Finite Group Databasebeta

← #13125993

Subgroups — #13125993

Order 1664.

326 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719327C211yesmaximal, characteristic
2#11719222C211yesmaximal, characteristic
3C13×#485C211yesmaximal, characteristic
4#11718706C211yesmaximal, characteristic
5#11718657C211yesmaximal, characteristic
6#11718538C211yesmaximal, characteristic, complemented
7#11718535C211yesmaximal, characteristic, complemented
8#11718518C211yesmaximal, characteristic, complemented
9#11718516C211yesmaximal, characteristic, complemented
10#11718460C211yesmaximal, characteristic, complemented
11#11718457C211yesmaximal, characteristic, complemented
12#11718453C211yesmaximal, characteristic, complemented
13#11718453C211yesmaximal, characteristic, complemented
14#11718384C211yesmaximal, characteristic
15#11718379C211yesmaximal, characteristic
16C13×C22⋊Q8C2211yescharacteristic
17C13×#117C2211yescharacteristic
18Q8×Dic13C2211yescharacteristic
19#88198C2211yescharacteristic
20#88180C2211yescharacteristic
21#88178C2211yescharacteristic
22C2×C4×Dic13C2211yescharacteristic
23#88144C2211yescharacteristic
24#88144C2211yescharacteristic
25#88143—21no—
26#88142C2211yescharacteristic
27#88142C2211yescharacteristic
28#88142C2211yescharacteristic
29#88141—21no—
30#88141C2211yescharacteristic
31#88132—21no—
32#88132—21no—
33#88132—21no—
34#88131—21no—
35C4×Dic26—21no—
36C4×Dic26—21no—
37C13×#107C2211yescharacteristic
38C13×#106C2211yescharacteristic
39C13×#103C2211yescharacteristic
40C13×#103C2211yescharacteristic
41C13×C22⋊C8C2211yescharacteristic
42#88075C2211yescharacteristic
43#88075C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88058C2211yescharacteristic
46#88057C2211yescharacteristic
47#88056C2211yescharacteristic
48#88056C2211yescharacteristic
49#88054C2211yescharacteristic
50#88054C2211yescharacteristic
51C8×Dic13C2211yescharacteristic
52C8×Dic13C2211yescharacteristic
53#88050C2211yescharacteristic
54#88050C2211yescharacteristic
55#88048C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×Dic13D411yescharacteristic
62C22×Dic13D411yescharacteristic
63C2×Dic26—21no—
64C2×Dic26—21no—
65C2×Dic26—21no—
66C2×Dic26C2311yescharacteristic
67C2×C8×C13C2311yescharacteristic
68C2×C8×C13C2311yescharacteristic
69C13×C4⋊C4—21no—
70C13×C4⋊C4C2311yescharacteristic
71C13×C4⋊C4C2311yescharacteristic
72C13×C4⋊C4C2311yescharacteristic
73C13×C22⋊C4—21no—
74C13×C22⋊C4—21no—
75C42×C13—21no—
76C22⋊Dic13—21no—
77C22⋊Dic13—21no—
78C4⋊Dic13—21no—
79C4⋊Dic13—21no—
80C4⋊Dic13—21no—
81C4⋊Dic13C2311yescharacteristic
82C4⋊Dic13C2311yescharacteristic
83C4⋊Dic13C2311yescharacteristic
84#6101—21no—
85#6101—21no—
86#6101—21no—
87#6101—21no—
88#6101—21no—
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93C4×Dic13—21no—
94C4×Dic13—21no—
95C4×Dic13—21no—
96C4×Dic13D411yescharacteristic
97C4×Dic13D411yescharacteristic
98C4×Dic13C2311yescharacteristic
99C4×Dic13C2311yescharacteristic
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102#3231—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—22no—
115C2×Dic13—22no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13C2×D411yescharacteristic
121C2×Dic13C2×D411yescharacteristic
122C2×Dic13C2×D411yescharacteristic
123C2×Dic13C2×D411yescharacteristic
124Dic26—21no—
125Dic26—21no—
126Dic26—42no—
127Dic26—42no—
128Dic26—42no—
129C8×C13—21no—
130C8×C13—21no—
131#1055—21no—
132#1055—21no—
133#533—131no—
134#533—131no—
135#500—131no—
136#498—131no—
137#487—131no—
138#487—131no—
139#485—131no—
