Finite Group Databasebeta

← #34098525

Subgroups — #34098525

Order 20096.

312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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#23757325C211yesmaximal, characteristic, complemented
3#23757324C211yesmaximal, 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—
10C4×D628C2211yescharacteristic
11D4×Dic157C411yescharacteristic
12#19097733C411yescharacteristic
13C4×C22⋊D157—21no—
14#19097731—21no—
15C4⋊C4×D157C411yescharacteristic
16C22⋊C4×D157—21no—
17C42×D157C2211yescharacteristic
18C4⋊#11929434C2211yescharacteristic, complemented
19#19097700—21no—
20#19097683—21no—
21#19097683—21no—
22C4×#11929434C2211yescharacteristic, complemented
23C8×Dic157—21no—
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×D157C814yescomplemented
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
41C2×#11929434—21no—
42C2×#11929434—21no—
43C4⋊Dic157C2×C411yescharacteristic
44#14578933—21no—
45C22⋊Dic157—21no—
46#14578931—21no—
47#14578931—21no—
48C4×Dic157C2×C411yescharacteristic
49C4×Dic157D411yescharacteristic
50C4×Dic157D411yescharacteristic
51C2×D4×C157C2×C411yescharacteristic
52C22×C4×C157—21no—
53C2×C8×C157—21no—
54C2×C8×C157—21no—
55C4⋊C4×C157C2×C411yescharacteristic
56C22⋊C4×C157—21no—
57C42×C157C2311yescharacteristic
58C22×D157—21no—
59C22×D157—24no—
60C22×D157—42no—
61C22×D157—42no—
62C22×D157C22⋊C411yescharacteristic
63D628—21no—
64D628C2×C812yes—
65C22⋊D157—24no—
66C2×Dic157—21no—
67C2×Dic157—42no—
68C2×Dic157C22⋊C411yescharacteristic
69C2×Dic157C22⋊C411yescharacteristic
70C2×Dic157C22⋊C411yescharacteristic
71C4×D157—21no—
72C4×D157—21no—
73C4×D157—41no—
74C4×D157—42no—
75C4×D157—42no—
76C4×D157—41no—
77C4×D157—41no—
78C4×D157C2×C812yes—
79C4×D157M1612yes—
80#11929434—41no—
81#11929434—41no—
82C23×C157—21no—
83D4×C157—21no—
84D4×C157C2×C812yes—
85C2×C4×C157—21no—
86C2×C4×C157—41no—
87C2×C4×C157—41no—
88C2×C4×C157C22×C411yescharacteristic
89C2×C4×C157C2×D411yescharacteristic
90C2×C4×C157C2×D411yescharacteristic
91C8×C157—41no—
92C8×C157—41no—
93C22×C157—22no—
94C22×C157—41no—
95C22×C157—41no—
96C22×C157C2×C22⋊C411yescharacteristic
97C2×D157—21no—
98C2×D157—21no—
99C2×D157—22no—
100C2×D157—48no—
101C2×D157—41no—
102C2×D157—41no—
103C2×D157C22⋊C812yes—
104C4×C157—21no—
105C4×C157—41no—
106C4×C157C22×C811yescharacteristic
107C4×C157C2×M1611yescharacteristic
108C4×C157AGL(1,ℤ/8)11yescharacteristic
109C4×C157AGL(1,ℤ/8)11yescharacteristic
110Dic157—21no—
111Dic157—21no—
112Dic157—41no—
113Dic157C22⋊C812yes—
114C2×C157—42no—
115C2×C157C2×C22⋊C811yescharacteristic
116C2×C157#41811yescharacteristic
117C2×C157#42111yescharacteristic
118D157—22no—
119D157—42no—
120C157#147811yescharacteristic, complemented, Sylow
121#1478—1571nomaximal, Sylow
122C2×C4×D4—1571no—
123#431—1571no—
124#431—1571no—
125D4⋊C8—1571no—
126D4⋊C8—1571no—
127D4⋊C8—1571no—
128D4⋊C8D15711yescharacteristic, complemented
129C22×D4—1571no—
130C23×C4—3141no—
131C4×D4—3141no—
