Finite Group Databasebeta

← #28405995

Subgroups — #28405995

Order 14464.

252 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 56 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#20299621C211yesmaximal, characteristic, complemented
2#20299543C211yesmaximal, characteristic, complemented
3#20299450C214yesmaximal, complemented
4#20299149C211yesmaximal, characteristic
5#16813689—21no—
6#16813679C2212yes—
7#16813677—21no—
8(C2×#90673)⋊C4—21no—
9(C2×#90673)⋊C4—21no—
10(C2×#90673)⋊C4C2212yes—
11C2×#14268648—21no—
12#16813619C411yescharacteristic, complemented
13#16813611—21no—
14#16813597—21no—
15#16813597C2212yes—
16#16813584—21no—
17#16813584C412yescomplemented
18C42×D113C2211yescharacteristic
19C4⋊Q8×C113C411yescharacteristic, complemented
20C22×#90673—22no—
21C2×#11744753—22no—
22#14268648—44no—
23C2×D452—22no—
24C2×D452—21no—
25C2×D452—21no—
26C2×D452C2×C412yes—
27C2×C4×D113—22no—
28C2×C4×D113D411yescharacteristic
29C2×C4×D113D411yescharacteristic
30C2×C4×D113C2311yescharacteristic
31#14268624—22no—
32#14268624—22no—
33C4×Dic113C2×C411yescharacteristic
34C4×Dic113D411yescharacteristic
35C4×Dic113D411yescharacteristic
36C2×Q8×C113—21no—
37C4⋊C4×C113—21no—
38C4⋊C4×C113C2×C412yes—
39C42×C113C2×C411yescharacteristic
40C22×D113—22no—
41C22×D113C2×D411yescharacteristic
42C2×#90673—42no—
43C2×#90673—42no—
44C2×#90673—42no—
45Q8×C113—42no—
46C2×C4×C113—22no—
47C2×C4×C113C22⋊C411yescharacteristic
48C2×C4×C113C22⋊C411yescharacteristic
49C2×C4×C113C22×C411yescharacteristic
50C2×Dic113C22⋊C411yescharacteristic
51C2×Dic113C22⋊C411yescharacteristic
52C2×Dic113C2×D411yescharacteristic
53D452—42no—
54D452—42no—
55D452—42no—
56D452—44no—
57C4×D113—22no—
58C4×D113—41no—
59C4×D113—41no—
60C4×D113—44no—
61#11744753—42no—
62C22×C113C2×C22⋊C411yescharacteristic
63C2×D113—21no—
64C2×D113—21no—
65C2×D113—42no—
66C2×D113—42no—
67C2×D113—42no—
68C2×D113AGL(1,ℤ/8)12yes—
69#90673—82no—
70C4×C113—21no—
71C4×C113—21no—
72C4×C113—21no—
73C4×C113—42no—
74Dic113—21no—
75Dic113—21no—
76Dic113—21no—
77C2×C113#41011yescharacteristic
78C2×C113#41811yescharacteristic
79C2×C113#42111yescharacteristic
80D113—22no—
81D113—82no—
82#1514—1131nomaximal, Sylow
83C113#151411yescharacteristic, complemented, Sylow
84#532—1131no—
85#432—1131no—
86#383—1131no—
87#327—1134no—
88C2×#41—2261no—
89C4⋊Q8#9067311yescharacteristic, complemented
90#127—1131no—
91#124—2261no—
92#121—1132no—
93#121—2261no—
94C4×D4—1132no—
95C4×D4—2261no—
96C2×C42—1131no—
97C4⋊C8—2261no—
98C22⋊C8—1132no—
99#97—2261no—
100#95—1132no—
101#95—2261no—
102#95—2261no—
103#41—4524no—
104C2×Q8—21no—
105C2×D4—1132no—
106C2×D4—2262no—
107C2×D4—2261no—
108C2×D4—2261no—
109C22×C4—1131no—
110C22×C4—1131no—
111C22×C4—1131no—
112C22×C4—2262no—
113C22×C4—2262no—
114C2×C8—2262no—
115C4⋊C4—21no—
116C4⋊C4C2×#9067312yes—
117C22⋊C4—2262no—
118C22⋊C4—2262no—
119C42—1131no—
120C42—1131no—
121C42—1131no—
122C42C2×#9067311yescharacteristic
123C23—1131no—
124C23—2262no—
125Q8—42no—
126D4—4522no—
127D4—4522no—
128D4—4522no—
129D4—4524no—
130C2×C4—22no—
131C2×C4—1131no—
132C2×C4—1131no—
133C2×C4—1131no—
134C2×C4—4521no—
135C2×C4—4521no—
136C2×C4—4524no—
137C2×C4—4522no—
138C2×C4—4522no—
139C2×C4—4522no—
140C2×C4—2262no—
141C2×C4C22⋊#9067311yescharacteristic
142C2×C4C22⋊#9067311yescharacteristic
143C2×C4C22×#9067311yescharacteristic
144C8—4522no—
145C22—1132no—
146C22—4522no—
147C22—4522no—
148C22—4522no—
149C22—2261no—
150C22—2261no—
151C22C2×C22⋊#9067311yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—42no—
156C4—9042no—
157C4—2261no—
158C4—2261no—
159C4—2261no—
160C2—9042no—
161C2—2262no—
162C2#2029957911yescharacteristic
163C2#2029959011yescharacteristic
164C2#2029959711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC4⋊Q8×C113C4
socleC22×C113C2×C22⋊C4
prime radical#20299149C2
cosocleC2×C4×D113C23
hypercenterC4⋊Q8#90673
hypocenterC113#1514
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
1. #20299621C2semidirect
2. #20299543C2semidirect
3. #20299450C2semidirect
12. #16813619C4semidirect
17. #16813584C4semidirect
19. C4⋊Q8×C113C4semidirect
83. C113#1514semidirect
89. C4⋊Q8#90673semidirect

Maximal subgroups

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

subgroupindex
#202996212
#202995432
#202994502
#202991492
#1514113