Finite Group Databasebeta

← #34101826

Subgroups — #34101826

Order 20096.

262 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 55 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#23757841C211yesmaximal, characteristic
2#23757256C212yesmaximal, complemented
3#23757070C211yesmaximal, characteristic, complemented
4#23757069C212yesmaximal, complemented
5#355×C157C211yesmaximal, characteristic, complemented
6C2×#14578955C2211yescharacteristic
7C2×D4×D157C411yescharacteristic
8M16×D157—22no—
9#19097768C411yescharacteristic
10#19097767C411yescharacteristic
11#19097760C2211yescharacteristic
12#19097744—22no—
13#19097741—22no—
14#19097728C411yescharacteristic
15#19097690C2212yescomplemented
16#19097687—22no—
17#124×C157C2211yescharacteristic
18#101×C157C2212yescomplemented
19C23×D157—21no—
20#14578955—42no—
21C2×D628—22no—
22C2×D628C2×C411yescharacteristic
23C2×D628C2×C411yescharacteristic
24C2×D628D412yes—
25C2×C22⋊D157—22no—
26C2×C22⋊D157—21no—
27D4×D157—42no—
28C2×C4×D157C2×C411yescharacteristic
29C2×C4×D157D412yes—
30#14578938—22no—
31#14578937—42no—
32C8×D157—42no—
33#14578933—21no—
34#14578931—21no—
35#14578931—22no—
36C4×Dic157C2×C411yescharacteristic
37C2×Q8×C157C2311yescharacteristic
38C2×D4×C157C2×C411yescharacteristic
39M16×C157—22no—
40C22⋊C4×C157—22no—
41C42×C157C2×C411yescharacteristic
42C22×D157—21no—
43C22×D157—42no—
44C22×D157—82no—
45C22×D157C22⋊C411yescharacteristic
46C22×D157C22⋊C412yes—
47D628—41no—
48D628—42no—
49D628—41no—
50D628—82no—
51C22⋊D157—42no—
52C22⋊D157—82no—
53C2×Dic157—21no—
54C2×Dic157C22⋊C411yescharacteristic
55C4×D157—22no—
56C4×D157—22no—
57C4×D157—22no—
58#11929434—42no—
59C23×C157—21no—
60Q8×C157—41no—
61D4×C157—41no—
62C2×C4×C157—21no—
63C2×C4×C157C22×C411yescharacteristic
64C2×C4×C157C2×D412yes—
65C8×C157—42no—
66C22×C157—42no—
67C22×C157—41no—
68C22×C157C2×C22⋊C411yescharacteristic
69C2×D157—21no—
70C2×D157—22no—
71C2×D157—42no—
72C2×D157—41no—
73C2×D157—42no—
74C2×D157—41no—
75C2×D157—84no—
76C4×C157—22no—
77C4×C157—21no—
78C4×C157—41no—
79Dic157—41no—
80Dic157#9912yes—
81C2×C157—21no—
82C2×C157—81no—
83C2×C157C2×#9911yescharacteristic
84D157—42no—
85D157—41no—
86D157—81no—
87C157#213411yescharacteristic, complemented, Sylow
88#2134—1571nomaximal, Sylow
89#535—1571no—
90#413—1572no—
91#355—1571no—
92#355—1572no—
93#355D15711yescharacteristic, complemented
94C2×#41—1571no—
95C22×D4—1571no—
96C2×M16—3142no—
97#127—1571no—
98#127—1571no—
99#124—1571no—
100#124C2×D15711yescharacteristic
101#121—3142no—
102#120—3142no—
103#117—1571no—
104#101—1572no—
105#101C2×D15712yescomplemented
106#100—3142no—
107C24—3141no—
108#41—6282no—
109C2×Q8C22×D15711yescharacteristic
110C2×D4—3142no—
111C2×D4—3142no—
112C2×D4—3141no—
113C2×D4—6282no—
114C2×D4—1571no—
115C2×D4—1571no—
116C2×D4—1572no—
117C2×D4C4×D15711yescharacteristic
118C22×C4—1571no—
119C22×C4—1572no—
120M16—22no—
121M16—3142no—
122M16—6282no—
123C2×C8—6282no—
124C4⋊C4—3141no—
125C22⋊C4—22no—
126C22⋊C4—3141no—
127C22⋊C4—3142no—
128C42—1571no—
129C42C4×D15711yescharacteristic
130C23—21no—
131C23—3141no—
132C23—6282no—
133C23—1571no—
134C23—1572no—
135C23—12562no—
136Q8—41no—
137D4—41no—
138D4—6282no—
139D4—6281no—
140D4—6281no—
141D4—6282no—
142D4—12562no—
143D4—12562no—
144C2×C4—21no—
145C2×C4—3142no—
146C2×C4—3142no—
147C2×C4—3142no—
148C2×C4—3141no—
149C2×C4—1571no—
150C2×C4C2×C4×D15711yescharacteristic
151C2×C4D4×D15712yes—
152C8—42no—
153C8—6282no—
154C22—42no—
155C22—41no—
156C22—3141no—
157C22—3142no—
158C22—6282no—
159C22—6281no—
160C22—6282no—
161C22—6281no—
162C22—12564no—
163C22C22⋊C4×D15711yescharacteristic
164C4—22no—
165C4—21no—
166C4—41no—
167C4—6281no—
168C4—1572no—
169C2—21no—
170C2—81no—
171C2—6281no—
172C2—6282no—
173C2—12561no—
174C2#99×D15711yescharacteristic
subgroupG/H
centerC2#99×D157
commutatorC2×C4×C157C22×C4
FrattiniC2×Q8C22×D157
Fitting#355×C157C2
socleC2×C157C2×#99
prime radical#23757841C2
cosocleC2×Q8×C157C23
hypercenter#355D157
hypocenterC157#2134
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #23757256C2semidirect
3. #23757070C2semidirect
4. #23757069C2semidirect
5. #355×C157C2semidirect
15. #19097690C22semidirect
18. #101×C157C22semidirect
87. C157#2134semidirect
93. #355D157semidirect
105. #101C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237578412
#237572562
#237570702
#237570692
#355×C1572
#2134157