Finite Group Databasebeta

← #34099199

Subgroups — #34099199

Order 20096.

278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 57 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#23757945C211yesmaximal, characteristic, complemented
2#23757649C211yesmaximal, characteristic, complemented
3#23757465C211yesmaximal, characteristic, complemented
4#23757016C211yesmaximal, characteristic, complemented
5Q8⋊#11929434C211yesmaximal, characteristic, complemented
6#23757000C211yesmaximal, characteristic, complemented
7#460×C157C211yesmaximal, characteristic, complemented
8C2×#14578955—21no—
9C2×#14578939—22no—
10C2×#14578939—21no—
11#19097768—21no—
12#19097768C2211yescharacteristic
13#19097746—21no—
14#19097746—22no—
15C4×D628—21no—
16C4×D628C2211yescharacteristic
17C4⋊#11929434C2211yescharacteristic
18#19097692—21no—
19C4×#11929434C2211yescharacteristic
20C2×SD16×C157—21no—
21#127×C157C2211yescharacteristic
22C4×Q8×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24#102×C157—21no—
25#14578955—42no—
26#14578955—42no—
27C2×D628—22no—
28C2×D628—22no—
29C2×D628—21no—
30C2×D628—21no—
31C2×D628D411yescharacteristic
32C2×D628D412yes—
33C2×C4×D157—22no—
34C2×C4×D157—21no—
35#14578939—44no—
36#14578939—42no—
37C2×#11929434—21no—
38C2×#11929434—21no—
39C4⋊Dic157D411yescharacteristic
40#14578931—22no—
41#14578931—21no—
42C2×Q8×C157D411yescharacteristic
43C2×D4×C157—21no—
44C2×D4×C157—21no—
45C2×D4×C157—21no—
46SD16×C157—42no—
47C2×C8×C157—21no—
48C4⋊C4×C157—21no—
49C4⋊C4×C157D411yescharacteristic
50C42×C157—21no—
51C42×C157C2311yescharacteristic
52C22×D157—21no—
53C22×D157—22no—
54D628—21no—
55D628—21no—
56D628—42no—
57D628—44no—
58D628—41no—
59D628—41no—
60D628—41no—
61D628—41no—
62D628—82no—
63C2×Dic157—21no—
64C4×D157—44no—
65C4×D157—41no—
66C4×D157—41no—
67#11929434—22no—
68#11929434—41no—
69C23×C157—41no—
70Q8×C157—21no—
71Q8×C157D812yescomplemented
72D4×C157—42no—
73D4×C157—41no—
74D4×C157—41no—
75D4×C157—41no—
76D4×C157—41no—
77C2×C4×C157—21no—
78C2×C4×C157—21no—
79C2×C4×C157C2×D411yescharacteristic
80C2×C4×C157C2×D411yescharacteristic
81C2×C4×C157C2×D411yescharacteristic
82C8×C157—41no—
83C22×C157—81no—
84C22×C157—81no—
85C22×C157—81no—
86C22×C157#12011yescharacteristic
87C2×D157—42no—
88C2×D157—41no—
89C2×D157—41no—
90C2×D157—42no—
91C2×D157—42no—
92C2×D157—41no—
93C4×C157—22no—
94C4×C157—21no—
95C4×C157—41no—
96C4×C157C2×D811yescharacteristic
97C4×C157#13511yescharacteristic
98C4×C157AGL(1,ℤ/8)11yescharacteristic
99C4×C157AGL(1,ℤ/8)11yescharacteristic
100Dic157—41no—
101C2×C157—161no—
102C2×C157#44711yescharacteristic
103C2×C157#44911yescharacteristic
104C2×C157#45311yescharacteristic
105D157—81no—
106D157—82no—
107C157#162111yescharacteristic, complemented, Sylow
108#1621—1571nomaximal, Sylow
109#550—1571no—
110#493—1571no—
111#460D15711yescharacteristic, complemented
112#459—1571no—
113#331—1571no—
114Q8⋊C8—1571no—
115D4⋊C8—1571no—
116C2×#41—3141no—
117C2×SD16—21no—
118C2×D8—3141no—
119C2×D8—3142no—
120#127—3141no—
121#127—1571no—
122#127C2×D15711yescharacteristic
123#121—3142no—
124#121—3141no—
125C4×Q8C2×D15711yescharacteristic
126C4×D4—3141no—
127C4×D4—1571no—
128C4⋊C8—1571no—
129C4⋊C8C2×D15711yescharacteristic
130#102—21no—
131#102—3141no—
132C4×C8—1571no—
133#41—6282no—
134#41—6282no—
135C2×Q8C22⋊D15711yescharacteristic
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—3142no—
140C2×D4—3142no—
141C2×D4—3141no—
142C2×D4—3141no—
143C2×D4—1571no—
144C2×D4—1572no—
145C22×C4—3142no—
146C22×C4—3141no—
147SD16—42no—
148D8—6284no—
149D8—6282no—
150C2×C8—21no—
151C2×C8—3141no—
152C2×C8—3141no—
153C4⋊C4—21no—
154C4⋊C4—1571no—
155C4⋊C4C22⋊D15711yescharacteristic
156C22⋊C4—3142no—
157C22⋊C4—3141no—
158C42—21no—
159C42C22×D15711yescharacteristic
160C23—41no—
161C23—3141no—
162C23—3142no—
163Q8—21no—
164Q8#1457893912yescomplemented
165D4—42no—
166D4—41no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—3141no—
171D4—3141no—
172D4—6282no—
173D4—6284no—
174D4—6281no—
175D4—6281no—
176D4—6281no—
177D4—6281no—
178D4—12562no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—3141no—
182C2×C4—6284no—
183C2×C4—6281no—
184C2×C4—6281no—
185C2×C4D4×D15711yescharacteristic
186C2×C4D4×D15711yescharacteristic
187C2×C4C2×C22⋊D15711yescharacteristic
188C8—41no—
189C8—3142no—
190C8—6281no—
191C22—81no—
192C22—81no—
193C22—81no—
194C22—6282no—
195C22—6281no—
196C22—6281no—
197C22—6282no—
198C22—6282no—
199C22—6281no—
200C22#1909773911yescharacteristic
201C4—22no—
202C4—21no—
203C4—41no—
204C4—6281no—
205C4C2×#1457893911yescharacteristic
206C4#1909779211yescharacteristic
207C4#1909779611yescharacteristic
208C4#1909779811yescharacteristic
209C2—161no—
210C2—12561no—
211C2—12562no—
212C2#2375740611yescharacteristic
213C2#2375741711yescharacteristic
214C2#2375743911yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#460×C157C2
socleC22×C157#120
hypercenter#460D157
hypocenterC157#1621
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #23757945C2semidirect
2. #23757649C2semidirect
3. #23757465C2semidirect
4. #23757016C2semidirect
5. Q8⋊#11929434C2semidirect
6. #23757000C2semidirect
7. #460×C157C2semidirect
71. Q8×C157D8semidirect
107. C157#1621semidirect
111. #460D157semidirect
164. Q8#14578939semidirect

Maximal subgroups

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

subgroupindex
#237579452
#237576492
#237574652
#237570162
Q8⋊#119294342
#237570002
#460×C1572
#1621157