Finite Group Databasebeta

← #28389586

Subgroups — #28389586

Order 14464.

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

normal subgroups only

This group has 232 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#20299186C211yesmaximal, characteristic
2#20298928C211yesmaximal, characteristic, complemented
3#20298911C211yesmaximal, characteristic, complemented
4#20298334C211yesmaximal, characteristic, complemented
5#20298331C211yesmaximal, characteristic, complemented
6#20298322C211yesmaximal, characteristic, complemented
7#397×C113C211yesmaximal, characteristic, complemented
8#16813615—21no—
9#16813608—21no—
10#16813604—21no—
11#16813601C2211yescharacteristic
12#16813596C2211yescharacteristic
13#16813595—21no—
14#16813591—21no—
15C4×C22⋊D113—21no—
16#16813555—21no—
17#16813553—21no—
18#16813545—21no—
19#16813542—21no—
20C22⋊#11744751C2211yescharacteristic
21C22⋊#11744751C2211yescharacteristic
22C2×C4⋊C4×C113C2211yescharacteristic
23C2×C22⋊C4×C113—21no—
24C2×C22⋊C4×C113C2211yescharacteristic
25#95×C113—21no—
26#95×C113C2211yescharacteristic
27C2×Dic226D411yescharacteristic
28C2×D452D411yescharacteristic
29C2×C22⋊D113—21no—
30C2×C22⋊D113—21no—
31C2×C22⋊D113—21no—
32C2×C4×D113—21no—
33C2×#11744751—21no—
34C2×#11744751—21no—
35C4⋊Dic113D411yescharacteristic
36C4⋊Dic113D411yescharacteristic
37#14268626—21no—
38#14268626—21no—
39C22⋊Dic113—21no—
40C22⋊Dic113—21no—
41C22⋊Dic113—21no—
42#14268624—21no—
43#14268624—21no—
44C4×Dic113—21no—
45C24×C113D411yescharacteristic
46C22×C4×C113—21no—
47C22×C4×C113—21no—
48C22×C4×C113D411yescharacteristic
49C22×C4×C113C2311yescharacteristic
50C4⋊C4×C113—21no—
51C4⋊C4×C113—21no—
52C22⋊C4×C113—21no—
53C22⋊C4×C113—21no—
54C22⋊C4×C113—42no—
55C23×C113—21no—
56C23×C113—21no—
57C23×C113—21no—
58C23×C113—41no—
59C23×C113—41no—
60C23×C113C2×D411yescharacteristic
61C22×D113—21no—
62C2×C4×C113—21no—
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×C113—41no—
70C2×C4×C113—41no—
71C2×C4×C113C2×D411yescharacteristic
72C2×C4×C113C2×D411yescharacteristic
73C22⋊D113—41no—
74C22⋊D113—41no—
75C22⋊D113—81no—
76C22⋊D113—81no—
77C2×Dic113—21no—
78C2×Dic113—21no—
79C2×Dic113—21no—
80D452—41no—
81C4×D113—81no—
82Dic226—41no—
83#11744751—41no—
84#11744751—41no—
85C22×C113—21no—
86C22×C113—21no—
87C22×C113—42no—
88C22×C113—41no—
89C22×C113—41no—
90C22×C113—41no—
91C22×C113—81no—
92C22×C113#12011yescharacteristic
93C22×C113#13511yescharacteristic
94C22×C113AGL(1,ℤ/8)11yescharacteristic
95C2×D113—41no—
96C2×D113—41no—
97C2×D113—41no—
98C4×C113—21no—
99C4×C113—21no—
100C4×C113—41no—
101C4×C113—81no—
102C4×C113—81no—
103Dic113—41no—
104Dic113—41no—
105Dic113—41no—
106C2×C113—21no—
107C2×C113—21no—
108C2×C113—81no—
109C2×C113#44911yescharacteristic
110C2×C113#45511yescharacteristic
111C2×C113#45811yescharacteristic
112D113—81no—
113#1612—1131nomaximal, Sylow
114C113#161211yescharacteristic, complemented, Sylow
115#538—1131no—
116#483—1131no—
117#480—1131no—
118#397D11311yescharacteristic, complemented
119#328—1131no—
120#327—1131no—
121#323—1131no—
122#126—2261no—
123#124—2261no—
124#123—2261no—
125C22⋊Q8—1131no—
126#121—1131no—
127#121—2261no—
128#120—2261no—
129C4×D4—2261no—
130C2×C4⋊C4C2×D11311yescharacteristic
131C2×C22⋊C4—21no—
132C2×C22⋊C4C2×D11311yescharacteristic
133#107—2261no—
134#106—2261no—
135#103—2261no—
136#102—2261no—
137C22⋊C8—1131no—
138C22⋊C8—1131no—
139#95—21no—
140#95C2×D11311yescharacteristic
141C24C22⋊D11311yescharacteristic
142C2×Q8—1131no—
143C2×D4—1131no—
144C2×D4—2261no—
145C2×D4—2261no—
146C2×D4—2261no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—2261no—
150C22×C4C22⋊D11311yescharacteristic
151C22×C4C22×D11311yescharacteristic
152C2×C8—2261no—
153C2×C8—2261no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—1131no—
157C4⋊C4—1131no—
158C4⋊C4—2261no—
159C4⋊C4—2261no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—42no—
163C22⋊C4—2261no—
164C22⋊C4—2261no—
165C22⋊C4—2261no—
166C22⋊C4—2261no—
167C22⋊C4—2261no—
168C42—2261no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—2261no—
175C23C2×C22⋊D11311yescharacteristic
176Q8—4521no—
177D4—9041no—
178D4—9041no—
179D4—4521no—
180D4—4521no—
181D4—4521no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—9041no—
192C2×C4—2261no—
193C2×C4—2261no—
194C2×C4—2261no—
195C2×C4D4×D11311yescharacteristic
196C2×C4D4×D11311yescharacteristic
197C8—4521no—
198C8—4521no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22—4521no—
207C22—4521no—
208C22—4521no—
209C22#1681359011yescharacteristic
210C22#1681364211yescharacteristic
211C22#1681364811yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—81no—
217C4—4521no—
218C4—4521no—
219C4—4521no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—9041no—
224C2#2029874111yescharacteristic
225C2#2029877511yescharacteristic
226C2#2029878711yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#397×C113C2
socleC22×C113#120
prime radical#20299186C2
hypercenter#397D113
hypocenterC113#1612
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #20298928C2semidirect
3. #20298911C2semidirect
4. #20298334C2semidirect
5. #20298331C2semidirect
6. #20298322C2semidirect
7. #397×C113C2semidirect
114. C113#1612semidirect
118. #397D113semidirect

Maximal subgroups

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

subgroupindex
#202991862
#202989282
#202989112
#202983342
#202983312
#202983222
#397×C1132
#1612113