Finite Group Databasebeta

← #28406003

Subgroups — #28406003

Order 14464.

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

normal subgroups only

This group has 264 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, complemented
2#20299542C211yesmaximal, characteristic, complemented
3#20299449C214yesmaximal, complemented
4#20299146C211yesmaximal, characteristic
5C2×C4⋊#90673—21no—
6#16813689—21no—
7#16813679C2212yes—
8C4×#11744753—21no—
9(C2×#90673)⋊C4—21no—
10(C2×#90673)⋊C4C2212yes—
11C2×#14268646—21no—
12#16813622C411yescharacteristic, complemented
13#16813609—21no—
14#16813593—21no—
15#16813593C2212yes—
16D4×Dic113—21no—
17D4×Dic113C412yescomplemented
18C42×D113C2211yescharacteristic
19#127×C113C411yescharacteristic, complemented
20C22×#90673—22no—
21C2×#11744753—22no—
22C4⋊#90673—42no—
23#14268646—42no—
24#14268646—42no—
25C2×Dic226—21no—
26C2×C22⋊D113—22no—
27C22×Dic113—22no—
28C2×C4×D113D411yescharacteristic
29C2×C4×D113D411yescharacteristic
30C2×C4×D113C2311yescharacteristic
31C4⋊Dic113—21no—
32C4⋊Dic113C2×C412yes—
33C22⋊Dic113—22no—
34C22⋊Dic113—22no—
35C4×Dic113C2×C411yescharacteristic
36C4×Dic113D411yescharacteristic
37C4×Dic113D411yescharacteristic
38C2×D4×C113—21no—
39C2×D4×C113—21no—
40C2×D4×C113C2×C412yes—
41C42×C113C2×C411yescharacteristic
42C23×C113—22no—
43C22×D113C2×D411yescharacteristic
44C2×#90673—42no—
45C2×#90673—42no—
46C2×#90673—42no—
47D4×C113—42no—
48D4×C113—42no—
49D4×C113—42no—
50C2×C4×C113C22⋊C411yescharacteristic
51C2×C4×C113C22⋊C411yescharacteristic
52C2×C4×C113C22×C411yescharacteristic
53C22⋊D113—42no—
54C22⋊D113—42no—
55C2×Dic113—22no—
56C2×Dic113—44no—
57C2×Dic113C22⋊C411yescharacteristic
58C2×Dic113C22⋊C411yescharacteristic
59C2×Dic113C2×D411yescharacteristic
60C4×D113—41no—
61C4×D113—41no—
62C4×D113D812yes—
63C4×D113SD1612yes—
64Dic226—42no—
65#11744753—42no—
66C22×C113—42no—
67C22×C113—42no—
68C22×C113—42no—
69C22×C113C2×C22⋊C411yescharacteristic
70C2×D113—21no—
71C2×D113—21no—
72C2×D113C2×D811yescharacteristic
73C2×D113C2×SD1611yescharacteristic
74#90673—82no—
75C4×C113—21no—
76C4×C113—21no—
77C4×C113#10212yes—
78Dic113—21no—
79Dic113—21no—
80Dic113—42no—
81Dic113#10212yes—
82C2×C113—82no—
83C2×C113#41011yescharacteristic
84C2×C113C2×#10211yescharacteristic
85C2×C113#42111yescharacteristic
86D113—21no—
87D113—21no—
88#1517—1131nomaximal, Sylow
89C113#151711yescharacteristic, complemented, Sylow
90#532—1131no—
91#431—1131no—
92#382—1131no—
93#327—1134no—
94C2×#41—2261no—
95C4⋊Q8—1131no—
96#127#9067311yescharacteristic, complemented
97#124—2261no—
98#121—1132no—
99#121—2261no—
100C4×D4—1132no—
101C4×D4—2261no—
102C2×C4⋊C4—2261no—
103C2×C42—1131no—
104C4⋊C8—2261no—
105C22⋊C8—1132no—
106C4×C8—2261no—
107#95—1132no—
108#95—2261no—
109#41—4522no—
110#41—4522no—
111C2×Q8—2261no—
112C2×D4—21no—
113C2×D4—21no—
114C2×D4—2262no—
115C2×D4C2×#9067312yes—
116C22×C4—1131no—
117C22×C4—1131no—
118C22×C4—1131no—
119C22×C4—2262no—
120C22×C4—2262no—
121C2×C8—2262no—
122C4⋊C4—1132no—
123C4⋊C4—4522no—
124C4⋊C4—2261no—
125C22⋊C4—2262no—
126C22⋊C4—2262no—
127C42—1131no—
128C42—1131no—
129C42—1131no—
130C42C2×#9067311yescharacteristic
131C23—22no—
132C23—1131no—
133Q8—4522no—
134D4—42no—
135D4—42no—
136D4—42no—
137D4—4522no—
138D4—4522no—
139C2×C4—1131no—
140C2×C4—1132no—
141C2×C4—1132no—
142C2×C4—1131no—
143C2×C4—1131no—
144C2×C4—4521no—
145C2×C4—4521no—
146C2×C4—4524no—
147C2×C4—4522no—
148C2×C4—4522no—
149C2×C4—4522no—
150C2×C4—2262no—
151C2×C4C22⋊#9067311yescharacteristic
152C2×C4C22⋊#9067311yescharacteristic
153C2×C4C22×#9067311yescharacteristic
154C8—4522no—
155C22—42no—
156C22—42no—
157C22—42no—
158C22—1131no—
159C22—1131no—
160C22—2261no—
161C22—2261no—
162C22C2×C22⋊#9067311yescharacteristic
163C4—21no—
164C4—21no—
165C4—1132no—
166C4—9042no—
167C4—4522no—
168C4—2261no—
169C4—2261no—
170C4#1681368412yes—
171C2—82no—
172C2—2261no—
173C2—2261no—
174C2#2029957811yescharacteristic
175C2C2×#1681368411yescharacteristic
176C2#2029959611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#127×C113C4
socleC22×C113C2×C22⋊C4
prime radical#20299146C2
cosocleC2×C4×D113C23
hypercenter#127#90673
hypocenterC113#1517
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #20299616C2semidirect
2. #20299542C2semidirect
3. #20299449C2semidirect
12. #16813622C4semidirect
17. D4×Dic113C4semidirect
19. #127×C113C4semidirect
89. C113#1517semidirect
96. #127#90673semidirect

Maximal subgroups

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

subgroupindex
#202996162
#202995422
#202994492
#202991462
#1517113