Finite Group Databasebeta

← #34098769

Subgroups — #34098769

Order 20096.

238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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#23757328C212yesmaximal, complemented
3#23757013C211yesmaximal, characteristic, complemented
4#23757012C212yesmaximal, complemented
5#329×C157C211yesmaximal, characteristic, complemented
6C2×#14578955C411yescharacteristic
7C2×#14578953C411yescharacteristic
8#19097769C411yescharacteristic
9#19097767C411yescharacteristic
10#19097759C2211yescharacteristic
11#19097744—22no—
12#19097731—22no—
13C42×D157C2211yescharacteristic
14#19097700—22no—
15#19097683—22no—
16#19097682C2212yes—
17#124×C157C2211yescharacteristic
18#97×C157C2212yes—
19#14578955—42no—
20#14578953—42no—
21C2×Dic314C2×C411yescharacteristic
22C2×D628—21no—
23C2×D628C2×C411yescharacteristic
24C2×C22⋊D157—21no—
25C2×C22⋊D157—22no—
26C22×Dic157—21no—
27C2×C4×D157—21no—
28C2×C4×D157C2×C411yescharacteristic
29C2×C4×D157D412yes—
30C2×#11929434—22no—
31#14578933—22no—
32#14578931—22no—
33C4×Dic157C2×C411yescharacteristic
34C4×Dic157D412yes—
35C2×Q8×C157C2×C411yescharacteristic
36C2×D4×C157C2×C411yescharacteristic
37C2×C8×C157—22no—
38C22⋊C4×C157—22no—
39C42×C157C2311yescharacteristic
40C22×D157—21no—
41C22×D157C22⋊C411yescharacteristic
42Dic314—41no—
43D628—41no—
44D628—42no—
45C22⋊D157—44no—
46C22⋊D157—42no—
47C2×Dic157—21no—
48C2×Dic157—42no—
49C2×Dic157C22⋊C412yes—
50C2×Dic157C22⋊C411yescharacteristic
51C4×D157—22no—
52C4×D157—42no—
53C4×D157—42no—
54#11929434—42no—
55C23×C157—21no—
56Q8×C157—41no—
57D4×C157—41no—
58C2×C4×C157—21no—
59C2×C4×C157C22×C411yescharacteristic
60C2×C4×C157C2×D412yes—
61C8×C157—42no—
62C22×C157—41no—
63C22×C157—42no—
64C22×C157C2×C22⋊C411yescharacteristic
65C2×D157—21no—
66C2×D157—22no—
67C2×D157—41no—
68C2×D157—42no—
69C4×C157—21no—
70C4×C157—22no—
71C4×C157—41no—
72Dic157—22no—
73Dic157—41no—
74Dic157#10012yes—
75C2×C157—81no—
76C2×C157C2×#10011yescharacteristic
77C2×C157#42112yes—
78D157—41no—
79D157—81no—
80C157#153611yescharacteristic, complemented, Sylow
81#1536—1571nomaximal, Sylow
82#532—1571no—
83#432—1572no—
84#329—1571no—
85#329—1572no—
86#329D15711yescharacteristic, complemented
87C2×#41—1571no—
88C2×#41—1571no—
89C4⋊Q8—1571no—
90#127—1571no—
91#124—1571no—
92#124C2×D15711yescharacteristic
93#121—3142no—
94C4×D4—3142no—
95C2×C42—1571no—
96C4⋊C8—3142no—
97C22⋊C8—3142no—
98#97—1572no—
99#97C2×D15712yes—
100#41—6282no—
101#41—6282no—
102C2×Q8—1571no—
103C2×Q8C4×D15711yescharacteristic
104C2×D4—3141no—
105C2×D4—3141no—
106C2×D4—3142no—
107C2×D4—1571no—
108C2×D4C4×D15711yescharacteristic
109C22×C4—3141no—
110C22×C4—3141no—
111C22×C4—1571no—
112C22×C4—1572no—
113C2×C8—22no—
114C2×C8—3142no—
115C4⋊C4—3142no—
116C22⋊C4—22no—
117C22⋊C4—3142no—
118C42—1571no—
119C42—1572no—
120C42C22×D15711yescharacteristic
121C23—21no—
122C23—3141no—
123C23—1571no—
124Q8—41no—
125Q8—6281no—
126D4—41no—
127D4—6281no—
128D4—6282no—
129D4—6284no—
130D4—6282no—
131C2×C4—21no—
132C2×C4—3142no—
133C2×C4—3141no—
134C2×C4—6282no—
135C2×C4—6282no—
136C2×C4—6282no—
137C2×C4—1572no—
138C2×C4—1571no—
139C2×C4C2×C4×D15711yescharacteristic
140C2×C4D4×D15712yes—
141C8—42no—
142C8—6282no—
143C22—41no—
144C22—42no—
145C22—3141no—
146C22—3142no—
147C22—6281no—
148C22—6282no—
149C22C22⋊C4×D15711yescharacteristic
150C4—21no—
151C4—22no—
152C4—41no—
153C4—3142no—
154C4—6281no—
155C4—1572no—
156C2—81no—
157C2—6281no—
158C2—12561no—
159C2#100×D15711yescharacteristic
160C2#2375728812yes—
subgroupG/H
centerC22C22⋊C4×D157
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
Fitting#329×C157C2
socleC22×C157C2×C22⋊C4
prime radical#23757822C2
cosocleC42×C157C23
hypercenter#329D157
hypocenterC157#1536
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #23757328C2semidirect
3. #23757013C2semidirect
4. #23757012C2semidirect
5. #329×C157C2semidirect
80. C157#1536semidirect
86. #329D157semidirect

Maximal subgroups

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

subgroupindex
#237578222
#237573282
#237570132
#237570122
#329×C1572
#1536157