Finite Group Databasebeta

← #34101161

Subgroups — #34101161

Order 20096.

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

normal subgroups only

This group has 382 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
1C2×#19097799C211yesmaximal, characteristic
2#23757849C211yesmaximal, characteristic, complemented
3C2×#19097759C211yesmaximal, characteristic, complemented
4C2×#19097699C211yesmaximal, characteristic, complemented
5#23757277C211yesmaximal, characteristic, complemented
6C2×#19097689C211yesmaximal, characteristic, complemented
7#339×C157C211yesmaximal, characteristic, complemented
8C2×#14578954C2211yescharacteristic
9C22×Dic314C2211yescharacteristic
10C22×D628C2211yescharacteristic
11#19097799—22no—
12#19097799—22no—
13C2×#14578943—21no—
14C2×D1256—21no—
15C2×#14578938C2211yescharacteristic
16#19097771—21no—
17#19097759—22no—
18#19097759—21no—
19#19097759—22no—
20#19097755—22no—
21#19097751—22no—
22C2×#14578931—22no—
23#19097699—22no—
24#19097691—22no—
25#19097689—22no—
26C2×M16×C157C2211yescharacteristic
27#117×C157C2211yescharacteristic
28C2×C42×C157C2211yescharacteristic
29C23×D157—21no—
30#14578954—21no—
31#14578954—21no—
32#14578954—21no—
33#14578954—21no—
34C2×Dic314—21no—
35C2×Dic314—21no—
36C2×Dic314—21no—
37C2×Dic314—21no—
38C2×Dic314—21no—
39C2×Dic314—21no—
40C2×Dic314D411yescharacteristic
41C2×D628—21no—
42C2×D628—21no—
43C2×D628—21no—
44C2×D628—21no—
45C2×D628—21no—
46C2×D628D411yescharacteristic
47C2×D628D412yes—
48C2×C22⋊D157—21no—
49C22×Dic157D412yes—
50C2×C4×D157—21no—
51#14578943—24no—
52D1256—24no—
53#14578938—21no—
54#14578938—21no—
55C2×#11929434—21no—
56C4⋊Dic157—24no—
57#14578931—28no—
58#14578931—24no—
59C22×C4×C157—21no—
60C22×C4×C157C2311yescharacteristic
61M16×C157—21no—
62M16×C157D412yes—
63C2×C8×C157—21no—
64C4⋊C4×C157D412yes—
65C22⋊C4×C157—21no—
66C42×C157—21no—
67C42×C157—21no—
68C42×C157D412yes—
69C22×D157—21no—
70C22×D157—22no—
71C22×D157—44no—
72C22×D157—41no—
73C22×D157—41no—
74Dic314—21no—
75Dic314—21no—
76Dic314—41no—
77Dic314—41no—
78Dic314—41no—
79Dic314—41no—
80D628—22no—
81D628—21no—
82D628—22no—
83D628—21no—
84D628—41no—
85D628—41no—
86C22⋊D157—41no—
87C22⋊D157—41no—
88C2×Dic157—21no—
89C2×Dic157—22no—
90C2×Dic157—22no—
91C2×Dic157—22no—
92C4×D157—41no—
93C4×D157—41no—
94#11929434—41no—
95C23×C157C2×D411yescharacteristic
96C2×C4×C157—22no—
97C2×C4×C157—22no—
98C2×C4×C157—42no—
99C2×C4×C157C2×D411yescharacteristic
100C2×C4×C157C2×D411yescharacteristic
101C2×C4×C157C2×D411yescharacteristic
102C2×C4×C157C2×D411yescharacteristic
103C2×C4×C157C2×D411yescharacteristic
104C2×C4×C157#4111yescharacteristic
105C8×C157—22no—
106C22×C157—22no—
107C22×C157#12011yescharacteristic
108C22×C157#12011yescharacteristic
109C22×C157#12111yescharacteristic
110C2×D157—44no—
111C2×D157—41no—
112C2×D157—42no—
113C2×D157—42no—
114C2×D157—82no—
115C2×D157—82no—
116C4×C157—42no—
117C4×C157—42no—
118C4×C157#12011yescharacteristic
119C4×C157#12111yescharacteristic
120C4×C157#12111yescharacteristic
121C4×C157#12711yescharacteristic
122Dic157—41no—
123Dic157—42no—
124C2×C157—21no—
125C2×C157—21no—
126C2×C157#39211yescharacteristic
