Finite Group Databasebeta

← #28392564

Subgroups — #28392564

Order 14464.

258 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 45 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#20298787C211yesmaximal, characteristic, complemented
2#20298784C211yesmaximal, characteristic
3#20298775C211yesmaximal, characteristic, complemented
4#20298393C211yesmaximal, characteristic, complemented
5#20298388C211yesmaximal, characteristic, complemented
6#20298385C211yesmaximal, characteristic, complemented
7#551×C113C211yesmaximal, characteristic, complemented
8#16813667C2211yescharacteristic
9#16813653—21no—
10#16813605—21no—
11#16813591—21no—
12#16813550—21no—
13#16813539C2211yescharacteristic
14#16813537C2211yescharacteristic
15#16813537C2211yescharacteristic
16#16813536—21no—
17#16813536—21no—
18#126×C113—21no—
19#124×C113C2211yescharacteristic
20#123×C113—21no—
21#123×C113C2211yescharacteristic
22C22⋊Q8×C113—21no—
23#120×C113C2211yescharacteristic
24C4×D4×C113—21no—
25#117×C113—21no—
26C2×C22⋊C4×C113—21no—
27#14268647—21no—
28#14268646—41no—
29C2×C22⋊D113—21no—
30C2×C22⋊D113—21no—
31C2×C22⋊D113—41no—
32D4×D113—41no—
33#14268637—41no—
34#14268634—41no—
35#14268631—21no—
36#14268626—41no—
37C22⋊Dic113—21no—
38C22⋊Dic113—21no—
39C22⋊Dic113—41no—
40#14268624—41no—
41C24×C113D411yescharacteristic
42C2×Q8×C113D411yescharacteristic, complemented
43C2×D4×C113—21no—
44C2×D4×C113C2311yescharacteristic
45C22×C4×C113—21no—
46C22×C4×C113—21no—
47C22×C4×C113D411yescharacteristic, complemented
48C4⋊C4×C113—21no—
49C4⋊C4×C113—21no—
50C4⋊C4×C113—21no—
51C4⋊C4×C113—21no—
52C22⋊C4×C113—21no—
53C22⋊C4×C113—21no—
54C22⋊C4×C113—21no—
55C22⋊C4×C113—21no—
56C22⋊C4×C113—21no—
57C22⋊C4×C113—21no—
58C22⋊C4×C113D411yescharacteristic
59C22⋊C4×C113D411yescharacteristic, complemented
60C42×C113—21no—
61C42×C113D411yescharacteristic, complemented
62C23×C113—21no—
63C23×C113—42no—
64C23×C113—41no—
65C23×C113C2×D411yescharacteristic
66C23×C113C2×D411yescharacteristic
67C22×D113—21no—
68C22×D113—21no—
69Q8×C113—41no—
70D4×C113—41no—
71D4×C113—42no—
72C2×C4×C113—21no—
73C2×C4×C113—21no—
74C2×C4×C113—21no—
75C2×C4×C113—21no—
76C2×C4×C113—21no—
77C2×C4×C113—42no—
78C2×C4×C113—41no—
79C2×C4×C113—81no—
80C2×C4×C113C2×D411yescharacteristic
81C22⋊D113—41no—
82C22⋊D113—41no—
83C22⋊D113—41no—
84C22⋊D113—82no—
85C2×Dic113—21no—
86C2×Dic113—21no—
87C2×Dic113—41no—
88C2×Dic113—41no—
89D452—21no—
90C4×D113—41no—
91Dic226—21no—
92#11744751—41no—
93C22×C113—22no—
94C22×C113—21no—
95C22×C113—21no—
96C22×C113—41no—
97C22×C113—41no—
98C22×C113—41no—
99C22×C113—42no—
100C22×C113—41no—
101C22×C113—81no—
102C22×C113#12011yescharacteristic
103C2×D113—41no—
104C2×D113—81no—
105C2×D113—81no—
106C4×C113—21no—
107C4×C113—41no—
108C4×C113—41no—
109C4×C113—41no—
110C4×C113—41no—
111C4×C113—41no—
112Dic113—41no—
113Dic113—81no—
114Dic113—81no—
115C2×C113—21no—
116C2×C113—41no—
117C2×C113—41no—
118C2×C113—42no—
119C2×C113B(4,𝔽2)11yescharacteristic
120D113—81no—
121#2197—1131nomaximal, Sylow
122C113#219711yescharacteristic, complemented, Sylow
