Finite Group Databasebeta

← #28389604

Subgroups — #28389604

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#20299197C211yesmaximal, characteristic
2#20298916C211yesmaximal, characteristic
3#20298536C211yesmaximal, characteristic, complemented
4#20298335C211yesmaximal, characteristic, complemented
5#20298333C211yesmaximal, characteristic
6#20298323C211yesmaximal, characteristic, complemented
7#484×C113C211yesmaximal, characteristic, complemented
8#16813617—21no—
9#16813613—21no—
10#16813607—21no—
11#16813606—21no—
12#16813598—21no—
13#16813596C2211yescharacteristic
14#16813582—21no—
15C2×#14268626C2211yescharacteristic
16#16813553—21no—
17#16813542—21no—
18C22⋊#11744751C2211yescharacteristic
19#16813529—21no—
20#16813529—21no—
21#16813529C2211yescharacteristic
22C22⋊Q8×C113C2211yescharacteristic
23C2×C4⋊C4×C113C2211yescharacteristic
24#107×C113—21no—
25#103×C113—21no—
26C22⋊C8×C113C2211yescharacteristic
27C2×D452D411yescharacteristic
28C2×C22⋊D113—21no—
29C22×Dic113—21no—
30C22×Dic113D411yescharacteristic
31C22×Dic113D411yescharacteristic
32C2×C4×D113—21no—
33C2×#11744751—21no—
34C4⋊Dic113—21no—
35C4⋊Dic113—21no—
36C4⋊Dic113D411yescharacteristic
37#14268626—21no—
38#14268626—21no—
39#14268626—21no—
40#14268624—21no—
41#14268624—21no—
42#14268624—21no—
43#14268624—21no—
44C4×Dic113—21no—
45C2×Q8×C113D411yescharacteristic
46C22×C4×C113—21no—
47C22×C4×C113C2311yescharacteristic
48C2×C8×C113—21no—
49C4⋊C4×C113—21no—
50C4⋊C4×C113—21no—
51C4⋊C4×C113—21no—
52C4⋊C4×C113D411yescharacteristic
53C22⋊C4×C113—21no—
54C23×C113C2×D411yescharacteristic
55C22×D113—21no—
56Q8×C113—41no—
57C2×C4×C113—21no—
58C2×C4×C113—21no—
59C2×C4×C113—41no—
60C2×C4×C113—42no—
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—21no—
70C2×Dic113—21no—
71C2×Dic113—41no—
72C2×Dic113—41no—
73C2×Dic113—41no—
74C2×Dic113—41no—
75D452—41no—
76C4×D113—81no—
77C8×C113—41no—
78#11744751—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—
91C4×C113—81no—
92Dic113—41no—
93Dic113—41no—
94Dic113—41no—
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#484D11311yescharacteristic, complemented
106#481—1131no—
107#400—1131no—
108#328—1131no—
109#327—1131no—
110#324—1131no—
111#126—2261no—
112#125—2261no—
113#123—2261no—
114#123—2261no—
115C22⋊Q8—2261no—
116C22⋊Q8C2×D11311yescharacteristic
117#121—1131no—
118C4×D4—2261no—
119C2×C4⋊C4—1131no—
120C2×C4⋊C4C2×D11311yescharacteristic
121#107—21no—
122#106—2261no—
123#103—21no—
124#102—2261no—
125C22⋊C8—1131no—
126C22⋊C8C2×D11311yescharacteristic
127#95—1131no—
128#95—2261no—
129#95—2261no—
130C2×Q8C22⋊D11311yescharacteristic
131C2×D4—1131no—
132C2×D4—2261no—
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—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—1131no—
145C4⋊C4—2261no—
146C4⋊C4—2261no—
147C4⋊C4—2261no—
148C4⋊C4—2261no—
149C4⋊C4—2261no—
150C4⋊C4C22⋊D11311yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—2261no—
153C22⋊C4—2261no—
154C22⋊C4—2261no—
155C22⋊C4—2261no—
156C42—2261no—
157C23—2261no—
158C23D4×D11311yescharacteristic
159Q8—41no—
160D4—4521no—
161D4—4521no—
162D4—4521no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—42no—
167C2×C4—41no—
168C2×C4—9041no—
169C2×C4—4521no—
170C2×C4—4521no—
171C2×C4—4521no—
172C2×C4—4521no—
173C2×C4—2261no—
174C2×C4—2261no—
175C2×C4—2261no—
176C2×C4—2261no—
177C2×C4—2261no—
178C2×C4D4×D11311yescharacteristic
179C2×C4C2×C22⋊D11311yescharacteristic
180C8—41no—
181C8—4521no—
182C22—21no—
183C22—21no—
184C22—4521no—
185C22—4521no—
186C22—4521no—
187C22#1681359011yescharacteristic
188C22#1681364511yescharacteristic
189C22#1681365411yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—9041no—
196C4—4521no—
197C4—4521no—
198C4—4521no—
199C2—21no—
200C2—21no—
201C2—9041no—
202C2#2029875911yescharacteristic
203C2#2029876911yescharacteristic
204C2#2029878711yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#484×C113C2
socleC22×C113#120
prime radical#16813596C22
hypercenter#484D113
hypocenterC113#1615
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #20298536C2semidirect
4. #20298335C2semidirect
6. #20298323C2semidirect
7. #484×C113C2semidirect
103. C113#1615semidirect
105. #484D113semidirect

Maximal subgroups

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

subgroupindex
#202991972
#202989162
#202985362
#202983352
#202983332
#202983232
#484×C1132
#1615113