Finite Group Databasebeta

← D113⋊#355 #28406860

Subgroups — D113⋊#355 #28406860

Order 14464.

260 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 54 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
1D113⋊#101C212yesmaximal, complemented
2#20299507C212yesmaximal, complemented
3#20299506C212yesmaximal, complemented
4#124×D113C211yesmaximal, characteristic
5D113⋊M16—22no—
6#16813683—22no—
7#16813683C2214yescomplemented
8C2×Q8×D113C2211yescharacteristic
9C2×D4×D113C411yescharacteristic
10#16813611C411yescharacteristic
11#16813610C2211yescharacteristic
12#16813609C2211yescharacteristic
13#16813608—22no—
14C22⋊C4×D113—22no—
15C42×D113C411yescharacteristic
16#124×C113C411yescharacteristic
17#14268657—42no—
18#14268656—24no—
19#14268655—42no—
20C23×D113—21no—
21C2×Dic226D412yes—
22C2×Dic226C2311yescharacteristic
23Q8×D113—41no—
24Q8×D113—41no—
25C2×D452C2×C411yescharacteristic
26C2×C22⋊D113—21no—
27D4×D113—41no—
28D4×D113—41no—
29C2×C4×D113—21no—
30C2×C4×D113C2×C411yescharacteristic
31C2×C4×D113D412yes—
32C22⋊Dic113—22no—
33#14268624—22no—
34#14268624—22no—
35C4×Dic113—21no—
36C4×Dic113C2×C411yescharacteristic
37C2×Q8×C113C2×C411yescharacteristic
38C2×D4×C113C2×C411yescharacteristic
39C22⋊C4×C113—22no—
40C42×C113C2×C411yescharacteristic
41C23×C113—21no—
42C22×D113—21no—
43C22×D113—44no—
44C22×D113—41no—
45C22×D113—41no—
46C22×D113C22⋊C411yescharacteristic
47Q8×C113—41no—
48D4×C113—41no—
49C2×C4×C113—21no—
50C2×C4×C113C22⋊C412yes—
51C2×C4×C113C22×C411yescharacteristic
52C22⋊D113—42no—
53C2×Dic113—21no—
54C2×Dic113C22⋊C411yescharacteristic
55C2×Dic113C2×D412yes—
56D452—41no—
57C4×D113—21no—
58C4×D113—21no—
59C4×D113—22no—
60C4×D113—22no—
61C4×D113—42no—
62Dic226—42no—
63Dic226—41no—
64#11744753—44no—
65C22×C113—42no—
66C22×C113—41no—
67C22×C113C2×C22⋊C411yescharacteristic
68C2×D113—22no—
69C2×D113—42no—
70C2×D113—41no—
71C2×D113—82no—
72C2×D113—82no—
73C2×D113#9911yescharacteristic
74C2×D113#9911yescharacteristic
75C4×C113—21no—
76C4×C113—22no—
77C4×C113—41no—
78Dic113—22no—
79Dic113—21no—
80Dic113—41no—
81C2×C113—21no—
82C2×C113—81no—
83C2×C113C2×#9911yescharacteristic
84D113—21no—
85D113—81no—
86D113#35512yescomplemented
87C2×#355—1131nomaximal, Sylow
88C113C2×#35511yescharacteristic, complemented, Sylow
89C2×#124—1131no—
90C2×#101—1132no—
91#355—1132no—
92#355—1132no—
93C22×Q8—1131no—
94C22×D4—1131no—
95C2×M16—2262no—
96#124—1131no—
97#124—1131no—
98#124—1131no—
99#124—2262no—
100#124#9067311yescharacteristic
101C2×C22⋊C4—2262no—
102C2×C42—1131no—
103#101—1134no—
104#101—2262no—
105C24—2261no—
106C2×Q8—1132no—
107C2×Q8—1131no—
108C2×Q8—4521no—
109C2×Q8—4521no—
110C2×Q8C2×#9067311yescharacteristic
111C2×D4—1131no—
112C2×D4—4521no—
113C2×D4—4521no—
114C2×D4—2261no—
115C2×D4C2×#9067311yescharacteristic
116C22×C4—1132no—
117C22×C4—1131no—
118C22×C4—2261no—
119M16—4522no—
120M16—2264no—
121C2×C8—4522no—
122C22⋊C4—22no—
123C22⋊C4—2262no—
124C22⋊C4—2262no—
125C22⋊C4—2262no—
126C42—1131no—
127C42—2261no—
128C42C2×#9067311yescharacteristic
129C23—21no—
130C23—1131no—
131C23—4521no—
132C23—4521no—
133C23—4524no—
134C23—2261no—
135Q8—41no—
136Q8—4522no—
137Q8—4521no—
138D4—41no—
139D4—4521no—
140D4—4522no—
141C2×C4—21no—
142C2×C4—1131no—
143C2×C4—1132no—
144C2×C4—4522no—
145C2×C4—2262no—
146C2×C4—2262no—
147C2×C4—2261no—
148C2×C4—2261no—
149C2×C4—2261no—
150C2×C4C22⋊#9067312yes—
151C2×C4C22×#9067311yescharacteristic
152C8—4524no—
153C22—42no—
154C22—41no—
155C22—1131no—
156C22—1131no—
157C22—9042no—
158C22—9042no—
159C22—4522no—
160C22—4521no—
161C22—2262no—
162C22C2×C22⋊#9067311yescharacteristic
163C4—22no—
164C4—21no—
165C4—41no—
166C4—4521no—
167C4—2262no—
168C4—2261no—
169C2—21no—
170C2—81no—
171C2—1132no—
172C2—9041no—
173C2—2261no—
174C2D113⋊#9911yescharacteristic
subgroupG/H
centerC2D113⋊#99
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#124×C113C4
socleC2×C113C2×#99
prime radicalC2×D4×D113C4
cosocleC2×Dic226C23
hypercenter#124#90673
hypocenterC113C2×#355
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #124

Complements

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

NH ≅ G/Ntype
1. D113⋊#101C2semidirect
2. #20299507C2semidirect
3. #20299506C2semidirect
7. #16813683C22semidirect
86. D113#355semidirect
88. C113C2×#355semidirect

Maximal subgroups

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

subgroupindex
D113⋊#1012
#202995072
#202995062
#124×D1132
C2×#355113