Finite Group Databasebeta

← #34101809

Subgroups — #34101809

Order 20096.

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

normal subgroups only

This group has 238 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#23757843C211yesmaximal, characteristic
2#23757245C212yesmaximal
3#23757068C211yesmaximal, characteristic, complemented
4#23757067C212yesmaximal, complemented
5#354×C157C211yesmaximal, characteristic, complemented
6C2×#14578953C2211yescharacteristic
7C2×Q8×D157C411yescharacteristic, complemented
8#19097771C411yescharacteristic, complemented
9#19097769C411yescharacteristic, complemented
10#19097758C2211yescharacteristic
11#19097753—22no—
12#19097748—22no—
13#19097728C411yescharacteristic, complemented
14#19097727—22no—
15#19097686C2212yes—
16#19097685—22no—
17#124×C157C2211yescharacteristic
18#99×C157C2212yes—
19#14578953—42no—
20C2×Dic314—21no—
21C2×Dic314C2×C411yescharacteristic
22C2×Dic314C2×C411yescharacteristic
23Q8×D157—42no—
24C2×C22⋊D157D412yes—
25C22×Dic157D412yes—
26C2×C4×D157—21no—
27C2×C4×D157C2×C411yescharacteristic
28C4⋊Dic157—22no—
29#14578933—21no—
30#14578933—22no—
31#14578933—42no—
32C22⋊Dic157—22no—
33C22⋊Dic157—22no—
34#14578931—21no—
35C4×Dic157—42no—
36C4×Dic157C2×C411yescharacteristic
37C2×Q8×C157C2×C411yescharacteristic
38C2×D4×C157C2311yescharacteristic
39C22⋊C4×C157—22no—
40C22⋊C4×C157—22no—
41C42×C157C2×C411yescharacteristic
42C22×D157C22⋊C411yescharacteristic
43Dic314—41no—
44Dic314—42no—
45Dic314—41no—
46C22⋊D157—42no—
47C2×Dic157—22no—
48C2×Dic157—22no—
49C2×Dic157—21no—
50C2×Dic157—21no—
51C2×Dic157—42no—
52C2×Dic157C22⋊C412yes—
53C2×Dic157C22⋊C411yescharacteristic
54C4×D157—22no—
55C4×D157—42no—
56C23×C157C2×D412yes—
57Q8×C157—41no—
58D4×C157—41no—
59C2×C4×C157—21no—
60C2×C4×C157—21no—
61C2×C4×C157—42no—
62C2×C4×C157C22×C411yescharacteristic
63C22×C157—22no—
64C22×C157—42no—
65C22×C157C2×C22⋊C411yescharacteristic
66C2×D157—21no—
67C2×D157—41no—
68C4×C157—21no—
69C4×C157—41no—
70C4×C157—41no—
71C4×C157—82no—
72Dic157—22no—
73Dic157—41no—
74Dic157—41no—
75Dic157—82no—
76Dic157#9912yes—
77C2×C157—21no—
78C2×C157—42no—
79C2×C157C2×#9911yescharacteristic
80D157—41no—
81C157#212911yescharacteristic, complemented, Sylow
82#2129—1571nomaximal, Sylow
83#536—1571no—
84#410—1572no—
85#354—1571no—
86#354—1572no—
87#354D15711yescharacteristic, complemented
88C2×#41—1571no—
89C22×Q8—1571no—
90C4⋊Q8—1571no—
91C4⋊Q8—1571no—
92#124—1571no—
93#124C2×D15711yescharacteristic
94#123—3142no—
95C22⋊Q8—3142no—
96#117—3142no—
97#117—1571no—
98#99—3142no—
99#99—1572no—
100#99C2×D15712yes—
101#41—6282no—
102C2×Q8—3141no—
103C2×Q8—6282no—
104C2×Q8—1571no—
105C2×Q8—1571no—
106C2×Q8C4×D15711yescharacteristic
107C2×D4—1572no—
108C2×D4C22×D15711yescharacteristic
109C22×C4—3141no—
110C22×C4—1572no—
111C22×C4—1571no—
112C4⋊C4—3141no—
113C4⋊C4—3142no—
114C4⋊C4—3142no—
115C4⋊C4—6282no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—3141no—
119C22⋊C4—3142no—
120C22⋊C4—3142no—
121C42—6282no—
122C42—1571no—
123C42C4×D15711yescharacteristic
124C23—1571no—
125C23D4×D15712yes—
126Q8—41no—
127Q8—6281no—
128Q8—6281no—
129Q8—6282no—
130D4—41no—
131D4—6282no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—42no—
135C2×C4—3142no—
136C2×C4—3142no—
137C2×C4—3142no—
138C2×C4—3141no—
139C2×C4—3141no—
140C2×C4—6282no—
141C2×C4—6282no—
142C2×C4—1572no—
143C2×C4—1571no—
144C2×C4C2×C4×D15711yescharacteristic
145C22—22no—
146C22—42no—
147C22—3141no—
148C22—6281no—
149C22C22⋊C4×D15711yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—3142no—
155C4—6281no—
156C4—6281no—
157C4—1572no—
158C4—12562no—
159C2—21no—
160C2—42no—
161C2—6281no—
162C2#99×D15711yescharacteristic
subgroupG/H
centerC2#99×D157
commutatorC2×C4×C157C22×C4
FrattiniC2×D4C22×D157
Fitting#354×C157C2
socleC2×C157C2×#99
prime radicalC2×#14578953C22
cosocleC2×D4×C157C23
hypercenter#354D157
hypocenterC157#2129
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #23757068C2semidirect
4. #23757067C2semidirect
5. #354×C157C2semidirect
7. C2×Q8×D157C4semidirect
8. #19097771C4semidirect
9. #19097769C4semidirect
13. #19097728C4semidirect
81. C157#2129semidirect
87. #354D157semidirect

Maximal subgroups

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

subgroupindex
#237578432
#237572452
#237570682
#237570672
#354×C1572
#2129157