Finite Group Databasebeta

← #28308111

Subgroups — #28308111

Order 13568.

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

normal subgroups only

This group has 364 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#20289662C212yesmaximal, complemented
3#20289649C212yesmaximal, complemented
4#20283431C211yesmaximal, characteristic
5D53⋊M32—22no—
6#16811520—22no—
7#16811519C2214yes—
8C2×#13133223C2211yescharacteristic
9#16811169C411yescharacteristic
10#16810694—22no—
11#16810692—22no—
12#16810646C2211yescharacteristic
13#16810591C411yescharacteristic
14#16810590C2211yescharacteristic
15C2×#13133127C411yescharacteristic
16C2×#131×C53C411yescharacteristic
17#13133292—42no—
18#13133291—24no—
19D53⋊C16—42no—
20C2×#11719945C2×C411yescharacteristic
21#13133223—42no—
22C2×#11719917C2311yescharacteristic
23C2×#11719912D412yes—
24C22×#88322C2×C411yescharacteristic
25C2×C8×D53D412yes—
26#13133215C811yescharacteristic
27#13133213C811yescharacteristic
28#13133206C811yescharacteristic
29#13133204C811yescharacteristic
30#13133189—22no—
31C4×C22⋊D53—22no—
32C2×C4×Dic53C2×C411yescharacteristic
33#13133146—22no—
34C22⋊#88322—22no—
35#13133129—22no—
36#13133127—21no—
37#13133127—21no—
38C2×#41×C53C2×C411yescharacteristic
39#131×C53—42no—
40C2×M16×C53—21no—
41C2×M16×C53C2×C411yescharacteristic
42C22×C8×C53—21no—
43C22×C8×C53C2×C411yescharacteristic
44#41×C53—41no—
45#41×C53—41no—
46C2×Q8×C53C2×C811yescharacteristic
47C2×D4×C53—21no—
48C2×D4×C53C2×C811yescharacteristic
49C22×C4×C53—21no—
50C22×C4×C53C22×C411yescharacteristic
51C2×C22⋊D53—22no—
52C2×C22⋊D53M1612yes—
53C22×Dic53—21no—
54#11719945—41no—
55#11719945—41no—
56C2×D212C2×C811yescharacteristic
57C2×C4×D53C22⋊C412yes—
58C2×Dic106C2×C811yescharacteristic
59M16×C53—42no—
60M16×C53—41no—
61C2×C8×C53—22no—
62C2×C8×C53—21no—
63C2×C8×C53—42no—
64C2×C8×C53C22⋊C411yescharacteristic
65C2×C8×C53C22⋊C411yescharacteristic
66C22⋊Dic53—22no—
67#11719921—22no—
68#11719919—22no—
69C4×Dic53—21no—
70C4×Dic53C2×C811yescharacteristic
71C4×Dic53C2×C811yescharacteristic
72#11719917—41no—
73C2×#88322—21no—
74C2×#88322—41no—
75C2×#88322C2×D412yes—
76#11719912—42no—
77C8×D53—22no—
78C8×D53—22no—
79#11719910—44no—
80C23×C53—21no—
81C23×C53C2×M1611yescharacteristic
82C22×D53C22⋊C812yes—
83Q8×C53—41no—
84D4×C53—41no—
85D4×C53—42no—
86C2×C4×C53—21no—
87C2×C4×C53—21no—
88C2×C4×C53—21no—
89C2×C4×C53—41no—
90C2×C4×C53—41no—
91C2×C4×C53C2×C22⋊C411yescharacteristic
92C2×C4×C53C22×C811yescharacteristic
93C22⋊D53—42no—
94C22⋊D53—82no—
95C2×Dic53—21no—
96C2×Dic53—21no—
97C2×Dic53—81no—
98C2×Dic53C22⋊C812yes—
99D212—41no—
100C4×D53—22no—
101C4×D53—22no—
102Dic106—41no—
103C8×C53—21no—
104C8×C53—41no—
105C8×C53#9912yes—
106#88322—22no—
107#88322—41no—
108#11486—531nomaximal, Sylow
109C22×C53—21no—
110C22×C53—41no—
111C22×C53—42no—
112C22×C53—41no—
113C22×C53C2×C22⋊C811yescharacteristic
114C2×D53—22no—
115C2×D53—42no—
116C4×C53—21no—
117C4×C53—41no—
118C4×C53C2×#9911yescharacteristic
119C4×C53#41311yescharacteristic
