Finite Group Databasebeta

← #28389573

Subgroups — #28389573

Order 14464.

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

normal subgroups only

This group has 216 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#20298929C211yesmaximal, characteristic, complemented
3#20298912C211yesmaximal, characteristic
4#20298528C211yesmaximal, 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
17C2×#14268626—21no—
18#16813556—21no—
19#16813554—21no—
20#16813547—21no—
21#16813544—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—
41#14268626—42no—
42C22⋊Dic113—21no—
43#14268624—21no—
44#14268624—21no—
45#14268624—21no—
46#14268624—21no—
47C4×Dic113—21no—
48C22×C4×C113D411yescharacteristic
49C22×C4×C113D411yescharacteristic
50C22×C4×C113C2311yescharacteristic
51C2×C8×C113—21no—
52C2×C8×C113—21no—
53C4⋊C4×C113—21no—
54C4⋊C4×C113—21no—
55C23×C113C2×D411yescharacteristic
56C22×D113—21no—
57C2×C4×C113—21no—
58C2×C4×C113—21no—
59C2×C4×C113—21no—
60C2×C4×C113—21no—
61C2×C4×C113—41no—
62C2×C4×C113—41no—
63C2×C4×C113C2×D411yescharacteristic
64C2×C4×C113C2×D411yescharacteristic
65C22⋊D113—41no—
66C22⋊D113—41no—
67C2×Dic113—22no—
68C2×Dic113—21no—
69C2×Dic113—21no—
70C2×Dic113—21no—
71C2×Dic113—41no—
72C2×Dic113—41no—
73C2×Dic113—41no—
74C2×Dic113—41no—
75C2×Dic113—41no—
76D452—41no—
77C4×D113—81no—
78Dic226—41no—
79C8×C113—41no—
80C8×C113—41no—
81C22×C113—21no—
82C22×C113—21no—
83C22×C113#12011yescharacteristic
84C22×C113#13511yescharacteristic
85C22×C113AGL(1,ℤ/8)11yescharacteristic
86C2×D113—41no—
87C2×D113—41no—
88C2×D113—41no—
89C4×C113—21no—
90C4×C113—21no—
91C4×C113—41no—
92C4×C113—41no—
93Dic113—42no—
94Dic113—41no—
95Dic113—41no—
96Dic113—41no—
97Dic113—81no—
98C2×C113—21no—
99C2×C113—21no—
100C2×C113#44911yescharacteristic
101C2×C113#45611yescharacteristic
102C2×C113#45811yescharacteristic
103D113—81no—
104#1609—1131nomaximal, Sylow
105C113#160911yescharacteristic, complemented, Sylow
106#539—1131no—
107#483—1131no—
108#480—1131no—
109#398—1131no—
110#328—1131no—
111#327—1131no—
112#324D11311yescharacteristic, complemented
113#126—2261no—
114#125—2261no—
115#123—2261no—
116#123—2261no—
117C22⋊Q8—1131no—
118C22⋊Q8—2261no—
119#121—1131no—
120C4×D4—2261no—
121C2×C4⋊C4—1131no—
122C2×C4⋊C4—2261no—
123C2×C4⋊C4C2×D11311yescharacteristic
124#107—2261no—
125#106—2261no—
126#103—2261no—
127#102—2261no—
128C22⋊C8C2×D11311yescharacteristic
129C22⋊C8C2×D11311yescharacteristic
130#95—1131no—
131#95—2261no—
132C2×Q8—1131no—
133C2×D4—1131no—
134C2×D4—2261no—
135C22×C4—2261no—
136C22×C4—2261no—
137C22×C4—2261no—
138C22×C4D45211yescharacteristic
139C22×C4D45211yescharacteristic
140C22×C4C22×D11311yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—1131no—
146C4⋊C4—1131no—
147C4⋊C4—4522no—
148C4⋊C4—2261no—
149C4⋊C4—2261no—
150C4⋊C4—2261no—
151C4⋊C4—2261no—
152C4⋊C4—2261no—
153C4⋊C4—2261no—
154C22⋊C4—2261no—
155C22⋊C4—2261no—
156C22⋊C4—2261no—
157C22⋊C4—2261no—
158C22⋊C4—2261no—
159C42—2261no—
160C23—2261no—
161C23C2×D45211yescharacteristic
162Q8—4521no—
163D4—4521no—
164D4—4521no—
165D4—4521no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—9041no—
173C2×C4—4521no—
174C2×C4—4521no—
175C2×C4—4521no—
176C2×C4—4521no—
177C2×C4—4521no—
178C2×C4—2262no—
179C2×C4—2261no—
180C2×C4—2261no—
181C2×C4—2261no—
182C2×C4D4×D11311yescharacteristic
183C2×C4D4×D11311yescharacteristic
184C8—41no—
185C8—41no—
186C22—21no—
187C22—21no—
188C22—4521no—
189C22—4521no—
190C22—4521no—
191C22#1681359211yescharacteristic
192C22#1681364411yescharacteristic
193C22#1681365011yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—9041no—
199C4—4522no—
200C4—4521no—
201C4—4521no—
202C4—4521no—
203C2—21no—
204C2—21no—
205C2—9041no—
206C2#2029874511yescharacteristic
207C2#2029878311yescharacteristic
208C2#2029878911yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#324×C113C2
socleC22×C113#120
prime radical#16813596C22
hypercenter#324D113
hypocenterC113#1609
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. #20298929C2semidirect
4. #20298528C2semidirect
5. #20298336C2semidirect
7. #324×C113C2semidirect
105. C113#1609semidirect
112. #324D113semidirect

Maximal subgroups

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

subgroupindex
#202991952
#202989292
#202989122
#202985282
#202983362
#202983332
#324×C1132
#1609113