Finite Group Databasebeta

← #16069345

Subgroups — #16069345

Order 3328.

1778 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123100C211yesmaximal, characteristic
2#13123100C212yesmaximal
3#13123093C214yesmaximal, complemented
4#13123091C218yesmaximal, complemented
5#13123089C211yesmaximal, characteristic
6#13118110C218yesmaximal, complemented
7#13118104C214yesmaximal, complemented
8#13117219C212yesmaximal
9C13×#2280C211yesmaximal, characteristic
10C24×C4×C13C2211yescharacteristic
11C2×C13×#117C2212yes—
12C2×#88180C2214yes—
13C2×C4×Dic26C2214yescomplemented
14C13×#381C2212yes—
15C13×#380C2214yes—
16C13×#379C2211yescharacteristic
17C13×#379C2211yescharacteristic
18C4×C13×C22⋊C4C2214yes—
19#11718908C2212yes—
20#11718908C2212yes—
21#11718873C2214yes—
22#11718873C2214yes—
23#11718872C2214yes—
24C4×C22⋊Dic13C2214yes—
25C4×C22⋊Dic13C2214yes—
26#11718647C2214yescomplemented
27#11718645C2218yescomplemented
28#11718640C2214yescomplemented
29#11718610C2218yes—
30#11718610C2214yes—
31#11718609C2218yes—
32#11718609C2218yes—
33#11718609C2218yes—
34#11718608C2218yes—
35#11718608C2214yes—
36C4×C4⋊Dic13C2214yescomplemented
37C4×#6101C2218yescomplemented
38#11718322C2218yescomplemented
39#11718321C2218yescomplemented
40#11718318C2218yescomplemented
41#11718317C2218yescomplemented
42C25×C13C2311yescharacteristic
43C23×C4×C13—44no—
44C23×C4×C13Q818yescomplemented
45C23×C4×C13C2312yes—
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2312yes—
48C23×C4×C13C2311yescharacteristic
49C22×Dic26C2314yes—
50C13×#117—44no—
51C2×C13×C4⋊C4C2314yes—
52C2×C13×C22⋊C4C2314yes—
53C2×C13×C22⋊C4C2314yes—
54C2×C13×C22⋊C4C2312yes—
55C2×C13×C22⋊C4C2312yes—
56C2×C42×C13C2314yes—
57C2×C22⋊Dic13C2314yes—
58C2×C22⋊Dic13C2314yes—
59C2×C22⋊Dic13C2314yes—
60C2×C22⋊Dic13C2314yes—
61C2×C22⋊Dic13C2314yes—
62C2×C22⋊Dic13C2314yes—
63#88180—48no—
64C2×C4⋊Dic13C2314yes—
65C2×C4⋊Dic13C2318yes—
66C2×C4⋊Dic13C2318yes—
67C2×#6101C2318yes—
68C2×#6101C2318yes—
69C2×#6101C2318yes—
70C2×C4×Dic13C2318yes—
71C4×Dic26—48no—
72C13×#95C2318yes—
73#88071C2318yes—
74#88071C2318yes—
75#88071C2314yes—
76#88071C2314yes—
77#88071C2318yes—
78#88071C2318yes—
79#36674—131nomaximal, Sylow
80C24×C13—42no—
81C24×C13—44no—
82C24×C13C2×Q814yes—
83C24×C13C2412yes—
84C24×C13C2411yescharacteristic
85C22×C4×C13—28no—
86C22×C4×C13—24no—
87C22×C4×C13—416no—
88C22×C4×C13—42no—
89C22×C4×C13—44no—
90C22×C4×C13C2×Q818yes—
91C22×C4×C13C2×Q814yes—
92C22×C4×C13C2×Q818yes—
93C22×C4×C13C2×Q814yes—
94C22×C4×C13C2414yes—
95C22×C4×C13C2414yes—
96C22×C4×C13C2411yescharacteristic
97C22×C4×C13C2412yes—
98C22×C4×C13C2411yescharacteristic
99C22×Dic13C2418yes—
100C22×Dic13C2418yes—
101C2×Dic26—44no—
102C2×Dic26—48no—
103C13×C4⋊C4—44no—
104C13×C22⋊C4—44no—
105C13×C22⋊C4—44no—
106C13×C22⋊C4—42no—
