Finite Group Databasebeta

← #34099292

Subgroups — #34099292

Order 20096.

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

normal subgroups only

This group has 188 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#23758001C211yesmaximal, characteristic
2#23757623C211yesmaximal, characteristic
3#23757565C211yesmaximal, characteristic
4#23757020C211yesmaximal, characteristic
5Q8⋊#11929434C211yesmaximal, characteristic
6#23757003C211yesmaximal, characteristic
7#477×C157C211yesmaximal, characteristic
8#19097771C2211yescharacteristic
9#19097769—21no—
10#19097763—21no—
11#19097761—22no—
12C4×Dic314—21no—
13C4×Dic314C2211yescharacteristic
14#19097736—21no—
15#19097704—21no—
16C4⋊#11929434C2211yescharacteristic
17#19097695—22no—
18#19097694—21no—
19C4×#11929434C2211yescharacteristic
20C4⋊Q8×C157C2211yescharacteristic
21C4×Q8×C157C2211yescharacteristic
22#107×C157—21no—
23C4⋊C8×C157C2211yescharacteristic
24#103×C157—21no—
25C2×Dic314—21no—
26C2×Dic314D411yescharacteristic
27C2×#11929434—21no—
28C2×#11929434—21no—
29C4⋊Dic157—21no—
30C4⋊Dic157D412yes—
31C4⋊Dic157D411yescharacteristic
32#14578933—22no—
33#14578933—22no—
34#14578933—22no—
35#14578933—21no—
36C4×Dic157—22no—
37C4×Dic157—21no—
38C2×Q8×C157—21no—
39C2×Q8×C157D411yescharacteristic
40C2×C8×C157—21no—
41C4⋊C4×C157—21no—
42C4⋊C4×C157—21no—
43C4⋊C4×C157—21no—
44C4⋊C4×C157D411yescharacteristic
45C42×C157—21no—
46C42×C157C2311yescharacteristic
47Dic314—21no—
48Dic314—41no—
49Dic314—41no—
50Dic314Q1612yes—
51C2×Dic157—21no—
52C2×Dic157—22no—
53C2×Dic157—21no—
54#11929434—41no—
55#11929434—41no—
56Q8×C157—21no—
57Q8×C157—21no—
58Q8×C157—42no—
59C2×C4×C157—21no—
60C2×C4×C157—21no—
61C2×C4×C157—41no—
62C2×C4×C157C2×D411yescharacteristic
63C2×C4×C157C2×D411yescharacteristic
64C2×C4×C157C2×D411yescharacteristic
65C8×C157—41no—
66C22×C157#12011yescharacteristic
67C4×C157—21no—
68C4×C157—41no—
69C4×C157—41no—
70C4×C157—81no—
71C4×C157C2×Q1611yescharacteristic
72C4×C157#13511yescharacteristic
73C4×C157#13711yescharacteristic
74C4×C157#13711yescharacteristic
75Dic157—22no—
76Dic157—42no—
77Dic157—41no—
78C2×C157#45111yescharacteristic
79C2×C157#45211yescharacteristic
80C2×C157#45411yescharacteristic
81C157#163611yescharacteristic, complemented, Sylow
82#1636—1571nomaximal, Sylow
83#557—1571no—
84#487—1571no—
85#477—1571no—
86#477D15711yescharacteristic
87#332—1571no—
88Q8⋊C8—1571no—
89Q8⋊C8—1571no—
90C4⋊Q8—3141no—
91C4⋊Q8—1571no—
92C4⋊Q8C2×D15711yescharacteristic
93#125—3141no—
94#125—3142no—
95C4×Q8—3141no—
96C4×Q8—3141no—
97C4×Q8—1571no—
98C4×Q8C2×D15711yescharacteristic
99#107—21no—
100#107—3141no—
101C4⋊C8—1571no—
102C4⋊C8C2×D15711yescharacteristic
103#103—21no—
104#103—3141no—
105#103—3142no—
106C4×C8—1571no—
107C2×Q8—21no—
108C2×Q8—3141no—
109C2×Q8—1571no—
110C2×Q8C22⋊D15711yescharacteristic
111C2×C8—21no—
112C2×C8—3141no—
113C2×C8—3141no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—3142no—
118C4⋊C4—3142no—
119C4⋊C4—3142no—
120C4⋊C4—3141no—
121C4⋊C4—3141no—
122C4⋊C4—1572no—
123C4⋊C4—1571no—
124C4⋊C4C22⋊D15711yescharacteristic
125C42—21no—
126C42—3142no—
127C42—3141no—
128C42C22×D15711yescharacteristic
129Q8—21no—
130Q8—21no—
131Q8—42no—
132Q8—3141no—
133Q8—6281no—
134Q8—6281no—
135Q8—1572no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—41no—
139C2×C4—3141no—
140C2×C4—3141no—
141C2×C4—3142no—
142C2×C4D4×D15711yescharacteristic
143C2×C4D4×D15711yescharacteristic
144C2×C4C2×C22⋊D15711yescharacteristic
145C8—41no—
146C8—6281no—
147C8—6281no—
148C22#1909773911yescharacteristic
149C4—21no—
150C4—41no—
151C4—41no—
152C4—81no—
153C4—3142no—
154C4—6282no—
155C4—6281no—
156C4Q16×D15711yescharacteristic
157C4#1909779111yescharacteristic
158C4#1909780211yescharacteristic
159C4#1909780311yescharacteristic
160C2#2375742711yescharacteristic
161C2#2375743311yescharacteristic
162C2#2375744411yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#477×C157C2
socle, prime radicalC22×C157#120
hypercenter#477D157
hypocenterC157#1636
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
81. C157#1636semidirect

Maximal subgroups

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

subgroupindex
#237580012
#237576232
#237575652
#237570202
Q8⋊#119294342
#237570032
#477×C1572
#1636157