Finite Group Databasebeta

← #38741718

Subgroups — #38741718

Order 25216.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#27161708C211yesmaximal, characteristic
2#27161409C211yesmaximal, characteristic
3#27161010C211yesmaximal, characteristic
4#27160817C211yesmaximal, characteristic
5#27160816C211yesmaximal, characteristic
6#27160804C211yesmaximal, characteristic
7#483×C197C211yesmaximal, characteristic
8#20263325—21no—
9#20263324—21no—
10#20263316—21no—
11#20263316—21no—
12#20263305C2211yescharacteristic
13#20263303—21no—
14#20263282—21no—
15C2×#15691337—21no—
16C2×#15691337C2211yescharacteristic
17#20263257—21no—
18#20263249—21no—
19C22⋊#13096802C2211yescharacteristic
20#20263233—21no—
21#20263233C2211yescharacteristic
22C22⋊Q8×C197C2211yescharacteristic
23C2×C4⋊C4×C197C2211yescharacteristic
24#106×C197—21no—
25#103×C197—21no—
26C22⋊C8×C197C2211yescharacteristic
27C2×Dic394—21no—
28C2×Dic394D411yescharacteristic
29C22×Dic197—21no—
30C22×Dic197D411yescharacteristic
31C22×Dic197D411yescharacteristic
32C2×#13096802—21no—
33C4⋊Dic197—21no—
34C4⋊Dic197D411yescharacteristic
35#15691337—21no—
36#15691337—21no—
37#15691337—21no—
38#15691337—21no—
39#15691337—21no—
40#15691337—21no—
41#15691337—21no—
42#15691337—42no—
43C22⋊Dic197—21no—
44C4×Dic197—21no—
45C4×Dic197—21no—
46C2×Q8×C197D411yescharacteristic
47C22×C4×C197—21no—
48C22×C4×C197C2311yescharacteristic
49C2×C8×C197—21no—
50C4⋊C4×C197—21no—
51C4⋊C4×C197—21no—
52C4⋊C4×C197—21no—
53C4⋊C4×C197D411yescharacteristic
54C22⋊C4×C197—21no—
55Dic394—41no—
56Dic394—81no—
57C2×Dic197—21no—
58C2×Dic197—21no—
59C2×Dic197—22no—
60C2×Dic197—21no—
61C2×Dic197—21no—
62C2×Dic197—21no—
63C2×Dic197—41no—
64C2×Dic197—41no—
65C2×Dic197—41no—
66C2×Dic197SD1612yes—
67#13096802—41no—
68C23×C197C2×D411yescharacteristic
69Q8×C197—41no—
70C2×C4×C197—21no—
71C2×C4×C197—21no—
72C2×C4×C197—41no—
73C2×C4×C197—41no—
74C2×C4×C197—41no—
75C2×C4×C197—41no—
76C2×C4×C197C2×D411yescharacteristic
77C2×C4×C197C2×D411yescharacteristic
78C8×C197—41no—
79C22×C197—21no—
80C22×C197—21no—
81C22×C197#12011yescharacteristic
82C22×C197C2×SD1611yescharacteristic
83C22×C197#13711yescharacteristic
84C4×C197—21no—
85C4×C197—21no—
86C4×C197—41no—
87C4×C197—41no—
88C4×C197—81no—
89Dic197—22no—
90Dic197—42no—
91Dic197—41no—
92Dic197—41no—
93Dic197—41no—
94C2×C197—21no—
95C2×C197—21no—
96C2×C197#44811yescharacteristic
97C2×C197#45611yescharacteristic
98C2×C197#45811yescharacteristic
99C197#161111yescharacteristic, complemented, Sylow
100#1611—1971nomaximal, Sylow
101#544—1971no—
102#483—1971no—
103#483D19711yescharacteristic
104#398—1971no—
105#328—1971no—
106#328—1971no—
107#324—1971no—
108C4⋊Q8—3941no—
109C4⋊Q8—3941no—
110#125—3941no—
111#125—3941no—
112C22⋊Q8—3941no—
113C22⋊Q8—1971no—
114C22⋊Q8C2×D19711yescharacteristic
115#117—3941no—
116C2×C4⋊C4—3941no—
117C2×C4⋊C4—1971no—
118C2×C4⋊C4C2×D19711yescharacteristic
119#106—21no—
120#106—3941no—
121#103—21no—
122#103—3941no—
123C22⋊C8—1971no—
124C22⋊C8C2×D19711yescharacteristic
125#95—3941no—
126#95—1971no—
127C2×Q8—3941no—
128C2×Q8—1971no—
129C2×Q8C22⋊D19711yescharacteristic
130C22×C4—21no—
131C22×C4—3941no—
132C22×C4—1971no—
133C22×C4—1971no—
134C22×C4C22×D19711yescharacteristic
135C2×C8—21no—
136C2×C8—3941no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—7882no—
141C4⋊C4—3941no—
142C4⋊C4—3941no—
143C4⋊C4—3941no—
144C4⋊C4—3941no—
145C4⋊C4—3941no—
146C4⋊C4—3941no—
147C4⋊C4—3941no—
148C4⋊C4—3941no—
149C4⋊C4—1971no—
150C4⋊C4C22⋊D19711yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—3941no—
153C42—3941no—
154C42—3941no—
155C23D4×D19711yescharacteristic
156Q8—41no—
157Q8—7881no—
158Q8—15761no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—7881no—
166C2×C4—7881no—
167C2×C4—7881no—
168C2×C4—3942no—
169C2×C4—3941no—
170C2×C4—3941no—
171C2×C4—3941no—
172C2×C4—3941no—
173C2×C4—3941no—
174C2×C4—1972no—
175C2×C4D4×D19711yescharacteristic
176C2×C4C2×C22⋊D19711yescharacteristic
177C8—41no—
178C8—7881no—
179C22—21no—
180C22—21no—
181C22#2026329411yescharacteristic
182C22SD16×D19711yescharacteristic
183C22#2026335511yescharacteristic
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—81no—
189C4—7882no—
190C4—7881no—
191C4—7881no—
192C4—7881no—
193C4—3942no—
194C2—21no—
195C2—21no—
196C2#2716121611yescharacteristic
197C2#2716126011yescharacteristic
198C2#2716126811yescharacteristic
subgroupG/H
centerC22#20263294
commutator, cosocleC22×C4×C197C23
FrattiniC22×C4C22×D197
Fitting#483×C197C2
socleC22×C197#120
prime radicalC23×C197C2×D4
hypercenter#483D197
hypocenterC197#1611
LCSG ▷ C22×C4×C197 ▷ C22×C197 ▷ C197
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
99. C197#1611semidirect

Maximal subgroups

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

subgroupindex
#271617082
#271614092
#271610102
#271608172
#271608162
#271608042
#483×C1972
#1611197