Finite Group Databasebeta

← #28389649

Subgroups — #28389649

Order 14464.

236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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#20299308C211yesmaximal, characteristic, complemented
2#20298971C211yesmaximal, characteristic, complemented
3#20298798C211yesmaximal, characteristic, complemented
4#20298794C211yesmaximal, characteristic
5#20298346C211yesmaximal, characteristic, complemented
6#20298327C211yesmaximal, characteristic, complemented
7Q8⋊C8×C113C211yesmaximal, characteristic, complemented
8C2×#14268636—22no—
9C2×#14268634—21no—
10C2×D904—21no—
11#16813622C2211yescharacteristic
12#16813619C2211yescharacteristic
13#16813614—21no—
14#16813600—22no—
15#16813598—21no—
16C4×D452—21no—
17C4×D452C2211yescharacteristic
18C4⋊C4×D113—21no—
19C4⋊#11744751C2211yescharacteristic
20#16813544—21no—
21#16813542—21no—
22C4×Q8×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4×C8×C113C2211yescharacteristic
25C2×Dic226D412yes—
26C2×D452—21no—
27C2×D452—21no—
28C2×D452—21no—
29C2×D452D411yescharacteristic
30C2×C4×D113—21no—
31C2×C4×D113—22no—
32#14268636—44no—
33#14268634—42no—
34D904—42no—
35C2×#11744751—21no—
36C4⋊Dic113—21no—
37C4⋊Dic113—21no—
38C4⋊Dic113D411yescharacteristic
39#14268626—22no—
40#14268626—22no—
41#14268624—22no—
42#14268624—21no—
43C2×Q8×C113D411yescharacteristic
44C2×C8×C113—21no—
45C2×C8×C113—21no—
46C4⋊C4×C113—21no—
47C4⋊C4×C113D411yescharacteristic
48C42×C113—21no—
49C42×C113C2311yescharacteristic
50C22×D113—21no—
51C22×D113—41no—
52Q8×C113—21no—
53Q8×C113—21no—
54C2×C4×C113—21no—
55C2×C4×C113—21no—
56C2×C4×C113C2×D411yescharacteristic
57C2×C4×C113C2×D411yescharacteristic
58C2×C4×C113C2×D411yescharacteristic
59C2×Dic113—21no—
60C2×Dic113—22no—
61D452—21no—
62D452—42no—
63D452—41no—
64D452—41no—
65D452—41no—
66D452—41no—
67D452SD1612yescomplemented
68C4×D113—41no—
69C4×D113—41no—
70C4×D113—82no—
71Dic226—42no—
72C8×C113—22no—
73C8×C113—41no—
74#11744751—41no—
75C22×C113#12011yescharacteristic
76C2×D113—22no—
77C2×D113—41no—
78C2×D113—41no—
79C2×D113—81no—
80C2×D113—81no—
81C2×D113—81no—
82C4×C113—21no—
83C4×C113—41no—
84C4×C113—41no—
85C4×C113C2×SD1611yescharacteristic
86C4×C113#13511yescharacteristic
87C4×C113AGL(1,ℤ/8)11yescharacteristic
88C4×C113#13711yescharacteristic
89Dic113—41no—
90Dic113—42no—
91C2×C113#44811yescharacteristic
92C2×C113#44911yescharacteristic
93C2×C113#45311yescharacteristic
94D113—42no—
95D113—161no—
96#1622—1131nomaximal, Sylow
97C113#162211yescharacteristic, complemented, Sylow
98#554—1131no—
99#492—1131no—
100#460—1131no—
101#459—1131no—
102#333—1131no—
103Q8⋊C8D11311yescharacteristic, complemented
104D4⋊C8—1131no—
105C2×SD16—2262no—
106C2×SD16—2261no—
107C2×D8—2261no—
108C4⋊Q8—1131no—
109#127—1131no—
110#125—2261no—
111C22⋊Q8—2262no—
112C22⋊Q8—2261no—
113C4×Q8C2×D11311yescharacteristic
114C4×D4—1131no—
115C4×D4—2261no—
116C2×C4⋊C4—2261no—
117C4⋊C8—1131no—
118C4⋊C8C2×D11311yescharacteristic
119#102—2261no—
120#102—2261no—
121C4×C8C2×D11311yescharacteristic
122C2×Q8—1132no—
123C2×Q8D45211yescharacteristic
124C2×D4—1131no—
125C2×D4—2261no—
126C2×D4—2261no—
127C2×D4—2261no—
128C22×C4—2262no—
129C22×C4—2261no—
130SD16—4524no—
131SD16—4522no—
132D8—4522no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—2261no—
136C4⋊C4—21no—
137C4⋊C4—1131no—
138C4⋊C4—2262no—
139C4⋊C4—2262no—
140C4⋊C4—2261no—
141C4⋊C4—2261no—
142C4⋊C4D45211yescharacteristic
143C22⋊C4—2262no—
144C22⋊C4—2261no—
145C42—21no—
146C42C22×D11311yescharacteristic
147C23—4521no—
148C23—2261no—
149Q8—21no—
150Q8—21no—
151Q8—4522no—
152D4—1132no—
153D4—4522no—
154D4—4521no—
155D4—4521no—
156D4—4521no—
157D4—4521no—
158D4—2261no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—9042no—
162C2×C4—4521no—
163C2×C4—4521no—
164C2×C4—2261no—
165C2×C4—2262no—
166C2×C4D4×D11311yescharacteristic
167C2×C4D4×D11311yescharacteristic
168C2×C4C2×D45211yescharacteristic
169C8—22no—
170C8—41no—
171C8—4521no—
172C22—9041no—
173C22—9041no—
174C22—9041no—
175C22—4521no—
176C22—4521no—
177C22—2262no—
178C22#1681359211yescharacteristic
179C4—21no—
180C4—41no—
181C4—41no—
182C4—4522no—
183C4—4521no—
184C4SD16×D11311yescharacteristic
185C4#1681364411yescharacteristic
186C4#1681365011yescharacteristic
187C4#1681365411yescharacteristic
188C2—18081no—
189C2—4522no—
190C2#2029873811yescharacteristic
191C2#2029874511yescharacteristic
192C2#2029876711yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
FittingQ8⋊C8×C113C2
socleC22×C113#120
prime radical#20298794C2
hypercenterQ8⋊C8D113
hypocenterC113#1622
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #20299308C2semidirect
2. #20298971C2semidirect
3. #20298798C2semidirect
5. #20298346C2semidirect
6. #20298327C2semidirect
7. Q8⋊C8×C113C2semidirect
67. D452SD16semidirect
97. C113#1622semidirect
103. Q8⋊C8D113semidirect

Maximal subgroups

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

subgroupindex
#202993082
#202989712
#202987982
#202987942
#202983462
#202983272
Q8⋊C8×C1132
#1622113