Finite Group Databasebeta

← #34098603

Subgroups — #34098603

Order 20096.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#23757820C211yesmaximal, characteristic
2#23757329C211yesmaximal, characteristic, complemented
3#23757324C211yesmaximal, characteristic, complemented
4#23757002C211yesmaximal, characteristic, complemented
5D4⋊#11929434C211yesmaximal, characteristic, complemented
6#23757000C211yesmaximal, characteristic, complemented
7D4⋊C8×C157C211yesmaximal, characteristic, complemented
8C2×#14578954—21no—
9#19097770C411yescharacteristic
10#19097767C411yescharacteristic
11#19097757—21no—
12#19097746C411yescharacteristic
13#19097744—21no—
14#19097742C411yescharacteristic
15C4×D628C2211yescharacteristic
16C4×C22⋊D157—21no—
17C42×D157C2211yescharacteristic
18C4⋊#11929434C2211yescharacteristic
19#19097700—21no—
20#19097683—21no—
21#19097683—21no—
22#19097681—21no—
23C4×#11929434C2211yescharacteristic
24C4×D4×C157C2211yescharacteristic
25C4⋊C8×C157C2211yescharacteristic
26C4×C8×C157C2211yescharacteristic
27#14578954—42no—
28#14578954—42no—
29C2×Dic314—21no—
30C2×D628—21no—
31C2×D628C2×C411yescharacteristic
32C2×C22⋊D157—21no—
33C2×C22⋊D157—21no—
34C2×C22⋊D157—21no—
35C2×C4×D157—21no—
36C2×C4×D157C2×C411yescharacteristic
37C2×C4×D157D411yescharacteristic
38C2×C4×D157D411yescharacteristic
39C2×#11929434—21no—
40C2×#11929434—21no—
41C4⋊Dic157C2×C411yescharacteristic
42#14578933—21no—
43C22⋊Dic157—21no—
44#14578931—21no—
45#14578931—21no—
46C4×Dic157C2×C411yescharacteristic
47C4×Dic157D411yescharacteristic
48C4×Dic157D411yescharacteristic
49C2×D4×C157C2×C411yescharacteristic
50C22×C4×C157—21no—
51C2×C8×C157—21no—
52C2×C8×C157—21no—
53C4⋊C4×C157C2×C411yescharacteristic
54C22⋊C4×C157—21no—
55C42×C157C2311yescharacteristic
56C22×D157—21no—
57C22×D157C22⋊C411yescharacteristic
58Dic314—42no—
59D628—21no—
60D628—21no—
61D628—42no—
62C22⋊D157—42no—
63C22⋊D157—42no—
64C22⋊D157—42no—
65C2×Dic157—21no—
66C2×Dic157C22⋊C411yescharacteristic
67C2×Dic157C22⋊C411yescharacteristic
68C2×Dic157C22⋊C411yescharacteristic
69C4×D157—21no—
70C4×D157—21no—
71C4×D157—21no—
72C4×D157—21no—
73C4×D157—41no—
74C4×D157—41no—
75C4×D157—41no—
76#11929434—41no—
77#11929434—41no—
78C23×C157—21no—
79D4×C157—21no—
80D4×C157—21no—
81C2×C4×C157—21no—
82C2×C4×C157—41no—
83C2×C4×C157—41no—
84C2×C4×C157C22×C411yescharacteristic
85C2×C4×C157C2×D411yescharacteristic
86C2×C4×C157C2×D411yescharacteristic
87C8×C157—41no—
88C8×C157—41no—
89C22×C157—41no—
90C22×C157—41no—
91C22×C157—41no—
92C22×C157C2×C22⋊C411yescharacteristic
93C2×D157—21no—
94C2×D157—21no—
95C2×D157—21no—
96C2×D157—41no—
97C2×D157—41no—
98C2×D157—41no—
99C4×C157—21no—
100C4×C157—41no—
101C4×C157#13111yescharacteristic
102C4×C157#13111yescharacteristic
103C4×C157AGL(1,ℤ/8)11yescharacteristic
104C4×C157AGL(1,ℤ/8)11yescharacteristic
105Dic157—21no—
106Dic157—21no—
107Dic157—21no—
108Dic157—41no—
109C2×C157—81no—
110C2×C157#40811yescharacteristic
111C2×C157#41811yescharacteristic
