Finite Group Databasebeta

← #28389748

Subgroups — #28389748

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#20299318C211yesmaximal, characteristic
2#20298949C211yesmaximal, characteristic, complemented
3#20298894C211yesmaximal, characteristic, complemented
4#20298888C211yesmaximal, characteristic
5#20298343C211yesmaximal, characteristic, complemented
6#20298330C211yesmaximal, characteristic, complemented
7D4⋊C8×C113C211yesmaximal, characteristic
8#16813622C2211yescharacteristic
9#16813622C2211yescharacteristic
10#16813615—22no—
11#16813609—21no—
12#16813601—21no—
13C4×Dic226C2211yescharacteristic
14#16813587—21no—
15#16813581—21no—
16#16813556—21no—
17#16813553—21no—
18C4⋊#11744751C2211yescharacteristic
19#16813547—21no—
20#16813547—22no—
21#16813543—21no—
22C4×D4×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4×C8×C113C2211yescharacteristic
25C2×Dic226—21no—
26C2×Dic226—21no—
27C2×Dic226D411yescharacteristic
28C2×#11744751—21no—
29C4⋊Dic113—21no—
30C4⋊Dic113—21no—
31C4⋊Dic113—21no—
32C4⋊Dic113D411yescharacteristic
33C4⋊Dic113D412yes—
34#14268626—22no—
35#14268626—21no—
36C22⋊Dic113—22no—
37C22⋊Dic113—22no—
38C4×Dic113—22no—
39C4×Dic113—21no—
40C2×D4×C113D411yescharacteristic
41C22×C4×C113—21no—
42C2×C8×C113—21no—
43C2×C8×C113—21no—
44C4⋊C4×C113D411yescharacteristic
45C22⋊C4×C113—21no—
46C42×C113C2311yescharacteristic
47C23×C113—21no—
48D4×C113—21no—
49D4×C113—21no—
50C2×C4×C113—21no—
51C2×C4×C113—41no—
52C2×C4×C113—41no—
53C2×C4×C113C2×D411yescharacteristic
54C2×C4×C113C2×D411yescharacteristic
55C2×C4×C113C2×D411yescharacteristic
56C2×Dic113—21no—
57C2×Dic113—21no—
58C2×Dic113—22no—
59C2×Dic113—41no—
60Dic226—21no—
61Dic226—21no—
62Dic226—41no—
63Dic226—41no—
64Dic226—42no—
65C8×C113—41no—
66C8×C113—41no—
67#11744751—41no—
68C22×C113—41no—
69C22×C113—41no—
70C22×C113—41no—
71C22×C113#12011yescharacteristic
72C4×C113—21no—
73C4×C113—41no—
74C4×C113#13511yescharacteristic
75C4×C113#13511yescharacteristic
76C4×C113#13711yescharacteristic
77C4×C113#13711yescharacteristic
78Dic113—41no—
79Dic113—42no—
80Dic113—41no—
81Dic113—81no—
82C2×C113—81no—
83C2×C113#45211yescharacteristic
84C2×C113#45211yescharacteristic
85C2×C113#45411yescharacteristic
86#1638—1131nomaximal, Sylow
87C113#163811yescharacteristic, complemented, Sylow
88#556—1131no—
89#487—1131no—
90#477—1131no—
91#476—1131no—
92#332—1131no—
93Q8⋊C8—1131no—
94D4⋊C8D11311yescharacteristic
95C4⋊Q8—1131no—
96C4⋊Q8—1131no—
97#126—2262no—
98#124—2261no—
99C22⋊Q8—2261no—
100C4×Q8—1131no—
101C4×Q8—2261no—
102C4×D4C2×D11311yescharacteristic
103#117—2261no—
104#107—2261no—
105#106—2261no—
106C4⋊C8—1131no—
107C4⋊C8C2×D11311yescharacteristic
108#103—2262no—
109#103—2261no—
110#102—2261no—
111C4×C8C2×D11311yescharacteristic
112C2×Q8—1131no—
113C2×Q8—2261no—
114C2×Q8—2261no—
115C2×D4D45211yescharacteristic
116C22×C4—21no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—2261no—
120C4⋊C4—1132no—
121C4⋊C4—1131no—
122C4⋊C4—2262no—
123C4⋊C4—2261no—
124C4⋊C4—2261no—
125C4⋊C4—2261no—
126C4⋊C4—2261no—
127C4⋊C4D45211yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—2262no—
130C22⋊C4—2262no—
131C42—2262no—
132C42—2261no—
133C42C22×D11311yescharacteristic
134C23—21no—
135Q8—4522no—
136Q8—4521no—
137Q8—4521no—
138Q8—2261no—
139Q8—2261no—
140D4—21no—
141D4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—4521no—
146C2×C4—2261no—
147C2×C4—2262no—
148C2×C4—2261no—
149C2×C4D4×D11311yescharacteristic
150C2×C4D4×D11311yescharacteristic
151C2×C4C2×D45211yescharacteristic
152C8—41no—
153C8—41no—
154C8—4521no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#1681359211yescharacteristic
159C4—21no—
160C4—41no—
161C4—9041no—
162C4—4521no—
163C4—4522no—
164C4—4521no—
165C4#1681364111yescharacteristic
166C4#1681364411yescharacteristic
167C4#1681365111yescharacteristic
168C4#1681365511yescharacteristic
169C2—81no—
170C2#2029876111yescharacteristic
171C2#2029876211yescharacteristic
172C2#2029877211yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
FittingD4⋊C8×C113C2
socleC22×C113#120
prime radicalC2×D4×C113D4
hypercenterD4⋊C8D113
hypocenterC113#1638
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #20298949C2semidirect
3. #20298894C2semidirect
5. #20298343C2semidirect
6. #20298330C2semidirect
87. C113#1638semidirect

Maximal subgroups

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

subgroupindex
#202993182
#202989492
#202988942
#202988882
#202983432
#202983302
D4⋊C8×C1132
#1638113