Finite Group Databasebeta

← D53⋊#1328 #28307998

Subgroups — D53⋊#1328 #28307998

Order 13568.

378 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 88 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
1D53⋊#349C212yesmaximal
2#20289664C212yesmaximal, complemented
3#20289663C212yesmaximal, complemented
4#424×D53C211yesmaximal, characteristic
5D53⋊M32—22no—
6#16811520—22no—
7#16811519C2214yes—
8C2×M16×D53C2211yescharacteristic
9C22×C8×D53C411yescharacteristic
10#117×D53C411yescharacteristic
11#16810651C411yescharacteristic
12#16810650C2211yescharacteristic
13#16810649C2211yescharacteristic
14#16810648—22no—
15C4⋊C8×D53—22no—
16C53×#424C411yescharacteristic
17#13133292—42no—
18#13133291—24no—
19D53⋊C16—42no—
20C22×C4×D53C2×C411yescharacteristic
21C2×#11719917C2311yescharacteristic
22C2×#11719912D412yes—
23M16×D53—41no—
24M16×D53—41no—
25C22×#88322C2×C411yescharacteristic
26C2×C8×D53—21no—
27C2×C8×D53—21no—
28C2×C8×D53—41no—
29C2×C8×D53—41no—
30C2×C8×D53D412yes—
31#13133176C2×C411yescharacteristic
32#13133175—21no—
33#13133174—21no—
34#13133173C812yes—
35C4⋊C4×D53—21no—
36C22⋊C4×D53C812yes—
37C42×D53—21no—
38C4⋊#88322—22no—
39#13133146—22no—
40#13133146—22no—
41C2×M16×C53C2×C411yescharacteristic
42C22×C8×C53C2×C411yescharacteristic
43#117×C53C2×C411yescharacteristic
44C4⋊C8×C53—22no—
45C23×D53C2×C811yescharacteristic
46C22×C4×C53C22×C411yescharacteristic
47C22×Dic53C2×C811yescharacteristic
48C2×C4×D53—21no—
49C2×C4×D53—21no—
50C2×C4×D53—21no—
51C2×C4×D53—21no—
52C2×C4×D53—22no—
53C2×C4×D53C22⋊C411yescharacteristic
54C2×C4×D53C22⋊C411yescharacteristic
55C2×C4×D53M1611yescharacteristic
56C2×C4×D53M1611yescharacteristic
57M16×C53—41no—
58C2×C8×C53—21no—
59C2×C8×C53—41no—
60C2×C8×C53C22⋊C412yes—
61C4⋊C4×C53—21no—
62C22⋊C4×C53C2×C812yes—
63C42×C53—21no—
64C22⋊Dic53C2×C812yes—
65#11719921—22no—
66C4⋊Dic53—21no—
67#11719919—22no—
68C4×Dic53—21no—
69C4×Dic53—22no—
70#11719917—41no—
71C2×#88322—21no—
72C2×#88322—41no—
73C2×#88322C2×D412yes—
74#11719912—42no—
75C8×D53—22no—
76C8×D53—22no—
77C8×D53—42no—
78C8×D53—41no—
79C8×D53—41no—
80#11719910—44no—
81C23×C53C22×C811yescharacteristic
82C22×D53—21no—
83C22×D53—21no—
84C22×D53—42no—
85C22×D53C22⋊C811yescharacteristic
86C22×D53C22⋊C811yescharacteristic
87C2×C4×C53—21no—
88C2×C4×C53—21no—
89C2×C4×C53—22no—
90C2×C4×C53C2×C22⋊C411yescharacteristic
91C2×C4×C53C2×M1611yescharacteristic
92C2×Dic53—21no—
93C2×Dic53—21no—
94C2×Dic53—22no—
95C2×Dic53C22⋊C811yescharacteristic
96C2×Dic53C22⋊C811yescharacteristic
97C4×D53—21no—
98C4×D53—21no—
99C4×D53—21no—
100C4×D53—21no—
101C4×D53—21no—
102C4×D53—21no—
103C4×D53—44no—
104C4×D53#9911yescharacteristic
105C4×D53#9911yescharacteristic
106C4×D53#10111yescharacteristic
107C4×D53#10111yescharacteristic
108C8×C53—22no—
109C8×C53—41no—
110#88322—22no—
111#88322—41no—
112C2×#1328—531nomaximal, Sylow
113C22×C53—21no—
114C22×C53—41no—
115C22×C53C2×C22⋊C811yescharacteristic
116C2×D53—22no—
117C2×D53—21no—
118C2×D53—42no—
119C2×D53—42no—
120C2×D53—41no—
121C2×D53#32411yescharacteristic
122C2×D53#32411yescharacteristic
123C4×C53—21no—
124C4×C53—42no—
125C4×C53C2×#9911yescharacteristic
126C4×C53C2×#10111yescharacteristic
127Dic53—21no—
