Finite Group Databasebeta

← #34099202

Subgroups — #34099202

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#23757943C211yesmaximal, characteristic, complemented
2#23757649C211yesmaximal, characteristic, complemented
3#23757474C211yesmaximal, characteristic, complemented
4#23757469C211yesmaximal, characteristic, complemented
5#23757003C211yesmaximal, characteristic, complemented
6#23757000C211yesmaximal, characteristic, complemented
7#331×C157C211yesmaximal, characteristic, complemented
8C2×#14578953—21no—
9C2×#14578943—21no—
10C2×D1256—21no—
11C2×#14578939—22no—
12#19097768C2211yescharacteristic
13#19097767—21no—
14#19097743—22no—
15#19097742—21no—
16C4×Dic314C2211yescharacteristic
17C4×D628C2211yescharacteristic
18D4×Dic157—21no—
19#19097693—21no—
20#19097693—21no—
21C4×#11929434C2211yescharacteristic
22#127×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4⋊C8×C157C2211yescharacteristic
25#14578953—42no—
26#14578953—42no—
27C2×Dic314D411yescharacteristic
28C2×D628—21no—
29C2×D628—21no—
30C2×D628—21no—
31C2×D628D411yescharacteristic
32C2×C22⋊D157—22no—
33C2×C22⋊D157—22no—
34C22×Dic157—22no—
35C2×C4×D157—21no—
36#14578943—42no—
37D1256—42no—
38#14578939—44no—
39C2×#11929434—21no—
40C4⋊Dic157D411yescharacteristic
41C4⋊Dic157D411yescharacteristic
42#14578933—21no—
43C22⋊Dic157—22no—
44#14578931—21no—
45C4×Dic157—21no—
46C2×D4×C157—21no—
47C2×D4×C157—21no—
48C2×D4×C157D412yes—
49C2×C8×C157—21no—
50C2×C8×C157—21no—
51C42×C157C2311yescharacteristic
52C22×D157—21no—
53C22×D157—41no—
54Dic314—21no—
55Dic314D812yescomplemented
56D628—21no—
57D628—21no—
58D628—42no—
59D628—41no—
60D628—41no—
61D628—41no—
62D628—41no—
63C22⋊D157—44no—
64C22⋊D157—82no—
65C2×Dic157—21no—
66C2×Dic157—21no—
67C2×Dic157—21no—
68C2×Dic157—44no—
69C4×D157—41no—
70C4×D157—41no—
71#11929434—22no—
72C23×C157—22no—
73D4×C157—42no—
74D4×C157—41no—
75D4×C157—41no—
76D4×C157—41no—
77D4×C157—41no—
78C2×C4×C157C2×D411yescharacteristic
79C2×C4×C157C2×D411yescharacteristic
80C2×C4×C157C2×D411yescharacteristic
81C8×C157—41no—
82C8×C157—41no—
83C22×C157—42no—
84C22×C157—42no—
85C22×C157—42no—
86C22×C157#12011yescharacteristic
87C2×D157—41no—
88C2×D157—41no—
89C2×D157—41no—
90C2×D157—81no—
91C2×D157—81no—
92C2×D157—81no—
93C4×C157—21no—
94C4×C157C2×D811yescharacteristic
95C4×C157#13511yescharacteristic
96C4×C157AGL(1,ℤ/8)11yescharacteristic
97C4×C157AGL(1,ℤ/8)11yescharacteristic
98Dic157—22no—
99Dic157—41no—
100Dic157—41no—
101C2×C157—82no—
102C2×C157#44711yescharacteristic
103C2×C157#44911yescharacteristic
104C2×C157#45311yescharacteristic
105D157—81no—
106D157—161no—
107C157#162111yescharacteristic, complemented, Sylow
108#1621—1571nomaximal, Sylow
109#550—1571no—
110#493—1571no—
111#460—1571no—
112#459—1571no—
113#331D15711yescharacteristic, complemented
114Q8⋊C8—1571no—
115D4⋊C8—1571no—
116C2×#41—3141no—
117C2×SD16—3141no—
118C2×D8—3141no—
119C2×D8—3142no—
120#127—3141no—
121#127—1571no—
122#127C2×D15711yescharacteristic
123#121—3142no—
124#121—3141no—
125C4×Q8—1571no—
126C4×D4—3141no—
127C4×D4—1571no—
128C4⋊C8C2×D15711yescharacteristic
129C4⋊C8C2×D15711yescharacteristic
130#102—3141no—
131#102—3141no—
132C4×C8—1571no—
133#41—6282no—
134#41—6282no—
135C2×Q8—1571no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—3142no—
139C2×D4—3142no—
140C2×D4—3141no—
141C2×D4—3141no—
142C2×D4—3141no—
143C2×D4—1571no—
144C2×D4D62812yes—
145C22×C4—3142no—
146C22×C4—3141no—
147SD16—6282no—
148D8—6282no—
149D8—6284no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—3141no—
153C4⋊C4—3141no—
154C4⋊C4—1571no—
155C4⋊C4—1571no—
156C22⋊C4—3142no—
157C22⋊C4—3141no—
158C42—3141no—
159C42C22×D15711yescharacteristic
160C23—22no—
161C23—3141no—
162C23—6281no—
163Q8—3141no—
164Q8—1572no—
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—3141no—
180C2×C4—3141no—
181C2×C4—3141no—
182C2×C4—6284no—
183C2×C4—6281no—
184C2×C4—6281no—
185C2×C4D4×D15711yescharacteristic
186C2×C4D4×D15711yescharacteristic
187C2×C4C2×D62811yescharacteristic
188C8—41no—
189C8—41no—
190C8—3142no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—6281no—
195C22—6281no—
196C22—6281no—
197C22—12561no—
198C22—12561no—
199C22—12561no—
200C22#1909774111yescharacteristic
201C4—21no—
202C4—3142no—
203C4—6281no—
204C4—6281no—
205C4D8×D15711yescharacteristic
206C4#1909779211yescharacteristic
207C4#1909779511yescharacteristic
208C4#1909779811yescharacteristic
209C2—82no—
210C2—25121no—
211C2—12561no—
212C2#2375740811yescharacteristic
213C2#2375741911yescharacteristic
214C2#2375744311yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#331×C157C2
socleC22×C157#120
hypercenter#331D157
hypocenterC157#1621
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #23757943C2semidirect
2. #23757649C2semidirect
3. #23757474C2semidirect
4. #23757469C2semidirect
5. #23757003C2semidirect
6. #23757000C2semidirect
7. #331×C157C2semidirect
55. Dic314D8semidirect
107. C157#1621semidirect
113. #331D157semidirect

Maximal subgroups

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

subgroupindex
#237579432
#237576492
#237574742
#237574692
#237570032
#237570002
#331×C1572
#1621157