112C2×C157#42111yescharacteristic
113D157—41no—
114D157—81no—
115C157#149611yescharacteristic, complemented, Sylow
116#1496—1571nomaximal, Sylow
117#532—1571no—
118#432—1571no—
119#431—1571no—
120D4⋊C8—1571no—
121D4⋊C8—1571no—
122D4⋊C8—1571no—
123D4⋊C8D15711yescharacteristic, complemented
124C2×#41—3141no—
125C4⋊Q8—1571no—
126#127—1571no—
127#124—3141no—
128#121—3141no—
129#121—1571no—
130#121—1571no—
131C4×D4—3141no—
132C4×D4—1571no—
133C4×D4C2×D15711yescharacteristic
134C2×C42—1571no—
135C4⋊C8—3141no—
136C4⋊C8—1571no—
137C4⋊C8C2×D15711yescharacteristic
138C22⋊C8—3141no—
139C22⋊C8—3141no—
140#97—3141no—
141C4×C8—1571no—
142C4×C8C2×D15711yescharacteristic
143#41—6282no—
144#41—6282no—
145C2×Q8—3141no—
146C2×D4—3141no—
147C2×D4—3141no—
148C2×D4—3141no—
149C2×D4—3141no—
150C2×D4—1571no—
151C2×D4C4×D15711yescharacteristic
152C22×C4—21no—
153C22×C4—3141no—
154C22×C4—1571no—
155C22×C4—1571no—
156C22×C4—1571no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—3141no—
160C2×C8—3141no—
161C4⋊C4—3141no—
162C4⋊C4—1571no—
163C4⋊C4C4×D15711yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—3141no—
166C22⋊C4—3141no—
167C22⋊C4—3141no—
168C42—1571no—
169C42—1571no—
170C42—1571no—
171C42C22×D15711yescharacteristic
172C23—21no—
173C23—3141no—
174C23—1571no—
175Q8—6282no—
176D4—21no—
177D4—21no—
178D4—3141no—
179D4—3141no—
180D4—6282no—
181D4—6282no—
182D4—6282no—
183D4—6282no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—3141no—
188C2×C4—3141no—
189C2×C4—3141no—
190C2×C4—3141no—
191C2×C4—3141no—
192C2×C4—6281no—
193C2×C4—6281no—
194C2×C4—6281no—
195C2×C4—1571no—
196C2×C4—1571no—
197C2×C4—1571no—
198C2×C4C2×C4×D15711yescharacteristic
199C2×C4D4×D15711yescharacteristic
200C2×C4D4×D15711yescharacteristic
201C8—41no—
202C8—41no—
203C8—6281no—
204C8—6281no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—3141no—
209C22—3141no—
210C22—3141no—
211C22—6281no—
212C22—6281no—
213C22—6281no—
214C22C22⋊C4×D15711yescharacteristic
215C4—21no—
216C4—41no—
217C4—3141no—
218C4—3141no—
219C4—3141no—
220C4—6281no—
221C4#1909777711yescharacteristic
222C4#1909777911yescharacteristic
223C4#1909779511yescharacteristic
224C4#1909779811yescharacteristic
225C2—81no—
226C2—6281no—
227C2—12561no—
228C2#2375723811yescharacteristic
229C2#2375727611yescharacteristic
230C2#2375728811yescharacteristic
subgroupG/H
centerC2×C4D4×D157
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
FittingD4⋊C8×C157C2
socleC22×C157C2×C22⋊C4
prime radical#23757820C2
cosocleC42×C157C23
hypercenterD4⋊C8D157
hypocenterC157#1496
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #23757329C2semidirect
3. #23757324C2semidirect
4. #23757002C2semidirect
5. D4⋊#11929434C2semidirect
6. #23757000C2semidirect
7. D4⋊C8×C157C2semidirect
115. C157#1496semidirect
123. D4⋊C8D157semidirect

Maximal subgroups

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

subgroupindex
#237578202
#237573292
#237573242
#237570022
D4⋊#119294342
#237570002
D4⋊C8×C1572
#1496157