Finite Group Databasebeta

← #13126117

Subgroups — #13126117

Order 1664.

320 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719308C211yesmaximal, characteristic
2#11719224C211yesmaximal, characteristic, complemented
3C13×#482C211yesmaximal, characteristic
4#11718694C211yesmaximal, characteristic
5#11718657C211yesmaximal, characteristic, complemented
6#11718536C211yesmaximal, characteristic, complemented
7#11718535C211yesmaximal, characteristic, complemented
8#11718518C211yesmaximal, characteristic, complemented
9#11718517C211yesmaximal, characteristic, complemented
10#11718429C211yesmaximal, characteristic, complemented
11#11718427C211yesmaximal, characteristic, complemented
12#11718426C211yesmaximal, characteristic, complemented
13#11718420C211yesmaximal, characteristic, complemented
14#11718383C211yesmaximal, characteristic, complemented
15#11718381C211yesmaximal, characteristic, complemented
16C13×#121C2211yescharacteristic
17C13×#117C2211yescharacteristic
18#88190—21no—
19#88190C2211yescharacteristic
20#88189—21no—
21D4×Dic13C2211yescharacteristic
22#88180C2211yescharacteristic
23C2×C4⋊Dic13C2211yescharacteristic
24#88178C2211yescharacteristic
25#88144C2211yescharacteristic
26#88144C2211yescharacteristic
27#88142C2211yescharacteristic
28#88142C2211yescharacteristic
29#88142C2211yescharacteristic
30#88141C2211yescharacteristic
31#88133—21no—
32#88132—21no—
33#88132—21no—
34#88132—21no—
35#88124—21no—
36#88123—21no—
37C13×#107C2211yescharacteristic
38C13×#106C2211yescharacteristic
39C13×#102C2211yescharacteristic
40C13×#102C2211yescharacteristic
41C13×C22⋊C8C2211yescharacteristic
42#88072C2211yescharacteristic
43#88072C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88058C2211yescharacteristic
46#88058C2211yescharacteristic
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×D4×C13—21no—
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×Dic13—21no—
63C22×Dic13—21no—
64C2×Dic26—21no—
65C2×Dic26—21no—
66C2×Dic26—21no—
67C2×Dic26C2311yescharacteristic
68C2×C8×C13C2311yescharacteristic
69C2×C8×C13C2311yescharacteristic
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—
78C22⋊Dic13—21no—
79C22⋊Dic13—21no—
80C22⋊Dic13D411yescharacteristic
81C22⋊Dic13D411yescharacteristic
82C4⋊Dic13—21no—
83C4⋊Dic13—21no—
84C4⋊Dic13—21no—
85C4⋊Dic13D411yescharacteristic
86C4⋊Dic13D411yescharacteristic
87C4⋊Dic13C2311yescharacteristic
88C4⋊Dic13C2311yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97C4×Dic13—21no—
98C4×Dic13C2311yescharacteristic
99C4×Dic13C2311yescharacteristic
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102#3243—131nomaximal, Sylow
103C23×C13—21no—
104C23×C13C2×D411yescharacteristic
105D4×C13—21no—
106D4×C13—21no—
107D4×C13—81no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13C2×D411yescharacteristic
114C2×C4×C13C2411yescharacteristic
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—81no—
120C2×Dic13—81no—
121C2×Dic13C2×D411yescharacteristic
122C2×Dic13C2×D411yescharacteristic
123C2×Dic13C2×D411yescharacteristic
124C2×Dic13C2×D411yescharacteristic
125Dic26—21no—
126Dic26—21no—
127Dic26—81no—
128Dic26—81no—
129Dic26—81no—
130C8×C13—21no—
131C8×C13—21no—
132#1055—21no—
133#1055—21no—
134#544—131no—
135#542—131no—
136#501—131no—
137#500—131no—
138#489—131no—
139#488—131no—
140#485—131no—
141#484—131no—
142#482D1311yescharacteristic
143#480—131no—
144#479—131no—
145#478—131no—
146#477—131no—
147#474—131no—
148#433—131no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13C22×D411yescharacteristic
