Finite Group Databasebeta

← #28299968

Subgroups — #28299968

Order 13568.

352 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 86 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#20290642C211yesmaximal, characteristic
2#20290631C211yesmaximal, characteristic
3#20289534C212yesmaximal
4#20289533C212yesmaximal
5#20283101C211yesmaximal, characteristic
6C2×#13133284—21no—
7#16811489—21no—
8#16811489—21no—
9#16811489—21no—
10#16811489C2212yes—
11#16811489C2212yes—
12#16810522C2211yescharacteristic
13#16810521C411yescharacteristic
14#16810519C2211yescharacteristic
15#16810509—21no—
16#16810508—21no—
17#16810505—21no—
18#16810504—21no—
19#16810488C411yescharacteristic
20#16810488C411yescharacteristic
21C42×Dic53C2211yescharacteristic
22C53×#389C411yescharacteristic
23C22×#88324—22no—
24C22×#88324—22no—
25#13133284—42no—
26C2×C4⋊Dic53—21no—
27C2×C4⋊Dic53C2×C411yescharacteristic
28C2×C4⋊Dic53C2×C411yescharacteristic
29C2×#11719919—21no—
30C2×#11719919—21no—
31C2×C4×Dic53C2×C411yescharacteristic
32C2×C4×Dic53D411yescharacteristic
33C2×C4×Dic53D411yescharacteristic
34C2×C4×Dic53D411yescharacteristic
35C2×C4×Dic53D411yescharacteristic
36C2×C4×Dic53C2311yescharacteristic
37#13133124—21no—
38#13133124—21no—
39#13133124—21no—
40#13133124—21no—
41#13133124—21no—
42#13133124—21no—
43#13133124—21no—
44C2×C4⋊C4×C53—21no—
45C2×C4⋊C4×C53C2×C411yescharacteristic
46C2×C4⋊C4×C53C2×C411yescharacteristic
47C2×C42×C53C2×C411yescharacteristic
48#95×C53—21no—
49C22×C4×C53—21no—
50C22×C4×C53—21no—
51C22×C4×C53C22⋊C411yescharacteristic
52C22×C4×C53C22⋊C411yescharacteristic
53C22×C4×C53C22×C411yescharacteristic
54C22×Dic53—21no—
55C22×Dic53—21no—
56C22×Dic53C22⋊C411yescharacteristic
57C22×Dic53C22⋊C411yescharacteristic
58C22×Dic53C2×D411yescharacteristic
59C22×Dic53C2×D411yescharacteristic
60C2×#88324—42no—
61C2×#88324—42no—
62C2×#88324—42no—
63C2×#88324—42no—
64C2×#88324—42no—
65C2×#88324—42no—
66C4⋊C4×C53—22no—
67C4⋊C4×C53—42no—
68C4⋊C4×C53—41no—
69C42×C53—22no—
70C4⋊Dic53—22no—
71C4⋊Dic53—41no—
72C4⋊Dic53—41no—
73C4⋊Dic53—41no—
74#11719919—42no—
75#11719919—42no—
76C4×Dic53—22no—
77C4×Dic53—22no—
78C4×Dic53—21no—
79C4×Dic53—21no—
80C4×Dic53—41no—
81C4×Dic53—41no—
82C4×Dic53—41no—
83C23×C53C2×C22⋊C411yescharacteristic
84C2×C4×C53—21no—
85C2×C4×C53—21no—
86C2×C4×C53—21no—
87C2×C4×C53—21no—
88C2×C4×C53—21no—
89C2×C4×C53—21no—
90C2×C4×C53—21no—
91C2×C4×C53—21no—
92C2×C4×C53—41no—
93C2×C4×C53—41no—
94C2×C4×C53—41no—
95C2×C4×C53—41no—
96C2×C4×C53—41no—
97C2×C4×C53—41no—
98C2×C4×C53#13112yes—
99C2×Dic53—21no—
100C2×Dic53—21no—
101C2×Dic53—21no—
102C2×Dic53—21no—
103C2×Dic53—21no—
104C2×Dic53—21no—
105C2×Dic53—21no—
106C2×Dic53—21no—
107C2×Dic53—21no—
108C2×Dic53—41no—
109C2×Dic53—41no—
110C2×Dic53—41no—
111C2×Dic53—41no—
112C2×Dic53—41no—
113C2×Dic53—41no—
114C2×Dic53#10112yes—
115C2×Dic53#13512yes—
116C2×Dic53AGL(1,ℤ/8)11yescharacteristic
117C2×Dic53#13711yescharacteristic
118#88324—82no—
119#88324—82no—
120#7717—531nomaximal, Sylow
121C22×C53#40811yescharacteristic
122C22×C53#41011yescharacteristic
123C22×C53C2×#10111yescharacteristic
124C22×C53#41611yescharacteristic
125C22×C53#41711yescharacteristic
126C22×C53#42111yescharacteristic
127C22×C53#42111yescharacteristic
128C4×C53—22no—
129C4×C53—41no—
130C4×C53—41no—
131C4×C53—81no—
132C4×C53—81no—
133Dic53—22no—
134Dic53—21no—
135Dic53—21no—
136Dic53—22no—
137Dic53—41no—
138Dic53—81no—
