Finite Group Databasebeta

← #38745817

Subgroups — #38745817

Order 25216.

448 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 185 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
1C2×#20263318C211yesmaximal, characteristic
2#27160964C212yesmaximal
3#27160963C212yesmaximal
4#27160962C212yesmaximal
5#27160961C212yesmaximal
6C4×#15691337C212yesmaximal
7#27160930C212yesmaximal
8#27160925C211yesmaximal, characteristic
9#376×C197C211yesmaximal, characteristic
10#20263318C418yescomplemented
11C2×C4⋊Dic197C2211yescharacteristic
12C2×C4⋊Dic197C2211yescharacteristic
13C2×#15691337C2212yes—
14C2×#15691337C2212yes—
15C2×#15691337C2212yes—
16C2×#15691337C2212yes—
17C2×C4×Dic197C2212yes—
18C2×C4×Dic197C2212yes—
19C2×C4×Dic197C2212yes—
20#20263233C2211yescharacteristic
21#20263233C2212yes—
22#20263233C2211yescharacteristic
23#20263233C2212yes—
24#20263233C2212yes—
25#20263233C2212yes—
26#20263233C2212yes—
27C2×C42×C197C2212yes—
28C2×C42×C197C2211yescharacteristic
29#95×C197C2211yescharacteristic
30#95×C197C2211yescharacteristic
31#95×C197C2212yes—
32C22×Dic197C2312yes—
33C22×Dic197C2312yes—
34C22×Dic197C2312yes—
35C22×Dic197C2312yes—
36C4⋊Dic197C2×C414yes—
37C4⋊Dic197C2×C414yes—
38#15691337—24no—
39#15691337—24no—
40#15691337C2×C418yes—
41#15691337C2×C418yes—
42C4×Dic197—24no—
43C4×Dic197—24no—
44C4×Dic197—24no—
45C22×C4×C197C2312yes—
46C22×C4×C197C2311yescharacteristic
47C22×C4×C197C2311yescharacteristic
48C22×C4×C197C2311yescharacteristic
49C22×C4×C197C2312yes—
50C42×C197—24no—
51C42×C197C2×C414yes—
52C2×Dic197—22no—
53C2×Dic197—22no—
54C2×Dic197—22no—
55C2×Dic197—22no—
56C2×Dic197—22no—
57C2×Dic197—22no—
58C2×Dic197—22no—
59C2×Dic197—22no—
60C2×Dic197—22no—
61C2×Dic197C22×C414yes—
62C2×Dic197C22×C414yes—
63C2×Dic197#4114yes—
64C23×C197C2411yescharacteristic
65C2×C4×C197—22no—
66C2×C4×C197—22no—
67C2×C4×C197—22no—
68C2×C4×C197—21no—
69C2×C4×C197—21no—
70C2×C4×C197—22no—
71C2×C4×C197—22no—
72C2×C4×C197—22no—
73C2×C4×C197—22no—
74C2×C4×C197C22×C412yes—
75C2×C4×C197C22×C412yes—
76C2×C4×C197C22×C412yes—
77C2×C4×C197#4114yes—
78C22×C197C23×C411yescharacteristic
79C22×C197C2×#4112yes—
80C22×C197C2×#4112yes—
81C22×C1972−1+411yescharacteristic
82C22×C1972−1+411yescharacteristic
83C4×C197—22no—
84C4×C197—22no—
85C4×C197—22no—
86C4×C197—24no—
87C4×C197—42no—
88Dic197—24no—
89Dic197—24no—
90Dic197—24no—
91Dic197—42no—
92C2×C197C4×#4111yescharacteristic
93C2×C197C4×#4111yescharacteristic
94C2×C197#51911yescharacteristic
95C2×C197#55212yes—
96C2×C197#55212yes—
97C197#237111yescharacteristic, complemented, Sylow
98#2371—1971nomaximal, Sylow
99C2×#125—1971no—
100#387—1972no—
101#387—1972no—
102#387—1972no—
103#387—1972no—
104C4×C4⋊C4—1972no—
105C4×C4⋊C4—1972no—
106#376—1971no—
107#376D19711yescharacteristic
108#125—1978no—
109C2×C4⋊C4—1972no—
110C2×C4⋊C4—1972no—
111C2×C4⋊C4—1972no—
112C2×C4⋊C4—1972no—
113C2×C4⋊C4—1971no—
114C2×C4⋊C4—1971no—
115C2×C42—1972no—
116C2×C42—1972no—
117C2×C42—1972no—
118C2×C42C2×D19712yes—
119C2×C42C2×D19711yescharacteristic
120#95—1971no—
121#95—1971no—
122#95—1972no—
123#95—1972no—
124#95—1972no—
125#95—1972no—
126#95—1972no—
127#95C2×D19711yescharacteristic
128#95C2×D19711yescharacteristic
129#95C2×D19712yes—
130C22×C4—1972no—
131C22×C4—1972no—
132C22×C4—1972no—
133C22×C4—1972no—
134C22×C4C22×D19712yes—
135C22×C4C22×D19711yescharacteristic
136C22×C4C22×D19711yescharacteristic
137C22×C4C22×D19711yescharacteristic
138C22×C4C22×D19712yes—
139C4⋊C4—3944no—
140C4⋊C4—3944no—
141C4⋊C4—1978no—
142C4⋊C4—1978no—
143C4⋊C4—1974no—
144C4⋊C4—1974no—
145C42—24no—
146C42—3944no—
147C42—3944no—
148C42—3944no—
149C42C4×D19714yes—
150C23C23×D19711yescharacteristic
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—3942no—
161C2×C4—3942no—
162C2×C4—3942no—
163C2×C4—3942no—
164C2×C4—3942no—
165C2×C4—3942no—
166C2×C4—3942no—
167C2×C4—3942no—
168C2×C4—3942no—
169C2×C4—1974no—
170C2×C4—1974no—
171C2×C4—1974no—
172C2×C4C2×C4×D19712yes—
173C2×C4C2×C4×D19712yes—
174C2×C4C2×C4×D19712yes—
175C2×C4#1569135814yes—
176C22C22×C4×D19711yescharacteristic
177C22#41×D19712yes—
178C22C2×#1569135812yes—
179C22#2026337311yescharacteristic
180C22#2026337311yescharacteristic
181C4—24no—
182C4—22no—
183C4—22no—
184C4—22no—
185C4—42no—
186C4—7882no—
187C4—3944no—
188C4—3944no—
189C4—3944no—
190C2#2716154711yescharacteristic
191C2C4×#1569135811yescharacteristic
192C2#2716155611yescharacteristic
193C2#2716176212yes—
194C2#2716176812yes—
subgroupG/H
center, FrattiniC23C23×D197
commutatorC22×C197C23×C4
Fitting#376×C197C2
socle, prime radical, cosocleC23×C197C24
hypercenter#376D197
hypocenterC197#2371
LCSG ▷ C22×C197 ▷ C197
UCSC1 ◁ C23 ◁ #376

Complements

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

NH ≅ G/Ntype
10. #20263318C4semidirect
97. C197#2371semidirect

Maximal subgroups

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

subgroupindex
C2×#202633182
#271609642
#271609632
#271609622
#271609612
C4×#156913372
#271609302
#271609252
#376×C1972
#2371197