Finite Group Databasebeta

← #34098559

Subgroups — #34098559

Order 20096.

312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C4×D4×D157C211yesmaximal, characteristic
2#23757324C211yesmaximal, characteristic, complemented
3#23757295C211yesmaximal, characteristic, complemented
4#23757002C211yesmaximal, characteristic, complemented
5D4⋊#11929434C211yesmaximal, characteristic, complemented
6#23757000C211yesmaximal, characteristic, complemented
7D4⋊C8×C157C211yesmaximal, characteristic, complemented
8C2×D4×D157C411yescharacteristic
9C22×C4×D157—21no—
10C2×#14578937—21no—
11C4×D628C2211yescharacteristic
12D4×Dic157C411yescharacteristic
13#19097733C411yescharacteristic
14C4×C22⋊D157—21no—
15#19097731—21no—
16C4⋊C4×D157C411yescharacteristic
17C22⋊C4×D157—21no—
18C42×D157C2211yescharacteristic
19C4⋊#11929434C2211yescharacteristic, complemented
20#19097700—21no—
21#19097700—21no—
22#19097683—21no—
23C4×#11929434C2211yescharacteristic, complemented
24C4×D4×C157C2211yescharacteristic
25C4⋊C8×C157C2211yescharacteristic, complemented
26C4×C8×C157C2211yescharacteristic, complemented
27C23×D157—21no—
28C2×D628C2×C411yescharacteristic
29C2×C22⋊D157—21no—
30D4×D157—22no—
31D4×D157—22no—
32C22×Dic157—21no—
33C2×C4×D157—21no—
34C2×C4×D157—21no—
35C2×C4×D157—21no—
36C2×C4×D157—42no—
37C2×C4×D157—42no—
38C2×C4×D157C2×C411yescharacteristic
39C2×C4×D157D411yescharacteristic
40C2×C4×D157D411yescharacteristic
41#14578937—42no—
42C2×#11929434—21no—
43C2×#11929434—21no—
44C4⋊Dic157C2×C411yescharacteristic
45#14578933—21no—
46C22⋊Dic157—21no—
47#14578931—21no—
48#14578931—21no—
49C4×Dic157C2×C411yescharacteristic
50C4×Dic157D411yescharacteristic
51C4×Dic157D411yescharacteristic
52C2×D4×C157C2×C411yescharacteristic
53C22×C4×C157—21no—
54C2×C8×C157—21no—
55C2×C8×C157—21no—
56C4⋊C4×C157C2×C411yescharacteristic
57C22⋊C4×C157—21no—
58C42×C157C2311yescharacteristic
59C22×D157—24no—
60C22×D157—21no—
61C22×D157—42no—
62C22×D157—42no—
63C22×D157C22⋊C411yescharacteristic
64D628—21no—
65D628M1612yescomplemented
66C22⋊D157—24no—
67C2×Dic157—21no—
68C2×Dic157—42no—
69C2×Dic157C22⋊C411yescharacteristic
70C2×Dic157C22⋊C411yescharacteristic
71C2×Dic157C22⋊C411yescharacteristic
72C4×D157—21no—
73C4×D157—21no—
74C4×D157—41no—
75C4×D157—42no—
76C4×D157—41no—
77C4×D157—41no—
78C4×D157—42no—
79C4×D157D812yes—
80C4×D157SD1612yes—
81#11929434—41no—
82#11929434—41no—
83C23×C157—21no—
84D4×C157—21no—
85D4×C157M1612yescomplemented
86C2×C4×C157—21no—
87C2×C4×C157—41no—
88C2×C4×C157—41no—
89C2×C4×C157C22×C411yescharacteristic
90C2×C4×C157C2×D411yescharacteristic
91C2×C4×C157C2×D411yescharacteristic
92C8×C157—41no—
93C8×C157—41no—
94C22×C157—22no—
95C22×C157—41no—
96C22×C157—41no—
97C22×C157C2×C22⋊C411yescharacteristic
98C2×D157—21no—
99C2×D157—21no—
100C2×D157—22no—
101C2×D157—48no—
102C2×D157—41no—
103C2×D157—41no—
104C2×D157#10212yes—
105C4×C157—21no—
106C4×C157—41no—
107C4×C157C2×M1611yescharacteristic
108C4×C157C2×M1611yescharacteristic
109C4×C157C2×D811yescharacteristic
110C4×C157C2×SD1611yescharacteristic
111Dic157—21no—
112Dic157—21no—
113Dic157—41no—
114Dic157#10212yes—
115C2×C157—42no—
116C2×C157#40711yescharacteristic
117C2×C157C2×#10211yescharacteristic
118C2×C157#42111yescharacteristic
119D157—22no—
120D157—42no—
121C157#148611yescharacteristic, complemented, Sylow