127C2×C157#45412yes—
128D157—81no—
129D157—82no—
130C157#200311yescharacteristic, complemented, Sylow
131#2003—1571nomaximal, Sylow
132C2×AGL(1,ℤ/8)—1571no—
133#536—1571no—
134C2×#124—1571no—
135C2×#104—1571no—
136#418—1571no—
137C2×#101—1571no—
138#339D15711yescharacteristic, complemented
139C2×#41—1571no—
140C22×Q8—1571no—
141C22×D4—1571no—
142AGL(1,ℤ/8)—3142no—
143AGL(1,ℤ/8)—3142no—
144C2×SD16—3141no—
145C2×D8—3141no—
146C2×M16—1571no—
147C2×M16C2×D15711yescharacteristic
148C4⋊Q8—3141no—
149#124—3142no—
150#124—3141no—
151#124—3142no—
152#123—3142no—
153C22⋊Q8—3142no—
154#117C2×D15711yescharacteristic
155C2×C22⋊C4—3142no—
156C2×C42C2×D15711yescharacteristic
157#104—3142no—
158#102—3142no—
159#101—3142no—
160C24—3141no—
161#41—3141no—
162#41—3141no—
163#41—3141no—
164#41—3141no—
165C2×Q8—3141no—
166C2×Q8—3141no—
167C2×Q8—3141no—
168C2×Q8—3141no—
169C2×Q8—3141no—
170C2×Q8—3141no—
171C2×Q8—1571no—
172C2×D4—3141no—
173C2×D4—3141no—
174C2×D4—3141no—
175C2×D4—3141no—
176C2×D4—3141no—
177C2×D4—3141no—
178C2×D4—1571no—
179C2×D4—1572no—
180C22×C4—21no—
181C22×C4—3141no—
182C22×C4—1572no—
183C22×C4C22×D15711yescharacteristic
184SD16—3144no—
185D8—3144no—
186M16—21no—
187M16—3141no—
188M16—3141no—
189M16D62812yes—
190C2×C8—21no—
191C2×C8—3141no—
192C4⋊C4—3144no—
193C4⋊C4D62812yes—
194C22⋊C4—21no—
195C22⋊C4—3148no—
196C22⋊C4—3144no—
197C42—21no—
198C42—21no—
199C42D62812yes—
200C23—3142no—
201C23—3141no—
202C23—6284no—
203C23—6281no—
204C23—6281no—
205C23D4×D15711yescharacteristic
206Q8—3141no—
207Q8—3141no—
208Q8—6281no—
209Q8—6281no—
210Q8—6281no—
211Q8—6281no—
212D4—3141no—
213D4—3142no—
214D4—3142no—
215D4—3141no—
216D4—6281no—
217D4—6281no—
218D4—6281no—
219D4—6281no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—42no—
223C2×C4—3142no—
224C2×C4—3142no—
225C2×C4—3141no—
226C2×C4—3142no—
227C2×C4—6281no—
228C2×C4—6281no—
229C2×C4D4×D15711yescharacteristic
230C2×C4D4×D15711yescharacteristic
231C2×C4C2×D62811yescharacteristic
232C2×C4C2×D62811yescharacteristic
233C2×C4C2×D62811yescharacteristic
234C2×C4#1457895511yescharacteristic
235C8—22no—
236C8—6281no—
237C22—22no—
238C22—6284no—
239C22—6281no—
240C22—6282no—
241C22—6282no—
242C22—12562no—
243C22—12562no—
244C22#1909774111yescharacteristic
245C22#1909774111yescharacteristic
246C22#1909774611yescharacteristic
247C4—42no—
248C4—42no—
249C4—6282no—
250C4—6281no—
251C4#1909774111yescharacteristic
252C4#1909774611yescharacteristic
253C4#1909774611yescharacteristic
254C4#1909776811yescharacteristic
255C2—21no—
256C2—21no—
257C2—12562no—
258C2—12561no—
259C2#2375718311yescharacteristic
260C2#2375744712yes—
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#339×C157C2
socleC22×C157#120
prime radicalC2×#19097799C2
hypercenter#339D157
hypocenterC157#2003
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #23757849C2semidirect
3. C2×#19097759C2semidirect
4. C2×#19097699C2semidirect
5. #23757277C2semidirect
6. C2×#19097689C2semidirect
7. #339×C157C2semidirect
130. C157#2003semidirect
138. #339D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977992
#237578492
C2×#190977592
C2×#190976992
#237572772
C2×#190976892
#339×C1572
#2003157