107C13×C22⋊C4—42no—
108C42×C13—28no—
109C22⋊Dic13—44no—
110C22⋊Dic13—44no—
111C22⋊Dic13—44no—
112C22⋊Dic13—44no—
113C22⋊Dic13—44no—
114C22⋊Dic13—44no—
115C4⋊Dic13—44no—
116C4⋊Dic13—48no—
117C4⋊Dic13—48no—
118#6101—48no—
119#6101—48no—
120#6101—48no—
121C4×Dic13—216no—
122#2842—132no—
123#2842—131no—
124#2841—134no—
125#2841—138no—
126#2840—131no—
127#2396—138no—
128#2396—134no—
129#2280—132no—
130#2280D1311yescharacteristic
131C23×C13—24no—
132C23×C13—22no—
133C23×C13—24no—
134C23×C13—24no—
135C23×C13—24no—
136C23×C13—44no—
137C23×C13—48no—
138C23×C13—416no—
139C23×C13C22×Q814yes—
140C23×C13C22×Q812yes—
141C23×C13C2511yescharacteristic
142C2×C4×C13—24no—
143C2×C4×C13—22no—
144C2×C4×C13—216no—
145C2×C4×C13—28no—
146C2×C4×C13—24no—
147C2×C4×C13—24no—
148C2×C4×C13—28no—
149C2×C4×C13—28no—
150C2×C4×C13—44no—
151C2×C4×C13—48no—
152C2×C4×C13C22×Q812yes—
153C2×C4×C13C22×Q814yes—
154C2×C4×C13C22×Q812yes—
155C2×C4×C13H(5,𝔽2)14yes—
156C2×Dic13—28no—
157C2×Dic13—28no—
158C2×Dic13—28no—
159C2×Dic13—28no—
160C2×Dic13—28no—
161C2×Dic13—28no—
162Dic26—416no—
163C24×C4C2×D1311yescharacteristic
164C2×C4×Q8—134no—
165C2×#117—134no—
166C2×#117C2×D1312yes—
167#400—134no—
168#400—138no—
169#399—138no—
170#399—134no—
171#398—138no—
172#398—138no—
173#398—138no—
174#396—138no—
175#396—138no—
176#396—138no—
177#395—134no—
178#395—138no—
179#393—138no—
180#393—134no—
181#381—134no—
182#381C2×D1312yes—
183#380—134no—
184#380—134no—
185#380C2×D1314yes—
186#379—132no—
187#379—132no—
188#379C2×D1311yescharacteristic
189#379C2×D1311yescharacteristic
190C4×C4⋊C4—138no—
191C4×C4⋊C4—134no—
192C4×C22⋊C4—134no—
193C4×C22⋊C4—134no—
194C4×C22⋊C4C2×D1314yes—
195C22×C13—24no—
196C22×C13—22no—
197C22×C13—24no—
198C22×C13—24no—
199C22×C13—24no—
200C22×C13—416no—
201C22×C13—48no—
202C22×C13—44no—
203C22×C13C23×Q811yescharacteristic
204C22×C13C2×H(5,𝔽2)12yes—
205C22×C13#58514yes—
206C4×C13—24no—
207C4×C13—22no—
208C4×C13—44no—
209C4×C13—44no—
210C4×C13#54314yes—
211Dic13—48no—
212Dic13—48no—
213C25C22×D1311yescharacteristic
214C22×Q8—134no—
215C23×C4—44no—
216C23×C4Dic2618yescomplemented
217C23×C4C22×D1312yes—
218C23×C4C22×D1311yescharacteristic
219C23×C4C22×D1311yescharacteristic
220C23×C4C22×D1312yes—
221C4×Q8—528no—
222#117—44no—
223#117—528no—
224C2×C4⋊C4—138no—
225C2×C4⋊C4—138no—
226C2×C4⋊C4—134no—
227C2×C4⋊C4—138no—
228C2×C4⋊C4—138no—
229C2×C4⋊C4—138no—
230C2×C4⋊C4C22×D1314yes—
231C2×C22⋊C4—134no—
232C2×C22⋊C4—134no—
233C2×C22⋊C4—134no—
234C2×C22⋊C4—134no—
235C2×C22⋊C4—134no—
236C2×C22⋊C4—134no—
237C2×C22⋊C4C22×D1312yes—
238C2×C22⋊C4C22×D1312yes—
239C2×C22⋊C4C22×D1314yes—
240C2×C22⋊C4C22×D1314yes—
241C2×C42—138no—
242C2×C42C22×D1314yes—
243#95—138no—
244#95—138no—
245#95—134no—
246#95—138no—
247#95—138no—
248#95—134no—
249#95C22×D1318yes—
