Finite Group Databasebeta

← D53×#1412 #27304435

Subgroups — D53×#1412 #27304435

Order 13568.

390 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 61 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#490×D53C211yesmaximal, characteristic
2#353×D53C212yesmaximal
3#20272886C211yesmaximal, characteristic, complemented
4#20272885C212yesmaximal, complemented
5C53×#1412C211yesmaximal, characteristic, complemented
6#127×D53C2211yescharacteristic
7#125×D53C411yescharacteristic, complemented
8#16810989C411yescharacteristic, complemented
9#16810988C411yescharacteristic, complemented
10#16810987C2211yescharacteristic
11#16810986—22no—
12#102×D53—22no—
13#99×D53—22no—
14#97×D53C411yescharacteristic, complemented
15#16810416C2212yes—
16#16810415—22no—
17C53×#490C2211yescharacteristic
18C53×#353C2212yes—
19C2×D4×D53—41no—
20C2×D4×D53D412yes—
21C2×C8×D53—21no—
22#13133214C2×C411yescharacteristic
23#13133213—41no—
24#13133213D412yes—
25#13133209C2×C411yescharacteristic, complemented
26#13133208—21no—
27#13133207—41no—
28C4⋊C4×D53—21no—
29C4⋊C4×D53—41no—
30C22⋊C4×D53—42no—
31C42×D53C2×C411yescharacteristic
32#13133139—22no—
33#13133138—22no—
34#13133137—22no—
35#13133132—22no—
36#13133131—42no—
37#13133128C2×C411yescharacteristic, complemented
38#13133127—21no—
39#127×C53C2311yescharacteristic
40#125×C53C2×C411yescharacteristic, complemented
41#102×C53—22no—
42#99×C53—22no—
43#97×C53C2×C411yescharacteristic, complemented
44C23×D53—22no—
45C2×D4×C53—41no—
46C2×D4×C53C2×D412yes—
47C2×C22⋊D53—22no—
48C2×C22⋊D53—42no—
49D4×D53—42no—
50D4×D53—42no—
51D4×D53—84no—
52C2×D212—41no—
53C2×D212C22⋊C412yes—
54C2×C4×D53—21no—
55C2×C4×D53—41no—
56C2×C4×D53—82no—
57C2×C4×D53C22⋊C411yescharacteristic
58C2×C8×C53—21no—
59C4⋊C4×C53—21no—
60C4⋊C4×C53—41no—
61C22⋊C4×C53—42no—
62C42×C53C22×C411yescharacteristic
63C22⋊Dic53—42no—
64#11719921—82no—
65C4⋊Dic53—21no—
66C4⋊Dic53—41no—
67#11719919—41no—
68#11719919—41no—
69#11719919—41no—
70C4×Dic53—21no—
71C4×Dic53C22⋊C411yescharacteristic
72C2×#88322—21no—
73C8×D53—41no—
74C8×D53—41no—
75C23×C53—22no—
76C22×D53—22no—
77C22×D53—42no—
78C22×D53—42no—
79C22×D53—84no—
80C22×D53#9911yescharacteristic
81D4×C53—42no—
82D4×C53—82no—
83C2×C4×C53—21no—
84C2×C4×C53—41no—
85C2×C4×C53—82no—
86C2×C4×C53C2×C22⋊C411yescharacteristic
87C22⋊D53—82no—
88C22⋊D53—84no—
89C2×Dic53—21no—
90C2×Dic53—41no—
91C2×Dic53—82no—
92C2×Dic53#9911yescharacteristic
93D212—42no—
94D212—82no—
95C4×D53—21no—
96C4×D53—21no—
97C4×D53—42no—
98C4×D53—82no—
99C4×D53—164no—
100C8×C53—41no—
101#88322—41no—
102C2×#1412—531nomaximal, Sylow
103C22×C53—42no—
104C22×C53—82no—
105C22×C53C2×#9911yescharacteristic
106C2×D53—22no—
107C2×D53—42no—
108C2×D53—84no—
109C2×D53—82no—
110C2×D53—162no—
111C2×D53#35411yescharacteristic
112C2×D53#35411yescharacteristic
113C4×C53—21no—
114C4×C53—41no—
115C4×C53—81no—
116C4×C53—162no—
117Dic53—21no—
118Dic53—41no—
119Dic53—81no—
120Dic53—162no—
121C2×#490—531no—
122C2×#353—532no—
123#1412—531no—
124#1412—532no—
125#1412D5311yescharacteristic, direct product factor
126C2×C53—21no—
127C2×C53—82no—
128C2×C53C2×#35411yescharacteristic
129D53—21no—
