Finite Group Databasebeta

← #15755094

Subgroups — #15755094

Order 3328.

1014 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 1014 conjugacy classes of subgroups — too many to draw. Only its 139 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#13114754C211yesmaximal, characteristic, complemented
2#13114748C211yesmaximal, characteristic, complemented
3#13113392C214yesmaximal, complemented
4C13×#3485C211yesmaximal, characteristic
5C2×C13×H(5,𝔽2)C411yescharacteristic, complemented
6C22×C13×#41C2211yescharacteristic
7C13×#547—24no—
8C13×#546—24no—
9C13×#536C412yescomplemented
10C13×#534—22no—
11C13×#525C2212yes—
12C2×C13×#123—22no—
13C13×#518C411yescharacteristic, complemented
14C2×#88074—22no—
15#11718872C2212yescomplemented
16C2×C22⋊#1055—22no—
17C2×C22⋊#1055C2212yescomplemented
18#11718130—24no—
19#11718129—24no—
20C13×H(5,𝔽2)—44no—
21C2×C13×#41—22no—
22C2×C13×#41—24no—
23C2×C13×#41—44no—
24C2×C13×#41C2×C412yes—
25C22×Q8×C13C2×C411yescharacteristic
26C22×D4×C13—22no—
27C22×D4×C13—22no—
28C22×D4×C13C2×C411yescharacteristic
29C22×D4×C13D412yes—
30C23×C4×C13D412yes—
31C23×C4×C13C2311yescharacteristic
32C13×C4⋊Q8—22no—
33C13×#124—22no—
34C13×#123—28no—
35C13×#123—24no—
36C13×#123—24no—
37C13×#123—22no—
38C13×C22⋊Q8—24no—
39C13×C22⋊Q8D414yes—
40C13×#121—28no—
41C13×#121D414yes—
42C13×#120—24no—
43C13×#120—22no—
44C4×D4×C13—24no—
45C4×D4×C13—24no—
46C13×#117C2×C412yes—
47C2×C13×C4⋊C4—24no—
48C2×C13×C22⋊C4—24no—
49C2×C13×C22⋊C4—22no—
50C2×C22⋊Dic13—22no—
51C22×#1055—22no—
52#88074—44no—
53#88071—24no—
54C22⋊#1055—24no—
55C22⋊#1055—44no—
56#8462—131nomaximal, Sylow
57C24×C13—22no—
58C24×C13C22⋊C412yes—
59C24×C13C2×D411yescharacteristic
60C13×#41—44no—
61C13×#41—416no—
62C13×#41—48no—
63C2×Q8×C13—22no—
64C2×Q8×C13—42no—
65C2×Q8×C13C22⋊C412yes—
66C2×D4×C13—24no—
67C2×D4×C13—24no—
68C2×D4×C13—24no—
69C2×D4×C13—22no—
70C2×D4×C13—24no—
71C2×D4×C13—24no—
72C2×D4×C13—22no—
73C2×D4×C13—42no—
74C2×D4×C13—48no—
75C2×D4×C13—44no—
76C2×D4×C13—44no—
77C2×D4×C13C22⋊C412yes—
78C22×C4×C13—22no—
79C22×C4×C13—24no—
80C22×C4×C13—24no—
81C22×C4×C13—22no—
82C22×C4×C13—24no—
83C22×C4×C13—42no—
84C22×C4×C13—42no—
85C22×C4×C13C22⋊C412yes—
86C22×C4×C13C22×C411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D414yes—
89C22×Dic13—42no—
90C13×C4⋊C4—28no—
91C13×C4⋊C4—24no—
92C13×C4⋊C4C22⋊C414yes—
93C13×C22⋊C4—24no—
94C13×C22⋊C4—28no—
95C13×C22⋊C4—22no—
96C13×C22⋊C4—24no—
97C13×C22⋊C4—24no—
98C42×C13—22no—
99C22⋊Dic13—44no—
100C2×#1055—44no—
101C2×#1055—42no—
102#3485D1311yescharacteristic
103#1782—131no—
104#1780—131no—
105#1516—134no—
106C23×C13—22no—
107C23×C13—22no—
108C23×C13—22no—
109C23×C13—22no—
110C23×C13—42no—
111C23×C13—44no—
112C23×C13—44no—
113C23×C13—84no—
114C23×C13#9914yes—
115C23×C13C2×C22⋊C411yescharacteristic
116C23×C13#12012yes—
117Q8×C13—44no—
118Q8×C13—42no—
119D4×C13—28no—
120D4×C13—42no—
121D4×C13—48no—
122D4×C13—48no—
123D4×C13—44no—
124D4×C13—84no—
125C2×C4×C13—22no—
126C2×C4×C13—22no—
127C2×C4×C13—24no—
128C2×C4×C13—22no—
129C2×C4×C13—22no—
130C2×C4×C13—22no—
131C2×C4×C13—22no—
132C2×C4×C13—44no—
133C2×C4×C13—48no—
134C2×C4×C13—44no—
135C2×C4×C13—44no—
136C2×C4×C13—84no—
137C2×C4×C13C2×C22⋊C412yes—
138C2×C4×C13#12012yes—
139C2×Dic13—82no—
140C2×Dic13—84no—
141#1055—82no—
142C2×H(5,𝔽2)Dic1311yescharacteristic, complemented
143C22×#41C2×D1311yescharacteristic
144#547—24no—
145#546—24no—
146#536Dic1312yescomplemented
147#534—22no—
148#525C2×D1312yes—
149C2×#123—22no—
150#518Dic1311yescharacteristic, complemented
151C2×#99—262no—
152C2×C22⋊C8—132no—
153C2×C22⋊C8—262no—
154#381—132no—
155#328—264no—
156#327—264no—
157C22×C13—22no—
158C22×C13—24no—
159C22×C13—22no—
