Finite Group Databasebeta

← #13074740

Subgroups — #13074740

Order 1408.

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

normal subgroups only

This group has 448 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×#66943C211yesmaximal, characteristic
2C2×#66941C211yesmaximal, characteristic
3C11×#382C211yesmaximal, characteristic
4#10622590C211yesmaximal, characteristic
5#10622589C211yesmaximal, characteristic
6#10622548C211yesmaximal, characteristic
7#10622545C211yesmaximal, characteristic
8#10622270C214yesmaximal
9#10622269C214yesmaximal
10C22×Dic22C2212yes—
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C42×C11C2211yescharacteristic
14C2×C4⋊Dic11C2211yescharacteristic
15C2×C4⋊Dic11C2212yes—
16C2×C4⋊Dic11C2211yescharacteristic
17C2×C4⋊Dic11C2214yes—
18C2×Dic11⋊C4C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2214yes—
21C2×C4×Dic11C2211yescharacteristic
22C2×C4×Dic11C2211yescharacteristic
23#66943—24no—
24#66941—24no—
25C11×#95C2214yes—
26C11⋊#95C2212yes—
27C11⋊#95C2214yes—
28C11⋊#95C2212yes—
29C22×C4×C11C2312yes—
30C22×C4×C11C2312yes—
31C22×C4×C11C2312yes—
32C22×C4×C11C2311yescharacteristic
33C22×Dic11C2312yes—
34C22×Dic11C2312yes—
35C22×Dic11C2311yescharacteristic
36C22×Dic11C2311yescharacteristic
37C22×Dic11C2312yes—
38C2×Dic22—24no—
39C2×Dic22—44no—
40C11×C4⋊C4—22no—
41C11×C4⋊C4—22no—
42C42×C11Q814yescomplemented
43C4⋊Dic11—24no—
44C4⋊Dic11—22no—
45C4⋊Dic11—22no—
46C4⋊Dic11—44no—
47Dic11⋊C4—24no—
48Dic11⋊C4—24no—
49Dic11⋊C4—44no—
50C4×Dic11D414yes—
51C4×Dic11Q814yescomplemented
52#2660—111nomaximal, Sylow
53C23×C11C2411yescharacteristic
54C2×C4×C11—22no—
55C2×C4×C11—22no—
56C2×C4×C11—22no—
57C2×C4×C11—22no—
58C2×C4×C11—24no—
59C2×C4×C11—24no—
60C2×C4×C11C2×D412yes—
61C2×C4×C11C2×Q814yes—
62C2×C4×C11C2×Q812yes—
63C2×C4×C11C2×Q812yes—
64C2×Dic11—22no—
65C2×Dic11—22no—
66C2×Dic11—22no—
67C2×Dic11—22no—
68C2×Dic11—22no—
69C2×Dic11—22no—
70C2×Dic11—24no—
71C2×Dic11—24no—
72C2×Dic11C2×D412yes—
73C2×Dic11C2×D412yes—
74C2×Dic11C2×Q814yes—
75Dic22—48no—
76C2×C4⋊Q8—111no—
77C2×#125—111no—
78#398—114no—
79#395—114no—
80#384—111no—
81#384—111no—
82#382—111no—
83#382D1111yescharacteristic
84#376—111no—
85C22×C11C22×D411yescharacteristic
86C22×C11C22×Q811yescharacteristic
87C22×C11C22×Q811yescharacteristic
88C22×C11H(5,𝔽2)12yes—
89C22×C112−1+412yes—
90C4×C11—24no—
91C4×C11—42no—
92C4×C11—42no—
93C4×C11C4⋊Q814yes—
94Dic11—22no—
95Dic11—22no—
96Dic11—24no—
97Dic11—42no—
98Dic11—42no—
99C22×Q8—112no—
100C4⋊Q8—224no—
101#125—224no—
102C2×C4⋊C4—111no—
103C2×C4⋊C4—112no—
104C2×C4⋊C4—112no—
105C2×C4⋊C4—111no—
106C2×C4⋊C4—112no—
107C2×C4⋊C4—114no—
108C2×C4⋊C4—114no—
109C2×C4⋊C4C2×D1111yescharacteristic
110C2×C4⋊C4C2×D1111yescharacteristic
111C2×C42—111no—
112C2×C42—111no—
113C2×C42C2×D1111yescharacteristic
114#95—112no—
115#95—112no—
116#95—114no—
117#95C2×D1114yes—
118C2×C11C2×C4⋊Q811yescharacteristic
119C2×C11#53511yescharacteristic
120C2×C11#53611yescharacteristic
121C2×C11#54412yes—
122C2×C11#54412yes—
123C2×Q8—224no—
124C2×Q8—444no—
125C22×C4—112no—
126C22×C4—111no—
127C22×C4—111no—
128C22×C4—112no—
129C22×C4—112no—
130C22×C4C22×D1112yes—
131C22×C4C22×D1112yes—
132C22×C4C22×D1112yes—
133C22×C4C22×D1111yescharacteristic
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—224no—
137C4⋊C4—224no—
138C4⋊C4—224no—
139C4⋊C4—222no—
140C4⋊C4—222no—
141C4⋊C4—444no—
142C4⋊C4—444no—
143C42—114no—
144C42—114no—
145C42Dic2214yescomplemented
146C11#266011yescharacteristic, complemented, Sylow
147C23C23×D1111yescharacteristic
148Q8—448no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—24no—
154C2×C4—24no—
155C2×C4—112no—
156C2×C4—112no—
157C2×C4—114no—
158C2×C4—222no—
159C2×C4—222no—
160C2×C4—222no—
161C2×C4—222no—
162C2×C4—222no—
163C2×C4—222no—
164C2×C4—224no—
165C2×C4—224no—
166C2×C4C2×Dic2214yes—
167C2×C4C2×Dic2212yes—
168C2×C4D4×D1112yes—
169C2×C4Q8×D1112yes—
170C22C22×Dic2211yescharacteristic
171C22C2×D4×D1111yescharacteristic
172C22C2×Q8×D1111yescharacteristic
173C22#6704212yes—
174C22#6704312yes—
175C4—24no—
176C4—42no—
177C4—42no—
178C4—222no—
179C4—222no—
180C4—224no—
181C4—442no—
182C4—442no—
183C4#6694114yes—
184C2C2×#6694111yescharacteristic
185C2#1062305012yes—
186C2#1062320511yescharacteristic
187C2#1062320611yescharacteristic
188C2#1062322012yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#382C2
hypercenter#382D11
hypocenterC11#2660
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
42. C42×C11Q8semidirect
51. C4×Dic11Q8semidirect
145. C42Dic22semidirect
146. C11#2660semidirect

Maximal subgroups

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

subgroupindex
C2×#669432
C2×#669412
C11×#3822
#106225902
#106225892
#106225482
#106225452
#106222702
#106222692
#266011