Finite Group Databasebeta

← #34100375

Subgroups — #34100375

Order 20096.

262 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 79 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#23758039C211yesmaximal, characteristic
2#23757321C211yesmaximal, characteristic, complemented
3#23757289C211yesmaximal, characteristic
4C2×#19097699C211yesmaximal, characteristic
5#23757044C211yesmaximal, characteristic, complemented
6#23757033C211yesmaximal, characteristic, complemented
7#423×C157C211yesmaximal, characteristic, complemented
8C2×#14578954C2211yescharacteristic
9#19097779—22no—
10#19097777—22no—
11C2×#14578938C2211yescharacteristic
12C2×#14578938C2211yescharacteristic
13M16×D157—22no—
14#19097730C2211yescharacteristic
15#19097706—22no—
16#19097699C412yescomplemented
17#19097699C412yescomplemented
18#19097697—22no—
19C2×M16×C157C2211yescharacteristic
20C2×M16×C157C2211yescharacteristic
21C2×C42×C157C2211yescharacteristic
22C4⋊C8×C157—22no—
23#14578954—21no—
24#14578954—21no—
25#14578954C2×C412yes—
26#14578954D412yes—
27C2×Dic314Q811yescharacteristic
28C2×D628Q811yescharacteristic
29C2×C22⋊D157—21no—
30C2×C4×D157—21no—
31#14578938—21no—
32#14578938—21no—
33#14578938C2×C412yes—
34#14578938D412yes—
35#14578937—24no—
36C2×#11929434—21no—
37C2×#11929434—21no—
38C8×D157—24no—
39C4⋊Dic157—21no—
40C22⋊Dic157—21no—
41C4×Dic157—21no—
42C22×C4×C157—21no—
43C22×C4×C157C2311yescharacteristic
44M16×C157—21no—
45M16×C157—21no—
46M16×C157—21no—
47M16×C157—21no—
48C2×C8×C157—21no—
49C2×C8×C157D412yes—
50C42×C157—21no—
51C42×C157C2×C411yescharacteristic
52C42×C157C2×C411yescharacteristic
53C22×D157—21no—
54Dic314—21no—
55Dic314C4⋊C412yes—
56D628—21no—
57D628C4⋊C412yes—
58C22⋊D157—22no—
59C22⋊D157—22no—
60C2×Dic157—21no—
61C2×Dic157—41no—
62C4×D157—22no—
63C4×D157—22no—
64#11929434—22no—
65#11929434—22no—
66C23×C157#4111yescharacteristic
67C2×C4×C157—21no—
68C2×C4×C157—21no—
69C2×C4×C157—42no—
70C2×C4×C157C22×C411yescharacteristic
71C2×C4×C157C2×D411yescharacteristic
72C2×C4×C157C2×D411yescharacteristic
73C2×C4×C157C2×D411yescharacteristic
74C2×C4×C157C2×Q811yescharacteristic
75C2×C4×C157#4111yescharacteristic
76C8×C157—22no—
77C8×C157—41no—
78C22×C157—41no—
79C22×C157C4×D411yescharacteristic
80C22×C157C22⋊Q811yescharacteristic
81C22×C157#12311yescharacteristic
82C2×D157—22no—
83C2×D157—81no—
84C4×C157—22no—
85C4×C157—41no—
86C4×C157C2×C4⋊C411yescharacteristic
87C4×C157C4×D411yescharacteristic
88C4×C157#12011yescharacteristic
89C4×C157C22⋊Q811yescharacteristic
90Dic157—22no—
91Dic157—81no—
92C2×C157—21no—
93C2×C157—21no—
94C2×C157—21no—
95C2×C157#38511yescharacteristic
96D157—42no—
97C157#186111yescharacteristic, complemented, Sylow
98#1861—1571nomaximal, Sylow
99#568—1571no—
100#430—1571no—
101#423D15711yescharacteristic, complemented
102#421—1571no—
103C2×#104—1571no—
104#344—1571no—
105#339—1571no—
106C2×#41—1571no—
107#131—3142no—
108#131—3142no—
109C2×M16—3142no—
110C2×M16—1571no—
111C2×M16—1571no—
112C2×M16C2×D15711yescharacteristic
113C2×M16C2×D15711yescharacteristic
114#117—1571no—
115C2×C42C2×D15711yescharacteristic
116#108—3142no—
117C4⋊C8—22no—
118#104—3142no—
119#104—1572no—
120#104—1572no—
121#41—3141no—
122#41—3141no—
123#41—1572no—
124#41—1572no—
125C2×Q8—1571no—
126C2×D4—3141no—
127C2×D4—1571no—
128C22×C4—21no—
129C22×C4—3141no—
130C22×C4C22×D15711yescharacteristic
131M16—21no—
132M16—21no—
133M16—21no—
134M16—21no—
135M16—3144no—
136M16—3141no—
137M16—3141no—
138M16—1572no—
139M16—1572no—
140C2×C8—21no—
141C2×C8—3144no—
142C2×C8—3141no—
143C2×C8—3141no—
144C2×C8C22⋊D15712yes—
145C4⋊C4—3141no—
146C22⋊C4—3141no—
147C42—21no—
148C42—3141no—
149C42C4×D15711yescharacteristic
150C42C4×D15711yescharacteristic
151C23—3141no—
152C23#1457895411yescharacteristic
153Q8—3141no—
154Q8—1572no—
155D4—3142no—
156D4—3142no—
157D4—3141no—
158D4—1572no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—42no—
162C2×C4—3141no—
163C2×C4—3142no—
164C2×C4—3142no—
165C2×C4—6281no—
166C2×C4C2×C4×D15711yescharacteristic
167C2×C4D4×D15711yescharacteristic
168C2×C4D4×D15711yescharacteristic
169C2×C4C2×C22⋊D15711yescharacteristic
170C2×C4Q8×D15711yescharacteristic
171C2×C4#1457895511yescharacteristic
172C8—22no—
173C8—41no—
174C8—3142no—
175C8—3142no—
176C22—41no—
177C22—3142no—
178C22—12561no—
179C22C4×C22⋊D15711yescharacteristic
180C22#1909774911yescharacteristic
181C22#1909775611yescharacteristic
182C4—22no—
183C4—41no—
184C4—3142no—
185C4—12561no—
186C4C4⋊C4×D15711yescharacteristic
187C4#1909773311yescharacteristic
188C4#1909773911yescharacteristic
189C4#1909774711yescharacteristic
190C2—21no—
191C2—21no—
192C2—21no—
193C2—6282no—
194C2#2375714411yescharacteristic
subgroupG/H
centerC4#19097739
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#423×C157C2
socleC2×C157#385
prime radicalC2×#14578954C22
cosocleC22×C4×C157C23
hypercenter#423D157
hypocenterC157#1861
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C4 ◁ C22×C4 ◁ #423

Complements

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

NH ≅ G/Ntype
2. #23757321C2semidirect
5. #23757044C2semidirect
6. #23757033C2semidirect
7. #423×C157C2semidirect
16. #19097699C4semidirect
17. #19097699C4semidirect
97. C157#1861semidirect
101. #423D157semidirect

Maximal subgroups

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

subgroupindex
#237580392
#237573212
#237572892
C2×#190976992
#237570442
#237570332
#423×C1572
#1861157