Finite Group Databasebeta

← #28406018

Subgroups — #28406018

Order 14464.

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

normal subgroups only

This group has 218 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#20299616C211yesmaximal, characteristic, complemented
2#20299543C211yesmaximal, characteristic, complemented
3#20299452C212yesmaximal, complemented
4#20299450C212yesmaximal
5#20299135C211yesmaximal, characteristic
6#16813689—21no—
7#16813679C2212yes—
8C4×#11744753—21no—
9(C2×#90673)⋊C4—21no—
10(C2×#90673)⋊C4—21no—
11(C2×#90673)⋊C4C2212yes—
12#16813617—21no—
13#16813613C411yescharacteristic, complemented
14#16813611C411yescharacteristic, complemented
15#16813607—21no—
16#16813598C2211yescharacteristic
17#16813597C2211yescharacteristic
18C4×D452—21no—
19C4×D452C411yescharacteristic, complemented
20#16813579—21no—
21C42×D113C2211yescharacteristic
22C4×Q8×C113C411yescharacteristic, complemented
23C22×#90673—22no—
24C2×#11744753—22no—
25C2×D452—21no—
26C2×D452C2×C411yescharacteristic
27C2×C4×D113—21no—
28C2×C4×D113D411yescharacteristic
29C2×C4×D113D411yescharacteristic
30C2×C4×D113C2311yescharacteristic
31C4⋊Dic113—21no—
32C4⋊Dic113C2×C411yescharacteristic
33#14268626—21no—
34#14268626—21no—
35#14268624—21no—
36#14268624—21no—
37#14268624—21no—
38#14268624—21no—
39#14268624—21no—
40C4×Dic113C2×C411yescharacteristic
41C4×Dic113D411yescharacteristic
42C4×Dic113D411yescharacteristic
43C2×Q8×C113C2×C411yescharacteristic
44C4⋊C4×C113—21no—
45C4⋊C4×C113C2×C411yescharacteristic
46C42×C113—21no—
47C42×C113C2×C411yescharacteristic
48C22×D113—21no—
49C22×D113C2×D411yescharacteristic
50C2×#90673—42no—
51C2×#90673—42no—
52C2×#90673—42no—
53Q8×C113—41no—
54C2×C4×C113—21no—
55C2×C4×C113—21no—
56C2×C4×C113C22⋊C411yescharacteristic
57C2×C4×C113C22⋊C411yescharacteristic
58C2×C4×C113C22×C411yescharacteristic
59C2×Dic113—21no—
60C2×Dic113C22⋊C411yescharacteristic
61C2×Dic113C22⋊C411yescharacteristic
62C2×Dic113C2×D411yescharacteristic
63D452—41no—
64D452—42no—
65C4×D113—22no—
66C4×D113—41no—
67C4×D113—41no—
68C4×D113—42no—
69#11744753—42no—
70C22×C113C2×C22⋊C411yescharacteristic
71C2×D113—21no—
72C2×D113—21no—
73C2×D113—41no—
74C2×D113—41no—
75C2×D113—41no—
76C2×D113#13512yes—
77#90673—82no—
78C4×C113—21no—
79C4×C113—21no—
80C4×C113—21no—
81C4×C113—41no—
82C4×C113—41no—
83Dic113—21no—
84Dic113—21no—
85Dic113—21no—
86Dic113—41no—
87C2×C113#41011yescharacteristic
88C2×C113#41611yescharacteristic
89C2×C113#42111yescharacteristic
90D113—22no—
91D113—81no—
92#1521—1131nomaximal, Sylow
93C113#152111yescharacteristic, complemented, Sylow
94#529—1131no—
95#431—1131no—
96#383—1131no—
97#328—1132no—
98#327—1132no—
99#126—2261no—
100#125—1131no—
101#124—1131no—
102#123—2261no—
103C22⋊Q8—1131no—
104#121—1131no—
105C4×Q8#9067311yescharacteristic, complemented
106C4×D4—1131no—
107C4×D4—2261no—
108#117—2261no—
109C2×C42—1131no—
110C4⋊C8—2261no—
111C22⋊C8—1132no—
112C4×C8—2261no—
113#95—1132no—
114#95—2261no—
115#95—2261no—
116C2×Q8C2×#9067311yescharacteristic
117C2×D4—1131no—
118C2×D4—2261no—
119C22×C4—1131no—
120C22×C4—1131no—
121C22×C4—1131no—
122C22×C4—2262no—
123C22×C4—2261no—
124C2×C8—2262no—
125C4⋊C4—21no—
126C4⋊C4—1131no—
127C4⋊C4—2261no—
128C4⋊C4—2261no—
129C4⋊C4—2261no—
130C4⋊C4C2×#9067311yescharacteristic
131C22⋊C4—2261no—
132C22⋊C4—2261no—
133C22⋊C4—2261no—
134C22⋊C4—2261no—
135C22⋊C4—2261no—
136C42—21no—
137C42—1131no—
138C42—1131no—
139C42—1131no—
140C42C2×#9067311yescharacteristic
141C23—1131no—
142C23—2261no—
143Q8—41no—
144D4—4521no—
145D4—4522no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—1131no—
149C2×C4—1131no—
150C2×C4—1131no—
151C2×C4—4522no—
152C2×C4—4521no—
153C2×C4—4521no—
154C2×C4—4522no—
155C2×C4—4522no—
156C2×C4—4522no—
157C2×C4—2262no—
158C2×C4—2261no—
159C2×C4C22⋊#9067311yescharacteristic
160C2×C4C22⋊#9067311yescharacteristic
161C2×C4C22×#9067311yescharacteristic
162C8—4522no—
163C22—1132no—
164C22—4521no—
165C22—4521no—
166C22—4521no—
167C22—2261no—
168C22—2261no—
169C22C2×C22⋊#9067311yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—41no—
174C4—41no—
175C4—9042no—
176C4—4521no—
177C4—2261no—
178C4—2261no—
179C4—2261no—
180C2—9041no—
181C2—2262no—
182C2#2029957711yescharacteristic
183C2#2029958811yescharacteristic
184C2#2029959711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC4×Q8×C113C4
socleC22×C113C2×C22⋊C4
prime radical#16813597C22
cosocleC2×C4×D113C23
hypercenterC4×Q8#90673
hypocenterC113#1521
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. #20299616C2semidirect
2. #20299543C2semidirect
3. #20299452C2semidirect
13. #16813613C4semidirect
14. #16813611C4semidirect
19. C4×D452C4semidirect
22. C4×Q8×C113C4semidirect
93. C113#1521semidirect
105. C4×Q8#90673semidirect

Maximal subgroups

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

subgroupindex
#202996162
#202995432
#202994522
#202994502
#202991352
#1521113