Finite Group Databasebeta

← #28298803

Subgroups — #28298803

Order 13568.

518 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 62 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#20290549C212yesmaximal
2#20272985C211yesmaximal, characteristic
3C2×#13133278—22no—
4C2×#13133278C414yescomplemented
5#16811593—22no—
6C23×Dic106C2211yescharacteristic
7C2×#13133124—22no—
8C2×#13133124C411yescharacteristic
9C2×#95×C53C411yescharacteristic
10C2×#11719940—24no—
11#13133278—44no—
12#13133278—44no—
13C22⋊#88324—42no—
14C22⋊#88324—42no—
15C22×Dic106—44no—
16C22×Dic106—41no—
17C22×Dic106—41no—
18C22×Dic106C2×C412yes—
19C22×Dic106D411yescharacteristic
20C22×Dic106Q811yescharacteristic
21C23×Dic53—21no—
22C23×Dic53D412yes—
23#13133124—44no—
24#13133124—41no—
25C23×C4×C53—21no—
26C23×C4×C53C2×C411yescharacteristic
27#95×C53—41no—
28C24×C53C22⋊C411yescharacteristic
29C22×C4×C53—21no—
30C22×C4×C53—21no—
31C22×C4×C53—22no—
32C22×C4×C53—42no—
33C22×C4×C53—41no—
34C22×C4×C53—42no—
35C22×C4×C53—42no—
36C22×C4×C53—41no—
37C22×C4×C53C4211yescharacteristic
38C22×C4×C53C4⋊C411yescharacteristic
39C22×Dic53—22no—
40C22×Dic53—22no—
41C22×Dic53—24no—
42C22×Dic53—22no—
43C22×Dic53—42no—
44C22×Dic53—42no—
45C22×Dic53—41no—
46C22×Dic53—42no—
47C22×Dic53—41no—
48C22×Dic53C22⋊C412yes—
49C22×Dic53C4⋊C412yes—
50C2×Dic106—24no—
51C2×Dic106—24no—
52C2×Dic106—42no—
53C2×Dic106—42no—
54C2×Dic106—41no—
55C2×Dic106—42no—
56C2×Dic106—41no—
57C2×Dic106—48no—
58C2×Dic106—48no—
59#11719940—44no—
60#11719940—44no—
61C2×#88324—44no—
62C23×C53—22no—
63C23×C53—21no—
64C23×C53—21no—
65C23×C53—21no—
66C23×C53—21no—
67C23×C53#9511yescharacteristic
68C23×C53#9911yescharacteristic
69C23×C53#9911yescharacteristic
70C2×C4×C53—22no—
71C2×C4×C53—22no—
72C2×C4×C53—21no—
73C2×C4×C53—21no—
74C2×C4×C53—42no—
75C2×C4×C53—42no—
76C2×C4×C53—44no—
77C2×C4×C53—42no—
78C2×C4×C53—82no—
79C2×C4×C53—81no—
80C2×C4×C53—81no—
81C2×Dic53—22no—
82C2×Dic53—22no—
83C2×Dic53—22no—
84C2×Dic53—22no—
85C2×Dic53—22no—
86C2×Dic53—44no—
87C2×Dic53—44no—
88C2×Dic53—44no—
89C2×Dic53—42no—
90C2×Dic53—82no—
91C2×Dic53—81no—
92C2×Dic53—81no—
93C2×Dic53#9914yes—
94Dic106—44no—
95Dic106—48no—
96Dic106—44no—
97#88324—84no—
98#7308—531nomaximal, Sylow
99C22×C53—22no—
100C22×C53—22no—
101C22×C53—22no—
102C22×C53—22no—
103C22×C53—21no—
104C22×C53—21no—
105C22×C53—21no—
106C22×C53—21no—
107C22×C53—21no—
108C22×C53—21no—
109C22×C53#34212yes—
110C22×C53#34211yescharacteristic
111C22×C53#35511yescharacteristic
112C22×C53#35511yescharacteristic
113C22×C53#35611yescharacteristic
114C22×C53#35611yescharacteristic
115C4×C53—41no—
116C4×C53—41no—
117C4×C53—82no—
118Dic53—24no—
119Dic53—42no—
120Dic53—82no—
121#1784—532no—
122#1446—531no—
123C2×C53—21no—
124C2×C53—21no—
125C2×C53—22no—
126C2×C53—21no—
127C2×C53—21no—
128C2×C53#130411yescharacteristic
