Finite Group Databasebeta

← #28389301

Subgroups — #28389301

Order 14464.

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

normal subgroups only

This group has 202 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#20299153C211yesmaximal, characteristic
2#20298654C211yesmaximal, characteristic
3#20298620C211yesmaximal, characteristic
4#20298347C211yesmaximal, characteristic, complemented
5#20298345C211yesmaximal, characteristic, complemented
6#20298343C211yesmaximal, characteristic, complemented
7#333×C113C211yesmaximal, characteristic, complemented
8C2×#14268630—21no—
9#16813622C2211yescharacteristic
10#16813613—21no—
11#16813602—21no—
12#16813598C412yes—
13Q8×Dic113C412yes—
14#16813587—21no—
15#16813580—21no—
16C42×D113C2211yescharacteristic
17C4⋊#11744751C2211yescharacteristic
18C4⋊#11744751C2211yescharacteristic
19#16813551—21no—
20#16813534—21no—
21#16813532—21no—
22C4⋊Q8×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4⋊C8×C113C2211yescharacteristic
25C2×Dic226—21no—
26C2×C4×D113C2×C411yescharacteristic
27C2×C4×D113D411yescharacteristic
28C2×C4×D113D411yescharacteristic
29#14268630—42no—
30C2×#11744751—21no—
31C2×#11744751—21no—
32C4⋊Dic113—21no—
33C4⋊Dic113—22no—
34C4⋊Dic113C2×C412yes—
35#14268626—22no—
36#14268624—22no—
37C4×Dic113—22no—
38C4×Dic113C2×C411yescharacteristic
39C4×Dic113D411yescharacteristic
40C4×Dic113D411yescharacteristic
41C2×Q8×C113C2×C412yes—
42C2×C8×C113—21no—
43C2×C8×C113—21no—
44C4⋊C4×C113—21no—
45C4⋊C4×C113—21no—
46C42×C113C2311yescharacteristic
47C22×D113C22⋊C411yescharacteristic
48Q8×C113—42no—
49C2×C4×C113—22no—
50C2×C4×C113C22×C411yescharacteristic
51C2×C4×C113C2×D411yescharacteristic
52C2×C4×C113C2×D411yescharacteristic
53C2×Dic113—22no—
54C2×Dic113C22⋊C411yescharacteristic
55C2×Dic113C22⋊C411yescharacteristic
56C2×Dic113C22⋊C411yescharacteristic
57C4×D113—21no—
58C4×D113—21no—
59C4×D113—21no—
60C4×D113—21no—
61C4×D113—41no—
62Dic226—41no—
63Dic226—41no—
64C8×C113—41no—
65C8×C113—41no—
66#11744751—41no—
67#11744751—41no—
68C22×C113C2×C22⋊C411yescharacteristic
69C2×D113—21no—
70C2×D113—21no—
71C2×D113—21no—
72C4×C113—21no—
73C4×C113—42no—
74C4×C113AGL(1,ℤ/8)11yescharacteristic
75C4×C113#13711yescharacteristic
76C4×C113#13711yescharacteristic
77C4×C113#13711yescharacteristic
78Dic113—21no—
79Dic113—21no—
80Dic113—21no—
81Dic113—42no—
82C2×C113#41311yescharacteristic
83C2×C113#41711yescharacteristic
84C2×C113#41911yescharacteristic
85D113—41no—
86#1559—1131nomaximal, Sylow
87C113#155911yescharacteristic, complemented, Sylow
88#533—1131no—
89#432—1131no—
90#423—1131no—
91#333—1131no—
92#333D11311yescharacteristic, complemented
93#332—1131no—
94#332—1131no—
95C2×M16—2261no—
96C4⋊Q8—1131no—
97C4⋊Q8C2×D11311yescharacteristic
98#125—2261no—
99C22⋊Q8—1132no—
100C22⋊Q8—2261no—
101C4×Q8—1132no—
102C4×Q8—2261no—
103#117—2261no—
104C2×C42—1131no—
105C4⋊C8—1131no—
106C4⋊C8—1131no—
107C4⋊C8—2261no—
108C4⋊C8C2×D11311yescharacteristic
109C4⋊C8C2×D11311yescharacteristic
110C22⋊C8—2261no—
111#97—2261no—
112C2×Q8—2261no—
113C2×Q8C4×D11312yes—
114C22×C4—1131no—
115C22×C4—1131no—
116C22×C4—1131no—
117M16—4522no—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—2261no—
121C2×C8—2261no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—1132no—
125C4⋊C4—2262no—
126C4⋊C4—2262no—
127C4⋊C4—2261no—
128C22⋊C4—2262no—
129C42—1131no—
130C42—1131no—
131C42—1131no—
132C42—2262no—
133C42C22×D11311yescharacteristic
134C23—1131no—
135Q8—42no—
136Q8—4521no—
137Q8—4521no—
138C2×C4—22no—
139C2×C4—1131no—
140C2×C4—1131no—
141C2×C4—1131no—
142C2×C4—4521no—
143C2×C4—2262no—
144C2×C4—2261no—
145C2×C4—2261no—
146C2×C4—2261no—
147C2×C4—2261no—
148C2×C4C2×C4×D11311yescharacteristic
149C2×C4D4×D11311yescharacteristic
150C2×C4D4×D11311yescharacteristic
151C8—41no—
152C8—41no—
153C8—4521no—
154C8—4521no—
155C22—2261no—
156C22—2261no—
157C22—2261no—
158C22C22⋊C4×D11311yescharacteristic
159C4—21no—
160C4—42no—
161C4—4522no—
162C4—2261no—
163C4—2261no—
164C4—2261no—
165C4#1681364911yescharacteristic
166C4#1681365111yescharacteristic
167C4#1681365411yescharacteristic
168C4#1681365411yescharacteristic
169C2—4521no—
170C2#2029857911yescharacteristic
171C2#2029859811yescharacteristic
172C2#2029860511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D113
commutatorC2×C4×C113C22×C4
FrattiniC42C22×D113
Fitting#333×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC22×D113C22⋊C4
cosocleC42×C113C23
hypercenter#333D113
hypocenterC113#1559
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
4. #20298347C2semidirect
5. #20298345C2semidirect
6. #20298343C2semidirect
7. #333×C113C2semidirect
87. C113#1559semidirect
92. #333D113semidirect

Maximal subgroups

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

subgroupindex
#202991532
#202986542
#202986202
#202983472
#202983452
#202983432
#333×C1132
#1559113