Finite Group Databasebeta

← #28303500

Subgroups — #28303500

Order 13568.

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

normal subgroups only

This group has 384 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
1C4×#13133278C211yesmaximal, characteristic
2#20289977C211yesmaximal, characteristic
3#20289603C212yesmaximal
4#20289574C212yesmaximal
5#20277675C211yesmaximal, characteristic
6#16811644C2212yes—
7C2×#13133278—21no—
8C4×#11719940C2212yes—
9#16811503—21no—
10#16811469—21no—
11#16811468—21no—
12C2×C4×Dic106C2211yescharacteristic
13#16810527—21no—
14#16810506—21no—
15#16810505—21no—
16#16810490C2211yescharacteristic
17#16810487C411yescharacteristic
18#16810474—21no—
19#16810474C411yescharacteristic
20#16810469C411yescharacteristic
21#16810468C2211yescharacteristic
22C53×#383C411yescharacteristic
23C2×#11719940—22no—
24C4⋊#88324—22no—
25#13133278—24no—
26C22⋊#88324—22no—
27#13133272—22no—
28#13133272—22no—
29C4×#88324—22no—
30C22×Dic106D411yescharacteristic
31C4×Dic106—22no—
32C4×Dic106—22no—
33C2×C4⋊Dic53D411yescharacteristic
34C2×#11719919—21no—
35C2×#11719919—21no—
36C2×#11719919D411yescharacteristic
37C2×#11719919D411yescharacteristic
38C2×C4×Dic53—21no—
39C2×C4×Dic53—21no—
40C2×C4×Dic53—21no—
41C2×C4×Dic53C2×C411yescharacteristic
42C2×C4×Dic53C2311yescharacteristic
43#13133124—21no—
44#13133124—21no—
45#13133124—21no—
46#13133124—21no—
47#13133124—21no—
48#13133124C2×C411yescharacteristic
49#13133124C2×C411yescharacteristic
50C2×C42×C53C2×C411yescharacteristic
51#95×C53—21no—
52#95×C53—21no—
53#95×C53C2×C411yescharacteristic
54#95×C53C2×C411yescharacteristic
55C22×C4×C53—21no—
56C22×C4×C53—21no—
57C22×C4×C53C22⋊C411yescharacteristic
58C22×C4×C53C22⋊C411yescharacteristic
59C22×C4×C53C22×C411yescharacteristic
60C22×Dic53—21no—
61C22×Dic53—21no—
62C22×Dic53C22⋊C411yescharacteristic
63C22×Dic53C22⋊C411yescharacteristic
64C22×Dic53C2×D411yescharacteristic
65C22×Dic53C2×D411yescharacteristic
66C2×Dic106—22no—
67C2×Dic106—22no—
68C2×Dic106—41no—
69#11719940—24no—
70#11719940—42no—
71C2×#88324—42no—
72C2×#88324—42no—
73C42×C53—21no—
74C42×C53—21no—
75C4⋊Dic53—22no—
76#11719919—22no—
77#11719919—22no—
78#11719919—42no—
79#11719919—42no—
80C4×Dic53—21no—
81C4×Dic53—21no—
82C4×Dic53—42no—
83C4×Dic53—42no—
84C4×Dic53—42no—
85C4×Dic53#4112yes—
86C4×Dic53#4112yes—
87C23×C53C2×C22⋊C411yescharacteristic
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—41no—
99C2×C4×C53—41no—
100C2×C4×C53#11711yescharacteristic
101C2×C4×C53#11711yescharacteristic
102C2×Dic53—21no—
103C2×Dic53—21no—
104C2×Dic53—21no—
105C2×Dic53—21no—
106C2×Dic53—22no—
107C2×Dic53—21no—
108C2×Dic53—41no—
109C2×Dic53—41no—
110C2×Dic53—41no—
111C2×Dic53—41no—
112C2×Dic53—41no—
113C2×Dic53—41no—
114C2×Dic53—41no—
115C2×Dic53#10412yes—
116C2×Dic53#12312yes—
117C2×Dic53#12312yes—
118Dic106—44no—
119#88324—44no—
120#88324—82no—
121#8775—531nomaximal, Sylow
122C22×C53—21no—
123C22×C53—21no—
124C22×C53#38111yescharacteristic
125C22×C53C2×#10411yescharacteristic
126C22×C53#42111yescharacteristic
127C4×C53—21no—
128C4×C53—21no—
129C4×C53—41no—
130C4×C53—41no—
131C4×C53—81no—
132C4×C53—81no—
133Dic53—22no—
134Dic53—22no—
135Dic53—22no—
136Dic53—42no—
137Dic53—41no—
138Dic53—81no—
