Finite Group Databasebeta

← #13074414

Subgroups — #13074414

Order 1408.

464 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 149 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
2C2×#66979C211yesmaximal, characteristic
3#10622843C212yesmaximal, complemented
4#10622825C211yesmaximal, characteristic
5#10622599C212yesmaximal, complemented
6#10622596C212yesmaximal, complemented
7#10622586C212yesmaximal, complemented
8#10622565C214yesmaximal
9C22×Q8×C11C2211yescharacteristic
10C23×C4×C11C2211yescharacteristic
11C11×C22⋊Q8—24no—
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C4⋊C4C2212yes—
14C2×C11×C22⋊C4C2212yes—
15C2×C22⋊Dic11C2212yes—
16C2×C22⋊Dic11C2212yes—
17#66979—24no—
18C2×C4⋊Dic11C2211yescharacteristic
19C2×C4⋊Dic11C2211yescharacteristic
20C2×C4⋊Dic11C2212yes—
21C2×Dic11⋊C4C2214yes—
22C2×C4×Dic11C2212yes—
23C11⋊#95C2214yes—
24C11⋊#95C2214yes—
25C11⋊#95C2214yes—
26C11⋊#95C2212yes—
27C24×C11C2311yescharacteristic
28C2×Q8×C11—22no—
29C2×Q8×C11—24no—
30C22×C4×C11—24no—
31C22×C4×C11D414yes—
32C22×C4×C11C2312yes—
33C22×C4×C11C2312yes—
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C22×Dic11C2312yes—
37C22×Dic11C2314yes—
38C22×Dic11C2312yes—
39C11×C4⋊C4—22no—
40C11×C4⋊C4—24no—
41C11×C22⋊C4—24no—
42C22⋊Dic11—24no—
43C22⋊Dic11—42no—
44C4⋊Dic11—22no—
45C4⋊Dic11—22no—
46C4⋊Dic11—24no—
47Dic11⋊C4—44no—
48C4×Dic11—24no—
49#2625—111nomaximal, Sylow
50C23×C11—22no—
51C23×C11—21no—
52C23×C11—22no—
53C23×C11—21no—
54C23×C11C2×D412yes—
55C23×C11C2411yescharacteristic
56Q8×C11—44no—
57C2×C4×C11—22no—
58C2×C4×C11—28no—
59C2×C4×C11—22no—
60C2×C4×C11—22no—
61C2×C4×C11—24no—
62C2×C4×C11—22no—
63C2×C4×C11—22no—
64C2×C4×C11C2×D412yes—
65C2×C4×C11C2×D412yes—
66C2×C4×C11#4114yes—
67C2×Dic11—22no—
68C2×Dic11—22no—
69C2×Dic11—24no—
70C2×Dic11—22no—
71C2×Dic11—24no—
72C2×Dic11—24no—
73C2×Dic11—24no—
74C2×Dic11—22no—
75C2×C22⋊Q8D1111yescharacteristic
76C2×#117—111no—
77#400—112no—
78#398—112no—
79#397—114no—
80#391—112no—
81#389—112no—
82#380—111no—
83C22×C11—22no—
84C22×C11—22no—
85C22×C11—22no—
86C22×C11—42no—
87C22×C11—42no—
88C22×C11C22×D411yescharacteristic
89C22×C11C2×#4112yes—
90C22×C11H(5,𝔽2)11yescharacteristic
91C22×C112−1+412yes—
92C22×C112−1+411yescharacteristic
93C4×C11—22no—
94C4×C11—42no—
95C4×C11—42no—
96C4×C11#12314yes—
97Dic11—42no—
98Dic11—42no—
99Dic11—44no—
100C22×Q8C2×D1111yescharacteristic
101C23×C4C2×D1111yescharacteristic
102C22⋊Q8—24no—
103#117—224no—
104C2×C4⋊C4—111no—
105C2×C4⋊C4—111no—
106C2×C4⋊C4—112no—
107C2×C4⋊C4—114no—
108C2×C4⋊C4C2×D1111yescharacteristic
109C2×C4⋊C4C2×D1112yes—
110C2×C22⋊C4—112no—
111C2×C22⋊C4—112no—
112C2×C22⋊C4C2×D1112yes—
113C2×C42—112no—
114#95—112no—
115#95—114no—
116#95—114no—
117#95—114no—
118C2×C11—42no—
119C2×C11C2×#12311yescharacteristic
120C2×C11#53611yescharacteristic
121C2×C11#53711yescharacteristic
122C2×C11#54112yes—
123C2×C11#54212yes—
124C24C22×D1111yescharacteristic
125C2×Q8—24no—
126C2×Q8—22no—
127C22×C4—24no—
128C22×C4—112no—
129C22×C4—114no—
130C22×C4—112no—
131C22×C4C22⋊D1114yes—
132C22×C4C22×D1112yes—
133C22×C4C22×D1112yes—
134C22×C4C22×D1111yescharacteristic
135C22×C4C22×D1111yescharacteristic
136C4⋊C4—22no—
137C4⋊C4—24no—
138C4⋊C4—224no—
139C4⋊C4—222no—
140C4⋊C4—222no—
141C4⋊C4—444no—
142C22⋊C4—24no—
143C22⋊C4—224no—
144C22⋊C4—442no—
145C42—224no—
146C11#262511yescharacteristic, complemented, Sylow
147C23—22no—
148C23—22no—
149C23—21no—
150C23—21no—
151C23C2×C22⋊D1112yes—
152C23C23×D1111yescharacteristic
153Q8—44no—
154C2×C4—22no—
155C2×C4—28no—
156C2×C4—24no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—224no—
162C2×C4—224no—
163C2×C4—224no—
164C2×C4—224no—
165C2×C4—222no—
166C2×C4—222no—
167C2×C4—222no—
168C2×C4—222no—
169C2×C4#434114yes—
170C2×C4C2×C22⋊D1112yes—
171C2×C4C2×C22⋊D1112yes—
172C22—22no—
173C22—22no—
174C22—22no—
175C22—42no—
176C22—42no—
177C22C2×#434112yes—
178C22#6704012yes—
179C22#6704211yescharacteristic
180C22#6704311yescharacteristic
181C22C22×C22⋊D1111yescharacteristic
182C4—22no—
183C4—42no—
184C4—42no—
185C4—442no—
186C4—442no—
187C4—444no—
188C4#6698814yes—
189C2—42no—
190C2#1062315612yes—
191C2#1062317412yes—
192C2C2×#6698811yescharacteristic
193C2#1062334711yescharacteristic
194C2#1062336411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C22⋊Q8C2
prime radicalC24×C11C23
hypercenterC2×C22⋊Q8D11
hypocenterC11#2625
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. #10622599C2semidirect
6. #10622596C2semidirect
7. #10622586C2semidirect
146. C11#2625semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊Q82
C2×#669792
#106228432
#106228252
#106225992
#106225962
#106225862
#106225652
#262511