Finite Group Databasebeta

← #13076644

Subgroups — #13076644

Order 1408.

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

normal subgroups only

This group has 528 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×C11×#121C211yesmaximal, characteristic
2C2×#66977C211yesmaximal, characteristic, complemented
3#10622835C214yesmaximal, complemented
4#10622835C212yesmaximal, complemented
5#10622824C211yesmaximal, characteristic, complemented
6#10622593C212yesmaximal, complemented
7#10622562C212yesmaximal, complemented
8#10622560C212yesmaximal, complemented
9C22×D4×C11C2212yes—
10C22×D4×C11C2211yescharacteristic
11C23×C4×C11C2211yescharacteristic
12C22×Dic22C2211yescharacteristic
13C11×#121—24no—
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C22⋊C4C2212yes—
16C2×C22⋊Dic11C2212yes—
17C2×C22⋊Dic11C2214yes—
18C2×C22⋊Dic11C2214yes—
19C2×C22⋊Dic11C2212yes—
20C2×C4⋊Dic11C2211yescharacteristic
21#66977—24no—
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2214yes—
24C11⋊#95C2212yes—
25C11⋊#95C2214yes—
26C11⋊#95C2212yes—
27C24×C11C2312yes—
28C24×C11C2311yescharacteristic
29C2×D4×C11—24no—
30C2×D4×C11—22no—
31C2×D4×C11—42no—
32C2×D4×C11—44no—
33C22×C4×C11—42no—
34C22×C4×C11D414yes—
35C22×C4×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C22×Dic11C2314yes—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C2×Dic22—22no—
42C2×Dic22—42no—
43C11×C4⋊C4—22no—
44C11×C22⋊C4—24no—
45C22⋊Dic11—24no—
46C22⋊Dic11—42no—
47C22⋊Dic11—44no—
48C22⋊Dic11—44no—
49C4⋊Dic11—22no—
50Dic11⋊C4—24no—
51Dic11⋊C4—44no—
52#2816—111nomaximal, Sylow
53C23×C11—22no—
54C23×C11—22no—
55C23×C11—22no—
56C23×C11—22no—
57C23×C11—24no—
58C23×C11—24no—
59C23×C11—24no—
60C23×C11C2×D412yes—
61C23×C11C2411yescharacteristic
62D4×C11—44no—
63D4×C11—48no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—24no—
68C2×C4×C11—44no—
69C2×C4×C11C2×D412yes—
70C2×C4×C11C2×D412yes—
71C2×Dic11—22no—
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—24no—
75C2×Dic11—22no—
76C2×Dic11—24no—
77C2×Dic11—24no—
78C2×Dic11—24no—
79Dic22—44no—
80C2×C22⋊Q8—111no—
81C2×#121D1111yescharacteristic
82#399—112no—
83#398—112no—
84#394—112no—
85#394—114no—
86#393—112no—
87#381—111no—
88C22×C11—22no—
89C22×C11—22no—
90C22×C11—22no—
91C22×C11—44no—
92C22×C11—42no—
93C22×C11—42no—
94C22×C11—42no—
95C22×C11—48no—
96C22×C11C22×D411yescharacteristic
97C22×C11H(5,𝔽2)12yes—
98C22×C11H(5,𝔽2)12yes—
99C22×C112−1+412yes—
100C4×C11—22no—
101C4×C11—22no—
102C4×C11—42no—
103Dic11—42no—
104Dic11—42no—
105Dic11—44no—
106C22×Q8—111no—
107C22×D4C2×D1112yes—
108C22×D4C2×D1111yescharacteristic
109C23×C4C2×D1111yescharacteristic
110C22⋊Q8—224no—
111#121—24no—
112C2×C4⋊C4—112no—
113C2×C4⋊C4—111no—
114C2×C4⋊C4—114no—
115C2×C4⋊C4C2×D1111yescharacteristic
116C2×C22⋊C4—112no—
117C2×C22⋊C4—112no—
118C2×C22⋊C4—114no—
119C2×C22⋊C4—114no—
120C2×C22⋊C4C2×D1112yes—
121#95—112no—
122#95—112no—
123#95—114no—
124C2×C11—42no—
125C2×C11—82no—
126C2×C11#53411yescharacteristic
127C2×C11#53511yescharacteristic
128C2×C11#53611yescharacteristic
129C2×C11#56214yes—
130C24C22×D1112yes—
131C24C22×D1111yescharacteristic
132C2×Q8—222no—
133C2×Q8—442no—
134C2×D4—24no—
135C2×D4—22no—
136C2×D4—42no—
137C2×D4—44no—
138C22×C4—42no—
139C22×C4—114no—
140C22×C4—112no—
141C22×C4—112no—
142C22×C4C22⋊D1114yes—
143C22×C4C22×D1112yes—
144C22×C4C22×D1111yescharacteristic
145C22×C4C22×D1111yescharacteristic
146C4⋊C4—22no—
147C4⋊C4—224no—
148C4⋊C4—222no—
149C4⋊C4—444no—
150C22⋊C4—24no—
151C22⋊C4—224no—
152C22⋊C4—442no—
153C22⋊C4—444no—
154C22⋊C4—444no—
155C11#281611yescharacteristic, complemented, Sylow
156C23—22no—
157C23—22no—
158C23—22no—
159C23—24no—
160C23—24no—
161C23—24no—
162C23—22no—
163C23C2×C22⋊D1112yes—
164C23C23×D1111yescharacteristic
165Q8—444no—
166D4—44no—
167D4—48no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—22no—
172C2×C4—44no—
173C2×C4—222no—
174C2×C4—224no—
175C2×C4—224no—
176C2×C4—224no—
177C2×C4—222no—
178C2×C4—224no—
179C2×C4—222no—
180C2×C4—222no—
181C2×C4C2×C22⋊D1112yes—
182C2×C4C2×C22⋊D1112yes—
183C22—22no—
184C22—22no—
185C22—22no—
186C22—44no—
187C22—42no—
188C22—42no—
189C22—42no—
190C22—48no—
191C22#6703712yes—
192C22#6703712yes—
193C22#6704312yes—
194C22C22×C22⋊D1111yescharacteristic
195C4—22no—
196C4—22no—
197C4—42no—
198C4—442no—
199C4—442no—
200C4—444no—
201C2—42no—
202C2—82no—
203C2#1062315214yes—
204C2#1062333511yescharacteristic
205C2#1062333611yescharacteristic
206C2#1062335611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
Fitting, prime radicalC2×C11×#121C2
hypercenterC2×#121D11
hypocenterC11#2816
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C2×#66977C2semidirect
3. #10622835C2semidirect
4. #10622835C2semidirect
5. #10622824C2semidirect
6. #10622593C2semidirect
7. #10622562C2semidirect
8. #10622560C2semidirect
155. C11#2816semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×#669772
#106228352
#106228242
#106225932
#106225622
#106225602
#281611