Finite Group Databasebeta

← #28308099

Subgroups — #28308099

Order 13568.

382 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 82 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#20290952C212yesmaximal, complemented
2#20289664C212yesmaximal, complemented
3#20289647C212yesmaximal, complemented
4#20283409C211yesmaximal, characteristic
5D53⋊M32—22no—
6#16811520—22no—
7#16811519C2214yes—
8C2×#13133223C2211yescharacteristic
9#16811134C411yescharacteristic
10#16810694—22no—
11C8×C22⋊D53—22no—
12#16810649C2211yescharacteristic
13#16810589C411yescharacteristic
14#16810587C2211yescharacteristic
15#16810578C411yescharacteristic
16C23×C8×C53C411yescharacteristic
17#13133292—42no—
18#13133291—24no—
19D53⋊C16—42no—
20C2×#11719945C2×C411yescharacteristic
21#13133223—41no—
22#13133223—41no—
23C2×#11719917C2×C411yescharacteristic
24C2×#11719917C2311yescharacteristic
25C2×#11719912D412yes—
26C2×C8×D53D412yes—
27#13133200C812yes—
28#13133196—21no—
29#13133191—21no—
30#13133186C812yes—
31C4×C22⋊D53—22no—
32#13133176C2×C411yescharacteristic
33#13133146—22no—
34C22⋊#88322—22no—
35#13133129—22no—
36#13133127—21no—
37C8×Dic53—21no—
38C23×C4×C53C2×C411yescharacteristic
39C22×C8×C53—21no—
40C22×C8×C53—21no—
41C22×C8×C53—41no—
42C22×C8×C53—41no—
43C22×C8×C53C2×C411yescharacteristic
44C22×C8×C53C2×C411yescharacteristic
45C24×C53C2×C811yescharacteristic
46C22×C4×C53—21no—
47C22×C4×C53—21no—
48C22×C4×C53—41no—
49C22×C4×C53—41no—
50C22×C4×C53C2×C811yescharacteristic
51C22×C4×C53C22×C411yescharacteristic
52C2×C22⋊D53—22no—
53C2×C22⋊D53C2×C812yes—
54#11719945—41no—
55#11719945—41no—
56C2×D212M1611yescharacteristic
57C2×C4×D53C22⋊C412yes—
58C2×Dic106M1611yescharacteristic
59C2×C8×C53—21no—
60C2×C8×C53—21no—
61C2×C8×C53—21no—
62C2×C8×C53—42no—
63C2×C8×C53—41no—
64C2×C8×C53—41no—
65C2×C8×C53—41no—
66C2×C8×C53C22⋊C411yescharacteristic
67C2×C8×C53C22⋊C411yescharacteristic
68C22⋊Dic53—22no—
69C22⋊Dic53C2×C812yes—
70#11719921—22no—
71C4⋊Dic53—21no—
72#11719919—22no—
73C4×Dic53—21no—
74#11719917—41no—
75#11719917—41no—
76C2×#88322—21no—
77C2×#88322C2×D412yes—
78#11719912—42no—
79C8×D53—22no—
80C8×D53—22no—
81#11719910—44no—
82C23×C53—21no—
83C23×C53—41no—
84C23×C53—42no—
85C23×C53C22×C811yescharacteristic
86C22×D53C22⋊C812yes—
87C2×C4×C53—21no—
88C2×C4×C53—21no—
89C2×C4×C53—21no—
90C2×C4×C53—42no—
91C2×C4×C53—41no—
92C2×C4×C53—41no—
93C2×C4×C53—41no—
94C2×C4×C53C2×C22⋊C411yescharacteristic
95C2×C4×C53C2×M1611yescharacteristic
96C22⋊D53—42no—
97C22⋊D53—44no—
98C2×Dic53—22no—
99C2×Dic53C22⋊C812yes—
100D212—41no—
101C4×D53—22no—
102C4×D53—22no—
103Dic106—41no—
104C8×C53—21no—
105C8×C53—41no—
106C8×C53#9911yescharacteristic
107C8×C53#9911yescharacteristic
108#88322—22no—
109#88322—41no—
110#11483—531nomaximal, Sylow
111C22×C53—22no—
112C22×C53—21no—
113C22×C53—41no—
114C22×C53—41no—
115C22×C53—42no—
116C22×C53—42no—
117C22×C53—41no—
118C22×C53C2×C22⋊C811yescharacteristic
119C2×D53—22no—
120C2×D53—42no—
121C4×C53—21no—
122C4×C53—41no—
123C4×C53C2×#9911yescharacteristic
124C4×C53#41311yescharacteristic
125Dic53—22no—