130D53—82no—
131D53#141212yesdirect product factor
132C2×#127—531no—
133C2×#125—531no—
134#490—531no—
135#490—531no—
136#490—531no—
137#490—1062no—
138#490C2×D5311yescharacteristic
139C2×#102—1062no—
140C2×#99—1062no—
141C2×#97—531no—
142#353—532no—
143#353—1062no—
144#353C2×D5312yes—
145C53C2×#141211yescharacteristic, complemented, Sylow
146C22×D4—532no—
147C22×D4—2121no—
148C22×C8—1061no—
149#127—532no—
150#127—531no—
151#127—2121no—
152#127C22×D5311yescharacteristic
153#125—531no—
154#125—1061no—
155#125—2121no—
156#125C4×D5311yescharacteristic, complemented
157C2×C4⋊C4—1061no—
158C2×C4⋊C4—2121no—
159C2×C22⋊C4—2122no—
160C2×C42—531no—
161#102—22no—
162#102—1062no—
163#102—1062no—
164#102—1062no—
165#99—22no—
166#99—1062no—
167#99—2122no—
168#97—531no—
169#97—1061no—
170#97C4×D5311yescharacteristic, complemented
171C24—1062no—
172C2×D4—41no—
173C2×D4—532no—
174C2×D4—1062no—
175C2×D4—4244no—
176C2×D4—2121no—
177C2×D4—2122no—
178C2×D4—2122no—
179C2×D4—2122no—
180C2×D4D4×D5312yes—
181C22×C4—531no—
182C22×C4—1061no—
183C22×C4—4242no—
184C22×C4—2121no—
185C2×C8—21no—
186C2×C8—1061no—
187C2×C8—2121no—
188C2×C8—2121no—
189C4⋊C4—21no—
190C4⋊C4—41no—
191C4⋊C4—1061no—
192C4⋊C4—2121no—
193C4⋊C4—2121no—
194C4⋊C4—2121no—
195C4⋊C4—2121no—
196C22⋊C4—42no—
197C22⋊C4—4242no—
198C22⋊C4—2122no—
199C42—531no—
200C42—1061no—
201C42C2×C4×D5311yescharacteristic
202C23—22no—
203C23—531no—
204C23—1062no—
205C23—4244no—
206C23—2122no—
207C23—2122no—
208D4—42no—
209D4—82no—
210D4—4242no—
211D4—4242no—
212D4—4244no—
213D4—2122no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—82no—
217C2×C4—531no—
218C2×C4—8484no—
219C2×C4—1061no—
220C2×C4—1061no—
221C2×C4—1061no—
222C2×C4—4242no—
223C2×C4—4242no—
224C2×C4—2122no—
225C2×C4—2121no—
226C2×C4C22⋊C4×D5311yescharacteristic
227C8—41no—
228C8—2121no—
229C22—42no—
230C22—82no—
231C22—531no—
232C22—531no—
233C22—8482no—
234C22—1062no—
235C22—4242no—
236C22—4244no—
237C22—2122no—
238C22#99×D5311yescharacteristic
239C4—21no—
240C4—41no—
241C4—81no—
242C4—162no—
243C4—8482no—
244C4—1061no—
245C4—4241no—
246C4—2121no—
247C2—21no—
248C2—82no—
249C2—532no—
250C2—1061no—
251C2—4242no—
252C2#354×D5311yescharacteristic
subgroupG/H
centerC2#354×D53
commutatorC42×C53C22×C4
Frattini#127C22×D53
FittingC53×#1412C2
socleC2×C53C2×#354
prime radical#127×D53C22
cosocle#127×C53C23
hypercenter#1412D53
hypocenterC53C2×#1412
LCSG ▷ C42×C53 ▷ C2×C4×C53 ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #1412

Complements

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

NH ≅ G/Ntype
3. #20272886C2semidirect
4. #20272885C2semidirect
5. C53×#1412C2semidirect
7. #125×D53C4semidirect
8. #16810989C4semidirect
9. #16810988C4semidirect
14. #97×D53C4semidirect
25. #13133209C2×C4semidirect
37. #13133128C2×C4semidirect
40. #125×C53C2×C4semidirect
43. #97×C53C2×C4semidirect
125. #1412D53direct (N × H)
131. D53#1412direct (N × H)
145. C53C2×#1412semidirect
156. #125C4×D53semidirect
170. #97C4×D53semidirect

Maximal subgroups

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

subgroupindex
#490×D532
#353×D532
#202728862
#202728852
C53×#14122
C2×#141253