Finite Group Databasebeta

← #28389643

Subgroups — #28389643

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#20299309C211yesmaximal, characteristic, complemented
2#20298795C211yesmaximal, characteristic, complemented
3#20298790C211yesmaximal, characteristic
4#20298347C211yesmaximal, characteristic, complemented
5#20298330C211yesmaximal, characteristic, complemented
6#20298327C211yesmaximal, characteristic, complemented
7#492×C113C211yesmaximal, characteristic, complemented
8C2×#14268635—21no—
9C2×#14268632—21no—
10#16813613—21no—
11#16813602—21no—
12#16813598—22no—
13C4×Dic226C2211yescharacteristic
14C4×D452C2211yescharacteristic
15#16813584—21no—
16C4⋊C4×D113—21no—
17C4⋊#11744751C2211yescharacteristic
18C4⋊#11744751C2211yescharacteristic
19#16813543—21no—
20#16813543—21no—
21C2×SD16×C113—22no—
22C4⋊Q8×C113C2211yescharacteristic
23#127×C113C2211yescharacteristic
24C4×C8×C113C2211yescharacteristic
25C2×Dic226D411yescharacteristic
26C2×D452D411yescharacteristic
27C2×C4×D113—21no—
28C2×C4×D113—22no—
29#14268635—42no—
30#14268632—42no—
31C2×#11744751—21no—
32C2×#11744751—21no—
33C4⋊Dic113—22no—
34C4⋊Dic113D411yescharacteristic
35C4⋊Dic113D411yescharacteristic
36#14268626—22no—
37#14268626—21no—
38#14268624—22no—
39#14268624—21no—
40C4×Dic113—21no—
41C2×Q8×C113D412yes—
42C2×D4×C113—21no—
43C2×D4×C113—21no—
44C2×D4×C113—21no—
45SD16×C113—44no—
46C2×C8×C113—21no—
47C4⋊C4×C113—21no—
48C4⋊C4×C113—21no—
49C42×C113C2311yescharacteristic
50C23×C113—41no—
51C22×D113—21no—
52Q8×C113—42no—
53D4×C113—42no—
54D4×C113—41no—
55D4×C113—41no—
56D4×C113—41no—
57D4×C113—41no—
58C2×C4×C113—22no—
59C2×C4×C113C2×D411yescharacteristic
60C2×C4×C113C2×D411yescharacteristic
61C2×C4×C113C2×D411yescharacteristic
62C2×Dic113—21no—
63C2×Dic113—21no—
64C2×Dic113—21no—
65D452—21no—
66D452SD1612yescomplemented
67C4×D113—41no—
68C4×D113—41no—
69C4×D113—82no—
70Dic226—21no—
71Dic226—21no—
72C8×C113—22no—
73#11744751—41no—
74#11744751—41no—
75C22×C113—81no—
76C22×C113—81no—
77C22×C113—81no—
78C22×C113#12011yescharacteristic
79C2×D113—22no—
80C2×D113—41no—
81C2×D113—41no—
82C4×C113—21no—
83C4×C113—42no—
84C4×C113C2×SD1611yescharacteristic
85C4×C113#13511yescharacteristic
86C4×C113AGL(1,ℤ/8)11yescharacteristic
87C4×C113#13711yescharacteristic
88Dic113—41no—
89Dic113—41no—
90Dic113—41no—
91C2×C113—161no—
92C2×C113#44811yescharacteristic
93C2×C113#44911yescharacteristic
94C2×C113#45311yescharacteristic
95D113—42no—
96#1622—1131nomaximal, Sylow
97C113#162211yescharacteristic, complemented, Sylow
98#554—1131no—
99#492D11311yescharacteristic, complemented
100#460—1131no—
101#459—1131no—
102#333—1131no—
103Q8⋊C8—1131no—
104D4⋊C8—1131no—
105C2×SD16—22no—
106C2×SD16—2261no—
107C2×D8—2261no—
108C4⋊Q8C2×D11311yescharacteristic
109#127C2×D11311yescharacteristic
110#125—2261no—
111C22⋊Q8—2261no—
112C22⋊Q8—2262no—
113C4×Q8—1131no—
114C4×D4—1131no—
115C4×D4—2261no—
116C2×C4⋊C4—2261no—
117C4⋊C8—1131no—
118C4⋊C8—1131no—
119#102—2261no—
120#102—2261no—
121C4×C8C2×D11311yescharacteristic
122C2×Q8—1131no—
123C2×Q8C22⋊D11312yes—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—1131no—
128C22×C4—2262no—
129C22×C4—2261no—
130SD16—44no—
131SD16—4522no—
132D8—4522no—
133C2×C8—21no—
134C2×C8—2261no—
135C2×C8—2261no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—1131no—
139C4⋊C4—1131no—
140C4⋊C4—2262no—
141C4⋊C4—2262no—
142C4⋊C4—2261no—
143C22⋊C4—2262no—
144C22⋊C4—2261no—
145C42—2261no—
146C42C22×D11311yescharacteristic
147C23—41no—
148C23—2261no—
149Q8—42no—
150Q8—2261no—
151Q8—2261no—
152D4—42no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—1132no—
158D4—2261no—
159C2×C4—22no—
160C2×C4—9042no—
161C2×C4—4521no—
162C2×C4—4521no—
163C2×C4—2261no—
164C2×C4—2261no—
165C2×C4—2261no—
166C2×C4D4×D11311yescharacteristic
167C2×C4D4×D11311yescharacteristic
168C2×C4C2×C22⋊D11311yescharacteristic
169C8—22no—
170C8—4521no—
171C8—4521no—
172C22—81no—
173C22—81no—
174C22—81no—
175C22—4521no—
176C22—4521no—
177C22—2262no—
178C22#1681359011yescharacteristic
179C4—21no—
180C4—42no—
181C4—4521no—
182C4—4521no—
183C4—4521no—
184C4SD16×D11311yescharacteristic
185C4#1681364311yescharacteristic
186C4#1681364911yescharacteristic
187C4#1681365111yescharacteristic
188C2—161no—
189C2—4522no—
190C2#2029873511yescharacteristic
191C2#2029874211yescharacteristic
192C2#2029876511yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#492×C113C2
socleC22×C113#120
prime radical#20298790C2
hypercenter#492D113
hypocenterC113#1622
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #20299309C2semidirect
2. #20298795C2semidirect
4. #20298347C2semidirect
5. #20298330C2semidirect
6. #20298327C2semidirect
7. #492×C113C2semidirect
66. D452SD16semidirect
97. C113#1622semidirect
99. #492D113semidirect

Maximal subgroups

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

subgroupindex
#202993092
#202987952
#202987902
#202983472
#202983302
#202983272
#492×C1132
#1622113