Finite Group Databasebeta

← #34099072

Subgroups — #34099072

Order 20096.

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

normal subgroups only

This group has 310 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#23757850C211yesmaximal, characteristic, complemented
2#23757409C211yesmaximal, characteristic, complemented
3#23757406C211yesmaximal, characteristic, complemented
4#23757191C211yesmaximal, characteristic, complemented
5#23757006C211yesmaximal, characteristic, complemented
6#23756998C211yesmaximal, characteristic, complemented
7#327×C157C211yesmaximal, characteristic, complemented
8C2×#14578953—21no—
9C22×D628C2211yescharacteristic
10C2×D1256—21no—
11C2×#14578939—21no—
12#19097749—21no—
13#19097748—21no—
14#19097745C2211yescharacteristic
15#19097744—21no—
16#19097743—21no—
17#19097743—21no—
18C2×#14578933C2211yescharacteristic
19C2×#14578931—21no—
20C2×#14578931—21no—
21#19097693—21no—
22#19097691—21no—
23C22⋊#11929434C2211yescharacteristic
24#121×C157C2211yescharacteristic
25C22⋊C8×C157C2211yescharacteristic
26#95×C157C2211yescharacteristic
27C23×D157—21no—
28#14578953—42no—
29#14578953—42no—
30C2×Dic314—21no—
31C2×D628—21no—
32C2×D628—21no—
33C2×D628—42no—
34C2×D628D411yescharacteristic
35C2×C22⋊D157—21no—
36C2×C22⋊D157—21no—
37C2×C22⋊D157—21no—
38C22×Dic157—21no—
39C22×Dic157D411yescharacteristic
40C22×Dic157D411yescharacteristic
41C2×C4×D157—21no—
42D1256—42no—
43#14578939—42no—
44C2×#11929434—21no—
45C4⋊Dic157D411yescharacteristic
46#14578933—21no—
47#14578933—21no—
48#14578933—21no—
49C22⋊Dic157—21no—
50#14578931—21no—
51#14578931—21no—
52#14578931—42no—
53#14578931—42no—
54C2×D4×C157—21no—
55C2×D4×C157D411yescharacteristic
56C22×C4×C157—21no—
57C22×C4×C157C2311yescharacteristic
58C2×C8×C157—21no—
59C4⋊C4×C157D411yescharacteristic
60C22⋊C4×C157—21no—
61C22×D157—22no—
62C22×D157—21no—
63C22×D157—41no—
64C22×D157—41no—
65C22×D157—41no—
66C22×D157—41no—
67C22×D157—41no—
68C22×D157—41no—
69Dic314—42no—
70D628—22no—
71D628—22no—
72D628—41no—
73D628—41no—
74D628—41no—
75C22⋊D157—42no—
76C22⋊D157—41no—
77C22⋊D157—41no—
78C22⋊D157—81no—
79C2×Dic157—21no—
80C2×Dic157—21no—
81C2×Dic157—21no—
82C2×Dic157—21no—
83C2×Dic157—42no—
84C2×Dic157—41no—
85C2×Dic157D812yescomplemented
86C4×D157—42no—
87#11929434—41no—
88C23×C157—21no—
89C23×C157C2×D411yescharacteristic
90D4×C157—41no—
91D4×C157—41no—
92D4×C157—41no—
93C2×C4×C157—21no—
94C2×C4×C157—41no—
95C2×C4×C157—41no—
96C2×C4×C157—41no—
97C2×C4×C157—41no—
98C2×C4×C157C2×D411yescharacteristic
99C2×C4×C157C2×D411yescharacteristic
100C8×C157—41no—
101C22×C157—21no—
102C22×C157—21no—
103C22×C157—41no—
104C22×C157—41no—
105C22×C157—41no—
106C22×C157#12011yescharacteristic
107C22×C157C2×D811yescharacteristic
108C22×C157AGL(1,ℤ/8)11yescharacteristic
109C2×D157—42no—
110C2×D157—42no—
111C2×D157—41no—
112C2×D157—41no—
113C2×D157—41no—
114C2×D157—42no—
115C2×D157—81no—
116C2×D157—81no—
117C2×D157—81no—
118C2×D157—81no—
119C4×C157—21no—
120C4×C157—21no—
121C4×C157—41no—
122C4×C157—81no—
123Dic157—22no—
124Dic157—41no—
125Dic157—41no—
126C2×C157—21no—
127C2×C157—21no—
128C2×C157—81no—
129C2×C157#44711yescharacteristic
