Finite Group Databasebeta

← #38745293

Subgroups — #38745293

Order 25216.

1104 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 229 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
1C23×C22⋊D197C211yesmaximal, characteristic
2C2×#20263282C212yesmaximal, complemented
3#27160979C218yesmaximal, complemented
4#27160935C211yesmaximal, characteristic, complemented
5#27160934C212yesmaximal, complemented
6#379×C197C211yesmaximal, characteristic, complemented
7C24×D197C2211yescharacteristic
8C22×C22⋊D197—28no—
9C22×C22⋊D197C418yescomplemented
10C22×C22⋊D197C2214yes—
11C23×Dic197C2211yescharacteristic
12#20263282—28no—
13C2×#15691337C2214yescomplemented
14C2×C22⋊Dic197C2212yes—
15C2×C22⋊Dic197C2214yescomplemented
16C2×#15691335C2218yescomplemented
17C2×C4×Dic197C2214yescomplemented
18C25×C197C2211yescharacteristic
19C2×C22⋊C4×C197C2212yes—
20C2×C22⋊C4×C197C2214yescomplemented
21C23×D197—24no—
22C23×D197—44no—
23C23×D197C2×C414yes—
24C23×D197C2312yes—
25C2×C22⋊D197—232no—
26C2×C22⋊D197—28no—
27C2×C22⋊D197—28no—
28C2×C22⋊D197C2×C4116yes—
29C22×Dic197C2×C414yes—
30C22×Dic197D418yes—
31C22×Dic197C2314yes—
32C22×Dic197C2312yes—
33#15691337—28no—
34C22⋊Dic197—24no—
35C22⋊Dic197—44no—
36#15691335—48no—
37C4×Dic197—28no—
38C24×C197—24no—
39C24×C197—44no—
40C24×C197C2×C414yes—
41C24×C197C2312yes—
42C24×C197C2311yescharacteristic
43C22×C4×C197C2314yes—
44C22⋊C4×C197—24no—
45C22⋊C4×C197—44no—
46C22×D197—28no—
47C22×D197—24no—
48C22×D197—28no—
49C22×D197—48no—
50C22×D197—416no—
51C22×D197C22×C414yes—
52C22⋊D197—232no—
53C2×Dic197—24no—
54C2×Dic197—28no—
55C2×Dic197C22⋊C4116yescomplemented
56C2×Dic197C22×C414yes—
57C2×Dic197C2×D414yes—
58C2×Dic197C2×D414yes—
59C23×C197—24no—
60C23×C197—28no—
61C23×C197—24no—
62C23×C197—24no—
63C23×C197—24no—
64C23×C197—48no—
65C23×C197—416no—
66C23×C197C22×C414yes—
67C23×C197C22×C412yes—
68C23×C197C2×D414yes—
69C23×C197C2411yescharacteristic
70C2×C4×C197—24no—
71C2×C4×C197—28no—
72C22×C197—24no—
73C22×C197—28no—
74C22×C197—24no—
75C22×C197—24no—
76C22×C197—24no—
77C22×C197—416no—
78C22×C197—48no—
79C22×C197C2×C22⋊C414yes—
80C22×C197C23×C411yescharacteristic
81C22×C197C22×D412yes—
82C22×C197H(5,𝔽2)14yes—
83C2×D197—24no—
84C2×D197—28no—
85C2×D197—416no—
86C2×D197—48no—
87C4×C197—44no—
88Dic197—44no—
89Dic197C2×C22⋊C418yes—
90C2×C197—24no—
91C2×C197—44no—
92C2×C197C22×C22⋊C411yescharacteristic
93C2×C197#51812yes—
94C2×C197#53514yes—
95D197—44no—
96C197#230911yescharacteristic, complemented, Sylow
97#2309—1971nomaximal, Sylow
98C23×D4—1971no—
99C2×#117—1972no—
100#390—1978no—
101#379—1971no—
102#379—1972no—
103#379D19711yescharacteristic, complemented
104C25—1971no—
105C25C2×D19711yescharacteristic
106C22×D4—3948no—
107C22×D4—1978no—
108C22×D4—1974no—
109C23×C4—1971no—
110#117—3948no—
111C2×C4⋊C4—1974no—
112C2×C22⋊C4—1974no—
113C2×C22⋊C4—1978no—
114C2×C22⋊C4—1972no—
115C2×C22⋊C4C2×D19712yes—
116C2×C22⋊C4C2×D19714yescomplemented
117C2×C42—1974no—
118C24—24no—
119C24—44no—
120C24—7884no—
121C24—3944no—
122C24—1974no—
123C24—1972no—
124C24C4×D19714yes—
125C24C22×D19712yes—
126C24C22×D19711yescharacteristic
127C2×D4—39432no—
128C2×D4—3948no—
129C2×D4—3948no—
130C2×D4—19716no—
131C22×C4—1974no—
132C22×C4—1974no—
133C22×C4—1978no—
134C22×C4—1972no—
135C22×C4C22×D19714yes—
136C4⋊C4—3948no—
137C22⋊C4—24no—
138C22⋊C4—44no—
139C22⋊C4—7888no—
140C22⋊C4—7884no—
141C22⋊C4—3944no—
142C42—3948no—
143C23—24no—
144C23—28no—
145C23—24no—
146C23—24no—
147C23—24no—
148C23—48no—
149C23—416no—
150C23—78816no—
151C23—7888no—
152C23—3948no—
153C23—3944no—
154C23—3948no—
155C23—1974no—
156C23C2×C4×D19714yes—
157C23C2×C4×D19712yes—
158C23D4×D19714yes—
159C23C23×D19711yescharacteristic
160D4—39432no—
161C2×C4—24no—
162C2×C4—28no—
163C2×C4—3944no—
164C2×C4—3948no—
165C2×C4—19716no—
166C2×C4—1974no—
167C2×C4—1974no—
168C2×C4—1974no—
169C22—28no—
170C22—24no—
171C22—24no—
172C22—24no—
173C22—24no—
174C22—416no—
175C22—48no—
176C22—78816no—
177C22—7888no—
178C22—3944no—
179C22—3948no—
180C22C22⋊C4×D19714yes—
181C22C22×C4×D19711yescharacteristic
182C22C2×D4×D19712yes—
183C22#2026337114yes—
184C4—44no—
185C4—7884no—
186C4—1978no—
187C2—24no—
188C2—44no—
189C2—7884no—
190C2C2×C22⋊C4×D19711yescharacteristic
191C2#2716155212yes—
192C2#2716164414yes—
subgroupG/H
center, FrattiniC23C23×D197
commutatorC22×C197C23×C4
Fitting#379×C197C2
socle, cosocleC23×C197C24
prime radicalC23×C22⋊D197C2
hypercenter#379D197
hypocenterC197#2309
LCSG ▷ C22×C197 ▷ C197
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×#20263282C2semidirect
3. #27160979C2semidirect
4. #27160935C2semidirect
5. #27160934C2semidirect
6. #379×C197C2semidirect
9. C22×C22⋊D197C4semidirect
13. C2×#15691337C22semidirect
15. C2×C22⋊Dic197C22semidirect
16. C2×#15691335C22semidirect
17. C2×C4×Dic197C22semidirect
20. C2×C22⋊C4×C197C22semidirect
55. C2×Dic197C22⋊C4semidirect
96. C197#2309semidirect
103. #379D197semidirect
116. C2×C22⋊C4C2×D197semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊D1972
C2×#202632822
#271609792
#271609352
#271609342
#379×C1972
#2309197