250C2×C13—44no—
251C2×C13—42no—
252C2×C13C2×#54311yescharacteristic
253C2×C13#345812yes—
254C2×C13#352914yes—
255C24—42no—
256C24—44no—
257C24C2×Dic2614yes—
258C24C23×D1311yescharacteristic
259C24C23×D1312yes—
260C2×Q8—524no—
261C2×Q8—528no—
262C22×C4—24no—
263C22×C4—28no—
264C22×C4—416no—
265C22×C4—44no—
266C22×C4—42no—
267C22×C4—138no—
268C22×C4—138no—
269C22×C4C2×Dic2618yes—
270C22×C4C2×Dic2614yes—
271C22×C4C2×Dic2614yes—
272C22×C4C2×Dic2618yes—
273C22×C4C23×D1314yes—
274C22×C4C23×D1314yes—
275C22×C4C23×D1311yescharacteristic
276C22×C4C23×D1312yes—
277C22×C4C23×D1311yescharacteristic
278C4⋊C4—44no—
279C4⋊C4—528no—
280C4⋊C4—528no—
281C4⋊C4—524no—
282C4⋊C4—528no—
283C4⋊C4—528no—
284C4⋊C4—528no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—44no—
288C22⋊C4—44no—
289C22⋊C4—524no—
290C22⋊C4—524no—
291C22⋊C4—524no—
292C22⋊C4—524no—
293C22⋊C4—524no—
294C22⋊C4—524no—
295C42—28no—
296C42—2616no—
297C13#3667411yescharacteristic, complemented, Sylow
298C23—22no—
299C23—24no—
300C23—24no—
301C23—24no—
302C23—24no—
303C23—44no—
304C23—48no—
305C23—416no—
306C23C22×Dic2612yes—
307C23C22×Dic2614yes—
308C23C24×D1311yescharacteristic
309Q8—5216no—
310C2×C4—22no—
311C2×C4—24no—
312C2×C4—28no—
313C2×C4—216no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—28no—
317C2×C4—28no—
318C2×C4—48no—
319C2×C4—44no—
320C2×C4—268no—
321C2×C4—268no—
322C2×C4—268no—
323C2×C4—268no—
324C2×C4—268no—
325C2×C4—268no—
326C2×C4C22×Dic2612yes—
327C2×C4C22×Dic2614yes—
328C2×C4C22×Dic2612yes—
329C2×C4#8825114yes—
330C22—22no—
331C22—24no—
332C22—24no—
333C22—24no—
334C22—24no—
335C22—416no—
336C22—44no—
337C22—48no—
338C22C23×Dic2611yescharacteristic
339C22C2×#8825112yes—
340C22#1171964814yes—
341C4—22no—
342C4—24no—
343C4—44no—
344C4—44no—
345C4—528no—
346C4—528no—
347C4#1171918814yes—
348C2—42no—
349C2—44no—
350C2C2×#1171918811yescharacteristic
351C2#1312824112yes—
352C2#1312897414yes—
subgroupG/H
centerC22×C4C23×D13
commutator, socle, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC13×#2280C2
prime radicalC25×C13C23
hypercenter#2280D13
hypocenterC13#36674
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
3. #13123093C2semidirect
4. #13123091C2semidirect
6. #13118110C2semidirect
7. #13118104C2semidirect
13. C2×C4×Dic26C22semidirect
26. #11718647C22semidirect
27. #11718645C22semidirect
28. #11718640C22semidirect
36. C4×C4⋊Dic13C22semidirect
37. C4×#6101C22semidirect
38. #11718322C22semidirect
39. #11718321C22semidirect
40. #11718318C22semidirect
41. #11718317C22semidirect
44. C23×C4×C13Q8semidirect
216. C23×C4Dic26semidirect
297. C13#36674semidirect

Maximal subgroups

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

subgroupindex
#131231002
#131230932
#131230912
#131230892
#131181102
#131181042
#131172192
C13×#22802
#3667413