Finite Group Databasebeta

← #34112743

Subgroups — #34112743

Order 20096.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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#23757973C212yesmaximal, complemented
2#23757675C211yesmaximal, characteristic, complemented
3#23757595C212yesmaximal, complemented
4#23757585C212yesmaximal, complemented
5#23757573C212yesmaximal, complemented
6#23757523C212yesmaximal, complemented
7#23757352C211yesmaximal, characteristic, complemented
8#23757314C212yesmaximal, complemented
9C4×D8×C157C211yesmaximal, characteristic, complemented
10C2×#14578937C2212yes—
11#19097764—22no—
12#19097763C2212yes—
13#19097754—22no—
14#19097744—22no—
15#19097742C2212yes—
16#19097742C2212yes—
17C4×D628C2211yescharacteristic
18C4×C22⋊D157—22no—
19#19097729C2212yes—
20C4⋊C4×D157C2212yes—
21#19097705C2211yescharacteristic
22#19097705C2211yescharacteristic
23#19097704C2212yes—
24#19097703C2212yes—
25#19097702C2212yes—
26C4⋊#11929434C2211yescharacteristic
27#19097692C2212yes—
28#19097692C2212yes—
29#19097683C2212yes—
30C2×D8×C157C2211yescharacteristic
31C4×D4×C157C2212yes—
32#107×C157C2211yescharacteristic
33#102×C157C2212yes—
34C4×C8×C157C2211yescharacteristic
35C2×D628D411yescharacteristic
36C2×C22⋊D157—22no—
37C2×C22⋊D157—22no—
38C2×C4×D157—22no—
39C2×C4×D157C2312yes—
40#14578937—24no—
41C2×#11929434C2312yes—
42C4⋊Dic157D411yescharacteristic
43C4⋊Dic157C2312yes—
44C4⋊Dic157C2312yes—
45#14578933—22no—
46#14578933—22no—
47#14578933—22no—
48C22⋊Dic157—22no—
49C22⋊Dic157—22no—
50#14578931—22no—
51#14578931D412yes—
52C4×Dic157—22no—
53C2×D4×C157C2312yes—
54C22×C4×C157—22no—
55D8×C157—22no—
56C2×C8×C157C2311yescharacteristic
57C2×C8×C157C2311yescharacteristic
58C4⋊C4×C157C2312yes—
59C22⋊C4×C157—22no—
60C42×C157C2311yescharacteristic
61C22×D157C2×D412yes—
62D628—41no—
63C22⋊D157—44no—
64C22⋊D157—82no—
65C2×Dic157—22no—
66C2×Dic157—22no—
67C2×Dic157C2×D412yes—
68C4×D157—22no—
69C4×D157—22no—
70C4×D157—82no—
71#11929434—22no—
72C23×C157—22no—
73D4×C157—22no—
74D4×C157—22no—
75C2×C4×C157—22no—
76C2×C4×C157—82no—
77C2×C4×C157C2×D411yescharacteristic
78C2×C4×C157C2×D411yescharacteristic
79C2×C4×C157C2411yescharacteristic
80C8×C157—21no—
81C8×C157#4112yes—
82C22×C157—42no—
83C22×C157—42no—
84C22×C157—42no—
85C22×C157C22×D411yescharacteristic
86C2×D157—22no—
87C2×D157—22no—
88C2×D157—22no—
89C4×C157—21no—
90C4×C157—21no—
91C4×C157—42no—
92C4×C157C2×#4111yescharacteristic
93C4×C1572−1+411yescharacteristic
94Dic157—22no—
95Dic157—42no—
96Dic157—42no—
97C2×C157—82no—
98C2×C157#54711yescharacteristic
99C2×C157#57511yescharacteristic
100C2×C157#57611yescharacteristic
101D157—42no—
102C157#335511yescharacteristic, complemented, Sylow
103#3355—1571nomaximal, Sylow
104#553—1572no—
105#499—1571no—
106#482—1572no—
107#480—1572no—
108#478—1572no—
109#469—1572no—
110C4×D8D15711yescharacteristic, complemented
111#436—1571no—
112#428—1572no—
113C2×D8C2×D15711yescharacteristic
114C2×M16—1572no—
115#126—3142no—
116#125—1572no—
117#123—3142no—
118#121—3142no—
119#121—1572no—
120#121—1572no—
121C4×D4—3142no—
122C4×D4—1571no—
123C4×D4C2×D15712yes—
124#117—1572no—
125C2×C4⋊C4—1572no—
126#107—1571no—
127#107—1571no—
128#107—1572no—
129#107C2×D15711yescharacteristic
130#106—1572no—
131#106—1572no—
132C4⋊C8—1571no—
133#102—1572no—
134#102—1572no—
135#102C2×D15712yes—
136C22⋊C8—1572no—
137C4×C8C2×D15711yescharacteristic
138C2×D4—3142no—
139C2×D4—3142no—
140C2×D4—1571no—
141C2×D4C22×D15712yes—
142C22×C4—22no—
143C22×C4—3142no—
144C22×C4—1572no—
145D8—22no—
146M16—3144no—
147C2×C8—1572no—
148C2×C8C22×D15711yescharacteristic
149C2×C8C22×D15711yescharacteristic
150C4⋊C4—3142no—
151C4⋊C4—3142no—
152C4⋊C4—3142no—
153C4⋊C4—1572no—
154C4⋊C4—1572no—
155C4⋊C4—1571no—
156C4⋊C4C22×D15712yes—
157C22⋊C4—22no—
158C22⋊C4—3142no—
159C22⋊C4—3142no—
160C22⋊C4—3142no—
161C22⋊C4—1572no—
162C42—3142no—
163C42C22×D15711yescharacteristic
164C23—22no—
165C23—1572no—
166D4—22no—
167D4—22no—
168D4—6281no—
169D4—6284no—
170D4—12562no—
171C2×C4—22no—
172C2×C4—82no—
173C2×C4—3142no—
174C2×C4—3142no—
175C2×C4—3142no—
176C2×C4—3142no—
177C2×C4—1572no—
178C2×C4—12562no—
179C2×C4D4×D15711yescharacteristic
180C2×C4D4×D15711yescharacteristic
181C2×C4C23×D15711yescharacteristic
182C8—21no—
183C8—3142no—
184C8#1457895412yes—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—3142no—
189C22—3142no—
190C22—3142no—
191C22C2×D4×D15711yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—3142no—
196C4—6282no—
197C4—6282no—
198C4C2×#1457895411yescharacteristic
199C4#1909781811yescharacteristic
200C2—82no—
201C2—6282no—
202C2#2375792811yescharacteristic
203C2#2375807011yescharacteristic
204C2#2375807411yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC4×D8×C157C2
socleC22×C157C22×D4
hypercenterC4×D8D157
hypocenterC157#3355
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #23757973C2semidirect
2. #23757675C2semidirect
3. #23757595C2semidirect
4. #23757585C2semidirect
5. #23757573C2semidirect
6. #23757523C2semidirect
7. #23757352C2semidirect
8. #23757314C2semidirect
9. C4×D8×C157C2semidirect
102. C157#3355semidirect
110. C4×D8D157semidirect

Maximal subgroups

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

subgroupindex
#237579732
#237576752
#237575952
#237575852
#237575732
#237575232
#237573522
#237573142
C4×D8×C1572
#3355157