Finite Group Databasebeta

← #28308441

Subgroups — #28308441

Order 13568.

424 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 74 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#20289970C211yesmaximal, characteristic
2#20289954C211yesmaximal, characteristic
3#20289659C214yesmaximal, complemented
4#20279033C211yesmaximal, characteristic
5#16811640—21no—
6#16811594—21no—
7#16811469—21no—
8#16811467—21no—
9#16811466C2212yes—
10#16811466C2212yes—
11C2×C4×C22⋊D53C2211yescharacteristic
12C22×C4⋊Dic53C411yescharacteristic
13#16810563—21no—
14#16810560—21no—
15#16810522—21no—
16#16810500C412yes—
17#16810498C2212yes—
18#16810480—21no—
19C53×#380C411yescharacteristic
20C2×#11719936—41no—
21#13133284—41no—
22#13133274—41no—
23C22⋊#88324—22no—
24C22⋊#88324—22no—
25C4×#88324—41no—
26C22×C22⋊D53C2×C411yescharacteristic
27C23×Dic53C2×C412yes—
28C22×C4×D53D411yescharacteristic
29C4×C22⋊D53—41no—
30C4×C22⋊D53—41no—
31C2×C4⋊Dic53—21no—
32C2×C4⋊Dic53—21no—
33C2×C4⋊Dic53—22no—
34C2×C4⋊Dic53—41no—
35C2×C4⋊Dic53—41no—
36C2×#11719919D411yescharacteristic
37C2×C22⋊Dic53C2311yescharacteristic
38C2×#11719921—22no—
39C2×#11719921D411yescharacteristic
40C2×C4×Dic53D411yescharacteristic
41#13133124—22no—
42#13133124—22no—
43C23×C4×C53C2×C411yescharacteristic
44C2×C4⋊C4×C53—21no—
45C2×C22⋊C4×C53C2×C412yes—
46#95×C53—21no—
47C24×C53C22×C411yescharacteristic
48C23×D53C22⋊C411yescharacteristic
49C22×C4×C53—21no—
50C22×C4×C53—21no—
51C22×C4×C53—22no—
52C22×C4×C53—42no—
53C22×C4×C53C22⋊C411yescharacteristic
54C22×C4×C53C22⋊C411yescharacteristic
55C2×C22⋊D53—22no—
56C2×C22⋊D53—22no—
57C2×C22⋊D53—41no—
58C22×Dic53—22no—
59C22×Dic53—42no—
60C22×Dic53—82no—
61C22×Dic53C22⋊C411yescharacteristic
62C22×Dic53C2×D411yescharacteristic
63C22×Dic53C2×D411yescharacteristic
64C2×C4×D53—21no—
65C2×C4×D53—21no—
66C2×C4×D53—42no—
67C2×#88324—42no—
68C2×#88324—42no—
69#11719936—82no—
70C4⋊C4×C53—42no—
71C22⋊C4×C53—24no—
72C22⋊Dic53—41no—
73#11719921—41no—
74#11719921—82no—
75C4⋊Dic53—42no—
76C4⋊Dic53—41no—
77C4⋊Dic53—41no—
78C4⋊Dic53—82no—
79#11719919—41no—
80C4×Dic53—21no—
81C4×Dic53—21no—
82C23×C53—21no—
83C23×C53—21no—
84C23×C53—41no—
85C23×C53—41no—
86C23×C53C2×C22⋊C411yescharacteristic
87C23×C53#13112yes—
88C22×D53—21no—
89C22×D53—21no—
90C22×D53—21no—
91C22×D53—41no—
92C22×D53—41no—
93C2×C4×C53—22no—
94C2×C4×C53—21no—
95C2×C4×C53—42no—
96C2×C4×C53—42no—
97C2×C4×C53—41no—
98C2×C4×C53—42no—
99C2×C4×C53—42no—
100C2×C4×C53—42no—
101C2×C4×C53#9911yescharacteristic
102C2×C4×C53#9911yescharacteristic
103C22⋊D53—44no—
104C2×Dic53—21no—
105C2×Dic53—21no—
106C2×Dic53—21no—
107C2×Dic53—21no—
108C2×Dic53—41no—
109C2×Dic53—41no—
110C2×Dic53—42no—
111C2×Dic53—42no—
112C2×Dic53—42no—
113C2×Dic53—84no—
114C2×Dic53#10112yes—
115C4×D53—42no—
116C4×D53—81no—
117#88324—82no—
118#88324—82no—
119#11579—531nomaximal, Sylow
120C22×C53—21no—
121C22×C53—21no—
122C22×C53—22no—
123C22×C53—42no—
124C22×C53—42no—
125C22×C53—41no—
126C22×C53—41no—
127C22×C53#40811yescharacteristic
128C22×C53C2×#9911yescharacteristic
129C22×C53C2×#10111yescharacteristic
130C2×D53—42no—
131C2×D53—41no—
132C2×D53—41no—
133C2×D53—41no—
134C2×D53—81no—
135C4×C53—21no—
136C4×C53—41no—
137C4×C53—82no—
138C4×C53#35212yes—
139Dic53—22no—
140Dic53—41no—
141Dic53—41no—
142Dic53—82no—
143#2487—531no—
144#1465—531no—