139#2356—531no—
140C4×#101—531no—
141#1467—531no—
142#1300—532no—
143#1288—532no—
144C2×C53—21no—
145C2×C53—21no—
146C2×C53#182611yescharacteristic
147C2×C53#182711yescharacteristic
148C2×C53#183011yescharacteristic
149C2×C4×Q8—531no—
150#432—532no—
151C2×#101—1061no—
152C4×M16—532no—
153#391—1061no—
154#387—1061no—
155#387—1061no—
156#383—531no—
157#383#615711yescharacteristic
158#382—531no—
159C4×C4⋊C4—531no—
160C4×C4⋊C4—1061no—
161#376—531no—
162#376—531no—
163#343—1061no—
164#324—1061no—
165#324—1061no—
166C53#877511yescharacteristic, complemented, Sylow
167C22×Q8—531no—
168C2×M16—1062no—
169C4×Q8—1062no—
170C4×Q8—1062no—
171C2×C4⋊C4—531no—
172C2×C4⋊C4—531no—
173C2×C4⋊C4—531no—
174C2×C4⋊C4—1061no—
175C2×C4⋊C4—1061no—
176C2×C42—531no—
177C2×C42—531no—
178C2×C42—1061no—
179C2×C42—1061no—
180C2×C42—1061no—
181C2×C42C2×#615711yescharacteristic
182C4⋊C8—1062no—
183#101—1064no—
184C22⋊C8—1062no—
185#97—1062no—
186#97—1062no—
187C4×C8—1062no—
188#95—21no—
189#95—21no—
190#95—531no—
191#95—531no—
192#95—1061no—
193#95—1061no—
194#95—1061no—
195#95—1061no—
196#95—1061no—
197#95C2×#615711yescharacteristic
198#95C2×#615711yescharacteristic
199C2×Q8—1062no—
200C2×Q8—1062no—
201C2×Q8—2121no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—531no—
205C22×C4—531no—
206C22×C4—531no—
207C22×C4—531no—
208C22×C4—1061no—
209C22×C4—1061no—
210C22×C4C22⋊#615711yescharacteristic
211C22×C4C22⋊#615711yescharacteristic
212C22×C4C22×#615711yescharacteristic
213M16—1064no—
214M16—2122no—
215C2×C8—2122no—
216C2×C8—2122no—
217C4⋊C4—1062no—
218C4⋊C4—1062no—
219C4⋊C4—1062no—
220C4⋊C4—2122no—
221C4⋊C4—2122no—
222C42—21no—
223C42—21no—
224C42—532no—
225C42—532no—
226C42—1061no—
227C42—1061no—
228C42—2122no—
229C42—2122no—
230C42—2122no—
231C23C2×C22⋊#615711yescharacteristic
232Q8—2124no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—41no—
238C2×C4—41no—
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—532no—
248C2×C4—1061no—
249C2×C4—1061no—
250C2×C4—1061no—
251C2×C4—1061no—
252C2×C4—1062no—
253C2×C4—1061no—
254C2×C4—2121no—
255C2×C4—2121no—
256C2×C4—2121no—
257C2×C4—2121no—
258C2×C4—2121no—
259C2×C4—2121no—
260C2×C4—2121no—
261C2×C4#1313329611yescharacteristic
262C2×C4#1313329611yescharacteristic
263C8—4242no—
264C8—2124no—
265C22—21no—
266C22—21no—
267C22#1681156611yescharacteristic
268C22D53⋊#10411yescharacteristic
269C22#1681162011yescharacteristic
270C4—21no—
271C4—21no—
272C4—41no—
273C4—41no—
274C4—81no—
275C4—81no—
276C4—1062no—
277C4—1062no—
278C4—1062no—
279C4—4241no—
280C4—2122no—
281C4—2121no—
282C2—21no—
283C2—21no—
284C2#2029062311yescharacteristic
285C2#2029062511yescharacteristic
286C2#2029062911yescharacteristic
subgroupG/H
centerC22#16811566
commutatorC22×C4×C53C22×C4
FrattiniC22×C4C22×#6157
FittingC53×#383C4
socleC22×C53#381
prime radicalC23×C53C2×C22⋊C4
cosocleC2×C4×Dic53C23
hypercenter#383#6157
hypocenterC53#8775
LCSG ▷ C22×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ #383

Complements

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

NH ≅ G/Ntype
166. C53#8775semidirect

Maximal subgroups

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

subgroupindex
C4×#131332782
#202899772
#202896032
#202895742
#202776752
#877553