Finite Group Databasebeta

← #28389203

Subgroups — #28389203

Order 14464.

200 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 65 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#20299132C211yesmaximal, characteristic
2#20298655C211yesmaximal, characteristic, complemented
3#20298339C212yesmaximal, complemented
4#20298337C212yesmaximal, complemented
5#432×C113C211yesmaximal, characteristic, complemented
6#16813616—21no—
7#16813614C2211yescharacteristic
8#16813610C2211yescharacteristic
9#16813605—21no—
10#16813601C411yescharacteristic
11#16813596C411yescharacteristic
12C4×Dic226C411yescharacteristic
13C4×D452C411yescharacteristic
14C4×C22⋊D113—21no—
15#16813579—21no—
16C4⋊#11744751—21no—
17C22⋊#11744751—21no—
18#16813533C2212yes—
19C2×C42×C113C2211yescharacteristic
20C4⋊C8×C113—21no—
21C22⋊C8×C113—21no—
22#97×C113C2212yes—
23C2×Dic226C2×C411yescharacteristic
24C2×D452C2×C411yescharacteristic
25C2×C22⋊D113—21no—
26C2×C4×D113—21no—
27C2×#11744751—22no—
28C4⋊Dic113C2×C411yescharacteristic
29C4⋊Dic113C2×C411yescharacteristic
30#14268626—21no—
31#14268626—21no—
32#14268626—21no—
33#14268626—21no—
34C22⋊Dic113—21no—
35#14268624—21no—
36#14268624—21no—
37#14268624—21no—
38#14268624—21no—
39C4×Dic113—21no—
40C22×C4×C113C2×C411yescharacteristic
41C22×C4×C113D411yescharacteristic
42C22×C4×C113D411yescharacteristic
43C2×C8×C113—22no—
44C42×C113C2×C411yescharacteristic
45C42×C113D411yescharacteristic
46C42×C113D411yescharacteristic
47C42×C113C2311yescharacteristic
48C23×C113C22⋊C411yescharacteristic
49C22×D113—21no—
50C2×C4×C113—41no—
51C2×C4×C113—41no—
52C2×C4×C113—41no—
53C2×C4×C113C22⋊C411yescharacteristic
54C2×C4×C113C22⋊C411yescharacteristic
55C2×C4×C113C22⋊C411yescharacteristic
56C2×C4×C113C22×C411yescharacteristic
57C2×C4×C113C2×D411yescharacteristic
58C2×C4×C113C2×D411yescharacteristic
59C22⋊D113—42no—
60C2×Dic113—21no—
61C2×Dic113—21no—
62C2×Dic113—21no—
63D452—41no—
64C4×D113—42no—
65Dic226—41no—
66C8×C113—42no—
67#11744751—42no—
68C22×C113—21no—
69C22×C113—21no—
70C22×C113—21no—
71C22×C113C2×C22⋊C411yescharacteristic
72C2×D113—41no—
73C2×D113—41no—
74C2×D113—41no—
75C4×C113—21no—
76C4×C113—21no—
77C4×C113—21no—
78C4×C113—21no—
79C4×C113—21no—
80C4×C113—21no—
81Dic113—41no—
82Dic113—41no—
83Dic113—41no—
84C2×C113—41no—
85C2×C113#41311yescharacteristic
86C2×C113#42111yescharacteristic
87C2×C113#42111yescharacteristic
88D113—81no—
89#1535—1131nomaximal, Sylow
90C113#153511yescharacteristic, complemented, Sylow
91#529—1131no—
92#432—1131no—
93#432D11311yescharacteristic, complemented
94#330—1132no—
95#329—1132no—
96#126—2261no—
97#125—1131no—
98#124—1131no—
99#123—2261no—
100C22⋊Q8—1131no—
101#121—1131no—
102C4×Q8—1131no—
103C4×D4—1131no—
104C4×D4—2261no—
105#117—2261no—
106C2×C42C2×D11311yescharacteristic
107C4⋊C8—21no—
108C4⋊C8—2261no—
109C22⋊C8—21no—
110C22⋊C8—2261no—
111#97—1132no—
112#97C2×D11312yes—
113C2×Q8—1131no—
114C2×D4—1131no—
115C2×D4—2261no—
116C22×C4—2261no—
117C22×C4C4×D11311yescharacteristic
118C22×C4D45211yescharacteristic
119C22×C4C22⋊D11311yescharacteristic
120C2×C8—22no—
121C2×C8—2262no—
122C4⋊C4—1131no—
123C4⋊C4—1131no—
124C4⋊C4—2261no—
125C4⋊C4—2261no—
126C4⋊C4—2261no—
127C4⋊C4—2261no—
128C22⋊C4—2261no—
129C22⋊C4—2261no—
130C22⋊C4—2261no—
131C22⋊C4—2261no—
132C22⋊C4—2261no—
133C42—2261no—
134C42C4×D11311yescharacteristic
135C42D45211yescharacteristic
136C42C22⋊D11311yescharacteristic
137C42C22×D11311yescharacteristic
138C23—2261no—
139C23#1426862411yescharacteristic
140Q8—4521no—
141D4—4521no—
142D4—4522no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—4522no—
147C2×C4—2261no—
148C2×C4—2261no—
149C2×C4—2261no—
150C2×C4#1426862411yescharacteristic
151C2×C4#1426862411yescharacteristic
152C2×C4#1426862411yescharacteristic
153C2×C4C2×C4×D11311yescharacteristic
154C2×C4C2×C22⋊D11311yescharacteristic
155C2×C4C2×D45211yescharacteristic
156C8—42no—
157C8—4522no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—4521no—
162C22—4521no—
163C22—4521no—
164C22C2×#1426862411yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—4521no—
172C4—4521no—
173C4—4521no—
174C2—41no—
175C2—9041no—
176C2#2029858011yescharacteristic
177C2#2029861411yescharacteristic
178C2#2029861611yescharacteristic
subgroupG/H
centerC22C2×#14268624
commutatorC2×C4×C113C22×C4
FrattiniC42C22×D113
Fitting#432×C113C2
socleC22×C113C2×C22⋊C4
prime radical#16813596C4
cosocleC42×C113C23
hypercenter#432D113
hypocenterC113#1535
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #20298655C2semidirect
3. #20298339C2semidirect
4. #20298337C2semidirect
5. #432×C113C2semidirect
90. C113#1535semidirect
93. #432D113semidirect

Maximal subgroups

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

subgroupindex
#202991322
#202986552
#202983392
#202983372
#432×C1132
#1535113