Finite Group Databasebeta

← #34099052

Subgroups — #34099052

Order 20096.

368 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 51 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#23757831C211yesmaximal, characteristic, complemented
2#23757407C211yesmaximal, characteristic, complemented
3#23757181C211yesmaximal, characteristic, complemented
4#23757008C211yesmaximal, characteristic, complemented
5#23757007C211yesmaximal, characteristic, complemented
6#23756996C211yesmaximal, characteristic, complemented
7#447×C157C211yesmaximal, characteristic, complemented
8C22×C22⋊D157—21no—
9C2×D4×D157—21no—
10C2×#14578939—21no—
11#19097756—21no—
12#19097753—21no—
13#19097745C2211yescharacteristic
14#19097743—21no—
15#19097741—21no—
16#19097739—21no—
17C2×C22⋊Dic157—21no—
18C2×#14578931C2211yescharacteristic
19#19097692—21no—
20C22⋊#11929434C2211yescharacteristic, complemented
21#19097678C2211yescharacteristic, complemented
22C22×D4×C157C2211yescharacteristic, complemented
23C2×D8×C157—21no—
24#121×C157C2211yescharacteristic
25#102×C157—21no—
26C22⋊C8×C157C2211yescharacteristic, complemented
27C23×D157—21no—
28C23×D157D411yescharacteristic
29C2×D628—21no—
30C2×D628D411yescharacteristic, complemented
31C2×C22⋊D157—21no—
32C2×C22⋊D157—21no—
33C2×C22⋊D157—21no—
34C2×C22⋊D157—42no—
35C2×C22⋊D157—42no—
36C2×C22⋊D157—42no—
37D4×D157—42no—
38D4×D157—42no—
39C22×Dic157—21no—
40C22×Dic157D411yescharacteristic
41C2×C4×D157—21no—
42#14578939—42no—
43C2×#11929434—21no—
44C4⋊Dic157D411yescharacteristic, complemented
45#14578933—21no—
46C22⋊Dic157—21no—
47C22⋊Dic157—42no—
48#14578931—21no—
49#14578931—21no—
50#14578931—21no—
51#14578931—21no—
52C24×C157—21no—
53C2×D4×C157—21no—
54C2×D4×C157—21no—
55C2×D4×C157—21no—
56C2×D4×C157—42no—
57C2×D4×C157D411yescharacteristic, complemented
58C22×C4×C157C2311yescharacteristic
59D8×C157—42no—
60C2×C8×C157—21no—
61C4⋊C4×C157D411yescharacteristic, complemented
62C22⋊C4×C157—21no—
63C22×D157—21no—
64C22×D157—21no—
65C22×D157—21no—
66C22×D157—42no—
67C22×D157—41no—
68C22×D157—41no—
69C22×D157—81no—
70C22×D157—81no—
71C22×D157D812yescomplemented
72D628—41no—
73D628—42no—
74C22⋊D157—42no—
75C22⋊D157—48no—
76C22⋊D157—41no—
77C22⋊D157—41no—
78C22⋊D157—81no—
79C2×Dic157—22no—
80C2×Dic157—21no—
81C2×Dic157—21no—
82C2×Dic157—41no—
83C2×Dic157—41no—
84C2×Dic157—41no—
85C4×D157—42no—
86#11929434—41no—
87C23×C157—22no—
88C23×C157—21no—
89C23×C157—41no—
90C23×C157—41no—
91C23×C157—41no—
92C23×C157—41no—
93C23×C157—41no—
94C23×C157—41no—
95C23×C157C2×D411yescharacteristic
96D4×C157—22no—
97D4×C157—22no—
98D4×C157—41no—
99D4×C157—41no—
100D4×C157—41no—
101D4×C157—41no—
102D4×C157—41no—
103C2×C4×C157—21no—
104C2×C4×C157—41no—
105C2×C4×C157C2×D411yescharacteristic
106C2×C4×C157C2×D411yescharacteristic
107C8×C157—41no—
108C22×C157—21no—
109C22×C157—21no—
110C22×C157—42no—
111C22×C157—42no—
112C22×C157—41no—
113C22×C157—41no—
114C22×C157—42no—
115C22×C157—41no—
116C22×C157—81no—
117C22×C157—81no—
118C22×C157—81no—
119C22×C157—81no—
120C22×C157#12011yescharacteristic
121C22×C157C2×D811yescharacteristic
122C22×C157AGL(1,ℤ/8)11yescharacteristic
123C2×D157—22no—
124C2×D157—41no—
125C2×D157—41no—
126C2×D157—42no—
127C2×D157—41no—
128C2×D157—41no—
129C2×D157—41no—
130C2×D157—81no—
131C2×D157—84no—
132C4×C157—21no—
133C4×C157—21no—
134C4×C157—41no—
135Dic157—42no—
136Dic157—41no—
137Dic157—41no—
138C2×C157—21no—
139C2×C157—21no—
140C2×C157—81no—
141C2×C157—82no—
142C2×C157#44711yescharacteristic
143C2×C157#45311yescharacteristic
144C2×C157B(4,𝔽2)11yescharacteristic
145D157—42no—
146D157—81no—
