Finite Group Databasebeta

← #28389607

Subgroups — #28389607

Order 14464.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#20299195C211yesmaximal, characteristic
2#20298934C211yesmaximal, characteristic, complemented
3#20298917C211yesmaximal, characteristic
4#20298537C211yesmaximal, characteristic, complemented
5#20298336C211yesmaximal, characteristic, complemented
6#20298333C211yesmaximal, characteristic
7#324×C113C211yesmaximal, characteristic, complemented
8#16813617—21no—
9#16813612—21no—
10#16813607—21no—
11#16813605—21no—
12#16813601C2211yescharacteristic
13#16813600—21no—
14#16813596C2211yescharacteristic
15C4×C22⋊D113—21no—
16C2×C4⋊Dic113C2211yescharacteristic
17#16813556—21no—
18#16813554—21no—
19#16813547—21no—
20#16813544—21no—
21#16813529—21no—
22#16813529—21no—
23#16813529C2211yescharacteristic
24C2×C4⋊C4×C113C2211yescharacteristic
25C22⋊C8×C113C2211yescharacteristic
26C22⋊C8×C113C2211yescharacteristic
27C2×Dic226D411yescharacteristic
28C2×D452D411yescharacteristic
29C2×C22⋊D113—21no—
30C22×Dic113—21no—
31C22×Dic113—21no—
32C2×C4×D113—21no—
33C4⋊Dic113—21no—
34C4⋊Dic113—21no—
35C4⋊Dic113D411yescharacteristic
36C4⋊Dic113D411yescharacteristic
37#14268626—21no—
38#14268626—21no—
39#14268626—21no—
40#14268626—21no—
41C22⋊Dic113—21no—
42#14268624—21no—
43#14268624—21no—
44#14268624—21no—
45#14268624—21no—
46C4×Dic113—21no—
47C22×C4×C113D411yescharacteristic
48C22×C4×C113D411yescharacteristic
49C22×C4×C113C2311yescharacteristic
50C2×C8×C113—21no—
51C2×C8×C113—21no—
52C4⋊C4×C113—21no—
53C4⋊C4×C113—21no—
54C23×C113C2×D411yescharacteristic
55C22×D113—21no—
56C2×C4×C113—21no—
57C2×C4×C113—21no—
58C2×C4×C113—21no—
59C2×C4×C113—21no—
60C2×C4×C113—41no—
61C2×C4×C113—41no—
62C2×C4×C113C2×D411yescharacteristic
63C2×C4×C113C2×D411yescharacteristic
64C22⋊D113—41no—
65C22⋊D113—41no—
66C2×Dic113—21no—
67C2×Dic113—21no—
68C2×Dic113—21no—
69C2×Dic113—41no—
70C2×Dic113—41no—
71C2×Dic113—42no—
72C2×Dic113—41no—
73C2×Dic113—41no—
74D452—41no—
75C4×D113—81no—
76Dic226—41no—
77C8×C113—41no—
78C8×C113—41no—
79C22×C113—21no—
80C22×C113—21no—
81C22×C113#12011yescharacteristic
82C22×C113#13511yescharacteristic
83C22×C113#13711yescharacteristic
84C2×D113—41no—
85C2×D113—41no—
86C2×D113—41no—
87C4×C113—21no—
88C4×C113—21no—
89C4×C113—41no—
90C4×C113—41no—
91Dic113—41no—
92Dic113—41no—
93Dic113—41no—
94Dic113—81no—
95Dic113—81no—
96C2×C113—21no—
97C2×C113—21no—
98C2×C113#45211yescharacteristic
99C2×C113#45411yescharacteristic
100C2×C113#45811yescharacteristic
101D113—81no—
102#1615—1131nomaximal, Sylow
103C113#161511yescharacteristic, complemented, Sylow
104#539—1131no—
105#484—1131no—
106#481—1131no—
107#400—1131no—
108#328—1131no—
109#327—1131no—
110#324D11311yescharacteristic, complemented
111#126—2261no—
112#125—2261no—
113#123—2261no—
114#123—2261no—
115C22⋊Q8—1131no—
116C22⋊Q8—2261no—
117#121—1131no—
118C4×D4—2261no—
119C2×C4⋊C4—1131no—
120C2×C4⋊C4C2×D11311yescharacteristic
121#107—2261no—
122#106—2261no—
123#103—2261no—
124#102—2261no—
125C22⋊C8C2×D11311yescharacteristic
126C22⋊C8C2×D11311yescharacteristic
127#95—1131no—
128#95—2261no—
129#95—2261no—
130C2×Q8—1131no—
131C2×D4—1131no—
132C2×D4—2261no—
133C22×C4—2261no—
134C22×C4—2261no—
135C22×C4—2261no—
136C22×C4D45211yescharacteristic
137C22×C4D45211yescharacteristic
138C22×C4C22×D11311yescharacteristic
139C2×C8—21no—
140C2×C8—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—1131no—
144C4⋊C4—1131no—
145C4⋊C4—2261no—
146C4⋊C4—2261no—
147C4⋊C4—2261no—
148C4⋊C4—2261no—
149C4⋊C4—2261no—
150C4⋊C4—2261no—
151C22⋊C4—2261no—
152C22⋊C4—2261no—
153C22⋊C4—2261no—
154C22⋊C4—2261no—
155C22⋊C4—2261no—
156C42—2261no—
157C23—2261no—
158C23C2×D45211yescharacteristic
159Q8—4521no—
160D4—4521no—
161D4—4521no—
162D4—4521no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—9041no—
170C2×C4—4521no—
171C2×C4—4521no—
172C2×C4—4522no—
173C2×C4—4521no—
174C2×C4—4521no—
175C2×C4—2261no—
176C2×C4—2261no—
177C2×C4—2261no—
178C2×C4D4×D11311yescharacteristic
179C2×C4D4×D11311yescharacteristic
180C8—41no—
181C8—41no—
182C22—21no—
183C22—21no—
184C22—4521no—
185C22—4521no—
186C22—4521no—
187C22#1681359211yescharacteristic
188C22#1681364411yescharacteristic
189C22#1681365511yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—9041no—
195C4—9041no—
196C4—4521no—
197C4—4521no—
198C4—4521no—
199C2—21no—
200C2—21no—
201C2—9041no—
202C2#2029876211yescharacteristic
203C2#2029877311yescharacteristic
204C2#2029878911yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#324×C113C2
socleC22×C113#120
prime radical#16813596C22
hypercenter#324D113
hypocenterC113#1615
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #20298934C2semidirect
4. #20298537C2semidirect
5. #20298336C2semidirect
7. #324×C113C2semidirect
103. C113#1615semidirect
110. #324D113semidirect

Maximal subgroups

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

subgroupindex
#202991952
#202989342
#202989172
#202985372
#202983362
#202983332
#324×C1132
#1615113