Finite Group Databasebeta

← #34098504

Subgroups — #34098504

Order 20096.

214 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C2×#19097766C211yesmaximal, characteristic
2#23757327C211yesmaximal, characteristic, complemented
3#23757323C211yesmaximal, characteristic, complemented
4#23756999C211yesmaximal, characteristic, complemented
5#23756996C211yesmaximal, characteristic
6#23756996C211yesmaximal, characteristic
7#324×C157C211yesmaximal, characteristic, complemented
8#19097766—21no—
9#19097766—21no—
10#19097766—21no—
11#19097766—21no—
12C2×C4⋊Dic157C411yescharacteristic
13C2×#14578933C411yescharacteristic
14C2×#14578931C411yescharacteristic
15C2×#14578931C411yescharacteristic
16C2×#14578931C2211yescharacteristic
17C2×C4×Dic157C2211yescharacteristic
18#19097700—21no—
19#19097700—21no—
20C22⋊#11929434C2211yescharacteristic
21C22⋊#11929434C2211yescharacteristic
22#19097681—21no—
23C8×Dic157—21no—
24C2×C4⋊C4×C157C2211yescharacteristic
25C22⋊C8×C157C2211yescharacteristic
26C22⋊C8×C157C2211yescharacteristic
27C23×D157C2×C411yescharacteristic
28C22×Dic157C2×C411yescharacteristic
29C22×Dic157C2×C411yescharacteristic
30C22×Dic157C2×C411yescharacteristic
31C2×#11929434—21no—
32C2×#11929434—21no—
33C4⋊Dic157—21no—
34C4⋊Dic157—21no—
35#14578933—21no—
36#14578933—21no—
37#14578931—21no—
38#14578931—21no—
39#14578931—21no—
40#14578931—21no—
41#14578931—21no—
42#14578931—21no—
43C4×Dic157D411yescharacteristic
44C4×Dic157D411yescharacteristic
45C4×Dic157D411yescharacteristic
46C4×Dic157D411yescharacteristic
47C22×C4×C157C2×C411yescharacteristic
48C22×C4×C157C2×C411yescharacteristic
49C22×C4×C157C2311yescharacteristic
50C2×C8×C157—21no—
51C2×C8×C157—21no—
52C4⋊C4×C157—21no—
53C4⋊C4×C157—21no—
54C22×D157—21no—
55C22×D157—21no—
56C22×D157—21no—
57C22×D157—41no—
58C22×D157—41no—
59C2×Dic157—21no—
60C2×Dic157—21no—
61C2×Dic157—21no—
62C2×Dic157—41no—
63C2×Dic157—41no—
64C2×Dic157C22⋊C411yescharacteristic
65C2×Dic157C22⋊C411yescharacteristic
66C2×Dic157C22⋊C411yescharacteristic
67C2×Dic157C22⋊C411yescharacteristic
68#11929434—41no—
69#11929434—41no—
70C23×C157C22×C411yescharacteristic
71C2×C4×C157—21no—
72C2×C4×C157—21no—
73C2×C4×C157—21no—
74C2×C4×C157—21no—
75C2×C4×C157—41no—
76C2×C4×C157—41no—
77C2×C4×C157C2×D411yescharacteristic
78C2×C4×C157C2×D411yescharacteristic
79C8×C157—41no—
80C8×C157—41no—
81C22×C157—21no—
82C22×C157—21no—
83C22×C157C2×C22⋊C411yescharacteristic
84C22×C157#13111yescharacteristic
85C22×C157#13111yescharacteristic
86C2×D157—41no—
87C2×D157—41no—
88C2×D157—41no—
89C2×D157—81no—
90C2×D157—81no—
91C4×C157—21no—
92C4×C157—21no—
93C4×C157—41no—
94C4×C157—41no—
95Dic157—21no—
96Dic157—21no—
97Dic157—21no—
98Dic157—21no—
99Dic157—41no—
100C2×C157—21no—
101C2×C157—21no—
102C2×C157#40811yescharacteristic
103C2×C157#41011yescharacteristic
104C2×C157#41311yescharacteristic
105D157—81no—
106C157#147311yescharacteristic, complemented, Sylow
107#1473—1571nomaximal, Sylow
108C2×#126—1571no—
109#432—1571no—
110#431—1571no—
111#324—1571no—
112#324D15711yescharacteristic, complemented
113#323—1571no—
114#323—1571no—
115#126—3141no—
116#126—3141no—
117#126—3141no—
118#126—3141no—
119C2×C4⋊C4—1571no—
120C2×C4⋊C4—1571no—
121C2×C4⋊C4C2×D15711yescharacteristic
122C2×C22⋊C4—1571no—
123C2×C22⋊C4—1571no—
124C2×C22⋊C4—1571no—
125C2×C42—1571no—
126C4⋊C8—3141no—
127C4⋊C8—3141no—
128C22⋊C8—1571no—
129C22⋊C8—1571no—
130C22⋊C8C2×D15711yescharacteristic
131C22⋊C8C2×D15711yescharacteristic
132#97—3141no—
133C4×C8—3141no—
134C24—1571no—
135C22×C4—1571no—
136C22×C4—1571no—
137C22×C4—1571no—
138C22×C4C4×D15711yescharacteristic
139C22×C4C4×D15711yescharacteristic
140C22×C4C22×D15711yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—3141no—
144C2×C8—3141no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—3141no—
148C4⋊C4—3141no—
149C4⋊C4—3141no—
150C4⋊C4—3141no—
151C22⋊C4—3141no—
152C22⋊C4—3141no—
153C22⋊C4—3141no—
154C22⋊C4—3141no—
155C22⋊C4—3141no—
156C22⋊C4—3141no—
157C42—1571no—
158C42—1571no—
159C42—1571no—
160C42—1571no—
161C23—3141no—
162C23—3141no—
163C23—3141no—
164C23—6281no—
165C23—6281no—
166C23C2×C4×D15711yescharacteristic
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—3141no—
174C2×C4—3141no—
175C2×C4—3141no—
176C2×C4—6281no—
177C2×C4—6281no—
178C2×C4—1571no—
179C2×C4—1571no—
180C2×C4—1571no—
181C2×C4—1571no—
182C2×C4D4×D15711yescharacteristic
183C2×C4D4×D15711yescharacteristic
184C8—41no—
185C8—41no—
186C8—6281no—
187C8—6281no—
188C22—21no—
189C22—21no—
190C22—6281no—
191C22—6281no—
192C22—6281no—
193C22—12561no—
194C22—12561no—
195C22C22⋊C4×D15711yescharacteristic
196C22#1909777711yescharacteristic
197C22#1909777911yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—3141no—
203C4—3141no—
204C4—3141no—
205C4—3141no—
206C4—6281no—
207C2—21no—
208C2—21no—
209C2—12561no—
210C2#2375723811yescharacteristic
211C2#2375724511yescharacteristic
212C2#2375725611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC23×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#324×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC23×D157C2×C4
cosocleC22×C4×C157C23
hypercenter#324D157
hypocenterC157#1473
LCSG ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #23757327C2semidirect
3. #23757323C2semidirect
4. #23756999C2semidirect
7. #324×C157C2semidirect
106. C157#1473semidirect
112. #324D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977662
#237573272
#237573232
#237569992
#237569962
#324×C1572
#1473157