Finite Group Databasebeta

← #34098689

Subgroups — #34098689

Order 20096.

284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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#23757783C211yesmaximal, characteristic
2C22⋊C8×D157C211yesmaximal, characteristic, complemented
3#23757135C211yesmaximal, characteristic, complemented
4#23757011C211yesmaximal, characteristic, complemented
5#23757009C211yesmaximal, characteristic, complemented
6#23757007C211yesmaximal, characteristic, complemented
7#327×C157C211yesmaximal, characteristic, complemented
8C2×#14578953C411yescharacteristic, complemented
9C22×C4×D157C2211yescharacteristic
10C2×C8×D157—21no—
11#19097753—21no—
12#19097751C411yescharacteristic, complemented
13#19097750C2211yescharacteristic
14#19097742C411yescharacteristic, complemented
15#19097739—21no—
16D4×Dic157—21no—
17#19097731—21no—
18#19097729C411yescharacteristic, complemented
19C2×#14578931—21no—
20C22⋊#11929434C2211yescharacteristic
21#19097683—21no—
22#19097678—21no—
23#19097678C2211yescharacteristic
24#121×C157C2211yescharacteristic
25C22⋊C8×C157C2211yescharacteristic
26#95×C157C2211yescharacteristic
27C23×D157D411yescharacteristic
28#14578953—42no—
29C2×Dic314C2×C411yescharacteristic
30C2×C22⋊D157—21no—
31C2×C22⋊D157—21no—
32C22×Dic157—21no—
33C22×Dic157—21no—
34C22×Dic157D411yescharacteristic
35C2×C4×D157—42no—
36C2×C4×D157C2×C411yescharacteristic
37C2×C4×D157C2×C411yescharacteristic
38C2×C4×D157D411yescharacteristic
39C2×C4×D157D411yescharacteristic
40C2×#11929434—21no—
41C8×D157—42no—
42C4⋊Dic157—21no—
43C4⋊Dic157C2×C411yescharacteristic
44#14578933—21no—
45C22⋊Dic157—21no—
46C22⋊Dic157—21no—
47#14578931—21no—
48#14578931—21no—
49#14578931—42no—
50C4×Dic157—21no—
51C2×D4×C157—21no—
52C2×D4×C157C2×C411yescharacteristic
53C22×C4×C157—21no—
54C22×C4×C157C2311yescharacteristic
55C2×C8×C157—21no—
56C4⋊C4×C157C2×C411yescharacteristic
57C22⋊C4×C157—21no—
58C22×D157—21no—
59C22×D157—21no—
60C22×D157—22no—
61C22×D157—41no—
62C22×D157C22⋊C411yescharacteristic
63C22×D157C22⋊C411yescharacteristic
64Dic314—41no—
65C22⋊D157—42no—
66C22⋊D157—42no—
67C2×Dic157—21no—
68C2×Dic157—21no—
69C2×Dic157—41no—
70C2×Dic157—42no—
71C2×Dic157—41no—
72C2×Dic157—41no—
73C2×Dic157—41no—
74C2×Dic157C22⋊C411yescharacteristic
75C2×Dic157C22⋊C411yescharacteristic
76C4×D157—22no—
77C4×D157—22no—
78C4×D157—41no—
79C4×D157—41no—
80#11929434—41no—
81C23×C157—21no—
82C23×C157C2×D411yescharacteristic
83D4×C157—41no—
84D4×C157—41no—
85D4×C157—41no—
86C2×C4×C157—21no—
87C2×C4×C157—41no—
88C2×C4×C157—41no—
89C2×C4×C157—41no—
90C2×C4×C157—41no—
91C2×C4×C157C22×C411yescharacteristic
92C2×C4×C157C2×D411yescharacteristic
93C8×C157—41no—
94C22×C157—21no—
95C22×C157—21no—
96C22×C157—41no—
97C22×C157—41no—
98C22×C157—41no—
99C22×C157C2×C22⋊C411yescharacteristic
100C22×C157#13511yescharacteristic
101C22×C157#13511yescharacteristic
102C2×D157—21no—
103C2×D157—21no—
104C2×D157—21no—
105C2×D157—21no—
106C2×D157—21no—
107C2×D157—42no—
108C2×D157—42no—
109C2×D157#9912yes—
110C4×C157—21no—
111C4×C157—21no—
112C4×C157—41no—
113C4×C157—81no—
114Dic157—21no—
115Dic157—21no—
116Dic157—41no—
117Dic157—41no—
118Dic157—81no—
119C2×C157—21no—
120C2×C157—21no—
