Finite Group Databasebeta

← #28392264

Subgroups — #28392264

Order 14464.

262 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 55 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#20299166C211yesmaximal, characteristic
2#20298581C212yesmaximal, complemented
3#20298395C211yesmaximal, characteristic, complemented
4#20298394C212yesmaximal, complemented
5#355×C113C211yesmaximal, characteristic, complemented
6C2×#14268648C2211yescharacteristic
7C2×D4×D113C411yescharacteristic
8M16×D113—22no—
9#16813619C411yescharacteristic
10#16813618C411yescharacteristic
11#16813611C2211yescharacteristic
12#16813595—22no—
13#16813592—22no—
14#16813579C411yescharacteristic
15#16813541C2212yescomplemented
16#16813538—22no—
17#124×C113C2211yescharacteristic
18#101×C113C2212yescomplemented
19C23×D113—21no—
20#14268648—42no—
21C2×D452—22no—
22C2×D452C2×C411yescharacteristic
23C2×D452C2×C411yescharacteristic
24C2×D452D412yes—
25C2×C22⋊D113—22no—
26C2×C22⋊D113—21no—
27D4×D113—42no—
28C2×C4×D113C2×C411yescharacteristic
29C2×C4×D113D412yes—
30#14268631—22no—
31#14268630—42no—
32C8×D113—42no—
33#14268626—21no—
34#14268624—21no—
35#14268624—22no—
36C4×Dic113C2×C411yescharacteristic
37C2×Q8×C113C2311yescharacteristic
38C2×D4×C113C2×C411yescharacteristic
39M16×C113—22no—
40C22⋊C4×C113—22no—
41C42×C113C2×C411yescharacteristic
42C23×C113—21no—
43C22×D113—21no—
44C22×D113—42no—
45C22×D113—82no—
46C22×D113C22⋊C411yescharacteristic
47C22×D113C22⋊C412yes—
48Q8×C113—41no—
49D4×C113—41no—
50C2×C4×C113—21no—
51C2×C4×C113C22×C411yescharacteristic
52C2×C4×C113C2×D412yes—
53C22⋊D113—42no—
54C22⋊D113—82no—
55C2×Dic113—21no—
56C2×Dic113C22⋊C411yescharacteristic
57D452—41no—
58D452—42no—
59D452—41no—
60D452—82no—
61C4×D113—22no—
62C4×D113—22no—
63C4×D113—22no—
64C8×C113—42no—
65#11744751—42no—
66C22×C113—42no—
67C22×C113—41no—
68C22×C113C2×C22⋊C411yescharacteristic
69C2×D113—21no—
70C2×D113—22no—
71C2×D113—42no—
72C2×D113—41no—
73C2×D113—42no—
74C2×D113—41no—
75C2×D113—84no—
76C4×C113—22no—
77C4×C113—21no—
78C4×C113—41no—
79Dic113—41no—
80Dic113#9912yes—
81C2×C113—21no—
82C2×C113—81no—
83C2×C113C2×#9911yescharacteristic
84D113—42no—
85D113—41no—
86D113—81no—
87#2134—1131nomaximal, Sylow
88C113#213411yescharacteristic, complemented, Sylow
89#535—1131no—
90#413—1132no—
91#355—1131no—
92#355—1132no—
93#355D11311yescharacteristic, complemented
94C2×#41—1131no—
95C22×D4—1131no—
96C2×M16—2262no—
97#127—1131no—
98#127—1131no—
99#124—1131no—
100#124C2×D11311yescharacteristic
101#121—2262no—
102#120—2262no—
103#117—1131no—
104#101—1132no—
105#101C2×D11312yescomplemented
106#100—2262no—
107C24—2261no—
108#41—4522no—
109C2×Q8C22×D11311yescharacteristic
110C2×D4—1131no—
111C2×D4—1131no—
112C2×D4—1132no—
113C2×D4—4522no—
114C2×D4—2262no—
115C2×D4—2261no—
116C2×D4—2262no—
117C2×D4C4×D11311yescharacteristic
118C22×C4—1131no—
119C22×C4—1132no—
120M16—22no—
121M16—4522no—
122M16—2262no—
123C2×C8—4522no—
124C4⋊C4—2261no—
125C22⋊C4—22no—
126C22⋊C4—2261no—
127C22⋊C4—2262no—
128C42—1131no—
129C42C4×D11311yescharacteristic
130C23—21no—
131C23—1131no—
132C23—1132no—
133C23—9042no—
134C23—4522no—
135C23—2261no—
136Q8—41no—
137D4—41no—
138D4—9042no—
139D4—9042no—
140D4—4521no—
141D4—4522no—
142D4—4521no—
143D4—4522no—
144C2×C4—21no—
145C2×C4—1131no—
146C2×C4—2262no—
147C2×C4—2262no—
148C2×C4—2262no—
149C2×C4—2261no—
150C2×C4C2×C4×D11311yescharacteristic
151C2×C4D4×D11312yes—
152C8—42no—
153C8—4522no—
154C22—42no—
155C22—41no—
156C22—9044no—
157C22—4522no—
158C22—4522no—
159C22—4521no—
160C22—4521no—
161C22—2261no—
162C22—2262no—
163C22C22⋊C4×D11311yescharacteristic
164C4—22no—
165C4—21no—
166C4—41no—
167C4—1132no—
168C4—4521no—
169C2—21no—
170C2—81no—
171C2—9041no—
172C2—4521no—
173C2—4522no—
174C2#99×D11311yescharacteristic
subgroupG/H
centerC2#99×D113
commutatorC2×C4×C113C22×C4
FrattiniC2×Q8C22×D113
Fitting#355×C113C2
socleC2×C113C2×#99
prime radical#20299166C2
cosocleC2×Q8×C113C23
hypercenter#355D113
hypocenterC113#2134
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #20298581C2semidirect
3. #20298395C2semidirect
4. #20298394C2semidirect
5. #355×C113C2semidirect
15. #16813541C22semidirect
18. #101×C113C22semidirect
88. C113#2134semidirect
93. #355D113semidirect
105. #101C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991662
#202985812
#202983952
#202983942
#355×C1132
#2134113