Finite Group Databasebeta

← #28389743

Subgroups — #28389743

Order 14464.

194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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#20299322C211yesmaximal, characteristic
2#20298890C211yesmaximal, characteristic, complemented
3#20298885C211yesmaximal, characteristic
4#20298344C211yesmaximal, characteristic, complemented
5#20298330C211yesmaximal, characteristic, complemented
6#20298327C211yesmaximal, characteristic
7#487×C113C211yesmaximal, characteristic, complemented
8#16813617—22no—
9#16813611—21no—
10#16813602—21no—
11Q8×Dic113—21no—
12C4×Dic226C2211yescharacteristic
13C4×D452C2211yescharacteristic
14#16813580—21no—
15#16813555—21no—
16#16813553—21no—
17C4⋊#11744751C2211yescharacteristic
18C4⋊#11744751C2211yescharacteristic
19#16813545—21no—
20#16813542—21no—
21C4⋊Q8×C113C2211yescharacteristic
22C4⋊Q8×C113C2211yescharacteristic
23#103×C113—22no—
24C4×C8×C113C2211yescharacteristic
25C2×Dic226D411yescharacteristic
26C2×D452D411yescharacteristic
27C2×C4×D113—21no—
28C2×#11744751—21no—
29C2×#11744751—21no—
30C4⋊Dic113—22no—
31C4⋊Dic113D411yescharacteristic
32C4⋊Dic113D411yescharacteristic
33#14268626—21no—
34#14268624—22no—
35#14268624—22no—
36#14268624—21no—
37C4×Dic113—22no—
38C4×Dic113—21no—
39C2×Q8×C113—21no—
40C2×Q8×C113—21no—
41C2×C8×C113—21no—
42C4⋊C4×C113—21no—
43C4⋊C4×C113—21no—
44C4⋊C4×C113—21no—
45C4⋊C4×C113D412yes—
46C42×C113C2311yescharacteristic
47C22×D113—21no—
48Q8×C113—42no—
49Q8×C113—41no—
50Q8×C113—41no—
51C2×C4×C113—22no—
52C2×C4×C113—41no—
53C2×C4×C113C2×D411yescharacteristic
54C2×C4×C113C2×D411yescharacteristic
55C2×C4×C113C2×D411yescharacteristic
56C2×Dic113—21no—
57C2×Dic113—21no—
58C2×Dic113—21no—
59D452—21no—
60D452—21no—
61C4×D113—41no—
62C4×D113—41no—
63Dic226—21no—
64Dic226—21no—
65C8×C113—41no—
66#11744751—41no—
67#11744751—41no—
68C22×C113#12011yescharacteristic
69C2×D113—41no—
70C2×D113—41no—
71C2×D113—41no—
72C4×C113—21no—
73C4×C113—42no—
74C4×C113—81no—
75C4×C113#13511yescharacteristic
76C4×C113#13511yescharacteristic
77C4×C113#13711yescharacteristic
78C4×C113#13711yescharacteristic
79Dic113—41no—
80Dic113—41no—
81Dic113—41no—
82C2×C113#45211yescharacteristic
83C2×C113#45211yescharacteristic
84C2×C113#45411yescharacteristic
85D113—81no—
86#1638—1131nomaximal, Sylow
87C113#163811yescharacteristic, complemented, Sylow
88#556—1131no—
89#487D11311yescharacteristic, complemented
90#477—1131no—
91#476—1131no—
92#332—1131no—
93Q8⋊C8—1131no—
94D4⋊C8—1131no—
95C4⋊Q8C2×D11311yescharacteristic
96C4⋊Q8C2×D11311yescharacteristic
97#126—2262no—
98#124—2261no—
99C22⋊Q8—2261no—
100C4×Q8—1131no—
101C4×Q8—2261no—
102C4×D4—1131no—
103#117—2261no—
104#107—2261no—
105#106—2261no—
106C4⋊C8—1131no—
107C4⋊C8—1131no—
108#103—22no—
109#103—2261no—
110#102—2261no—
111C4×C8C2×D11311yescharacteristic
112C2×Q8—21no—
113C2×Q8—21no—
114C2×Q8—1131no—
115C2×D4—1131no—
116C22×C4—2261no—
117C2×C8—21no—
118C2×C8—2261no—
119C2×C8—2261no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—1131no—
124C4⋊C4—1131no—
125C4⋊C4—2262no—
126C4⋊C4—2261no—
127C4⋊C4C22⋊D11312yes—
128C22⋊C4—2262no—
129C22⋊C4—2262no—
130C22⋊C4—2261no—
131C42—2262no—
132C42—2261no—
133C42C22×D11311yescharacteristic
134C23—2261no—
135Q8—42no—
136Q8—41no—
137Q8—41no—
138Q8—2261no—
139Q8—2261no—
140D4—2261no—
141D4—2261no—
142C2×C4—22no—
143C2×C4—41no—
144C2×C4—4521no—
145C2×C4—4521no—
146C2×C4—2261no—
147C2×C4—2261no—
148C2×C4—2261no—
149C2×C4D4×D11311yescharacteristic
150C2×C4D4×D11311yescharacteristic
151C2×C4C2×C22⋊D11311yescharacteristic
152C8—41no—
153C8—4521no—
154C8—4521no—
155C22—4521no—
156C22—4521no—
157C22—4521no—
158C22#1681359011yescharacteristic
159C4—21no—
160C4—42no—
161C4—81no—
162C4—4521no—
163C4—4521no—
164C4—4521no—
165C4#1681364311yescharacteristic
166C4#1681364511yescharacteristic
167C4#1681365111yescharacteristic
168C4#1681365411yescharacteristic
169C2—9041no—
170C2#2029875711yescharacteristic
171C2#2029875911yescharacteristic
172C2#2029877011yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#487×C113C2
socleC22×C113#120
prime radicalC2×D452D4
hypercenter#487D113
hypocenterC113#1638
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #20298890C2semidirect
4. #20298344C2semidirect
5. #20298330C2semidirect
7. #487×C113C2semidirect
87. C113#1638semidirect
89. #487D113semidirect

Maximal subgroups

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

subgroupindex
#202993222
#202988902
#202988852
#202983442
#202983302
#202983272
#487×C1132
#1638113