Finite Group Databasebeta

← #34101359

Subgroups — #34101359

Order 20096.

306 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 69 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#23757851C211yesmaximal, characteristic
2C2×#19097699C211yesmaximal, characteristic, complemented
3#23757275C211yesmaximal, characteristic, complemented
4#23757274C211yesmaximal, characteristic, complemented
5#23757143C211yesmaximal, characteristic, complemented
6#23757041C211yesmaximal, characteristic, complemented
7C2×#104×C157C211yesmaximal, characteristic, complemented
8C2×#14578954C2211yescharacteristic
9C2×#14578938C2211yescharacteristic
10#19097750—21no—
11#19097747—21no—
12#19097745—21no—
13#19097743—22no—
14#19097742—21no—
15C2×C4⋊Dic157—22no—
16C2×C4⋊Dic157C2211yescharacteristic
17C2×C4⋊Dic157C2211yescharacteristic
18#19097699—22no—
19#19097696—21no—
20#19097695—21no—
21#19097693—21no—
22#19097692—21no—
23C2×#41×C157C2211yescharacteristic
24C2×M16×C157C2211yescharacteristic
25C2×C42×C157C2211yescharacteristic
26#104×C157—22no—
27#14578954—21no—
28#14578954—21no—
29#14578954—21no—
30#14578954—21no—
31C2×Dic314D411yescharacteristic
32C2×D628D411yescharacteristic
33C2×C22⋊D157—22no—
34C2×C22⋊D157—21no—
35C22×Dic157—21no—
36C22×Dic157D412yes—
37C2×C4×D157—21no—
38#14578938—21no—
39#14578938—21no—
40C2×#11929434—21no—
41C4⋊Dic157—21no—
42C4⋊Dic157—21no—
43C4⋊Dic157—21no—
44C4⋊Dic157—21no—
45C4⋊Dic157—44no—
46#14578933—22no—
47C22⋊Dic157—22no—
48#14578931—22no—
49#41×C157—21no—
50#41×C157—21no—
51#41×C157—21no—
52#41×C157—21no—
53C2×Q8×C157D411yescharacteristic
54C2×D4×C157—21no—
55C2×D4×C157D411yescharacteristic
56C22×C4×C157—21no—
57C22×C4×C157—21no—
58C22×C4×C157C2311yescharacteristic
59M16×C157—21no—
60M16×C157—21no—
61C2×C8×C157—21no—
62C42×C157—21no—
63C42×C157D412yescomplemented
64C22×D157—21no—
65Dic314—21no—
66Dic314—21no—
67D628—21no—
68D628—21no—
69C22⋊D157—41no—
70C22⋊D157—41no—
71C22⋊D157—82no—
72C2×Dic157—21no—
73C2×Dic157—22no—
74C2×Dic157—42no—
75C2×Dic157—42no—
76C2×Dic157—41no—
77C4×D157—41no—
78C4×D157—41no—
79#11929434—41no—
80C23×C157—21no—
81C23×C157C2×D411yescharacteristic
82Q8×C157—21no—
83Q8×C157—21no—
84D4×C157—21no—
85D4×C157—21no—
86D4×C157—41no—
87D4×C157—41no—
88C2×C4×C157—22no—
89C2×C4×C157—22no—
90C2×C4×C157—22no—
91C2×C4×C157—21no—
92C2×C4×C157—41no—
93C2×C4×C157—41no—
94C2×C4×C157C2×D411yescharacteristic
95C2×C4×C157C2×D411yescharacteristic
96C2×C4×C157C2×D411yescharacteristic
97C2×C4×C157#4111yescharacteristic
98C2×C4×C157#4111yescharacteristic
99C2×C4×C157#4111yescharacteristic
100C8×C157—41no—
101C22×C157—21no—
102C22×C157—21no—
103C22×C157—41no—
104C22×C157—41no—
105C22×C157—41no—
106C22×C157#12011yescharacteristic
107C22×C157#12111yescharacteristic
108C22×C157#12411yescharacteristic
109C2×D157—41no—
110C2×D157—41no—
111C2×D157—41no—
112C4×C157—24no—
113C4×C157—41no—
114C4×C157#12111yescharacteristic
115C4×C157#12111yescharacteristic
116C4×C157#12311yescharacteristic
117C4×C157#12311yescharacteristic
118Dic157—41no—
119Dic157—42no—
120Dic157—81no—
121C2×C157—21no—
122C2×C157—21no—
123C2×C157—81no—
124C2×C157#39411yescharacteristic
125C2×C157#45311yescharacteristic
