Finite Group Databasebeta

← #13073998

Subgroups — #13073998

Order 1408.

468 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 161 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×#66942C211yesmaximal, characteristic
3C11×#395C211yesmaximal, characteristic
4#10622842C211yesmaximal, characteristic
5#10622598C212yesmaximal
6#10622596C211yesmaximal, characteristic
7#10622585C212yesmaximal
8#10622274C211yesmaximal, characteristic
9#10622262C211yesmaximal, characteristic
10#10622260C212yesmaximal
11#10622260C212yesmaximal
12C22×Q8×C11C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2212yes—
15Q8×Dic11—24no—
16C2×C4⋊Dic11C2212yes—
17C2×C4⋊Dic11C2211yescharacteristic
18C2×C4⋊Dic11C2211yescharacteristic
19C2×C4⋊Dic11C2212yes—
20C2×Dic11⋊C4C2211yescharacteristic
21C2×Dic11⋊C4C2211yescharacteristic
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2211yescharacteristic
24C2×Dic11⋊C4C2211yescharacteristic
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2212yes—
27C2×C4×Dic11C2212yes—
28C2×C4×Dic11C2212yes—
29C2×C4×Dic11C2211yescharacteristic
30#66942—24no—
31C11×#95C2212yes—
32C11×#95C2211yescharacteristic
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C2×Q8×C11—22no—
38C2×Q8×C11—24no—
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2312yes—
43C22×C4×C11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C22×Dic11C2312yes—
49C22×Dic11C2311yescharacteristic
50C11×C4⋊C4—22no—
51C11×C4⋊C4—24no—
52C4⋊Dic11—22no—
53C4⋊Dic11—24no—
54C4⋊Dic11—22no—
55C4⋊Dic11—42no—
56Dic11⋊C4—22no—
57Dic11⋊C4—22no—
58Dic11⋊C4—22no—
59Dic11⋊C4—22no—
60Dic11⋊C4—24no—
61Dic11⋊C4—42no—
62Dic11⋊C4Q818yescomplemented
63C4×Dic11—24no—
64C4×Dic11—42no—
65C4×Dic11D414yes—
66#2584—111nomaximal, Sylow
67C23×C11C2411yescharacteristic
68Q8×C11—28no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—22no—
77C2×C4×C11—21no—
78C2×C4×C11—21no—
79C2×C4×C11C2×D412yes—
80C2×C4×C11C2×Q814yes—
81C2×C4×C11#4114yes—
82C2×Dic11—22no—
83C2×Dic11—21no—
84C2×Dic11—22no—
85C2×Dic11—21no—
86C2×Dic11—22no—
87C2×Dic11—21no—
88C2×Dic11—21no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—21no—
92C2×Dic11—22no—
93C2×Dic11—21no—
94C2×Dic11C2×D412yes—
95C2×Dic11C2×D412yes—
96C2×Dic11C2×Q814yes—
97C2×Dic11C2×Q814yes—
98C2×#125—111no—
99C2×C4×Q8—111no—
100#398—111no—
101#398—111no—
102#395—111no—
103#395D1111yescharacteristic
104#389—112no—
105#389—112no—
106#389—112no—
107#389—112no—
108C4×C4⋊C4—111no—
109C22×C11C22×D411yescharacteristic
110C22×C11C22×Q812yes—
111C22×C11C2×#4112yes—
112C22×C11H(5,𝔽2)11yescharacteristic
113C22×C112−1+411yescharacteristic
114C4×C11—22no—
115C4×C11—24no—
116C4×C11—24no—
117C4×C11—41no—
118C4×C11—41no—
119Dic11—22no—
120Dic11—24no—
121Dic11—41no—
122Dic11—42no—
123Dic11—41no—
124Dic11C4⋊Q814yes—
125C22×Q8C2×D1111yescharacteristic
126#125—224no—
127C4×Q8—224no—
128C2×C4⋊C4—112no—
129C2×C4⋊C4—112no—
130C2×C4⋊C4—111no—
131C2×C4⋊C4—111no—
132C2×C4⋊C4—111no—
133C2×C4⋊C4—111no—
134C2×C4⋊C4—111no—
135C2×C4⋊C4—111no—
136C2×C4⋊C4—112no—
137C2×C4⋊C4—112no—
138C2×C4⋊C4—112no—
139C2×C4⋊C4C2×D1111yescharacteristic
140C2×C4⋊C4C2×D1112yes—
141C2×C42—111no—
142C2×C42—112no—
143C2×C42—112no—
144#95—111no—
145#95—112no—
146#95—112no—
147#95—112no—
148#95C2×D1111yescharacteristic
149#95C2×D1112yes—
150C2×C11#52511yescharacteristic
151C2×C11C2×C4⋊Q811yescharacteristic
152C2×C11#53711yescharacteristic
153C2×C11#55412yes—
154C2×C11#55712yes—
155C2×Q8—22no—
156C2×Q8—24no—
157C22×C4—111no—
158C22×C4—112no—
159C22×C4—111no—
160C22×C4—112no—
161C22×C4—111no—
162C22×C4—111no—
163C22×C4C22×D1111yescharacteristic
164C22×C4C22×D1111yescharacteristic
165C22×C4C22×D1111yescharacteristic
166C22×C4C22×D1112yes—
167C22×C4C22×D1112yes—
168C4⋊C4—22no—
169C4⋊C4—24no—
170C4⋊C4—118no—
171C4⋊C4—224no—
172C4⋊C4—222no—
173C4⋊C4—222no—
174C4⋊C4—222no—
175C4⋊C4—222no—
176C4⋊C4—222no—
177C4⋊C4—222no—
178C4⋊C4—224no—
179C4⋊C4—442no—
180C4⋊C4—442no—
181C42—114no—
182C42—224no—
183C42—442no—
184C11#258411yescharacteristic, complemented, Sylow
185C23C23×D1111yescharacteristic
186Q8—28no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—112no—
198C2×C4—114no—
199C2×C4—112no—
200C2×C4—114no—
201C2×C4—222no—
202C2×C4—221no—
203C2×C4—221no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4—221no—
207C2×C4—221no—
208C2×C4—222no—
209C2×C4—222no—
210C2×C4—221no—
211C2×C4—222no—
212C2×C4—221no—
213C2×C4D4×D1112yes—
214C2×C4#434114yes—
215C2×C4Q8×D1114yes—
216C22C2×D4×D1111yescharacteristic
217C22C2×#434112yes—
218C22C2×Q8×D1112yes—
219C22#6704011yescharacteristic
220C22#6704211yescharacteristic
221C4—22no—
222C4—24no—
223C4—24no—
224C4—41no—
225C4—41no—
226C4—114no—
227C4—222no—
228C4—224no—
229C4—441no—
230C4—442no—
231C4—441no—
232C2#1062311711yescharacteristic
233C2#1062316011yescharacteristic
234C2#1062316612yes—
235C2#1062325212yes—
236C2D11×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#395C2
hypercenter#395D11
hypocenterC11#2584
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
62. Dic11⋊C4Q8semidirect
184. C11#2584semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic112
C2×#669422
C11×#3952
#106228422
#106225982
#106225962
#106225852
#106222742
#106222622
#106222602
#258411