Finite Group Databasebeta

← #34101491

Subgroups — #34101491

Order 20096.

228 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 69 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#23757315C211yesmaximal, characteristic, complemented
2#23757299C211yesmaximal, characteristic, complemented
3#23757279C211yesmaximal, characteristic
4C2×#19097693C211yesmaximal, characteristic
5C2×#19097687C211yesmaximal, characteristic
6#23757041C211yesmaximal, characteristic, complemented
7C2×#108×C157C211yesmaximal, characteristic, complemented
8C22×D628C2211yescharacteristic
9C2×#14578938C2211yescharacteristic
10#19097730C2211yescharacteristic
11C2×C4⋊Dic157C2211yescharacteristic
12#19097705—21no—
13#19097703—21no—
14#19097700—22no—
15#19097693—21no—
16#19097693—21no—
17#19097693—22no—
18#19097687—22no—
19C2×M16×C157C2211yescharacteristic
20C2×M16×C157C2211yescharacteristic
21C22×C8×C157C2211yescharacteristic
22#108×C157—22no—
23C23×D157—21no—
24C2×D628—21no—
25C2×D628—21no—
26C2×D628—21no—
27C2×D628—21no—
28C2×D628—21no—
29C2×D628Q812yes—
30C22×Dic157—21no—
31#14578938—21no—
32#14578938—21no—
33C2×#11929434—21no—
34C4⋊Dic157—21no—
35C4⋊Dic157—21no—
36C4⋊Dic157D411yescharacteristic
37C4⋊Dic157D411yescharacteristic
38C22⋊Dic157—21no—
39C4×Dic157—21no—
40C22×C4×C157C2311yescharacteristic
41M16×C157—21no—
42M16×C157—21no—
43M16×C157—21no—
44M16×C157D412yes—
45C2×C8×C157—21no—
46C2×C8×C157—21no—
47C2×C8×C157—21no—
48C2×C8×C157—21no—
49C2×C8×C157D412yes—
50C22×D157—22no—
51C22×D157—41no—
52C22×D157—41no—
53C22×D157—81no—
54C22×D157—81no—
55D628—22no—
56D628—22no—
57D628—41no—
58D628—41no—
59C2×Dic157—21no—
60C2×Dic157—21no—
61C2×Dic157—41no—
62C2×Dic157—81no—
63#11929434—41no—
64C23×C157#4111yescharacteristic
65C2×C4×C157C2×D411yescharacteristic
66C2×C4×C157C2×D411yescharacteristic
67C2×C4×C157C2×D411yescharacteristic
68C2×C4×C157C2×Q811yescharacteristic
69C2×C4×C157#4111yescharacteristic
70C2×C4×C157#4111yescharacteristic
71C8×C157—22no—
72C8×C157—22no—
73C8×C157—41no—
74C22×C157—21no—
75C22×C157—21no—
76C22×C157#12111yescharacteristic
77C22×C157C22⋊Q811yescharacteristic
78C22×C157#12611yescharacteristic
79C2×D157—42no—
80C2×D157—82no—
81C2×D157—81no—
82C2×D157—81no—
83C2×D157—82no—
84C4×C157#12111yescharacteristic
85C4×C157#12111yescharacteristic
86C4×C157C22⋊Q811yescharacteristic
87C4×C157C22⋊Q811yescharacteristic
88Dic157—41no—
89Dic157—41no—
90Dic157—81no—
91C2×C157—21no—
92C2×C157—21no—
93C2×C157#39611yescharacteristic
94C2×C157#47111yescharacteristic
95C2×C157#47211yescharacteristic
96D157—82no—
97C157#206311yescharacteristic, complemented, Sylow
98#2063—1571nomaximal, Sylow
99C2×#108D15711yescharacteristic, complemented
100#428—1571no—
101#424—1571no—
102#418—1571no—
103C2×#102—1571no—
104C2×#100—1571no—
105#343—1571no—
106C22×D4—1571no—
107C2×M16—1571no—
108C2×M16C2×D15711yescharacteristic
109C2×M16C2×D15711yescharacteristic
110C22×C8C2×D15711yescharacteristic
111#117—1571no—
112C2×C4⋊C4—1571no—
113#108—22no—
114#107—3141no—
115#106—3141no—
116C4⋊C8—3142no—
117#102—3142no—
118#102—3141no—
119#102—3141no—
120#100—3142no—
121C24—3141no—
122C2×D4—3141no—
123C2×D4—3141no—
124C2×D4—3141no—
125C2×D4—3141no—
126C2×D4—3141no—
127C2×D4—1572no—
128C22×C4—3141no—
129C22×C4C22×D15711yescharacteristic
130M16—21no—
131M16—21no—
132M16—21no—
133M16—3141no—
134M16—3141no—
135M16C22⋊D15712yes—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—3141no—
141C2×C8D62812yes—
142C4⋊C4—3141no—
143C4⋊C4—3141no—
144C4⋊C4—1571no—
145C4⋊C4—1571no—
146C22⋊C4—3141no—
147C42—3141no—
148C23—3142no—
149C23—6281no—
150C23—6281no—
151C23—12561no—
152C23—12561no—
153C23#1457895511yescharacteristic
154D4—3142no—
155D4—3142no—
156D4—6281no—
157D4—6281no—
158C2×C4—3141no—
159C2×C4—3141no—
160C2×C4—6281no—
161C2×C4—12561no—
162C2×C4D4×D15711yescharacteristic
163C2×C4C2×C22⋊D15711yescharacteristic
164C2×C4C2×D62811yescharacteristic
165C2×C4Q8×D15711yescharacteristic
166C2×C4#1457895311yescharacteristic
167C2×C4#1457895411yescharacteristic
168C8—22no—
169C8—22no—
170C8—41no—
171C8—6281no—
172C22—21no—
173C22—21no—
174C22—6282no—
175C22—12562no—
176C22—12562no—
177C22—12561no—
178C22—12561no—
179C22#1909774611yescharacteristic
180C22#1909774711yescharacteristic
181C22#1909776611yescharacteristic
182C4—6281no—
183C4—6281no—
184C4—12561no—
185C4#1909774311yescharacteristic
186C4#1909774511yescharacteristic
187C4#1909774911yescharacteristic
188C4#1909775111yescharacteristic
189C2—21no—
190C2—21no—
191C2—12562no—
192C2#2375719511yescharacteristic
193C2#2375753711yescharacteristic
194C2#2375754411yescharacteristic
subgroupG/H
centerC22#19097746
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
FittingC2×#108×C157C2
socleC22×C157#121
prime radicalC22×D628C22
hypercenterC2×#108D157
hypocenterC157#2063
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
1. #23757315C2semidirect
2. #23757299C2semidirect
6. #23757041C2semidirect
7. C2×#108×C157C2semidirect
97. C157#2063semidirect
99. C2×#108D157semidirect

Maximal subgroups

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

subgroupindex
#237573152
#237572992
#237572792
C2×#190976932
C2×#190976872
#237570412
C2×#108×C1572
#2063157