Finite Group Databasebeta

← #34099198

Subgroups — #34099198

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#23757470C211yesmaximal, characteristic, complemented
3#23757465C211yesmaximal, characteristic, complemented
4#23757017C211yesmaximal, characteristic, complemented
5#23757005C211yesmaximal, characteristic, complemented
6#23757002C211yesmaximal, characteristic, complemented
7#493×C157C211yesmaximal, characteristic, complemented
8C2×#14578953—21no—
9C2×#14578942—21no—
10C2×#14578939—21no—
11#19097767—21no—
12#19097743—22no—
13#19097742—21no—
14C4×Dic314C2211yescharacteristic
15C4×D628C2211yescharacteristic
16D4×Dic157—21no—
17C4⋊#11929434C2211yescharacteristic
18C4⋊#11929434C2211yescharacteristic
19#19097692—21no—
20#19097692—21no—
21C2×D8×C157—22no—
22#127×C157C2211yescharacteristic
23#127×C157C2211yescharacteristic
24C4×C8×C157C2211yescharacteristic
25#14578953—42no—
26#14578953—42no—
27C2×Dic314D411yescharacteristic
28C2×D628D411yescharacteristic
29C2×C22⋊D157—22no—
30C2×C22⋊D157—22no—
31C22×Dic157—22no—
32C2×C4×D157—21no—
33#14578942—42no—
34#14578939—42no—
35C2×#11929434—21no—
36C2×#11929434—21no—
37C4⋊Dic157D411yescharacteristic
38C4⋊Dic157D411yescharacteristic
39#14578933—21no—
40C22⋊Dic157—22no—
41#14578931—21no—
42C4×Dic157—21no—
43C2×D4×C157—21no—
44C2×D4×C157—21no—
45C2×D4×C157—21no—
46C2×D4×C157—21no—
47C2×D4×C157—21no—
48C2×D4×C157D412yes—
49D8×C157—44no—
50C2×C8×C157—21no—
51C42×C157C2311yescharacteristic
52C22×D157—21no—
53Dic314—21no—
54Dic314D812yescomplemented
55D628—21no—
56D628—21no—
57C22⋊D157—44no—
58C22⋊D157—82no—
59C2×Dic157—21no—
60C2×Dic157—21no—
61C2×Dic157—21no—
62C2×Dic157—44no—
63C4×D157—41no—
64C4×D157—41no—
65#11929434—41no—
66#11929434—41no—
67C23×C157—22no—
68C23×C157—41no—
69D4×C157—42no—
70D4×C157—42no—
71D4×C157—41no—
72D4×C157—41no—
73D4×C157—41no—
74D4×C157—41no—
75D4×C157—41no—
76D4×C157—41no—
77D4×C157—41no—
78D4×C157—41no—
79C2×C4×C157C2×D411yescharacteristic
80C2×C4×C157C2×D411yescharacteristic
81C2×C4×C157C2×D411yescharacteristic
82C8×C157—22no—
83C22×C157—42no—
84C22×C157—42no—
85C22×C157—42no—
86C22×C157—81no—
87C22×C157—81no—
88C22×C157—81no—
89C22×C157#12011yescharacteristic
90C2×D157—41no—
91C2×D157—41no—
92C2×D157—41no—
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—161no—
103C2×C157#44711yescharacteristic
104C2×C157#44911yescharacteristic
105C2×C157#45311yescharacteristic
106D157—81no—
107C157#162111yescharacteristic, complemented, Sylow
108#1621—1571nomaximal, Sylow
109#550—1571no—
110#493D15711yescharacteristic, complemented
111#460—1571no—
112#459—1571no—
113#331—1571no—
114Q8⋊C8—1571no—
115D4⋊C8—1571no—
116C2×#41—3141no—
117C2×SD16—3141no—
118C2×D8—22no—
119C2×D8—3141no—
120#127—3141no—
121#127C2×D15711yescharacteristic
122#127C2×D15711yescharacteristic
123#121—3142no—
124#121—3141no—
125C4×Q8—1571no—
126C4×D4—3141no—
127C4×D4—1571no—
128C4⋊C8—1571no—
129C4⋊C8—1571no—
130#102—3141no—
131#102—3141no—
132C4×C8C2×D15711yescharacteristic
133#41—6282no—
134#41—6282no—
135C2×Q8—1571no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—3142no—
142C2×D4—3142no—
143C2×D4—1571no—
144C2×D4C22⋊D15712yes—
145C22×C4—3142no—
146C22×C4—3141no—
147SD16—6282no—
148D8—44no—
149D8—6282no—
150C2×C8—21no—
151C2×C8—3141no—
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—41no—
162C23—3141no—
163Q8—3141no—
164Q8—1572no—
165D4—42no—
166D4—42no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—41no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—3141no—
176D4—3141no—
177D4—6284no—
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×C22⋊D15711yescharacteristic
188C8—22no—
189C8—6281no—
190C8—6281no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—81no—
195C22—81no—
196C22—81no—
197C22—6281no—
198C22—6281no—
199C22—6281no—
200C22#1909773911yescharacteristic
201C4—21no—
202C4—3142no—
203C4—6281no—
204C4—6281no—
205C4D8×D15711yescharacteristic
206C4#1909779011yescharacteristic
207C4#1909779511yescharacteristic
208C4#1909779511yescharacteristic
209C2—82no—
210C2—161no—
211C2—12561no—
212C2#2375740511yescharacteristic
213C2#2375741511yescharacteristic
214C2#2375744011yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#493×C157C2
socleC22×C157#120
hypercenter#493D157
hypocenterC157#1621
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #23757943C2semidirect
2. #23757470C2semidirect
3. #23757465C2semidirect
4. #23757017C2semidirect
5. #23757005C2semidirect
6. #23757002C2semidirect
7. #493×C157C2semidirect
54. Dic314D8semidirect
107. C157#1621semidirect
110. #493D157semidirect

Maximal subgroups

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

subgroupindex
#237579432
#237574702
#237574652
#237570172
#237570052
#237570022
#493×C1572
#1621157