126Dic53—42no—
127#2929—531no—
128#2115—532no—
129#1328—532no—
130#1320—532no—
131C2×C53—21no—
132C2×C53—42no—
133C2×C53—41no—
134C2×C53#145911yescharacteristic
135D53—42no—
136C2×#131—531no—
137C23×C8#615711yescharacteristic
138#525—531no—
139C2×M32—1062no—
140#435—1062no—
141C8×D4—1062no—
142#424—531no—
143#408—531no—
144#407—531no—
145#405—531no—
146#349—534no—
147#349—1062no—
148C53#1148311yescharacteristic, complemented, Sylow
149C2×#41—531no—
150C23×C4C2×#615711yescharacteristic
151#131—2121no—
152#131—2121no—
153C2×M16—531no—
154C2×M16—532no—
155C2×M16—531no—
156C22×C8—21no—
157C22×C8—21no—
158C22×C8—41no—
159C22×C8—41no—
160C22×C8—532no—
161C22×C8C2×#615711yescharacteristic
162C22×C8C2×#615711yescharacteristic
163#123—532no—
164C22⋊Q8—1061no—
165#121—1061no—
166#120—532no—
167C4×D4—1062no—
168#117—531no—
169M32—1064no—
170M32—2122no—
171C2×C16—2122no—
172C4⋊C8—1062no—
173C22⋊C8—1062no—
174C22⋊C8—1062no—
175#97—1061no—
176C4×C8—1061no—
177C24D53⋊C811yescharacteristic
178#41—2121no—
179#41—2121no—
180C2×Q8—531no—
181C2×D4—532no—
182C2×D4—531no—
183C2×D4—1062no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—532no—
189C22×C4D53⋊C811yescharacteristic
190C22×C4C22×#615711yescharacteristic
191M16—2122no—
192M16—2121no—
193M16—2121no—
194C2×C8—21no—
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—42no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—532no—
202C2×C8—1062no—
203C2×C8—1062no—
204C2×C8—1061no—
205C2×C8C22⋊#615711yescharacteristic
206C2×C8C22⋊#615711yescharacteristic
207C4⋊C4—1062no—
208C4⋊C4—1061no—
209C22⋊C4—532no—
210C22⋊C4—1062no—
211C22⋊C4—1062no—
212C42—1061no—
213C16—2124no—
214C23—21no—
215C23—41no—
216C23—42no—
217C23—532no—
218C23C2×D53⋊C811yescharacteristic
219Q8—2121no—
220D4—2121no—
221D4—2122no—
222D4—2124no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—532no—
231C2×C4—1062no—
232C2×C4—1062no—
233C2×C4—1062no—
234C2×C4C2×C22⋊#615711yescharacteristic
235C2×C4D53⋊M1611yescharacteristic
236C8—21no—
237C8—41no—
238C8—1062no—
239C8—2121no—
240C8#1313327511yescharacteristic
241C8#1313327511yescharacteristic
242C22—22no—
243C22—21no—
244C22—41no—
245C22—41no—
246C22—42no—
247C22—42no—
248C22—41no—
249C22—1062no—
250C22—2122no—
251C22D53⋊(C22⋊C8)11yescharacteristic
252C4—21no—
253C4—41no—
254C4—1062no—
255C4—2122no—
256C4C2×#1313327511yescharacteristic
257C4#1681160911yescharacteristic
258C2—21no—
259C2—42no—
260C2—41no—
261C2—2122no—
262C2#2028995011yescharacteristic
subgroupG/H
centerC8#13133275
commutatorC23×C53C22×C8
FrattiniC22×C4C22×#6157
FittingC23×C8×C53C4
socleC2×C53#1459
prime radical#16811134C4
cosocleC2×#11719917C23
hypercenterC23×C8#6157
hypocenterC53#11483
LCSG ▷ C23×C53 ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C8 ◁ C2×C8 ◁ C22×C8 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. #20290952C2semidirect
2. #20289664C2semidirect
3. #20289647C2semidirect
148. C53#11483semidirect

Maximal subgroups

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

subgroupindex
#202909522
#202896642
#202896472
#202834092
#1148353