Finite Group Databasebeta

← #28303380

Subgroups — #28303380

Order 13568.

522 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 112 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#20289948C212yesmaximal
2#20289543C212yesmaximal, complemented
3#20289539C212yesmaximal, complemented
4#20277054C211yesmaximal, characteristic
5#16811639C2214yes—
6#16811469—22no—
7#16811467—22no—
8C2×#13133174C411yescharacteristic
9C2×#13133174C2211yescharacteristic
10C2×C42×D53C411yescharacteristic
11#16810474—22no—
12#16810470—22no—
13#16810469C2211yescharacteristic
14C42×Dic53C411yescharacteristic
15C42×Dic53C2211yescharacteristic
16C53×#376C411yescharacteristic
17C4⋊#88324—24no—
18C22⋊#88324—24no—
19C4×#88324—24no—
20C22×C4×D53—21no—
21C22×C4×D53C2×C411yescharacteristic
22#13133174—22no—
23#13133174—22no—
24#13133174—22no—
25#13133174C814yescomplemented
26C2×#11719919—21no—
27C2×#11719919D412yes—
28C2×#11719921—21no—
29C2×#11719921D412yes—
30C2×C4×Dic53—22no—
31C2×C4×Dic53—21no—
32C2×C4×Dic53—22no—
33C2×C4×Dic53C2×C411yescharacteristic
34C2×C4×Dic53C2×C411yescharacteristic
35C2×C4×Dic53C2311yescharacteristic
36C42×D53—22no—
37C42×D53—22no—
38#13133124—22no—
39C2×C42×C53C2×C411yescharacteristic
40C2×C42×C53C2×C411yescharacteristic
41C2×C42×C53C2×C411yescharacteristic
42#95×C53—22no—
43C23×D53C22⋊C411yescharacteristic
44C22×C4×C53—21no—
45C22×C4×C53—21no—
46C22×C4×C53C22⋊C412yes—
47C22×C4×C53C22×C411yescharacteristic
48C22×Dic53—21no—
49C22×Dic53—21no—
50C22×Dic53C22⋊C411yescharacteristic
51C22×Dic53C2×D412yes—
52C2×C4×D53—21no—
53C2×C4×D53—21no—
54C2×C4×D53—21no—
55C2×C4×D53—21no—
56C2×C4×D53—24no—
57C2×C4×D53—44no—
58C2×C4×D53C2×C812yes—
59C2×C4×D53M1612yes—
60C2×#88324—44no—
61C42×C53—21no—
62C42×C53—21no—
63C42×C53—21no—
64C42×C53—21no—
65C42×C53C2×C812yes—
66C42×C53M1612yes—
67#11719921—24no—
68#11719921—24no—
69#11719919—24no—
70#11719919—24no—
71C4×Dic53—24no—
72C4×Dic53—21no—
73C4×Dic53—21no—
74C4×Dic53—44no—
75C4×Dic53—44no—
76C4×Dic53C2×C812yes—
77C4×Dic53M1612yes—
78C4×Dic53#4112yes—
79C4×Dic53#4112yes—
80C23×C53C2×C22⋊C411yescharacteristic
81C22×D53—21no—
82C22×D53—21no—
83C22×D53—42no—
84C22×D53C22⋊C812yes—
85C2×C4×C53—22no—
86C2×C4×C53—22no—
87C2×C4×C53—22no—
88C2×C4×C53—42no—
89C2×C4×C53—42no—
90C2×C4×C53—42no—
91C2×C4×C53#11711yescharacteristic
92C2×C4×C53#11711yescharacteristic
93C2×C4×C53C22×C811yescharacteristic
94C2×C4×C53C2×M1611yescharacteristic
95C2×C4×C53C2×M1611yescharacteristic
96C2×C4×C53C2×M1611yescharacteristic
97C2×Dic53—24no—
98C2×Dic53—21no—
99C2×Dic53—22no—
100C2×Dic53—21no—
101C2×Dic53—22no—
102C2×Dic53—42no—
103C2×Dic53—42no—
104C2×Dic53C22⋊C812yes—
105C2×Dic53#12314yes—
106C4×D53—22no—
107C4×D53—22no—
108C4×D53—22no—
109C4×D53—22no—
110C4×D53—48no—
111#88324—84no—
112#8731—531nomaximal, Sylow
113C22×C53—22no—
114C22×C53#38111yescharacteristic
115C22×C53C2×C22⋊C811yescharacteristic
116C22×C53#40711yescharacteristic
117C2×D53—22no—
118C2×D53—42no—
119C2×D53—42no—
120C2×D53—42no—
121C4×C53—42no—
122C4×C53—42no—
123C4×C53—42no—
124C4×C53#43111yescharacteristic
125C4×C53#43111yescharacteristic
126C4×C53#43211yescharacteristic
127C4×C53#43211yescharacteristic
128Dic53—24no—
129Dic53—22no—
130Dic53—24no—
131Dic53—42no—