132C4×D4—3141no—
133C4×D4—1571no—
134C4×D4—1571no—
135C4×D4—1571no—
136C4×D4C2×D15711yescharacteristic
137C2×C4⋊C4—1571no—
138C2×C22⋊C4—3141no—
139C2×C42—1571no—
140C4⋊C8—3141no—
141C4⋊C8—1571no—
142C4⋊C8C2×D15711yescharacteristic, complemented
143C22⋊C8—3141no—
144C22⋊C8—3141no—
145C4×C8—3141no—
146C4×C8—1571no—
147C4×C8C2×D15711yescharacteristic, complemented
148C24—3141no—
149C2×D4—3142no—
150C2×D4—3141no—
151C2×D4—1574no—
152C2×D4—1571no—
153C2×D4C4×D15711yescharacteristic
154C22×C4—21no—
155C22×C4—3141no—
156C22×C4—3141no—
157C22×C4—3141no—
158C22×C4—3141no—
159C22×C4—6282no—
160C22×C4—6282no—
161C22×C4—1571no—
162C22×C4—1571no—
163C22×C4—1571no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—3141no—
167C2×C8—3141no—
168C4⋊C4—3141no—
169C4⋊C4—1571no—
170C4⋊C4C4×D15711yescharacteristic
171C22⋊C4—21no—
172C22⋊C4—3141no—
173C22⋊C4—3141no—
174C22⋊C4—3141no—
175C42—1571no—
176C42—1571no—
177C42—1571no—
178C42C22×D15711yescharacteristic
179C23—21no—
180C23—3144no—
181C23—3141no—
182C23—6282no—
183C23—6282no—
184C23—1571no—
185D4—21no—
186D4—3144no—
187D4—3141no—
188D4—1572no—
189D4C8×D15712yes—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—3141no—
194C2×C4—3141no—
195C2×C4—3141no—
196C2×C4—6281no—
197C2×C4—6282no—
198C2×C4—6282no—
199C2×C4—6282no—
200C2×C4—6281no—
201C2×C4—6281no—
202C2×C4—1571no—
203C2×C4—1571no—
204C2×C4—1571no—
205C2×C4—1572no—
206C2×C4—1572no—
207C2×C4C2×C4×D15711yescharacteristic
208C2×C4D4×D15711yescharacteristic
209C2×C4D4×D15711yescharacteristic
210C8—41no—
211C8—41no—
212C8—6281no—
213C8—6281no—
214C22—22no—
215C22—41no—
216C22—41no—
217C22—3141no—
218C22—3141no—
219C22—3142no—
220C22—6288no—
221C22—6281no—
222C22—6281no—
223C22—1572no—
224C22C22⋊C4×D15711yescharacteristic
225C4—21no—
226C4—41no—
227C4—3141no—
228C4—3141no—
229C4—6281no—
230C4—1572no—
231C4C2×C8×D15711yescharacteristic
232C4M16×D15711yescharacteristic
233C4#1909779511yescharacteristic
234C4#1909779811yescharacteristic
235C2—42no—
236C2—3142no—
237C2—6282no—
238C2C22⋊C8×D15711yescharacteristic
239C2#2375727611yescharacteristic
240C2#2375728811yescharacteristic
subgroupG/H
centerC2×C4D4×D157
commutatorC4×C157C22×C8
FrattiniC42C22×D157
FittingD4⋊C8×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC2×D4×D157C4
cosocleC42×C157C23
hypercenterD4⋊C8D157
hypocenterC157#1478
LCSG ▷ 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. #23757325C2semidirect
3. #23757324C2semidirect
4. #23757002C2semidirect
5. D4⋊#11929434C2semidirect
6. #23757000C2semidirect
7. D4⋊C8×C157C2semidirect
18. C4⋊#11929434C22semidirect
22. C4×#11929434C22semidirect
25. C4⋊C8×C157C22semidirect
26. C4×C8×C157C22semidirect
31. D4×D157C8semidirect
120. C157#1478semidirect
128. D4⋊C8D157semidirect
142. C4⋊C8C2×D157semidirect
147. C4×C8C2×D157semidirect

Maximal subgroups

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

subgroupindex
C4×D4×D1572
#237573252
#237573242
#237570022
D4⋊#119294342
#237570002
D4⋊C8×C1572
#1478157