Finite Group Databasebeta

← #38744230

Subgroups — #38744230

Order 25216.

274 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 83 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×#20263257C211yesmaximal, characteristic, complemented
2C2×#20263248C211yesmaximal, characteristic
3C2×#20263246C211yesmaximal, characteristic
4#27160980C211yesmaximal, characteristic
5#27160944C211yesmaximal, characteristic, complemented
6#27160833C211yesmaximal, characteristic, complemented
7C2×#107×C197C211yesmaximal, characteristic, complemented
8C22×D788C2211yescharacteristic
9C22×#13096802C2211yescharacteristic
10C2×C4⋊Dic197C2211yescharacteristic
11C2×#15691335—22no—
12C2×C4×Dic197C2211yescharacteristic
13#20263257—22no—
14#20263248—22no—
15#20263246—22no—
16#20263233—22no—
17C22×C8×C197C2211yescharacteristic
18C2×C4⋊C4×C197C2211yescharacteristic
19C2×C4⋊C4×C197C2211yescharacteristic
20#107×C197—22no—
21C23×D197—21no—
22C2×D788—21no—
23C2×D788—21no—
24C2×D788—21no—
25C2×D788—21no—
26C2×D788—21no—
27C2×D788Q812yes—
28C22×Dic197—21no—
29C22×Dic197D412yes—
30C2×#13096802—21no—
31C2×#13096802—21no—
32C2×#13096802D412yes—
33C4⋊Dic197—21no—
34C4⋊Dic197—21no—
35#15691335—44no—
36C4×Dic197—21no—
37C4×Dic197—21no—
38C22×C4×C197—21no—
39C22×C4×C197—21no—
40C22×C4×C197C2311yescharacteristic
41C2×C8×C197—21no—
42C2×C8×C197—21no—
43C2×C8×C197D412yes—
44C4⋊C4×C197—21no—
45C4⋊C4×C197—21no—
46C4⋊C4×C197—21no—
47C4⋊C4×C197—21no—
48C22×D197—22no—
49C22×D197—41no—
50C22×D197—41no—
51C22×D197—42no—
52C22×D197—42no—
53D788—22no—
54D788—22no—
55D788—41no—
56D788—41no—
57C2×Dic197—22no—
58C2×Dic197—22no—
59C2×Dic197—22no—
60C2×Dic197—41no—
61C2×Dic197—42no—
62#13096802—22no—
63C23×C197C2×D411yescharacteristic
64C2×C4×C197—41no—
65C2×C4×C197—41no—
66C2×C4×C197—42no—
67C2×C4×C197—42no—
68C2×C4×C197C2×D411yescharacteristic
69C2×C4×C197C2×D411yescharacteristic
70C2×C4×C197C2×Q811yescharacteristic
71C2×C4×C197#4111yescharacteristic
72C2×C4×C197#4111yescharacteristic
73C2×C4×C197#4111yescharacteristic
74C8×C197—22no—
75C22×C197C22⋊Q811yescharacteristic
76C22×C197#12311yescharacteristic
77C22×C197#12711yescharacteristic
78C22×C197#13512yes—
79C22×C197AGL(1,ℤ/8)12yes—
80C2×D197—42no—
81C2×D197—44no—
82C2×D197—82no—
83C2×D197—81no—
84C2×D197—81no—
85C4×C197—81no—
86C4×C197—81no—
87C4×C197C22⋊Q811yescharacteristic
88C4×C197C22⋊Q811yescharacteristic
89C4×C197#12311yescharacteristic
90C4×C197#12311yescharacteristic
91Dic197—42no—
92Dic197—81no—
93C2×C197#39911yescharacteristic
94C2×C197#47812yes—
95C2×C197#48212yes—
96C2×C197#49511yescharacteristic
97C2×C197#49611yescharacteristic
98D197—82no—
99C197#209211yescharacteristic, complemented, Sylow
100#2092—1971nomaximal, Sylow
101C2×#107D19711yescharacteristic, complemented
102C2×#106—1971no—
103C2×#102—1971no—
104C2×#102—1971no—
105#390—1971no—
106#382—1971no—
107#336—1971no—
108C22×D4—1971no—
109C22×C8—1971no—
110C22×C8C2×D19711yescharacteristic
111C2×C4⋊C4—1971no—
112C2×C4⋊C4C2×D19711yescharacteristic
113C2×C4⋊C4C2×D19711yescharacteristic
114C2×C22⋊C4—3942no—
115C2×C42—1971no—
116#107—22no—
117#106—3942no—
118#102—3942no—
119#102—3942no—
120#95—3942no—
121C24—3941no—
122C2×D4—3941no—
123C2×D4—3941no—
124C2×D4—3941no—
125C2×D4—3941no—
126C2×D4—3941no—
127C2×D4—1972no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—3941no—
131C22×C4—1972no—
132C22×C4C22×D19711yescharacteristic
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—3941no—
136C2×C8—3941no—
137C2×C8—1972no—
138C2×C8C22⋊D19712yes—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—3941no—
144C4⋊C4—3941no—
145C22⋊C4—7884no—
146C42—3941no—
147C42—3941no—
148C23—7881no—
149C23—7881no—
150C23—7882no—
151C23—7882no—
152C23—3942no—
153C23D4×D19711yescharacteristic
154D4—7881no—
155D4—7881no—
156D4—3942no—
157D4—3942no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—7881no—
163C2×C4—7882no—
164C2×C4—3942no—
165C2×C4—3942no—
166C2×C4—3942no—
167C2×C4D4×D19711yescharacteristic
168C2×C4C2×C22⋊D19711yescharacteristic
169C2×C4Q8×D19711yescharacteristic
170C2×C4#1569135811yescharacteristic
171C2×C4#1569135811yescharacteristic
172C2×C4#1569135911yescharacteristic
173C8—22no—
174C8—3942no—
175C22—7884no—
176C22—7882no—
177C22—15762no—
178C22—15761no—
179C22—15761no—
180C22#2026330411yescharacteristic
181C22#2026331111yescharacteristic
182C22#2026332211yescharacteristic
183C22#2026334912yes—
184C22#2026335012yes—
185C4—81no—
186C4—81no—
187C4—7882no—
188C4—15761no—
189C4#2026330211yescharacteristic
190C4#2026330411yescharacteristic
191C4#2026330911yescharacteristic
192C4#2026331111yescharacteristic
193C2—15762no—
194C2#2716101411yescharacteristic
195C2#2716138212yes—
196C2#2716140612yes—
197C2#2716146411yescharacteristic
198C2#2716146711yescharacteristic
subgroupG/H
centerC23D4×D197
commutator, cosocleC22×C4×C197C23
FrattiniC22×C4C22×D197
FittingC2×#107×C197C2
socleC23×C197C2×D4
prime radicalC22×D788C22
hypercenterC2×#107D197
hypocenterC197#2092
LCSG ▷ C22×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
1. C2×#20263257C2semidirect
5. #27160944C2semidirect
6. #27160833C2semidirect
7. C2×#107×C197C2semidirect
99. C197#2092semidirect
101. C2×#107D197semidirect

Maximal subgroups

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

subgroupindex
C2×#202632572
C2×#202632482
C2×#202632462
#271609802
#271609442
#271608332
C2×#107×C1972
#2092197