Finite Group Databasebeta

← #28406006

Subgroups — #28406006

Order 14464.

220 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 66 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#20299616C211yesmaximal, characteristic
2#20299542C211yesmaximal, characteristic
3#20299451C214yesmaximal
4#20299153C211yesmaximal, characteristic
5C2×C4⋊#90673—21no—
6#16813689—21no—
7#16813679C2212yes—
8C4×#11744753—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—
22C4⋊#90673—42no—
23C2×Dic226C2×C412yes—
24C2×C4×D113D411yescharacteristic
25C2×C4×D113D411yescharacteristic
26C2×C4×D113C2311yescharacteristic
27C4⋊Dic113—21no—
28C4⋊Dic113—21no—
29C4⋊Dic113—22no—
30#14268626—22no—
31#14268624—22no—
32C4×Dic113—22no—
33C4×Dic113C2×C411yescharacteristic
34C4×Dic113D411yescharacteristic
35C4×Dic113D411yescharacteristic
36C2×Q8×C113—21no—
37C4⋊C4×C113—21no—
38C4⋊C4×C113C2×C412yes—
39C42×C113C2×C411yescharacteristic
40C22×D113C2×D411yescharacteristic
41C2×#90673—42no—
42C2×#90673—42no—
43C2×#90673—42no—
44Q8×C113—42no—
45C2×C4×C113—22no—
46C2×C4×C113C22⋊C411yescharacteristic
47C2×C4×C113C22⋊C411yescharacteristic
48C2×C4×C113C22×C411yescharacteristic
49C2×Dic113—22no—
50C2×Dic113C22⋊C411yescharacteristic
51C2×Dic113C22⋊C411yescharacteristic
52C2×Dic113C2×D411yescharacteristic
53C4×D113—41no—
54C4×D113—41no—
55C4×D113SD1612yes—
56C4×D113Q1612yes—
57Dic226—42no—
58#11744753—42no—
59C22×C113C2×C22⋊C411yescharacteristic
60C2×D113—21no—
61C2×D113—21no—
62C2×D113C2×SD1611yescharacteristic
63C2×D113C2×Q1611yescharacteristic
64#90673—82no—
65C4×C113—21no—
66C4×C113—21no—
67C4×C113—42no—
68C4×C113#10312yes—
69Dic113—21no—
70Dic113—21no—
71Dic113—42no—
72Dic113#10312yes—
73C2×C113#41011yescharacteristic
74C2×C113C2×#10311yescharacteristic
75C2×C113#42111yescharacteristic
76D113—21no—
77D113—21no—
78#1518—1131nomaximal, Sylow
79C113#151811yescharacteristic, complemented, Sylow
80#533—1131no—
81#431—1131no—
82#382—1131no—
83#328—1134no—
84C4⋊Q8—1131no—
85C4⋊Q8#9067311yescharacteristic, complemented
86#125—2261no—
87C22⋊Q8—1132no—
88C22⋊Q8—2261no—
89C4×Q8—1132no—
90C4×Q8—2261no—
91#117—2261no—
92C2×C4⋊C4—2261no—
93C2×C42—1131no—
94C4⋊C8—2261no—
95C22⋊C8—1132no—
96C4×C8—2261no—
97#95—1132no—
98#95—2261no—
99C2×Q8—21no—
100C2×Q8—1132no—
101C22×C4—1131no—
102C22×C4—1131no—
103C22×C4—1131no—
104C22×C4—2262no—
105C2×C8—2262no—
106C4⋊C4—21no—
107C4⋊C4—4522no—
108C4⋊C4—2262no—
109C4⋊C4—2262no—
110C4⋊C4—2261no—
111C4⋊C4—2261no—
112C4⋊C4C2×#9067312yes—
113C22⋊C4—2262no—
114C42—1131no—
115C42—1131no—
116C42—1131no—
117C42—2262no—
118C42C2×#9067311yescharacteristic
119C23—1131no—
120Q8—42no—
121Q8—4522no—
122C2×C4—22no—
123C2×C4—1131no—
124C2×C4—1132no—
125C2×C4—1132no—
126C2×C4—1131no—
127C2×C4—1131no—
128C2×C4—4521no—
129C2×C4—4521no—
130C2×C4—4522no—
131C2×C4—4522no—
132C2×C4—4522no—
133C2×C4—2262no—
134C2×C4C22⋊#9067311yescharacteristic
135C2×C4C22⋊#9067311yescharacteristic
136C2×C4C22×#9067311yescharacteristic
137C8—4522no—
138C22—1131no—
139C22—1131no—
140C22—2261no—
141C22—2261no—
142C22C2×C22⋊#9067311yescharacteristic
143C4—21no—
144C4—21no—
145C4—42no—
146C4—1132no—
147C4—9042no—
148C4—4522no—
149C4—2261no—
150C4—2261no—
151C4#1681368512yes—
152C2—2261no—
153C2—2261no—
154C2#2029957911yescharacteristic
155C2C2×#1681368511yescharacteristic
156C2#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#1518
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
79. C113#1518semidirect
85. C4⋊Q8#90673semidirect

Maximal subgroups

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

subgroupindex
#202996162
#202995422
#202994512
#202991532
#1518113