Finite Group Databasebeta

← #34101493

Subgroups — #34101493

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#23757300C211yesmaximal, characteristic, complemented
3#23757277C211yesmaximal, characteristic
4C2×#19097691C211yesmaximal, characteristic
5C2×#19097687C211yesmaximal, characteristic
6#23757042C211yesmaximal, characteristic, complemented
7#428×C157C211yesmaximal, characteristic, complemented
8C22×D628C2211yescharacteristic
9C2×#14578938C2211yescharacteristic
10C2×#14578938C2211yescharacteristic
11C22×#11929434C2211yescharacteristic
12#19097706—22no—
13C4⋊#11929434—22no—
14#19097691—22no—
15#19097691—21no—
16#19097691—21no—
17#19097687—22no—
18C2×M16×C157C2211yescharacteristic
19#117×C157C2211yescharacteristic
20C2×C4⋊C4×C157C2211yescharacteristic
21#107×C157—21no—
22#106×C157—21no—
23C23×D157—21no—
24C2×D628—21no—
25C2×D628—21no—
26C2×D628—21no—
27C2×D628—21no—
28C2×D628—21no—
29C2×D628Q812yes—
30#14578938—21no—
31#14578938—21no—
32#14578938—21no—
33#14578938—21no—
34C2×#11929434—21no—
35C2×#11929434—21no—
36C2×#11929434—21no—
37C2×#11929434—21no—
38C2×#11929434D412yes—
39C22×C4×C157—21no—
40C22×C4×C157C2311yescharacteristic
41M16×C157—21no—
42M16×C157D412yes—
43C2×C8×C157—21no—
44C4⋊C4×C157—21no—
45C4⋊C4×C157—21no—
46C4⋊C4×C157D411yescharacteristic
47C4⋊C4×C157D411yescharacteristic
48C22⋊C4×C157—21no—
49C42×C157—21no—
50C22×D157—22no—
51C22×D157—41no—
52C22×D157—41no—
53C22×D157—81no—
54C22×D157—81no—
55D628—22no—
56D628—22no—
57D628—41no—
58D628—41no—
59#11929434—22no—
60#11929434—41no—
61#11929434—41no—
62C23×C157#4111yescharacteristic
63C2×C4×C157—21no—
64C2×C4×C157—21no—
65C2×C4×C157—41no—
66C2×C4×C157—81no—
67C2×C4×C157C2×D411yescharacteristic
68C2×C4×C157C2×D411yescharacteristic
69C2×C4×C157C2×D411yescharacteristic
70C2×C4×C157C2×Q811yescharacteristic
71C2×C4×C157#4111yescharacteristic
72C2×C4×C157#4111yescharacteristic
73C8×C157—22no—
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—41no—
85C4×C157—41no—
86C4×C157—81no—
87C4×C157#12111yescharacteristic
88C4×C157#12111yescharacteristic
89C4×C157C22⋊Q811yescharacteristic
90C4×C157C22⋊Q811yescharacteristic
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×#108—1571no—
100#428D15711yescharacteristic, complemented
101#424—1571no—
102#418—1571no—
103C2×#102—1571no—
104C2×#100—1571no—
105#343—1571no—
106C22×D4—1571no—
107C2×M16—1571no—
108C2×M16—1571no—
109C2×M16C2×D15711yescharacteristic
110C22×C8—1571no—
111#117C2×D15711yescharacteristic
112C2×C4⋊C4C2×D15711yescharacteristic
113#108—3142no—
114#107—21no—
115#106—21no—
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—21no—
129C22×C4C22×D15711yescharacteristic
130M16—21no—
131M16—3141no—
132M16—3141no—
133M16—3141no—
134M16—3141no—
135M16D62812yes—
136C2×C8—21no—
137C2×C8—3141no—
138C2×C8—3141no—
139C2×C8—3141no—
140C2×C8—3141no—
141C2×C8—1572no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4C22⋊D15711yescharacteristic
145C4⋊C4C22⋊D15711yescharacteristic
146C22⋊C4—21no—
147C42—21no—
148C23—3142no—
149C23—6281no—
150C23—6281no—
151C23—12561no—
152C23—12561no—
153C23#1457895311yescharacteristic
154D4—3142no—
155D4—3142no—
156D4—6281no—
157D4—6281no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—81no—
162C2×C4D4×D15711yescharacteristic
163C2×C4C2×C22⋊D15711yescharacteristic
164C2×C4C2×D62811yescharacteristic
165C2×C4Q8×D15711yescharacteristic
166C2×C4#1457895411yescharacteristic
167C2×C4#1457895511yescharacteristic
168C8—22no—
169C8—3142no—
170C8—6281no—
171C8—6281no—
172C22—21no—
173C22—21no—
174C22—6282no—
175C22—12562no—
176C22—12562no—
177C22—12561no—
178C22—12561no—
179C22#1909774311yescharacteristic
180C22#1909775111yescharacteristic
181C22#1909776611yescharacteristic
182C4—41no—
183C4—41no—
184C4—81no—
185C4#1909774511yescharacteristic
186C4#1909774611yescharacteristic
187C4#1909774711yescharacteristic
188C4#1909774911yescharacteristic
189C2—21no—
190C2—21no—
191C2—12562no—
192C2#2375719511yescharacteristic
193C2#2375753811yescharacteristic
194C2#2375754111yescharacteristic
subgroupG/H
centerC22#19097743
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#428×C157C2
socleC22×C157#121
prime radicalC22×D628C22
hypercenter#428D157
hypocenterC157#2063
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. C2×#19097706C2semidirect
2. #23757300C2semidirect
6. #23757042C2semidirect
7. #428×C157C2semidirect
97. C157#2063semidirect
100. #428D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977062
#237573002
#237572772
C2×#190976912
C2×#190976872
#237570422
#428×C1572
#2063157