Finite Group Databasebeta

← #28309170

Subgroups — #28309170

Order 13568.

378 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 70 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
1C4×#13133278C211yesmaximal, characteristic
2#20289977C211yesmaximal, characteristic
3#20289715C212yesmaximal
4#20289713C212yesmaximal
5#20280082C211yesmaximal, characteristic
6#16811644—21no—
7C2×#13133278—21no—
8C4×#11719940—21no—
9#16811503C2212yes—
10#16811469C2212yes—
11#16811468—21no—
12C2×C4×Dic106C411yescharacteristic
13C2×C4×Dic106C2211yescharacteristic
14#16810563C411yescharacteristic
15#16810563C2211yescharacteristic
16#16810544C411yescharacteristic
17#16810544C2211yescharacteristic
18#16810528—21no—
19#16810522—21no—
20#16810508—21no—
21#16810508—21no—
22C53×#382C411yescharacteristic
23C2×#11719940—22no—
24C4⋊#88324—41no—
25#13133278—24no—
26C22⋊#88324—22no—
27#13133272—41no—
28#13133272—41no—
29C4×#88324—41no—
30C22×Dic106C2×C411yescharacteristic
31C22×Dic106D411yescharacteristic
32C4×Dic106—41no—
33C4×Dic106—41no—
34C4×Dic106—41no—
35C4×Dic106—41no—
36C2×C4⋊Dic53—21no—
37C2×C4⋊Dic53—21no—
38C2×C4⋊Dic53C2×C411yescharacteristic
39C2×C4⋊Dic53D411yescharacteristic
40C2×#11719919—21no—
41C2×#11719919C2×C411yescharacteristic
42C2×#11719919C2311yescharacteristic
43C2×C4×Dic53—21no—
44C2×C4×Dic53D411yescharacteristic
45C2×C4×Dic53D411yescharacteristic
46#13133124—21no—
47#13133124—21no—
48#13133124—21no—
49#13133124—21no—
50#13133124—21no—
51#13133124—21no—
52C2×C4⋊C4×C53—21no—
53C2×C42×C53C2×C411yescharacteristic
54#95×C53—21no—
55#95×C53C2×C411yescharacteristic
56#95×C53C2×C411yescharacteristic
57C22×C4×C53—21no—
58C22×C4×C53—21no—
59C22×C4×C53C22⋊C411yescharacteristic
60C22×C4×C53C22⋊C411yescharacteristic
61C22×C4×C53C22×C411yescharacteristic
62C22×Dic53—21no—
63C22×Dic53—21no—
64C22×Dic53C22⋊C411yescharacteristic
65C22×Dic53C22⋊C411yescharacteristic
66C22×Dic53C2×D411yescharacteristic
67C22×Dic53C2×D411yescharacteristic
68C2×Dic106—22no—
69C2×Dic106—22no—
70C2×Dic106—41no—
71C2×Dic106—41no—
72C2×Dic106—42no—
73#11719940—24no—
74#11719940—42no—
75C2×#88324—42no—
76C2×#88324—42no—
77C4⋊C4×C53—42no—
78C42×C53—21no—
79C42×C53—21no—
80C4⋊Dic53—41no—
81C4⋊Dic53—42no—
82C4⋊Dic53—42no—
83C4⋊Dic53—41no—
84#11719919—41no—
85#11719919—41no—
86#11719919—41no—
87#11719919—41no—
88C4×Dic53—21no—
89C4×Dic53—21no—
90C4×Dic53—21no—
91C4×Dic53—21no—
92C4×Dic53—42no—
93C23×C53C2×C22⋊C411yescharacteristic
94C2×C4×C53—21no—
95C2×C4×C53—21no—
96C2×C4×C53—21no—
97C2×C4×C53—41no—
98C2×C4×C53—41no—
99C2×C4×C53—41no—
100C2×C4×C53—41no—
101C2×C4×C53—41no—
102C2×C4×C53—41no—
103C2×C4×C53—41no—
104C2×C4×C53—41no—
105C2×C4×C53#9911yescharacteristic
106C2×C4×C53#9911yescharacteristic
107C2×C4×C53#10412yes—
108C2×Dic53—21no—
109C2×Dic53—21no—
110C2×Dic53—22no—
111C2×Dic53—21no—
112C2×Dic53—21no—
113C2×Dic53—21no—
114C2×Dic53—21no—
115C2×Dic53—21no—
116C2×Dic53—41no—
117C2×Dic53—41no—
118C2×Dic53—41no—
119C2×Dic53—41no—
120C2×Dic53—42no—
121C2×Dic53—41no—
122C2×Dic53#13712yes—
123Dic106—44no—
124Dic106—42no—
125Dic106—42no—
126#88324—44no—
127#88324—82no—
128#11792—531nomaximal, Sylow
129C22×C53—21no—
130C22×C53—21no—
131C22×C53C2×#9911yescharacteristic
132C22×C53#41911yescharacteristic
133C22×C53C2×#10411yescharacteristic
134C4×C53—21no—
135C4×C53—21no—
136C4×C53—22no—
137C4×C53—41no—
138C4×C53—81no—
139C4×C53—81no—