120Dic53—22no—
121Dic53—41no—
122Dic53—41no—
123#2932—531no—
124#2115—532no—
125#1327—532no—
126#1321—532no—
127C2×C53—21no—
128C2×C53—41no—
129C2×C53—81no—
130C2×C53#145911yescharacteristic
131D53—42no—
132C2×#131—531no—
133C2×#131#615711yescharacteristic
134#532—531no—
135C2×M32—1062no—
136#435—1062no—
137#435—1062no—
138#423—531no—
139#408—531no—
140#408—531no—
141C2×#97—531no—
142#349—534no—
143#349—1062no—
144C53#1148611yescharacteristic, complemented, Sylow
145C2×#41—531no—
146C2×#41C2×#615711yescharacteristic
147#131—42no—
148#131—2122no—
149C2×M16—21no—
150C2×M16—531no—
151C2×M16—532no—
152C2×M16C2×#615711yescharacteristic
153C22×C8—21no—
154C22×C8—532no—
155C22×C8—531no—
156C22×C8C2×#615711yescharacteristic
157C4⋊Q8—531no—
158#127—531no—
159#124—531no—
160#124—531no—
161#121—1062no—
162C4×D4—1062no—
163C2×C42—531no—
164M32—1064no—
165M32—2122no—
166C2×C16—2122no—
167C4⋊C8—1062no—
168C22⋊C8—1062no—
169C22⋊C8—1062no—
170#97—1061no—
171#97—1061no—
172#41—41no—
173#41—41no—
174#41—2121no—
175#41—2121no—
176C2×Q8—531no—
177C2×Q8D53⋊C811yescharacteristic
178C2×D4—21no—
179C2×D4—532no—
180C2×D4—531no—
181C2×D4—1062no—
182C2×D4D53⋊C811yescharacteristic
183C22×C4—21no—
184C22×C4—532no—
185C22×C4—1061no—
186C22×C4C22×#615711yescharacteristic
187M16—42no—
188M16—41no—
189M16—2122no—
190M16—2121no—
191C2×C8—22no—
192C2×C8—21no—
193C2×C8—42no—
194C2×C8—532no—
195C2×C8—1062no—
196C2×C8—1062no—
197C2×C8—1061no—
198C2×C8—2121no—
199C2×C8C22⋊#615711yescharacteristic
200C2×C8C22⋊#615711yescharacteristic
201C4⋊C4—1062no—
202C22⋊C4—1062no—
203C22⋊C4—1062no—
204C42—531no—
205C42—531no—
206C42—1061no—
207C16—2124no—
208C23—21no—
209C23—532no—
210C23D53⋊M1611yescharacteristic
211Q8—41no—
212Q8—2121no—
213D4—41no—
214D4—42no—
215D4—4242no—
216D4—2121no—
217D4—2122no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—532no—
224C2×C4—1062no—
225C2×C4—1062no—
226C2×C4—1061no—
227C2×C4—1061no—
228C2×C4—4241no—
229C2×C4C2×C22⋊#615711yescharacteristic
230C2×C4C2×D53⋊C811yescharacteristic
231C8—21no—
232C8—41no—
233C8—1062no—
234C8—2121no—
235C8#1313327512yes—
236C22—21no—
237C22—41no—
238C22—42no—
239C22—41no—
240C22—1062no—
241C22—2122no—
242C22D53⋊(C22⋊C8)11yescharacteristic
243C4—21no—
244C4—41no—
245C4—1062no—
246C4—2121no—
247C4—2121no—
248C4C2×#1313327511yescharacteristic
249C4#1681160911yescharacteristic
250C2—21no—
251C2—41no—
252C2—81no—
253C2—2122no—
254C2#2028995011yescharacteristic
subgroupG/H
centerC4C2×#13133275
commutatorC2×C4×C53C22×C8
FrattiniC22×C4C22×#6157
FittingC2×#131×C53C4
socleC2×C53#1459
prime radical#16811169C4
cosocleC2×#11719917C23
hypercenterC2×#131#6157
hypocenterC53#11486
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C8 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. #20290952C2semidirect
2. #20289662C2semidirect
3. #20289649C2semidirect
144. C53#11486semidirect

Maximal subgroups

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

subgroupindex
#202909522
#202896622
#202896492
#202834312
#1148653