Finite Group Databasebeta

← #13073977

Subgroups — #13073977

Order 1408.

468 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 151 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×Q8×Dic11C211yesmaximal, characteristic
2C2×#66940C211yesmaximal, characteristic
3C11×#395C211yesmaximal, characteristic
4#10622842C211yesmaximal, characteristic
5#10622599C211yesmaximal, characteristic
6#10622594C212yesmaximal
7#10622585C212yesmaximal
8#10622272C211yesmaximal, characteristic
9#10622268C212yesmaximal
10#10622263C211yesmaximal, characteristic
11#10622259C212yesmaximal
12C22×Q8×C11C2211yescharacteristic
13C22×Dic22C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C4⋊C4C2212yes—
16Q8×Dic11—24no—
17C2×C4⋊Dic11C2212yes—
18C2×C4⋊Dic11C2211yescharacteristic
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2211yescharacteristic
21C2×Dic11⋊C4C2211yescharacteristic
22C2×Dic11⋊C4C2212yes—
23C2×C4×Dic11C2212yes—
24C2×C4×Dic11C2211yescharacteristic
25C2×C4×Dic11C2211yescharacteristic
26C2×C4×Dic11C2211yescharacteristic
27#66940—24no—
28C11×#95C2212yes—
29C11×#95C2211yescharacteristic
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2211yescharacteristic
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C2×Q8×C11—22no—
38C2×Q8×C11—24no—
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C22×Dic11C2311yescharacteristic
49C22×Dic11C2311yescharacteristic
50C2×Dic22—22no—
51C2×Dic22—22no—
52C2×Dic22Q814yescomplemented
53C11×C4⋊C4—22no—
54C11×C4⋊C4—24no—
55C4⋊Dic11—24no—
56C4⋊Dic11—22no—
57Dic11⋊C4—22no—
58Dic11⋊C4—24no—
59Dic11⋊C4—22no—
60Dic11⋊C4—24no—
61C4×Dic11—22no—
62C4×Dic11—22no—
63C4×Dic11—24no—
64C4×Dic11D414yes—
65#2581—111nomaximal, Sylow
66C23×C11C2411yescharacteristic
67Q8×C11—28no—
68C2×C4×C11—22no—
69C2×C4×C11—21no—
70C2×C4×C11—21no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—21no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11C2×D412yes—
79C2×C4×C11C2×Q812yes—
80C2×C4×C11#4114yes—
81C2×Dic11—21no—
82C2×Dic11—21no—
83C2×Dic11—22no—
84C2×Dic11—21no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—24no—
90C2×Dic11—22no—
91C2×Dic11C2×D412yes—
92C2×Dic11C2×D412yes—
93C2×Dic11C2×Q812yes—
94C2×Dic11C2×Q812yes—
95C2×Dic11#4112yes—
96Dic22—28no—
97C2×C4×Q8—111no—
98C2×C4×Q8—111no—
99#400—111no—
100#400—111no—
101#395—111no—
102#395D1111yescharacteristic
103#391—112no—
104#389—112no—
105#387—112no—
106#387—112no—
107#382—111no—
108C22×C11C22×D411yescharacteristic
109C22×C11C22×Q811yescharacteristic
110C22×C11C2×#4112yes—
111C22×C11C2×#4111yescharacteristic
112C22×C112−1+412yes—
113C4×C11—22no—
114C4×C11—22no—
115C4×C11—24no—
116C4×C11—41no—
117C4×C11—42no—
118Dic11—22no—
119Dic11—22no—
120Dic11—41no—
121Dic11—42no—
122Dic11—42no—
123Dic11C22⋊Q814yes—
124C22×Q8—111no—
125C22×Q8C2×D1111yescharacteristic
126C4×Q8—224no—
127C4×Q8—224no—
128C2×C4⋊C4—112no—
129C2×C4⋊C4—111no—
130C2×C4⋊C4—111no—
131C2×C4⋊C4—111no—
132C2×C4⋊C4—112no—
133C2×C4⋊C4—112no—
134C2×C4⋊C4C2×D1111yescharacteristic
135C2×C4⋊C4C2×D1112yes—
136C2×C42—111no—
137C2×C42—111no—
138C2×C42—111no—
139C2×C42—112no—
140#95—112no—
141#95—111no—
142#95—112no—
143#95—112no—
144#95—112no—
145#95—112no—
146#95—112no—
147#95C2×D1111yescharacteristic
148#95C2×D1112yes—
149C2×C11C2×C22⋊Q811yescharacteristic
150C2×C11#52511yescharacteristic
151C2×C11#53611yescharacteristic
152C2×C11#55612yes—
153C2×C11#55712yes—
154C2×Q8—22no—
155C2×Q8—24no—
156C2×Q8—114no—
157C2×Q8—222no—
158C2×Q8—222no—
159C22×C4—111no—
160C22×C4—111no—
161C22×C4—111no—
162C22×C4—112no—
163C22×C4—112no—
164C22×C4—111no—
165C22×C4C22×D1112yes—
166C22×C4C22×D1111yescharacteristic
167C22×C4C22×D1111yescharacteristic
168C22×C4C22×D1112yes—
169C22×C4C22×D1111yescharacteristic
170C4⋊C4—22no—
171C4⋊C4—24no—
172C4⋊C4—222no—
173C4⋊C4—224no—
174C4⋊C4—224no—
175C4⋊C4—222no—
176C4⋊C4—222no—
177C4⋊C4—224no—
178C42—114no—
179C42—222no—
180C42—224no—
181C42—222no—
182C11#258111yescharacteristic, complemented, Sylow
183C23C23×D1111yescharacteristic
184Q8—28no—
185Q8—228no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—112no—
197C2×C4—112no—
198C2×C4—112no—
199C2×C4—112no—
200C2×C4—112no—
201C2×C4—221no—
202C2×C4—222no—
203C2×C4—221no—
204C2×C4—222no—
205C2×C4—221no—
206C2×C4—222no—
207C2×C4—222no—
208C2×C4—224no—
209C2×C4—222no—
210C2×C4—222no—
211C2×C4D4×D1112yes—
212C2×C4#434114yes—
213C2×C4Q8×D1112yes—
214C22C2×D4×D1111yescharacteristic
215C22C2×#434112yes—
216C22C2×Q8×D1111yescharacteristic
217C22#6704012yes—
218C22#41×D1111yescharacteristic
219C4—22no—
220C4—24no—
221C4—22no—
222C4—41no—
223C4—42no—
224C4—114no—
225C4—222no—
226C4—222no—
227C4—442no—
228C4—441no—
229C4—442no—
230C2#1062311711yescharacteristic
231C2D11×C22⋊Q811yescharacteristic
232C2#1062317212yes—
233C2#1062325212yes—
234C2#1062325511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#395C2
hypercenter#395D11
hypocenterC11#2581
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
52. C2×Dic22Q8semidirect
182. C11#2581semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic112
C2×#669402
C11×#3952
#106228422
#106225992
#106225942
#106225852
#106222722
#106222682
#106222632
#106222592
#258111