Finite Group Databasebeta

← #28401293

Subgroups — #28401293

Order 14464.

402 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 129 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#20299148C211yesmaximal, characteristic
2#20299001C211yesmaximal, characteristic, complemented
3#20298972C211yesmaximal, characteristic, complemented
4#20298948C211yesmaximal, characteristic, complemented
5#20298946C211yesmaximal, characteristic, complemented
6#20298846C214yesmaximal, complemented
7#20298696C214yesmaximal, complemented
8C4×#14268631C211yesmaximal, characteristic, complemented
9#533×C113C211yesmaximal, characteristic, complemented
10C2×#14268647—21no—
11C2×#14268634C2214yes—
12C2×#14268631C2212yes—
13#16813622C2211yescharacteristic
14#16813619C2211yescharacteristic
15#16813610—21no—
16#16813596—21no—
17#16813596C2212yes—
18C4×D452—21no—
19C4×D452C2212yes—
20#16813555C2214yes—
21#16813546C2214yes—
22#16813542C2214yes—
23#16813533C2212yes—
24C4×#11744751C2211yescharacteristic
25C4×#11744751C2211yescharacteristic
26C4⋊Q8×C113C2211yescharacteristic
27C4⋊Q8×C113C2211yescharacteristic
28#125×C113—21no—
29C22⋊Q8×C113—21no—
30C22⋊Q8×C113C2212yes—
31C4×Q8×C113—21no—
32C4×Q8×C113C2212yes—
33#117×C113—21no—
34C2×C42×C113C2211yescharacteristic
35#14268647—44no—
36C2×Dic226—21no—
37C2×D452—21no—
38C2×D452—21no—
39C2×D452C2312yes—
40C2×C22⋊D113—22no—
41C2×C4×D113—22no—
42#14268634—28no—
43#14268631—24no—
44C2×#11744751C2312yes—
45C2×#11744751C2312yes—
46C4⋊Dic113—21no—
47C4⋊Dic113C2312yes—
48#14268624—22no—
49#14268624—22no—
50C2×Q8×C113—21no—
51C2×Q8×C113C2312yes—
52C22×C4×C113D411yescharacteristic
53C22×C4×C113D411yescharacteristic
54C22×C4×C113C2311yescharacteristic
55C4⋊C4×C113—21no—
56C4⋊C4×C113—21no—
57C4⋊C4×C113—21no—
58C4⋊C4×C113—22no—
59C4⋊C4×C113—22no—
60C4⋊C4×C113C2312yes—
61C22⋊C4×C113—22no—
62C42×C113—22no—
63C42×C113D411yescharacteristic
64C42×C113D411yescharacteristic
65C42×C113C2311yescharacteristic
66C42×C113C2311yescharacteristic
67C23×C113C2×D411yescharacteristic
68C22×D113—22no—
69Q8×C113—24no—
70Q8×C113—42no—
71C2×C4×C113—22no—
72C2×C4×C113—22no—
73C2×C4×C113—22no—
74C2×C4×C113—22no—
75C2×C4×C113—22no—
76C2×C4×C113C2×D411yescharacteristic
77C2×C4×C113C2×D411yescharacteristic
78C2×C4×C113C2×D411yescharacteristic
79C2×C4×C113C2×D411yescharacteristic
80C2×C4×C113C2×D411yescharacteristic
81C2×C4×C113C2411yescharacteristic
82C22⋊D113—44no—
83C2×Dic113—22no—
84D452—24no—
85D452—42no—
86D452—42no—
87C4×D113—44no—
88Dic226—42no—
89#11744751—22no—
90#11744751#4114yescomplemented
91C22×C113—21no—
92C22×C113—21no—
93C22×C113—21no—
94C22×C113C22×D411yescharacteristic
95C2×D113—42no—
96C2×D113—42no—
97C2×D113—42no—
98C4×C113—21no—
99C4×C113—21no—
100C4×C113—21no—
101C4×C113—42no—
102C4×C113—42no—
103C4×C113AGL(1,ℤ/8)12yes—
104C4×C113#13712yes—
105C4×C113C2×#4112yes—
106Dic113—42no—
107C2×C113—41no—
108C2×C113#53211yescharacteristic
109C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
