Finite Group Databasebeta

← #34101186

Subgroups — #34101186

Order 20096.

380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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×#19097796C211yesmaximal, characteristic, complemented
2#23757837C211yesmaximal, characteristic, complemented
3#23757290C211yesmaximal, characteristic, complemented
4#23757279C211yesmaximal, characteristic, complemented
5#23757247C211yesmaximal, characteristic, complemented
6#23757044C211yesmaximal, characteristic, complemented
7#575×C157C211yesmaximal, characteristic, complemented
8C22×D628C2211yescharacteristic
9#19097796—22no—
10#19097796—22no—
11C2×#14578941—21no—
12C2×#14578939—21no—
13C2×#14578938C2211yescharacteristic
14#19097767—21no—
15#19097760—21no—
16#19097745—22no—
17#19097739—22no—
18#19097730C2211yescharacteristic
19#19097730C2211yescharacteristic
20#19097698—22no—
21#19097693—22no—
22#19097686—22no—
23C2×#41×C157C2211yescharacteristic
24C2×#41×C157C2211yescharacteristic
25#137×C157—21no—
26#137×C157—21no—
27AGL(1,ℤ/8)×C157—21no—
28AGL(1,ℤ/8)×C157—21no—
29#135×C157—22no—
30C2×M16×C157C2211yescharacteristic
31C23×D157—21no—
32C2×D628—21no—
33C2×D628—21no—
34C2×D628—21no—
35C2×D628—21no—
36C2×D628—21no—
37C2×D628D412yes—
38C2×C22⋊D157—24no—
39#14578941—24no—
40#14578939—24no—
41#14578938—21no—
42#14578938D412yescomplemented
43C2×#11929434—21no—
44C4⋊Dic157—21no—
45C4⋊Dic157—21no—
46C22⋊Dic157—21no—
47C22⋊Dic157D412yes—
48#14578931—24no—
49C4×Dic157—21no—
50C4×Dic157—21no—
51#41×C157—21no—
52#41×C157—21no—
53#41×C157—21no—
54#41×C157—21no—
55#41×C157—21no—
56#41×C157—21no—
57#41×C157—21no—
58#41×C157—21no—
59C2×Q8×C157D411yescharacteristic
60C2×Q8×C157D411yescharacteristic, complemented
61C2×D4×C157—21no—
62C2×D4×C157—21no—
63C2×D4×C157D411yescharacteristic
64C2×D4×C157D411yescharacteristic, complemented
65C22×C4×C157—21no—
66C22×C4×C157—21no—
67C22×C4×C157C2311yescharacteristic
68Q16×C157—22no—
69SD16×C157—22no—
70SD16×C157—22no—
71D8×C157—22no—
72M16×C157—21no—
73M16×C157—21no—
74C2×C8×C157D412yescomplemented
75C22×D157—22no—
76C22×D157—41no—
77C22×D157—41no—
78C22×D157—82no—
79D628—22no—
80D628—22no—
81D628—41no—
82D628—41no—
83C22⋊D157—84no—
84C2×Dic157—22no—
85C2×Dic157—41no—
86#11929434—22no—
87C23×C157—21no—
88C23×C157—21no—
89C23×C157C2×D411yescharacteristic
90Q8×C157—21no—
91Q8×C157—21no—
92Q8×C157—21no—
93Q8×C157—21no—
94D4×C157—21no—
95D4×C157—21no—
96D4×C157—21no—
97D4×C157—21no—
98D4×C157—41no—
99D4×C157—41no—
100D4×C157—41no—
101D4×C157—41no—
102C2×C4×C157—21no—
103C2×C4×C157—21no—
104C2×C4×C157—41no—
105C2×C4×C157—41no—
106C2×C4×C157—41no—
107C2×C4×C157—41no—
108C2×C4×C157C2×D411yescharacteristic
109C2×C4×C157C2×D411yescharacteristic
110C2×C4×C157C2×D411yescharacteristic
111C2×C4×C157C2×D411yescharacteristic
112C2×C4×C157C2×D411yescharacteristic
113C2×C4×C157#4111yescharacteristic
114C8×C157—22no—
115C22×C157—41no—
116C22×C157—42no—
117C22×C157—41no—
118C22×C157—41no—
119C22×C157—81no—
120C22×C157#12011yescharacteristic
121C22×C157#12111yescharacteristic
122C22×C157#12711yescharacteristic
123C2×D157—44no—
124C2×D157—42no—
125C2×D157—82no—
126C2×D157—82no—
127C4×C157—41no—
128C4×C157—41no—
129C4×C157#12011yescharacteristic
130C4×C157#12011yescharacteristic
131C4×C157#12111yescharacteristic
132C4×C157#12111yescharacteristic
133Dic157—42no—
134Dic157—81no—
135C2×C157—21no—
136C2×C157—21no—
137C2×C157—21no—
138C2×C157—81no—
139C2×C157—81no—
140C2×C157#39211yescharacteristic
