Finite Group Databasebeta

← #13126110

Subgroups — #13126110

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#11719330C211yesmaximal, characteristic
2#11719224C211yesmaximal, characteristic
3C13×#485C211yesmaximal, characteristic
4#11718705C211yesmaximal, characteristic
5#11718657C211yesmaximal, characteristic
6#11718537C211yesmaximal, characteristic, complemented
7#11718536C211yesmaximal, characteristic, complemented
8#11718519C211yesmaximal, characteristic, complemented
9#11718518C211yesmaximal, characteristic, complemented
10#11718460C211yesmaximal, characteristic, complemented
11#11718458C211yesmaximal, characteristic, complemented
12#11718453C211yesmaximal, characteristic, complemented
13#11718452C211yesmaximal, characteristic, complemented
14#11718382C211yesmaximal, characteristic
15#11718381C211yesmaximal, characteristic
16C13×C22⋊Q8C2211yescharacteristic
17C13×#117C2211yescharacteristic
18Q8×Dic13C2211yescharacteristic
19#88198C2211yescharacteristic
20#88180C2211yescharacteristic
21C2×C4⋊Dic13C2211yescharacteristic
22#88178C2211yescharacteristic
23#88144—21no—
24#88144C2211yescharacteristic
25#88144C2211yescharacteristic
26#88144C2211yescharacteristic
27#88143—21no—
28#88142C2211yescharacteristic
29#88142C2211yescharacteristic
30#88141C2211yescharacteristic
31#88133—21no—
32#88133—21no—
33#88132—21no—
34#88132—21no—
35#88124—21no—
36#88123—21no—
37C13×#107C2211yescharacteristic
38C13×#106C2211yescharacteristic
39C13×#103C2211yescharacteristic
40C13×#103C2211yescharacteristic
41C13×C22⋊C8C2211yescharacteristic
42#88075C2211yescharacteristic
43#88075C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88057C2211yescharacteristic
46#88057C2211yescharacteristic
47#88056C2211yescharacteristic
48#88056C2211yescharacteristic
49#88055C2211yescharacteristic
50#88054C2211yescharacteristic
51#88054C2211yescharacteristic
52C8×Dic13C2211yescharacteristic
53#88050C2211yescharacteristic
54#88050C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×Dic13—21no—
62C2×Dic26—21no—
63C2×Dic26—21no—
64C2×Dic26C2311yescharacteristic
65C2×C8×C13C2311yescharacteristic
66C2×C8×C13C2311yescharacteristic
67C13×C4⋊C4—21no—
68C13×C4⋊C4C2311yescharacteristic
69C13×C4⋊C4C2311yescharacteristic
70C13×C4⋊C4C2311yescharacteristic
71C13×C22⋊C4—21no—
72C13×C22⋊C4—21no—
73C42×C13—21no—
74C22⋊Dic13—21no—
75C22⋊Dic13D411yescharacteristic
76C22⋊Dic13D411yescharacteristic
77C4⋊Dic13—21no—
78C4⋊Dic13—21no—
79C4⋊Dic13—21no—
80C4⋊Dic13—21no—
81C4⋊Dic13—21no—
82C4⋊Dic13D411yescharacteristic
83C4⋊Dic13D411yescharacteristic
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#6101—21no—
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13C2311yescharacteristic
99C4×Dic13C2311yescharacteristic
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102#3242—131nomaximal, Sylow
103C23×C13C2×D411yescharacteristic
104Q8×C13—21no—
105Q8×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13C2×D411yescharacteristic
113C2×C4×C13C2411yescharacteristic
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—81no—
119C2×Dic13C2×D411yescharacteristic
120C2×Dic13C2×D411yescharacteristic
121C2×Dic13C2×D411yescharacteristic
122C2×Dic13C2×D411yescharacteristic
123Dic26—21no—
124Dic26—21no—
125Dic26—81no—
126Dic26—81no—
127C8×C13—21no—
128C8×C13—21no—
129#1055—21no—