145#1460—531no—
146#1326—534no—
147C2×C53—21no—
148C2×C53—21no—
149C2×C53—42no—
150C2×C53#147211yescharacteristic
151C2×C53C2×#35211yescharacteristic
152C2×C53#212211yescharacteristic
153D53—81no—
154C2×C4×D4—531no—
155C22×C4⋊C4—531no—
156#431—1061no—
157#407—1061no—
158#400—1061no—
159#399—1061no—
160#389—1061no—
161#386—532no—
162#385—532no—
163#380—1061no—
164#380#615711yescharacteristic
165#324—1061no—
166#323—532no—
167#323—532no—
168#323—1061no—
169C53#1157911yescharacteristic, complemented, Sylow
170C22×D4—531no—
171C23×C4—531no—
172C23×C4—532no—
173C23×C4C2×#615711yescharacteristic
174C2×M16—2121no—
175C4×D4—2121no—
176C4×D4—2121no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—531no—
179C2×C4⋊C4—1062no—
180C2×C4⋊C4—1061no—
181C2×C4⋊C4—1061no—
182C2×C4⋊C4—2121no—
183C2×C4⋊C4—2121no—
184C2×C22⋊C4—531no—
185C2×C22⋊C4—531no—
186C2×C22⋊C4—1062no—
187C2×C22⋊C4C2×#615712yes—
188C2×C42—531no—
189C4⋊C8—2121no—
190C22⋊C8—1062no—
191C22⋊C8—1062no—
192C22⋊C8—2121no—
193C4×C8—2121no—
194#95—21no—
195#95—1062no—
196#95—1062no—
197C24—531no—
198C24C22×#615711yescharacteristic
199C2×D4—1062no—
200C2×D4—1062no—
201C2×D4—2121no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—22no—
205C22×C4—42no—
206C22×C4—531no—
207C22×C4—531no—
208C22×C4—531no—
209C22×C4—1061no—
210C22×C4—1061no—
211C22×C4—1062no—
212C22×C4—4242no—
213C22×C4—2122no—
214C22×C4—2122no—
215C22×C4C22⋊#615711yescharacteristic
216C22×C4C22⋊#615711yescharacteristic
217M16—4242no—
218C2×C8—2122no—
219C2×C8—2122no—
220C4⋊C4—42no—
221C4⋊C4—4242no—
222C4⋊C4—2121no—
223C4⋊C4—2122no—
224C4⋊C4—2121no—
225C4⋊C4—2121no—
226C22⋊C4—24no—
227C22⋊C4—4242no—
228C22⋊C4—2121no—
229C22⋊C4—2121no—
230C42—1061no—
231C42—1061no—
232C23—21no—
233C23—21no—
234C23—41no—
235C23—41no—
236C23—1061no—
237C23—1061no—
238C23—1061no—
239C23—2121no—
240C23—2121no—
241C23C2×C22⋊#615711yescharacteristic
242C23#1313330412yes—
243D4—2124no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—532no—
253C2×C4—1061no—
254C2×C4—1061no—
255C2×C4—1061no—
256C2×C4—1061no—
257C2×C4—4241no—
258C2×C4—4244no—
259C2×C4—2122no—
260C2×C4—2122no—
261C2×C4—2122no—
262C2×C4—2122no—
263C2×C4—2121no—
264C2×C4—2121no—
265C2×C4#1313327611yescharacteristic
266C2×C4#1313327611yescharacteristic
267C8—4242no—
268C8—4242no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—42no—
273C22—42no—
274C22—41no—
275C22—41no—
276C22—4241no—
277C22—2122no—
278C22—2121no—
279C22—2121no—
280C22—2121no—
281C22#1681159711yescharacteristic
282C22C2×#1313327611yescharacteristic
283C22D53⋊#10111yescharacteristic
284C4—21no—
285C4—41no—
286C4—82no—
287C4—1062no—
288C4—4242no—
289C4—2121no—
290C4—2121no—
291C4#1681152612yes—
292C2—21no—
293C2—21no—
294C2—42no—
295C2—4241no—
296C2#2028999311yescharacteristic
297C2C2×#1681152611yescharacteristic
298C2#2029097611yescharacteristic
subgroupG/H
centerC22C2×#13133276
commutatorC24×C53C22×C4
FrattiniC24C22×#6157
FittingC53×#380C4
socleC22×C53C2×#99
prime radicalC22×C22⋊D53C2×C4
cosocleC2×C22⋊Dic53C23
hypercenter#380#6157
hypocenterC53#11579
LCSG ▷ C24×C53 ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #20289659C2semidirect
169. C53#11579semidirect

Maximal subgroups

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

subgroupindex
#202899702
#202899542
#202896592
#202790332
#1157953