Finite Group Databasebeta

← #34102046

Subgroups — #34102046

Order 20096.

266 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 53 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×D8×D157C211yesmaximal, characteristic, complemented
2C2×#19097712C211yesmaximal, characteristic, complemented
3#23757506C211yesmaximal, characteristic, complemented
4#23757075C211yesmaximal, characteristic, complemented
5#23757074C211yesmaximal, characteristic, complemented
6#23757052C211yesmaximal, characteristic, complemented
7C2×D16×C157C211yesmaximal, characteristic, complemented
8C2×D4×D157—21no—
9C2×D1256C2211yescharacteristic
10C2×#14578939—21no—
11D8×D157—22no—
12D8×D157—22no—
13C2×C8×D157C2211yescharacteristic
14#19097742—21no—
15#19097712—22no—
16C2×#14578929C2211yescharacteristic, complemented
17#19097705C2211yescharacteristic, complemented
18#19097692—21no—
19C2×D8×C157C2211yescharacteristic
20C2×D8×C157C2211yescharacteristic, complemented
21D16×C157—22no—
22C2×C16×C157C2211yescharacteristic, complemented
23C23×D157—41no—
24C2×D628—21no—
25C2×C22⋊D157—41no—
26C2×C22⋊D157—41no—
27D4×D157—24no—
28D4×D157—42no—
29C2×C4×D157D411yescharacteristic
30D1256—21no—
31D1256D412yescomplemented
32#14578939—24no—
33C2×#11929434D411yescharacteristic
34C8×D157—21no—
35C8×D157—21no—
36C4⋊Dic157—21no—
37C22⋊Dic157—41no—
38#14578929—21no—
39C2×D4×C157—21no—
40C2×D4×C157—21no—
41D8×C157—21no—
42D8×C157—21no—
43D8×C157—21no—
44D8×C157D412yescomplemented
45C2×C8×C157C2311yescharacteristic
46C16×C157—21no—
47C22×D157—44no—
48C22×D157—41no—
49C22×D157—82no—
50C22×D157—82no—
51C22×D157D811yescharacteristic
52D628—22no—
53D628—41no—
54C22⋊D157—44no—
55C22⋊D157—82no—
56C2×Dic157—41no—
57C2×Dic157D811yescharacteristic
58C4×D157—21no—
59C4×D157—21no—
60#11929434—21no—
61C23×C157—41no—
62C23×C157—41no—
63D4×C157—22no—
64D4×C157—41no—
65D4×C157—41no—
66D4×C157—41no—
67C2×C4×C157C2×D411yescharacteristic
68C8×C157C2×D411yescharacteristic
69C8×C157C2×D411yescharacteristic
70C22×C157—42no—
71C22×C157—81no—
72C22×C157—81no—
73C22×C157—81no—
74C22×C157—81no—
75C22×C157—81no—
76C22×C157C2×D811yescharacteristic
77C2×D157—21no—
78C2×D157—21no—
79C2×D157—42no—
80C2×D157—88no—
81C2×D157—81no—
82C2×D157—81no—
83C2×D157D1612yescomplemented
84C4×C157#12011yescharacteristic
85C4×C157AGL(1,ℤ/8)11yescharacteristic
86Dic157—21no—
87Dic157—81no—
88C2×C157—82no—
89C2×C157—161no—
90C2×C157#44711yescharacteristic
91C2×C157C2×D1611yescharacteristic
92C2×C157#50911yescharacteristic
93D157—22no—
94D157—82no—
95C157#218411yescharacteristic, complemented, Sylow
96#2184—1571nomaximal, Sylow
97C22×D8—1571no—
98C2×D16—1571no—
99C2×D16D15711yescharacteristic, complemented
100#466—1571no—
101#357—1571no—
102#357—1571no—
103C22⋊C16—1571no—
104C22×D4—3141no—
105C2×D8—3142no—
106C2×D8—3142no—
107C2×D8—3141no—
108C2×D8—1571no—
109C2×D8C2×D15711yescharacteristic
110C2×D8C2×D15711yescharacteristic, complemented
111C22×C8—1571no—
112#121—3141no—
113D16—22no—
114D16—3142no—
115C2×C16—1571no—
116C2×C16C2×D15711yescharacteristic, complemented
117#107—1571no—
118#102—3141no—
119C24—6281no—
120C2×D4—21no—
121C2×D4—21no—
122C2×D4—3144no—
123C2×D4—3141no—
124C2×D4—6282no—
125C2×D4—6281no—
126C2×D4—6281no—
127C22×C4—1571no—
128D8—21no—
129D8—21no—
130D8—21no—
131D8—3144no—
132D8—3141no—
133D8—1572no—
134D8C22⋊D15712yescomplemented
135C2×C8—3141no—
136C2×C8—3141no—
137C2×C8—1571no—
138C2×C8C22×D15711yescharacteristic
139C4⋊C4—3141no—
140C22⋊C4—6281no—
141C16—21no—
142C16—3141no—
143C23—41no—
144C23—41no—
145C23—6284no—
146C23—6281no—
147C23—1571no—
148C23—12562no—
149C23—12562no—
150D4—22no—
151D4—41no—
152D4—41no—
153D4—41no—
154D4—3142no—
155D4—6284no—
156D4—6281no—
157D4—12562no—
158C2×C4—3141no—
159C2×C4—3141no—
160C2×C4—6281no—
161C2×C4—1571no—
162C2×C4D4×D15711yescharacteristic
163C8—3141no—
164C8D4×D15711yescharacteristic
165C8C2×C22⋊D15711yescharacteristic
166C22—42no—
167C22—81no—
168C22—81no—
169C22—81no—
170C22—81no—
171C22—81no—
172C22—3141no—
173C22—3141no—
174C22—6282no—
175C22—1572no—
176C22—12568no—
177C22—12561no—
178C22—12561no—
179C22D8×D15711yescharacteristic
180C4—3141no—
181C4—12561no—
182C4#1909773911yescharacteristic
183C4#1909779511yescharacteristic
184C2—82no—
185C2—161no—
186C2—3142no—
187C2—12562no—
188C2#2375740511yescharacteristic
189C2D16×D15711yescharacteristic
190C2#2375770711yescharacteristic
subgroupG/H
centerC22D8×D157
commutator, cosocleC2×C8×C157C23
FrattiniC2×C8C22×D157
FittingC2×D16×C157C2
socleC22×C157C2×D8
hypercenterC2×D16D157
hypocenterC157#2184
LCSG ▷ C2×C8×C157 ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. C2×D8×D157C2semidirect
2. C2×#19097712C2semidirect
3. #23757506C2semidirect
4. #23757075C2semidirect
5. #23757074C2semidirect
6. #23757052C2semidirect
7. C2×D16×C157C2semidirect
16. C2×#14578929C22semidirect
17. #19097705C22semidirect
20. C2×D8×C157C22semidirect
22. C2×C16×C157C22semidirect
31. D1256D4semidirect
44. D8×C157D4semidirect
83. C2×D157D16semidirect
95. C157#2184semidirect
99. C2×D16D157semidirect
110. C2×D8C2×D157semidirect
116. C2×C16C2×D157semidirect
134. D8C22⋊D157semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1572
C2×#190977122
#237575062
#237570752
#237570742
#237570522
C2×D16×C1572
#2184157