Finite Group Databasebeta

← #13125363

Subgroups — #13125363

Order 1664.

340 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719434C211yesmaximal, characteristic
2#11719394C211yesmaximal, characteristic
3C13×#501C211yesmaximal, characteristic, complemented
4#11718740C211yesmaximal, characteristic, complemented
5#11718725C211yesmaximal, characteristic, complemented
6#11718542C211yesmaximal, characteristic
7#11718541C211yesmaximal, characteristic
8#11718539C211yesmaximal, characteristic, complemented
9#11718537C211yesmaximal, characteristic, complemented
10#11718522C211yesmaximal, characteristic
11D13×#106C211yesmaximal, characteristic
12#11718517C211yesmaximal, characteristic, complemented
13#11718516C211yesmaximal, characteristic, complemented
14#11718369C211yesmaximal, characteristic
15#11718363C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8C2211yescharacteristic
17C13×#125C2211yescharacteristic
18#88200—21no—
19#88198—21no—
20C2×#6094C2211yescharacteristic
21C2×C8×D13C2211yescharacteristic
22#88151—21no—
23#88150—21no—
24#88150—21no—
25#88146C2211yescharacteristic
26#88146C2211yescharacteristic
27C4⋊C4×D13C2211yescharacteristic
28C4⋊C4×D13C2211yescharacteristic
29#88144C2211yescharacteristic
30#88144C2211yescharacteristic
31#88143—21no—
32#88143—21no—
33#88142—21no—
34#88142C2211yescharacteristic
35#88142C2211yescharacteristic
36#88126C2211yescharacteristic
37#88124C2211yescharacteristic
38#88123C2211yescharacteristic
39C13×#107C2211yescharacteristic
40C13×#107C2211yescharacteristic
41C13×#106C2211yescharacteristic
42C13×#106C2211yescharacteristic
43C13×#97C2211yescharacteristic
44#88058C2211yescharacteristic
45#88058C2211yescharacteristic
46#88057C2211yescharacteristic
47#88057C2211yescharacteristic
48#88055C2211yescharacteristic
49C8×Dic13C2211yescharacteristic
50#88048C2211yescharacteristic
51#88048C2211yescharacteristic
52#88048C2211yescharacteristic
53#88048C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×C4×D13—21no—
61C2×C4×D13—21no—
62C2×C4×D13C2311yescharacteristic
63C2×Dic26—21no—
64C2×Dic26—21no—
65C2×Dic26—21no—
66C2×C8×C13C2311yescharacteristic
67C2×C8×C13C2311yescharacteristic
68C13×C4⋊C4—21no—
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4C2311yescharacteristic
72C13×C4⋊C4C2311yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C42×C13C2311yescharacteristic
76#6103—21no—
77#6103—21no—
78#6103D411yescharacteristic
79#6103D411yescharacteristic
80C4⋊Dic13—21no—
81C4⋊Dic13—21no—
82C4⋊Dic13—21no—
83C4⋊Dic13C2311yescharacteristic
84C4⋊Dic13C2311yescharacteristic
85C4⋊Dic13C2311yescharacteristic
86C4⋊Dic13C2311yescharacteristic
87#6101—21no—
88#6101—21no—
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101D411yescharacteristic
96#6101D411yescharacteristic
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13C2311yescharacteristic
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102#6094Q814yescomplemented
103C8×D13Q814yescomplemented
104#3163—131nomaximal, Sylow
105C22×D13C2×D411yescharacteristic
106Q8×C13—81no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13C2×D411yescharacteristic
112C2×C4×C13C2×D411yescharacteristic
113C2×C4×C13C2411yescharacteristic
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13C2×D411yescharacteristic
119C2×Dic13C2×D411yescharacteristic
120C2×Dic13C2×D411yescharacteristic
121C4×D13—81no—
122C4×D13—81no—
123C4×D13C2×Q812yes—
124C4×D13C2×Q812yes—
125Dic26—81no—
126Dic26—81no—
127Dic26—81no—
128C8×C13C2×Q812yes—
129C8×C13C2×Q812yes—
130#1055C2×Q812yes—
131#1055C2×Q812yes—
132#544—131no—
133#544—131no—
134#501—131no—
135#501—131no—
136#501—131no—
137#501D1311yescharacteristic, complemented
138#499—131no—
139#499—131no—
140#498—131no—
141#498—131no—
142#428—131no—
143#428—131no—
144#427—131no—
145C2×#106—131no—
146#405—131no—
