Finite Group Databasebeta

← #13073109

Subgroups — #13073109

Order 1408.

596 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 165 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
2C22×C4⋊Dic11C211yesmaximal, characteristic, complemented
3#10622834C212yesmaximal, complemented
4#10622833C214yesmaximal, complemented
5C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
6#10622590C212yesmaximal, complemented
7#10622566C214yesmaximal, complemented
8C22×D4×C11C2212yes—
9C22×D4×C11C2211yescharacteristic
10C23×C4×C11C2211yescharacteristic
11C23×Dic11C2212yes—
12C11×#121—24no—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C22⋊C4C2212yes—
15C2×C22⋊Dic11C2212yes—
16C2×C22⋊Dic11C2218yes—
17C2×C4⋊Dic11—24no—
18C2×C4⋊Dic11C2212yes—
19C2×C4⋊Dic11C2212yes—
20C2×C4×Dic11C2212yes—
21C11⋊#95C2212yes—
22C11⋊#95C2218yes—
23C24×C11C2312yes—
24C24×C11C2311yescharacteristic
25C2×D4×C11—24no—
26C2×D4×C11—28no—
27C2×D4×C11—22no—
28C2×D4×C11—24no—
29C22×C4×C11—24no—
30C22×C4×C11D414yes—
31C22×C4×C11C2312yes—
32C22×C4×C11C2311yescharacteristic
33C22×C4×C11C2311yescharacteristic
34C22×Dic11—24no—
35C22×Dic11—44no—
36C22×Dic11C2314yes—
37C22×Dic11C2314yes—
38C11×C4⋊C4—22no—
39C11×C22⋊C4—24no—
40C22⋊Dic11—24no—
41C22⋊Dic11—48no—
42C4⋊Dic11—24no—
43C4⋊Dic11—24no—
44C4×Dic11—24no—
45#2504—111nomaximal, Sylow
46C23×C11—22no—
47C23×C11—22no—
48C23×C11—22no—
49C23×C11—24no—
50C23×C11—24no—
51C23×C11—24no—
52C23×C11C2×D412yes—
53C23×C11#4114yes—
54C23×C11C2411yescharacteristic
55D4×C11—48no—
56D4×C11—44no—
57C2×C4×C11—22no—
58C2×C4×C11—28no—
59C2×C4×C11—22no—
60C2×C4×C11—24no—
61C2×C4×C11C2×D412yes—
62C2×C4×C11C2×D412yes—
63C2×C4×C11#4114yes—
64C2×Dic11—24no—
65C2×Dic11—24no—
66C2×Dic11—24no—
67C2×Dic11—24no—
68C2×Dic11—28no—
69C2×Dic11—48no—
70C2×#121D1111yescharacteristic
71C22×C4⋊C4—111no—
72#397—114no—
73#390—112no—
74#386—114no—
75#382—112no—
76C4×C22⋊C4—111no—
77C22×C11—22no—
78C22×C11—22no—
79C22×C11—28no—
80C22×C11—42no—
81C22×C11—42no—
82C22×C11—42no—
83C22×C11—48no—
84C22×C11#12414yes—
85C22×C11C22×D411yescharacteristic
86C22×C11C2×#4112yes—
87C22×C11C2×#4112yes—
88C22×C11H(5,𝔽2)12yes—
89C4×C11—22no—
90C4×C11—42no—
91C4×C11#12314yes—
92Dic11—44no—
93Dic11—44no—
94C22×D4C2×D1112yes—
95C22×D4C2×D1111yescharacteristic
96C23×C4—112no—
97C23×C4C2×D1111yescharacteristic
98#121—24no—
99C2×C4⋊C4—112no—
100C2×C4⋊C4—112no—
101C2×C4⋊C4—224no—
102C2×C4⋊C4C2×D1111yescharacteristic
103C2×C22⋊C4—112no—
104C2×C22⋊C4—118no—
105C2×C22⋊C4C2×D1112yes—
106C2×C42—112no—
107#95—112no—
108#95—118no—
109C2×C11—24no—
110C2×C11—82no—
111C2×C11C2×#12311yescharacteristic
112C2×C11C2×#12411yescharacteristic
113C2×C11#53511yescharacteristic
114C2×C11#55314yes—
115C24C22×D1112yes—
116C24C22×D1111yescharacteristic
117C2×D4—28no—
118C2×D4—24no—
119C2×D4—24no—
120C2×D4—22no—
121C22×C4—24no—
122C22×C4—114no—
123C22×C4—114no—
124C22×C4—224no—
125C22×C4—444no—
126C22×C4C22⋊D1114yes—
127C22×C4C22×D1112yes—
128C22×C4C22×D1111yescharacteristic
129C22×C4C22×D1111yescharacteristic
130C4⋊C4—22no—
131C4⋊C4—224no—
132C4⋊C4—224no—
133C22⋊C4—24no—
134C22⋊C4—224no—
135C22⋊C4—448no—
136C42—224no—
137C11#250411yescharacteristic, complemented, Sylow
138C23—22no—
139C23—22no—
140C23—24no—
141C23—24no—
142C23—24no—
143C23—22no—
144C23#434114yes—
145C23C2×C22⋊D1112yes—
146C23C23×D1111yescharacteristic
147D4—48no—
148D4—44no—
149C2×C4—22no—
150C2×C4—28no—
151C2×C4—24no—
152C2×C4—22no—
153C2×C4—224no—
154C2×C4—224no—
155C2×C4—224no—
156C2×C4—228no—
157C2×C4—224no—
158C2×C4—448no—
159C2×C4#434114yes—
160C2×C4C2×C22⋊D1112yes—
161C2×C4C2×C22⋊D1112yes—
162C22—22no—
163C22—22no—
164C22—28no—
165C22—42no—
166C22—42no—
167C22—42no—
168C22—48no—
169C22#6698914yes—
170C22C2×#434112yes—
171C22C2×#434112yes—
172C22#6704212yes—
173C22C22×C22⋊D1111yescharacteristic
174C4—22no—
175C4—42no—
176C4—444no—
177C4—444no—
178C4#6698814yes—
179C2—24no—
180C2—82no—
181C2#1062314914yes—
182C2C2×#6698811yescharacteristic
183C2C2×#6698911yescharacteristic
184C2#1062336111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
Fitting, prime radicalC2×C11×#121C2
hypercenterC2×#121D11
hypocenterC11#2504
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic11C2semidirect
3. #10622834C2semidirect
4. #10622833C2semidirect
5. C4×C22⋊Dic11C2semidirect
6. #10622590C2semidirect
7. #10622566C2semidirect
137. C11#2504semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C22×C4⋊Dic112
#106228342
#106228332
C4×C22⋊Dic112
#106225902
#106225662
#250411