Finite Group Databasebeta

← #28389135

Subgroups — #28389135

Order 14464.

264 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 85 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#20299148C211yesmaximal, characteristic
2#20298464C211yesmaximal, characteristic, complemented
3#20298333C214yesmaximal, complemented
4#431×C113C211yesmaximal, characteristic, complemented
5C2×#14268647—21no—
6#16813622C411yescharacteristic, complemented
7#16813619C411yescharacteristic, complemented
8#16813610—21no—
9#16813596—21no—
10#16813596C2212yes—
11C4×D452—21no—
12C4×D452C412yescomplemented
13C2×C4⋊Dic113—21no—
14#16813529—21no—
15#16813529C2212yes—
16C2×C42×C113C2211yescharacteristic
17C4⋊C8×C113—21no—
18C22⋊C8×C113C2212yes—
19C4×C8×C113—21no—
20#14268647—42no—
21#14268647—42no—
22C2×Dic226—21no—
23C2×D452—21no—
24C2×D452—21no—
25C2×D452C2×C412yes—
26C2×C22⋊D113—22no—
27C22×Dic113—22no—
28C2×C4×D113—22no—
29C4⋊Dic113—21no—
30C4⋊Dic113—42no—
31C4⋊Dic113C2×C412yes—
32#14268624—22no—
33#14268624—22no—
34C22×C4×C113D411yescharacteristic
35C22×C4×C113D411yescharacteristic
36C22×C4×C113C2311yescharacteristic
37C2×C8×C113—22no—
38C42×C113C2×C411yescharacteristic
39C42×C113C2×C411yescharacteristic
40C42×C113D411yescharacteristic
41C42×C113D411yescharacteristic
42C23×C113C2×D411yescharacteristic
43C22×D113—22no—
44C2×C4×C113—41no—
45C2×C4×C113—41no—
46C2×C4×C113C22⋊C411yescharacteristic
47C2×C4×C113C22⋊C411yescharacteristic
48C2×C4×C113C22⋊C411yescharacteristic
49C2×C4×C113C22⋊C411yescharacteristic
50C2×C4×C113D812yes—
51C2×C4×C113SD1612yes—
52C2×C4×C113C22×C411yescharacteristic
53C2×C4×C113C2×D411yescharacteristic
54C22⋊D113—42no—
55C22⋊D113—42no—
56C2×Dic113—22no—
57C2×Dic113—42no—
58C2×Dic113—42no—
59C2×Dic113—42no—
60D452—42no—
61D452—42no—
62D452—42no—
63C4×D113—44no—
64Dic226—42no—
65C8×C113—42no—
66C22×C113—21no—
67C22×C113—21no—
68C22×C113C2×C22⋊C411yescharacteristic
69C22×C113C2×D811yescharacteristic
70C22×C113C2×SD1611yescharacteristic
71C2×D113—42no—
72C2×D113—42no—
73C2×D113—42no—
74C4×C113—21no—
75C4×C113—21no—
76C4×C113—21no—
77C4×C113—21no—
78C4×C113#10212yes—
79C4×C113#10212yes—
80Dic113—42no—
81Dic113—82no—
82C2×C113—21no—
83C2×C113—21no—
84C2×C113#41011yescharacteristic
85C2×C113C2×#10211yescharacteristic
86C2×C113#42111yescharacteristic
87D113—82no—
88#1517—1131nomaximal, Sylow
89C113#151711yescharacteristic, complemented, Sylow
90#532—1131no—
91#431D11311yescharacteristic, complemented
92#382—1131no—
93#327—1134no—
94C2×#41—2261no—
95C4⋊Q8—1131no—
96#127—1131no—
97#124—2261no—
98#121—1132no—
99#121—2261no—
100C4×D4—1132no—
101C4×D4—2261no—
102C2×C4⋊C4—2261no—
103C2×C42C2×D11311yescharacteristic
104C4⋊C8—21no—
105C22⋊C8C2×D11312yes—
106C4×C8—21no—
107#95—1132no—
108#95—2261no—
109#41—4522no—
110#41—4522no—
111C2×Q8—2261no—
112C2×D4—1132no—
113C2×D4—2262no—
114C2×D4—2261no—
115C2×D4—2261no—
116C22×C4—2262no—
117C22×C4—2262no—
118C22×C4D45211yescharacteristic
119C22×C4D45211yescharacteristic
120C22×C4C22×D11311yescharacteristic
121C2×C8—22no—
122C4⋊C4—1132no—
123C4⋊C4—4522no—
124C4⋊C4—2261no—
125C22⋊C4—2262no—
126C22⋊C4—2262no—
127C42C4×D11311yescharacteristic
128C42C4×D11311yescharacteristic
129C42C22⋊D11311yescharacteristic
130C42C22⋊D11311yescharacteristic
131C23—2262no—
132C23C2×D45211yescharacteristic
133Q8—4522no—
134D4—4522no—
135D4—4522no—
136D4—4522no—
137D4—4522no—
138D4—4522no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—4522no—
142C2×C4—4522no—
143C2×C4—4522no—
144C2×C4—4524no—
145C2×C4—2262no—
146C2×C4#1426862411yescharacteristic
147C2×C4#1426862411yescharacteristic
148C2×C4#1426862411yescharacteristic
149C2×C4#1426862411yescharacteristic
150C2×C4D90412yes—
151C2×C4#1426863612yes—
152C2×C4C2×C4×D11311yescharacteristic
153C2×C4C2×C22⋊D11311yescharacteristic
154C8—42no—
155C22—21no—
156C22—21no—
157C22—4522no—
158C22—4522no—
159C22—4522no—
160C22C2×#1426862411yescharacteristic
161C22C2×D90411yescharacteristic
162C22C2×#1426863611yescharacteristic
163C4—21no—
164C4—21no—
165C4—21no—
166C4—21no—
167C4—9042no—
168C4—4522no—
169C4#1681354412yes—
170C4#1681354412yes—
171C2—21no—
172C2—21no—
173C2—9042no—
174C2#2029857111yescharacteristic
175C2C2×#1681354411yescharacteristic
176C2#2029861411yescharacteristic
subgroupG/H
centerC22C2×#14268624
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#431×C113C2
socleC22×C113C2×C22⋊C4
prime radical#20299148C2
cosocleC22×C4×C113C23
hypercenter#431D113
hypocenterC113#1517
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #20298464C2semidirect
3. #20298333C2semidirect
4. #431×C113C2semidirect
6. #16813622C4semidirect
7. #16813619C4semidirect
12. C4×D452C4semidirect
89. C113#1517semidirect
91. #431D113semidirect

Maximal subgroups

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

subgroupindex
#202991482
#202984642
#202983332
#431×C1132
#1517113