Finite Group Databasebeta

← #34099372

Subgroups — #34099372

Order 20096.

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

normal subgroups only

This group has 240 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#23757926C211yesmaximal, characteristic
2#23757676C211yesmaximal, characteristic, complemented
3#23757554C211yesmaximal, characteristic, complemented
4#23757479C211yesmaximal, characteristic, complemented
5#23757000C211yesmaximal, characteristic, complemented
6#23757000C211yesmaximal, characteristic, complemented
7#332×C157C211yesmaximal, characteristic, complemented
8C2×#14578955—21no—
9C2×#14578943—21no—
10#19097771C2211yescharacteristic
11#19097756—22no—
12#19097747—21no—
13#19097746—21no—
14C4×D628C2211yescharacteristic
15C4×D628C2211yescharacteristic
16C4⋊C4×D157—21no—
17#19097705—21no—
18#19097704—22no—
19#19097696—21no—
20#19097693—21no—
21C4×#11929434C2211yescharacteristic
22C4⋊Q8×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4⋊C8×C157C2211yescharacteristic
25#14578955—42no—
26#14578955—42no—
27C2×Dic314—21no—
28C2×D628—22no—
29C2×D628D411yescharacteristic
30C2×D628D411yescharacteristic
31C2×C4×D157—22no—
32C2×C4×D157—21no—
33C2×C4×D157—21no—
34#14578943—42no—
35C2×#11929434—21no—
36C4⋊Dic157—21no—
37C4⋊Dic157—21no—
38C4⋊Dic157D411yescharacteristic
39C4⋊Dic157D411yescharacteristic
40#14578933—22no—
41#14578931—22no—
42#14578931—21no—
43#14578931—21no—
44C2×Q8×C157—21no—
45C2×C8×C157—21no—
46C2×C8×C157—21no—
47C4⋊C4×C157—21no—
48C4⋊C4×C157D412yes—
49C42×C157C2311yescharacteristic
50C22×D157—21no—
51C22×D157—21no—
52Dic314—41no—
53Dic314—41no—
54D628—21no—
55D628—21no—
56D628—21no—
57D628—44no—
58D628D812yes—
59C2×Dic157—21no—
60C2×Dic157—21no—
61C2×Dic157—41no—
62C4×D157—44no—
63C4×D157—41no—
64C4×D157—41no—
65C4×D157—41no—
66C4×D157—41no—
67#11929434—22no—
68Q8×C157—41no—
69Q8×C157—41no—
70C2×C4×C157—22no—
71C2×C4×C157C2×D411yescharacteristic
72C2×C4×C157C2×D411yescharacteristic
73C2×C4×C157C2×D411yescharacteristic
74C8×C157—41no—
75C8×C157—41no—
76C22×C157#12011yescharacteristic
77C2×D157—22no—
78C2×D157—41no—
79C2×D157—41no—
80C2×D157—41no—
81C2×D157—41no—
82C2×D157—41no—
83C4×C157—21no—
84C4×C157—42no—
85C4×C157C2×D811yescharacteristic
86C4×C157#13511yescharacteristic
87C4×C157AGL(1,ℤ/8)11yescharacteristic
88C4×C157#13711yescharacteristic
89Dic157—41no—
90Dic157—41no—
91Dic157—81no—
92C2×C157#44711yescharacteristic
93C2×C157#45211yescharacteristic
94C2×C157#45611yescharacteristic
95D157—42no—
96D157—81no—
97C157#164711yescharacteristic, complemented, Sylow
98#1647—1571nomaximal, Sylow
99#547—1571no—
100#500—1571no—
101#474—1571no—
102#461—1571no—
103#332D15711yescharacteristic, complemented
104D4⋊C8—1571no—
105D4⋊C8—1571no—
106C2×#41—3141no—
107C2×SD16—3141no—
108C4⋊Q8—1571no—
109C4⋊Q8C2×D15711yescharacteristic
110#123—3142no—
111C22⋊Q8—3141no—
112#121—3141no—
113C4×D4—1571no—
114C4×D4—1571no—
115C2×C4⋊C4—3141no—
116#107—3141no—
117#107—3142no—
118C4⋊C8C2×D15711yescharacteristic
119C4⋊C8C2×D15711yescharacteristic
120#103—3141no—
121#102—3141no—
122C4×C8—1571no—
123#41—6282no—
124#41—6282no—
125C2×Q8—21no—
126C2×Q8—3141no—
127C2×D4—3142no—
128C2×D4—1571no—
129C2×D4—1571no—
130C22×C4—3142no—
131C22×C4—3141no—
132C22×C4—3141no—
133SD16—6282no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—3141no—
137C4⋊C4—21no—
138C4⋊C4—3142no—
139C4⋊C4—3141no—
140C4⋊C4—3141no—
141C4⋊C4—1571no—
142C4⋊C4—1571no—
143C4⋊C4D62812yes—
144C22⋊C4—3142no—
145C22⋊C4—3141no—
146C22⋊C4—3141no—
147C42C22×D15711yescharacteristic
148C23—3141no—
149C23—3141no—
150Q8—41no—
151Q8—41no—
152Q8—6281no—
153Q8—6281no—
154D4—3141no—
155D4—3141no—
156D4—3141no—
157D4—6284no—
158D4—1572no—
159C2×C4—22no—
160C2×C4—3141no—
161C2×C4—3141no—
162C2×C4—6284no—
163C2×C4—6281no—
164C2×C4—6281no—
165C2×C4—6281no—
166C2×C4—6281no—
167C2×C4—6281no—
168C2×C4D4×D15711yescharacteristic
169C2×C4D4×D15711yescharacteristic
170C2×C4C2×D62811yescharacteristic
171C8—41no—
172C8—41no—
173C8—3142no—
174C22—3142no—
175C22—6281no—
176C22—6281no—
177C22—6281no—
178C22—6281no—
179C22—6281no—
180C22#1909774111yescharacteristic
181C4—21no—
182C4—42no—
183C4—6281no—
184C4—6281no—
185C4—12561no—
186C4D8×D15711yescharacteristic
187C4#1909779211yescharacteristic
188C4#1909779811yescharacteristic
189C4#1909780311yescharacteristic
190C2—6282no—
191C2—12561no—
192C2#2375740811yescharacteristic
193C2#2375743811yescharacteristic
194C2#2375745811yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#332×C157C2
socleC22×C157#120
prime radical#23757926C2
hypercenter#332D157
hypocenterC157#1647
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #23757676C2semidirect
3. #23757554C2semidirect
4. #23757479C2semidirect
5. #23757000C2semidirect
6. #23757000C2semidirect
7. #332×C157C2semidirect
97. C157#1647semidirect
103. #332D157semidirect

Maximal subgroups

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

subgroupindex
#237579262
#237576762
#237575542
#237574792
#237570002
#332×C1572
#1647157