156C4×C13—21no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C13—41no—
160C4×C132−1+411yescharacteristic
161C4×C132−1+411yescharacteristic
162Dic13—21no—
163Dic13—21no—
164Dic13—21no—
165Dic13—21no—
166Dic13—41no—
167Dic13—41no—
168Dic13—41no—
169Dic13—41no—
170C4⋊Q8—131no—
171C4⋊Q8—131no—
172C4⋊Q8—131no—
173C4⋊Q8—261no—
174#126—261no—
175#125—131no—
176#125—131no—
177#125—261no—
178#124—131no—
179#124—261no—
180#123—261no—
181C22⋊Q8—131no—
182C22⋊Q8—261no—
183C22⋊Q8—261no—
184C22⋊Q8—261no—
185#121C2×D1311yescharacteristic
186C4×Q8—131no—
187C4×D4—131no—
188#117—131no—
189#117C2×D1311yescharacteristic
190C2×C4⋊C4—131no—
191#107—131no—
192#107—131no—
193#107—131no—
194#107—131no—
195#107—131no—
196#107C2×D1311yescharacteristic
197#106—131no—
198#106C2×D1311yescharacteristic
199C4⋊C8—131no—
200C4⋊C8—131no—
201#103—131no—
202#103—131no—
203#103—131no—
204#103—131no—
205#102—131no—
206#102—131no—
207#102C2×D1311yescharacteristic
208#102C2×D1311yescharacteristic
209C22⋊C8—131no—
210C22⋊C8C2×D1311yescharacteristic
211#97—131no—
212C4×C8—131no—
213C2×C13—41no—
214C2×C13—81no—
215C2×C13#53611yescharacteristic
216C2×C13#57611yescharacteristic
217C2×C13#57811yescharacteristic
218C2×Q8—131no—
219C2×Q8—261no—
220C2×Q8—261no—
221C2×Q8—261no—
222C2×D4—21no—
223C2×D4C22×D1311yescharacteristic
224C22×C4—261no—
225C22×C4—261no—
226C22×C4C22×D1311yescharacteristic
227C2×C8—131no—
228C2×C8—131no—
229C2×C8C22×D1311yescharacteristic
230C2×C8C22×D1311yescharacteristic
231C4⋊C4—131no—
232C4⋊C4—131no—
233C4⋊C4—131no—
234C4⋊C4—131no—
235C4⋊C4—131no—
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
249C22⋊C4—21no—
250C22⋊C4—21no—
251C22⋊C4—131no—
252C22⋊C4—131no—
253C22⋊C4—261no—
254C22⋊C4—261no—
255C22⋊C4—261no—
256C22⋊C4—261no—
257C42—21no—
258C42—131no—
259C42—131no—
260C42—261no—
261C13#324311yescharacteristic, complemented, Sylow
262C23—21no—
263C23D4×D1311yescharacteristic
264Q8—261no—
265Q8—261no—
266Q8—1041no—
267Q8—1041no—
268Q8—1041no—
269D4—21no—
270D4—21no—
271D4—81no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—131no—
278C2×C4—131no—
279C2×C4—131no—
280C2×C4—131no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—1041no—
286C2×C4—1041no—
287C2×C4D4×D1311yescharacteristic
288C2×C4C23×D1311yescharacteristic
289C8—21no—
290C8—21no—
291C8—261no—
292C8—261no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22C2×D4×D1311yescharacteristic
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—261no—
305C4—261no—
306C4—261no—
307C4—261no—
308C4—521no—
309C4—521no—
310C4—521no—
311C4—521no—
312C4#8825711yescharacteristic
313C4#8825711yescharacteristic
314C2—41no—
315C2—81no—
316C2#1171935311yescharacteristic
317C2#1171947611yescharacteristic
318C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#482C2
socleC22×C13C22×D4
prime radicalC13×#121C22
hypercenter#482D13
hypocenterC13#3243
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #11719224C2semidirect
5. #11718657C2semidirect
6. #11718536C2semidirect
7. #11718535C2semidirect
8. #11718518C2semidirect
9. #11718517C2semidirect
10. #11718429C2semidirect
11. #11718427C2semidirect
12. #11718426C2semidirect
13. #11718420C2semidirect
14. #11718383C2semidirect
15. #11718381C2semidirect
261. C13#3243semidirect

Maximal subgroups

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

subgroupindex
#117193082
#117192242
C13×#4822
#117186942
#117186572
#117185362
#117185352
#117185182
#117185172
#117184292
#117184272
#117184262
#117184202
#117183832
#117183812
#324313