132C4×#117—531no—
133#1458—532no—
134#1276—532no—
135#1274—532no—
136C2×C53—21no—
137C2×C53—21no—
138C2×C53#181711yescharacteristic
139C2×C53#182712yes—
140D53—42no—
141C2×#117—531no—
142C2×#117—531no—
143C22×C42—531no—
144#431—534no—
145C4×C4⋊C4—1062no—
146C4×C22⋊C4—1062no—
147#376—531no—
148#376#615711yescharacteristic
149C43—531no—
150C43—531no—
151#324—1062no—
152#323—1062no—
153C53#873111yescharacteristic, complemented, Sylow
154C23×C4—531no—
155C23×C4—1061no—
156#117—534no—
157#117—1062no—
158#117—1062no—
159#117—1062no—
160C2×C4⋊C4—532no—
161C2×C4⋊C4—1061no—
162C2×C22⋊C4—532no—
163C2×C22⋊C4—1061no—
164C2×C42—531no—
165C2×C42—531no—
166C2×C42—531no—
167C2×C42—1062no—
168C2×C42—1061no—
169C2×C42—1062no—
170C2×C42—1062no—
171C2×C42—1062no—
172C2×C42C2×#615711yescharacteristic
173C2×C42C2×#615711yescharacteristic
174C2×C42C2×#615711yescharacteristic
175C4⋊C8—1064no—
176C22⋊C8—1064no—
177C4×C8—1064no—
178#95—22no—
179#95—1062no—
180C24—531no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—531no—
184C22×C4—532no—
185C22×C4—532no—
186C22×C4—532no—
187C22×C4—1064no—
188C22×C4—1061no—
189C22×C4—1061no—
190C22×C4—1061no—
191C22×C4—1061no—
192C22×C4—1061no—
193C22×C4—1061no—
194C22×C4—2124no—
195C22×C4C22⋊#615712yes—
196C22×C4C22×#615711yescharacteristic
197C2×C8—2124no—
198C4⋊C4—1064no—
199C4⋊C4—1064no—
200C22⋊C4—1064no—
201C22⋊C4—1064no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—532no—
207C42—532no—
208C42—532no—
209C42—532no—
210C42—1064no—
211C42—1061no—
212C42—1061no—
213C42—2124no—
214C42—2124no—
215C42D53⋊C812yes—
216C42#1171993612yes—
217C23—532no—
218C23—1061no—
219C23—1061no—
220C23—2122no—
221C23C2×C22⋊#615711yescharacteristic
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—534no—
229C2×C4—532no—
230C2×C4—1064no—
231C2×C4—1061no—
232C2×C4—1062no—
233C2×C4—1061no—
234C2×C4—1062no—
235C2×C4—1062no—
236C2×C4—1062no—
237C2×C4—1062no—
238C2×C4—1062no—
239C2×C4—2128no—
240C2×C4—2122no—
241C2×C4—2122no—
242C2×C4#1313329611yescharacteristic
243C2×C4#1313329611yescharacteristic
244C2×C4C2×D53⋊C811yescharacteristic
245C2×C4D53⋊M1611yescharacteristic
246C2×C4D53⋊M1611yescharacteristic
247C2×C4C2×#1171993611yescharacteristic
248C8—4244no—
249C22—22no—
250C22—1062no—
251C22—2122no—
252C22—2122no—
253C22—2122no—
254C22#1681156611yescharacteristic
255C22D53⋊(C22⋊C8)11yescharacteristic
256C22#1681159411yescharacteristic
257C4—42no—
258C4—42no—
259C4—42no—
260C4—1064no—
261C4—1062no—
262C4—1064no—
263C4—2122no—
264C4#1681164111yescharacteristic
265C4#1681164211yescharacteristic
266C4#1681164511yescharacteristic
267C4#1681164611yescharacteristic
268C2—21no—
269C2—21no—
270C2—2122no—
271C2#2029060711yescharacteristic
272C2#2029062512yes—
subgroupG/H
centerC2×C4#13133296
commutatorC2×C4×C53C22×C8
FrattiniC22×C4C22×#6157
FittingC53×#376C4
socleC22×C53#381
prime radicalC23×D53C22⋊C4
cosocleC2×C4×Dic53C23
hypercenter#376#6157
hypocenterC53#8731
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
2. #20289543C2semidirect
3. #20289539C2semidirect
25. #13133174C8semidirect
153. C53#8731semidirect

Maximal subgroups

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

subgroupindex
#202899482
#202895432
#202895392
#202770542
#873153