Finite Group Databasebeta

← #28405997

Subgroups — #28405997

Order 14464.

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

normal subgroups only

This group has 208 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
2#20299543C211yesmaximal, characteristic
3#20299451C214yesmaximal
4#20299153C211yesmaximal, characteristic
5#16813689—21no—
6#16813679C2212yes—
7#16813677—21no—
8(C2×#90673)⋊C4—21no—
9(C2×#90673)⋊C4—21no—
10(C2×#90673)⋊C4C2212yes—
11#16813622C411yescharacteristic, complemented
12#16813613—21no—
13#16813602C2212yes—
14#16813598—21no—
15Q8×Dic113—21no—
16#16813587C412yescomplemented
17#16813580—21no—
18C42×D113C2211yescharacteristic
19C4⋊Q8×C113C411yescharacteristic, complemented
20C22×#90673—22no—
21C2×#11744753—22no—
22C2×Dic226C2×C412yes—
23C2×C4×D113D411yescharacteristic
24C2×C4×D113D411yescharacteristic
25C2×C4×D113C2311yescharacteristic
26C4⋊Dic113—21no—
27C4⋊Dic113—21no—
28C4⋊Dic113—22no—
29#14268626—22no—
30#14268624—22no—
31C4×Dic113—22no—
32C4×Dic113C2×C411yescharacteristic
33C4×Dic113D411yescharacteristic
34C4×Dic113D411yescharacteristic
35C2×Q8×C113—21no—
36C4⋊C4×C113—21no—
37C4⋊C4×C113C2×C412yes—
38C42×C113C2×C411yescharacteristic
39C22×D113C2×D411yescharacteristic
40C2×#90673—42no—
41C2×#90673—42no—
42C2×#90673—42no—
43Q8×C113—42no—
44C2×C4×C113—22no—
45C2×C4×C113C22⋊C411yescharacteristic
46C2×C4×C113C22⋊C411yescharacteristic
47C2×C4×C113C22×C411yescharacteristic
48C2×Dic113—22no—
49C2×Dic113C22⋊C411yescharacteristic
50C2×Dic113C22⋊C411yescharacteristic
51C2×Dic113C2×D411yescharacteristic
52C4×D113—22no—
53C4×D113—41no—
54C4×D113—41no—
55Dic226—42no—
56#11744753—42no—
57C22×C113C2×C22⋊C411yescharacteristic
58C2×D113—21no—
59C2×D113—21no—
60C2×D113#13712yes—
61#90673—82no—
62C4×C113—21no—
63C4×C113—21no—
64C4×C113—21no—
65C4×C113—42no—
66Dic113—21no—
67Dic113—21no—
68Dic113—21no—
69Dic113—42no—
70C2×C113#41011yescharacteristic
71C2×C113#41911yescharacteristic
72C2×C113#42111yescharacteristic
73D113—22no—
74#1515—1131nomaximal, Sylow
75C113#151511yescharacteristic, complemented, Sylow
76#533—1131no—
77#432—1131no—
78#383—1131no—
79#328—1134no—
80C4⋊Q8—1131no—
81C4⋊Q8#9067311yescharacteristic, complemented
82#125—2261no—
83C22⋊Q8—1132no—
84C22⋊Q8—2261no—
85C4×Q8—1132no—
86C4×Q8—2261no—
87#117—2261no—
88C2×C42—1131no—
89C4⋊C8—2261no—
90C22⋊C8—1132no—
91#97—2261no—
92#95—1132no—
93#95—2261no—
94#95—2261no—
95C2×Q8—21no—
96C2×Q8—1132no—
97C22×C4—1131no—
98C22×C4—1131no—
99C22×C4—1131no—
100C22×C4—2262no—
101C2×C8—2262no—
102C4⋊C4—21no—
103C4⋊C4—2262no—
104C4⋊C4—2262no—
105C4⋊C4—2261no—
106C4⋊C4—2261no—
107C4⋊C4C2×#9067312yes—
108C22⋊C4—2262no—
109C42—1131no—
110C42—1131no—
111C42—1131no—
112C42—2262no—
113C42C2×#9067311yescharacteristic
114C23—1131no—
115Q8—42no—
116Q8—4522no—
117C2×C4—22no—
118C2×C4—1131no—
119C2×C4—1131no—
120C2×C4—1131no—
121C2×C4—4521no—
122C2×C4—4521no—
123C2×C4—4522no—
124C2×C4—4522no—
125C2×C4—4522no—
126C2×C4—2262no—
127C2×C4—2262no—
128C2×C4C22⋊#9067311yescharacteristic
129C2×C4C22⋊#9067311yescharacteristic
130C2×C4C22×#9067311yescharacteristic
131C8—4522no—
132C22—1132no—
133C22—2261no—
134C22—2261no—
135C22C2×C22⋊#9067311yescharacteristic
136C4—21no—
137C4—21no—
138C4—21no—
139C4—42no—
140C4—9042no—
141C4—4522no—
142C4—2261no—
143C4—2261no—
144C4—2261no—
145C2—2262no—
146C2#2029957911yescharacteristic
147C2#2029959111yescharacteristic
148C2#2029959611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC4⋊Q8×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC22×D113C2×D4
cosocleC2×C4×D113C23
hypercenterC4⋊Q8#90673
hypocenterC113#1515
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
11. #16813622C4semidirect
16. #16813587C4semidirect
19. C4⋊Q8×C113C4semidirect
75. C113#1515semidirect
81. 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
#202994512
#202991532
#1515113