160C22×C13—24no—
161C22×C13—44no—
162C22×C13—44no—
163C22×C13—44no—
164C22×C13—42no—
165C22×C13—82no—
166C22×C13—82no—
167C22×C13—164no—
168C22×C13#37911yescharacteristic
169C22×C13C2×#9912yes—
170C4×C13—22no—
171C4×C13—22no—
172C4×C13—44no—
173C4×C13—42no—
174C4×C13—42no—
175Dic13—162no—
176H(5,𝔽2)—44no—
177C2×#41—22no—
178C2×#41—24no—
179C2×#41—44no—
180C2×#41C2×Dic1312yes—
181C22×Q8C2×Dic1311yescharacteristic
182C22×D4—22no—
183C22×D4—22no—
184C22×D4C2×Dic1311yescharacteristic
185C22×D4C22⋊D1312yes—
186C23×C4C22⋊D1312yes—
187C23×C4C22×D1311yescharacteristic
188C22×C8—262no—
189C4⋊Q8—22no—
190#124—22no—
191#123—28no—
192#123—24no—
193#123—24no—
194#123—22no—
195C22⋊Q8—24no—
196C22⋊Q8C22⋊D1314yes—
197#121—28no—
198#121C22⋊D1314yes—
199#120—24no—
200#120—22no—
201C4×D4—24no—
202C4×D4—24no—
203#117C2×Dic1312yes—
204C2×C4⋊C4—24no—
205C2×C22⋊C4—24no—
206C2×C22⋊C4—22no—
207C2×C22⋊C4—262no—
208#99—524no—
209C22⋊C8—264no—
210C22⋊C8—524no—
211#95—264no—
212C2×C13—22no—
213C2×C13—42no—
214C2×C13—44no—
215C2×C13—82no—
216C2×C13#178111yescharacteristic
217C2×C13#179412yes—
218C24—22no—
219C24C22⋊Dic1312yes—
220C24C2×C22⋊D1311yescharacteristic
221#41—44no—
222#41—416no—
223#41—48no—
224C2×Q8—22no—
225C2×Q8—42no—
226C2×Q8C22⋊Dic1312yes—
227C2×D4—24no—
228C2×D4—24no—
229C2×D4—24no—
230C2×D4—22no—
231C2×D4—24no—
232C2×D4—24no—
233C2×D4—22no—
234C2×D4—42no—
235C2×D4—48no—
236C2×D4—44no—
237C2×D4—44no—
238C2×D4C22⋊Dic1312yes—
239C22×C4—22no—
240C22×C4—24no—
241C22×C4—24no—
242C22×C4—22no—
243C22×C4—24no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—522no—
247C22×C4C22⋊Dic1312yes—
248C22×C4C22×Dic1311yescharacteristic
249C22×C4C2×C22⋊D1311yescharacteristic
250C22×C4C2×C22⋊D1314yes—
251C2×C8—524no—
252C2×C8—522no—
253C4⋊C4—28no—
254C4⋊C4—24no—
255C4⋊C4C22⋊Dic1314yes—
256C22⋊C4—24no—
257C22⋊C4—28no—
258C22⋊C4—22no—
259C22⋊C4—24no—
260C22⋊C4—24no—
261C22⋊C4—524no—
262C42—22no—
263C13#846211yescharacteristic, complemented, Sylow
264C23—22no—
265C23—22no—
266C23—22no—
267C23—22no—
268C23—42no—
269C23—44no—
270C23—44no—
271C23—84no—
272C23#8807414yes—
273C23C2×C22⋊Dic1311yescharacteristic
274C23#8820712yes—
275Q8—42no—
276Q8—44no—
277D4—28no—
278D4—42no—
279D4—48no—
280D4—48no—
281D4—44no—
282D4—84no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—44no—
291C2×C4—48no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—84no—
295C2×C4—1042no—
296C2×C4—1044no—
297C2×C4C2×C22⋊Dic1312yes—
298C2×C4#8820712yes—
299C8—1042no—
300C22—22no—
301C22—24no—
302C22—22no—
303C22—24no—
304C22—44no—
305C22—44no—
306C22—42no—
307C22—44no—
308C22—82no—
309C22—82no—
310C22—164no—
311C22C2×#8807412yes—
312C22#1171890811yescharacteristic
313C4—22no—
314C4—22no—
315C4—42no—
316C4—42no—
317C4—44no—
318C4—2082no—
319C2—22no—
320C2—42no—
321C2—44no—
322C2—82no—
323C2#1311475111yescharacteristic
324C2#1311480012yes—
subgroupG/H
centerC22#11718908
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
Fitting, prime radicalC13×#3485C2
socleC22×C13#379
cosocleC23×C4×C13C23
hypercenter#3485D13
hypocenterC13#8462
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3485

Complements

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

NH ≅ G/Ntype
1. #13114754C2semidirect
2. #13114748C2semidirect
3. #13113392C2semidirect
5. C2×C13×H(5,𝔽2)C4semidirect
9. C13×#536C4semidirect
13. C13×#518C4semidirect
15. #11718872C22semidirect
17. C2×C22⋊#1055C22semidirect
142. C2×H(5,𝔽2)Dic13semidirect
146. #536Dic13semidirect
150. #518Dic13semidirect
263. C13#8462semidirect

Maximal subgroups

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

subgroupindex
#131147542
#131147482
#131133922
C13×#34852
#846213