Finite Group Databasebeta

← #28303474

Subgroups — #28303474

Order 13568.

422 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 90 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#20277635C211yesmaximal, characteristic
6#16811640C2212yes—
7#16811626C2212yes—
8C2×#13133278—21no—
9#16811503—21no—
10#16811469—21no—
11#16811468—21no—
12C2×C4×Dic106—21no—
13C2×C4×Dic106C2211yescharacteristic
14#16810521—21no—
15#16810518—21no—
16#16810518—21no—
17#16810489C411yescharacteristic
18#16810487C411yescharacteristic
19#16810487C2211yescharacteristic
20#16810474C411yescharacteristic
21#16810474C2211yescharacteristic
22C4×C4⋊C4×C53C411yescharacteristic
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—
33C4×Dic106—42no—
34C4×Dic106—42no—
35C2×C4⋊Dic53—21no—
36C2×C4⋊Dic53D411yescharacteristic
37C2×#11719919—21no—
38C2×#11719919—21no—
39C2×#11719919—21no—
40C2×#11719919—21no—
41C2×#11719919D411yescharacteristic
42C2×#11719919D411yescharacteristic
43C2×C4×Dic53—21no—
44C2×C4×Dic53—21no—
45C2×C4×Dic53C2×C411yescharacteristic
46C2×C4×Dic53C2311yescharacteristic
47#13133124—21no—
48#13133124—21no—
49#13133124—21no—
50#13133124C2×C411yescharacteristic
51#13133124C2×C411yescharacteristic
52C2×C4⋊C4×C53—21no—
53C2×C42×C53—21no—
54C2×C42×C53C2×C411yescharacteristic
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×Dic106D812yes—
71C2×Dic106SD1612yes—
72#11719940—42no—
73#11719940—42no—
74C2×#88324—42no—
75C2×#88324—42no—
76C4⋊C4×C53—42no—
77C42×C53—21no—
78C42×C53—21no—
79C42×C53—42no—
80C4⋊Dic53—22no—
81C4⋊Dic53—42no—
82#11719919—22no—
83#11719919—22no—
84#11719919—42no—
85#11719919—42no—
86#11719919—42no—
87#11719919—41no—
88#11719919—41no—
89C4×Dic53—21no—
90C4×Dic53—21no—
91C4×Dic53—42no—
92C4×Dic53—41no—
93C4×Dic53—41no—
94C4×Dic53#4112yes—
95C4×Dic53#4112yes—
96C23×C53C2×C22⋊C411yescharacteristic
97C2×C4×C53—21no—
98C2×C4×C53—21no—
99C2×C4×C53—22no—
100C2×C4×C53—21no—
101C2×C4×C53—41no—
102C2×C4×C53—41no—
103C2×C4×C53—41no—
104C2×C4×C53—41no—
105C2×C4×C53—41no—
106C2×C4×C53—41no—
107C2×C4×C53—41no—
108C2×C4×C53#10212yes—
109C2×C4×C53#11711yescharacteristic
110C2×C4×C53#11711yescharacteristic
111C2×Dic53—21no—
112C2×Dic53—21no—
113C2×Dic53—21no—
114C2×Dic53—41no—
115C2×Dic53—41no—
116C2×Dic53—41no—
117C2×Dic53—41no—
118C2×Dic53—41no—
119C2×Dic53—41no—
120C2×Dic53—41no—
121C2×Dic53—41no—
122C2×Dic53#10212yes—
123C2×Dic53#12312yes—
124C2×Dic53#12312yes—
125C2×Dic53C2×D811yescharacteristic
126C2×Dic53C2×SD1611yescharacteristic
127C2×Dic53#13712yes—
128Dic106—24no—
129Dic106—24no—
130#88324—82no—
131#88324—82no—
132#8766—531nomaximal, Sylow
133C22×C53—21no—
134C22×C53—21no—
135C22×C53#38111yescharacteristic
136C22×C53C2×#10211yescharacteristic
137C22×C53#41911yescharacteristic
138C4×C53—22no—
139C4×C53—21no—
140C4×C53—21no—
141C4×C53—42no—
142C4×C53—41no—
143C4×C53—81no—
144Dic53—22no—
145Dic53—22no—
146Dic53—41no—
147Dic53—81no—
148Dic53—81no—
149Dic53#48012yes—
150Dic53#48312yes—
151#2351—531no—
152#1801—531no—
153#1461—531no—
154#1303—532no—
155#1286—532no—
156C2×C53—21no—
157C2×C53—21no—
158C2×C53#182311yescharacteristic
159C2×C53#182711yescharacteristic
160C2×C53#183011yescharacteristic
