Finite Group Databasebeta

← #13073997

Subgroups — #13073997

Order 1408.

544 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 169 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×Dic11⋊C4C211yesmaximal, characteristic
3#10622842C212yesmaximal, complemented
4C4×C22⋊Dic11C211yesmaximal, characteristic
5#10622593C212yesmaximal, complemented
6#10622585C214yesmaximal, complemented
7#10622559C212yesmaximal
8#10622559C212yesmaximal
9C22×Q8×C11C2211yescharacteristic
10C23×C4×C11C2211yescharacteristic
11C23×Dic11C2211yescharacteristic
12C23×Dic11C2211yescharacteristic
13C11×C22⋊Q8—24no—
14C2×C11×C4⋊C4C2212yes—
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C22⋊C4C2212yes—
17C2×C22⋊Dic11C2212yes—
18C2×Dic11⋊C4—24no—
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2214yes—
22C2×Dic11⋊C4C2214yes—
23C2×C4×Dic11C2212yes—
24C11⋊#95C2214yes—
25C11⋊#95C2214yes—
26C11⋊#95C2212yes—
27C24×C11C2311yescharacteristic
28C2×Q8×C11—22no—
29C2×Q8×C11—42no—
30C22×C4×C11—42no—
31C22×C4×C11D414yes—
32C22×C4×C11C2312yes—
33C22×C4×C11C2312yes—
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C22×Dic11—24no—
37C22×Dic11—22no—
38C22×Dic11—22no—
39C22×Dic11—42no—
40C22×Dic11C2312yes—
41C22×Dic11C2314yes—
42C22×Dic11C2312yes—
43C11×C4⋊C4—22no—
44C11×C4⋊C4—24no—
45C11×C22⋊C4—24no—
46C22⋊Dic11Q818yescomplemented
47Dic11⋊C4—28no—
48Dic11⋊C4—24no—
49Dic11⋊C4—24no—
50Dic11⋊C4—44no—
51C4×Dic11—42no—
52#2583—111nomaximal, Sylow
53C23×C11—22no—
54C23×C11—22no—
55C23×C11C2×D412yes—
56C23×C11C2×Q814yes—
57C23×C11C2411yescharacteristic
58Q8×C11—44no—
59C2×C4×C11—22no—
60C2×C4×C11—22no—
61C2×C4×C11—22no—
62C2×C4×C11—22no—
63C2×C4×C11—24no—
64C2×C4×C11—24no—
65C2×C4×C11—44no—
66C2×C4×C11C2×D412yes—
67C2×C4×C11C2×D412yes—
68C2×Dic11—28no—
69C2×Dic11—22no—
70C2×Dic11—24no—
71C2×Dic11—22no—
72C2×Dic11—24no—
73C2×Dic11—22no—
74C2×Dic11—24no—
75C2×Dic11—44no—
76C2×Dic11C2×Q818yes—
77C2×Dic11#4114yes—
78C2×C22⋊Q8D1111yescharacteristic
79C22×C4⋊C4—111no—
80#398—112no—
81#395—112no—
82#389—114no—
83#385—112no—
84#385—112no—
85C4×C22⋊C4—111no—
86C22×C11—22no—
87C22×C11—22no—
88C22×C11—28no—
89C22×C11C4⋊Q814yes—
90C22×C11C22×D411yescharacteristic
91C22×C11C22×Q812yes—
92C22×C11C2×#4112yes—
93C22×C11H(5,𝔽2)12yes—
94C4×C11—22no—
95C4×C11—22no—
96C4×C11—42no—
97C4×C11—42no—
98Dic11—24no—
99Dic11—28no—
100Dic11—42no—
101C22×Q8C2×D1111yescharacteristic
102C23×C4—111no—
103C23×C4—111no—
104C23×C4C2×D1111yescharacteristic
105C22⋊Q8—24no—
106C2×C4⋊C4—112no—
107C2×C4⋊C4—112no—
108C2×C4⋊C4—114no—
109C2×C4⋊C4—114no—
110C2×C4⋊C4—224no—
111C2×C4⋊C4C2×D1112yes—
112C2×C4⋊C4C2×D1111yescharacteristic
113C2×C22⋊C4—112no—
114C2×C22⋊C4C2×D1112yes—
115C2×C42—112no—
116#95—112no—
117#95—114no—
118#95—114no—
119C2×C11—24no—
120C2×C11#52511yescharacteristic
121C2×C11C2×C4⋊Q811yescharacteristic
122C2×C11#53411yescharacteristic
123C2×C11#55414yes—
124C24C22×D1111yescharacteristic
125C2×Q8—22no—
126C2×Q8—42no—
127C22×C4—42no—
128C22×C4—114no—
129C22×C4—112no—
130C22×C4—112no—
131C22×C4—224no—
132C22×C4—222no—
133C22×C4—222no—
134C22×C4—442no—
135C22×C4C22⋊D1114yes—
136C22×C4C22×D1112yes—
137C22×C4C22×D1112yes—
138C22×C4C22×D1111yescharacteristic
139C22×C4C22×D1111yescharacteristic
140C4⋊C4—22no—
141C4⋊C4—24no—
142C4⋊C4—228no—
143C4⋊C4—224no—
144C4⋊C4—224no—
145C4⋊C4—444no—
146C22⋊C4—24no—
147C22⋊C4—118no—
148C42—442no—
149C11#258311yescharacteristic, complemented, Sylow
150C23—22no—
151C23—22no—
152C23Q8×D1114yes—
153C23C2×C22⋊D1112yes—
154C23C23×D1111yescharacteristic
155Q8—44no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—44no—
163C2×C4—118no—
164C2×C4—114no—
165C2×C4—228no—
166C2×C4—224no—
167C2×C4—224no—
168C2×C4—222no—
169C2×C4—222no—
170C2×C4—224no—
171C2×C4—222no—
172C2×C4—444no—
173C2×C4C2×C22⋊D1112yes—
174C2×C4C2×C22⋊D1112yes—
175C22—22no—
176C22—22no—
177C22—28no—
178C22#6699714yes—
179C22#6703712yes—
180C22C2×Q8×D1112yes—
181C22#41×D1112yes—
182C22C22×C22⋊D1111yescharacteristic
183C4—22no—
184C4—22no—
185C4—42no—
186C4—42no—
187C4—224no—
188C4—228no—
189C4—442no—
190C2—24no—
191C2#1062316714yes—
192C2#1062333511yescharacteristic
193C2C2×#6699711yescharacteristic
194C2#1062335911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C22⋊Q8C2
prime radicalC24×C11C23
hypercenterC2×C22⋊Q8D11
hypocenterC11#2583
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #10622842C2semidirect
5. #10622593C2semidirect
6. #10622585C2semidirect
46. C22⋊Dic11Q8semidirect
149. C11#2583semidirect

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×Dic11⋊C42
#106228422
C4×C22⋊Dic112
#106225932
#106225852
#106225592
#258311