130#1055—21no—
131#544—131no—
132#541—131no—
133#501—131no—
134#499—131no—
135#491—131no—
136#487—131no—
137#485—131no—
138#485D1311yescharacteristic
139#484—131no—
140#483—131no—
141#479—131no—
142#479—131no—
143#477—131no—
144#475—131no—
145#433—131no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13C22×D411yescharacteristic
150C4×C13—21no—
151C4×C13—41no—
152C4×C13—41no—
153C4×C13—41no—
154C4×C13—41no—
155C4×C132−1+411yescharacteristic
156C4×C132−1+411yescharacteristic
157Dic13—21no—
158Dic13—21no—
159Dic13—21no—
160Dic13—21no—
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—261no—
179C22⋊Q8—261no—
180C22⋊Q8C2×D1311yescharacteristic
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#107C2×D1311yescharacteristic
190#106—131no—
191#106—131no—
192#106—131no—
193#106C2×D1311yescharacteristic
194C4⋊C8—131no—
195C4⋊C8—131no—
196#103—131no—
197#103—131no—
198#103—131no—
199#103—131no—
200#103—131no—
201#103—131no—
202#103C2×D1311yescharacteristic
203#103C2×D1311yescharacteristic
204C22⋊C8—131no—
205C22⋊C8C2×D1311yescharacteristic
206#97—131no—
207C4×C8—131no—
208C2×C13—41no—
209C2×C13#53611yescharacteristic
210C2×C13#57711yescharacteristic
211C2×C13#57811yescharacteristic
212C2×Q8—131no—
213C2×Q8—261no—
214C2×Q8—261no—
215C2×Q8C22×D1311yescharacteristic
216C22×C4—261no—
217C22×C4C22×D1311yescharacteristic
218C2×C8—131no—
219C2×C8—131no—
220C2×C8C22×D1311yescharacteristic
221C2×C8C22×D1311yescharacteristic
222C4⋊C4—21no—
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⋊C4C22×D1311yescharacteristic
243C4⋊C4C22×D1311yescharacteristic
244C4⋊C4C22×D1311yescharacteristic
245C22⋊C4—21no—
246C22⋊C4—21no—
247C22⋊C4—131no—
248C22⋊C4—131no—
249C22⋊C4—261no—
250C42—21no—
251C42—131no—
252C42—131no—
253C42—261no—
254C42—261no—
255C13#324211yescharacteristic, complemented, Sylow
256C23D4×D1311yescharacteristic
257Q8—21no—
258Q8—21no—
259Q8—261no—
260Q8—261no—
261Q8—1041no—
262Q8—1041no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—131no—
270C2×C4—131no—
271C2×C4—131no—
272C2×C4—131no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4—1041no—
278C2×C4D4×D1311yescharacteristic
279C2×C4C23×D1311yescharacteristic
280C8—21no—
281C8—21no—
282C8—261no—
283C8—261no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22C2×D4×D1311yescharacteristic
288C4—21no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—261no—
294C4—261no—
295C4—261no—
296C4—261no—
297C4—521no—
298C4—521no—
299C4—521no—
300C4—521no—
301C4#8825711yescharacteristic
302C4#8825711yescharacteristic
303C2—41no—
304C2#1171935311yescharacteristic
305C2#1171947511yescharacteristic
306C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#485C2
socleC22×C13C22×D4
prime radicalC23×C13C2×D4
hypercenter#485D13
hypocenterC13#3242
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
6. #11718537C2semidirect
7. #11718536C2semidirect
8. #11718519C2semidirect
9. #11718518C2semidirect
10. #11718460C2semidirect
11. #11718458C2semidirect
12. #11718453C2semidirect
13. #11718452C2semidirect
255. C13#3242semidirect

Maximal subgroups

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

subgroupindex
#117193302
#117192242
C13×#4852
#117187052
#117186572
#117185372
#117185362
#117185192
#117185182
#117184602
#117184582
#117184532
#117184522
#117183822
#117183812
#324213