123#551D11311yescharacteristic, complemented
124#458—1131no—
125B(4,𝔽2)—1131no—
126#455—1131no—
127#354—1131no—
128#352—1131no—
129AΣL(1,𝔽16)—1131no—
130H(5,𝔽2)—1131no—
131#137—2261no—
132#126—21no—
133#124C2×D11311yescharacteristic
134#123—21no—
135#123—2261no—
136#123C2×D11311yescharacteristic
137C22⋊Q8—21no—
138#120—2261no—
139#120C2×D11311yescharacteristic
140C4×D4—21no—
141#117—21no—
142C2×C22⋊C4—21no—
143#104—2261no—
144#100—1131no—
145#99—1131no—
146#99—1131no—
147#99—2261no—
148#99—2261no—
149C24C22⋊D11311yescharacteristic
150#41—4521no—
151#41—2261no—
152C2×Q8C22⋊D11311yescharacteristic, complemented
153C2×D4—21no—
154C2×D4—4521no—
155C2×D4—4521no—
156C2×D4—2261no—
157C2×D4—2261no—
158C2×D4C22×D11311yescharacteristic
159C22×C4—21no—
160C22×C4—21no—
161C22×C4C22⋊D11311yescharacteristic, complemented
162Q16—4521no—
163SD16—4521no—
164M16—2261no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—4521no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—21no—
173C22⋊C4—21no—
174C22⋊C4—21no—
175C22⋊C4—21no—
176C22⋊C4—4521no—
177C22⋊C4—4521no—
178C22⋊C4—2261no—
179C22⋊C4—2261no—
180C22⋊C4C22⋊D11311yescharacteristic
181C22⋊C4C22⋊D11311yescharacteristic, complemented
182C42—21no—
183C42C22⋊D11311yescharacteristic, complemented
184C23—21no—
185C23—41no—
186C23—42no—
187C23—2261no—
188C23—2261no—
189C23C2×C22⋊D11311yescharacteristic
190C23C2×C22⋊D11311yescharacteristic
191Q8—41no—
192Q8—2261no—
193D4—41no—
194D4—42no—
195D4—9042no—
196D4—4521no—
197D4—4521no—
198D4—4521no—
199D4—2261no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—81no—
208C2×C4—4521no—
209C2×C4—4521no—
210C2×C4—4521no—
211C2×C4—2261no—
212C2×C4—2261no—
213C2×C4C2×C22⋊D11311yescharacteristic
214C8—4521no—
215C22—22no—
216C22—21no—
217C22—21no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—42no—
222C22—41no—
223C22—81no—
224C22—9041no—
225C22—9041no—
226C22—4521no—
227C22#1681359111yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4—41no—
234C4—9041no—
235C4—9041no—
236C4—4521no—
237C2—21no—
238C2—41no—
239C2—41no—
240C2—42no—
241C2—9041no—
242C2#2029878511yescharacteristic
subgroupG/H
centerC2#20298785
commutator, cosocleC2×D4×C113C23
FrattiniC2×D4C22×D113
Fitting#551×C113C2
socleC2×C113B(4,𝔽2)
prime radical#20298784C2
hypercenter#551D113
hypocenterC113#2197
LCSG ▷ C2×D4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #551

Complements

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

NH ≅ G/Ntype
1. #20298787C2semidirect
3. #20298775C2semidirect
4. #20298393C2semidirect
5. #20298388C2semidirect
6. #20298385C2semidirect
7. #551×C113C2semidirect
42. C2×Q8×C113D4semidirect
47. C22×C4×C113D4semidirect
59. C22⋊C4×C113D4semidirect
61. C42×C113D4semidirect
122. C113#2197semidirect
123. #551D113semidirect
152. C2×Q8C22⋊D113semidirect
161. C22×C4C22⋊D113semidirect
181. C22⋊C4C22⋊D113semidirect
183. C42C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
#202987872
#202987842
#202987752
#202983932
#202983882
#202983852
#551×C1132
#2197113