Finite Group Databasebeta

← #34116145

Subgroups — #34116145

Order 20096.

578 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 68 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#23758340C211yesmaximal, characteristic, complemented
2D157⋊#99C211yesmaximal, characteristic, complemented
3#23758214C212yesmaximal, complemented
4#23758150C212yesmaximal, complemented
5#120×D157C211yesmaximal, characteristic
6D4×#10597845—24no—
7#19097850—21no—
8C2×C22⋊#10597845—24no—
9C2×C22⋊#10597845—21no—
10C2×C22⋊#10597845C2212yes—
11C2×C22⋊#10597845C2212yes—
12#19097830—21no—
13#19097829—21no—
14C24×D157C2211yescharacteristic
15C2×D4×D157—21no—
16C2×D4×D157C2211yescharacteristic
17#19097741—21no—
18#19097741C411yescharacteristic, complemented
19#19097740C411yescharacteristic, complemented
20#19097739—21no—
21#19097739C411yescharacteristic, complemented
22C22⋊C4×D157—21no—
23C22⋊C4×D157C2211yescharacteristic
24#120×C157C411yescharacteristic, complemented
25C22×#10597845—22no—
26C22×#10597845—22no—
27C22×#10597845D414yescomplemented
28C4⋊#10597845—22no—
29C22⋊#10597845—22no—
30C22⋊#10597845—22no—
31C22⋊#10597845—22no—
32C22⋊#10597845—22no—
33C22⋊#10597845—22no—
34C22⋊#10597845—48no—
35C4×#10597845—22no—
36C23×D157—21no—
37C23×D157—22no—
38C23×D157—21no—
39C23×D157—22no—
40C23×D157—44no—
41C23×D157C2×C411yescharacteristic, complemented
42C23×D157D411yescharacteristic
43C23×D157C2311yescharacteristic
44C2×D628—21no—
45C2×D628D411yescharacteristic
46C2×C22⋊D157—21no—
47C2×C22⋊D157—21no—
48C2×C22⋊D157C2×C411yescharacteristic
49C2×C22⋊D157D411yescharacteristic
50D4×D157—22no—
51D4×D157—22no—
52D4×D157—44no—
53C2×C4×D157—21no—
54C2×C4×D157D411yescharacteristic
55C22⋊Dic157—21no—
56C22⋊Dic157C2×C411yescharacteristic, complemented
57#14578931—21no—
58#14578931—21no—
59#14578931—21no—
60C24×C157C2×C411yescharacteristic, complemented
61C2×D4×C157—21no—
62C2×D4×C157C2×C411yescharacteristic
63C22⋊C4×C157—21no—
64C22⋊C4×C157C2×C411yescharacteristic, complemented
65C2×#10597845—24no—
66C2×#10597845—44no—
67C2×#10597845—44no—
68C2×#10597845—42no—
69C2×#10597845—82no—
70C22×D157—24no—
71C22×D157—28no—
72C22×D157—21no—
73C22×D157—22no—
74C22×D157—21no—
75C22×D157—21no—
76C22×D157—42no—
77C22×D157—42no—
78C22×D157—42no—
79C22×D157—44no—
80C22×D157—42no—
81C22×D157—44no—
82C22×D157—42no—
83C22×D157—42no—
84C22×D157—44no—
85C22×D157—41no—
86C22×D157—42no—
87C22×D157—41no—
88C22×D157C22⋊C411yescharacteristic, complemented
89C22×D157C2×D412yes—
90C22×D157C2×D411yescharacteristic
91C22×D157C2×D411yescharacteristic
92C22×D157#4112yes—
93D628—22no—
94D628—42no—
95C22⋊D157—22no—
96C22⋊D157—22no—
97C22⋊D157—42no—
98C22⋊D157—42no—
99C2×Dic157—21no—
100C2×Dic157C22⋊C411yescharacteristic, complemented
101C4×D157—21no—
102C4×D157—21no—
103C4×D157—42no—
104C23×C157—21no—
105C23×C157—22no—
106C23×C157—42no—
107C23×C157C22⋊C411yescharacteristic, complemented
108C23×C157C22×C411yescharacteristic
109D4×C157—22no—
110D4×C157—42no—
111C2×C4×C157—21no—
112C2×C4×C157C22⋊C411yescharacteristic, complemented
113C22×C157—22no—
114C22×C157—24no—
115C22×C157—21no—
116C22×C157—41no—
117C22×C157—41no—
118C22×C157—41no—
119C22×C157—42no—
120C22×C157—41no—
121C22×C157C2×C22⋊C411yescharacteristic
122C22×C157C4×D412yes—
123C2×D157—22no—
124C2×D157—24no—
125C2×D157—22no—
126C2×D157—24no—
127C2×D157—21no—
128C2×D157—41no—
129C2×D157—42no—
130C2×D157—48no—
131C2×D157—44no—
132C2×D157—41no—
133C2×D157—42no—
134C2×D157—41no—
135C2×D157—44no—
136C2×D157—42no—
137C2×D157—41no—
138C2×D157—81no—
139C2×D157#12011yescharacteristic
140C2×D157#12112yes—
141C2×D157#12311yescharacteristic
142#10597845—44no—
143#10597845—82no—
144C4×C157—21no—
145C4×C157—41no—
146Dic157—21no—
147Dic157—41no—
148C2×C157—21no—
149C2×C157—22no—
150C2×C157—42no—
151C2×C157—41no—
152C2×C157#38611yescharacteristic
153D157—22no—
154D157—21no—
155D157—42no—
156D157—41no—
157D157B(4,𝔽2)12yes—
158C157#188911yescharacteristic, complemented, Sylow
