Finite Group Databasebeta

← #13068731

Subgroups — #13068731

Order 1408.

260 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 117 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×Dic11⋊C8C212yesmaximal
2C42×Dic11C211yesmaximal, characteristic
3C11×#336C211yesmaximal, characteristic
4#10622188C212yesmaximal
5#10622162C211yesmaximal, characteristic
6C22×C8×C11C2212yes—
7C2×C42×C11C2211yescharacteristic
8C2×C4×Dic11C411yescharacteristic
9C2×C4×Dic11C411yescharacteristic
10C2×C4×Dic11C411yescharacteristic
11C2×C4×Dic11C411yescharacteristic
12C2×C4×Dic11C2211yescharacteristic
13C2×C4×Dic11C2211yescharacteristic
14C22×C11⋊C8C2212yes—
15Dic11⋊C8—24no—
16C22×C4×C11C2×C411yescharacteristic
17C22×C4×C11C2×C411yescharacteristic
18C22×C4×C11C2311yescharacteristic
19C22×Dic11C2×C411yescharacteristic
20C22×Dic11C2×C411yescharacteristic
21C22×Dic11C2×C411yescharacteristic
22C22×Dic11C2×C411yescharacteristic
23C2×C8×C11—22no—
24C2×C8×C11—22no—
25C2×C8×C11—22no—
26C42×C11—22no—
27C4×Dic11—22no—
28C4×Dic11—22no—
29C4×Dic11—22no—
30C4×Dic11—22no—
31C4×Dic11C814yescomplemented
32C4×Dic11D412yes—
33C4×Dic11Q812yes—
34C2×C11⋊C8—22no—
35C2×C11⋊C8—22no—
36C2×C11⋊C8—22no—
37#1831—111nomaximal, Sylow
38C23×C11C22×C411yescharacteristic
39C2×C4×C11—21no—
40C2×C4×C11—21no—
41C2×C4×C11—21no—
42C2×C4×C11—21no—
43C2×C4×C11C2×C812yes—
44C2×C4×C11M1612yes—
45C2×C4×C11C2×D411yescharacteristic
46C2×C4×C11C2×Q811yescharacteristic
47C2×C4×C11#4112yes—
48C2×C4×C11#4112yes—
49C2×Dic11—21no—
50C2×Dic11—21no—
51C2×Dic11—21no—
52C2×Dic11—21no—
53C2×Dic11—21no—
54C2×Dic11—21no—
55C2×Dic11C4⋊C412yes—
56C2×Dic11C4⋊C412yes—
57C2×Dic11C2×C812yes—
58C2×Dic11C2×C812yes—
59C2×Dic11M1612yes—
60C2×Dic11M1612yes—
61C8×C11—42no—
62C11⋊C8—42no—
63C2×C4⋊C8—112no—
64C43—111no—
65#336—112no—
66#336—111no—
67#336D1111yescharacteristic
68C22×C11C2×C4⋊C411yescharacteristic
69C22×C11#11711yescharacteristic
70C22×C11#11711yescharacteristic
71C22×C11C22×C811yescharacteristic
72C22×C11C2×M1611yescharacteristic
73C22×C11C2×M1611yescharacteristic
74C22×C11C2×M1611yescharacteristic
75C4×C11—22no—
76C4×C11—22no—
77C4×C11#12412yes—
78C4×C11#12512yes—
79Dic11—22no—
80Dic11—22no—
81Dic11—22no—
82Dic11C4⋊C814yes—
83C22×C8—112no—
84C22×C8C2×D1112yes—
85C2×C42—111no—
86C2×C42—111no—
87C2×C42—111no—
88C2×C42—111no—
89C2×C42—111no—
90C2×C42—111no—
91C2×C42C2×D1111yescharacteristic
92C4⋊C8—224no—
93C2×C11#38211yescharacteristic
94C2×C11C2×C4⋊C811yescharacteristic
95C2×C11#42311yescharacteristic
96C2×C11#43111yescharacteristic
97C2×C11#43111yescharacteristic
98C2×C11#43211yescharacteristic
99C2×C11#43211yescharacteristic
100C22×C4—111no—
101C22×C4—111no—
102C22×C4—111no—
103C22×C4—111no—
104C22×C4C4×D1111yescharacteristic
105C22×C4C4×D1111yescharacteristic
106C22×C4C22×D1111yescharacteristic
107C2×C8—22no—
108C2×C8—22no—
109C2×C8—22no—
110C2×C8—222no—
111C2×C8—222no—
112C2×C8—222no—
113C42—22no—
114C42—114no—
115C42—112no—
116C42—112no—
117C42—222no—
118C42—222no—
119C42—222no—
120C42—222no—
121C11#183111yescharacteristic, complemented, Sylow
122C23C2×C4×D1111yescharacteristic
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—112no—
128C2×C4—112no—
129C2×C4—112no—
130C2×C4—112no—
131C2×C4—112no—
132C2×C4—112no—
133C2×C4—221no—
134C2×C4—221no—
135C2×C4—221no—
136C2×C4—221no—
137C2×C4—221no—
138C2×C4—221no—
139C2×C4C8×D1112yes—
140C2×C4#431312yes—
141C2×C4#433912yes—
142C2×C4D4×D1111yescharacteristic
143C2×C4#434112yes—
144C2×C4Q8×D1111yescharacteristic
145C8—42no—
146C8—442no—
147C22#6692511yescharacteristic
148C22#6693011yescharacteristic
149C22C4⋊C4×D1111yescharacteristic
150C22C2×C8×D1111yescharacteristic
151C22C2×#431311yescharacteristic
152C22M16×D1111yescharacteristic
153C22M16×D1111yescharacteristic
154C4—22no—
155C4—22no—
156C4—114no—
157C4—222no—
158C4—222no—
159C4—222no—
160C4#6693812yes—
161C4#6694212yes—
162C2#1062226311yescharacteristic
163C2#1062229811yescharacteristic
164C2#1062231811yescharacteristic
165C2#1062233111yescharacteristic
166C2#1062233211yescharacteristic
167C2D11×C4⋊C811yescharacteristic
168C2#1062245011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×D11
commutatorC22×C11C22×C8
FittingC11×#336C2
socle, prime radicalC23×C11C22×C4
cosocleC22×C4×C11C23
hypercenter#336D11
hypocenterC11#1831
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #336

Complements

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

NH ≅ G/Ntype
31. C4×Dic11C8semidirect
121. C11#1831semidirect

Maximal subgroups

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

subgroupindex
C2×Dic11⋊C82
C42×Dic112
C11×#3362
#106221882
#106221622
#183111