Finite Group Databasebeta

← #34101202

Subgroups — #34101202

Order 20096.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#23758071C211yesmaximal, characteristic, complemented
2#23757785C211yesmaximal, characteristic, complemented
3#23757780C211yesmaximal, characteristic, complemented
4#23757289C211yesmaximal, characteristic, complemented
5#23757236C211yesmaximal, characteristic, complemented
6#23757029C211yesmaximal, characteristic, complemented
7#421×C157C211yesmaximal, characteristic, complemented
8C2×#14578954C2211yescharacteristic
9C22×C4×D157C2211yescharacteristic
10#19097802—21no—
11#19097801—21no—
12#19097797—21no—
13#19097796—21no—
14#19097791—22no—
15C2×#14578938C2211yescharacteristic
16#19097755—21no—
17#19097752—21no—
18#19097751—21no—
19#19097747—21no—
20#19097746—21no—
21#19097742—21no—
22#19097741—21no—
23#19097739—21no—
24C4×D628—22no—
25C4×C22⋊D157—22no—
26#19097730C2211yescharacteristic
27#19097697—22no—
28#19097683—22no—
29C2×#41×C157C2211yescharacteristic
30C2×M16×C157C2211yescharacteristic
31#117×C157C2211yescharacteristic
32#104×C157—22no—
33C23×D157D411yescharacteristic
34#14578954—21no—
35#14578954—21no—
36#14578954—21no—
37#14578954—21no—
38C2×Dic314D411yescharacteristic, complemented
39C2×D628—22no—
40C2×D628D411yescharacteristic, complemented
41C2×C22⋊D157—22no—
42C2×C22⋊D157—21no—
43C22×Dic157D411yescharacteristic
44C2×C4×D157—21no—
45C2×C4×D157—21no—
46C2×C4×D157—21no—
47C2×C4×D157—21no—
48C2×C4×D157—21no—
49C2×C4×D157—21no—
50C2×C4×D157—21no—
51#14578944—22no—
52#14578942—22no—
53#14578941—22no—
54#14578939—22no—
55#14578938—21no—
56#14578938—21no—
57C2×#11929434D412yescomplemented
58C4⋊Dic157—22no—
59C4⋊Dic157—21no—
60#14578933—22no—
61C22⋊Dic157—22no—
62C22⋊Dic157—21no—
63#14578931—22no—
64#14578931—22no—
65#14578931—22no—
66C4×Dic157D412yescomplemented
67#41×C157—21no—
68#41×C157—21no—
69#41×C157—21no—
70#41×C157—21no—
71C2×Q8×C157D411yescharacteristic, complemented
72C2×D4×C157—21no—
73C2×D4×C157D411yescharacteristic, complemented
74C22×C4×C157—21no—
75C22×C4×C157C2311yescharacteristic
76M16×C157—21no—
77M16×C157—21no—
78C2×C8×C157—21no—
79C4⋊C4×C157—21no—
80C22⋊C4×C157—21no—
81C42×C157D412yescomplemented
82C22×D157—21no—
83C22×D157—21no—
84C22×D157—21no—
85C22×D157—21no—
86C22×D157—42no—
87Dic314—21no—
88Dic314—21no—
89D628—21no—
90D628—21no—
91D628—44no—
92C22⋊D157—44no—
93C22⋊D157—41no—
94C22⋊D157—41no—
95C2×Dic157—21no—
96C2×Dic157—21no—
97C2×Dic157—21no—
98C2×Dic157—22no—
99C2×Dic157—21no—
100C4×D157—41no—
101C4×D157—41no—
102C4×D157—41no—
103C4×D157—41no—
104C4×D157—41no—
105C4×D157—41no—
106#11929434—22no—
107C23×C157—21no—
108C23×C157C2×D411yescharacteristic
109Q8×C157—21no—
110Q8×C157—21no—
111D4×C157—21no—
112D4×C157—21no—
113D4×C157—41no—
114D4×C157—41no—
115C2×C4×C157—22no—
116C2×C4×C157—21no—
117C2×C4×C157—41no—
118C2×C4×C157—41no—
119C2×C4×C157C2×D411yescharacteristic
120C2×C4×C157C2×D411yescharacteristic
121C2×C4×C157C2×D411yescharacteristic
122C2×C4×C157C2×D411yescharacteristic
123C2×C4×C157C2×D411yescharacteristic
124C2×C4×C157#4111yescharacteristic
125C8×C157—41no—
126C22×C157—41no—
127C22×C157—42no—
128C22×C157—41no—
129C22×C157#12011yescharacteristic
130C22×C157#12011yescharacteristic
131C22×C157#12111yescharacteristic
132C2×D157—22no—
133C2×D157—22no—
134C2×D157—22no—
135C2×D157—41no—
136C2×D157—41no—
137C2×D157—41no—
138C2×D157—41no—
139C2×D157—42no—
140C2×D157—41no—
141C4×C157—42no—
142C4×C157—41no—
143C4×C157#12011yescharacteristic
144C4×C157#12111yescharacteristic
145C4×C157#12111yescharacteristic
146C4×C157#12711yescharacteristic
147Dic157—42no—
148Dic157—41no—
149Dic157—41no—
150C2×C157—21no—
151C2×C157—21no—
152C2×C157—21no—
153C2×C157—81no—
154C2×C157#39211yescharacteristic
155D157—42no—
156D157—81no—
157C157#201011yescharacteristic, complemented, Sylow