128Dic53—42no—
129Dic53#32411yescharacteristic
130Dic53#32411yescharacteristic
131C2×#424—531no—
132C2×#349—532no—
133#1328—532no—
134#1328—532no—
135C2×C53—21no—
136C2×C53—41no—
137C2×C53C2×#32411yescharacteristic
138D53—21no—
139D53—41no—
140D53#132812yescomplemented
141C22×M16—531no—
142C23×C8—531no—
143C2×#117—531no—
144C2×M32—1062no—
145#424—531no—
146#424—531no—
147#424—531no—
148#424—1062no—
149#424#615711yescharacteristic
150C2×C4⋊C8—1062no—
151#349—534no—
152#349—1062no—
153C53C2×#132811yescharacteristic, complemented, Sylow
154C23×C4—531no—
155C2×M16—531no—
156C2×M16—532no—
157C2×M16—2121no—
158C2×M16—2121no—
159C2×M16C2×#615711yescharacteristic
160C22×C8—532no—
161C22×C8—531no—
162C22×C8—1061no—
163C22×C8—1061no—
164C22×C8—2121no—
165C22×C8—2121no—
166C22×C8C2×#615711yescharacteristic
167#117—531no—
168#117—532no—
169#117—1061no—
170#117—1061no—
171#117C2×#615711yescharacteristic
172C2×C4⋊C4—1061no—
173C2×C22⋊C4—532no—
174C2×C42—1061no—
175M32—1064no—
176M32—2122no—
177C2×C16—2122no—
178C4⋊C8—22no—
179C4⋊C8—1062no—
180C4⋊C8—1062no—
181C4⋊C8—1062no—
182C24—531no—
183C22×C4—531no—
184C22×C4—531no—
185C22×C4—531no—
186C22×C4—531no—
187C22×C4—531no—
188C22×C4—1061no—
189C22×C4—1061no—
190C22×C4—1061no—
191C22×C4—1061no—
192C22×C4—1062no—
193C22×C4C22×#615711yescharacteristic
194M16—41no—
195M16—2122no—
196M16—2121no—
197C2×C8—21no—
198C2×C8—41no—
199C2×C8—532no—
200C2×C8—1062no—
201C2×C8—1062no—
202C2×C8—1061no—
203C2×C8—2121no—
204C2×C8—2121no—
205C2×C8—2122no—
206C2×C8—2121no—
207C2×C8C22⋊#615712yes—
208C4⋊C4—21no—
209C4⋊C4—1062no—
210C4⋊C4—1061no—
211C22⋊C4—532no—
212C22⋊C4—1062no—
213C22⋊C4D53⋊C812yes—
214C42—21no—
215C42—1062no—
216C42—1061no—
217C16—2124no—
218C23—531no—
219C23—531no—
220C23—1061no—
221C23—1061no—
222C23—2122no—
223C23C2×D53⋊C811yescharacteristic
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—531no—
228C2×C4—531no—
229C2×C4—531no—
230C2×C4—531no—
231C2×C4—531no—
232C2×C4—531no—
233C2×C4—1061no—
234C2×C4—1061no—
235C2×C4—1061no—
236C2×C4—1061no—
237C2×C4—1061no—
238C2×C4—1061no—
239C2×C4—1061no—
240C2×C4—1061no—
241C2×C4—1062no—
242C2×C4—2124no—
243C2×C4C2×C22⋊#615711yescharacteristic
244C2×C4D53⋊M1611yescharacteristic
245C8—22no—
246C8—41no—
247C8—1062no—
248C8—2121no—
249C22—21no—
250C22—41no—
251C22—531no—
252C22—531no—
253C22—1062no—
254C22—1061no—
255C22—2121no—
256C22—2122no—
257C22—2122no—
258C22D53⋊(C22⋊C8)11yescharacteristic
259C4—21no—
260C4—42no—
261C4—531no—
262C4—531no—
263C4—1061no—
264C4—2122no—
265C4D53⋊#9911yescharacteristic
266C4D53⋊#10111yescharacteristic
267C2—21no—
268C2—41no—
269C2—532no—
270C2—1061no—
271C2—2121no—
272C2D53⋊#32411yescharacteristic
subgroupG/H
centerC4D53⋊#99
commutatorC23×C53C22×C8
FrattiniC22×C4C22×#6157
FittingC53×#424C4
socleC2×C53C2×#324
prime radicalC23×D53C2×C8
cosocleC2×#11719917C23
hypercenter#424#6157
hypocenterC53C2×#1328
LCSG ▷ C23×C53 ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #20289664C2semidirect
3. #20289663C2semidirect
140. D53#1328semidirect
153. C53C2×#1328semidirect

Maximal subgroups

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

subgroupindex
D53⋊#3492
#202896642
#202896632
#424×D532
C2×#132853