Finite Group Databasebeta

← #13074582

Subgroups — #13074582

Order 1408.

352 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C11×#391C211yesmaximal, characteristic
2#10622843C211yesmaximal, characteristic
3#10622843C211yesmaximal, characteristic
4#10622598C211yesmaximal, characteristic
5#10622586C211yesmaximal, characteristic
6#10622545C211yesmaximal, characteristic
7#10622541C211yesmaximal, characteristic
8C11⋊#401C212yesmaximal
9#10622273C212yesmaximal
10#10622272C212yesmaximal
11#10622271C212yesmaximal
12C22×Q8×C11C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C42×C11C2211yescharacteristic
15C2×C4⋊Dic11C2211yescharacteristic
16C2×C4⋊Dic11C2211yescharacteristic
17C2×C4⋊Dic11C2212yes—
18C2×Dic11⋊C4C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×C4×Dic11C2211yescharacteristic
21C2×C4×Dic11C2211yescharacteristic
22C11×#95C2212yes—
23C11×#95C2212yes—
24C11⋊#95C2211yescharacteristic
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2211yescharacteristic
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2211yescharacteristic
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2211yescharacteristic
35C2×Q8×C11—22no—
36C2×Q8×C11—22no—
37C2×Q8×C11—22no—
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2312yes—
42C22×C4×C11C2311yescharacteristic
43C22×Dic11C2311yescharacteristic
44C22×Dic11C2311yescharacteristic
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2312yes—
48C22×Dic11C2312yes—
49C11×C4⋊C4—22no—
50C42×C11—22no—
51C4⋊Dic11—22no—
52C4⋊Dic11—22no—
53C4⋊Dic11—42no—
54Dic11⋊C4—42no—
55Dic11⋊C4—42no—
56C4×Dic11—22no—
57C4×Dic11—22no—
58#2645—111nomaximal, Sylow
59C23×C11C2411yescharacteristic
60Q8×C11—44no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—21no—
68C2×C4×C11—22no—
69C2×C4×C11—21no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—22no—
73C2×C4×C11#4112yes—
74C2×C4×C11#4112yes—
75C2×C4×C11#4112yes—
76C2×Dic11—21no—
77C2×Dic11—21no—
78C2×Dic11—21no—
79C2×Dic11—21no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—21no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—21no—
86C2×Dic11—21no—
87C2×Dic11—21no—
88C2×Dic11—21no—
89C2×Dic11—21no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—21no—
93C2×Dic11—21no—
94#401—112no—
95#400—112no—
96#400—112no—
97#400—112no—
98#391—111no—
99#391—111no—
100#391D1111yescharacteristic
101#389—111no—
102#389—111no—
103#389—111no—
104#376—111no—
105C22×C11C2×#4111yescharacteristic
106C22×C11C2×#4111yescharacteristic
107C22×C11C2×#4111yescharacteristic
108C22×C11H(5,𝔽2)11yescharacteristic
109C22×C112−1+411yescharacteristic
110C22×C112−1+411yescharacteristic
111C22×C112−1+411yescharacteristic
112C4×C11—42no—
113C4×C11—41no—
114C4×C11—41no—
115C4×C11—42no—
116C4×C11#12614yes—
117Dic11—41no—
118Dic11—41no—
119Dic11—41no—
120Dic11—42no—
121Dic11—42no—
122Dic11—41no—
123C22×Q8C2×D1111yescharacteristic
124C2×C4⋊C4—111no—
125C2×C4⋊C4—111no—
126C2×C4⋊C4—112no—
127C2×C4⋊C4—112no—
128C2×C4⋊C4—112no—
129C2×C4⋊C4C2×D1111yescharacteristic
130C2×C42—111no—
131C2×C42—111no—
132C2×C42C2×D1111yescharacteristic
133#95—111no—
134#95—111no—
135#95—111no—
136#95—111no—
137#95—112no—
138#95—112no—
139#95—112no—
140#95—112no—
141#95—112no—
142#95—112no—
143#95—112no—
144#95C2×D1112yes—
145#95C2×D1112yes—
146C2×C11C2×#12611yescharacteristic
147C2×C11#54111yescharacteristic
148C2×C11#54111yescharacteristic
149C2×C11#54111yescharacteristic
150C2×C11#54211yescharacteristic
151C2×C11#54211yescharacteristic
152C2×C11#54211yescharacteristic
153C2×Q8—22no—
154C2×Q8—22no—
155C2×Q8—22no—
156C22×C4—111no—
157C22×C4—111no—
158C22×C4—111no—
159C22×C4—111no—
160C22×C4—112no—
161C22×C4—112no—
162C22×C4C22×D1111yescharacteristic
163C22×C4C22×D1112yes—
164C22×C4C22×D1111yescharacteristic
165C22×C4C22×D1112yes—
166C22×C4C22×D1111yescharacteristic
167C4⋊C4—22no—
168C4⋊C4—222no—
169C4⋊C4—222no—
170C4⋊C4—442no—
171C4⋊C4—442no—
172C4⋊C4—442no—
173C42—22no—
174C42—222no—
175C42—222no—
176C11#264511yescharacteristic, complemented, Sylow
177C23C23×D1111yescharacteristic
178Q8—44no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—221no—
192C2×C4—221no—
193C2×C4—222no—
194C2×C4—221no—
195C2×C4—221no—
196C2×C4—222no—
197C2×C4—221no—
198C2×C4—221no—
199C2×C4—221no—
200C2×C4—222no—
201C2×C4—221no—
202C2×C4—222no—
203C2×C4—222no—
204C2×C4—221no—
205C2×C4—222no—
206C2×C4—221no—
207C2×C4—221no—
208C2×C4—221no—
209C2×C4#433912yes—
210C2×C4#434112yes—
211C2×C4#434112yes—
212C22C2×#433911yescharacteristic
213C22C2×#434111yescharacteristic
214C22C2×#434111yescharacteristic
215C22#6704011yescharacteristic
216C22#6704011yescharacteristic
217C22#6704211yescharacteristic
218C22#6704311yescharacteristic
219C4—42no—
220C4—41no—
221C4—41no—
222C4—42no—
223C4—441no—
224C4—441no—
225C4—442no—
226C4—441no—
227C4—442no—
228C4—441no—
229C4#6693214yes—
230C2C2×#6693211yescharacteristic
231C2#1062311311yescharacteristic
232C2#1062311411yescharacteristic
233C2#1062315611yescharacteristic
234C2#1062317411yescharacteristic
235C2#1062321311yescharacteristic
236C2#1062326211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#391C2
hypercenter#391D11
hypocenterC11#2645
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
176. C11#2645semidirect

Maximal subgroups

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

subgroupindex
C11×#3912
#106228432
#106225982
#106225862
#106225452
#106225412
C11⋊#4012
#106222732
#106222722
#106222712
#264511