Finite Group Databasebeta

← #13069859

Subgroups — #13069859

Order 1408.

298 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 95 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×C4⋊Q8C211yesmaximal, characteristic
2C2×#66899C212yesmaximal
3C2×#66899C212yesmaximal
4#10622541C211yesmaximal, characteristic
5#10622162C211yesmaximal, characteristic
6C22×Q8×C11C2212yes—
7C11×C4⋊Q8—24no—
8C2×C11×C4⋊C4—21no—
9C2×C11×C4⋊C4—21no—
10C2×C42×C11C2211yescharacteristic
11C2×C4⋊Dic11C2211yescharacteristic
12C2×C4⋊Dic11C2211yescharacteristic
13C2×Dic11⋊C4—21no—
14C22×C11⋊C8C2212yes—
15#66899—24no—
16#66899—24no—
17C11⋊#95—21no—
18C2×Q8×C11—22no—
19C2×Q8×C11—22no—
20C2×Q8×C11—22no—
21C2×Q8×C11—22no—
22C2×Q8×C11—22no—
23C2×Q8×C11D414yes—
24C22×C4×C11—22no—
25C22×C4×C11D411yescharacteristic
26C22×C4×C11D411yescharacteristic
27C22×C4×C11C2311yescharacteristic
28C22×Dic11—21no—
29C22×Dic11—21no—
30C11×C4⋊C4—24no—
31C11×C4⋊C4—24no—
32C42×C11—22no—
33C4⋊Dic11—22no—
34C4⋊Dic11—21no—
35C4⋊Dic11D412yes—
36Dic11⋊C4—42no—
37C2×C11⋊C8—22no—
38C2×C11⋊C8—22no—
39C2×C11⋊C8—22no—
40#2043—111nomaximal, Sylow
41C23×C11C2×D411yescharacteristic
42Q8×C11—24no—
43Q8×C11—24no—
44Q8×C11—42no—
45Q8×C11—42no—
46C2×C4×C11—21no—
47C2×C4×C11—21no—
48C2×C4×C11—21no—
49C2×C4×C11—21no—
50C2×C4×C11—24no—
51C2×C4×C11—42no—
52C2×C4×C11—42no—
53C2×C4×C11SD1612yes—
54C2×C4×C11Q1612yes—
55C2×C4×C11C2×D411yescharacteristic
56C2×C4×C11C2×D412yes—
57C2×C4×C11#4112yes—
58C2×C4×C11#4111yescharacteristic
59C2×Dic11—22no—
60C2×Dic11—41no—
61C2×Dic11—41no—
62C2×Dic11—41no—
63C2×Dic11—41no—
64C2×Dic11—41no—
65C11⋊C8—42no—
66C2×C4⋊Q8D1111yescharacteristic
67C2×#103—112no—
68C2×#103—112no—
69#389—111no—
70#336—111no—
71C22×C11#12011yescharacteristic
72C22×C11#12111yescharacteristic
73C22×C11#12411yescharacteristic
74C22×C11C2×SD1611yescharacteristic
75C22×C11C2×Q1611yescharacteristic
76C22×C11#13711yescharacteristic
77C22×C11#13711yescharacteristic
78C4×C11—22no—
79C4×C11—22no—
80C4×C11—44no—
81C4×C11#12112yes—
82C4×C11#12312yes—
83Dic11—42no—
84Dic11—81no—
85C22×Q8C2×D1112yes—
86C22×C8—112no—
87C4⋊Q8—24no—
88C2×C4⋊C4—21no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4—111no—
91C2×C4⋊C4—111no—
92C2×C4⋊C4—221no—
93C2×C42C2×D1111yescharacteristic
94#103—224no—
95#103—224no—
96#95—221no—
97C2×C11#39411yescharacteristic
98C2×C11#44811yescharacteristic
99C2×C11#45111yescharacteristic
100C2×C11#46111yescharacteristic
101C2×C11#46211yescharacteristic
102C2×C11#48711yescharacteristic
103C2×C11#49111yescharacteristic
104C2×Q8—22no—
105C2×Q8—22no—
106C2×Q8—22no—
107C2×Q8—22no—
108C2×Q8—22no—
109C2×Q8C22⋊D1114yes—
110C22×C4—22no—
111C22×C4—221no—
112C22×C4—221no—
113C22×C4C22⋊D1111yescharacteristic
114C22×C4C22⋊D1111yescharacteristic
115C22×C4C22×D1111yescharacteristic
116C2×C8—222no—
117C2×C8—222no—
118C2×C8—222no—
119C4⋊C4—24no—
120C4⋊C4—24no—
121C4⋊C4—112no—
122C4⋊C4—221no—
123C4⋊C4—222no—
124C4⋊C4—442no—
125C42—22no—
126C11#204311yescharacteristic, complemented, Sylow
127C23C2×C22⋊D1111yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—42no—
131Q8—42no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—24no—
137C2×C4—42no—
138C2×C4—42no—
139C2×C4—222no—
140C2×C4—441no—
141C2×C4—441no—
142C2×C4—441no—
143C2×C4—441no—
144C2×C4—441no—
145C2×C4#432512yes—
146C2×C4#432612yes—
147C2×C4D4×D1111yescharacteristic
148C2×C4#434111yescharacteristic
149C2×C4#434112yes—
150C2×C4C2×C22⋊D1112yes—
151C8—442no—
152C22#6698911yescharacteristic
153C22#6699111yescharacteristic
154C22C2×#432511yescharacteristic
155C22#6699511yescharacteristic
156C22#6699511yescharacteristic
157C22C2×#432611yescharacteristic
158C22#6700611yescharacteristic
159C4—22no—
160C4—22no—
161C4—44no—
162C4—442no—
163C4—881no—
164C4#6698812yes—
165C4#6699212yes—
166C2#1062269411yescharacteristic
167C2#1062269511yescharacteristic
168C2#1062269611yescharacteristic
169C2#1062270311yescharacteristic
170C2#1062283511yescharacteristic
171C2#1062284011yescharacteristic
172C2#1062284111yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×C4⋊Q8C2
socle, prime radicalC23×C11C2×D4
hypercenterC2×C4⋊Q8D11
hypocenterC11#2043
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
126. C11#2043semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C4⋊Q82
C2×#668992
#106225412
#106221622
#204311