Finite Group Databasebeta

← #27294488

Subgroups — #27294488

Order 13568.

358 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 71 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#20280596C211yesmaximal, characteristic
2#20274510C211yesmaximal, characteristic
3#20273037C211yesmaximal, characteristic
4#20272743C211yesmaximal, characteristic
5#20272741C211yesmaximal, characteristic
6#20272721C211yesmaximal, characteristic
7C53×#1346C211yesmaximal, characteristic
8C2×#13133208C411yescharacteristic
9C2×#13133182C2211yescharacteristic
10#16810673—21no—
11C2×#13133135—21no—
12M16×Dic53—21no—
13#16810564—21no—
14#16810563C411yescharacteristic
15#16810562C2211yescharacteristic
16#16810554C411yescharacteristic
17#16810543—21no—
18#16810510—21no—
19#16810509—21no—
20#16810490C411yescharacteristic
21#16810392C2211yescharacteristic
22#16810349C2211yescharacteristic
23#16810348—21no—
24C53×#398C2211yescharacteristic
25C53×#343C2211yescharacteristic
26C53×#324C2211yescharacteristic
27C22×Dic106D411yescharacteristic
28C2×#11719917—21no—
29#13133208—41no—
30#13133208—41no—
31#13133182—41no—
32#13133182—41no—
33C2×C4⋊Dic53—21no—
34C2×C4⋊Dic53C2×C411yescharacteristic
35C2×#11719919—21no—
36C2×#11719919—21no—
37C2×#11719919C2×C411yescharacteristic
38C2×#11719919D411yescharacteristic
39C2×C4×Dic53C2×C411yescharacteristic
40C2×C4×Dic53D411yescharacteristic
41C2×C4×Dic53D411yescharacteristic
42#13133146—41no—
43#13133135—24no—
44C22⋊#88322—21no—
45#13133127—41no—
46C8×Dic53—41no—
47C8×Dic53—41no—
48#13133124—21no—
49#13133124—21no—
50#13133124—21no—
51#13133124—21no—
52#13133124—21no—
53#13133124—21no—
54#13133124—21no—
55#13133124C2×C411yescharacteristic
56C2×M16×C53—21no—
57C2×C4⋊C4×C53—21no—
58C2×C4⋊C4×C53C2×C411yescharacteristic
59C2×C4⋊C4×C53C2311yescharacteristic
60C22⋊C8×C53—21no—
61#95×C53—21no—
62#95×C53C2×C411yescharacteristic
63C22×C4×C53—21no—
64C22×C4×C53—21no—
65C22×C4×C53C22×C411yescharacteristic
66C22×C4×C53C2×D411yescharacteristic
67C22×C4×C53C2×D411yescharacteristic
68C22×Dic53—21no—
69C22×Dic53—21no—
70C22×Dic53C22⋊C411yescharacteristic
71C22×Dic53C22⋊C411yescharacteristic
72C22×Dic53C22⋊C411yescharacteristic
73C22×Dic53C22⋊C411yescharacteristic
74C2×Dic106—21no—
75C2×Dic106—21no—
76C2×Dic106—22no—
77C2×Dic106—41no—
78M16×C53—22no—
79M16×C53—41no—
80C2×C8×C53—41no—
81C2×C8×C53—41no—
82C4⋊C4×C53—41no—
83C4⋊C4×C53—41no—
84C4⋊C4×C53—41no—
85C4⋊C4×C53—41no—
86C4⋊Dic53—41no—
87C4⋊Dic53—41no—
88C4⋊Dic53—41no—
89#11719919—41no—
90#11719919—41no—
91#11719919—42no—
92#11719919—42no—
93C4×Dic53—21no—
94C4×Dic53—21no—
95C4×Dic53—21no—
96C4×Dic53—21no—
97C4×Dic53—21no—
98C4×Dic53—21no—
99#11719917—22no—
100#11719917—41no—
101C2×#88322—41no—
102C2×#88322—41no—
103C23×C53C2×C22⋊C411yescharacteristic
104C2×C4×C53—21no—
105C2×C4×C53—21no—
106C2×C4×C53—21no—
107C2×C4×C53—21no—
108C2×C4×C53—41no—
109C2×C4×C53—41no—
110C2×C4×C53—41no—
111C2×C4×C53—41no—
112C2×C4×C53—41no—
113C2×C4×C53—41no—
114C2×C4×C53—41no—
115C2×C4×C53—41no—
116C2×C4×C53#13511yescharacteristic
117C2×C4×C53#13511yescharacteristic
118C2×Dic53—21no—
119C2×Dic53—21no—
120C2×Dic53—21no—
121C2×Dic53—21no—
122C2×Dic53—21no—
123C2×Dic53—21no—
124C2×Dic53—41no—
125C2×Dic53—41no—
126C2×Dic53—41no—
127C2×Dic53—41no—
128C2×Dic53—42no—
129C2×Dic53—41no—
130C2×Dic53—41no—
131C2×Dic53#9911yescharacteristic
132C2×Dic53#9911yescharacteristic
133C2×Dic53#10412yes—
134Dic106—42no—
135Dic106—42no—
136C8×C53—42no—
137C8×C53—81no—
138#88322—42no—
139#88322—81no—
140#11740—531nomaximal, Sylow
141C22×C53—21no—
142C22×C53—21no—
143C22×C53C2×#9911yescharacteristic
144C22×C53#41611yescharacteristic
145C22×C53C2×#10411yescharacteristic
146C4×C53—21no—