122#1486—1571nomaximal, Sylow
123C2×C4×D4—1571no—
124#431—1571no—
125#423—1571no—
126D4⋊C8—1571no—
127D4⋊C8—1571no—
128D4⋊C8—1571no—
129D4⋊C8D15711yescharacteristic, complemented
130C22×D4—1571no—
131C23×C4—3141no—
132C2×M16—3141no—
133C4×D4—3141no—
134C4×D4—3141no—
135C4×D4—1571no—
136C4×D4—1571no—
137C4×D4—1571no—
138C4×D4C2×D15711yescharacteristic
139C2×C4⋊C4—1571no—
140C2×C22⋊C4—3141no—
141C2×C42—1571no—
142C4⋊C8—3141no—
143C4⋊C8—3141no—
144C4⋊C8—1571no—
145C4⋊C8C2×D15711yescharacteristic, complemented
146C22⋊C8—3141no—
147C4×C8—1571no—
148C4×C8C2×D15711yescharacteristic, complemented
149C24—3141no—
150C2×D4—3142no—
151C2×D4—3142no—
152C2×D4—3141no—
153C2×D4—1571no—
154C2×D4C4×D15711yescharacteristic
155C22×C4—21no—
156C22×C4—3141no—
157C22×C4—3141no—
158C22×C4—3141no—
159C22×C4—3141no—
160C22×C4—6282no—
161C22×C4—6282no—
162C22×C4—1571no—
163C22×C4—1571no—
164C22×C4—1571no—
165M16—6282no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—3141no—
169C2×C8—3141no—
170C4⋊C4—3141no—
171C4⋊C4—1571no—
172C4⋊C4C4×D15711yescharacteristic
173C22⋊C4—21no—
174C22⋊C4—3141no—
175C22⋊C4—3141no—
176C22⋊C4—3141no—
177C42—1571no—
178C42—1571no—
179C42—1571no—
180C42C22×D15711yescharacteristic
181C23—21no—
182C23—3144no—
183C23—3141no—
184C23—6282no—
185C23—6282no—
186C23—1571no—
187D4—21no—
188D4—3144no—
189D4—3141no—
190D4—1572no—
191D4#1457893712yescomplemented
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—3141no—
196C2×C4—3141no—
197C2×C4—3141no—
198C2×C4—6281no—
199C2×C4—6282no—
200C2×C4—6282no—
201C2×C4—6282no—
202C2×C4—6281no—
203C2×C4—6281no—
204C2×C4—1571no—
205C2×C4—1571no—
206C2×C4—1571no—
207C2×C4—1572no—
208C2×C4—1572no—
209C2×C4C2×C4×D15711yescharacteristic
210C2×C4D4×D15711yescharacteristic
211C2×C4D4×D15711yescharacteristic
212C8—41no—
213C8—41no—
214C8—6281no—
215C8—6281no—
216C22—22no—
217C22—41no—
218C22—41no—
219C22—3141no—
220C22—3141no—
221C22—3142no—
222C22—6288no—
223C22—6281no—
224C22—6281no—
225C22—1572no—
226C22C22⋊C4×D15711yescharacteristic
227C4—21no—
228C4—41no—
229C4—3141no—
230C4—3141no—
231C4—6281no—
232C4—1572no—
233C4M16×D15711yescharacteristic
234C4C2×#1457893711yescharacteristic
235C4D8×D15711yescharacteristic
236C4SD16×D15711yescharacteristic
237C2—42no—
238C2—3142no—
239C2—6282no—
240C2#2375723511yescharacteristic
241C2#102×D15711yescharacteristic
242C2#2375728811yescharacteristic
subgroupG/H
centerC2×C4D4×D157
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
FittingD4⋊C8×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC2×D4×D157C4
cosocleC42×C157C23
hypercenterD4⋊C8D157
hypocenterC157#1486
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. #23757295C2semidirect
4. #23757002C2semidirect
5. D4⋊#11929434C2semidirect
6. #23757000C2semidirect
7. D4⋊C8×C157C2semidirect
19. C4⋊#11929434C22semidirect
23. C4×#11929434C22semidirect
25. C4⋊C8×C157C22semidirect
26. C4×C8×C157C22semidirect
65. D628M16semidirect
85. D4×C157M16semidirect
121. C157#1486semidirect
129. D4⋊C8D157semidirect
145. C4⋊C8C2×D157semidirect
148. C4×C8C2×D157semidirect
191. D4#14578937semidirect

Maximal subgroups

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

subgroupindex
C4×D4×D1572
#237573242
#237572952
#237570022
D4⋊#119294342
#237570002
D4⋊C8×C1572
#1486157