Finite Group Databasebeta

← #34099452

Subgroups — #34099452

Order 20096.

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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#23758017C211yesmaximal, characteristic
2#23757679C211yesmaximal, characteristic, complemented
3#23757665C211yesmaximal, characteristic, complemented
4#23757014C211yesmaximal, characteristic, complemented
5#23757013C211yesmaximal, characteristic, complemented
6#23757012C211yesmaximal, characteristic, complemented
7#489×C157C211yesmaximal, characteristic, complemented
8C2×#14578944—21no—
9C2×#14578941—21no—
10#19097763C2211yescharacteristic
11#19097759C2211yescharacteristic
12#19097755—21no—
13#19097753—21no—
14#19097748—21no—
15#19097747—21no—
16#19097744—21no—
17#19097743—21no—
18#19097704—21no—
19#19097702—21no—
20#19097682C2211yescharacteristic
21#19097682C2211yescharacteristic
22C4⋊Q8×C157C2211yescharacteristic
23#124×C157C2211yescharacteristic
24#103×C157—21no—
25#102×C157—21no—
26#97×C157C2211yescharacteristic
27C2×Dic314D411yescharacteristic
28C2×D628D411yescharacteristic
29C2×C22⋊D157—21no—
30C2×C22⋊D157—21no—
31C22×Dic157—21no—
32C2×C4×D157—21no—
33#14578944—42no—
34#14578941—42no—
35C2×#11929434—21no—
36C2×#11929434—21no—
37C4⋊Dic157—21no—
38C4⋊Dic157D411yescharacteristic
39C4⋊Dic157D411yescharacteristic
40#14578933—21no—
41#14578933—21no—
42#14578933—21no—
43C22⋊Dic157—21no—
44#14578931—21no—
45#14578931—21no—
46#14578931—21no—
47C2×Q8×C157—21no—
48C2×Q8×C157D411yescharacteristic
49C2×D4×C157D411yescharacteristic
50C2×C8×C157—21no—
51C4⋊C4×C157—21no—
52C4⋊C4×C157—21no—
53C22⋊C4×C157—21no—
54C22⋊C4×C157—21no—
55C42×C157C2311yescharacteristic
56C22×D157—21no—
57Dic314—41no—
58D628—41no—
59C22⋊D157—81no—
60C22⋊D157—81no—
61C2×Dic157—21no—
62C2×Dic157—21no—
63C2×Dic157—21no—
64C2×Dic157—81no—
65C4×D157—81no—
66#11929434—22no—
67#11929434—22no—
68C23×C157—21no—
69Q8×C157—41no—
70Q8×C157—41no—
71Q8×C157—41no—
72D4×C157—41no—
73C2×C4×C157—21no—
74C2×C4×C157—41no—
75C2×C4×C157C2×D411yescharacteristic
76C2×C4×C157C2×D411yescharacteristic
77C2×C4×C157C2×D411yescharacteristic
78C8×C157—41no—
79C22×C157—41no—
80C22×C157—41no—
81C22×C157—41no—
82C22×C157#12011yescharacteristic
83C2×D157—41no—
84C2×D157—41no—
85C2×D157—41no—
86C4×C157—21no—
87C4×C157—21no—
88C4×C157—21no—
89C4×C157—41no—
90C4×C157—81no—
91Dic157—41no—
92Dic157—41no—
93Dic157—41no—
94C2×C157—81no—
95C2×C157#45311yescharacteristic
96C2×C157#45511yescharacteristic
97C2×C157#45611yescharacteristic
98D157—81no—
99C157#166111yescharacteristic, complemented, Sylow
100#1661—1571nomaximal, Sylow
101#562—1571no—
102#501—1571no—
103#497—1571no—
104#489D15711yescharacteristic, complemented
105#330—1571no—
106#329—1571no—
107#329—1571no—
108C2×Q16—3141no—
109C2×SD16—3141no—
110C4⋊Q8C2×D15711yescharacteristic
111#125—1571no—
112#124—1571no—
113#124C2×D15711yescharacteristic
114#123—3141no—
115#123—3141no—
116C22⋊Q8—3141no—
117C22⋊Q8—3141no—
118#121—3141no—
119#121—3141no—
120#107—3141no—
121#106—3141no—
122#103—21no—
123#102—21no—
124#97—1571no—
125#97—1571no—
126#97C2×D15711yescharacteristic
127C2×Q8—21no—
128C2×Q8—1571no—
129C2×Q8C22⋊D15711yescharacteristic
130C2×D4—3141no—
131C2×D4—3141no—
132C2×D4—1571no—
133C2×D4C22⋊D15711yescharacteristic
134C22×C4—3141no—
135C22×C4—3141no—
136Q16—6282no—
137SD16—6282no—
138C2×C8—21no—
139C2×C8—3141no—
140C2×C8—3141no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—3141no—
144C4⋊C4—3141no—
145C4⋊C4—3141no—
146C4⋊C4—3141no—
147C4⋊C4—1571no—
148C4⋊C4—1571no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—3141no—
152C22⋊C4—3141no—
153C22⋊C4—3141no—
154C22⋊C4—3141no—
155C42C22×D15711yescharacteristic
156C23—21no—
157C23—3141no—
158Q8—41no—
159Q8—41no—
160Q8—41no—
161Q8—6281no—
162D4—41no—
163D4—6281no—
164D4—12561no—
165D4—12561no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—3141no—
169C2×C4—3141no—
170C2×C4—3141no—
171C2×C4—12561no—
172C2×C4—12561no—
173C2×C4D4×D15711yescharacteristic
174C2×C4D4×D15711yescharacteristic
175C2×C4C2×C22⋊D15711yescharacteristic
176C8—41no—
177C8—3142no—
178C8—3142no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—6281no—
183C22—6281no—
184C22—6281no—
185C22#1909773911yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—81no—
191C4—6281no—
192C4—6281no—
193C4—6281no—
194C2—81no—
195C2—12561no—
196C2#2375743911yescharacteristic
197C2#2375745011yescharacteristic
198C2#2375745411yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#489×C157C2
socleC22×C157#120
prime radical#23758017C2
hypercenter#489D157
hypocenterC157#1661
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #23757679C2semidirect
3. #23757665C2semidirect
4. #23757014C2semidirect
5. #23757013C2semidirect
6. #23757012C2semidirect
7. #489×C157C2semidirect
99. C157#1661semidirect
104. #489D157semidirect

Maximal subgroups

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

subgroupindex
#237580172
#237576792
#237576652
#237570142
#237570132
#237570122
#489×C1572
#1661157