Finite Group Databasebeta

← #28303481

Subgroups — #28303481

Order 13568.

378 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 80 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#20290581C211yesmaximal, characteristic
2#20289957C211yesmaximal, characteristic
3#20289613C212yesmaximal
4#20289568C212yesmaximal
5#20277675C211yesmaximal, characteristic
6#16811640C2212yes—
7#16811626C2212yes—
8C2×#13133278—21no—
9#16811503—21no—
10#16811469—21no—
11#16811468—21no—
12C2×C4×Dic106C2211yescharacteristic
13#16810527—21no—
14#16810506—21no—
15#16810505—21no—
16#16810490C411yescharacteristic
17#16810487C2211yescharacteristic
18#16810474—21no—
19#16810474C2211yescharacteristic
20#16810469C411yescharacteristic
21#16810468C411yescharacteristic
22C53×#383C411yescharacteristic
23C2×#11719940—22no—
24#13133284—22no—
25#13133284—22no—
26C4⋊#88324—22no—
27#13133278—42no—
28C22⋊#88324—22no—
29C4×#88324—22no—
30C22×Dic106D411yescharacteristic
31C4×Dic106—22no—
32C4×Dic106—22no—
33C2×C4⋊Dic53D411yescharacteristic
34C2×#11719919—21no—
35C2×#11719919—21no—
36C2×#11719919D411yescharacteristic
37C2×#11719919D411yescharacteristic
38C2×C4×Dic53—21no—
39C2×C4×Dic53—21no—
40C2×C4×Dic53—21no—
41C2×C4×Dic53C2×C411yescharacteristic
42C2×C4×Dic53C2311yescharacteristic
43#13133124—21no—
44#13133124—21no—
45#13133124—21no—
46#13133124—21no—
47#13133124—21no—
48#13133124C2×C411yescharacteristic
49#13133124C2×C411yescharacteristic
50C2×C42×C53C2×C411yescharacteristic
51#95×C53—21no—
52#95×C53—21no—
53#95×C53C2×C411yescharacteristic
54#95×C53C2×C411yescharacteristic
55C22×C4×C53—21no—
56C22×C4×C53—21no—
57C22×C4×C53C22⋊C411yescharacteristic
58C22×C4×C53C22⋊C411yescharacteristic
59C22×C4×C53C22×C411yescharacteristic
60C22×Dic53—21no—
61C22×Dic53—21no—
62C22×Dic53C22⋊C411yescharacteristic
63C22×Dic53C22⋊C411yescharacteristic
64C22×Dic53C2×D411yescharacteristic
65C22×Dic53C2×D411yescharacteristic
66C2×Dic106—22no—
67C2×Dic106—22no—
68C2×Dic106—21no—
69C2×Dic106—21no—
70#11719940—42no—
71#11719940—42no—
72C2×#88324—42no—
73C2×#88324—42no—
74C42×C53—21no—
75C42×C53—21no—
76C4⋊Dic53—22no—
77#11719919—22no—
78#11719919—22no—
79#11719919—42no—
80#11719919—41no—
81#11719919—41no—
82C4×Dic53—21no—
83C4×Dic53—21no—
84C4×Dic53—42no—
85C4×Dic53—42no—
86C4×Dic53—42no—
87C4×Dic53#4112yes—
88C4×Dic53#4112yes—
89C23×C53C2×C22⋊C411yescharacteristic
90C2×C4×C53—21no—
91C2×C4×C53—21no—
92C2×C4×C53—21no—
93C2×C4×C53—21no—
94C2×C4×C53—41no—
95C2×C4×C53—41no—
96C2×C4×C53—41no—
97C2×C4×C53—41no—
98C2×C4×C53—41no—
99C2×C4×C53—41no—
100C2×C4×C53—41no—
101C2×C4×C53—41no—
102C2×C4×C53#11711yescharacteristic
103C2×C4×C53#11711yescharacteristic
104C2×Dic53—22no—
105C2×Dic53—21no—
106C2×Dic53—21no—
107C2×Dic53—21no—
108C2×Dic53—21no—
109C2×Dic53—41no—
110C2×Dic53—41no—
111C2×Dic53—41no—
112C2×Dic53—41no—
113C2×Dic53—41no—
114C2×Dic53—41no—
115C2×Dic53—41no—
116C2×Dic53#12312yes—
117C2×Dic53#12312yes—
118C2×Dic53#13512yes—
119C2×Dic53AGL(1,ℤ/8)11yescharacteristic
120C2×Dic53#13711yescharacteristic
121Dic106—42no—
122Dic106—42no—
123#88324—82no—
124#88324—82no—
125#8769—531nomaximal, Sylow
126C22×C53—21no—
127C22×C53—21no—
128C22×C53#38111yescharacteristic
129C22×C53#41611yescharacteristic
130C22×C53#41711yescharacteristic
131C4×C53—21no—
132C4×C53—21no—
133C4×C53—41no—
134C4×C53—41no—
135C4×C53—81no—
136C4×C53—81no—
137Dic53—22no—