130C2×C157#45411yescharacteristic
131C2×C157B(4,𝔽2)11yescharacteristic
132D157—81no—
133D157—82no—
134C157#159811yescharacteristic, complemented, Sylow
135#1598—1571nomaximal, Sylow
136#537—1571no—
137#447—1571no—
138#447—1571no—
139#394—1571no—
140#327—1571no—
141#327D15711yescharacteristic, complemented
142#324—1571no—
143C2×#41—3141no—
144C22×D4—1571no—
145C2×D8—3141no—
146C2×D8—3141no—
147C22⋊Q8—3141no—
148C22⋊Q8—3141no—
149#121—3141no—
150#121—3141no—
151#121—3141no—
152#121—1571no—
153#121C2×D15711yescharacteristic
154C2×C4⋊C4—1571no—
155C2×C22⋊C4—3141no—
156C2×C22⋊C4—3141no—
157#102—3141no—
158#102—3141no—
159C22⋊C8—1571no—
160C22⋊C8C2×D15711yescharacteristic
161#95C2×D15711yescharacteristic
162C24—3141no—
163#41—6282no—
164#41—6282no—
165C2×Q8—3141no—
166C2×D4—21no—
167C2×D4—3141no—
168C2×D4—3141no—
169C2×D4—3141no—
170C2×D4—3141no—
171C2×D4—3141no—
172C2×D4—6282no—
173C2×D4—1571no—
174C2×D4D62811yescharacteristic
175C22×C4—21no—
176C22×C4—3141no—
177C22×C4—3141no—
178C22×C4—1571no—
179C22×C4—1571no—
180C22×C4C22×D15711yescharacteristic
181D8—6282no—
182D8—6282no—
183C2×C8—21no—
184C2×C8—3141no—
185C4⋊C4—3141no—
186C4⋊C4—3141no—
187C4⋊C4—3141no—
188C4⋊C4—1571no—
189C4⋊C4D62811yescharacteristic
190C22⋊C4—21no—
191C22⋊C4—3141no—
192C22⋊C4—3141no—
193C22⋊C4—3141no—
194C22⋊C4—6282no—
195C22⋊C4—6282no—
196C23—21no—
197C23—3142no—
198C23—3141no—
199C23—6281no—
200C23—6281no—
201C23—6281no—
202C23—6281no—
203C23—6281no—
204C23—6281no—
205C23D4×D15711yescharacteristic
206Q8—6282no—
207D4—41no—
208D4—41no—
209D4—41no—
210D4—3142no—
211D4—3142no—
212D4—6281no—
213D4—6281no—
214D4—6281no—
215D4—6282no—
216D4—6281no—
217D4—6281no—
218D4—12561no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—3141no—
225C2×C4—3141no—
226C2×C4—3141no—
227C2×C4—3141no—
228C2×C4—6282no—
229C2×C4—6282no—
230C2×C4—6281no—
231C2×C4—1572no—
232C2×C4D4×D15711yescharacteristic
233C2×C4C2×D62811yescharacteristic
234C8—41no—
235C8—6281no—
236C22—21no—
237C22—21no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—6282no—
242C22—6282no—
243C22—6281no—
244C22—6281no—
245C22—6282no—
246C22—6281no—
247C22—12561no—
248C22—12561no—
249C22—12561no—
250C22—12561no—
251C22#1909774111yescharacteristic
252C22D8×D15711yescharacteristic
253C22#1909779811yescharacteristic
254C4—21no—
255C4—21no—
256C4—41no—
257C4—81no—
258C4—3142no—
259C4—6281no—
260C4—6281no—
261C2—21no—
262C2—21no—
263C2—81no—
264C2—12562no—
265C2—12561no—
266C2#2375740811yescharacteristic
267C2#2375744711yescharacteristic
268C2#2375746111yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#327×C157C2
socleC22×C157#120
hypercenter#327D157
hypocenterC157#1598
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. #23757850C2semidirect
2. #23757409C2semidirect
3. #23757406C2semidirect
4. #23757191C2semidirect
5. #23757006C2semidirect
6. #23756998C2semidirect
7. #327×C157C2semidirect
85. C2×Dic157D8semidirect
134. C157#1598semidirect
141. #327D157semidirect

Maximal subgroups

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

subgroupindex
#237578502
#237574092
#237574062
#237571912
#237570062
#237569982
#327×C1572
#1598157