Finite Group Databasebeta

← #34098585

Subgroups — #34098585

Order 20096.

276 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 75 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#23757295C211yesmaximal, 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×#14578937—21no—
10C2×C8×D157—21no—
11#19097770C411yescharacteristic
12#19097767C411yescharacteristic
13#19097757—21no—
14#19097746C411yescharacteristic
15#19097744—21no—
16#19097742C411yescharacteristic
17C4×D628C2211yescharacteristic
18C4×C22⋊D157—21no—
19C42×D157C2211yescharacteristic
20C4⋊#11929434C2211yescharacteristic
21#19097700—21no—
22C4×#11929434C2211yescharacteristic
23C8×Dic157—21no—
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
39#14578937—42no—
40C2×#11929434—21no—
41C2×#11929434—21no—
42C8×D157—24no—
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×D157C22⋊C411yescharacteristic
60Dic314—42no—
61D628—21no—
62D628—21no—
63D628—42no—
64C22⋊D157—42no—
65C22⋊D157—42no—
66C22⋊D157—42no—
67C2×Dic157—21no—
68C2×Dic157C22⋊C411yescharacteristic
69C2×Dic157C22⋊C411yescharacteristic
70C2×Dic157C22⋊C411yescharacteristic
71C4×D157—21no—
72C4×D157—21no—
73C4×D157—22no—
74C4×D157—41no—
75C4×D157—41no—
76C4×D157D812yes—
77C4×D157SD1612yes—
78#11929434—22no—
79#11929434—41no—
80C23×C157—21no—
81D4×C157—21no—
82D4×C157—21no—
83C2×C4×C157—21no—
84C2×C4×C157—41no—
85C2×C4×C157—41no—
86C2×C4×C157C22×C411yescharacteristic
87C2×C4×C157C2×D411yescharacteristic
88C2×C4×C157C2×D411yescharacteristic
89C8×C157—22no—
90C8×C157—41no—
91C22×C157—41no—
92C22×C157—41no—
93C22×C157—41no—
94C22×C157C2×C22⋊C411yescharacteristic
95C2×D157—21no—
96C2×D157—21no—
97C2×D157—41no—
98C2×D157—41no—
99C2×D157—41no—
100C2×D157#10212yes—
101C4×C157—21no—
102C4×C157—41no—
103C4×C157#13111yescharacteristic
104C4×C157#13111yescharacteristic
105C4×C157C2×D811yescharacteristic
106C4×C157C2×SD1611yescharacteristic
107Dic157—21no—
108Dic157—41no—
109Dic157#10212yes—
110Dic157#10412yes—
111C2×C157—81no—
112C2×C157#40811yescharacteristic
113C2×C157C2×#10211yescharacteristic
114C2×C157C2×#10411yescharacteristic
115D157—22no—
116D157—81no—
117C157#149211yescharacteristic, complemented, Sylow
118#1492—1571nomaximal, Sylow
119#532—1571no—
120#423—1571no—
121C2×C4×C8—1571no—
122D4⋊C8—1571no—
123D4⋊C8—1571no—
124D4⋊C8—1571no—
125D4⋊C8D15711yescharacteristic, complemented
126C2×#41—3141no—
127C2×M16—3141no—
128C22×C8—3141no—
129C4⋊Q8—1571no—
130#127—1571no—
131#124—3141no—
132#121—3141no—
133#121—1571no—
134#121—1571no—
135C4×D4—3141no—
136C4×D4—1571no—
137C4×D4C2×D15711yescharacteristic
138C2×C42—1571no—
139C4⋊C8—3141no—
140C4⋊C8—1571no—
141C4⋊C8C2×D15711yescharacteristic
142C4×C8—3141no—
143C4×C8—1571no—
144C4×C8C2×D15711yescharacteristic
145#41—6282no—
146#41—6282no—
147C2×Q8—3141no—
148C2×D4—3141no—
149C2×D4—3141no—
150C2×D4—3141no—
151C2×D4—3141no—
152C2×D4—1571no—
153C2×D4C4×D15711yescharacteristic
154C22×C4—21no—
155C22×C4—3141no—
156C22×C4—1571no—
157C22×C4—1571no—
158C22×C4—1571no—
159M16—6282no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—3144no—
163C2×C8—3141no—
164C2×C8—3141no—
165C4⋊C4—3141no—
166C4⋊C4—1571no—
167C4⋊C4C4×D15711yescharacteristic
168C22⋊C4—21no—
169C22⋊C4—3141no—
170C22⋊C4—3141no—
171C22⋊C4—3141no—
172C42—1571no—
173C42—1571no—
174C42—1571no—
175C42C22×D15711yescharacteristic
176C23—21no—
177C23—3141no—
178C23—1571no—
179Q8—6282no—
180D4—21no—
181D4—21no—
182D4—3141no—
183D4—3141no—
184D4—6282no—
185D4—6282no—
186D4—6282no—
187D4—6282no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—3142no—
192C2×C4—3141no—
193C2×C4—3141no—
194C2×C4—3141no—
195C2×C4—6281no—
196C2×C4—6281no—
197C2×C4—1571no—
198C2×C4—1571no—
199C2×C4—1571no—
200C2×C4—1572no—
201C2×C4—1572no—
202C2×C4C2×C4×D15711yescharacteristic
203C2×C4D4×D15711yescharacteristic
204C2×C4D4×D15711yescharacteristic
205C8—22no—
206C8—41no—
207C8—3142no—
208C8—6281no—
209C22—41no—
210C22—41no—
211C22—41no—
212C22—3141no—
213C22—3141no—
214C22—6281no—
215C22—6281no—
216C22—6281no—
217C22—1572no—
218C22C22⋊C4×D15711yescharacteristic
219C4—21no—
220C4—41no—
221C4—3141no—
222C4—6281no—
223C4—1572no—
224C4—1572no—
225C4#1909777711yescharacteristic
226C4#1909777911yescharacteristic
227C4D8×D15711yescharacteristic
228C4SD16×D15711yescharacteristic
229C2—81no—
230C2—3142no—
231C2—12561no—
232C2#2375723811yescharacteristic
233C2#102×D15711yescharacteristic
234C2#104×D15711yescharacteristic
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#1492
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. #23757295C2semidirect
3. C4×C8×D157C2semidirect
4. #23757002C2semidirect
5. D4⋊#11929434C2semidirect
6. #23757000C2semidirect
7. D4⋊C8×C157C2semidirect
117. C157#1492semidirect
125. D4⋊C8D157semidirect

Maximal subgroups

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

subgroupindex
#237578202
#237572952
C4×C8×D1572
#237570022
D4⋊#119294342
#237570002
D4⋊C8×C1572
#1492157