Finite Group Databasebeta

← #34099458

Subgroups — #34099458

Order 20096.

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

normal subgroups only

This group has 196 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#23757641C211yesmaximal, characteristic, complemented
3#23757635C211yesmaximal, characteristic, complemented
4#23757014C211yesmaximal, characteristic, complemented
5#23757013C211yesmaximal, characteristic, complemented
6#23757012C211yesmaximal, characteristic, complemented
7#489×C157C211yesmaximal, characteristic, complemented
8#19097763C2211yescharacteristic
9#19097759C2211yescharacteristic
10#19097755—21no—
11#19097753—21no—
12#19097748—21no—
13#19097747—21no—
14#19097744—21no—
15#19097743—21no—
16#19097695—21no—
17#19097695—21no—
18#19097694—21no—
19#19097691—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—
33C2×#11929434—21no—
34C2×#11929434—21no—
35C4⋊Dic157—21no—
36C4⋊Dic157D411yescharacteristic
37C4⋊Dic157D411yescharacteristic
38#14578933—21no—
39#14578933—21no—
40#14578933—21no—
41C22⋊Dic157—21no—
42#14578931—21no—
43#14578931—21no—
44#14578931—21no—
45C2×Q8×C157—21no—
46C2×Q8×C157D411yescharacteristic
47C2×D4×C157D411yescharacteristic
48C2×C8×C157—21no—
49C4⋊C4×C157—21no—
50C4⋊C4×C157—21no—
51C22⋊C4×C157—21no—
52C22⋊C4×C157—21no—
53C42×C157C2311yescharacteristic
54C22×D157—21no—
55Dic314—41no—
56D628—41no—
57C22⋊D157—81no—
58C22⋊D157—81no—
59C2×Dic157—21no—
60C2×Dic157—21no—
61C2×Dic157—21no—
62C2×Dic157—81no—
63C4×D157—81no—
64#11929434—41no—
65#11929434—41no—
66C23×C157—21no—
67Q8×C157—41no—
68Q8×C157—42no—
69D4×C157—41no—
70C2×C4×C157—21no—
71C2×C4×C157—41no—
72C2×C4×C157C2×D411yescharacteristic
73C2×C4×C157C2×D411yescharacteristic
74C2×C4×C157C2×D411yescharacteristic
75C8×C157—41no—
76C22×C157—41no—
77C22×C157—41no—
78C22×C157—41no—
79C22×C157#12011yescharacteristic
80C2×D157—41no—
81C2×D157—41no—
82C2×D157—41no—
83C4×C157—21no—
84C4×C157—21no—
85C4×C157—21no—
86C4×C157—41no—
87C4×C157—81no—
88Dic157—41no—
89Dic157—41no—
90Dic157—41no—
91C2×C157—81no—
92C2×C157#45411yescharacteristic
93C2×C157#45511yescharacteristic
94C2×C157#45511yescharacteristic
95D157—81no—
96C157#166211yescharacteristic, complemented, Sylow
97#1662—1571nomaximal, Sylow
98#562—1571no—
99#491—1571no—
100#489—1571no—
101#489D15711yescharacteristic, complemented
102#330—1571no—
103#329—1571no—
104#329—1571no—
105C4⋊Q8C2×D15711yescharacteristic
106#125—1571no—
107#124—1571no—
108#124C2×D15711yescharacteristic
109#123—3141no—
110#123—3141no—
111C22⋊Q8—3141no—
112C22⋊Q8—3141no—
113#121—3141no—
114#121—3141no—
115#103—21no—
116#103—3141no—
117#103—3141no—
118#103—3141no—
119#102—21no—
120#102—3141no—
121#97—1571no—
122#97—1571no—
123#97C2×D15711yescharacteristic
124C2×Q8—21no—
125C2×Q8—1571no—
126C2×Q8C22⋊D15711yescharacteristic
127C2×D4—3141no—
128C2×D4—3141no—
129C2×D4—1571no—
130C2×D4C22⋊D15711yescharacteristic
131C22×C4—3141no—
132C22×C4—3141no—
133C2×C8—21no—
134C2×C8—3141no—
135C2×C8—3141no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—3141no—
139C4⋊C4—3141no—
140C4⋊C4—3141no—
141C4⋊C4—3141no—
142C4⋊C4—1571no—
143C4⋊C4—1571no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—3141no—
147C22⋊C4—3141no—
148C22⋊C4—3141no—
149C22⋊C4—3141no—
150C42C22×D15711yescharacteristic
151C23—21no—
152C23—3141no—
153Q8—41no—
154Q8—42no—
155Q8—6281no—
156D4—41no—
157D4—6281no—
158D4—12561no—
159D4—12561no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—3141no—
163C2×C4—3141no—
164C2×C4—3141no—
165C2×C4—12561no—
166C2×C4—12561no—
167C2×C4D4×D15711yescharacteristic
168C2×C4D4×D15711yescharacteristic
169C2×C4C2×C22⋊D15711yescharacteristic
170C8—41no—
171C8—6281no—
172C8—6281no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—6281no—
177C22—6281no—
178C22—6281no—
179C22#1909773911yescharacteristic
180C4—21no—
181C4—21no—
182C4—21no—
183C4—41no—
184C4—81no—
185C4—6281no—
186C4—6281no—
187C4—6281no—
188C2—81no—
189C2—12561no—
190C2#2375744411yescharacteristic
191C2#2375744911yescharacteristic
192C2#2375745011yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#489×C157C2
socleC22×C157#120
prime radical#23758017C2
hypercenter#489D157
hypocenterC157#1662
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. #23757641C2semidirect
3. #23757635C2semidirect
4. #23757014C2semidirect
5. #23757013C2semidirect
6. #23757012C2semidirect
7. #489×C157C2semidirect
96. C157#1662semidirect
101. #489D157semidirect

Maximal subgroups

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

subgroupindex
#237580172
#237576412
#237576352
#237570142
#237570132
#237570122
#489×C1572
#1662157