Finite Group Databasebeta

← #34101154

Subgroups — #34101154

Order 20096.

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

normal subgroups only

This group has 478 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, complemented
2#23757842C211yesmaximal, characteristic, complemented
3C2×#19097768C211yesmaximal, characteristic, complemented
4C2×#19097699C211yesmaximal, characteristic, complemented
5#23757277C211yesmaximal, characteristic, complemented
6C2×#19097687C211yesmaximal, characteristic, complemented
7#339×C157C211yesmaximal, characteristic, complemented
8C2×#14578954C2211yescharacteristic
9C22×D628—22no—
10C22×D628C2211yescharacteristic
11C22×D628C2211yescharacteristic
12#19097799—22no—
13#19097799—22no—
14C2×#14578943—21no—
15C2×D1256—21no—
16C2×#14578938C2211yescharacteristic
17#19097768—22no—
18#19097768—21no—
19#19097768—22no—
20#19097759—21no—
21#19097746—22no—
22#19097741—22no—
23#19097699—22no—
24#19097691—22no—
25#19097687—22no—
26C2×M16×C157C2211yescharacteristic
27#117×C157C2211yescharacteristic
28C2×C42×C157C2211yescharacteristic
29C23×D157—21no—
30C23×D157D412yes—
31#14578954—21no—
32#14578954—21no—
33#14578954—21no—
34#14578954—21no—
35C2×Dic314D411yescharacteristic, complemented
36C2×D628—28no—
37C2×D628—24no—
38C2×D628—21no—
39C2×D628—21no—
40C2×D628—21no—
41C2×D628—21no—
42C2×D628—21no—
43C2×D628—21no—
44C2×D628—21no—
45C2×D628—21no—
46C2×D628—21no—
47C2×D628—21no—
48C2×D628—21no—
49C2×D628—48no—
50C2×D628D411yescharacteristic, complemented
51C2×D628D412yescomplemented
52C2×C22⋊D157—21no—
53C2×C4×D157—21no—
54#14578943—24no—
55D1256—24no—
56#14578938—21no—
57#14578938—21no—
58C2×#11929434—21no—
59#14578931—24no—
60C22×C4×C157—21no—
61C22×C4×C157C2311yescharacteristic
62M16×C157—21no—
63M16×C157D412yescomplemented
64C2×C8×C157—21no—
65C4⋊C4×C157D412yescomplemented
66C22⋊C4×C157—21no—
67C42×C157—21no—
68C42×C157—21no—
69C42×C157D412yescomplemented
70C22×D157—21no—
71C22×D157—22no—
72C22×D157—22no—
73C22×D157—22no—
74C22×D157—22no—
75C22×D157—44no—
76C22×D157—44no—
77C22×D157—41no—
78C22×D157—41no—
79Dic314—21no—
80Dic314—21no—
81D628—22no—
82D628—21no—
83D628—22no—
84D628—21no—
85D628—416no—
86D628—41no—
87D628—41no—
88D628—41no—
89D628—41no—
90D628—41no—
91D628—41no—
92D628—84no—
93C22⋊D157—41no—
94C22⋊D157—41no—
95C2×Dic157—21no—
96C4×D157—41no—
97C4×D157—41no—
98#11929434—41no—
99C23×C157C2×D411yescharacteristic
100C2×C4×C157—24no—
101C2×C4×C157—22no—
102C2×C4×C157—22no—
103C2×C4×C157C2×D411yescharacteristic
104C2×C4×C157C2×D411yescharacteristic
105C2×C4×C157C2×D411yescharacteristic
106C2×C4×C157C2×D411yescharacteristic
107C2×C4×C157C2×D411yescharacteristic
108C2×C4×C157#4111yescharacteristic
109C8×C157—22no—
110C22×C157—22no—
111C22×C157#12011yescharacteristic
112C22×C157#12011yescharacteristic
113C22×C157#12111yescharacteristic
114C2×D157—44no—
115C2×D157—44no—
116C2×D157—41no—
117C2×D157—42no—
118C2×D157—42no—
119C2×D157—42no—
120C2×D157—44no—
121C2×D157—82no—
122C2×D157—82no—
123C2×D157—82no—
124C4×C157—24no—
125C4×C157—42no—
126C4×C157#12011yescharacteristic
127C4×C157#12111yescharacteristic
128C4×C157#12111yescharacteristic
129C4×C157#12711yescharacteristic
130Dic157—41no—
131C2×C157—21no—
132C2×C157—21no—
133C2×C157#39211yescharacteristic
134C2×C157#45312yes—
135D157—81no—
136D157—82no—
137D157—82no—
138C157#200211yescharacteristic, complemented, Sylow
139#2002—1571nomaximal, Sylow
