Finite Group Databasebeta

← #28389569

Subgroups — #28389569

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#20298928C211yesmaximal, characteristic, complemented
3#20298911C211yesmaximal, characteristic
4#20298334C211yesmaximal, characteristic, complemented
5#20298331C211yesmaximal, characteristic
6#20298324C211yesmaximal, characteristic, complemented
7#398×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—
16#16813555—21no—
17#16813553—21no—
18#16813545—21no—
19#16813542—21no—
20C22⋊#11744751C2211yescharacteristic
21C22⋊#11744751C2211yescharacteristic
22C2×C4⋊C4×C113—21no—
23C2×C4⋊C4×C113C2211yescharacteristic
24C2×C4⋊C4×C113C2211yescharacteristic
25#95×C113—21no—
26#95×C113C2211yescharacteristic
27C2×Dic226D411yescharacteristic
28C2×D452D411yescharacteristic
29C2×C22⋊D113—21no—
30C2×C4×D113—21no—
31C2×#11744751—21no—
32C2×#11744751—21no—
33C4⋊Dic113D411yescharacteristic
34C4⋊Dic113D411yescharacteristic
35#14268626—21no—
36#14268626—21no—
37#14268626—21no—
38#14268626—21no—
39C22⋊Dic113—21no—
40#14268624—21no—
41#14268624—21no—
42#14268624—21no—
43#14268624—21no—
44C4×Dic113—21no—
45C22×C4×C113—21no—
46C22×C4×C113—21no—
47C22×C4×C113D411yescharacteristic
48C22×C4×C113D411yescharacteristic
49C22×C4×C113C2311yescharacteristic
50C4⋊C4×C113—21no—
51C4⋊C4×C113—21no—
52C4⋊C4×C113—21no—
53C4⋊C4×C113—21no—
54C4⋊C4×C113—42no—
55C23×C113C2×D411yescharacteristic
56C22×D113—21no—
57C2×C4×C113—22no—
58C2×C4×C113—21no—
59C2×C4×C113—21no—
60C2×C4×C113—21no—
61C2×C4×C113—21no—
62C2×C4×C113—41no—
63C2×C4×C113—41no—
64C2×C4×C113—41no—
65C2×C4×C113—41no—
66C2×C4×C113—41no—
67C2×C4×C113—41no—
68C2×C4×C113—41no—
69C2×C4×C113C2×D411yescharacteristic
70C2×C4×C113C2×D411yescharacteristic
71C22⋊D113—41no—
72C22⋊D113—41no—
73C2×Dic113—21no—
74C2×Dic113—21no—
75C2×Dic113—21no—
76D452—41no—
77C4×D113—81no—
78Dic226—41no—
79#11744751—41no—
80#11744751—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—42no—
92C4×C113—41no—
93C4×C113—41no—
94C4×C113—81no—
95Dic113—41no—
96Dic113—41no—
97Dic113—41no—
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#398D11311yescharacteristic, complemented
110#328—1131no—
111#327—1131no—
112#324—1131no—
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—21no—
122C2×C4⋊C4C2×D11311yescharacteristic
123C2×C4⋊C4C2×D11311yescharacteristic
124#107—2261no—
125#106—2261no—
126#103—2261no—
127#102—2261no—
128C22⋊C8—1131no—
129C22⋊C8—1131no—
130#95—21no—
131#95C2×D11311yescharacteristic
132C2×Q8—1131no—
133C2×D4—1131no—
134C2×D4—2261no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—2261no—
138C22×C4C22⋊D11311yescharacteristic
139C22×C4C22⋊D11311yescharacteristic
140C22×C4C22×D11311yescharacteristic
141C2×C8—2261no—
142C2×C8—2261no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—42no—
148C4⋊C4—1131no—
149C4⋊C4—1131no—
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×C22⋊D11311yescharacteristic
162Q8—4521no—
163D4—4521no—
164D4—4521no—
165D4—4521no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—9041no—
179C2×C4—2261no—
180C2×C4—2261no—
181C2×C4—2261no—
182C2×C4D4×D11311yescharacteristic
183C2×C4D4×D11311yescharacteristic
184C8—4521no—
185C8—4521no—
186C22—21no—
187C22—21no—
188C22—4521no—
189C22—4521no—
190C22—4521no—
191C22#1681359011yescharacteristic
192C22#1681364211yescharacteristic
193C22#1681364811yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4—81no—
200C4—4521no—
201C4—4521no—
202C4—4521no—
203C2—21no—
204C2—21no—
205C2—9041no—
206C2#2029874111yescharacteristic
207C2#2029878011yescharacteristic
208C2#2029878711yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#398×C113C2
socleC22×C113#120
prime radical#16813596C22
hypercenter#398D113
hypocenterC113#1609
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
2. #20298928C2semidirect
4. #20298334C2semidirect
6. #20298324C2semidirect
7. #398×C113C2semidirect
105. C113#1609semidirect
109. #398D113semidirect

Maximal subgroups

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

subgroupindex
#202991952
#202989282
#202989112
#202983342
#202983312
#202983242
#398×C1132
#1609113