Finite Group Databasebeta

← #28406095

Subgroups — #28406095

Order 14464.

208 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 62 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#20299618C211yesmaximal, characteristic
2C2×#16813689C211yesmaximal, characteristic
3#20299457C212yesmaximal, complemented
4#20299457C212yesmaximal, complemented
5#20299151C211yesmaximal, characteristic
6C22×#11744753—21no—
7#16813689—21no—
8#16813689C2212yes—
9#16813689C2212yes—
10C22⋊#11744753—21no—
11#16813677—21no—
12#16813621C2211yescharacteristic
13#16813621C2211yescharacteristic
14#16813613C411yescharacteristic
15#16813613C411yescharacteristic
16#16813599—21no—
17#16813599—21no—
18C4×Dic226—21no—
19C4×Dic226—21no—
20#16813581C411yescharacteristic
21C2×C4×Dic113C2211yescharacteristic
22#117×C113C411yescharacteristic
23C2×#11744753—22no—
24C2×#11744753—22no—
25C2×#11744753—42no—
26C2×Dic226—21no—
27C2×Dic226—21no—
28C22×Dic113D411yescharacteristic
29C22×Dic113D411yescharacteristic
30C4⋊Dic113—21no—
31C4⋊Dic113—21no—
32C4⋊Dic113C2×C411yescharacteristic
33C4⋊Dic113C2×C411yescharacteristic
34#14268626—21no—
35#14268626—21no—
36#14268626—21no—
37#14268626—21no—
38C22⋊Dic113—21no—
39C4×Dic113—21no—
40C4×Dic113C2×C411yescharacteristic
41C4×Dic113D411yescharacteristic
42C4×Dic113D411yescharacteristic
43C4×Dic113C2311yescharacteristic
44C22×C4×C113C2×C411yescharacteristic
45C4⋊C4×C113C2×C411yescharacteristic
46C4⋊C4×C113C2×C411yescharacteristic
47C22⋊C4×C113—21no—
48C42×C113—21no—
49C23×C113C22⋊C411yescharacteristic
50C2×C4×C113—22no—
51C2×C4×C113—21no—
52C2×C4×C113—21no—
53C2×C4×C113C22⋊C411yescharacteristic
54C2×C4×C113C22×C411yescharacteristic
55C2×Dic113—22no—
56C2×Dic113—21no—
57C2×Dic113—21no—
58C2×Dic113—21no—
59C2×Dic113—21no—
60C2×Dic113C22⋊C411yescharacteristic
61C2×Dic113C22⋊C411yescharacteristic
62C2×Dic113C2×D411yescharacteristic
63C2×Dic113C2×D411yescharacteristic
64Dic226—42no—
65Dic226—41no—
66Dic226—41no—
67#11744753—42no—
68#11744753—42no—
69C22×C113—21no—
70C22×C113—21no—
71C22×C113#10112yes—
72C22×C113C2×C22⋊C411yescharacteristic
73C4×C113—21no—
74C4×C113—21no—
75C4×C113—41no—
76C4×C113—41no—
77Dic113—21no—
78Dic113—21no—
79Dic113—41no—
80Dic113—41no—
81Dic113#13512yes—
82Dic113AGL(1,ℤ/8)11yescharacteristic
83Dic113#13711yescharacteristic
84C2×C113—22no—
85C2×C113C2×#10111yescharacteristic
86C2×C113#41611yescharacteristic
87C2×C113#41711yescharacteristic
88#1552—1131nomaximal, Sylow
89C113#155211yescharacteristic, complemented, Sylow
90#533—1131no—
91#432—1131no—
92C2×C4⋊C8—1131no—
93#332—1132no—
94#332—1132no—
95C22×C8—2261no—
96C4⋊Q8—1131no—
97C4⋊Q8—1131no—
98#125—1131no—
99#125—1131no—
100C22⋊Q8—2261no—
101C22⋊Q8—2261no—
102C4×Q8—2261no—
103C4×Q8—2261no—
104#117—1131no—
105#117#9067311yescharacteristic
106C2×C42—1131no—
107C4⋊C8—1132no—
108C4⋊C8—1132no—
109C4⋊C8—2261no—
110C22⋊C8—2261no—
111#97—2261no—
112C2×Q8—2261no—
113C2×Q8—2261no—
114C22×C4—1131no—
115C22×C4—1131no—
116C22×C4C2×#9067311yescharacteristic
117C2×C8—4522no—
118C2×C8—2262no—
119C2×C8—2262no—
120C4⋊C4—1131no—
121C4⋊C4—1131no—
122C4⋊C4—2261no—
123C4⋊C4—2261no—
124C4⋊C4—2261no—
125C4⋊C4—2261no—
126C4⋊C4—2261no—
127C4⋊C4—2261no—
128C4⋊C4C2×#9067311yescharacteristic
129C4⋊C4C2×#9067311yescharacteristic
130C22⋊C4—21no—
131C22⋊C4—2261no—
132C42—21no—
133C42—1131no—
134C42—1131no—
135C42—1131no—
136C42—1131no—
137C42—2261no—
138C23C22⋊#9067311yescharacteristic
139Q8—4522no—
140Q8—4521no—
141Q8—4521no—
142C2×C4—22no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—1131no—
146C2×C4—1131no—
147C2×C4—1131no—
148C2×C4—1131no—
149C2×C4—2261no—
150C2×C4—2262no—
151C2×C4—2261no—
152C2×C4—2261no—
153C2×C4—2261no—
154C2×C4C22⋊#9067311yescharacteristic
155C2×C4C22×#9067311yescharacteristic
156C8—4522no—
157C8—4522no—
158C22—21no—
159C22—21no—
160C22#1681368312yes—
161C22C2×C22⋊#9067311yescharacteristic
162C4—21no—
163C4—21no—
164C4—41no—
165C4—41no—
166C4—1132no—
167C4—1131no—
168C4—1131no—
169C4—4521no—
170C4—4521no—
171C4—2261no—
172C4—2261no—
173C2—22no—
174C2C2×#1681368311yescharacteristic
175C2#2029958811yescharacteristic
176C2#2029958911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#117×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC23×C113C22⋊C4
cosocleC4×Dic113C23
hypercenter#117#90673
hypocenterC113#1552
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #20299457C2semidirect
4. #20299457C2semidirect
89. C113#1552semidirect

Maximal subgroups

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

subgroupindex
#202996182
C2×#168136892
#202994572
#202991512
#1552113