126C2×C157#45611yescharacteristic
127D157—81no—
128C157#203911yescharacteristic, complemented, Sylow
129#2039—1571nomaximal, Sylow
130#537—1571no—
131C2×#104—1571no—
132C2×#104D15711yescharacteristic, complemented
133#417—1571no—
134#417—1571no—
135#384—1571no—
136#343—1571no—
137C2×#41—1571no—
138C2×#41C2×D15711yescharacteristic
139C2×M16—1571no—
140C2×M16C2×D15711yescharacteristic
141C22⋊Q8—3141no—
142C22⋊Q8—3141no—
143#121—3141no—
144#121—3141no—
145#121—3142no—
146C2×C4⋊C4—3142no—
147C2×C4⋊C4—1571no—
148C2×C4⋊C4—1571no—
149C2×C42C2×D15711yescharacteristic
150#104—22no—
151#104—3142no—
152#103—3141no—
153#103—3141no—
154#102—3141no—
155#102—3141no—
156#41—21no—
157#41—21no—
158#41—21no—
159#41—21no—
160#41—3141no—
161#41—3141no—
162#41—3141no—
163#41—3141no—
164C2×Q8—1571no—
165C2×Q8D62811yescharacteristic
166C2×D4—21no—
167C2×D4—3141no—
168C2×D4—3142no—
169C2×D4—1571no—
170C2×D4D62811yescharacteristic
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—3141no—
174C22×C4—3141no—
175C22×C4—1572no—
176C22×C4C22×D15711yescharacteristic
177M16—21no—
178M16—21no—
179M16—3141no—
180M16—3141no—
181C2×C8—21no—
182C2×C8—3141no—
183C4⋊C4—3142no—
184C4⋊C4—3141no—
185C4⋊C4—3141no—
186C4⋊C4—3141no—
187C4⋊C4—3141no—
188C4⋊C4—6284no—
189C22⋊C4—3142no—
190C22⋊C4—3142no—
191C42—21no—
192C42C22⋊D15712yescomplemented
193C23—21no—
194C23—3141no—
195C23D4×D15711yescharacteristic
196Q8—21no—
197Q8—21no—
198Q8—3141no—
199Q8—3141no—
200D4—21no—
201D4—21no—
202D4—41no—
203D4—41no—
204D4—3141no—
205D4—3141no—
206D4—6281no—
207D4—6281no—
208D4—12562no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—3142no—
216C2×C4—3141no—
217C2×C4—6281no—
218C2×C4—6281no—
219C2×C4—6282no—
220C2×C4—6282no—
221C2×C4—6281no—
222C2×C4D4×D15711yescharacteristic
223C2×C4C2×C22⋊D15711yescharacteristic
224C2×C4C2×D62811yescharacteristic
225C2×C4#1457895311yescharacteristic
226C2×C4#1457895311yescharacteristic
227C2×C4#1457895411yescharacteristic
228C8—41no—
229C8—6281no—
230C22—21no—
231C22—21no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22—6281no—
236C22—6281no—
237C22—6281no—
238C22#1909774111yescharacteristic
239C22#1909774311yescharacteristic
240C22#1909775711yescharacteristic
241C4—24no—
242C4—41no—
243C4—6282no—
244C4—6281no—
245C4—12561no—
246C4#1909774211yescharacteristic
247C4#1909774511yescharacteristic
248C4#1909775311yescharacteristic
249C4#1909775511yescharacteristic
250C2—21no—
251C2—21no—
252C2—81no—
253C2—12561no—
254C2#2375718911yescharacteristic
255C2#2375744211yescharacteristic
256C2#2375745711yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
FittingC2×#104×C157C2
socleC22×C157#120
prime radical#23757851C2
hypercenterC2×#104D157
hypocenterC157#2039
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#19097699C2semidirect
3. #23757275C2semidirect
4. #23757274C2semidirect
5. #23757143C2semidirect
6. #23757041C2semidirect
7. C2×#104×C157C2semidirect
63. C42×C157D4semidirect
128. C157#2039semidirect
132. C2×#104D157semidirect
192. C42C22⋊D157semidirect

Maximal subgroups

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

subgroupindex
#237578512
C2×#190976992
#237572752
#237572742
#237571432
#237570412
C2×#104×C1572
#2039157