Finite Group Databasebeta

← #13073820

Subgroups — #13073820

Order 1408.

500 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 171 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×#66997C211yesmaximal, characteristic
2C2×#66940C211yesmaximal, characteristic
3C11×#395C211yesmaximal, characteristic
4#10622842C211yesmaximal, characteristic
5#10622592C211yesmaximal, characteristic
6#10622589C212yesmaximal
7#10622585C212yesmaximal
8#10622269C211yesmaximal, characteristic
9#10622262C211yesmaximal, characteristic
10#10622260C212yesmaximal
11#10622259C212yesmaximal
12C22×Q8×C11C2211yescharacteristic
13C22×Dic22C2211yescharacteristic
14C22×Dic22C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C4⋊C4C2212yes—
17#66997—24no—
18C2×C4⋊Dic11C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2211yescharacteristic
21C2×Dic11⋊C4C2211yescharacteristic
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×C4×Dic11C2212yes—
27C2×C4×Dic11C2211yescharacteristic
28C2×C4×Dic11C2211yescharacteristic
29C2×C4×Dic11C2211yescharacteristic
30#66940—24no—
31C11×#95C2212yes—
32C11×#95C2211yescharacteristic
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2211yescharacteristic
37C2×Q8×C11—22no—
38C2×Q8×C11—42no—
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2312yes—
48C22×Dic11C2311yescharacteristic
49C22×Dic11C2311yescharacteristic
50C2×Dic22—22no—
51C2×Dic22—22no—
52C2×Dic22—22no—
53C2×Dic22—42no—
54C2×Dic22Q814yescomplemented
55C11×C4⋊C4—22no—
56C11×C4⋊C4—42no—
57C4⋊Dic11—42no—
58Dic11⋊C4—22no—
59Dic11⋊C4—24no—
60Dic11⋊C4—24no—
61Dic11⋊C4—22no—
62Dic11⋊C4—42no—
63Dic11⋊C4—42no—
64Dic11⋊C4Q818yescomplemented
65C4×Dic11—22no—
66C4×Dic11—22no—
67C4×Dic11—24no—
68C4×Dic11D414yes—
69#2567—111nomaximal, Sylow
70C23×C11C2411yescharacteristic
71Q8×C11—44no—
72C2×C4×C11—21no—
73C2×C4×C11—22no—
74C2×C4×C11—21no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—21no—
78C2×C4×C11—22no—
79C2×C4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11C2×D412yes—
83C2×C4×C11C2×Q814yes—
84C2×C4×C11C2×Q812yes—
85C2×Dic11—21no—
86C2×Dic11—22no—
87C2×Dic11—21no—
88C2×Dic11—22no—
89C2×Dic11—21no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—22no—
93C2×Dic11—22no—
94C2×Dic11C2×D412yes—
95C2×Dic11C2×D412yes—
96C2×Dic11C2×Q814yes—
97C2×Dic11C2×Q812yes—
98C2×Dic11C2×Q812yes—
99C2×Dic11C2×Q814yes—
100C2×Dic11#4112yes—
101Dic22—28no—
102Dic22—44no—
103C2×C4⋊Q8—111no—
104C2×C4×Q8—111no—
105#395—111no—
106#395—111no—
107#395—111no—
108#395D1111yescharacteristic
109#391—112no—
110#389—112no—
111#389—112no—
112#384—112no—
113C4×C4⋊C4—111no—
114C22×C11C22×D411yescharacteristic
115C22×C11C22×Q811yescharacteristic
116C22×C11C22×Q812yes—
117C22×C11C2×#4111yescharacteristic
118C22×C11H(5,𝔽2)12yes—
