Finite Group Databasebeta

← #13126106

Subgroups — #13126106

Order 1664.

308 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719224C211yesmaximal, characteristic
2#11719223C211yesmaximal, characteristic
3C13×#433C211yesmaximal, characteristic
4#11718512C211yesmaximal, characteristic, complemented
5#11718511C211yesmaximal, characteristic, complemented
6#11718490C211yesmaximal, characteristic, complemented
7#11718490C211yesmaximal, characteristic, complemented
8#11718384C211yesmaximal, characteristic
9#11718384C211yesmaximal, characteristic
10#11718383C211yesmaximal, characteristic
11#11718382C211yesmaximal, characteristic
12#11718364C211yesmaximal, characteristic, complemented
13#11718363C211yesmaximal, characteristic, complemented
14#11718344C211yesmaximal, characteristic, complemented
15#11718342C211yesmaximal, characteristic, complemented
16C13×#117C2211yescharacteristic
17#88180C2211yescharacteristic
18C2×C4⋊Dic13C2211yescharacteristic
19#88178C2211yescharacteristic
20#88178C2211yescharacteristic
21#88144—21no—
22#88143—21no—
23#88143—21no—
24#88142—21no—
25#88133—21no—
26#88133—21no—
27#88132—21no—
28#88132—21no—
29#88124C2211yescharacteristic
30#88124C2211yescharacteristic
31#88124C2211yescharacteristic
32#88123C2211yescharacteristic
33#88123C2211yescharacteristic
34#88123C2211yescharacteristic
35C4×Dic26C2211yescharacteristic
36C4×Dic26C2211yescharacteristic
37C13×C4⋊C8C2211yescharacteristic
38C13×C4⋊C8C2211yescharacteristic
39C13×C22⋊C8C2211yescharacteristic
40C13×C22⋊C8C2211yescharacteristic
41C13×#97C2211yescharacteristic
42C4×C8×C13C2211yescharacteristic
43#88058C2211yescharacteristic
44#88058C2211yescharacteristic
45#88058C2211yescharacteristic
46#88058C2211yescharacteristic
47#88057C2211yescharacteristic
48#88057C2211yescharacteristic
49#88057C2211yescharacteristic
50#88057C2211yescharacteristic
51#88056C2211yescharacteristic
52#88056C2211yescharacteristic
53#88056C2211yescharacteristic
54#88056C2211yescharacteristic
55#88056C2211yescharacteristic
56#88056C2211yescharacteristic
57#88056C2211yescharacteristic
58#88056C2211yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C22×Dic13—21no—
61C2×Dic26—21no—
62C2×Dic26—21no—
63C2×Dic26C2311yescharacteristic
64C2×Dic26C2311yescharacteristic
65C2×C8×C13C2311yescharacteristic
66C2×C8×C13C2311yescharacteristic
67C2×C8×C13C2311yescharacteristic
68C2×C8×C13C2311yescharacteristic
69C13×C4⋊C4D411yescharacteristic
70C13×C4⋊C4D411yescharacteristic
71C13×C22⋊C4D411yescharacteristic
72C13×C22⋊C4D411yescharacteristic
73C42×C13C2311yescharacteristic
74C42×C13C2311yescharacteristic
75C22⋊Dic13—21no—
76C22⋊Dic13—21no—
77C22⋊Dic13—21no—
78C4⋊Dic13—21no—
79C4⋊Dic13—21no—
80C4⋊Dic13—21no—
81C4⋊Dic13—21no—
82C4⋊Dic13—21no—
83C4⋊Dic13C2311yescharacteristic
84C4⋊Dic13C2311yescharacteristic
85C4⋊Dic13C2311yescharacteristic
86C4⋊Dic13C2311yescharacteristic
87C4⋊Dic13C2311yescharacteristic
88C4⋊Dic13C2311yescharacteristic
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102#3242—131nomaximal, Sylow
103C23×C13C2×D411yescharacteristic
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13C2×D411yescharacteristic
107C2×C4×C13C2×D411yescharacteristic
108C2×C4×C13C2×D411yescharacteristic
109C2×C4×C13C2×D411yescharacteristic
110C2×C4×C13C2×D411yescharacteristic
111C2×C4×C13C2411yescharacteristic
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—81no—
121Dic26—21no—
122Dic26—21no—
123Dic26—21no—
124Dic26—21no—
125Dic26—81no—
126Dic26—81no—
127C8×C13—21no—
128C8×C13—21no—
129C8×C13—21no—
130C8×C13—21no—
131#544—131no—
132#541—131no—
133#501—131no—
134#499—131no—
135#491—131no—
136#487—131no—
137#485—131no—
138#485—131no—
139#484—131no—
140#483—131no—
141#479—131no—
142#479—131no—
143#477—131no—
144#475—131no—