140C2×AGL(1,ℤ/8)—1571no—
141#535—1571no—
142C2×#127—1571no—
143C2×#104—1571no—
144#418—1571no—
145C2×#100—1571no—
146#339D15711yescharacteristic, complemented
147C2×#41—1571no—
148C22×D4—3142no—
149C22×D4—1571no—
150C22×D4—1571no—
151AGL(1,ℤ/8)—3142no—
152AGL(1,ℤ/8)—3142no—
153C2×SD16—3141no—
154C2×D8—3141no—
155C2×M16—1571no—
156C2×M16C2×D15711yescharacteristic
157#127—3142no—
158#127—3141no—
159#127—3142no—
160#124—3141no—
161#121—3142no—
162#120—3142no—
163#117C2×D15711yescharacteristic
164C2×C42C2×D15711yescharacteristic
165#104—3142no—
166#102—3142no—
167#100—3142no—
168C24—3141no—
169C24—1572no—
170#41—3141no—
171#41—3141no—
172#41—3141no—
173#41—3141no—
174C2×Q8—1571no—
175C2×D4—3148no—
176C2×D4—3144no—
177C2×D4—3141no—
178C2×D4—3141no—
179C2×D4—3141no—
180C2×D4—3141no—
181C2×D4—3141no—
182C2×D4—3141no—
183C2×D4—3141no—
184C2×D4—3141no—
185C2×D4—3141no—
186C2×D4—3141no—
187C2×D4—3141no—
188C2×D4—3141no—
189C2×D4—6288no—
190C2×D4—1571no—
191C2×D4—1572no—
192C22×C4—21no—
193C22×C4—3141no—
194C22×C4C22×D15711yescharacteristic
195SD16—3144no—
196D8—3144no—
197M16—21no—
198M16—3141no—
199M16—3141no—
200M16D62812yescomplemented
201C2×C8—21no—
202C2×C8—3141no—
203C4⋊C4D62812yescomplemented
204C22⋊C4—21no—
205C22⋊C4—3144no—
206C42—21no—
207C42—21no—
208C42D62812yescomplemented
209C23—3142no—
210C23—3142no—
211C23—3142no—
212C23—3141no—
213C23—3142no—
214C23—6284no—
215C23—6284no—
216C23—6281no—
217C23—6281no—
218C23D4×D15711yescharacteristic
219Q8—3141no—
220Q8—3141no—
221D4—3141no—
222D4—3142no—
223D4—3142no—
224D4—3141no—
225D4—62816no—
226D4—6281no—
227D4—6281no—
228D4—6281no—
229D4—6281no—
230D4—6281no—
231D4—6281no—
232D4—6281no—
233D4—6281no—
234D4—12564no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—3141no—
239C2×C4—6281no—
240C2×C4—6281no—
241C2×C4D4×D15711yescharacteristic
242C2×C4D4×D15711yescharacteristic
243C2×C4C2×D62811yescharacteristic
244C2×C4C2×D62811yescharacteristic
245C2×C4C2×D62811yescharacteristic
246C2×C4#1457895511yescharacteristic
247C8—22no—
248C8—6281no—
249C22—22no—
250C22—6284no—
251C22—6284no—
252C22—6281no—
253C22—6282no—
254C22—6282no—
255C22—6282no—
256C22—6284no—
257C22—12562no—
258C22—12562no—
259C22—12562no—
260C22#1909774111yescharacteristic
261C22#1909774111yescharacteristic
262C22#1909774611yescharacteristic
263C4—24no—
264C4—42no—
265C4—6281no—
266C4#1909774111yescharacteristic
267C4#1909774611yescharacteristic
268C4#1909774611yescharacteristic
269C4#1909776811yescharacteristic
270C2—21no—
271C2—21no—
272C2—12562no—
273C2—12562no—
274C2—12561no—
275C2#2375718311yescharacteristic
276C2#2375744212yes—
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#339×C157C2
socleC22×C157#120
hypercenter#339D157
hypocenterC157#2002
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
1. C2×#19097799C2semidirect
2. #23757842C2semidirect
3. C2×#19097768C2semidirect
4. C2×#19097699C2semidirect
5. #23757277C2semidirect
6. C2×#19097687C2semidirect
7. #339×C157C2semidirect
35. C2×Dic314D4semidirect
50. C2×D628D4semidirect
51. C2×D628D4semidirect
63. M16×C157D4semidirect
65. C4⋊C4×C157D4semidirect
69. C42×C157D4semidirect
138. C157#2002semidirect
146. #339D157semidirect
200. M16D628semidirect
203. C4⋊C4D628semidirect
208. C42D628semidirect

Maximal subgroups

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

subgroupindex
C2×#190977992
#237578422
C2×#190977682
C2×#190976992
#237572772
C2×#190976872
#339×C1572
#2002157