Finite Group Databasebeta

← #34099055

Subgroups — #34099055

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#23757409C211yesmaximal, characteristic, complemented
3#23757406C211yesmaximal, characteristic, complemented
4#23757183C211yesmaximal, characteristic, complemented
5#23757006C211yesmaximal, characteristic, complemented
6#23756996C211yesmaximal, characteristic, complemented
7#327×C157C211yesmaximal, characteristic, complemented
8C22×D628—21no—
9C22×D628C2211yescharacteristic, complemented
10C2×D4×D157—21no—
11C2×D1256—21no—
12C2×#14578939—21no—
13#19097756—21no—
14#19097753—21no—
15#19097745C2211yescharacteristic
16#19097743—21no—
17#19097741—21no—
18#19097739—21no—
19C2×#14578931—21no—
20C2×#14578931C2211yescharacteristic
21#19097693—21no—
22#19097691—21no—
23C22⋊#11929434C2211yescharacteristic, complemented
24#121×C157C2211yescharacteristic
25C22⋊C8×C157C2211yescharacteristic, complemented
26#95×C157C2211yescharacteristic, complemented
27C23×D157—21no—
28C23×D157—21no—
29C23×D157D411yescharacteristic
30C2×D628—21no—
31C2×D628—21no—
32C2×D628—21no—
33C2×D628—42no—
34C2×D628—42no—
35C2×D628—42no—
36C2×D628—42no—
37C2×D628D411yescharacteristic, complemented
38C2×C22⋊D157—21no—
39C2×C22⋊D157—21no—
40C2×C22⋊D157—21no—
41D4×D157—42no—
42D4×D157—42no—
43C22×Dic157D411yescharacteristic
44C2×C4×D157—21no—
45D1256—42no—
46#14578939—42no—
47C2×#11929434—21no—
48C4⋊Dic157D411yescharacteristic, complemented
49#14578933—21no—
50C22⋊Dic157—21no—
51#14578931—21no—
52#14578931—21no—
53#14578931—21no—
54#14578931—21no—
55#14578931—42no—
56C2×D4×C157—21no—
57C2×D4×C157D411yescharacteristic, complemented
58C22×C4×C157—21no—
59C22×C4×C157C2311yescharacteristic
60C2×C8×C157—21no—
61C4⋊C4×C157D411yescharacteristic, complemented
62C22⋊C4×C157—21no—
63C22×D157—21no—
64C22×D157—21no—
65C22×D157—22no—
66C22×D157—21no—
67C22×D157—42no—
68C22×D157—41no—
69C22×D157—41no—
70C22×D157—41no—
71C22×D157—41no—
72C22×D157—41no—
73C22×D157—41no—
74C22×D157—41no—
75C22×D157—41no—
76C22×D157—81no—
77C22×D157—81no—
78C22×D157D812yescomplemented
79D628—22no—
80D628—22no—
81D628—41no—
82D628—41no—
83D628—41no—
84D628—42no—
85D628—48no—
86C22⋊D157—42no—
87C22⋊D157—41no—
88C22⋊D157—41no—
89C22⋊D157—81no—
90C2×Dic157—21no—
91C2×Dic157—21no—
92C2×Dic157—41no—
93C4×D157—42no—
94#11929434—41no—
95C23×C157—21no—
96C23×C157C2×D411yescharacteristic
97D4×C157—41no—
98D4×C157—41no—
99D4×C157—41no—
100C2×C4×C157—22no—
101C2×C4×C157—21no—
102C2×C4×C157—41no—
103C2×C4×C157—41no—
104C2×C4×C157—41no—
105C2×C4×C157C2×D411yescharacteristic
106C2×C4×C157C2×D411yescharacteristic
107C8×C157—41no—
108C22×C157—21no—
109C22×C157—21no—
110C22×C157—41no—
111C22×C157—41no—
112C22×C157—41no—
113C22×C157#12011yescharacteristic
114C22×C157C2×D811yescharacteristic
115C22×C157AGL(1,ℤ/8)11yescharacteristic
116C2×D157—22no—
117C2×D157—41no—
118C2×D157—41no—
119C2×D157—42no—
120C2×D157—42no—
121C2×D157—42no—
122C2×D157—41no—
123C2×D157—41no—
124C2×D157—42no—
125C2×D157—41no—
126C2×D157—81no—
127C2×D157—84no—
128C2×D157—81no—
129C2×D157—81no—
130C2×D157—81no—
131C2×D157—81no—
132C4×C157—21no—
133C4×C157—21no—
134C4×C157—42no—
135C4×C157—41no—
136Dic157—41no—
137Dic157—41no—
138C2×C157—21no—
139C2×C157—21no—
140C2×C157—81no—
141C2×C157#44711yescharacteristic
142C2×C157#45311yescharacteristic
143C2×C157B(4,𝔽2)11yescharacteristic
144D157—42no—
145D157—82no—
146D157—81no—
147C157#159511yescharacteristic, complemented, Sylow