121C2×C157—81no—
122C2×C157C2×#9911yescharacteristic
123C2×C157#41611yescharacteristic
124C2×C157#42111yescharacteristic
125D157—22no—
126D157—41no—
127C157#151611yescharacteristic, complemented, Sylow
128#1516—1571nomaximal, Sylow
129#525—1571no—
130C2×C22⋊C8—1571no—
131#381—1571no—
132#328—1571no—
133#328—1571no—
134#327—1571no—
135#327D15711yescharacteristic, complemented
136C2×#41—1571no—
137C23×C4—1571no—
138C22×C8—3141no—
139#123—3141no—
140C22⋊Q8—1571no—
141C22⋊Q8—1571no—
142#121—1571no—
143#121C2×D15711yescharacteristic
144#120—3141no—
145C4×D4—3141no—
146C4×D4—3141no—
147#117—1571no—
148C2×C22⋊C4—3141no—
149C22⋊C8—3141no—
150C22⋊C8—1571no—
151C22⋊C8C2×D15711yescharacteristic
152#95—3141no—
153#95—1571no—
154#95C2×D15711yescharacteristic
155C24—1571no—
156#41—6282no—
157C2×Q8—1571no—
158C2×D4—21no—
159C2×D4—3141no—
160C2×D4—3141no—
161C2×D4C4×D15711yescharacteristic
162C22×C4—21no—
163C22×C4—3141no—
164C22×C4—3141no—
165C22×C4—6282no—
166C22×C4—1571no—
167C22×C4—1571no—
168C22×C4—1571no—
169C22×C4—1571no—
170C22×C4—1571no—
171C22×C4C22×D15711yescharacteristic
172C2×C8—21no—
173C2×C8—3141no—
174C2×C8—6282no—
175C4⋊C4—3141no—
176C4⋊C4—3141no—
177C4⋊C4—1571no—
178C4⋊C4C4×D15711yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—3141no—
181C22⋊C4—3141no—
182C22⋊C4—3141no—
183C22⋊C4—3141no—
184C22⋊C4—6282no—
185C42—3141no—
186C23—21no—
187C23—3142no—
188C23—3141no—
189C23—3141no—
190C23—6281no—
191C23—1571no—
192C23—1571no—
193C23D4×D15711yescharacteristic
194Q8—6281no—
195D4—41no—
196D4—41no—
197D4—41no—
198D4—6282no—
199D4—6282no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—3142no—
206C2×C4—3142no—
207C2×C4—3141no—
208C2×C4—3141no—
209C2×C4—6281no—
210C2×C4—6281no—
211C2×C4—6281no—
212C2×C4—6282no—
213C2×C4—6281no—
214C2×C4—6281no—
215C2×C4—6281no—
216C2×C4—1571no—
217C2×C4—1571no—
218C2×C4C2×C4×D15711yescharacteristic
219C2×C4D4×D15711yescharacteristic
220C8—41no—
221C8—6281no—
222C22—21no—
223C22—21no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—3141no—
228C22—3141no—
229C22—3141no—
230C22—3141no—
231C22—3141no—
232C22—6282no—
233C22—6282no—
234C22—1572no—
235C22C22⋊C4×D15711yescharacteristic
236C22#1909779011yescharacteristic
237C22#1909779211yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—81no—
242C4—3141no—
243C4—3141no—
244C4—6281no—
245C4—6281no—
246C4—12561no—
247C2—21no—
248C2—21no—
249C2—81no—
250C2—3142no—
251C2—6281no—
252C2#99×D15711yescharacteristic
253C2#2375726611yescharacteristic
254C2#2375728811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#327×C157C2
socleC22×C157C2×C22⋊C4
prime radical#23757783C2
cosocleC22×C4×C157C23
hypercenter#327D157
hypocenterC157#1516
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D157C2semidirect
3. #23757135C2semidirect
4. #23757011C2semidirect
5. #23757009C2semidirect
6. #23757007C2semidirect
7. #327×C157C2semidirect
8. C2×#14578953C4semidirect
12. #19097751C4semidirect
14. #19097742C4semidirect
18. #19097729C4semidirect
127. C157#1516semidirect
135. #327D157semidirect

Maximal subgroups

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

subgroupindex
#237577832
C22⋊C8×D1572
#237571352
#237570112
#237570092
#237570072
#327×C1572
#1516157