141D157—82no—
142C157#200811yescharacteristic, complemented, Sylow
143#2008—1571nomaximal, Sylow
144#575D15711yescharacteristic, complemented
145C2×AGL(1,ℤ/8)—1571no—
146#535—1571no—
147#421—1571no—
148#418—1571no—
149#410—1571no—
150#344—1571no—
151C2×#41C2×D15711yescharacteristic
152C2×#41C2×D15711yescharacteristic
153C22×D4—1571no—
154#137—21no—
155#137—21no—
156AGL(1,ℤ/8)—21no—
157AGL(1,ℤ/8)—21no—
158AGL(1,ℤ/8)—3142no—
159AGL(1,ℤ/8)—3142no—
160#135—22no—
161C2×SD16—3141no—
162C2×D8—3141no—
163C2×M16—1571no—
164C2×M16C2×D15711yescharacteristic
165#127—3141no—
166#124—3141no—
167#121—3142no—
168#120—3142no—
169#117—1571no—
170#117—1571no—
171#104—3142no—
172#102—3142no—
173#99—3142no—
174C24—3141no—
175#41—21no—
176#41—21no—
177#41—21no—
178#41—21no—
179#41—21no—
180#41—21no—
181#41—21no—
182#41—21no—
183C2×Q8C22⋊D15711yescharacteristic
184C2×Q8C22⋊D15711yescharacteristic, complemented
185C2×D4—21no—
186C2×D4—21no—
187C2×D4—3144no—
188C2×D4—3141no—
189C2×D4—3141no—
190C2×D4—3141no—
191C2×D4—3141no—
192C2×D4—3141no—
193C2×D4—1572no—
194C2×D4C22⋊D15711yescharacteristic
195C2×D4C22⋊D15711yescharacteristic, complemented
196C22×C4—21no—
197C22×C4—21no—
198C22×C4C22×D15711yescharacteristic
199Q16—22no—
200SD16—22no—
201SD16—22no—
202SD16—3144no—
203D8—22no—
204D8—3144no—
205M16—21no—
206M16—21no—
207M16—3141no—
208M16—1572no—
209C2×C8—3141no—
210C2×C8C22⋊D15712yescomplemented
211C4⋊C4—3141no—
212C4⋊C4—3141no—
213C22⋊C4—3144no—
214C22⋊C4—3141no—
215C22⋊C4—1572no—
216C42—3141no—
217C42—3141no—
218C23—21no—
219C23—21no—
220C23—3142no—
221C23—6281no—
222C23—6281no—
223C23—12562no—
224C23D4×D15711yescharacteristic
225Q8—21no—
226Q8—21no—
227Q8—21no—
228Q8—21no—
229D4—21no—
230D4—21no—
231D4—21no—
232D4—21no—
233D4—41no—
234D4—41no—
235D4—41no—
236D4—41no—
237D4—3142no—
238D4—3142no—
239D4—6281no—
240D4—6281no—
241D4—12564no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—3142no—
249C2×C4—6281no—
250C2×C4D4×D15711yescharacteristic
251C2×C4D4×D15711yescharacteristic
252C2×C4C2×C22⋊D15711yescharacteristic
253C2×C4C2×C22⋊D15711yescharacteristic
254C2×C4C2×C22⋊D15711yescharacteristic
255C2×C4#1457895311yescharacteristic
256C8—22no—
257C8—3142no—
258C22—41no—
259C22—42no—
260C22—41no—
261C22—41no—
262C22—81no—
263C22—6284no—
264C22—6282no—
265C22—12562no—
266C22—12562no—
267C22#1909773911yescharacteristic
268C22#1909774311yescharacteristic
269C22#1909776711yescharacteristic
270C4—41no—
271C4—41no—
272C4—6282no—
273C4—12561no—
274C4#1909773911yescharacteristic
275C4#1909774011yescharacteristic
276C4#1909774211yescharacteristic
277C4#1909774311yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—81no—
282C2—81no—
283C2—12562no—
284C2#2375718111yescharacteristic
subgroupG/H
centerC2#23757181
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#575×C157C2
socleC2×C157#392
hypercenter#575D157
hypocenterC157#2008
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. C2×#19097796C2semidirect
2. #23757837C2semidirect
3. #23757290C2semidirect
4. #23757279C2semidirect
5. #23757247C2semidirect
6. #23757044C2semidirect
7. #575×C157C2semidirect
42. #14578938D4semidirect
60. C2×Q8×C157D4semidirect
64. C2×D4×C157D4semidirect
74. C2×C8×C157D4semidirect
142. C157#2008semidirect
144. #575D157semidirect
184. C2×Q8C22⋊D157semidirect
195. C2×D4C22⋊D157semidirect
210. C2×C8C22⋊D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977962
#237578372
#237572902
#237572792
#237572472
#237570442
#575×C1572
#2008157