148#1595—1571nomaximal, Sylow
149#534—1571no—
150#447—1571no—
151#447—1571no—
152#392—1571no—
153#327—1571no—
154#327D15711yescharacteristic, complemented
155#323—1571no—
156C22×D4—3141no—
157C22×D4—3141no—
158C22×D4—1571no—
159C2×D8—3141no—
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—3141no—
171#102—3141no—
172C22⋊C8—1571no—
173C22⋊C8C2×D15711yescharacteristic, complemented
174#95C2×D15711yescharacteristic, complemented
175C24—3141no—
176C24—3141no—
177C24—1571no—
178C2×D4—21no—
179C2×D4—3141no—
180C2×D4—3141no—
181C2×D4—3141no—
182C2×D4—3141no—
183C2×D4—3141no—
184C2×D4—3141no—
185C2×D4—6282no—
186C2×D4—6282no—
187C2×D4—6282no—
188C2×D4—6282no—
189C2×D4—6282no—
190C2×D4—6282no—
191C2×D4—1571no—
192C2×D4D62811yescharacteristic, complemented
193C22×C4—21no—
194C22×C4—3141no—
195C22×C4—1571no—
196C22×C4C22×D15711yescharacteristic
197D8—6282no—
198D8—6282no—
199C2×C8—21no—
200C2×C8—3141no—
201C4⋊C4—3141no—
202C4⋊C4—1571no—
203C4⋊C4D62811yescharacteristic, complemented
204C22⋊C4—21no—
205C22⋊C4—3141no—
206C22⋊C4—3141no—
207C22⋊C4—3141no—
208C22⋊C4—3141no—
209C22⋊C4—3141no—
210C22⋊C4—6282no—
211C23—21no—
212C23—3142no—
213C23—3141no—
214C23—3141no—
215C23—3141no—
216C23—6281no—
217C23—6281no—
218C23—6281no—
219C23—6281no—
220C23—6281no—
221C23—6282no—
222C23—6281no—
223C23—6281no—
224C23—6281no—
225C23—1572no—
226C23—12561no—
227C23—12561no—
228C23D4×D15711yescharacteristic
229D4—41no—
230D4—41no—
231D4—41no—
232D4—3142no—
233D4—3142no—
234D4—6281no—
235D4—6281no—
236D4—6281no—
237D4—6282no—
238D4—6288no—
239D4—6282no—
240D4—6281no—
241D4—6281no—
242D4—12561no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—3141no—
249C2×C4—3141no—
250C2×C4—6282no—
251C2×C4—6281no—
252C2×C4D4×D15711yescharacteristic
253C2×C4C2×D62811yescharacteristic
254C8—41no—
255C8—6281no—
256C22—21no—
257C22—21no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—3142no—
262C22—6282no—
263C22—6282no—
264C22—6282no—
265C22—6281no—
266C22—6281no—
267C22—6281no—
268C22—6281no—
269C22—6282no—
270C22—6281no—
271C22—12561no—
272C22—12561no—
273C22—12561no—
274C22—12564no—
275C22—12561no—
276C22—12561no—
277C22#1909774111yescharacteristic
278C22D8×D15711yescharacteristic
279C22#1909779811yescharacteristic
280C4—21no—
281C4—21no—
282C4—42no—
283C4—41no—
284C4—6281no—
285C4—6281no—
286C2—21no—
287C2—21no—
288C2—81no—
289C2—6282no—
290C2—12562no—
291C2—12561no—
292C2#2375740811yescharacteristic
293C2#2375744211yescharacteristic
294C2#2375746111yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#327×C157C2
socleC22×C157#120
hypercenter#327D157
hypocenterC157#1595
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
1. #23757831C2semidirect
2. #23757409C2semidirect
3. #23757406C2semidirect
4. #23757183C2semidirect
5. #23757006C2semidirect
6. #23756996C2semidirect
7. #327×C157C2semidirect
9. C22×D628C22semidirect
23. C22⋊#11929434C22semidirect
25. C22⋊C8×C157C22semidirect
26. #95×C157C22semidirect
37. C2×D628D4semidirect
48. C4⋊Dic157D4semidirect
57. C2×D4×C157D4semidirect
61. C4⋊C4×C157D4semidirect
78. C22×D157D8semidirect
147. C157#1595semidirect
154. #327D157semidirect
173. C22⋊C8C2×D157semidirect
174. #95C2×D157semidirect
192. C2×D4D628semidirect
203. C4⋊C4D628semidirect

Maximal subgroups

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

subgroupindex
#237578312
#237574092
#237574062
#237571832
#237570062
#237569962
#327×C1572
#1595157