Finite Group Databasebeta

← #34099427

Subgroups — #34099427

Order 20096.

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

normal subgroups only

This group has 230 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, complemented
2#23757660C211yesmaximal, characteristic, complemented
3#23757637C211yesmaximal, characteristic, complemented
4#23757014C211yesmaximal, characteristic, complemented
5#23757013C211yesmaximal, characteristic, complemented
6#23757012C211yesmaximal, characteristic, complemented
7#496×C157C211yesmaximal, characteristic, complemented
8C2×#14578942—21no—
9C2×#14578939—21no—
10#19097763C2211yescharacteristic
11#19097759C2211yescharacteristic
12#19097755—21no—
13#19097753—21no—
14#19097748—21no—
15#19097747—21no—
16#19097744—21no—
17#19097743—21no—
18#19097692—21no—
19#19097692—21no—
20#19097682C2211yescharacteristic
21#19097682C2211yescharacteristic
22C2×SD16×C157—21no—
23C2×D8×C157—21no—
24#127×C157C2211yescharacteristic
25#124×C157C2211yescharacteristic
26#97×C157C2211yescharacteristic
27C2×Dic314D411yescharacteristic
28C2×D628D411yescharacteristic
29C2×C22⋊D157—21no—
30C2×C22⋊D157—21no—
31C22×Dic157—21no—
32C2×C4×D157—21no—
33#14578942—42no—
34#14578939—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×C157D411yescharacteristic
48C2×D4×C157—21no—
49C2×D4×C157—21no—
50C2×D4×C157—21no—
51C2×D4×C157D411yescharacteristic
52SD16×C157—42no—
53D8×C157—42no—
54C2×C8×C157—21no—
55C22⋊C4×C157—21no—
56C22⋊C4×C157—21no—
57C42×C157C2311yescharacteristic
58C22×D157—21no—
59Dic314—41no—
60D628—41no—
61C22⋊D157—81no—
62C22⋊D157—81no—
63C2×Dic157—21no—
64C2×Dic157—21no—
65C2×Dic157—21no—
66C2×Dic157—81no—
67C4×D157—81no—
68#11929434—22no—
69#11929434—41no—
70C23×C157—21no—
71C23×C157—41no—
72Q8×C157—41no—
73D4×C157—41no—
74D4×C157—41no—
75D4×C157—41no—
76D4×C157—42no—
77D4×C157—41no—
78D4×C157—41no—
79C2×C4×C157—21no—
80C2×C4×C157C2×D411yescharacteristic
81C2×C4×C157C2×D411yescharacteristic
82C2×C4×C157C2×D411yescharacteristic
83C8×C157—22no—
84C22×C157—41no—
85C22×C157—41no—
86C22×C157—41no—
87C22×C157—81no—
88C22×C157—81no—
89C22×C157—81no—
90C22×C157#12011yescharacteristic
91C2×D157—41no—
92C2×D157—41no—
93C2×D157—41no—
94C4×C157—21no—
95C4×C157—21no—
96C4×C157—21no—
97C4×C157—41no—
98Dic157—41no—
99Dic157—41no—
100Dic157—41no—
101C2×C157—81no—
102C2×C157—161no—
103C2×C157#45311yescharacteristic
104C2×C157#45311yescharacteristic
105C2×C157#45411yescharacteristic
106D157—81no—
107C157#165611yescharacteristic, complemented, Sylow
108#1656—1571nomaximal, Sylow
109#562—1571no—
110#496—1571no—
111#496D15711yescharacteristic, complemented
112#490—1571no—
113#330—1571no—
114#329—1571no—
115#329—1571no—
116C2×SD16—21no—
117C2×SD16—3141no—
118C2×D8—21no—
119C2×D8—3141no—
120#127C2×D15711yescharacteristic
121#125—1571no—
122#124—1571no—
123#124C2×D15711yescharacteristic
124#123—3141no—
125#123—3141no—
126C22⋊Q8—3141no—
127C22⋊Q8—3141no—
128#121—3141no—
129#121—3141no—
130#102—3141no—
131#102—3141no—
132#97—1571no—
133#97—1571no—
134#97C2×D15711yescharacteristic
135C2×Q8—1571no—
136C2×Q8C22⋊D15711yescharacteristic
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—3141no—
141C2×D4—3141no—
142C2×D4—1571no—
143C2×D4C22⋊D15711yescharacteristic
144C22×C4—3141no—
145C22×C4—3141no—
146SD16—42no—
147SD16—6282no—
148D8—42no—
149D8—6282no—
150C2×C8—21no—
151C2×C8—3141no—
152C2×C8—3141no—
153C4⋊C4—3141no—
154C4⋊C4—3141no—
155C4⋊C4—3141no—
156C4⋊C4—3141no—
157C4⋊C4—1571no—
158C4⋊C4—1571no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—3141no—
162C22⋊C4—3141no—
163C22⋊C4—3141no—
164C22⋊C4—3141no—
165C42C22×D15711yescharacteristic
166C23—21no—
167C23—41no—
168C23—3141no—
169Q8—41no—
170Q8—6281no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—41no—
176D4—42no—
177D4—6281no—
178D4—12561no—
179D4—12561no—
180C2×C4—21no—
181C2×C4—3141no—
182C2×C4—3141no—
183C2×C4—3141no—
184C2×C4—12561no—
185C2×C4—12561no—
186C2×C4D4×D15711yescharacteristic
187C2×C4D4×D15711yescharacteristic
188C2×C4C2×C22⋊D15711yescharacteristic
189C8—22no—
190C8—3142no—
191C8—6281no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22—81no—
196C22—81no—
197C22—81no—
198C22—6281no—
199C22—6281no—
200C22—6281no—
201C22#1909773911yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—6281no—
207C4—6281no—
208C4—6281no—
209C2—81no—
210C2—161no—
211C2—12561no—
212C2#2375743911yescharacteristic
213C2#2375744011yescharacteristic
214C2#2375744411yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#496×C157C2
socleC22×C157#120
hypercenter#496D157
hypocenterC157#1656
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #23758017C2semidirect
2. #23757660C2semidirect
3. #23757637C2semidirect
4. #23757014C2semidirect
5. #23757013C2semidirect
6. #23757012C2semidirect
7. #496×C157C2semidirect
107. C157#1656semidirect
111. #496D157semidirect

Maximal subgroups

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

subgroupindex
#237580172
#237576602
#237576372
#237570142
#237570132
#237570122
#496×C1572
#1656157