Finite Group Databasebeta

← #28389622

Subgroups — #28389622

Order 14464.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#20298931C211yesmaximal, characteristic, complemented
2#20298914C211yesmaximal, characteristic, complemented
3#20298534C211yesmaximal, characteristic, complemented
4#20298335C211yesmaximal, characteristic, complemented
5#20298332C211yesmaximal, characteristic, complemented
6#20298322C211yesmaximal, characteristic, complemented
7#538×C113C211yesmaximal, characteristic
8C2×C4⋊Dic113C2211yescharacteristic
9C2×#14268626—21no—
10C2×C22⋊Dic113—21no—
11#16813555—21no—
12#16813553—21no—
13#16813546—21no—
14#16813543—21no—
15C22⋊#11744751C2211yescharacteristic
16C22⋊#11744751C2211yescharacteristic
17#16813529C2211yescharacteristic
18#126×C113—21no—
19#124×C113—21no—
20#123×C113—21no—
21C22⋊Q8×C113C2211yescharacteristic
22#121×C113—21no—
23#121×C113C2211yescharacteristic
24#120×C113—21no—
25C4×D4×C113—21no—
26C2×C22⋊C4×C113C2211yescharacteristic
27C22×Dic113—21no—
28C22×Dic113—21no—
29C2×#11744751—21no—
30C2×#11744751—21no—
31C4⋊Dic113—21no—
32C4⋊Dic113—21no—
33#14268626—42no—
34C22⋊Dic113—42no—
35C24×C113D411yescharacteristic
36C2×Q8×C113D411yescharacteristic
37C2×D4×C113—21no—
38C2×D4×C113—21no—
39C2×D4×C113—21no—
40C2×D4×C113D411yescharacteristic
41C22×C4×C113—21no—
42C22×C4×C113D411yescharacteristic
43C22×C4×C113C2311yescharacteristic
44C4⋊C4×C113—21no—
45C4⋊C4×C113—21no—
46C4⋊C4×C113D411yescharacteristic
47C4⋊C4×C113D411yescharacteristic
48C22⋊C4×C113—21no—
49C22⋊C4×C113—21no—
50C22⋊C4×C113—21no—
51C22⋊C4×C113—21no—
52C22⋊C4×C113—21no—
53C22⋊C4×C113—21no—
54C22⋊C4×C113—21no—
55C42×C113—21no—
56C23×C113—21no—
57C23×C113—21no—
58C23×C113—21no—
59C23×C113—21no—
60C23×C113—41no—
61C23×C113—41no—
62C23×C113C2×D411yescharacteristic
63Q8×C113—41no—
64D4×C113—41no—
65D4×C113—41no—
66D4×C113—41no—
67D4×C113—81no—
68D4×C113—81no—
69C2×C4×C113—21no—
70C2×C4×C113—21no—
71C2×C4×C113—21no—
72C2×C4×C113—21no—
73C2×C4×C113—41no—
74C2×C4×C113—41no—
75C2×C4×C113—81no—
76C2×C4×C113C2×D411yescharacteristic
77C2×C4×C113C2×D411yescharacteristic
78C2×Dic113—22no—
79C2×Dic113—41no—
80C2×Dic113—41no—
81C2×Dic113—41no—
82C2×Dic113—41no—
83C2×Dic113—41no—
84#11744751—41no—
85#11744751—41no—
86C22×C113—21no—
87C22×C113—21no—
88C22×C113—42no—
89C22×C113—41no—
90C22×C113—41no—
91C22×C113—41no—
92C22×C113—41no—
93C22×C113—41no—
94C22×C113—41no—
95C22×C113—81no—
96C22×C113#12011yescharacteristic
97C22×C113#13511yescharacteristic
98C22×C113#13711yescharacteristic
99C4×C113—21no—
100C4×C113—21no—
101C4×C113—41no—
102C4×C113—41no—
103C4×C113—41no—
104C4×C113—41no—
105Dic113—42no—
106Dic113—81no—
107C2×C113—21no—
108C2×C113—21no—
109C2×C113—81no—
110C2×C113—81no—
111C2×C113#45211yescharacteristic
112C2×C113#45311yescharacteristic
113C2×C113#45811yescharacteristic
114#1618—1131nomaximal, Sylow
115C113#161811yescharacteristic, complemented, Sylow
116#538D11311yescharacteristic
117#484—1131no—
118#481—1131no—
119#399—1131no—
120#328—1131no—
121#327—1131no—
122#323—1131no—
123#126—21no—
124#124—21no—
125#123—21no—
126C22⋊Q8C2×D11311yescharacteristic
127#121—21no—
128#121C2×D11311yescharacteristic
129#120—21no—
130C4×D4—21no—
131C2×C4⋊C4—1131no—
132C2×C4⋊C4—2261no—
133C2×C22⋊C4—2261no—
134C2×C22⋊C4C2×D11311yescharacteristic
135#107—2261no—
136#106—2261no—
137#103—2261no—
138#102—2261no—
139C22⋊C8—1131no—
140C22⋊C8—1131no—
141#95—1131no—
142C24C22⋊D11311yescharacteristic
143C2×Q8C22⋊D11311yescharacteristic
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4C22⋊D11311yescharacteristic
148C22×C4—21no—
149C22×C4—2261no—
150C22×C4—2261no—
151C22×C4C22⋊D11311yescharacteristic
152C22×C4C22×D11311yescharacteristic
153C2×C8—2261no—
154C2×C8—2261no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—4522no—
158C4⋊C4—2261no—
159C4⋊C4—2261no—
160C4⋊C4C22⋊D11311yescharacteristic
161C4⋊C4C22⋊D11311yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—21no—
166C22⋊C4—21no—
167C22⋊C4—21no—
168C22⋊C4—21no—
169C22⋊C4—4522no—
170C42—21no—
171C23—21no—
172C23—21no—
173C23—21no—
174C23—21no—
175C23—41no—
176C23—41no—
177C23C2×C22⋊D11311yescharacteristic
178Q8—41no—
179D4—41no—
180D4—41no—
181D4—41no—
182D4—81no—
183D4—81no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—81no—
191C2×C4—4521no—
192C2×C4—4521no—
193C2×C4—4521no—
194C2×C4—4521no—
195C2×C4—4521no—
196C2×C4—2262no—
197C2×C4C2×C22⋊D11311yescharacteristic
198C2×C4C2×C22⋊D11311yescharacteristic
199C8—4521no—
200C8—4521no—
201C22—21no—
202C22—21no—
203C22—42no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—81no—
211C22#1681359111yescharacteristic
212C22#1681364211yescharacteristic
213C22#1681365211yescharacteristic
214C4—21no—
215C4—21no—
216C4—41no—
217C4—41no—
218C4—41no—
219C4—41no—
220C4—9041no—
221C4—4522no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—81no—
226C2#2029876011yescharacteristic
227C2#2029876611yescharacteristic
228C2#2029878811yescharacteristic
subgroupG/H
centerC22#16813591
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting, prime radical#538×C113C2
socleC22×C113#120
hypercenter#538D113
hypocenterC113#1618
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #538

Complements

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

NH ≅ G/Ntype
1. #20298931C2semidirect
2. #20298914C2semidirect
3. #20298534C2semidirect
4. #20298335C2semidirect
5. #20298332C2semidirect
6. #20298322C2semidirect
115. C113#1618semidirect

Maximal subgroups

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

subgroupindex
#202989312
#202989142
#202985342
#202983352
#202983322
#202983222
#538×C1132
#1618113