Finite Group Databasebeta

← #13073095

Subgroups — #13073095

Order 1408.

544 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 181 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×C22⋊Q8C211yesmaximal, characteristic
2C22×C4⋊Dic11C211yesmaximal, characteristic
3#10622843C212yesmaximal, complemented
4C4×C22⋊Dic11C211yesmaximal, characteristic
5#10622596C214yesmaximal, complemented
6#10622589C212yesmaximal, complemented
7#10622559C214yesmaximal
8C22×Q8×C11C2211yescharacteristic
9C23×C4×C11C2211yescharacteristic
10C23×Dic11C2212yes—
11C11×C22⋊Q8—24no—
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C4⋊C4C2212yes—
14C2×C11×C22⋊C4C2212yes—
15C2×C22⋊Dic11C2212yes—
16C2×C4⋊Dic11—24no—
17C2×C4⋊Dic11C2212yes—
18C2×C4⋊Dic11C2212yes—
19C2×Dic11⋊C4C2218yes—
20C2×C4×Dic11C2212yes—
21C11⋊#95C2218yes—
22C11⋊#95C2212yes—
23C24×C11C2311yescharacteristic
24C2×Q8×C11—22no—
25C2×Q8×C11—24no—
26C22×C4×C11—24no—
27C22×C4×C11D414yes—
28C22×C4×C11C2312yes—
29C22×C4×C11C2312yes—
30C22×C4×C11C2311yescharacteristic
31C22×C4×C11C2311yescharacteristic
32C22×Dic11—24no—
33C22×Dic11—44no—
34C22×Dic11C2314yes—
35C22×Dic11C2314yes—
36C11×C4⋊C4—22no—
37C11×C4⋊C4—24no—
38C11×C22⋊C4—24no—
39C22⋊Dic11Q818yescomplemented
40C4⋊Dic11—24no—
41C4⋊Dic11—24no—
42Dic11⋊C4—48no—
43C4×Dic11—24no—
44#2502—111nomaximal, Sylow
45C23×C11—22no—
46C23×C11—22no—
47C23×C11C2×D412yes—
48C23×C11C2×Q814yes—
49C23×C11C2411yescharacteristic
50Q8×C11—44no—
51C2×C4×C11—22no—
52C2×C4×C11—28no—
53C2×C4×C11—22no—
54C2×C4×C11—22no—
55C2×C4×C11—24no—
56C2×C4×C11—24no—
57C2×C4×C11C2×D412yes—
58C2×C4×C11C2×D412yes—
59C2×C4×C11#4114yes—
60C2×Dic11—24no—
61C2×Dic11—24no—
62C2×Dic11—24no—
63C2×Dic11—28no—
64C2×Dic11—48no—
65C2×Dic11C2×Q818yes—
66C2×C22⋊Q8D1111yescharacteristic
67C22×C4⋊C4—111no—
68#398—114no—
69#391—112no—
70#385—114no—
71#384—112no—
72C4×C22⋊C4—111no—
73C22×C11—22no—
74C22×C11—22no—
75C22×C11—28no—
76C22×C11C4⋊Q814yes—
77C22×C11C22×D411yescharacteristic
78C22×C11C22×Q812yes—
79C22×C11C2×#4112yes—
80C22×C11H(5,𝔽2)12yes—
81C4×C11—22no—
82C4×C11—42no—
83C4×C11—42no—
84C4×C11#12314yes—
85Dic11—28no—
86Dic11—44no—
87C22×Q8C2×D1111yescharacteristic
88C23×C4—112no—
89C23×C4C2×D1111yescharacteristic
90C22⋊Q8—24no—
91C2×C4⋊C4—112no—
92C2×C4⋊C4—112no—
93C2×C4⋊C4—118no—
94C2×C4⋊C4—224no—
95C2×C4⋊C4C2×D1111yescharacteristic
96C2×C4⋊C4C2×D1112yes—
97C2×C22⋊C4—112no—
98C2×C22⋊C4C2×D1112yes—
99C2×C42—112no—
100#95—112no—
101#95—118no—
102C2×C11—24no—
103C2×C11C2×#12311yescharacteristic
104C2×C11C2×C4⋊Q811yescharacteristic
105C2×C11#53511yescharacteristic
106C2×C11#55414yes—
107C24C22×D1111yescharacteristic
108C2×Q8—24no—
109C2×Q8—22no—
110C22×C4—24no—
111C22×C4—114no—
112C22×C4—114no—
113C22×C4—224no—
114C22×C4—444no—
115C22×C4C22⋊D1114yes—
116C22×C4C22×D1112yes—
117C22×C4C22×D1112yes—
118C22×C4C22×D1111yescharacteristic
119C22×C4C22×D1111yescharacteristic
120C4⋊C4—22no—
121C4⋊C4—24no—
122C4⋊C4—224no—
123C4⋊C4—224no—
124C4⋊C4—448no—
125C22⋊C4—24no—
126C22⋊C4—118no—
127C42—224no—
128C11#250211yescharacteristic, complemented, Sylow
129C23—22no—
130C23—22no—
131C23Q8×D1114yes—
132C23C2×C22⋊D1112yes—
133C23C23×D1111yescharacteristic
134Q8—44no—
135C2×C4—22no—
136C2×C4—28no—
137C2×C4—24no—
138C2×C4—24no—
139C2×C4—22no—
140C2×C4—22no—
141C2×C4—118no—
142C2×C4—224no—
143C2×C4—224no—
144C2×C4—228no—
145C2×C4—224no—
146C2×C4—448no—
147C2×C4#434114yes—
148C2×C4C2×C22⋊D1112yes—
149C2×C4C2×C22⋊D1112yes—
150C22—22no—
151C22—22no—
152C22—28no—
153C22#6699714yes—
154C22C2×#434112yes—
155C22C2×Q8×D1112yes—
156C22#6704212yes—
157C22C22×C22⋊D1111yescharacteristic
158C4—22no—
159C4—42no—
160C4—42no—
161C4—228no—
162C4—444no—
163C4#6698814yes—
164C2—24no—
165C2#1062316614yes—
166C2C2×#6698811yescharacteristic
167C2C2×#6699711yescharacteristic
168C2#1062336111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C22⋊Q8C2
prime radicalC24×C11C23
hypercenterC2×C22⋊Q8D11
hypocenterC11#2502
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #10622843C2semidirect
5. #10622596C2semidirect
6. #10622589C2semidirect
39. C22⋊Dic11Q8semidirect
128. C11#2502semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊Q82
C22×C4⋊Dic112
#106228432
C4×C22⋊Dic112
#106225962
#106225892
#106225592
#250211