Finite Group Databasebeta

← #28389204

Subgroups — #28389204

Order 14464.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#20299133C211yesmaximal, characteristic
2#20298653C211yesmaximal, characteristic, complemented
3#20298653C211yesmaximal, characteristic, complemented
4#20298340C211yesmaximal, characteristic, complemented
5#20298337C211yesmaximal, characteristic, complemented
6#20298337C211yesmaximal, characteristic, complemented
7#330×C113C211yesmaximal, characteristic, complemented
8#16813617—21no—
9#16813610C2211yescharacteristic
10#16813607—21no—
11#16813602C411yescharacteristic
12#16813597C411yescharacteristic
13#16813587C411yescharacteristic
14#16813584—21no—
15#16813584C411yescharacteristic
16#16813580—21no—
17C42×D113C2211yescharacteristic
18#16813551—21no—
19#16813551—21no—
20#16813534—21no—
21#16813534—21no—
22#16813533C2211yescharacteristic
23#16813533C2211yescharacteristic
24#125×C113C2211yescharacteristic
25#97×C113C2211yescharacteristic
26#97×C113C2211yescharacteristic
27C2×Dic226C2×C411yescharacteristic
28C2×D452—21no—
29C2×D452C2×C411yescharacteristic
30C2×C4×D113—21no—
31C2×C4×D113C2×C411yescharacteristic
32C2×C4×D113D411yescharacteristic
33C2×C4×D113D411yescharacteristic
34C2×#11744751—21no—
35C2×#11744751—21no—
36C4⋊Dic113—21no—
37#14268626—21no—
38#14268624—21no—
39#14268624—21no—
40#14268624—21no—
41#14268624—21no—
42#14268624—21no—
43C4×Dic113—21no—
44C4×Dic113C2×C411yescharacteristic
45C4×Dic113D411yescharacteristic
46C4×Dic113D411yescharacteristic
47C2×C8×C113—21no—
48C2×C8×C113—21no—
49C4⋊C4×C113—21no—
50C4⋊C4×C113—21no—
51C4⋊C4×C113C2×C411yescharacteristic
52C4⋊C4×C113C2×C411yescharacteristic
53C42×C113C2311yescharacteristic
54C22×D113—21no—
55C22×D113C22⋊C411yescharacteristic
56C2×C4×C113—21no—
57C2×C4×C113—21no—
58C2×C4×C113C22×C411yescharacteristic
59C2×C4×C113C2×D411yescharacteristic
60C2×C4×C113C2×D411yescharacteristic
61C2×Dic113—21no—
62C2×Dic113C22⋊C411yescharacteristic
63C2×Dic113C22⋊C411yescharacteristic
64C2×Dic113C22⋊C411yescharacteristic
65D452—41no—
66D452—42no—
67C4×D113—41no—
68C4×D113—41no—
69C4×D113—41no—
70C4×D113—42no—
71Dic226—41no—
72C8×C113—41no—
73C8×C113—41no—
74#11744751—41no—
75#11744751—41no—
76C22×C113C2×C22⋊C411yescharacteristic
77C2×D113—21no—
78C2×D113—21no—
79C2×D113—21no—
80C2×D113—41no—
81C2×D113—41no—
82C2×D113—41no—
83C4×C113—21no—
84C4×C113—21no—
85C4×C113—21no—
86C4×C113—41no—
87C4×C113—41no—
88Dic113—21no—
89Dic113—21no—
90Dic113—21no—
91Dic113—41no—
92C2×C113#41311yescharacteristic
93C2×C113#42111yescharacteristic
94C2×C113#42111yescharacteristic
95D113—41no—
96D113—81no—
97#1535—1131nomaximal, Sylow
98C113#153511yescharacteristic, complemented, Sylow
99#529—1131no—
100#432—1131no—
101#432—1131no—
102#330—1131no—
103#330D11311yescharacteristic, complemented
104#329—1131no—
105#329—1131no—
106#126—2261no—
107#125C2×D11311yescharacteristic
108#124—1131no—
109#123—2261no—
110C22⋊Q8—1131no—
111#121—1131no—
112C4×Q8—1131no—
113C4×D4—1131no—
114C4×D4—2261no—
115#117—2261no—
116C2×C42—1131no—
117C4⋊C8—2261no—
118C4⋊C8—2261no—
119C22⋊C8—2261no—
120C22⋊C8—2261no—
121#97—1131no—
122#97—1131no—
123#97C2×D11311yescharacteristic
124#97C2×D11311yescharacteristic
125C2×Q8—1131no—
126C2×D4—1131no—
127C2×D4—2261no—
128C22×C4—1131no—
129C22×C4—1131no—
130C22×C4—1131no—
131C22×C4—2261no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—2261no—
135C2×C8—2261no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—2261no—
139C4⋊C4—2261no—
140C4⋊C4C4×D11311yescharacteristic
141C4⋊C4C4×D11311yescharacteristic
142C22⋊C4—2261no—
143C22⋊C4—2261no—
144C22⋊C4—2261no—
145C22⋊C4—2261no—
146C22⋊C4—2261no—
147C42—1131no—
148C42—1131no—
149C42—1131no—
150C42—2261no—
151C42C22×D11311yescharacteristic
152C23—1131no—
153C23—2261no—
154Q8—4521no—
155D4—4521no—
156D4—4522no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—1131no—
160C2×C4—1131no—
161C2×C4—1131no—
162C2×C4—4521no—
163C2×C4—4521no—
164C2×C4—4521no—
165C2×C4—4522no—
166C2×C4—2261no—
167C2×C4C2×C4×D11311yescharacteristic
168C2×C4D4×D11311yescharacteristic
169C2×C4D4×D11311yescharacteristic
170C8—41no—
171C8—41no—
172C8—4521no—
173C8—4521no—
174C22—4521no—
175C22—4521no—
176C22—4521no—
177C22—2261no—
178C22—2261no—
179C22—2261no—
180C22C22⋊C4×D11311yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—41no—
186C4—4521no—
187C4—2261no—
188C4—2261no—
189C4—2261no—
190C2—9041no—
191C2—4521no—
192C2#2029858111yescharacteristic
193C2#2029861311yescharacteristic
194C2#2029861311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D113
commutatorC2×C4×C113C22×C4
FrattiniC42C22×D113
Fitting#330×C113C2
socleC22×C113C2×C22⋊C4
prime radical#16813597C4
cosocleC42×C113C23
hypercenter#330D113
hypocenterC113#1535
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #20298653C2semidirect
3. #20298653C2semidirect
4. #20298340C2semidirect
5. #20298337C2semidirect
6. #20298337C2semidirect
7. #330×C113C2semidirect
98. C113#1535semidirect
103. #330D113semidirect

Maximal subgroups

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

subgroupindex
#202991332
#202986532
#202983402
#202983372
#330×C1132
#1535113