147C4×C53—21no—
148C4×C53—41no—
149C4×C53—41no—
150C4×C53—81no—
151C4×C53—81no—
152Dic53—21no—
153Dic53—21no—
154Dic53—22no—
155Dic53—41no—
156Dic53—41no—
157Dic53—81no—
158Dic53—81no—
159#2634—531no—
160C4×#101—531no—
161#1461—531no—
162#1353—531no—
163#1353—531no—
164#1346—531no—
165#1346D5311yescharacteristic
166C2×C53—21no—
167C2×C53—21no—
168C2×C53#150111yescharacteristic
169C2×C53#212311yescharacteristic
170C2×C53#213311yescharacteristic
171C2×#125—531no—
172C2×C4×Q8—531no—
173#431—1061no—
174C2×#101—1061no—
175C4×M16—1061no—
176#400—531no—
177#400—531no—
178#400—1061no—
179#398—531no—
180#398C2×D5311yescharacteristic
181#395—1061no—
182#387—1061no—
183#387—1061no—
184#383—531no—
185#343—531no—
186#343C2×D5311yescharacteristic
187#324—531no—
188#324—1061no—
189#324C2×D5311yescharacteristic
190C53#1174011yescharacteristic, complemented, Sylow
191C22×Q8—531no—
192C2×M16—21no—
193C2×M16—1061no—
194#125—2121no—
195#125—2121no—
196C4×Q8—2121no—
197C4×Q8—2121no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—531no—
200C2×C4⋊C4—531no—
201C2×C4⋊C4—531no—
202C2×C4⋊C4—1061no—
203C2×C4⋊C4—1061no—
204C2×C4⋊C4—1061no—
205C2×C4⋊C4C4×D5311yescharacteristic
206C2×C4⋊C4C22×D5311yescharacteristic
207C2×C42—531no—
208C2×C42—531no—
209C2×C42—531no—
210C4⋊C8—2121no—
211#101—1064no—
212C22⋊C8—21no—
213C22⋊C8—1061no—
214#97—2121no—
215C4×C8—2121no—
216C4×C8—2121no—
217#95—21no—
218#95—531no—
219#95—1061no—
220#95—1061no—
221#95—1061no—
222#95—1061no—
223#95—1061no—
224#95—1061no—
225#95—1061no—
226#95C4×D5311yescharacteristic
227C2×Q8—1062no—
228C2×Q8—1061no—
229C2×Q8—1061no—
230C2×Q8—2121no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—531no—
234C22×C4—531no—
235C22×C4—531no—
236C22×C4—531no—
237C22×C4—1061no—
238C22×C4—1061no—
239C22×C4C2×C4×D5311yescharacteristic
240C22×C4D4×D5311yescharacteristic
241C22×C4D4×D5311yescharacteristic
242M16—22no—
243M16—41no—
244M16—1062no—
245M16—2121no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—2121no—
249C2×C8—2121no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—2121no—
255C4⋊C4—2121no—
256C4⋊C4—2121no—
257C4⋊C4—2121no—
258C4⋊C4—2121no—
259C4⋊C4—2122no—
260C4⋊C4—2122no—
261C42—1061no—
262C42—1061no—
263C42—1061no—
264C42—1061no—
265C42—1061no—
266C42—1061no—
267C23C22⋊C4×D5311yescharacteristic
268Q8—2122no—
269Q8—2122no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—531no—
283C2×C4—531no—
284C2×C4—532no—
285C2×C4—1061no—
286C2×C4—1061no—
287C2×C4—1061no—
288C2×C4—1061no—
289C2×C4—1061no—
290C2×C4—1061no—
291C2×C4—2121no—
292C2×C4—2121no—
293C2×C4—2121no—
294C2×C4—2122no—
295C2×C4—2121no—
296C2×C4—2121no—
297C2×C4—2121no—
298C2×C4#1313323611yescharacteristic
299C2×C4#1313323811yescharacteristic
300C8—42no—
301C8—81no—
302C8—4241no—
303C8—2122no—
304C22—21no—
305C22—21no—
306C22#99×D5311yescharacteristic
307C22#1681061611yescharacteristic
308C22#104×D5311yescharacteristic
309C4—21no—
310C4—21no—
311C4—41no—
312C4—41no—
313C4—81no—
314C4—81no—
315C4—1062no—
316C4—1061no—
317C4—1061no—
318C4—4241no—
319C4—4241no—
320C4—2121no—
321C4—2121no—
322C2—21no—
323C2—21no—
324C2#2027320311yescharacteristic
325C2#2027636711yescharacteristic
326C2#2027640311yescharacteristic
subgroupG/H
centerC22#99×D53
commutatorC22×C4×C53C22×C4
FrattiniC2×C4⋊C4C22×D53
FittingC53×#1346C2
socleC22×C53C2×#99
prime radicalC23×C53C2×C22⋊C4
cosocleC2×C4⋊C4×C53C23
hypercenter#1346D53
hypocenterC53#11740
LCSG ▷ C22×C4×C53 ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
190. C53#11740semidirect

Maximal subgroups

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

subgroupindex
#202805962
#202745102
#202730372
#202727432
#202727412
#202727212
C53×#13462
#1174053