Finite Group Databasebeta

← #34098533

Subgroups — #34098533

Order 20096.

260 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 73 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#23757324C211yesmaximal, characteristic, complemented
3C4⋊C8×D157C211yesmaximal, characteristic, complemented
4#23757002C211yesmaximal, characteristic, complemented
5D4⋊#11929434C211yesmaximal, characteristic, complemented
6#23757000C211yesmaximal, characteristic, complemented
7D4⋊C8×C157C211yesmaximal, characteristic, complemented
8C2×#14578954—21no—
9C2×C8×D157—21no—
10#19097770C411yescharacteristic
11#19097767C411yescharacteristic
12#19097757—21no—
13#19097746C411yescharacteristic
14#19097744—21no—
15#19097742C411yescharacteristic
16C4×D628C2211yescharacteristic
17C4×C22⋊D157—21no—
18C42×D157C2211yescharacteristic
19C4⋊#11929434C2211yescharacteristic
20#19097700—21no—
21#19097700—21no—
22#19097683—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—
41C8×D157—42no—
42C4⋊Dic157C2×C411yescharacteristic
43#14578933—21no—
44C22⋊Dic157—21no—
45#14578931—21no—
46#14578931—21no—
47C4×Dic157C2×C411yescharacteristic
48C4×Dic157D411yescharacteristic
49C4×Dic157D411yescharacteristic
50C2×D4×C157C2×C411yescharacteristic
51C22×C4×C157—21no—
52C2×C8×C157—21no—
53C2×C8×C157—21no—
54C4⋊C4×C157C2×C411yescharacteristic
55C22⋊C4×C157—21no—
56C42×C157C2311yescharacteristic
57C22×D157—21no—
58C22×D157C22⋊C411yescharacteristic
59Dic314—42no—
60D628—21no—
61D628—21no—
62D628—42no—
63C22⋊D157—42no—
64C22⋊D157—42no—
65C22⋊D157—42no—
66C2×Dic157—21no—
67C2×Dic157C22⋊C411yescharacteristic
68C2×Dic157C22⋊C411yescharacteristic
69C2×Dic157C22⋊C411yescharacteristic
70C4×D157—21no—
71C4×D157—21no—
72C4×D157—41no—
73C4×D157—41no—
74C4×D157—41no—
75C4×D157D812yes—
76C4×D157SD1612yes—
77#11929434—41no—
78#11929434—41no—
79C23×C157—21no—
80D4×C157—21no—
81D4×C157—21no—
82C2×C4×C157—21no—
83C2×C4×C157—41no—
84C2×C4×C157—41no—
85C2×C4×C157C22×C411yescharacteristic
86C2×C4×C157C2×D411yescharacteristic
87C2×C4×C157C2×D411yescharacteristic
88C8×C157—41no—
89C8×C157—41no—
90C22×C157—41no—
91C22×C157—41no—
92C22×C157—41no—
93C22×C157C2×C22⋊C411yescharacteristic
94C2×D157—21no—
95C2×D157—21no—
96C2×D157—41no—
97C2×D157—41no—
98C2×D157—41no—
99C2×D157#10212yes—
100C4×C157—21no—
101C4×C157—41no—
102C4×C157#13111yescharacteristic
103C4×C157#13111yescharacteristic
104C4×C157C2×D811yescharacteristic
105C4×C157C2×SD1611yescharacteristic
106Dic157—21no—
107Dic157—21no—
108Dic157—41no—
109Dic157#10212yes—
110C2×C157—81no—
111C2×C157#40811yescharacteristic
112C2×C157C2×#10211yescharacteristic
113C2×C157#42111yescharacteristic
114D157—22no—
115D157—81no—
116C157#148011yescharacteristic, complemented, Sylow
117#1480—1571nomaximal, Sylow
118#532—1571no—
119#431—1571no—
120C2×C4⋊C8—1571no—
121D4⋊C8—1571no—
122D4⋊C8—1571no—
123D4⋊C8—1571no—
124D4⋊C8D15711yescharacteristic, complemented
125C2×#41—3141no—
126C22×C8—3141no—
127C4⋊Q8—1571no—
128#127—1571no—
129#124—3141no—
130#121—3141no—
131#121—1571no—
132#121—1571no—
133C4×D4—3141no—
134C4×D4—1571no—
135C4×D4C2×D15711yescharacteristic
136C2×C42—1571no—
137C4⋊C8—3141no—
138C4⋊C8—3141no—
139C4⋊C8—1571no—
140C4⋊C8C2×D15711yescharacteristic
141C22⋊C8—3141no—
142C4×C8—1571no—
143C4×C8C2×D15711yescharacteristic
144#41—6282no—
145#41—6282no—
146C2×Q8—3141no—
147C2×D4—3141no—
148C2×D4—3141no—
149C2×D4—3141no—
150C2×D4—3141no—
151C2×D4—1571no—
152C2×D4C4×D15711yescharacteristic
153C22×C4—21no—
154C22×C4—3141no—
155C22×C4—1571no—
156C22×C4—1571no—
157C22×C4—1571no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—3141no—
161C2×C8—3141no—
162C2×C8—6282no—
163C4⋊C4—3141no—
164C4⋊C4—1571no—
165C4⋊C4C4×D15711yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—3141no—
168C22⋊C4—3141no—
169C22⋊C4—3141no—
170C42—1571no—
171C42—1571no—
172C42—1571no—
173C42C22×D15711yescharacteristic
174C23—21no—
175C23—3141no—
176C23—1571no—
177Q8—6282no—
178D4—21no—
179D4—21no—
180D4—3141no—
181D4—3141no—
182D4—6282no—
183D4—6282no—
184D4—6282no—
185D4—6282no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
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×C4—1572no—
199C2×C4—1572no—
200C2×C4C2×C4×D15711yescharacteristic
201C2×C4D4×D15711yescharacteristic
202C2×C4D4×D15711yescharacteristic
203C8—41no—
204C8—41no—
205C8—6281no—
206C8—6281no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—3141no—
211C22—3141no—
212C22—6281no—
213C22—6281no—
214C22—6281no—
215C22—1572no—
216C22C22⋊C4×D15711yescharacteristic
217C4—21no—
218C4—41no—
219C4—3141no—
220C4—3141no—
221C4—6281no—
222C4—1572no—
223C4#1909777711yescharacteristic
224C4#1909777911yescharacteristic
225C4D8×D15711yescharacteristic
226C4SD16×D15711yescharacteristic
227C2—81no—
228C2—3142no—
229C2—12561no—
230C2#2375723811yescharacteristic
231C2#102×D15711yescharacteristic
232C2#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#1480
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. #23757324C2semidirect
3. C4⋊C8×D157C2semidirect
4. #23757002C2semidirect
5. D4⋊#11929434C2semidirect
6. #23757000C2semidirect
7. D4⋊C8×C157C2semidirect
116. C157#1480semidirect
124. D4⋊C8D157semidirect

Maximal subgroups

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

subgroupindex
#237578202
#237573242
C4⋊C8×D1572
#237570022
D4⋊#119294342
#237570002
D4⋊C8×C1572
#1480157