Finite Group Databasebeta

← #13074091

Subgroups — #13074091

Order 1408.

596 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 153 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×#66983C211yesmaximal, characteristic
2C22×Dic11⋊C4C211yesmaximal, characteristic, complemented
3C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
4#10622571C212yesmaximal, complemented
5#10622571C212yesmaximal, complemented
6#10622553C214yesmaximal, complemented
7#10622285C212yesmaximal, complemented
8#10622272C212yesmaximal, complemented
9C23×C4×C11C2211yescharacteristic
10C22×C22⋊D11C2212yes—
11C23×Dic11C2211yescharacteristic
12C23×Dic11C2211yescharacteristic
13C22×D44C2211yescharacteristic
14C2×C11×C22⋊C4C2212yes—
15C2×C42×C11C2212yes—
16#66983—24no—
17C2×(C2×D11)⋊C4C2214yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2214yes—
20C2×C4⋊Dic11C2211yescharacteristic
21C2×Dic11⋊C4—24no—
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2212yes—
24C11×#95C2212yes—
25C11⋊#95C2214yes—
26C11⋊#95C2214yes—
27C24×C11C2311yescharacteristic
28C23×D11C2312yes—
29C22×C4×C11—42no—
30C22×C4×C11D414yes—
31C22×C4×C11C2314yes—
32C22×C4×C11C2311yescharacteristic
33C22×C4×C11C2311yescharacteristic
34C2×C22⋊D11—24no—
35C2×C22⋊D11—28no—
36C22×Dic11—24no—
37C22×Dic11—22no—
38C22×Dic11—22no—
39C22×Dic11—42no—
40C22×Dic11C2312yes—
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C2×D44—22no—
44C2×D44—42no—
45C11×C22⋊C4—24no—
46C42×C11—42no—
47(C2×D11)⋊C4—28no—
48(C2×D11)⋊C4—24no—
49(C2×D11)⋊C4—44no—
50C4⋊Dic11—22no—
51Dic11⋊C4—24no—
52Dic11⋊C4—24no—
53#2591—111nomaximal, Sylow
54C23×C11—22no—
55C23×C11—22no—
56C23×C11C2×D412yes—
57C23×C11#4114yes—
58C23×C11C2411yescharacteristic
59C22×D11—22no—
60C22×D11—24no—
61C22×D11—24no—
62C22×D11—24no—
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—24no—
66C2×C4×C11—24no—
67C2×C4×C11—24no—
68C2×C4×C11—44no—
69C2×C4×C11C2×D412yes—
70C2×C4×C11C2×D412yes—
71C22⋊D11—48no—
72C2×Dic11—28no—
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—24no—
78C2×Dic11—24no—
79C2×Dic11—44no—
80C2×Dic11#4114yes—
81D44—44no—
82C2×#121—111no—
83C22×C4⋊C4—111no—
84#400—112no—
85#394—112no—
86#388—114no—
87#386—112no—
88#386—112no—
89C4×C22⋊C4D1111yescharacteristic, complemented
90C22×C11—22no—
91C22×C11—22no—
92C22×C11—28no—
93C22×C11#12414yes—
94C22×C11C22×D411yescharacteristic
95C22×C11C2×#4112yes—
96C22×C11C2×#4112yes—
97C22×C11H(5,𝔽2)12yes—
98C2×D11—42no—
99C2×D11—42no—
100C2×D11—42no—
101C2×D11—48no—
102C4×C11—22no—
103C4×C11—22no—
104C4×C11—44no—
105Dic11—24no—
106Dic11—42no—
107Dic11—42no—
108C22×D4—112no—
109C22×D4—111no—
110C23×C4—111no—
111C23×C4—111no—
112C23×C4C2×D1111yescharacteristic
113#121—224no—
114C2×C4⋊C4—112no—
115C2×C4⋊C4—112no—
116C2×C4⋊C4—111no—
117C2×C4⋊C4—224no—
118C2×C22⋊C4—112no—
119C2×C22⋊C4—114no—
120C2×C22⋊C4—114no—
121C2×C22⋊C4C2×D1112yes—
122C2×C42C2×D1112yes—
123#95—114no—
124#95—114no—
125#95C2×D1112yes—
126C2×C11—24no—
127C2×C11#52511yescharacteristic
128C2×C11C2×#12411yescharacteristic
129C2×C11#53411yescharacteristic
130C2×C11#55314yes—
131D11—82no—
132C24—112no—
133C24C22×D1111yescharacteristic
134C2×D4—224no—
135C2×D4—228no—
136C2×D4—222no—
137C2×D4—442no—
138C22×C4—42no—
139C22×C4—112no—
140C22×C4—112no—
141C22×C4—112no—
142C22×C4—224no—
143C22×C4—222no—
144C22×C4—222no—
145C22×C4—442no—
146C22×C4D4414yes—
147C22×C4C22×D1114yes—
148C22×C4C22×D1111yescharacteristic
149C22×C4C22×D1111yescharacteristic
150C4⋊C4—224no—
151C4⋊C4—224no—
152C4⋊C4—222no—
153C22⋊C4—24no—
154C22⋊C4—228no—
155C22⋊C4—224no—
156C22⋊C4—444no—
157C42—42no—
158C11#259111yescharacteristic, complemented, Sylow
159C23—22no—
160C23—22no—
161C23—222no—
162C23—224no—
163C23—224no—
164C23—224no—
165C23C2×D4412yes—
166C23#433914yes—
167C23C23×D1111yescharacteristic
168D4—444no—
169D4—448no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—24no—
173C2×C4—24no—
174C2×C4—24no—
175C2×C4—44no—
176C2×C4—114no—
177C2×C4—228no—
178C2×C4—222no—
179C2×C4—222no—
180C2×C4—222no—
181C2×C4—222no—
182C2×C4—224no—
183C2×C4—224no—
184C2×C4—444no—
185C2×C4C2×D4412yes—
186C2×C4C2×D4412yes—
187C22—22no—
188C22—22no—
189C22—28no—
190C22—442no—
191C22—442no—
192C22—442no—
193C22—448no—
194C22#6692814yes—
195C22C22×D4411yescharacteristic
196C22C2×#433912yes—
197C22#6703712yes—
198C22#41×D1112yes—
199C4—22no—
200C4—22no—
201C4—44no—
202C4—224no—
203C4—442no—
204C4—442no—
205C2—24no—
206C2—882no—
207C2C2×#6692811yescharacteristic
208C2#1062302411yescharacteristic
209C2#1062305511yescharacteristic
210C2#1062307114yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC4×C11×C22⋊C4C2
prime radicalC2×#66983C2
hypercenterC4×C22⋊C4D11
hypocenterC11#2591
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×Dic11⋊C4C2semidirect
3. C4×C11×C22⋊C4C2semidirect
4. #10622571C2semidirect
5. #10622571C2semidirect
6. #10622553C2semidirect
7. #10622285C2semidirect
8. #10622272C2semidirect
89. C4×C22⋊C4D11semidirect
158. C11#2591semidirect

Maximal subgroups

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

subgroupindex
C2×#669832
C22×Dic11⋊C42
C4×C11×C22⋊C42
#106225712
#106225532
#106222852
#106222722
#259111