Finite Group Databasebeta

← C2×#27161385 #38752488

Subgroups — C2×#27161385 #38752488

Order 25216.

384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 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×#20263317C211yesmaximal, characteristic
2C2×#20263291C211yesmaximal, characteristic
3#27161385C218yesmaximal, direct product factor
4C2×#20263257C211yesmaximal, characteristic
5C2×#20263255C211yesmaximal, characteristic
6C2×#20263251C211yesmaximal, characteristic
7C2×#20263249C211yesmaximal, characteristic
8C2×#107×C197C211yesmaximal, characteristic
9C22×Dic394C2211yescharacteristic
10C22×#13096802C2211yescharacteristic
11#20263317—22no—
12#20263317C2214yes—
13#20263291—22no—
14#20263291C2214yes—
15C2×C4⋊Dic197—21no—
16C2×C4⋊Dic197C2211yescharacteristic
17C2×#15691337—21no—
18C2×#15691337—21no—
19C2×C4×Dic197—21no—
20C2×C4×Dic197C2211yescharacteristic
21#20263257C2214yes—
22#20263255C2214yes—
23#20263251C2214yes—
24#20263249C2214yes—
25C22×C8×C197C2211yescharacteristic
26C2×C4⋊C4×C197C2211yescharacteristic
27C2×C4⋊C4×C197C2211yescharacteristic
28#107×C197C2214yes—
29C2×Dic394—21no—
30C2×Dic394—22no—
31C2×Dic394Q814yes—
32C2×Dic394C2312yes—
33C22×Dic197—21no—
34C22×Dic197—21no—
35C22×Dic197D411yescharacteristic
36C22×Dic197D411yescharacteristic
37C2×#13096802—22no—
38C2×#13096802C2312yes—
39C4⋊Dic197—24no—
40C4⋊Dic197—21no—
41C4⋊Dic197C2312yes—
42#15691337—24no—
43#15691337—24no—
44C4×Dic197—24no—
45C4×Dic197D412yes—
46C4×Dic197C2312yes—
47C22×C4×C197—21no—
48C22×C4×C197—21no—
49C22×C4×C197C2311yescharacteristic
50C2×C8×C197—22no—
51C2×C8×C197C2312yes—
52C4⋊C4×C197—21no—
53C4⋊C4×C197—21no—
54C4⋊C4×C197C2312yes—
55C4⋊C4×C197C2312yes—
56Dic394—24no—
57Dic394—22no—
58Dic394C2×Q814yes—
59C2×Dic197—24no—
60C2×Dic197—22no—
61C2×Dic197—22no—
62C2×Dic197—22no—
63C2×Dic197—22no—
64C2×Dic197—42no—
65C2×Dic197C2×D412yes—
66C2×Dic197C2×D412yes—
67#13096802—22no—
68C23×C197C2×D411yescharacteristic
69C2×C4×C197—22no—
70C2×C4×C197—22no—
71C2×C4×C197—42no—
72C2×C4×C197—42no—
73C2×C4×C197C2×D411yescharacteristic
74C2×C4×C197C2×Q812yes—
75C2×C4×C197#4112yes—
76C2×C4×C197C2411yescharacteristic
77C8×C197—22no—
78C22×C197C22⋊Q812yes—
79C22×C197#13512yes—
80C22×C197#13712yes—
81C22×C197C22×D411yescharacteristic
82C4×C197—42no—
83C4×C197—42no—
84C4×C197C22⋊Q812yes—
85C4×C197C22×Q811yescharacteristic
86C4×C197C2×#4111yescharacteristic
87Dic197—24no—
88Dic197—22no—
89Dic197—22no—
90Dic197—42no—
91C2×C197#47914yescomplemented
92C2×C197C2×C22⋊Q811yescharacteristic
93C2×C197C2×#13511yescharacteristic
94C2×C197C2×#13711yescharacteristic
95C197C2×#47911yescharacteristic, complemented, Sylow
96C2×#479—1971nomaximal, Sylow
97C2×#125—1971no—
98C2×C4×Q8—1971no—
99#479—1978no—
100C2×#107D19711yescharacteristic
101C2×#106—1971no—
102C2×C4⋊C8—1971no—
103C2×#103—1971no—
104C2×#103—1971no—
105C22×Q8—1971no—
106C22×C8—1971no—
107C22×C8C2×D19711yescharacteristic
108#125—3942no—
109#125—1974no—
110C4×Q8—3942no—
111C4×Q8—1974no—
112C2×C4⋊C4—3941no—
113C2×C4⋊C4—3941no—
114C2×C4⋊C4—3941no—
115C2×C4⋊C4—1971no—
116C2×C4⋊C4C2×D19711yescharacteristic
117C2×C4⋊C4C2×D19711yescharacteristic
118C2×C42—3941no—
119C2×C42—1971no—
120#107C2×D19714yes—
121#106—1974no—
122C4⋊C8—1974no—
123#103—1974no—
124#103—1974no—
125C2×Q8—3941no—
126C2×Q8—3942no—
127C2×Q8—1974no—
128C2×Q8—1972no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—3941no—
132C22×C4—3941no—
133C22×C4—1971no—
134C22×C4—1971no—
135C22×C4C22×D19711yescharacteristic
136C2×C8—22no—
137C2×C8—3942no—
138C2×C8—1972no—
139C2×C8C22×D19712yes—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—3944no—
143C4⋊C4—3944no—
144C4⋊C4—3944no—
145C4⋊C4—3941no—
146C4⋊C4—1972no—
147C4⋊C4C22×D19712yes—
148C4⋊C4C22×D19712yes—
149C42—3944no—
150C42—1972no—
151C42—1972no—
152C23D4×D19711yescharacteristic
153Q8—3944no—
154Q8—3942no—
155Q8—1974no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—7882no—
161C2×C4—3942no—
162C2×C4—3944no—
163C2×C4—3942no—
164C2×C4—3942no—
165C2×C4—3942no—
166C2×C4—1972no—
167C2×C4—1972no—
168C2×C4D4×D19711yescharacteristic
169C2×C4Q8×D19712yes—
170C2×C4#1569135812yes—
171C2×C4C23×D19711yescharacteristic
172C8—22no—
173C8—3942no—
174C22#2026330412yes—
175C22#2026334512yes—
176C22#2026335812yes—
177C22C2×D4×D19711yescharacteristic
178C4—42no—
179C4—42no—
180C4—7882no—
181C4—3942no—
182C4—3942no—
183C4—3944no—
184C4#2026330412yes—
185C4C2×Q8×D19711yescharacteristic
186C4C2×#1569135811yescharacteristic
187C2#2716138514yesdirect product factor
188C2C2×#2026330411yescharacteristic
189C2C2×#2026334511yescharacteristic
190C2C2×#2026335811yescharacteristic
subgroupG/H
centerC23D4×D197
commutator, cosocleC2×C4×C197C24
FrattiniC2×C4C23×D197
FittingC2×#107×C197C2
socle, prime radicalC23×C197C2×D4
hypercenterC2×#107D197
hypocenterC197C2×#479
LCSG ▷ C2×C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #27161385C2direct (N × H)
91. C2×C197#479semidirect
95. C197C2×#479semidirect
187. C2#27161385direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#202633172
C2×#202632912
#271613852
C2×#202632572
C2×#202632552
C2×#202632512
C2×#202632492
C2×#107×C1972
C2×#479197