Finite Group Databasebeta

← #38742639

Subgroups — #38742639

Order 25216.

584 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#15691359C211yesmaximal, characteristic
2C2×#20263245C211yesmaximal, characteristic, complemented
3C2×#20263242C212yesmaximal, complemented
4#27161042C212yesmaximal, complemented
5C2×#101×C197C211yesmaximal, characteristic, complemented
6C2×#15691359—24no—
7C2×#15691359—24no—
8C2×#15691359—22no—
9C2×#15691359—22no—
10C22×D788C412yes—
11C22×D788C2211yescharacteristic
12C22×C4×D197C412yes—
13C22×C4×D197C2211yescharacteristic
14C2×#15691342C2212yes—
15#20263245—22no—
16#20263242—24no—
17#20263238—24no—
18C22×Q8×C197C2211yescharacteristic
19C2×M16×C197C2212yes—
20#101×C197—22no—
21C23×D197C2×C412yes—
22C23×D197C2×C411yescharacteristic
23#15691359—216no—
24#15691359—216no—
25C2×D788—24no—
26C2×D788—24no—
27C2×D788—24no—
28C2×D788—22no—
29C2×D788—21no—
30C2×D788—21no—
31C2×D788D414yes—
32C22×Dic197C2×C411yescharacteristic
33C2×C4×D197—24no—
34C2×C4×D197—24no—
35C2×C4×D197—24no—
36C2×C4×D197—22no—
37C2×C4×D197—21no—
38C2×C4×D197—21no—
39C2×C4×D197D414yes—
40#15691342—22no—
41#15691342—22no—
42C2×#13096802—22no—
43C2×Q8×C197—22no—
44C2×Q8×C197—22no—
45C2×Q8×C197D412yes—
46C2×Q8×C197D412yes—
47C22×C4×C197C2×C412yes—
48C22×C4×C197C2311yescharacteristic
49M16×C197—22no—
50M16×C197—22no—
51C2×C8×C197—22no—
52C22×D197—21no—
53C22×D197—22no—
54C22×D197—22no—
55C22×D197—21no—
56C22×D197—42no—
57C22×D197—44no—
58C22×D197C22⋊C412yes—
59C22×D197C22⋊C414yes—
60D788—216no—
61D788—24no—
62D788—24no—
63C2×Dic197—21no—
64C2×Dic197—21no—
65C2×Dic197C22⋊C412yes—
66C4×D197—216no—
67C4×D197—24no—
68C4×D197—24no—
69#13096802—42no—
70C23×C197C22×C411yescharacteristic
71Q8×C197—24no—
72Q8×C197—24no—
73C2×C4×C197—22no—
74C2×C4×C197—22no—
75C2×C4×C197C22⋊C414yes—
76C2×C4×C197C2×D412yes—
77C2×C4×C197C2×D412yes—
78C2×C4×C197C2×D411yescharacteristic
79C2×C4×C197C2×D411yescharacteristic
80C8×C197—42no—
81C22×C197—22no—
82C22×C197C2×C22⋊C411yescharacteristic
83C22×C197C2×C22⋊C411yescharacteristic
84C22×C197C2×C22⋊C411yescharacteristic
85C2×D197—22no—
86C2×D197—24no—
87C2×D197—24no—
88C2×D197—42no—
89C2×D197—42no—
90C2×D197—44no—
91C2×D197—44no—
92C2×D197—44no—
93C4×C197—24no—
94C4×C197#12012yes—
95C4×C197#12012yes—
96Dic197—22no—
97C2×C197—21no—
98C2×C197—21no—
99C2×C197#37911yescharacteristic
100C2×C197#41312yes—
101D197—42no—
102D197—44no—
103C197#178511yescharacteristic, complemented, Sylow
104#1785—1971nomaximal, Sylow
105C22×#41—1971no—
106C2×#101—1971no—
107C2×#101D19711yescharacteristic, complemented
108C2×#100—1972no—
109#407—1972no—
110C2×#41—3942no—
111C2×#41—3942no—
112C2×#41—3944no—
113C2×#41—3944no—
114C22×Q8C2×D19711yescharacteristic
115C22×D4—1972no—
116C22×D4—1971no—
117C23×C4—1972no—
118C23×C4—1971no—
119C2×M16—1972no—
120C2×M16C2×D19712yes—
121#101—22no—
122#101—3942no—
123#100—3944no—
124C22⋊C8—3944no—
125C24—1972no—
126C24—1971no—
127#41—39416no—
128#41—39416no—
129C2×Q8—22no—
130C2×Q8—22no—
131C2×Q8C22⋊D19712yes—
132C2×Q8D78812yes—
133C2×D4—3944no—
134C2×D4—3944no—
135C2×D4—3944no—
136C2×D4—3942no—
137C2×D4—3941no—
138C2×D4—3941no—
139C2×D4—1974no—
140C22×C4—3944no—
141C22×C4—3944no—
142C22×C4—3944no—
143C22×C4—3942no—
144C22×C4—3941no—
145C22×C4—3941no—
146C22×C4—1971no—
147C22×C4—1974no—
148C22×C4C4×D19712yes—
149C22×C4C22×D19711yescharacteristic
150M16—22no—
151M16—22no—
152M16—3942no—
153M16—3942no—
154C2×C8—22no—
155C2×C8—3942no—
156C23—7884no—
157C23—7882no—
158C23—3941no—
159C23—3942no—
160C23—3942no—
161C23—3941no—
162C23—1974no—
163C23—1972no—
164C23C2×C4×D19711yescharacteristic
165Q8—24no—
166Q8—24no—
167D4—39416no—
168D4—3944no—
169D4—3944no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—39416no—
173C2×C4—3941no—
174C2×C4—3941no—
175C2×C4—3944no—
176C2×C4—3944no—
177C2×C4—1972no—
178C2×C4#1569133514yes—
179C2×C4D4×D19712yes—
180C2×C4D4×D19712yes—
181C2×C4C2×C22⋊D19711yescharacteristic
182C2×C4C2×D78811yescharacteristic
183C8—42no—
184C8—7882no—
185C22—22no—
186C22—7884no—
187C22—7882no—
188C22—7884no—
189C22—7882no—
190C22—7884no—
191C22—3944no—
192C22—3942no—
193C22—3944no—
194C22C22⋊C4×D19711yescharacteristic
195C22C22⋊C4×D19711yescharacteristic
196C22C2×#1569133511yescharacteristic
197C4—24no—
198C4—3942no—
199C4#2026329412yes—
200C4#2026329612yes—
201C2—21no—
202C2—21no—
203C2—7884no—
204C2—7882no—
205C2#2716093411yescharacteristic
206C2#2716106212yes—
subgroupG/H
centerC22C22⋊C4×D197
commutatorC23×C197C22×C4
FrattiniC22×C4C22×D197
FittingC2×#101×C197C2
socleC22×C197C2×C22⋊C4
prime radicalC22×#15691359C2
cosocleC22×C4×C197C23
hypercenterC2×#101D197
hypocenterC197#1785
LCSG ▷ C23×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#20263245C2semidirect
3. C2×#20263242C2semidirect
4. #27161042C2semidirect
5. C2×#101×C197C2semidirect
103. C197#1785semidirect
107. C2×#101D197semidirect

Maximal subgroups

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

subgroupindex
C22×#156913592
C2×#202632452
C2×#202632422
#271610422
C2×#101×C1972
#1785197