Finite Group Databasebeta

← #34099204

Subgroups — #34099204

Order 20096.

278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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#23757944C211yesmaximal, characteristic, complemented
2#23757650C211yesmaximal, characteristic, complemented
3#23757474C211yesmaximal, characteristic, complemented
4#23757468C211yesmaximal, characteristic, complemented
5#23757016C211yesmaximal, characteristic, complemented
6#23757005C211yesmaximal, characteristic, complemented
7D4⋊C8×C157C211yesmaximal, characteristic, complemented
8C2×#14578954—21no—
9C2×#14578943—21no—
10C2×D1256—22no—
11C2×#14578939—21no—
12#19097768C2211yescharacteristic
13#19097768C2211yescharacteristic
14#19097767—21no—
15#19097745—21no—
16#19097744—22no—
17C4×Dic314C2211yescharacteristic
18#19097733—21no—
19C4⋊#11929434C2211yescharacteristic
20#19097693—21no—
21#19097691—21no—
22C4×D4×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4×C8×C157C2211yescharacteristic
25#14578954—42no—
26#14578954—42no—
27C2×Dic314D411yescharacteristic
28C2×D628—21no—
29C2×D628—21no—
30C2×D628—21no—
31C2×D628—21no—
32C2×D628—21no—
33C2×D628D412yes—
34C2×C22⋊D157—22no—
35C2×C22⋊D157—22no—
36C2×C4×D157—22no—
37#14578943—42no—
38D1256—44no—
39#14578939—42no—
40C2×#11929434—21no—
41C4⋊Dic157D411yescharacteristic
42#14578933—21no—
43#14578931—22no—
44C4×Dic157—21no—
45C2×D4×C157D411yescharacteristic
46C22×C4×C157—21no—
47C2×C8×C157—21no—
48C2×C8×C157—21no—
49C4⋊C4×C157D411yescharacteristic
50C22⋊C4×C157—21no—
51C42×C157C2311yescharacteristic
52C22×D157—22no—
53C22×D157—41no—
54Dic314—21no—
55Dic314D812yescomplemented
56D628—42no—
57D628—42no—
58D628—41no—
59D628—41no—
60D628—41no—
61D628—41no—
62D628—41no—
63D628—41no—
64D628—41no—
65D628—41no—
66C22⋊D157—44no—
67C22⋊D157—82no—
68C2×Dic157—21no—
69C2×Dic157—21no—
70C4×D157—44no—
71#11929434—41no—
72C23×C157—21no—
73D4×C157—21no—
74D4×C157—21no—
75C2×C4×C157—21no—
76C2×C4×C157—41no—
77C2×C4×C157—41no—
78C2×C4×C157C2×D411yescharacteristic
79C2×C4×C157C2×D411yescharacteristic
80C2×C4×C157C2×D411yescharacteristic
81C8×C157—22no—
82C8×C157—41no—
83C22×C157—41no—
84C22×C157—41no—
85C22×C157—41no—
86C22×C157#12011yescharacteristic
87C2×D157—42no—
88C2×D157—42no—
89C2×D157—42no—
90C2×D157—81no—
91C2×D157—81no—
92C2×D157—81no—
93C4×C157—21no—
94C4×C157—41no—
95C4×C157C2×D811yescharacteristic
96C4×C157#13511yescharacteristic
97C4×C157AGL(1,ℤ/8)11yescharacteristic
98C4×C157AGL(1,ℤ/8)11yescharacteristic
99Dic157—22no—
100Dic157—41no—
101C2×C157—81no—
102C2×C157#44711yescharacteristic
103C2×C157#44911yescharacteristic
104C2×C157#45311yescharacteristic
105D157—82no—
106D157—161no—
107C157#162111yescharacteristic, complemented, Sylow
108#1621—1571nomaximal, Sylow
109#550—1571no—
110#493—1571no—
111#460—1571no—
112#459—1571no—
113#331—1571no—
114Q8⋊C8—1571no—
115D4⋊C8D15711yescharacteristic, complemented
116C2×#41—3141no—
117C2×SD16—3141no—
118C2×D8—3142no—
119C2×D8—3141no—
120#127—3141no—
121#127—1571no—
122#127—1571no—
123#121—3142no—
124#121—3141no—
125C4×Q8—1571no—
126C4×D4—3141no—
127C4×D4C2×D15711yescharacteristic
128C4⋊C8—1571no—
129C4⋊C8C2×D15711yescharacteristic
130#102—3141no—
131#102—3141no—
132C4×C8C2×D15711yescharacteristic
133#41—6282no—
134#41—6282no—
135C2×Q8—1571no—
136C2×D4—3142no—
137C2×D4—3142no—
138C2×D4—3141no—
139C2×D4—3141no—
140C2×D4—3141no—
141C2×D4—3141no—
142C2×D4—3141no—
143C2×D4—1572no—
144C2×D4D62811yescharacteristic
145C22×C4—21no—
146C22×C4—3142no—
147SD16—6282no—
148D8—6284no—
149D8—6282no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—3141no—
153C4⋊C4—3141no—
154C4⋊C4—1571no—
155C4⋊C4D62811yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—3142no—
158C42—3141no—
159C42C22×D15711yescharacteristic
160C23—21no—
161C23—3142no—
162C23—6281no—
163Q8—3141no—
164Q8—1572no—
165D4—21no—
166D4—21no—
167D4—6282no—
168D4—6282no—
169D4—6284no—
170D4—6281no—
171D4—6281no—
172D4—6281no—
173D4—6281no—
174D4—6281no—
175D4—6281no—
176D4—6281no—
177D4—6281no—
178D4—12562no—
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—3141no—
183C2×C4—3141no—
184C2×C4—6284no—
185C2×C4D4×D15711yescharacteristic
186C2×C4D4×D15711yescharacteristic
187C2×C4C2×D62811yescharacteristic
188C8—22no—
189C8—41no—
190C8—6281no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—6282no—
195C22—6282no—
196C22—6282no—
197C22—12561no—
198C22—12561no—
199C22—12561no—
200C22#1909774111yescharacteristic
201C4—21no—
202C4—41no—
203C4—3142no—
204C4—6281no—
205C4D8×D15711yescharacteristic
206C4#1909779311yescharacteristic
207C4#1909779811yescharacteristic
208C4#1909779911yescharacteristic
209C2—81no—
210C2—25121no—
211C2—12562no—
212C2#2375740811yescharacteristic
213C2#2375742011yescharacteristic
214C2#2375744211yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
FittingD4⋊C8×C157C2
socleC22×C157#120
hypercenterD4⋊C8D157
hypocenterC157#1621
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #23757944C2semidirect
2. #23757650C2semidirect
3. #23757474C2semidirect
4. #23757468C2semidirect
5. #23757016C2semidirect
6. #23757005C2semidirect
7. D4⋊C8×C157C2semidirect
55. Dic314D8semidirect
107. C157#1621semidirect
115. D4⋊C8D157semidirect

Maximal subgroups

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

subgroupindex
#237579442
#237576502
#237574742
#237574682
#237570162
#237570052
D4⋊C8×C1572
#1621157