Finite Group Databasebeta

← #34101492

Subgroups — #34101492

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
1C2×#19097706C211yesmaximal, characteristic, complemented
2#23757315C211yesmaximal, characteristic, complemented
3#23757301C211yesmaximal, characteristic, complemented
4#23757278C211yesmaximal, characteristic
5C2×#19097692C211yesmaximal, characteristic
6#23757041C211yesmaximal, characteristic, complemented
7C2×#100×C157C211yesmaximal, characteristic
8C2×#14578938C2211yescharacteristic
9C22×#11929434C2211yescharacteristic
10#19097730C2211yescharacteristic
11C2×C4⋊Dic157C2211yescharacteristic
12#19097706—22no—
13#19097705—21no—
14#19097703—21no—
15#19097700—22no—
16#19097692—22no—
17#19097692—21no—
18#19097692—21no—
19C22×D4×C157C2211yescharacteristic
20C2×M16×C157C2211yescharacteristic
21C2×M16×C157C2211yescharacteristic
22#100×C157—22no—
23C22×Dic157—21no—
24#14578938—21no—
25#14578938—21no—
26C2×#11929434—21no—
27C2×#11929434—21no—
28C2×#11929434—21no—
29C2×#11929434D412yes—
30C4⋊Dic157—21no—
31C4⋊Dic157—21no—
32C4⋊Dic157D411yescharacteristic
33C4⋊Dic157D411yescharacteristic
34C22⋊Dic157—21no—
35C4×Dic157—21no—
36C24×C157—21no—
37C2×D4×C157—21no—
38C2×D4×C157—21no—
39C2×D4×C157—21no—
40C2×D4×C157—21no—
41C2×D4×C157—21no—
42C2×D4×C157Q812yes—
43C22×C4×C157C2311yescharacteristic
44M16×C157—21no—
45M16×C157—21no—
46M16×C157—21no—
47M16×C157D412yes—
48C2×C8×C157—21no—
49C2×C8×C157—21no—
50C2×Dic157—21no—
51C2×Dic157—21no—
52C2×Dic157—41no—
53C2×Dic157—81no—
54#11929434—22no—
55#11929434—41no—
56C23×C157—22no—
57C23×C157—41no—
58C23×C157—41no—
59C23×C157—81no—
60C23×C157—81no—
61C23×C157#4111yescharacteristic
62D4×C157—22no—
63D4×C157—22no—
64D4×C157—41no—
65D4×C157—41no—
66C2×C4×C157C2×D411yescharacteristic
67C2×C4×C157C2×D411yescharacteristic
68C2×C4×C157C2×D411yescharacteristic
69C2×C4×C157C2×Q811yescharacteristic
70C2×C4×C157#4111yescharacteristic
71C2×C4×C157#4111yescharacteristic
72C8×C157—22no—
73C8×C157—41no—
74C22×C157—21no—
75C22×C157—21no—
76C22×C157—42no—
77C22×C157—82no—
78C22×C157—82no—
79C22×C157—81no—
80C22×C157—81no—
81C22×C157#12111yescharacteristic
82C22×C157C22⋊Q811yescharacteristic
83C22×C157#12611yescharacteristic
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—82no—
94C2×C157#39611yescharacteristic
95C2×C157#47111yescharacteristic
96C2×C157#47211yescharacteristic
97C157#206311yescharacteristic, complemented, Sylow
98#2063—1571nomaximal, Sylow
99C2×#108—1571no—
100#428—1571no—
101#424—1571no—
102#418—1571no—
103C2×#102—1571no—
104C2×#100D15711yescharacteristic
105#343—1571no—
106C22×D4C2×D15711yescharacteristic
107C2×M16—1571no—
108C2×M16C2×D15711yescharacteristic
109C2×M16C2×D15711yescharacteristic
110C22×C8—1571no—
111#117—1571no—
112C2×C4⋊C4—1571no—
113#108—3142no—
114#107—3141no—
115#106—3141no—
116C4⋊C8—3142no—
117#102—3142no—
118#102—3141no—
119#102—3141no—
120#100—22no—
121C24—21no—
122C2×D4—21no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4Dic31412yes—
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—3141no—
139C2×C8—3141no—
140C2×C8—3141no—
141C2×C8—1572no—
142C4⋊C4—3141no—
143C4⋊C4—3141no—
144C4⋊C4—1571no—
145C4⋊C4—1571no—
146C22⋊C4—3141no—
147C42—3141no—
148C23—22no—
149C23—41no—
150C23—41no—
151C23—81no—
152C23—81no—
153C23#1457895411yescharacteristic
154D4—22no—
155D4—22no—
156D4—41no—
157D4—41no—
158C2×C4—3141no—
159C2×C4—3141no—
160C2×C4—6281no—
161C2×C4—12561no—
162C2×C4D4×D15711yescharacteristic
163C2×C4D4×D15711yescharacteristic
164C2×C4C2×C22⋊D15711yescharacteristic
165C2×C4C2×Dic31411yescharacteristic
166C2×C4#1457895311yescharacteristic
167C2×C4#1457895311yescharacteristic
168C8—22no—
169C8—41no—
170C8—3142no—
171C8—6281no—
172C22—21no—
173C22—21no—
174C22—42no—
175C22—82no—
176C22—82no—
177C22—81no—
178C22—81no—
179C22#1909774411yescharacteristic
180C22#1909775011yescharacteristic
181C22#1909776411yescharacteristic
182C4—6281no—
183C4—6281no—
184C4—12561no—
185C4#1909774211yescharacteristic
186C4#1909774311yescharacteristic
187C4#1909774811yescharacteristic
188C4#1909774811yescharacteristic
189C2—21no—
190C2—21no—
191C2—82no—
192C2#2375719611yescharacteristic
193C2#2375753511yescharacteristic
194C2#2375754211yescharacteristic
subgroupG/H
centerC22#19097744
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
FittingC2×#100×C157C2
socleC22×C157#121
prime radicalC22×D4×C157C22
hypercenterC2×#100D157
hypocenterC157#2063
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#19097706C2semidirect
2. #23757315C2semidirect
3. #23757301C2semidirect
6. #23757041C2semidirect
97. C157#2063semidirect

Maximal subgroups

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

subgroupindex
C2×#190977062
#237573152
#237573012
#237572782
C2×#190976922
#237570412
C2×#100×C1572
#2063157