138Dic53—42no—
139Dic53—41no—
140Dic53—41no—
141Dic53—81no—
142Dic53#48212yes—
143Dic53#48512yes—
144#2356—531no—
145#1801—531no—
146#1461—531no—
147#1303—532no—
148#1286—532no—
149C2×C53—21no—
150C2×C53—21no—
151C2×C53#182511yescharacteristic
152C2×C53#182711yescharacteristic
153C2×C53#183011yescharacteristic
154C2×C4×Q8—531no—
155#431—532no—
156#423—532no—
157C2×#101—1061no—
158#391—1061no—
159#387—1061no—
160#387—1061no—
161#383—531no—
162#383#615711yescharacteristic
163#382—531no—
164C4×C4⋊C4—531no—
165C4×C4⋊C4—1061no—
166#376—531no—
167#376—531no—
168#343—1061no—
169#324—1061no—
170#324—1061no—
171C53#876911yescharacteristic, complemented, Sylow
172C22×Q8—531no—
173C2×M16—1062no—
174C4×Q8—1062no—
175C4×Q8—1062no—
176C2×C4⋊C4—531no—
177C2×C4⋊C4—531no—
178C2×C4⋊C4—531no—
179C2×C4⋊C4—1061no—
180C2×C4⋊C4—1061no—
181C2×C42—531no—
182C2×C42—531no—
183C2×C42—1061no—
184C2×C42—1061no—
185C2×C42—1061no—
186C2×C42C2×#615711yescharacteristic
187C4⋊C8—1062no—
188C4⋊C8—1062no—
189C4⋊C8—1062no—
190#101—2122no—
191C22⋊C8—1062no—
192C4×C8—1062no—
193#95—21no—
194#95—21no—
195#95—531no—
196#95—531no—
197#95—1061no—
198#95—1061no—
199#95—1061no—
200#95—1061no—
201#95—1061no—
202#95C2×#615711yescharacteristic
203#95C2×#615711yescharacteristic
204C2×Q8—1061no—
205C2×Q8—1062no—
206C2×Q8—1062no—
207C2×Q8—1061no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—531no—
211C22×C4—531no—
212C22×C4—531no—
213C22×C4—531no—
214C22×C4—1061no—
215C22×C4—1061no—
216C22×C4C22⋊#615711yescharacteristic
217C22×C4C22⋊#615711yescharacteristic
218C22×C4C22×#615711yescharacteristic
219M16—2122no—
220M16—2122no—
221C2×C8—2122no—
222C2×C8—2122no—
223C4⋊C4—1062no—
224C4⋊C4—1062no—
225C4⋊C4—1062no—
226C4⋊C4—2121no—
227C4⋊C4—2121no—
228C4⋊C4—2122no—
229C42—21no—
230C42—21no—
231C42—532no—
232C42—532no—
233C42—1061no—
234C42—1061no—
235C42—2122no—
236C42—2122no—
237C42—2122no—
238C23C2×C22⋊#615711yescharacteristic
239Q8—2122no—
240Q8—2122no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—532no—
254C2×C4—532no—
255C2×C4—531no—
256C2×C4—531no—
257C2×C4—532no—
258C2×C4—1062no—
259C2×C4—1061no—
260C2×C4—1061no—
261C2×C4—1061no—
262C2×C4—1061no—
263C2×C4—2121no—
264C2×C4—2121no—
265C2×C4—2121no—
266C2×C4—2121no—
267C2×C4—2121no—
268C2×C4—2121no—
269C2×C4—2121no—
270C2×C4#1313329611yescharacteristic
271C2×C4#1313329611yescharacteristic
272C8—4242no—
273C8—4242no—
274C22—21no—
275C22—21no—
276C22#1681156611yescharacteristic
277C22#1681161311yescharacteristic
278C22#1681161411yescharacteristic
279C4—21no—
280C4—21no—
281C4—41no—
282C4—41no—
283C4—81no—
284C4—81no—
285C4—532no—
286C4—532no—
287C4—1062no—
288C4—4241no—
289C4—2122no—
290C4—2121no—
291C4—2121no—
292C2—21no—
293C2—21no—
294C2#2029062011yescharacteristic
295C2#2029062511yescharacteristic
296C2#2029062911yescharacteristic
subgroupG/H
centerC22#16811566
commutatorC22×C4×C53C22×C4
FrattiniC22×C4C22×#6157
FittingC53×#383C4
socleC22×C53#381
prime radicalC23×C53C2×C22⋊C4
cosocleC2×C4×Dic53C23
hypercenter#383#6157
hypocenterC53#8769
LCSG ▷ C22×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ #383

Complements

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

NH ≅ G/Ntype
171. C53#8769semidirect

Maximal subgroups

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

subgroupindex
#202905812
#202899572
#202896132
#202895682
#202776752
#876953