139Dic53—81no—
140#2864—531no—
141#1839—531no—
142#1831—531no—
143#1271—532no—
144#1271—532no—
145C2×C53#147011yescharacteristic
146C2×C53#148211yescharacteristic
147C2×C53#149511yescharacteristic
148C2×C53#151211yescharacteristic
149C2×C53#152111yescharacteristic
150C2×C53#153711yescharacteristic
151C2×C53#155211yescharacteristic
152C2×C4⋊C8—1061no—
153#389—531no—
154#389—531no—
155#389—531no—
156#389#615711yescharacteristic
157#387—1061no—
158#387—1061no—
159#387—1061no—
160#387—1061no—
161#382—531no—
162#382—531no—
163C43—531no—
164#336—532no—
165#336—532no—
166#336—1061no—
167#336—1061no—
168#336—1061no—
169C53#771711yescharacteristic, complemented, Sylow
170C22×C8—1062no—
171C22×C8—1062no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—531no—
174C2×C4⋊C4—531no—
175C2×C4⋊C4—1061no—
176C2×C4⋊C4—1061no—
177C2×C4⋊C4—1061no—
178C2×C4⋊C4C2×#615711yescharacteristic
179C2×C4⋊C4C2×#615711yescharacteristic
180C2×C42—531no—
181C2×C42—531no—
182C2×C42—531no—
183C2×C42—531no—
184C2×C42—531no—
185C2×C42—531no—
186C2×C42C2×#615711yescharacteristic
187C4⋊C8—2122no—
188#95—21no—
189#95—1061no—
190#95—1061no—
191#95—1061no—
192#95—1061no—
193#95—1061no—
194#95—1061no—
195#95—1061no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—531no—
199C22×C4—531no—
200C22×C4—531no—
201C22×C4—531no—
202C22×C4—1061no—
203C22×C4—1061no—
204C22×C4C22⋊#615711yescharacteristic
205C22×C4C22⋊#615711yescharacteristic
206C22×C4C22×#615711yescharacteristic
207C2×C8—2122no—
208C2×C8—2122no—
209C2×C8—2122no—
210C2×C8—2122no—
211C2×C8—2122no—
212C2×C8—2122no—
213C4⋊C4—22no—
214C4⋊C4—41no—
215C4⋊C4—42no—
216C4⋊C4—1062no—
217C4⋊C4—2121no—
218C4⋊C4—2122no—
219C4⋊C4—2122no—
220C4⋊C4—2121no—
221C4⋊C4—2121no—
222C42—22no—
223C42—1061no—
224C42—1062no—
225C42—1062no—
226C42—1061no—
227C42—2121no—
228C42—2121no—
229C42—2121no—
230C23C2×C22⋊#615711yescharacteristic
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—532no—
246C2×C4—532no—
247C2×C4—531no—
248C2×C4—531no—
249C2×C4—1061no—
250C2×C4—1061no—
251C2×C4—1061no—
252C2×C4—1061no—
253C2×C4—1061no—
254C2×C4—1061no—
255C2×C4—1061no—
256C2×C4—1061no—
257C2×C4—1061no—
258C2×C4—2121no—
259C2×C4—2121no—
260C2×C4—2121no—
261C2×C4—2121no—
262C2×C4—2121no—
263C2×C4—2121no—
264C2×C4#1313330412yes—
265C8—4242no—
266C8—4242no—
267C22#1681159611yescharacteristic
268C22#1681160211yescharacteristic
269C22D53⋊#10111yescharacteristic
270C22#1681161311yescharacteristic
271C22#1681161411yescharacteristic
272C22#1681162111yescharacteristic
273C22#1681162211yescharacteristic
274C4—22no—
275C4—41no—
276C4—41no—
277C4—81no—
278C4—81no—
279C4—1061no—
280C4—1061no—
281C4—1062no—
282C4—1062no—
283C4—4241no—
284C4—4241no—
285C4—2121no—
286C2#2028998711yescharacteristic
287C2#2029002811yescharacteristic
288C2#2029007011yescharacteristic
289C2#2029012811yescharacteristic
290C2#2029015711yescharacteristic
291C2#2029020711yescharacteristic
292C2#2029023711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6157
commutatorC22×C4×C53C22×C4
FrattiniC22×C4C22×#6157
FittingC53×#389C4
socle, prime radicalC23×C53C2×C22⋊C4
cosocleC2×C4×Dic53C23
hypercenter#389#6157
hypocenterC53#7717
LCSG ▷ C22×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
169. C53#7717semidirect

Maximal subgroups

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

subgroupindex
#202906422
#202906312
#202895342
#202895332
#202831012
#771753