39#66882—28no—
40#66871—28no—
41C4⋊(C11⋊C8)—22no—
42C4⋊(C11⋊C8)D414yes—
43#10279—111nomaximal, Sylow
44C2×Q8×C11—21no—
45C2×Q8×C11—22no—
46C2×Q8×C11—22no—
47C2×Q8×C11Q1612yes—
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11C2×D411yescharacteristic
51C22×C4×C11C2×D411yescharacteristic
52C22×C4×C11#4111yescharacteristic
53C22×Dic11—42no—
54C2×Dic22—24no—
55C2×Dic22—42no—
56C2×Dic22—84no—
57C2×C8×C11—22no—
58C2×C8×C11—22no—
59C2×C8×C11—41no—
60C2×C8×C11—42no—
61C2×C8×C11Q1614yes—
62C11×C4⋊C4—22no—
63C11×C4⋊C4—42no—
64C42×C11—41no—
65C42×C11—41no—
66C42×C11C2×D412yes—
67C42×C11C2×D412yes—
68C4⋊Dic11—24no—
69C4⋊Dic11—24no—
70C4⋊Dic11—42no—
71C4⋊Dic11—42no—
72C2×C11⋊C8—24no—
73C2×C11⋊C8—42no—
74C2×C11⋊C8—42no—
75C2×#500—111no—
76C2×#477—112no—
77#1984D1111yescharacteristic
78C2×#333—112no—
79#1277—111no—
80C23×C11#12111yescharacteristic
81Q8×C11—24no—
82Q8×C11—42no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—41no—
86C2×C4×C11—41no—
87C2×C4×C11—41no—
88C2×C4×C11—42no—
89C2×C4×C11#12012yes—
90C2×C4×C11#12011yescharacteristic
91C2×C4×C11#12112yes—
92C2×C4×C11#12711yescharacteristic
93C2×C4×C11C2×Q1611yescharacteristic
94C2×C4×C11C2×Q1612yes—
95C2×C4×C11#13511yescharacteristic
96C2×C4×C11#13712yes—
97C2×C4×C11#13712yes—
98C2×Dic11—44no—
99C2×Dic11—84no—
100Dic22—84no—
101Dic22—84no—
102C8×C11—24no—
103C8×C11—81no—
104C11⋊C8—44no—
105C2×C4⋊Q8—112no—
106C2×C4×Q8C2×D1111yescharacteristic
107#500—224no—
108#477—224no—
109#477—224no—
110C2×#107—222no—
111C2×#107—222no—
112C2×C4⋊C8—112no—
113C2×C4⋊C8C2×D1111yescharacteristic
114C2×#103—222no—
115C2×C4×C8C2×D1111yescharacteristic
116#336—22no—
117#333—224no—
118C22×C11#39211yescharacteristic
119C22×C11#46212yes—
120C22×C11#46711yescharacteristic
121C22×C11#47011yescharacteristic
122C22×C11#47212yes—
123C4×C11—22no—
124C4×C11—42no—
125C4×C11—81no—
126C4×C11#45112yes—
127C4×C11#45112yes—
128C4×C11#45212yes—
129C4×C11#49411yescharacteristic
130C4×C11#49711yescharacteristic
131Dic11—84no—
132C22×Q8—222no—
133C22×Q8D4411yescharacteristic
134C22×C8—21no—
135C22×C8—222no—
136C22×C8C22⋊D1112yes—
137C4⋊Q8—114no—
138C4⋊Q8—222no—
139C4⋊Q8—222no—
140C4⋊Q8—222no—
141C4×Q8—22no—
142C4×Q8—22no—
143C2×C4⋊C4—21no—
144C2×C4⋊C4—222no—
145C2×C4⋊C4—222no—
146C2×C4⋊C4D4411yescharacteristic
147C2×C42—21no—
148C2×C42C22×D1111yescharacteristic
149#107—228no—
150#107—228no—
151C4⋊C8—22no—
152C4⋊C8—114no—
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—21no—
162C2×Q8—22no—
163C2×Q8—22no—
164C2×Q8—224no—
165C2×Q8—442no—
166C2×Q8—884no—
167C2×Q8Dic4412yes—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—442no—
171C22×C4C2×D4411yescharacteristic
172C22×C4#433911yescharacteristic
173C22×C4C2×C22⋊D1111yescharacteristic
174C2×C8—22no—
175C2×C8—22no—
176C2×C8—41no—
177C2×C8—42no—
178C2×C8—224no—
179C2×C8—442no—
180C2×C8—442no—
181C2×C8#432614yes—
182C4⋊C4—22no—
183C4⋊C4—42no—
184C4⋊C4—224no—
185C4⋊C4—224no—
186C4⋊C4—442no—
187C4⋊C4—442no—
188C42—41no—
189C42—41no—
190C42D4×D1112yes—
191C42D4×D1112yes—
192C11#1027911yescharacteristic, complemented, Sylow
193C23#6698311yescharacteristic
194Q8—24no—
195Q8—42no—
196Q8—884no—
197Q8—884no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—42no—
203C2×C4—41no—
204C2×C4—444no—
205C2×C4—884no—
206C2×C4#6693512yes—
207C2×C4#6693712yes—
208C2×C4#6695711yescharacteristic
209C2×C4C2×Dic4411yescharacteristic
210C2×C4#6696212yes—
211C2×C4#6699011yescharacteristic
212C2×C4#6699311yescharacteristic
213C2×C4C2×#432612yes—
214C2×C4#6700412yes—
215C8—24no—
216C8—81no—
217C8—444no—
218C22#1062257311yescharacteristic
219C22#1062264412yes—
220C22#1062272911yescharacteristic
221C22#1062275011yescharacteristic
222C22#1062275512yes—
223C4—22no—
224C4—42no—
225C4—81no—
226C4—884no—
227C4#1062234612yes—
228C4#1062235212yes—
229C4#1062266312yes—
230C4#1062267311yescharacteristic
231C4#1062270511yescharacteristic
232C2#1306802012yes—
233C2#1306814412yes—
234C2#1306962611yescharacteristic
235C2#1306971511yescharacteristic
236C2#1306972511yescharacteristic
subgroupG/H
centerC23#66983
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1984C2
socle, prime radicalC23×C11#121
hypercenter#1984D11
hypocenterC11#10279
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1984

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×#106222952
C2×#106226342
C2×#106221192
#130664512
C11×#19842
#1027911