Finite Group Databasebeta

← #28389606

Subgroups — #28389606

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#20299193C211yesmaximal, characteristic
2#20298934C211yesmaximal, characteristic, complemented
3#20298914C211yesmaximal, characteristic
4#20298538C211yesmaximal, characteristic, complemented
5#20298334C211yesmaximal, characteristic, complemented
6#20298323C211yesmaximal, characteristic, complemented
7#327×C113C211yesmaximal, characteristic
8#16813615—21no—
9#16813612—21no—
10#16813603—21no—
11#16813603—21no—
12#16813601C2211yescharacteristic
13#16813599—21no—
14D4×Dic113—21no—
15C2×C4⋊Dic113C2211yescharacteristic
16C2×#14268626C2211yescharacteristic
17#16813556—21no—
18#16813553—21no—
19#16813547—21no—
20#16813543—21no—
21C22⋊#11744751C2211yescharacteristic
22#16813529—21no—
23#16813529—21no—
24#121×C113C2211yescharacteristic
25C22⋊C8×C113C2211yescharacteristic
26#95×C113C2211yescharacteristic
27C2×Dic226D411yescharacteristic
28C22×Dic113—21no—
29C22×Dic113—21no—
30C22×Dic113D411yescharacteristic
31C22×Dic113D411yescharacteristic
32C2×#11744751—21no—
33C4⋊Dic113—21no—
34C4⋊Dic113—21no—
35C4⋊Dic113—21no—
36C4⋊Dic113D411yescharacteristic
37#14268626—21no—
38#14268626—21no—
39#14268626—21no—
40#14268626—21no—
41#14268626—21no—
42C22⋊Dic113—21no—
43C22⋊Dic113—21no—
44C22⋊Dic113—21no—
45C22⋊Dic113—21no—
46C4×Dic113—21no—
47C2×D4×C113—21no—
48C2×D4×C113D411yescharacteristic
49C22×C4×C113—21no—
50C22×C4×C113C2311yescharacteristic
51C2×C8×C113—21no—
52C4⋊C4×C113D411yescharacteristic
53C22⋊C4×C113—21no—
54C23×C113—21no—
55C23×C113C2×D411yescharacteristic
56D4×C113—41no—
57D4×C113—41no—
58D4×C113—41no—
59C2×C4×C113—21no—
60C2×C4×C113—41no—
61C2×C4×C113—41no—
62C2×C4×C113—41no—
63C2×C4×C113—41no—
64C2×C4×C113C2×D411yescharacteristic
65C2×C4×C113C2×D411yescharacteristic
66C2×Dic113—21no—
67C2×Dic113—21no—
68C2×Dic113—21no—
69C2×Dic113—21no—
70C2×Dic113—21no—
71C2×Dic113—21no—
72C2×Dic113—41no—
73C2×Dic113—42no—
74C2×Dic113—41no—
75C2×Dic113—81no—
76Dic226—41no—
77C8×C113—41no—
78#11744751—41no—
79C22×C113—21no—
80C22×C113—21no—
81C22×C113—41no—
82C22×C113—41no—
83C22×C113—41no—
84C22×C113#12011yescharacteristic
85C22×C113#13511yescharacteristic
86C22×C113#13711yescharacteristic
87C4×C113—21no—
88C4×C113—21no—
89C4×C113—41no—
90C4×C113—81no—
91Dic113—41no—
92Dic113—41no—
93Dic113—41no—
94Dic113—41no—
95Dic113—81no—
96C2×C113—21no—
97C2×C113—21no—
98C2×C113—81no—
99C2×C113#45211yescharacteristic
100C2×C113#45411yescharacteristic
101C2×C113#45811yescharacteristic
102#1615—1131nomaximal, Sylow
103C113#161511yescharacteristic, complemented, Sylow
104#539—1131no—
105#484—1131no—
106#481—1131no—
107#400—1131no—
108#328—1131no—
109#327D11311yescharacteristic
110#324—1131no—
111#126—2261no—
112#125—2261no—
113#123—2261no—
114#123—2261no—
115C22⋊Q8—1131no—
116C22⋊Q8—2261no—
117#121C2×D11311yescharacteristic
118C4×D4—2261no—
119C2×C4⋊C4—1131no—
120C2×C4⋊C4—1131no—
121#107—2261no—
122#106—2261no—
123#103—2261no—
124#102—2261no—
125C22⋊C8—1131no—
126C22⋊C8C2×D11311yescharacteristic
127#95—2261no—
128#95—2261no—
129#95C2×D11311yescharacteristic
130C2×Q8—1131no—
131C2×D4—21no—
132C2×D4D45211yescharacteristic
133C22×C4—21no—
134C22×C4—1131no—
135C22×C4—1131no—
136C22×C4—2261no—
137C22×C4—2261no—
138C22×C4C22×D11311yescharacteristic
139C2×C8—21no—
140C2×C8—2261no—
141C4⋊C4—1131no—
142C4⋊C4—2261no—
143C4⋊C4—2261no—
144C4⋊C4—2261no—
145C4⋊C4—2261no—
146C4⋊C4—2261no—
147C4⋊C4—2261no—
148C4⋊C4—2261no—
149C4⋊C4—2261no—
150C4⋊C4D45211yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—2261no—
153C22⋊C4—2261no—
154C22⋊C4—2261no—
155C22⋊C4—2261no—
156C42—2261no—
157C23—21no—
158C23D4×D11311yescharacteristic
159Q8—4521no—
160D4—41no—
161D4—41no—
162D4—41no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—9041no—
169C2×C4—4522no—
170C2×C4—4521no—
171C2×C4—4521no—
172C2×C4—2261no—
173C2×C4—2261no—
174C2×C4—2261no—
175C2×C4—2261no—
176C2×C4—2261no—
177C2×C4—2261no—
178C2×C4D4×D11311yescharacteristic
179C2×C4C2×D45211yescharacteristic
180C8—41no—
181C8—4521no—
182C22—21no—
183C22—21no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22#1681359211yescharacteristic
188C22#1681364111yescharacteristic
189C22#1681365111yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—81no—
194C4—9041no—
195C4—4521no—
196C4—4521no—
197C4—4521no—
198C4—4521no—
199C2—21no—
200C2—21no—
201C2—81no—
202C2#2029876111yescharacteristic
203C2#2029877211yescharacteristic
204C2#2029878911yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#327×C113C2
socleC22×C113#120
prime radical#121×C113C22
hypercenter#327D113
hypocenterC113#1615
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #20298934C2semidirect
4. #20298538C2semidirect
5. #20298334C2semidirect
6. #20298323C2semidirect
103. C113#1615semidirect

Maximal subgroups

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

subgroupindex
#202991932
#202989342
#202989142
#202985382
#202983342
#202983232
#327×C1132
#1615113