Finite Group Databasebeta

← #28406072

Subgroups — #28406072

Order 14464.

256 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 68 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#20299615C211yesmaximal, characteristic, complemented
2C2×#16813689C211yesmaximal, characteristic, complemented
3#20299457C212yesmaximal, complemented
4#20299456C212yesmaximal, complemented
5#20299143C211yesmaximal, characteristic
6C22×#11744753—21no—
7#16813689—21no—
8#16813689C2212yes—
9#16813689C2212yes—
10C22⋊#11744753—21no—
11C4×#11744753—21no—
12C2×#14268646—21no—
13#16813621C2211yescharacteristic
14#16813618C2211yescharacteristic
15#16813608—21no—
16#16813596C411yescharacteristic
17#16813594—21no—
18D4×Dic113C411yescharacteristic
19#16813584C411yescharacteristic
20#16813582—21no—
21C2×C4×Dic113C2211yescharacteristic
22#121×C113C411yescharacteristic
23C2×#11744753—22no—
24C2×#11744753—22no—
25C2×#11744753—42no—
26#14268646—42no—
27#14268646—42no—
28C2×Dic226—21no—
29C2×D452C2×C411yescharacteristic
30C2×C22⋊D113—21no—
31C2×C22⋊D113—21no—
32C2×C22⋊D113—21no—
33C22×Dic113—21no—
34C22×Dic113D411yescharacteristic
35C22×Dic113D411yescharacteristic
36C2×C4×D113—21no—
37C4⋊Dic113C2×C411yescharacteristic
38#14268626—21no—
39C22⋊Dic113—21no—
40#14268624—21no—
41#14268624—21no—
42C4×Dic113C2×C411yescharacteristic
43C4×Dic113D411yescharacteristic
44C4×Dic113D411yescharacteristic
45C4×Dic113C2311yescharacteristic
46C2×D4×C113—21no—
47C2×D4×C113C2×C411yescharacteristic
48C22×C4×C113C2×C411yescharacteristic
49C4⋊C4×C113C2×C411yescharacteristic
50C22⋊C4×C113—21no—
51C23×C113—21no—
52C23×C113C22⋊C411yescharacteristic
53C22×D113—21no—
54D4×C113—41no—
55D4×C113—42no—
56C2×C4×C113—21no—
57C2×C4×C113—41no—
58C2×C4×C113C22⋊C411yescharacteristic
59C2×C4×C113C22×C411yescharacteristic
60C22⋊D113—42no—
61C22⋊D113—41no—
62C22⋊D113—41no—
63C22⋊D113—42no—
64C2×Dic113—22no—
65C2×Dic113—21no—
66C2×Dic113—42no—
67C2×Dic113C22⋊C411yescharacteristic
68C2×Dic113C22⋊C411yescharacteristic
69C2×Dic113D812yes—
70C2×Dic113SD1612yes—
71C2×Dic113C2×D411yescharacteristic
72C2×Dic113C2×D411yescharacteristic
73D452—41no—
74C4×D113—42no—
75Dic226—41no—
76Dic226—41no—
77#11744753—42no—
78#11744753—42no—
79C22×C113—21no—
80C22×C113—21no—
81C22×C113—41no—
82C22×C113—41no—
83C22×C113—41no—
84C22×C113#10212yes—
85C22×C113C2×C22⋊C411yescharacteristic
86C2×D113—41no—
87C2×D113—41no—
88C2×D113—41no—
89C4×C113—21no—
90C4×C113—21no—
91C4×C113—41no—
92Dic113—21no—
93Dic113—41no—
94Dic113#10212yes—
95Dic113C2×D811yescharacteristic
96Dic113C2×SD1611yescharacteristic
97Dic113#13512yes—
98C2×C113—22no—
99C2×C113—81no—
100C2×C113#41311yescharacteristic
101C2×C113C2×#10211yescharacteristic
102C2×C113#41611yescharacteristic
103D113—81no—
104#1540—1131nomaximal, Sylow
105C113#154011yescharacteristic, complemented, Sylow
106#532—1131no—
107#431—1131no—
108C2×C4⋊C8—1131no—
109#332—1132no—
110#331—1132no—
111C2×#41—2261no—
112C22×C8—2261no—
113C4⋊Q8—1131no—
114#127—1131no—
115#124—2261no—
116#121—1131no—
117#121—2261no—
118#121#9067311yescharacteristic
119C4×D4—1131no—
120C4×D4—1131no—
121C4×D4—2261no—
122C2×C42—1131no—
123C4⋊C8—1132no—
124C4⋊C8—1132no—
125C4⋊C8—2261no—
126C22⋊C8—2261no—
127C4×C8—2261no—
128#41—4522no—
129#41—4522no—
130C2×Q8—2261no—
131C2×D4—21no—
132C2×D4—1131no—
133C2×D4—2261no—
134C2×D4—2261no—
135C2×D4—2261no—
136C2×D4C2×#9067311yescharacteristic
137C22×C4—1131no—
138C22×C4—1131no—
139C22×C4—2261no—
140C22×C4—2261no—
141C22×C4C2×#9067311yescharacteristic
142C2×C8—4522no—
143C2×C8—2262no—
144C2×C8—2262no—
145C4⋊C4—1131no—
146C4⋊C4—2261no—
147C4⋊C4C2×#9067311yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—2261no—
150C22⋊C4—2261no—
151C22⋊C4—2261no—
152C42—1131no—
153C42—1131no—
154C42—1131no—
155C42—1131no—
156C23—21no—
157C23—2261no—
158C23C22⋊#9067311yescharacteristic
159Q8—4521no—
160Q8—4521no—
161D4—41no—
162D4—42no—
163D4—4521no—
164D4—4521no—
165D4—4521no—
166D4—4522no—
167D4—4522no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—1132no—
171C2×C4—1132no—
172C2×C4—1131no—
173C2×C4—1131no—
174C2×C4—1131no—
175C2×C4—1131no—
176C2×C4—4522no—
177C2×C4—4522no—
178C2×C4—2262no—
179C2×C4—2261no—
180C2×C4C22⋊#9067311yescharacteristic
181C2×C4C22×#9067311yescharacteristic
182C8—4522no—
183C8—4522no—
184C22—21no—
185C22—21no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—4521no—
190C22—4521no—
191C22—4521no—
192C22#1681368412yes—
193C22C2×C22⋊#9067311yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—1131no—
198C4—1132no—
199C4—1131no—
200C4—1132no—
201C4—4521no—
202C4—2261no—
203C2—22no—
204C2—81no—
205C2—9041no—
206C2#2029958511yescharacteristic
207C2C2×#1681368411yescharacteristic
208C2#2029958811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#121×C113C4
socleC22×C113C2×C22⋊C4
prime radical#20299143C2
cosocleC4×Dic113C23
hypercenter#121#90673
hypocenterC113#1540
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #20299615C2semidirect
2. C2×#16813689C2semidirect
3. #20299457C2semidirect
4. #20299456C2semidirect
105. C113#1540semidirect

Maximal subgroups

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

subgroupindex
#202996152
C2×#168136892
#202994572
#202994562
#202991432
#1540113