140Dic53—22no—
141Dic53—41no—
142Dic53—42no—
143Dic53—41no—
144Dic53—41no—
145Dic53—81no—
146#2581—531no—
147C4×#101—531no—
148#1467—531no—
149#1354—532no—
150#1353—532no—
151C2×C53—21no—
152C2×C53—21no—
153C2×C53#150811yescharacteristic
154C2×C53#212011yescharacteristic
155C2×C53#213311yescharacteristic
156C2×C4×Q8—531no—
157C2×C4×Q8—531no—
158#432—1061no—
159C2×#101—1061no—
160C4×M16—1061no—
161#400—531no—
162#400—531no—
163#395—531no—
164#395—531no—
165#391—1061no—
166#389—1061no—
167#387—1061no—
168#387—1061no—
169#382#615711yescharacteristic
170#343—532no—
171#324—532no—
172#324—1061no—
173C53#1179211yescharacteristic, complemented, Sylow
174C22×Q8—531no—
175C22×Q8—531no—
176C2×M16—1062no—
177C4×Q8—2121no—
178C4×Q8—2121no—
179C4×Q8—2121no—
180C4×Q8—2121no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—531no—
183C2×C4⋊C4—531no—
184C2×C4⋊C4—531no—
185C2×C4⋊C4—531no—
186C2×C4⋊C4—1061no—
187C2×C4⋊C4—1061no—
188C2×C4⋊C4—1061no—
189C2×C42—531no—
190C2×C42—531no—
191C2×C42—1061no—
192C2×C42C2×#615711yescharacteristic
193C4⋊C8—2121no—
194#101—1064no—
195C22⋊C8—1062no—
196#97—2121no—
197#97—2121no—
198C4×C8—2121no—
199#95—21no—
200#95—1061no—
201#95—1061no—
202#95—1061no—
203#95—1061no—
204#95—1061no—
205#95—1061no—
206#95C2×#615711yescharacteristic
207#95C2×#615711yescharacteristic
208C2×Q8—1062no—
209C2×Q8—1062no—
210C2×Q8—2121no—
211C2×Q8—2121no—
212C2×Q8—2122no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—531no—
216C22×C4—531no—
217C22×C4—531no—
218C22×C4—531no—
219C22×C4—1061no—
220C22×C4—1061no—
221C22×C4C22⋊#615711yescharacteristic
222C22×C4C22⋊#615711yescharacteristic
223C22×C4C22×#615711yescharacteristic
224M16—1064no—
225M16—2122no—
226C2×C8—2122no—
227C2×C8—2122no—
228C4⋊C4—42no—
229C4⋊C4—2121no—
230C4⋊C4—2121no—
231C4⋊C4—2121no—
232C4⋊C4—2121no—
233C4⋊C4—2122no—
234C4⋊C4—2122no—
235C4⋊C4—2121no—
236C4⋊C4—2121no—
237C42—21no—
238C42—21no—
239C42—1061no—
240C42—1061no—
241C42—1061no—
242C42—1061no—
243C42—2122no—
244C23C2×C22⋊#615711yescharacteristic
245Q8—2124no—
246Q8—2122no—
247Q8—2122no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—532no—
260C2×C4—1061no—
261C2×C4—1061no—
262C2×C4—1062no—
263C2×C4—1061no—
264C2×C4—1061no—
265C2×C4—1061no—
266C2×C4—1061no—
267C2×C4—1061no—
268C2×C4—2122no—
269C2×C4—2121no—
270C2×C4—2121no—
271C2×C4—2121no—
272C2×C4—2121no—
273C2×C4—2121no—
274C2×C4#1313327611yescharacteristic
275C2×C4#1313327611yescharacteristic
276C2×C4#1313328112yes—
277C8—4242no—
278C8—2124no—
279C22—21no—
280C22—21no—
281C22C2×#1313327611yescharacteristic
282C22#1681161611yescharacteristic
283C22C2×#1313328111yescharacteristic
284C4—22no—
285C4—21no—
286C4—21no—
287C4—41no—
288C4—81no—
289C4—81no—
290C4—1062no—
291C4—4241no—
292C4—2121no—
293C4—2121no—
294C4—2122no—
295C4—2121no—
296C2—21no—
297C2—21no—
298C2#2029011411yescharacteristic
299C2#2029096811yescharacteristic
300C2#2029101211yescharacteristic
subgroupG/H
centerC22C2×#13133276
commutatorC22×C4×C53C22×C4
FrattiniC22×C4C22×#6157
FittingC53×#382C4
socleC22×C53C2×#99
prime radicalC23×C53C2×C22⋊C4
cosocleC2×#11719919C23
hypercenter#382#6157
hypocenterC53#11792
LCSG ▷ C22×C4×C53 ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
173. C53#11792semidirect

Maximal subgroups

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

subgroupindex
C4×#131332782
#202899772
#202897152
#202897132
#202800822
#1179253