Finite Group Databasebeta

← #28388942

Subgroups — #28388942

Order 14464.

214 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C2×#16813617C211yesmaximal, characteristic
2#20298652C211yesmaximal, characteristic, complemented
3#20298648C211yesmaximal, characteristic, complemented
4#20298324C211yesmaximal, characteristic, complemented
5#20298321C211yesmaximal, characteristic
6#20298321C211yesmaximal, characteristic
7#324×C113C211yesmaximal, characteristic, complemented
8#16813617—21no—
9#16813617—21no—
10#16813617—21no—
11#16813617—21no—
12C2×C4⋊Dic113C411yescharacteristic
13C2×#14268626C411yescharacteristic
14C2×#14268624C411yescharacteristic
15C2×#14268624C411yescharacteristic
16C2×#14268624C2211yescharacteristic
17C2×C4×Dic113C2211yescharacteristic
18#16813551—21no—
19#16813551—21no—
20C22⋊#11744751C2211yescharacteristic
21C22⋊#11744751C2211yescharacteristic
22#16813532—21no—
23C8×Dic113—21no—
24C2×C4⋊C4×C113C2211yescharacteristic
25C22⋊C8×C113C2211yescharacteristic
26C22⋊C8×C113C2211yescharacteristic
27C23×D113C2×C411yescharacteristic
28C22×Dic113C2×C411yescharacteristic
29C22×Dic113C2×C411yescharacteristic
30C22×Dic113C2×C411yescharacteristic
31C2×#11744751—21no—
32C2×#11744751—21no—
33C4⋊Dic113—21no—
34C4⋊Dic113—21no—
35#14268626—21no—
36#14268626—21no—
37#14268624—21no—
38#14268624—21no—
39#14268624—21no—
40#14268624—21no—
41#14268624—21no—
42#14268624—21no—
43C4×Dic113D411yescharacteristic
44C4×Dic113D411yescharacteristic
45C4×Dic113D411yescharacteristic
46C4×Dic113D411yescharacteristic
47C22×C4×C113C2×C411yescharacteristic
48C22×C4×C113C2×C411yescharacteristic
49C22×C4×C113C2311yescharacteristic
50C2×C8×C113—21no—
51C2×C8×C113—21no—
52C4⋊C4×C113—21no—
53C4⋊C4×C113—21no—
54C23×C113C22×C411yescharacteristic
55C22×D113—21no—
56C22×D113—21no—
57C22×D113—21no—
58C22×D113—41no—
59C22×D113—41no—
60C2×C4×C113—21no—
61C2×C4×C113—21no—
62C2×C4×C113—21no—
63C2×C4×C113—21no—
64C2×C4×C113—41no—
65C2×C4×C113—41no—
66C2×C4×C113C2×D411yescharacteristic
67C2×C4×C113C2×D411yescharacteristic
68C2×Dic113—21no—
69C2×Dic113—21no—
70C2×Dic113—21no—
71C2×Dic113—41no—
72C2×Dic113—41no—
73C2×Dic113C22⋊C411yescharacteristic
74C2×Dic113C22⋊C411yescharacteristic
75C2×Dic113C22⋊C411yescharacteristic
76C2×Dic113C22⋊C411yescharacteristic
77C8×C113—41no—
78C8×C113—41no—
79#11744751—41no—
80#11744751—41no—
81C22×C113—21no—
82C22×C113—21no—
83C22×C113C2×C22⋊C411yescharacteristic
84C22×C113#13111yescharacteristic
85C22×C113#13111yescharacteristic
86C2×D113—41no—
87C2×D113—41no—
88C2×D113—41no—
89C2×D113—81no—
90C2×D113—81no—
91C4×C113—21no—
92C4×C113—21no—
93C4×C113—41no—
94C4×C113—41no—
95Dic113—21no—
96Dic113—21no—
97Dic113—21no—
98Dic113—21no—
99Dic113—41no—
100C2×C113—21no—
101C2×C113—21no—
102C2×C113#40811yescharacteristic
103C2×C113#41011yescharacteristic
104C2×C113#41311yescharacteristic
105D113—81no—
106#1473—1131nomaximal, Sylow
107C113#147311yescharacteristic, complemented, Sylow
108C2×#126—1131no—
109#432—1131no—
110#431—1131no—
111#324—1131no—
112#324D11311yescharacteristic, complemented
113#323—1131no—
114#323—1131no—
115#126—2261no—
116#126—2261no—
117#126—2261no—
118#126—2261no—
119C2×C4⋊C4—1131no—
120C2×C4⋊C4—1131no—
121C2×C4⋊C4C2×D11311yescharacteristic
122C2×C22⋊C4—1131no—
123C2×C22⋊C4—1131no—
124C2×C22⋊C4—1131no—
125C2×C42—1131no—
126C4⋊C8—2261no—
127C4⋊C8—2261no—
128C22⋊C8—1131no—
129C22⋊C8—1131no—
130C22⋊C8C2×D11311yescharacteristic
131C22⋊C8C2×D11311yescharacteristic
132#97—2261no—
133C4×C8—2261no—
134C24—1131no—
135C22×C4—1131no—
136C22×C4—1131no—
137C22×C4—1131no—
138C22×C4C4×D11311yescharacteristic
139C22×C4C4×D11311yescharacteristic
140C22×C4C22×D11311yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—2261no—
144C2×C8—2261no—
145C4⋊C4—21no—
146C4⋊C4—21no—
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—
156C22⋊C4—2261no—
157C42—1131no—
158C42—1131no—
159C42—1131no—
160C42—1131no—
161C23—4521no—
162C23—4521no—
163C23—2261no—
164C23—2261no—
165C23—2261no—
166C23C2×C4×D11311yescharacteristic
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—1131no—
174C2×C4—1131no—
175C2×C4—1131no—
176C2×C4—1131no—
177C2×C4—4521no—
178C2×C4—4521no—
179C2×C4—2261no—
180C2×C4—2261no—
181C2×C4—2261no—
182C2×C4D4×D11311yescharacteristic
183C2×C4D4×D11311yescharacteristic
184C8—41no—
185C8—41no—
186C8—4521no—
187C8—4521no—
188C22—21no—
189C22—21no—
190C22—9041no—
191C22—9041no—
192C22—4521no—
193C22—4521no—
194C22—4521no—
195C22C22⋊C4×D11311yescharacteristic
196C22#1681362811yescharacteristic
197C22#1681363011yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—4521no—
203C4—2261no—
204C4—2261no—
205C4—2261no—
206C4—2261no—
207C2—21no—
208C2—21no—
209C2—9041no—
210C2#2029856311yescharacteristic
211C2#2029857011yescharacteristic
212C2#2029858111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D113
commutatorC23×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#324×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC23×D113C2×C4
cosocleC22×C4×C113C23
hypercenter#324D113
hypocenterC113#1473
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #20298652C2semidirect
3. #20298648C2semidirect
4. #20298324C2semidirect
7. #324×C113C2semidirect
107. C113#1473semidirect
112. #324D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136172
#202986522
#202986482
#202983242
#202983212
#324×C1132
#1473113