Finite Group Databasebeta

← #28406091

Subgroups — #28406091

Order 14464.

216 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 68 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#20299603C211yesmaximal, characteristic
2#20299599C211yesmaximal, characteristic
3#20299458C212yesmaximal, complemented
4#20299457C212yesmaximal, complemented
5#20299152C211yesmaximal, characteristic
6C2×#14268657—21no—
7C2×#14268655—21no—
8#16813689—21no—
9#16813689C2212yes—
10#16813689C2212yes—
11C4⋊#11744753—21no—
12#16813621C2211yescharacteristic
13#16813620C2211yescharacteristic
14#16813612—21no—
15#16813602C411yescharacteristic
16#16813600—21no—
17#16813598C411yescharacteristic
18C4×Dic226—21no—
19C4×Dic226C411yescharacteristic
20#16813579—21no—
21C42×D113C2211yescharacteristic
22C4×Q8×C113C411yescharacteristic
23#14268657—42no—
24#14268655—42no—
25C2×#11744753—22no—
26C2×#11744753—22no—
27C2×Dic226—21no—
28C2×Dic226C2×C411yescharacteristic
29C2×C4×D113C2×C411yescharacteristic
30C2×C4×D113D411yescharacteristic
31C2×C4×D113D411yescharacteristic
32C4⋊Dic113—21no—
33C4⋊Dic113C2×C411yescharacteristic
34#14268626—21no—
35#14268626—21no—
36#14268626—21no—
37#14268626—21no—
38#14268626—21no—
39#14268624—21no—
40#14268624—21no—
41C4×Dic113—21no—
42C4×Dic113D411yescharacteristic
43C4×Dic113D411yescharacteristic
44C4×Dic113C2311yescharacteristic
45C2×Q8×C113C2×C411yescharacteristic
46C4⋊C4×C113—21no—
47C4⋊C4×C113C2×C411yescharacteristic
48C42×C113—21no—
49C42×C113C2×C411yescharacteristic
50C22×D113C22⋊C411yescharacteristic
51Q8×C113—41no—
52C2×C4×C113—21no—
53C2×C4×C113—21no—
54C2×C4×C113C22⋊C411yescharacteristic
55C2×C4×C113C22⋊C411yescharacteristic
56C2×C4×C113C22×C411yescharacteristic
57C2×Dic113—21no—
58C2×Dic113—21no—
59C2×Dic113C22⋊C411yescharacteristic
60C2×Dic113C2×D411yescharacteristic
61C2×Dic113C2×D411yescharacteristic
62C4×D113—21no—
63C4×D113—21no—
64C4×D113—41no—
65C4×D113SD1612yes—
66C4×D113Q1612yes—
67Dic226—41no—
68Dic226—41no—
69Dic226—41no—
70#11744753—42no—
71#11744753—42no—
72C22×C113C2×C22⋊C411yescharacteristic
73C2×D113—21no—
74C2×D113—21no—
75C2×D113#10312yes—
76C4×C113—21no—
77C4×C113—21no—
78C4×C113—41no—
79C4×C113—41no—
80C4×C113#10312yes—
81Dic113—21no—
82Dic113—41no—
83Dic113—41no—
84Dic113C2×SD1611yescharacteristic
85Dic113C2×Q1611yescharacteristic
86Dic113AGL(1,ℤ/8)11yescharacteristic
87Dic113#13711yescharacteristic
88C2×C113#41311yescharacteristic
89C2×C113C2×#10311yescharacteristic
90C2×C113#41711yescharacteristic
91D113—22no—
92#1550—1131nomaximal, Sylow
93C113#155011yescharacteristic, complemented, Sylow
94#533—1131no—
95#423—1131no—
96C2×C4⋊C8—1131no—
97#333—1132no—
98#332—1132no—
99C2×M16—2261no—
100C22×C8—2261no—
101C4⋊Q8—1131no—
102C4⋊Q8—1131no—
103#125—2261no—
104C22⋊Q8—1131no—
105C22⋊Q8—1131no—
106C22⋊Q8—2261no—
107C4×Q8—1131no—
108C4×Q8—2261no—
109C4×Q8#9067311yescharacteristic
110#117—2261no—
111C2×C42—1131no—
112C4⋊C8—1132no—
113C4⋊C8—1132no—
114C4⋊C8—2261no—
115C4⋊C8—2261no—
116C2×Q8—1131no—
117C2×Q8—2261no—
118C2×Q8C2×#9067311yescharacteristic
119C22×C4—1131no—
120C22×C4—1131no—
121C22×C4—1131no—
122M16—4522no—
123C2×C8—4522no—
124C2×C8—2262no—
125C2×C8—2262no—
126C4⋊C4—21no—
127C4⋊C4—1131no—
128C4⋊C4—2261no—
129C4⋊C4—2261no—
130C4⋊C4—2261no—
131C4⋊C4—2261no—
132C4⋊C4—2261no—
133C4⋊C4—2261no—
134C4⋊C4C2×#9067311yescharacteristic
135C22⋊C4—2261no—
136C22⋊C4—2261no—
137C42—21no—
138C42—1131no—
139C42—1131no—
140C42—1131no—
141C42—2261no—
142C42C2×#9067311yescharacteristic
143C23—1131no—
144Q8—41no—
145Q8—4521no—
146Q8—4521no—
147Q8—4521no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—1131no—
151C2×C4—1131no—
152C2×C4—1132no—
153C2×C4—1132no—
154C2×C4—1131no—
155C2×C4—4521no—
156C2×C4—2261no—
157C2×C4—2261no—
158C2×C4—2261no—
159C2×C4—2261no—
160C2×C4C22⋊#9067311yescharacteristic
161C2×C4C22⋊#9067311yescharacteristic
162C2×C4C22×#9067311yescharacteristic
163C8—4522no—
164C8—4522no—
165C22—1132no—
166C22—2261no—
167C22—2261no—
168C22C2×C22⋊#9067311yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—1131no—
174C4—1131no—
175C4—1131no—
176C4—1131no—
177C4—4521no—
178C4—4521no—
179C4—2261no—
180C4#1681368512yes—
181C2—2262no—
182C2#2029958411yescharacteristic
183C2C2×#1681368511yescharacteristic
184C2#2029958911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC4×Q8×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC22×D113C22⋊C4
cosocleC4×Dic113C23
hypercenterC4×Q8#90673
hypocenterC113#1550
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #20299458C2semidirect
4. #20299457C2semidirect
93. C113#1550semidirect

Maximal subgroups

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

subgroupindex
#202996032
#202995992
#202994582
#202994572
#202991522
#1550113