Finite Group Databasebeta

← #13074431

Subgroups — #13074431

Order 1408.

508 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 157 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
4#10622825C211yesmaximal, characteristic
5#10622597C214yesmaximal, complemented
6#10622595C212yesmaximal, complemented
7#10622559C212yesmaximal
8#10622556C212yesmaximal
9C22×Q8×C11C2211yescharacteristic
10C23×C4×C11C2211yescharacteristic
11C23×Dic11C2211yescharacteristic
12C23×Dic11C2211yescharacteristic
13C11×C22⋊Q8—24no—
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C4⋊C4C2212yes—
16C2×C11×C22⋊C4C2212yes—
17C2×C22⋊Dic11C2212yes—
18C2×C4⋊Dic11C2212yes—
19C2×Dic11⋊C4—24no—
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2214yes—
23C11⋊#95C2214yes—
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—22no—
37C22×Dic11—22no—
38C22×Dic11—22no—
39C22×Dic11—42no—
40C22×Dic11Q814yescomplemented
41C22×Dic11C2314yes—
42C22×Dic11C2312yes—
43C22×Dic11C2312yes—
44C11×C4⋊C4—22no—
45C11×C4⋊C4—24no—
46C11×C22⋊C4—24no—
47C22⋊Dic11—24no—
48C4⋊Dic11—42no—
49Dic11⋊C4—24no—
50Dic11⋊C4—24no—
51Dic11⋊C4—44no—
52#2627—111nomaximal, Sylow
53C23×C11—22no—
54C23×C11—22no—
55C23×C11C2×D412yes—
56C23×C11C2×Q812yes—
57C23×C11#4112yes—
58C23×C11C2411yescharacteristic
59Q8×C11—44no—
60C2×C4×C11—22no—
61C2×C4×C11—22no—
62C2×C4×C11—22no—
63C2×C4×C11—22no—
64C2×C4×C11—24no—
65C2×C4×C11—24no—
66C2×C4×C11—44no—
67C2×C4×C11C2×D412yes—
68C2×C4×C11C2×D412yes—
69C2×Dic11—28no—
70C2×Dic11—22no—
71C2×Dic11—22no—
72C2×Dic11—22no—
73C2×Dic11—24no—
74C2×Dic11—24no—
75C2×Dic11—24no—
76C2×Dic11—24no—
77C2×Dic11—44no—
78C2×Dic11C2×Q814yes—
79C2×C22⋊Q8D1111yescharacteristic
80C22×C4⋊C4—111no—
81#400—112no—
82#398—114no—
83#395—112no—
84#385—112no—
85#381—112no—
86#380—111no—
87C22×C11—22no—
88C22×C11—22no—
89C22×C11—24no—
90C22×C11—24no—
91C22×C11C22⋊Q814yes—
92C22×C11C22×D411yescharacteristic
93C22×C11C22×Q811yescharacteristic
94C22×C11C2×#4111yescharacteristic
95C22×C11H(5,𝔽2)12yes—
96C22×C112−1+412yes—
97C4×C11—22no—
98C4×C11—22no—
99C4×C11—42no—
100C4×C11—42no—
101Dic11—24no—
102Dic11—42no—
103Dic11—44no—
104C22×Q8C2×D1111yescharacteristic
105C23×C4—111no—
106C23×C4—111no—
107C23×C4C2×D1111yescharacteristic
108C22⋊Q8—24no—
109C2×C4⋊C4—112no—
110C2×C4⋊C4—112no—
111C2×C4⋊C4—112no—
112C2×C4⋊C4—114no—
113C2×C4⋊C4—224no—
114C2×C4⋊C4C2×D1112yes—
115C2×C4⋊C4C2×D1111yescharacteristic
116C2×C22⋊C4—112no—
117C2×C22⋊C4C2×D1112yes—
118#95—112no—
119#95—114no—
120#95—114no—
121#95—114no—
122C2×C11—24no—
123C2×C11C2×C22⋊Q811yescharacteristic
124C2×C11#53411yescharacteristic
125C2×C11#53611yescharacteristic
126C2×C11#53912yes—
127C2×C11#54412yes—
128C24C22×D1111yescharacteristic
129C2×Q8—22no—
130C2×Q8—42no—
131C22×C4—42no—
132C22×C4—114no—
133C22×C4—112no—
134C22×C4—114no—
135C22×C4—112no—
136C22×C4—222no—
137C22×C4—222no—
138C22×C4—222no—
139C22×C4—442no—
140C22×C4C22⋊D1114yes—
141C22×C4C22×D1112yes—
142C22×C4C22×D1112yes—
143C22×C4C22×D1111yescharacteristic
144C22×C4C22×D1111yescharacteristic
145C4⋊C4—22no—
146C4⋊C4—24no—
147C4⋊C4—224no—
148C4⋊C4—224no—
149C4⋊C4—444no—
150C4⋊C4—442no—
151C22⋊C4—24no—
152C22⋊C4—224no—
153C11#262711yescharacteristic, complemented, Sylow
154C23—22no—
155C23—22no—
156C23Q8×D1112yes—
157C23#434312yes—
158C23C2×C22⋊D1112yes—
159C23C23×D1111yescharacteristic
160Q8—44no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—24no—
164C2×C4—24no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—44no—
168C2×C4—114no—
169C2×C4—228no—
170C2×C4—222no—
171C2×C4—222no—
172C2×C4—224no—
173C2×C4—224no—
174C2×C4—224no—
175C2×C4—224no—
176C2×C4—222no—
177C2×C4—444no—
178C2×C4C2×C22⋊D1112yes—
179C2×C4C2×C22⋊D1112yes—
180C22—22no—
181C22—22no—
182C22—24no—
183C22—24no—
184C22#6699914yes—
185C22#6703712yes—
186C22C2×Q8×D1111yescharacteristic
187C22C2×#434311yescharacteristic
188C22#6704312yes—
189C22C22×C22⋊D1111yescharacteristic
190C4—22no—
191C4—22no—
192C4—42no—
193C4—42no—
194C4—224no—
195C4—442no—
196C4—444no—
197C2—24no—
198C2#1062315412yes—
199C2#1062317612yes—
200C2#1062333511yescharacteristic
201C2C2×#6699911yescharacteristic
202C2#1062335611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C22⋊Q8C2
prime radicalC24×C11C23
hypercenterC2×C22⋊Q8D11
hypocenterC11#2627
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. #10622597C2semidirect
6. #10622595C2semidirect
40. C22×Dic11Q8semidirect
153. C11#2627semidirect

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
#106228252
#106225972
#106225952
#106225592
#106225562
#262711