147C157#159511yescharacteristic, complemented, Sylow
148#1595—1571nomaximal, Sylow
149#534—1571no—
150#447—1571no—
151#447D15711yescharacteristic, complemented
152#392—1571no—
153#327—1571no—
154#327—1571no—
155#323—1571no—
156C22×D4—3141no—
157C22×D4—3141no—
158C22×D4C2×D15711yescharacteristic, complemented
159C2×D8—21no—
160C2×D8—3141no—
161#123—3141no—
162#123—3141no—
163#121—3141no—
164#121—1571no—
165#121C2×D15711yescharacteristic
166#120—3141no—
167#120—3141no—
168C2×C22⋊C4—3141no—
169C2×C22⋊C4—1571no—
170#102—21no—
171#102—3141no—
172C22⋊C8—1571no—
173C22⋊C8C2×D15711yescharacteristic, complemented
174#95—1571no—
175C24—21no—
176C24—3141no—
177C24—1571no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—42no—
182C2×D4—3141no—
183C2×D4—3141no—
184C2×D4—3141no—
185C2×D4—3141no—
186C2×D4—6282no—
187C2×D4—6282no—
188C2×D4—6282no—
189C2×D4—6282no—
190C2×D4—6282no—
191C2×D4—1571no—
192C2×D4C22⋊D15711yescharacteristic, complemented
193C22×C4—3141no—
194C22×C4—3141no—
195C22×C4—1571no—
196C22×C4C22×D15711yescharacteristic
197D8—42no—
198D8—6282no—
199C2×C8—21no—
200C2×C8—3141no—
201C4⋊C4—3141no—
202C4⋊C4—1571no—
203C4⋊C4C22⋊D15711yescharacteristic, complemented
204C22⋊C4—21no—
205C22⋊C4—3141no—
206C22⋊C4—3141no—
207C22⋊C4—3141no—
208C22⋊C4—3141no—
209C22⋊C4—3141no—
210C22⋊C4—6282no—
211C23—22no—
212C23—21no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23—41no—
217C23—41no—
218C23—41no—
219C23—3141no—
220C23—3141no—
221C23—3141no—
222C23—6281no—
223C23—6281no—
224C23—6282no—
225C23—1572no—
226C23—12561no—
227C23—12561no—
228C23D4×D15711yescharacteristic
229D4—22no—
230D4—22no—
231D4—41no—
232D4—41no—
233D4—41no—
234D4—41no—
235D4—41no—
236D4—6281no—
237D4—6282no—
238D4—6282no—
239D4—6288no—
240D4—6281no—
241D4—6281no—
242D4—12561no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—3142no—
246C2×C4—3141no—
247C2×C4—3141no—
248C2×C4—6282no—
249C2×C4—6281no—
250C2×C4—6281no—
251C2×C4—6281no—
252C2×C4D4×D15711yescharacteristic
253C2×C4C2×C22⋊D15711yescharacteristic
254C8—41no—
255C8—6281no—
256C22—21no—
257C22—21no—
258C22—42no—
259C22—42no—
260C22—41no—
261C22—41no—
262C22—42no—
263C22—41no—
264C22—81no—
265C22—81no—
266C22—81no—
267C22—81no—
268C22—3142no—
269C22—6282no—
270C22—6281no—
271C22—6281no—
272C22—6281no—
273C22—6281no—
274C22—6281no—
275C22—12561no—
276C22—12564no—
277C22#1909773911yescharacteristic
278C22D8×D15711yescharacteristic
279C22#1909779511yescharacteristic
280C4—21no—
281C4—21no—
282C4—41no—
283C4—6282no—
284C4—6281no—
285C4—6281no—
286C2—21no—
287C2—21no—
288C2—82no—
289C2—81no—
290C2—6282no—
291C2—12561no—
292C2#2375740511yescharacteristic
293C2#2375743911yescharacteristic
294C2#2375745911yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#447×C157C2
socleC22×C157#120
hypercenter#447D157
hypocenterC157#1595
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #23757831C2semidirect
2. #23757407C2semidirect
3. #23757181C2semidirect
4. #23757008C2semidirect
5. #23757007C2semidirect
6. #23756996C2semidirect
7. #447×C157C2semidirect
20. C22⋊#11929434C22semidirect
21. #19097678C22semidirect
22. C22×D4×C157C22semidirect
26. C22⋊C8×C157C22semidirect
30. C2×D628D4semidirect
44. C4⋊Dic157D4semidirect
57. C2×D4×C157D4semidirect
61. C4⋊C4×C157D4semidirect
71. C22×D157D8semidirect
147. C157#1595semidirect
151. #447D157semidirect
158. C22×D4C2×D157semidirect
173. C22⋊C8C2×D157semidirect
192. C2×D4C22⋊D157semidirect
203. C4⋊C4C22⋊D157semidirect

Maximal subgroups

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

subgroupindex
#237578312
#237574072
#237571812
#237570082
#237570072
#237569962
#447×C1572
#1595157