159#1889—1571nomaximal, Sylow
160C2×#120—1571no—
161#518—1571no—
162C2×#99—1571no—
163#379—1572no—
164#342—1572no—
165C25—1571no—
166C22×D4—3141no—
167C22×D4—1571no—
168#120—3141no—
169#120—3141no—
170#120—1571no—
171#120—1571no—
172#120—1571no—
173#120#1059784511yescharacteristic, complemented
174C4×D4—3144no—
175#117—3141no—
176C2×C22⋊C4—3141no—
177C2×C22⋊C4—3141no—
178C2×C22⋊C4—3144no—
179C2×C22⋊C4—1572no—
180C2×C22⋊C4—1572no—
181C2×C22⋊C4—1571no—
182#99—3141no—
183#99—3141no—
184C24—3142no—
185C24—3141no—
186C24—3141no—
187C24—3142no—
188C24—6284no—
189C24—1571no—
190C24—1571no—
191C24—1571no—
192C24C2×#1059784511yescharacteristic, complemented
193C2×D4—21no—
194C2×D4—3141no—
195C2×D4—3142no—
196C2×D4—3142no—
197C2×D4—3141no—
198C2×D4—3141no—
199C2×D4—6284no—
200C2×D4—1571no—
201C2×D4—1571no—
202C2×D4—1571no—
203C2×D4C2×#1059784511yescharacteristic
204C22×C4—3141no—
205C22×C4—3142no—
206C22×C4—3142no—
207C22×C4—1571no—
208C22×C4—1574no—
209C4⋊C4—3142no—
210C22⋊C4—21no—
211C22⋊C4—3141no—
212C22⋊C4—3141no—
213C22⋊C4—3142no—
214C22⋊C4—3142no—
215C22⋊C4—3142no—
216C22⋊C4—3141no—
217C22⋊C4—3141no—
218C22⋊C4—3142no—
219C22⋊C4—3142no—
220C22⋊C4—6288no—
221C22⋊C4—1571no—
222C22⋊C4C2×#1059784511yescharacteristic, complemented
223C42—3142no—
224C23—21no—
225C23—22no—
226C23—42no—
227C23—3148no—
228C23—3144no—
229C23—3141no—
230C23—3141no—
231C23—3141no—
232C23—3142no—
233C23—6282no—
234C23—6284no—
235C23—6282no—
236C23—6282no—
237C23—6284no—
238C23—6282no—
239C23—6282no—
240C23—6284no—
241C23—6282no—
242C23—6281no—
243C23—6282no—
244C23—6281no—
245C23—1571no—
246C23—1572no—
247C23—1571no—
248C23—1571no—
249C23—1572no—
250C23C22⋊#1059784511yescharacteristic, complemented
251C23C22×#1059784511yescharacteristic
252D4—22no—
253D4—42no—
254D4—3142no—
255D4—3142no—
256D4—3142no—
257D4—6282no—
258D4—6282no—
259D4—6282no—
260C2×C4—21no—
261C2×C4—3141no—
262C2×C4—3141no—
263C2×C4—3144no—
264C2×C4—3141no—
265C2×C4—6282no—
266C2×C4—6284no—
267C2×C4—6284no—
268C2×C4—6282no—
269C2×C4—1571no—
270C2×C4—12562no—
271C2×C4C22⋊#1059784511yescharacteristic, complemented
272C22—22no—
273C22—24no—
274C22—21no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—41no—
280C22—3144no—
281C22—3142no—
282C22—3142no—
283C22—3144no—
284C22—3141no—
285C22—6281no—
286C22—6282no—
287C22—6281no—
288C22—6281no—
289C22—6282no—
290C22—6288no—
291C22—6284no—
292C22—6282no—
293C22—6284no—
294C22—6281no—
295C22—1571no—
296C22—1572no—
297C22—1571no—
298C22—12561no—
299C22C2×C22⋊#1059784511yescharacteristic
300C22D4×#1059784512yes—
301C4—21no—
302C4—41no—
303C4—3141no—
304C4—6281no—
305C4—6284no—
306C4—12562no—
307C2—21no—
308C2—22no—
309C2—42no—
310C2—41no—
311C2—3142no—
312C2—3141no—
313C2—6282no—
314C2—6281no—
315C2—1572no—
316C2#2375822111yescharacteristic
subgroupG/H
centerC2#23758221
commutatorC23×C157C22×C4
FrattiniC23C22×#10597845
Fitting#120×C157C4
socleC2×C157#386
prime radical#120×D157C2
cosocleC23×D157C23
hypercenter#120#10597845
hypocenterC157#1889
LCSG ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C23 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #23758340C2semidirect
2. D157⋊#99C2semidirect
3. #23758214C2semidirect
4. #23758150C2semidirect
18. #19097741C4semidirect
19. #19097740C4semidirect
21. #19097739C4semidirect
24. #120×C157C4semidirect
27. C22×#10597845D4semidirect
41. C23×D157C2×C4semidirect
56. C22⋊Dic157C2×C4semidirect
60. C24×C157C2×C4semidirect
64. C22⋊C4×C157C2×C4semidirect
88. C22×D157C22⋊C4semidirect
100. C2×Dic157C22⋊C4semidirect
107. C23×C157C22⋊C4semidirect
112. C2×C4×C157C22⋊C4semidirect
158. C157#1889semidirect
173. #120#10597845semidirect
192. C24C2×#10597845semidirect
222. C22⋊C4C2×#10597845semidirect
250. C23C22⋊#10597845semidirect
271. C2×C4C22⋊#10597845semidirect

Maximal subgroups

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

subgroupindex
#237583402
D157⋊#992
#237582142
#237581502
#120×D1572
#1889157