Finite Group Databasebeta

← #28406874

Subgroups — #28406874

Order 14464.

262 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 52 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
1#20299585C212yesmaximal, complemented
2#20299507C212yesmaximal, complemented
3#20299506C212yesmaximal, complemented
4#20299161C211yesmaximal, characteristic
5C2×#14268656—22no—
6#16813683C2214yescomplemented
7#16813682—22no—
8C2×#14268646C2211yescharacteristic
9C2×D4×D113C411yescharacteristic
10#16813618C411yescharacteristic
11#16813610C2211yescharacteristic
12#16813609C2211yescharacteristic
13#16813594—22no—
14#16813590—22no—
15#16813579C411yescharacteristic
16#127×C113C411yescharacteristic
17#14268656—24no—
18#14268656—42no—
19C2×#11744753—42no—
20C23×D113—21no—
21#14268646—42no—
22C2×Dic226C2311yescharacteristic
23C2×D452C2×C411yescharacteristic
24C2×C22⋊D113—22no—
25C2×C22⋊D113—21no—
26C2×C22⋊D113D412yes—
27D4×D113—42no—
28C22×Dic113D412yes—
29C2×C4×D113C2×C411yescharacteristic
30#14268626—21no—
31C22⋊Dic113—22no—
32#14268624—21no—
33#14268624—22no—
34C4×Dic113C2×C411yescharacteristic
35C2×D4×C113—22no—
36C2×D4×C113C2×C411yescharacteristic
37C2×D4×C113C2×C411yescharacteristic
38C42×C113C2×C411yescharacteristic
39C23×C113—21no—
40C23×C113C22⋊C412yes—
41C22×D113—21no—
42C22×D113—42no—
43C22×D113—82no—
44C22×D113C22⋊C411yescharacteristic
45D4×C113—41no—
46D4×C113—41no—
47D4×C113—82no—
48C2×C4×C113—21no—
49C2×C4×C113C22×C411yescharacteristic
50C22⋊D113—42no—
51C22⋊D113—42no—
52C22⋊D113—82no—
53C2×Dic113—22no—
54C2×Dic113—22no—
55C2×Dic113—21no—
56C2×Dic113C22⋊C411yescharacteristic
57C2×Dic113C2×D412yes—
58D452—41no—
59C4×D113—22no—
60Dic226—41no—
61#11744753—44no—
62C22×C113—22no—
63C22×C113—42no—
64C22×C113—42no—
65C22×C113—41no—
66C22×C113C2×C22⋊C411yescharacteristic
67C2×D113—21no—
68C2×D113—41no—
69C2×D113—42no—
70C2×D113—41no—
71C2×D113—84no—
72C4×C113—21no—
73C4×C113—41no—
74Dic113—22no—
75Dic113—41no—
76Dic113#9912yes—
77C2×C113—21no—
78C2×C113—42no—
79C2×C113—81no—
80C2×C113C2×#9911yescharacteristic
81D113—41no—
82D113—81no—
83#2134—1131nomaximal, Sylow
84C113#213411yescharacteristic, complemented, Sylow
85#535—1131no—
86#413—1132no—
87#355—1132no—
88#355—1132no—
89C2×#41—1131no—
90C22×D4—1131no—
91C2×M16—2262no—
92#127—1131no—
93#127#9067311yescharacteristic
94#124—1131no—
95#124—1131no—
96#121—2262no—
97#120—2262no—
98#117—1131no—
99#101—1134no—
100#100—2262no—
101C24—2261no—
102#41—4522no—
103C2×Q8—1131no—
104C2×D4—22no—
105C2×D4—1132no—
106C2×D4—1131no—
107C2×D4—4522no—
108C2×D4—2261no—
109C2×D4—2262no—
110C2×D4C2×#9067311yescharacteristic
111C2×D4C2×#9067311yescharacteristic
112C22×C4—1132no—
113C22×C4—1131no—
114M16—4522no—
115M16—2264no—
116C2×C8—4522no—
117C4⋊C4—2261no—
118C22⋊C4—2262no—
119C22⋊C4—2261no—
120C22⋊C4—2262no—
121C42—1131no—
122C42C2×#9067311yescharacteristic
123C23—21no—
124C23—1131no—
125C23—9042no—
126C23—4522no—
127C23—2261no—
128C23C22⋊#9067312yes—
129Q8—4521no—
130D4—41no—
131D4—41no—
132D4—82no—
133D4—9042no—
134D4—4521no—
135D4—4522no—
136D4—4522no—
137C2×C4—21no—
138C2×C4—1131no—
139C2×C4—1132no—
140C2×C4—2262no—
141C2×C4—2262no—
142C2×C4—2262no—
143C2×C4—2261no—
144C2×C4C22×#9067311yescharacteristic
145C8—4524no—
146C22—22no—
147C22—42no—
148C22—42no—
149C22—41no—
150C22—9044no—
151C22—4522no—
152C22—4521no—
153C22—4521no—
154C22—2261no—
155C22C2×C22⋊#9067311yescharacteristic
156C4—21no—
157C4—41no—
158C4—1132no—
159C4—4521no—
160C4—2262no—
161C2—21no—
162C2—42no—
163C2—81no—
164C2—9041no—
165C2—4521no—
166C2D113⋊#9911yescharacteristic
subgroupG/H
centerC2D113⋊#99
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#127×C113C4
socleC2×C113C2×#99
prime radical#20299161C2
cosocleC2×Dic226C23
hypercenter#127#90673
hypocenterC113#2134
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #20299585C2semidirect
2. #20299507C2semidirect
3. #20299506C2semidirect
6. #16813683C22semidirect
84. C113#2134semidirect

Maximal subgroups

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

subgroupindex
#202995852
#202995072
#202995062
#202991612
#2134113