140#485—131no—
141#485—131no—
142#485D1311yescharacteristic
143#479—131no—
144#479—131no—
145#479—131no—
146#479—131no—
147#431—131no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13C22×D411yescharacteristic
152C4×C13—21no—
153C4×C13—41no—
154C4×C13—41no—
155C4×C13—41no—
156C4×C13—41no—
157C4×C132−1+411yescharacteristic
158C4×C132−1+411yescharacteristic
159Dic13—21no—
160Dic13—21no—
161Dic13—41no—
162Dic13—41no—
163Dic13—41no—
164Dic13—41no—
165Dic13#13512yes—
166Dic13#13712yes—
167C4⋊Q8—131no—
168C4⋊Q8—131no—
169C4⋊Q8—131no—
170C4⋊Q8—131no—
171#125—131no—
172#125—131no—
173#125—261no—
174C22⋊Q8—131no—
175C22⋊Q8—261no—
176C22⋊Q8—261no—
177C22⋊Q8—261no—
178C22⋊Q8C2×D1311yescharacteristic
179C4×Q8—131no—
180C4×Q8—131no—
181C4×Q8—261no—
182C4×Q8—261no—
183C4×Q8—261no—
184#117—131no—
185#117—261no—
186#117C2×D1311yescharacteristic
187C2×C42—131no—
188#107—131no—
189#107—131no—
190#107—131no—
191#107C2×D1311yescharacteristic
192#106—131no—
193#106—131no—
194#106—131no—
195#106C2×D1311yescharacteristic
196C4⋊C8—131no—
197C4⋊C8—131no—
198#103—131no—
199#103—131no—
200#103—131no—
201#103—131no—
202#103—131no—
203#103—131no—
204#103C2×D1311yescharacteristic
205#103C2×D1311yescharacteristic
206C22⋊C8—131no—
207C22⋊C8C2×D1311yescharacteristic
208C4×C8—131no—
209C4×C8—131no—
210C2×C13—41no—
211C2×C13#53611yescharacteristic
212C2×C13C2×#13511yescharacteristic
213C2×C13C2×#13711yescharacteristic
214C2×Q8—131no—
215C2×Q8—261no—
216C2×Q8—261no—
217C2×Q8—261no—
218C2×Q8C22×D1311yescharacteristic
219C22×C4—131no—
220C22×C4—131no—
221C22×C4C22×D1311yescharacteristic
222C2×C8—131no—
223C2×C8—131no—
224C2×C8C22×D1311yescharacteristic
225C2×C8C22×D1311yescharacteristic
226C4⋊C4—21no—
227C4⋊C4—131no—
228C4⋊C4—131no—
229C4⋊C4—131no—
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—261no—
248C22⋊C4—261no—
249C42—21no—
250C42—131no—
251C42—131no—
252C42—131no—
253C42—131no—
254C42—261no—
255C42—261no—
256C42—261no—
257C13#323111yescharacteristic, complemented, Sylow
258C23D4×D1311yescharacteristic
259Q8—21no—
260Q8—21no—
261Q8—261no—
262Q8—261no—
263Q8—522no—
264Q8—522no—
265Q8—522no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—131no—
273C2×C4—131no—
274C2×C4—131no—
275C2×C4—131no—
276C2×C4—262no—
277C2×C4—262no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4D4×D1311yescharacteristic
283C2×C4C23×D1311yescharacteristic
284C8—21no—
285C8—21no—
286C8—261no—
287C8—261no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22C2×D4×D1311yescharacteristic
292C4—21no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—132no—
298C4—132no—
299C4—261no—
300C4—261no—
301C4—521no—
302C4—521no—
303C4—521no—
304C4—521no—
305C4#8825711yescharacteristic
306C4#8825711yescharacteristic
307C2—41no—
308C2#1171935311yescharacteristic
309C2D13×#13511yescharacteristic
310C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#485C2
socleC22×C13C22×D4
prime radicalC23×C13C2×D4
hypercenter#485D13
hypocenterC13#3231
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. #11718538C2semidirect
7. #11718535C2semidirect
8. #11718518C2semidirect
9. #11718516C2semidirect
10. #11718460C2semidirect
11. #11718457C2semidirect
12. #11718453C2semidirect
13. #11718453C2semidirect
257. C13#3231semidirect

Maximal subgroups

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

subgroupindex
#117193272
#117192222
C13×#4852
#117187062
#117186572
#117185382
#117185352
#117185182
#117185162
#117184602
#117184572
#117184532
#117183842
#117183792
#323113