119C4×C11—22no—
120C4×C11—22no—
121C4×C11—24no—
122C4×C11—41no—
123C4×C11—42no—
124Dic11—22no—
125Dic11—24no—
126Dic11—42no—
127Dic11—41no—
128Dic11C22⋊Q814yes—
129Dic11C4⋊Q814yes—
130C22×Q8—111no—
131C22×Q8—111no—
132C22×Q8C2×D1111yescharacteristic
133C4⋊Q8—224no—
134C4×Q8—224no—
135C2×C4⋊C4—112no—
136C2×C4⋊C4—111no—
137C2×C4⋊C4—111no—
138C2×C4⋊C4—112no—
139C2×C4⋊C4—112no—
140C2×C4⋊C4—112no—
141C2×C4⋊C4—112no—
142C2×C4⋊C4—112no—
143C2×C4⋊C4C2×D1111yescharacteristic
144C2×C4⋊C4C2×D1112yes—
145C2×C42—111no—
146C2×C42—111no—
147C2×C42—111no—
148C2×C42—112no—
149#95—111no—
150#95—112no—
151#95—112no—
152#95—112no—
153#95C2×D1111yescharacteristic
154#95C2×D1112yes—
155C2×C11C2×C22⋊Q811yescharacteristic
156C2×C11C2×C4⋊Q811yescharacteristic
157C2×C11#53511yescharacteristic
158C2×C11#55412yes—
159C2×C11Q8212yes—
160C2×Q8—22no—
161C2×Q8—42no—
162C2×Q8—114no—
163C2×Q8—222no—
164C2×Q8—222no—
165C2×Q8—222no—
166C2×Q8—442no—
167C22×C4—111no—
168C22×C4—111no—
169C22×C4—111no—
170C22×C4—112no—
171C22×C4—112no—
172C22×C4—111no—
173C22×C4C22×D1112yes—
174C22×C4C22×D1111yescharacteristic
175C22×C4C22×D1111yescharacteristic
176C22×C4C22×D1111yescharacteristic
177C22×C4C22×D1112yes—
178C4⋊C4—22no—
179C4⋊C4—42no—
180C4⋊C4—118no—
181C4⋊C4—222no—
182C4⋊C4—224no—
183C4⋊C4—224no—
184C4⋊C4—222no—
185C4⋊C4—442no—
186C4⋊C4—442no—
187C4⋊C4—442no—
188C42—114no—
189C42—222no—
190C42—222no—
191C42—224no—
192C11#256711yescharacteristic, complemented, Sylow
193C23C23×D1111yescharacteristic
194Q8—44no—
195Q8—228no—
196Q8—444no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—112no—
208C2×C4—112no—
209C2×C4—114no—
210C2×C4—112no—
211C2×C4—112no—
212C2×C4—114no—
213C2×C4—112no—
214C2×C4—221no—
215C2×C4—222no—
216C2×C4—222no—
217C2×C4—221no—
218C2×C4—221no—
219C2×C4—222no—
220C2×C4—222no—
221C2×C4—222no—
222C2×C4—222no—
223C2×C4D4×D1112yes—
224C2×C4Q8×D1114yes—
225C2×C4Q8×D1112yes—
226C22C2×D4×D1111yescharacteristic
227C22#6703712yes—
228C22C2×Q8×D1111yescharacteristic
229C22C2×Q8×D1112yes—
230C22#41×D1111yescharacteristic
231C4—22no—
232C4—22no—
233C4—24no—
234C4—42no—
235C4—41no—
236C4—114no—
237C4—114no—
238C4—222no—
239C4—224no—
240C4—442no—
241C4—441no—
242C2#1062312311yescharacteristic
243C2D11×C22⋊Q811yescharacteristic
244C2#1062316712yes—
245C2#1062325312yes—
246C2D11×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#395C2
hypercenter#395D11
hypocenterC11#2567
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
54. C2×Dic22Q8semidirect
64. Dic11⋊C4Q8semidirect
192. C11#2567semidirect

Maximal subgroups

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

subgroupindex
C2×#669972
C2×#669402
C11×#3952
#106228422
#106225922
#106225892
#106225852
#106222692
#106222622
#106222602
#106222592
#256711