Finite Group Databasebeta

← #13074563

Subgroups — #13074563

Order 1408.

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

normal subgroups only

This group has 416 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
1C2×#66942C211yesmaximal, characteristic
2C2×#66941C211yesmaximal, characteristic
3C11×#400C211yesmaximal, characteristic
4#10622599C211yesmaximal, characteristic
5#10622595C211yesmaximal, characteristic
6#10622273C212yesmaximal
7#10622272C211yesmaximal, characteristic
8#10622271C212yesmaximal
9#10622261C211yesmaximal, characteristic
10#10622259C212yesmaximal
11#10622259C212yesmaximal
12C22×Dic22C2212yes—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C4⋊Dic11C2211yescharacteristic
16C2×C4⋊Dic11C2211yescharacteristic
17C2×Dic11⋊C4C2211yescharacteristic
18C2×Dic11⋊C4C2211yescharacteristic
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2211yescharacteristic
21C2×Dic11⋊C4C2211yescharacteristic
22C2×C4×Dic11C2212yes—
23C2×C4×Dic11C2211yescharacteristic
24#66942—24no—
25#66941—24no—
26C11×#95C2212yes—
27C11×#95C2212yes—
28C11×#95C2211yescharacteristic
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2211yescharacteristic
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×Dic11C2312yes—
43C22×Dic11C2311yescharacteristic
44C22×Dic11C2311yescharacteristic
45C22×Dic11C2312yes—
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C2×Dic22—24no—
49C2×Dic22—28no—
50C11×C4⋊C4—22no—
51C11×C4⋊C4—22no—
52C4⋊Dic11—22no—
53C4⋊Dic11—22no—
54Dic11⋊C4—24no—
55Dic11⋊C4—22no—
56Dic11⋊C4—22no—
57Dic11⋊C4—22no—
58Dic11⋊C4—22no—
59C4×Dic11—24no—
60C4×Dic11D414yes—
61#2642—111nomaximal, Sylow
62C23×C11C2411yescharacteristic
63C2×C4×C11—22no—
64C2×C4×C11—21no—
65C2×C4×C11—21no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—24no—
69C2×C4×C11—21no—
70C2×C4×C11—21no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11C2×D412yes—
75C2×Dic11—21no—
76C2×Dic11—21no—
77C2×Dic11—21no—
78C2×Dic11—21no—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—24no—
82C2×Dic11—21no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—21no—
86C2×Dic11—22no—
87C2×Dic11C2×D412yes—
88C2×Dic11C2×D412yes—
89C2×Dic11#4114yes—
90Dic22—48no—
91C2×C4⋊Q8—111no—
92C2×#125—111no—
93#400—111no—
94#400—111no—
95#400—112no—
96#400—111no—
97#400—112no—
98#400D1111yescharacteristic
99#391—112no—
100#391—112no—
101#376—111no—
102C22×C11C22×D411yescharacteristic
103C22×C11C2×#4112yes—
104C22×C112−1+411yescharacteristic
105C22×C112−1+411yescharacteristic
106C22×C112−1+412yes—
107C4×C11—22no—
108C4×C11—42no—
109C4×C11—41no—
110C4×C11—41no—
111C4×C11—42no—
112Dic11—22no—
113Dic11—42no—
114Dic11—41no—
115Dic11—41no—
116Dic11—42no—
117Dic11#12414yes—
118C22×Q8—112no—
119C4⋊Q8—224no—
120#125—224no—
121C2×C4⋊C4—111no—
122C2×C4⋊C4—111no—
123C2×C4⋊C4—111no—
124C2×C4⋊C4—111no—
125C2×C4⋊C4—111no—
126C2×C4⋊C4—112no—
127C2×C4⋊C4—111no—
128C2×C4⋊C4C2×D1111yescharacteristic
129C2×C4⋊C4C2×D1111yescharacteristic
130C2×C42—111no—
131C2×C42—112no—
132#95—112no—
133#95—111no—
134#95—112no—
135#95—112no—
136#95—112no—
137#95—112no—
138#95—112no—
139#95—112no—
140#95C2×D1111yescharacteristic
141#95C2×D1112yes—
142#95C2×D1112yes—
143C2×C11C2×#12411yescharacteristic
144C2×C11#53611yescharacteristic
145C2×C11#53611yescharacteristic
146C2×C11#54112yes—
147C2×C11#54112yes—
148C2×Q8—224no—
149C2×Q8—228no—
150C22×C4—111no—
151C22×C4—111no—
152C22×C4—112no—
153C22×C4—111no—
154C22×C4—111no—
155C22×C4—112no—
156C22×C4C22×D1112yes—
157C22×C4C22×D1111yescharacteristic
158C22×C4C22×D1111yescharacteristic
159C22×C4C22×D1112yes—
160C22×C4C22×D1111yescharacteristic
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—222no—
164C4⋊C4—222no—
165C4⋊C4—222no—
166C4⋊C4—222no—
167C4⋊C4—224no—
168C4⋊C4—222no—
169C4⋊C4—222no—
170C42—114no—
171C42—224no—
172C11#264211yescharacteristic, complemented, Sylow
173C23C23×D1111yescharacteristic
174Q8—448no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—112no—
187C2×C4—114no—
188C2×C4—112no—
189C2×C4—221no—
190C2×C4—221no—
191C2×C4—221no—
192C2×C4—221no—
193C2×C4—222no—
194C2×C4—221no—
195C2×C4—222no—
196C2×C4—222no—
197C2×C4—224no—
198C2×C4—221no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4D4×D1112yes—
202C22C2×D4×D1111yescharacteristic
203C22#6704011yescharacteristic
204C22#41×D1112yes—
205C22#6704311yescharacteristic
206C22#6704312yes—
207C4—22no—
208C4—42no—
209C4—41no—
210C4—41no—
211C4—42no—
212C4—114no—
213C4—222no—
214C4—441no—
215C4—441no—
216C4—442no—
217C4—442no—
218C2#1062315911yescharacteristic
219C2#1062317911yescharacteristic
220C2D11×#12411yescharacteristic
221C2#1062322712yes—
222C2#1062323212yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#400C2
hypercenter#400D11
hypocenterC11#2642
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
172. C11#2642semidirect

Maximal subgroups

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

subgroupindex
C2×#669422
C2×#669412
C11×#4002
#106225992
#106225952
#106222732
#106222722
#106222712
#106222612
#106222592
#264211