161C2×C4×Q8—531no—
162C2×C4×Q8—1061no—
163#431—532no—
164#423—532no—
165C2×#101—1061no—
166#389—1061no—
167#389—1061no—
168#389—1061no—
169#382—531no—
170#382—531no—
171#382—531no—
172C4×C4⋊C4—531no—
173C4×C4⋊C4—531no—
174C4×C4⋊C4#615711yescharacteristic
175#343—1061no—
176#324—1061no—
177#324—1061no—
178C53#876611yescharacteristic, complemented, Sylow
179C22×Q8—531no—
180C2×M16—1062no—
181C4×Q8—1062no—
182C4×Q8—1062no—
183C4×Q8—2122no—
184C4×Q8—2122no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—531no—
187C2×C4⋊C4—531no—
188C2×C4⋊C4—531no—
189C2×C4⋊C4—1061no—
190C2×C4⋊C4—1061no—
191C2×C4⋊C4—1061no—
192C2×C4⋊C4—1061no—
193C2×C4⋊C4—1061no—
194C2×C42—21no—
195C2×C42—531no—
196C2×C42—531no—
197C2×C42—1061no—
198C2×C42—1061no—
199C2×C42C2×#615711yescharacteristic
200C4⋊C8—1062no—
201C4⋊C8—1062no—
202C4⋊C8—1062no—
203#101—2122no—
204C22⋊C8—1062no—
205C4×C8—1062no—
206#95—531no—
207#95—531no—
208#95—1061no—
209#95—1061no—
210#95—1061no—
211#95C2×#615711yescharacteristic
212#95C2×#615711yescharacteristic
213C2×Q8—532no—
214C2×Q8—532no—
215C2×Q8—1062no—
216C2×Q8—1062no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—531no—
220C22×C4—531no—
221C22×C4—531no—
222C22×C4—531no—
223C22×C4—1061no—
224C22×C4—1061no—
225C22×C4C22⋊#615711yescharacteristic
226C22×C4C22⋊#615711yescharacteristic
227C22×C4C22×#615711yescharacteristic
228M16—2122no—
229M16—2122no—
230C2×C8—2122no—
231C2×C8—2122no—
232C4⋊C4—42no—
233C4⋊C4—1062no—
234C4⋊C4—1062no—
235C4⋊C4—1062no—
236C4⋊C4—2122no—
237C4⋊C4—2122no—
238C4⋊C4—2121no—
239C4⋊C4—2121no—
240C4⋊C4—2122no—
241C4⋊C4—2122no—
242C42—21no—
243C42—21no—
244C42—42no—
245C42—532no—
246C42—532no—
247C42—1061no—
248C42—1061no—
249C42—2121no—
250C42—2121no—
251C42—2122no—
252C23C2×C22⋊#615711yescharacteristic
253Q8—1064no—
254Q8—1064no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—532no—
267C2×C4—531no—
268C2×C4—531no—
269C2×C4—532no—
270C2×C4—532no—
271C2×C4—532no—
272C2×C4—1061no—
273C2×C4—1061no—
274C2×C4—1061no—
275C2×C4—2121no—
276C2×C4—2121no—
277C2×C4—2121no—
278C2×C4—2121no—
279C2×C4—2121no—
280C2×C4—2121no—
281C2×C4—2121no—
282C2×C4—2121no—
283C2×C4#1313327912yes—
284C2×C4#1313329611yescharacteristic
285C2×C4#1313329611yescharacteristic
286C8—4242no—
287C8—4242no—
288C22—21no—
289C22—21no—
290C22#1681156611yescharacteristic
291C22C2×#1313327911yescharacteristic
292C22#1681161611yescharacteristic
293C4—22no—
294C4—21no—
295C4—21no—
296C4—42no—
297C4—41no—
298C4—81no—
299C4—532no—
300C4—532no—
301C4—1062no—
302C4—1062no—
303C4—4241no—
304C4—4241no—
305C4—2121no—
306C2—21no—
307C2—21no—
308C2#2029061811yescharacteristic
309C2#2029062411yescharacteristic
310C2#2029062911yescharacteristic
subgroupG/H
centerC22#16811566
commutatorC22×C4×C53C22×C4
FrattiniC22×C4C22×#6157
FittingC4×C4⋊C4×C53C4
socleC22×C53#381
prime radicalC23×C53C2×C22⋊C4
cosocleC2×C4×Dic53C23
hypercenterC4×C4⋊C4#6157
hypocenterC53#8766
LCSG ▷ C22×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
178. C53#8766semidirect

Maximal subgroups

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

subgroupindex
#202905812
#202899572
#202896132
#202895682
#202776352
#876653