158#2010—1571nomaximal, Sylow
159#575—1571no—
160#525—1571no—
161#525—1571no—
162#421—1571no—
163#421D15711yescharacteristic, complemented
164#407—1571no—
165H(3,ℤ/4)—1571no—
166C2×#41—1571no—
167C2×#41C2×D15711yescharacteristic
168C23×C4—1571no—
169#137—3141no—
170#137—3141no—
171AGL(1,ℤ/8)—3141no—
172AGL(1,ℤ/8)—3141no—
173#135—3142no—
174C2×M16—1571no—
175C2×M16C2×D15711yescharacteristic
176#123—3141no—
177#123—3141no—
178C22⋊Q8—3141no—
179C22⋊Q8—3141no—
180#121—3141no—
181#121—3141no—
182#120—3141no—
183#120—3141no—
184C4×D4—3142no—
185C4×D4—3142no—
186#117—1571no—
187#117C2×D15711yescharacteristic
188#104—22no—
189#104—3142no—
190C22⋊C8—3142no—
191C24—1571no—
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196#41—3141no—
197#41—3141no—
198#41—3141no—
199#41—3141no—
200C2×Q8—1571no—
201C2×Q8D62811yescharacteristic, complemented
202C2×D4—21no—
203C2×D4—3142no—
204C2×D4—3142no—
205C2×D4—3141no—
206C2×D4—1571no—
207C2×D4D62811yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—3141no—
210C22×C4—3141no—
211C22×C4—3141no—
212C22×C4—3141no—
213C22×C4—3141no—
214C22×C4—3141no—
215C22×C4—3141no—
216C22×C4—1571no—
217C22×C4C22×D15711yescharacteristic
218Q16—3142no—
219SD16—3142no—
220SD16—3142no—
221D8—3142no—
222M16—21no—
223M16—21no—
224M16—3141no—
225M16—3141no—
226C2×C8—21no—
227C2×C8—1572no—
228C4⋊C4—21no—
229C4⋊C4—3142no—
230C4⋊C4—3142no—
231C4⋊C4—3141no—
232C22⋊C4—21no—
233C22⋊C4—3142no—
234C22⋊C4—3142no—
235C22⋊C4—3142no—
236C22⋊C4—3142no—
237C22⋊C4—3141no—
238C42—1572no—
239C42C22⋊D15712yescomplemented
240C23—21no—
241C23—3141no—
242C23—3141no—
243C23—3141no—
244C23—3141no—
245C23—6282no—
246C23D4×D15711yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—3141no—
250Q8—3141no—
251D4—21no—
252D4—21no—
253D4—41no—
254D4—41no—
255D4—3141no—
256D4—3141no—
257D4—6284no—
258D4—6284no—
259D4—6281no—
260D4—6281no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—3141no—
266C2×C4—3141no—
267C2×C4—3142no—
268C2×C4—3141no—
269C2×C4—3141no—
270C2×C4—6281no—
271C2×C4—6281no—
272C2×C4—6281no—
273C2×C4—6281no—
274C2×C4—6281no—
275C2×C4—6281no—
276C2×C4D4×D15711yescharacteristic
277C2×C4D4×D15711yescharacteristic
278C2×C4D4×D15711yescharacteristic
279C2×C4C2×C22⋊D15711yescharacteristic
280C2×C4C2×D62811yescharacteristic
281C2×C4#1457895411yescharacteristic
282C8—41no—
283C8—3142no—
284C22—41no—
285C22—42no—
286C22—41no—
287C22—3142no—
288C22—3142no—
289C22—3142no—
290C22—6281no—
291C22—6281no—
292C22—6281no—
293C22—6282no—
294C22—6281no—
295C22—6281no—
296C22#1909773911yescharacteristic
297C22#1909774111yescharacteristic
298C22#1909774411yescharacteristic
299C4—42no—
300C4—41no—
301C4—6282no—
302C4—6281no—
303C4—6281no—
304C4#1909774111yescharacteristic
305C4#1909774411yescharacteristic
306C4#1909774511yescharacteristic
307C4#1909776711yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—81no—
312C2—6282no—
313C2—12561no—
314C2#2375718211yescharacteristic
subgroupG/H
centerC4#19097767
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#421×C157C2
socleC2×C157#392
hypercenter#421D157
hypocenterC157#2010
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #23758071C2semidirect
2. #23757785C2semidirect
3. #23757780C2semidirect
4. #23757289C2semidirect
5. #23757236C2semidirect
6. #23757029C2semidirect
7. #421×C157C2semidirect
38. C2×Dic314D4semidirect
40. C2×D628D4semidirect
57. C2×#11929434D4semidirect
66. C4×Dic157D4semidirect
71. C2×Q8×C157D4semidirect
73. C2×D4×C157D4semidirect
81. C42×C157D4semidirect
157. C157#2010semidirect
163. #421D157semidirect
201. C2×Q8D628semidirect
207. C2×D4D628semidirect
239. C42C22⋊D157semidirect

Maximal subgroups

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

subgroupindex
#237580712
#237577852
#237577802
#237572892
#237572362
#237570292
#421×C1572
#2010157