145#433D1311yescharacteristic
146C22×C13—21no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13C22×D411yescharacteristic
150C4×C13—21no—
151C4×C13—21no—
152C4×C13—21no—
153C4×C13—21no—
154C4×C13—21no—
155C4×C132−1+411yescharacteristic
156C4×C132−1+411yescharacteristic
157Dic13—41no—
158Dic13—41no—
159Dic13—41no—
160Dic13—41no—
161Dic13—41no—
162Dic13—41no—
163Dic13—41no—
164Dic13—41no—
165C4⋊Q8—131no—
166C4⋊Q8—131no—
167C4⋊Q8—131no—
168C4⋊Q8—261no—
169#126—261no—
170#126—261no—
171#125—131no—
172#125—131no—
173#125—131no—
174#125—261no—
175#125—261no—
176#125—261no—
177C22⋊Q8—131no—
178C22⋊Q8—131no—
179C22⋊Q8—261no—
180C22⋊Q8—261no—
181C4×Q8—131no—
182C4×Q8—131no—
183#117—131no—
184#117C2×D1311yescharacteristic
185C2×C4⋊C4—131no—
186#107—131no—
187#107—131no—
188#107—131no—
189#107—131no—
190#106—131no—
191#106—131no—
192#106—131no—
193#106—131no—
194C4⋊C8C2×D1311yescharacteristic
195C4⋊C8C2×D1311yescharacteristic
196#103—131no—
197#103—131no—
198#103—131no—
199#103—131no—
200#103—131no—
201#103—131no—
202#103—131no—
203#103—131no—
204C22⋊C8C2×D1311yescharacteristic
205C22⋊C8C2×D1311yescharacteristic
206#97C2×D1311yescharacteristic
207C4×C8C2×D1311yescharacteristic
208C2×C13—41no—
209C2×C13#53611yescharacteristic
210C2×C13#57711yescharacteristic
211C2×C13#57811yescharacteristic
212C2×Q8—131no—
213C2×Q8—131no—
214C2×Q8—261no—
215C2×Q8—261no—
216C22×C4—261no—
217C22×C4C22×D1311yescharacteristic
218C2×C8C22×D1311yescharacteristic
219C2×C8C22×D1311yescharacteristic
220C2×C8C22×D1311yescharacteristic
221C2×C8C22×D1311yescharacteristic
222C4⋊C4—131no—
223C4⋊C4—131no—
224C4⋊C4—131no—
225C4⋊C4—131no—
226C4⋊C4—131no—
227C4⋊C4—131no—
228C4⋊C4—261no—
229C4⋊C4—261no—
230C4⋊C4—261no—
231C4⋊C4—261no—
232C4⋊C4—261no—
233C4⋊C4—261no—
234C4⋊C4—261no—
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⋊C4D5211yescharacteristic
244C4⋊C4D5211yescharacteristic
245C22⋊C4—261no—
246C22⋊C4—261no—
247C22⋊C4—261no—
248C22⋊C4D5211yescharacteristic
249C22⋊C4D5211yescharacteristic
250C42—261no—
251C42—261no—
252C42—261no—
253C42C22×D1311yescharacteristic
254C42C22×D1311yescharacteristic
255C13#324211yescharacteristic, complemented, Sylow
256C23C2×D5211yescharacteristic
257Q8—261no—
258Q8—261no—
259Q8—261no—
260Q8—261no—
261Q8—1041no—
262Q8—1041no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—261no—
266C2×C4—261no—
267C2×C4—261no—
268C2×C4—261no—
269C2×C4—261no—
270C2×C4—261no—
271C2×C4—261no—
272C2×C4—261no—
273C2×C4—1041no—
274C2×C4C2×D5211yescharacteristic
275C2×C4C2×D5211yescharacteristic
276C2×C4C2×D5211yescharacteristic
277C2×C4C2×D5211yescharacteristic
278C2×C4C2×D5211yescharacteristic
279C2×C4C23×D1311yescharacteristic
280C8—21no—
281C8—21no—
282C8—21no—
283C8—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22C22×D5211yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—521no—
294C4—521no—
295C4—521no—
296C4—521no—
297C4—521no—
298C4—521no—
299C4—521no—
300C4—521no—
301C4#8825711yescharacteristic
302C4#8825711yescharacteristic
303C2—41no—
304C2#1171923111yescharacteristic
305C2#1171945611yescharacteristic
306C2#1171945811yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#433C2
socleC22×C13C22×D4
prime radicalC23×C13C2×D4
hypercenter#433D13
hypocenterC13#3242
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
4. #11718512C2semidirect
5. #11718511C2semidirect
6. #11718490C2semidirect
7. #11718490C2semidirect
12. #11718364C2semidirect
13. #11718363C2semidirect
14. #11718344C2semidirect
15. #11718342C2semidirect
255. C13#3242semidirect

Maximal subgroups

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

subgroupindex
#117192242
#117192232
C13×#4332
#117185122
#117185112
#117184902
#117183842
#117183832
#117183822
#117183642
#117183632
#117183442
#117183422
#324213