147C22×C13C22×D411yescharacteristic
148C2×D13—21no—
149C2×D13—21no—
150C2×D13C4⋊Q812yes—
151C4×C13—21no—
152C4×C13—21no—
153C4×C13—41no—
154C4×C13—41no—
155C4×C13—41no—
156C4×C13—41no—
157C4×C13C22×Q811yescharacteristic
158C4×C13C22×Q811yescharacteristic
159Dic13—21no—
160Dic13—21no—
161Dic13—41no—
162Dic13—41no—
163Dic13—41no—
164Dic13—41no—
165Dic13C4⋊Q812yes—
166C2×M16—131no—
167C22×C8—131no—
168C4⋊Q8—131no—
169C4⋊Q8—131no—
170C4⋊Q8—131no—
171C4⋊Q8—261no—
172C4⋊Q8—261no—
173C4⋊Q8C2×D1311yescharacteristic
174#125—131no—
175#125—131no—
176#125—131no—
177#125—261no—
178#125—261no—
179#125C2×D1311yescharacteristic
180C22⋊Q8—261no—
181C22⋊Q8—261no—
182C22⋊Q8—261no—
183C22⋊Q8—261no—
184#117—131no—
185#117—131no—
186#117—131no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—131no—
189#107—131no—
190#107—131no—
191#107—131no—
192#107—131no—
193#107C2×D1311yescharacteristic
194#107C2×D1311yescharacteristic
195#106—131no—
196#106—131no—
197#106—131no—
198#106—131no—
199#106—131no—
200#106—131no—
201#106—131no—
202#106—131no—
203#106C2×D1311yescharacteristic
204#106C2×D1311yescharacteristic
205#97—131no—
206#97C2×D1311yescharacteristic
207C4×C8—131no—
208C4×C8—131no—
209C2×C13C2×C4⋊Q811yescharacteristic
210C2×C13#57711yescharacteristic
211C2×C13#57711yescharacteristic
212D13—22no—
213C2×Q8—21no—
214C2×Q8—261no—
215C2×Q8—261no—
216C2×Q8—261no—
217C22×C4—131no—
218C22×C4—261no—
219C22×C4—261no—
220M16—134no—
221C2×C8—131no—
222C2×C8—131no—
223C2×C8—134no—
224C2×C8C22×D1311yescharacteristic
225C2×C8C22×D1311yescharacteristic
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—131no—
230C4⋊C4—131no—
231C4⋊C4—131no—
232C4⋊C4—131no—
233C4⋊C4—131no—
234C4⋊C4—131no—
235C4⋊C4—261no—
236C4⋊C4—261no—
237C4⋊C4—261no—
238C4⋊C4—261no—
239C4⋊C4—261no—
240C4⋊C4—261no—
241C4⋊C4—261no—
242C4⋊C4—261no—
243C4⋊C4—261no—
244C4⋊C4—261no—
245C4⋊C4—261no—
246C4⋊C4C22×D1311yescharacteristic
247C4⋊C4C22×D1311yescharacteristic
248C4⋊C4C22×D1311yescharacteristic
249C4⋊C4C22×D1311yescharacteristic
250C22⋊C4—131no—
251C22⋊C4—131no—
252C22⋊C4—261no—
253C22⋊C4—261no—
254C42—131no—
255C42—261no—
256C42—261no—
257C42C22×D1311yescharacteristic
258C13#316311yescharacteristic, complemented, Sylow
259C23—131no—
260Q8—81no—
261Q8—1041no—
262Q8—1041no—
263Q8—1041no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—131no—
269C2×C4—132no—
270C2×C4—132no—
271C2×C4—131no—
272C2×C4—131no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4—1041no—
278C2×C4—1041no—
279C2×C4D4×D1311yescharacteristic
280C2×C4D4×D1311yescharacteristic
281C2×C4C23×D1311yescharacteristic
282C8—132no—
283C8—132no—
284C8Q8×D1312yes—
285C8Q8×D1312yes—
286C22—132no—
287C22—261no—
288C22—261no—
289C22C2×D4×D1311yescharacteristic
290C4—21no—
291C4—21no—
292C4—41no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—132no—
297C4—261no—
298C4—261no—
299C4—521no—
300C4—521no—
301C4—521no—
302C4—521no—
303C4C2×Q8×D1311yescharacteristic
304C4C2×Q8×D1311yescharacteristic
305C2—262no—
306C2D13×C4⋊Q811yescharacteristic
307C2#1171948011yescharacteristic
308C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#501C2
socleC22×C13C22×D4
prime radicalC22×D13C2×D4
hypercenter#501D13
hypocenterC13#3163
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. C13×#501C2semidirect
4. #11718740C2semidirect
5. #11718725C2semidirect
8. #11718539C2semidirect
9. #11718537C2semidirect
12. #11718517C2semidirect
13. #11718516C2semidirect
15. #11718363C2semidirect
102. #6094Q8semidirect
103. C8×D13Q8semidirect
137. #501D13semidirect
258. C13#3163semidirect

Maximal subgroups

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

subgroupindex
#117194342
#117193942
C13×#5012
#117187402
#117187252
#117185422
#117185412
#117185392
#117185372
#117185222
D13×#1062
#117185172
#117185162
#117183692
#117183632
#316313