Finite Group Databasebeta

← #34101818

Subgroups — #34101818

Order 20096.

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

normal subgroups only

This group has 250 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#23757822C211yesmaximal, characteristic
2#23757256C212yesmaximal, complemented
3#23757071C212yesmaximal, complemented
4#23757070C211yesmaximal, characteristic, complemented
5#355×C157C211yesmaximal, characteristic, complemented
6C2×#14578955C2211yescharacteristic
7C2×#14578953C411yescharacteristic
8M16×D157—22no—
9#19097769C2211yescharacteristic
10#19097767C411yescharacteristic
11#19097759C411yescharacteristic
12#19097744—22no—
13#19097731—22no—
14C42×D157C411yescharacteristic
15#19097690C2212yes—
16#19097687—22no—
17#124×C157C2211yescharacteristic
18#101×C157C2212yes—
19#14578955—41no—
20#14578955—41no—
21#14578953—41no—
22#14578953—41no—
23C2×Dic314C2×C411yescharacteristic
24C2×D628C2×C411yescharacteristic
25C2×D628D412yes—
26C2×C22⋊D157—22no—
27C2×C22⋊D157—21no—
28C22×Dic157—21no—
29C2×C4×D157—21no—
30C2×C4×D157C2×C411yescharacteristic
31C2×C4×D157D412yes—
32#14578938—22no—
33#14578937—42no—
34C8×D157—42no—
35#14578933—22no—
36#14578931—22no—
37C4×Dic157—21no—
38C4×Dic157C2×C411yescharacteristic
39C2×Q8×C157C2311yescharacteristic
40C2×D4×C157C2×C411yescharacteristic
41M16×C157—22no—
42C22⋊C4×C157—22no—
43C42×C157C2×C411yescharacteristic
44C22×D157C22⋊C411yescharacteristic
45C22×D157C22⋊C412yes—
46Dic314—41no—
47D628—41no—
48D628—42no—
49C22⋊D157—44no—
50C22⋊D157—42no—
51C2×Dic157—21no—
52C2×Dic157—21no—
53C2×Dic157—41no—
54C2×Dic157—41no—
55C2×Dic157C22⋊C411yescharacteristic
56C4×D157—21no—
57C4×D157—21no—
58C4×D157—22no—
59C4×D157—22no—
60C4×D157—42no—
61#11929434—42no—
62C23×C157—21no—
63Q8×C157—41no—
64D4×C157—41no—
65C2×C4×C157—21no—
66C2×C4×C157C22×C411yescharacteristic
67C2×C4×C157C2×D412yes—
68C8×C157—42no—
69C22×C157—42no—
70C22×C157—41no—
71C22×C157C2×C22⋊C411yescharacteristic
72C2×D157—21no—
73C2×D157—22no—
74C2×D157—41no—
75C2×D157—42no—
76C4×C157—22no—
77C4×C157—21no—
78C4×C157—41no—
79Dic157—22no—
80Dic157—41no—
81Dic157#9911yescharacteristic
82Dic157#9911yescharacteristic
83C2×C157—21no—
84C2×C157—81no—
85C2×C157C2×#9911yescharacteristic
86D157—41no—
87D157—42no—
88C157#213211yescharacteristic, complemented, Sylow
89#2132—1571nomaximal, Sylow
90#532—1571no—
91#413—1572no—
92#356—1572no—
93#355—1571no—
94#355D15711yescharacteristic, complemented
95C2×#41—1571no—
96C2×#41—1571no—
97C2×M16—3142no—
98C4⋊Q8—1571no—
99#127—1571no—
100#124—1571no—
101#124C2×D15711yescharacteristic
102#121—3142no—
103C4×D4—3142no—
104C2×C42—1571no—
105#101—1572no—
106#101C2×D15712yes—
107#100—3142no—
108#41—6281no—
109#41—6281no—
110#41—6281no—
111#41—6281no—
112C2×Q8—1571no—
113C2×Q8C22×D15711yescharacteristic
114C2×D4—3142no—
115C2×D4—3141no—
116C2×D4—1571no—
117C2×D4—1572no—
118C2×D4C4×D15711yescharacteristic
119C22×C4—3141no—
120C22×C4—3141no—
121C22×C4—1571no—
122C22×C4—1572no—
123M16—22no—
124M16—3142no—
125M16—6282no—
126C2×C8—6282no—
127C4⋊C4—3142no—
128C22⋊C4—22no—
129C22⋊C4—3142no—
130C42—3141no—
131C42—1571no—
132C42C4×D15711yescharacteristic
133C23—21no—
134C23—1572no—
135C23—1571no—
136Q8—41no—
137Q8—6281no—
138D4—41no—
139D4—6282no—
140D4—6281no—
141D4—6284no—
142D4—6282no—
143C2×C4—21no—
144C2×C4—3142no—
145C2×C4—3142no—
146C2×C4—3141no—
147C2×C4—3141no—
148C2×C4—3141no—
149C2×C4—3141no—
150C2×C4—6282no—
151C2×C4—6281no—
152C2×C4—6281no—
153C2×C4—1571no—
154C2×C4C2×C4×D15711yescharacteristic
155C2×C4D4×D15712yes—
156C8—42no—
157C8—6282no—
158C22—42no—
159C22—41no—
160C22—3141no—
161C22—3142no—
162C22—6281no—
163C22—6282no—
164C22C22⋊C4×D15711yescharacteristic
165C4—22no—
166C4—21no—
167C4—41no—
168C4—3142no—
169C4—6281no—
170C4—1571no—
171C4—1571no—
172C2—21no—
173C2—81no—
174C2—6281no—
175C2—6282no—
176C2#99×D15711yescharacteristic
subgroupG/H
centerC2#99×D157
commutatorC2×C4×C157C22×C4
FrattiniC2×Q8C22×D157
Fitting#355×C157C2
socleC2×C157C2×#99
prime radical#23757822C2
cosocleC2×Q8×C157C23
hypercenter#355D157
hypocenterC157#2132
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. #23757071C2semidirect
4. #23757070C2semidirect
5. #355×C157C2semidirect
88. C157#2132semidirect
94. #355D157semidirect

Maximal subgroups

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

subgroupindex
#237578222
#237572562
#237570712
#237570702
#355×C1572
#2132157