110C2×C113C2×#13711yescharacteristic
111D113—82no—
112#3182—1131nomaximal, Sylow
113C113#318211yescharacteristic, complemented, Sylow
114#533D11311yescharacteristic, complemented
115#532—1131no—
116#500—1131no—
117#492—1131no—
118#487—1131no—
119#486—1131no—
120#468—1134no—
121#440—1134no—
122C4×M16—1131no—
123C2×#41—2261no—
124C2×SD16—1134no—
125C2×M16—1132no—
126C4⋊Q8—1131no—
127C4⋊Q8C2×D11311yescharacteristic
128C4⋊Q8C2×D11311yescharacteristic
129#127—1131no—
130#125—21no—
131#124—2261no—
132C22⋊Q8—21no—
133C22⋊Q8C2×D11312yes—
134#121—1132no—
135#121—2261no—
136C4×Q8—21no—
137C4×Q8C2×D11312yes—
138C4×D4—1132no—
139C4×D4—2261no—
140#117—21no—
141C2×C42C2×D11311yescharacteristic
142#107—1134no—
143#103—1134no—
144#102—1134no—
145#97—1132no—
146C4×C8—1131no—
147C4×C8—1131no—
148#41—4524no—
149C2×Q8—21no—
150C2×Q8—2261no—
151C2×Q8C22×D11312yes—
152C2×D4—1132no—
153C2×D4—2262no—
154C2×D4—2261no—
155C2×D4—2261no—
156C22×C4—2262no—
157C22×C4C22⋊D11311yescharacteristic
158C22×C4C22⋊D11311yescharacteristic
159C22×C4C22×D11311yescharacteristic
160SD16—2268no—
161M16—2264no—
162C2×C8—1132no—
163C2×C8—1132no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—22no—
168C4⋊C4—22no—
169C4⋊C4—1132no—
170C4⋊C4—2261no—
171C4⋊C4C22×D11312yes—
172C22⋊C4—22no—
173C22⋊C4—2262no—
174C22⋊C4—2262no—
175C42—22no—
176C42C22⋊D11311yescharacteristic
177C42C22⋊D11311yescharacteristic
178C42C22×D11311yescharacteristic
179C42C22×D11311yescharacteristic
180C23—2262no—
181C23C2×C22⋊D11311yescharacteristic
182Q8—24no—
183Q8—42no—
184Q8—4522no—
185D4—4524no—
186D4—4522no—
187D4—4522no—
188D4—2264no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—4524no—
195C2×C4—2262no—
196C2×C4C2×C22⋊D11311yescharacteristic
197C2×C4C2×C22⋊D11311yescharacteristic
198C2×C4C2×C22⋊D11311yescharacteristic
199C2×C4C2×C22⋊D11311yescharacteristic
200C2×C4C2×C22⋊D11311yescharacteristic
201C2×C4C23×D11311yescharacteristic
202C8—1134no—
203C8—2262no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—4522no—
208C22—4522no—
209C22—4522no—
210C22C22×C22⋊D11311yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—42no—
216C4—4522no—
217C4#1681364712yes—
218C4#1681365312yes—
219C4#41×D11312yes—
220C2—41no—
221C2—9042no—
222C2#2029914411yescharacteristic
223C2C2×#1681364711yescharacteristic
224C2C2×#1681365311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#533×C113C2
socleC22×C113C22×D4
prime radical#20299148C2
hypercenter#533D113
hypocenterC113#3182
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #20299001C2semidirect
3. #20298972C2semidirect
4. #20298948C2semidirect
5. #20298946C2semidirect
6. #20298846C2semidirect
7. #20298696C2semidirect
8. C4×#14268631C2semidirect
9. #533×C113C2semidirect
90. #11744751#41semidirect
113. C113#3182semidirect
114. #533D113semidirect

Maximal subgroups

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

subgroupindex
#202991482
#202990012
#202989722
#202989482
#202989462
#202988462
#202986962
C4×#142686312
#533×C1132
#3182113