Finite Group Databasebeta

← #28405448

Subgroups — #28405448

Order 14464.

276 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 60 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#20299566C211yesmaximal, characteristic
2#20299540C211yesmaximal, characteristic
3#95×D113C211yesmaximal, characteristic
4C2×#14268655—21no—
5C2×C4⋊#90673C412yescomplemented
6C2×C22⋊#90673—21no—
7#16813679C412yescomplemented
8C22⋊#11744753—21no—
9(C2×#90673)⋊C4—21no—
10C22×C4×D113—21no—
11C22×C4×D113C2211yescharacteristic
12#16813529—21no—
13#16813529C411yescharacteristic, complemented
14#95×C113C411yescharacteristic, complemented
15C22×#90673—22no—
16#14268655—42no—
17C2×#11744753—22no—
18C4⋊#90673—42no—
19C22⋊#90673—41no—
20C22⋊#90673—41no—
21C23×D113D411yescharacteristic
22C22×Dic113—21no—
23C22×Dic113D411yescharacteristic
24C2×C4×D113—24no—
25C2×C4×D113—42no—
26C2×C4×D113—42no—
27C2×C4×D113—41no—
28C2×C4×D113—41no—
29C2×C4×D113C2×C411yescharacteristic
30C2×C4×D113C2×C411yescharacteristic
31C2×C4×D113D411yescharacteristic
32C2×C4×D113Q811yescharacteristic
33C22×C4×C113—21no—
34C22×C4×C113C2×C411yescharacteristic
35C23×C113C22⋊C411yescharacteristic
36C22×D113—22no—
37C22×D113—22no—
38C22×D113C22⋊C411yescharacteristic
39C22×D113C4⋊C411yescharacteristic
40C22×D113D811yescharacteristic
41C22×D113SD1611yescharacteristic
42C22×D113SD1611yescharacteristic
43C22×D113Q1611yescharacteristic
44C2×#90673—42no—
45C2×#90673—42no—
46C2×#90673—42no—
47C2×C4×C113—22no—
48C2×C4×C113—41no—
49C2×C4×C113—41no—
50C2×C4×C113—41no—
51C2×C4×C113C4211yescharacteristic
52C2×C4×C113C4⋊C411yescharacteristic
53C2×Dic113—22no—
54C2×Dic113—41no—
55C2×Dic113—41no—
56C2×Dic113—41no—
57C2×Dic113C22⋊C411yescharacteristic
58C2×Dic113C4⋊C411yescharacteristic
59C4×D113—22no—
60C4×D113—22no—
61C4×D113—41no—
62C4×D113—41no—
63C4×D113—44no—
64C4×D113—44no—
65#11744753—42no—
66C22×C113—21no—
67C22×C113—21no—
68C22×C113#9511yescharacteristic
69C22×C113#10211yescharacteristic
70C22×C113#10311yescharacteristic
71C2×D113—21no—
72C2×D113—21no—
73C2×D113—22no—
74C2×D113—22no—
75C2×D113—22no—
76C2×D113—22no—
77C2×D113#9912yes—
78C2×D113#10211yescharacteristic
79C2×D113#10311yescharacteristic
80C2×D113#10412yes—
81C2×D113#10611yescharacteristic
82C2×D113#10711yescharacteristic
83#90673—82no—
84C4×C113—21no—
85C4×C113—21no—
86C4×C113—42no—
87Dic113—21no—
88Dic113—21no—
89Dic113—42no—
90C2×C113—21no—
91C2×C113—21no—
92C2×C113#33911yescharacteristic
93C2×C113#34011yescharacteristic
94C2×C113#34211yescharacteristic
95D113—21no—
96D113—21no—
97D113#32712yes—
98D113#32812yes—
99#1294—1131nomaximal, Sylow
100C113#129411yescharacteristic, complemented, Sylow
101C2×C22⋊C8—1131no—
102#380—1131no—
103C2×#95—1131no—
104C23×C4—1131no—
105C23×C4—2261no—
106C22×C8—2261no—
107C2×C4⋊C4—1132no—
108C2×C22⋊C4—2261no—
109C22⋊C8—1132no—
110C22⋊C8—2261no—
111#95—1131no—
112#95—2261no—
113#95—2261no—
114#95#9067311yescharacteristic, complemented
115C24—1131no—
116C22×C4—21no—
117C22×C4—1131no—
118C22×C4—1131no—
119C22×C4—1131no—
120C22×C4—1131no—
121C22×C4—1131no—
122C22×C4—4521no—
123C22×C4—4521no—
124C22×C4—4522no—
125C22×C4—4522no—
126C22×C4—2264no—
127C22×C4—2262no—
128C22×C4—2261no—
129C22×C4C2×#9067311yescharacteristic
130C2×C8—4522no—
131C2×C8—2262no—
132C4⋊C4—4522no—
133C22⋊C4—4521no—
134C22⋊C4—4521no—
135C23—1131no—
136C23—1131no—
137C23—1131no—
138C23—1131no—
139C23—1131no—
140C23—1131no—
141C23—2262no—
142C23—2262no—
143C23C22⋊#9067311yescharacteristic
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—1131no—
149C2×C4—1131no—
150C2×C4—4521no—
151C2×C4—4521no—
152C2×C4—4524no—
153C2×C4—4524no—
154C2×C4—4522no—
155C2×C4—4522no—
156C2×C4—4522no—
157C2×C4—4521no—
158C2×C4—4521no—
159C2×C4—4521no—
160C2×C4—2262no—
161C2×C4—2262no—
162C2×C4—2262no—
163C2×C4C4×#9067311yescharacteristic
164C2×C4C4⋊#9067311yescharacteristic
165C8—4522no—
166C22—21no—
167C22—21no—
168C22—1132no—
169C22—1131no—
170C22—1131no—
171C22—1132no—
172C22—1131no—
173C22—1131no—
174C22—2262no—
175C22—2262no—
176C22—2262no—
177C22—2262no—
178C22—2261no—
179C22—2261no—
180C22(C2×#90673)⋊C411yescharacteristic
181C22#1681368411yescharacteristic
182C22#1681368511yescharacteristic
183C4—21no—
184C4—21no—
185C4—42no—
186C4—9042no—
187C4—4522no—
188C4—2261no—
189C4—2261no—
190C2—21no—
191C2—21no—
192C2—1132no—
193C2—1132no—
194C2—2261no—
195C2—2261no—
196C2#2029946911yescharacteristic
197C2#2029947111yescharacteristic
198C2#2029947511yescharacteristic
subgroupG/H
centerC22(C2×#90673)⋊C4
commutatorC2×C4×C113C42
FrattiniC22×C4C2×#90673
Fitting#95×C113C4
socleC22×C113#95
prime radicalC23×D113D4
cosocleC22×C4×D113C22
hypercenter#95#90673
hypocenterC113#1294
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
5. C2×C4⋊#90673C4semidirect
7. #16813679C4semidirect
13. #16813529C4semidirect
14. #95×C113C4semidirect
100. C113#1294semidirect
114. #95#90673semidirect

Maximal subgroups

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

subgroupindex
#202995662
#202995402
#95×D1132
#1294113