129C2×C53#139411yescharacteristic
130C2×C53#139411yescharacteristic
131C23×Q8—531no—
132C2×#101—534no—
133C2×#101—1062no—
134#407—1062no—
135C2×#95—531no—
136C2×#95—1062no—
137C2×#95#615711yescharacteristic
138C53#730811yescharacteristic, complemented, Sylow
139C22×Q8—532no—
140C22×Q8—531no—
141C22×Q8—531no—
142C22×Q8—2121no—
143C22×Q8—2121no—
144C22×Q8—2124no—
145C23×C4—21no—
146C23×C4—532no—
147C23×C4—1061no—
148C23×C4C2×#615711yescharacteristic
149C2×M16—1064no—
150#101—2124no—
151#101—2124no—
152C22⋊C8—2122no—
153C22⋊C8—2122no—
154#95—41no—
155#95—2121no—
156#95—2124no—
157C24C22⋊#615711yescharacteristic
158C2×Q8—1064no—
159C2×Q8—1064no—
160C2×Q8—2122no—
161C2×Q8—2122no—
162C2×Q8—2122no—
163C2×Q8—2121no—
164C2×Q8—2121no—
165C2×Q8—2128no—
166C2×Q8—2128no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—22no—
170C22×C4—42no—
171C22×C4—42no—
172C22×C4—41no—
173C22×C4—42no—
174C22×C4—41no—
175C22×C4—532no—
176C22×C4—532no—
177C22×C4—1064no—
178C22×C4—1062no—
179C22×C4—1062no—
180C22×C4—1062no—
181C22×C4—2122no—
182C22×C4—2122no—
183C22×C4—2121no—
184C22×C4—2122no—
185C22×C4—2121no—
186C22×C4C4×#615711yescharacteristic
187C22×C4C4⋊#615711yescharacteristic
188M16—2124no—
189M16—2124no—
190C2×C8—2124no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23—21no—
195C23—22no—
196C23(C2×#6157)⋊C411yescharacteristic
197C23#1313327511yescharacteristic
198C23#1313327611yescharacteristic
199Q8—2124no—
200Q8—2128no—
201Q8—2124no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—44no—
209C2×C4—42no—
210C2×C4—82no—
211C2×C4—81no—
212C2×C4—81no—
213C2×C4—534no—
214C2×C4—1062no—
215C2×C4—1062no—
216C2×C4—1062no—
217C2×C4—1062no—
218C2×C4—1062no—
219C2×C4—4242no—
220C2×C4—4241no—
221C2×C4—4241no—
222C2×C4—2124no—
223C2×C4—2124no—
224C2×C4—2124no—
225C2×C4—2122no—
226C8—4244no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—21no—
232C22—21no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22#1681150012yes—
238C22#1681150111yescharacteristic
239C22#1681153111yescharacteristic
240C22#1681153211yescharacteristic
241C22#1681153311yescharacteristic
242C22#1681153411yescharacteristic
243C4—41no—
244C4—41no—
245C4—82no—
246C4—1064no—
247C4—4242no—
248C4—2122no—
249C2—21no—
250C2—21no—
251C2—21no—
252C2—21no—
253C2—22no—
254C2#2028961411yescharacteristic
255C2#2028981211yescharacteristic
256C2#2028981311yescharacteristic
subgroupG/H
centerC22#16811501
commutatorC22×C4×C53C42
FrattiniC23×C4C2×#6157
FittingC2×#95×C53C4
socleC22×C53#342
prime radicalC24×C53C22⋊C4
cosocleC23×Dic106C22
hypercenterC2×#95#6157
hypocenterC53#7308
LCSG ▷ C22×C4×C53 ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
4. C2×#13133278C4semidirect
138. C53#7308semidirect

Maximal subgroups

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

subgroupindex
#202905492
#202729852
#730853