Finite Group Databasebeta

← #13126010

Subgroups — #13126010

Order 1664.

332 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#11719393C211yesmaximal, characteristic, complemented
2#11719385C211yesmaximal, characteristic
3C13×#488C211yesmaximal, characteristic, complemented
4#11718725C211yesmaximal, characteristic, complemented
5#11718717C211yesmaximal, characteristic, complemented
6#11718476C211yesmaximal, characteristic, complemented
7#11718475C211yesmaximal, characteristic, complemented
8#11718455C211yesmaximal, characteristic, complemented
9#11718452C211yesmaximal, characteristic, complemented
10#11718445C211yesmaximal, characteristic
11#11718440C211yesmaximal, characteristic
12#11718422C211yesmaximal, characteristic, complemented
13#11718420C211yesmaximal, characteristic, complemented
14#11718346C211yesmaximal, characteristic, complemented
15#11718344C211yesmaximal, characteristic, complemented
16C13×#125C2211yescharacteristic
17C13×#124C2211yescharacteristic
18#88200C2211yescharacteristic
19Q8×Dic13C2211yescharacteristic
20#88192C2211yescharacteristic
21D4×Dic13C2211yescharacteristic
22#88150—21no—
23#88150—21no—
24#88146C2211yescharacteristic
25#88146C2211yescharacteristic
26#88142C2211yescharacteristic
27#88142C2211yescharacteristic
28#88141—21no—
29#88141—21no—
30#88137—21no—
31#88135—21no—
32#88133—21no—
33#88131—21no—
34C42×D13C2211yescharacteristic
35#88124C2211yescharacteristic
36#88124C2211yescharacteristic
37C13×#103C2211yescharacteristic
38C13×#103C2211yescharacteristic
39C13×#102C2211yescharacteristic
40C13×#102C2211yescharacteristic
41C4×C8×C13C2211yescharacteristic
42#88075C2211yescharacteristic
43#88075C2211yescharacteristic
44#88072C2211yescharacteristic
45#88072C2211yescharacteristic
46#88060C2211yescharacteristic
47#88060C2211yescharacteristic
48#88058C2211yescharacteristic
49#88058C2211yescharacteristic
50#88057C2211yescharacteristic
51#88057C2211yescharacteristic
52#88054C2211yescharacteristic
53#88054C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13C2311yescharacteristic
61C2×C22⋊D13—21no—
62C22×Dic13—21no—
63C2×C4×D13D411yescharacteristic
64C2×C4×D13D411yescharacteristic
65C2×C4×D13C2311yescharacteristic
66C2×Dic26—21no—
67C2×Dic26—21no—
68C2×C8×C13C2311yescharacteristic
69C2×C8×C13C2311yescharacteristic
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4C2311yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C22⋊C4—21no—
75C13×C22⋊C4—21no—
76C42×C13C2311yescharacteristic
77C22⋊Dic13—21no—
78C22⋊Dic13—21no—
79#6103—21no—
80#6103—21no—
81#6103—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—
94C4×Dic13—21no—
95C4×Dic13—21no—
96C4×Dic13—21no—
97C4×Dic13D411yescharacteristic
98C4×Dic13D411yescharacteristic
99C4×Dic13C2311yescharacteristic
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102#3233—131nomaximal, Sylow
103C23×C13—21no—
104C22×D13C2×D411yescharacteristic
105Q8×C13—21no—
106Q8×C13—21no—
107D4×C13—21no—
108D4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13C2×D411yescharacteristic
113C2×C4×C13C2×D411yescharacteristic
114C2×C4×C13C2411yescharacteristic
115C22⋊D13—42no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—42no—
121C2×Dic13C2×D411yescharacteristic
122C2×Dic13C2×D411yescharacteristic
123C2×Dic13C2×D411yescharacteristic
124C4×D13—21no—
125C4×D13—21no—
126C4×D13—22no—
127C4×D13—41no—
128Dic26—42no—
129Dic26—42no—
130C8×C13—21no—
131C8×C13—21no—
132#1055—21no—
133#1055—21no—
134#533—131no—
135#529—131no—
136#499—131no—
137#499—131no—
138#488—131no—
139#488D1311yescharacteristic, complemented
140#485—131no—
141#485—131no—
142#482—131no—
143#482—131no—
144#477—131no—
145#476—131no—
146#475—131no—
147#474—131no—
148#431—131no—
149C22×C13—41no—
150C22×C13—41no—
151C22×C13—41no—
152C22×C13C22×D411yescharacteristic
153C2×D13—21no—
154C2×D13—21no—
155C2×D13—21no—
156C4×C13—21no—
157C4×C13—21no—
158C4×C13—41no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C132−1+411yescharacteristic
162C4×C132−1+411yescharacteristic
163Dic13—21no—
164Dic13—21no—
165Dic13—41no—
166Dic13—41no—
167Dic13—41no—
168Dic13—41no—
169Dic13#13512yes—
170C4⋊Q8—131no—
171C4⋊Q8—131no—
172#126—261no—
173#125—131no—
174#125—131no—
175#125C2×D1311yescharacteristic
176#124C2×D1311yescharacteristic
177#123—261no—
178C22⋊Q8—131no—
179C22⋊Q8—261no—
180C22⋊Q8—261no—
181#121—131no—
182C4×Q8—131no—
183C4×Q8—261no—
184C4×Q8—261no—
185C4×D4—131no—
186C4×D4—261no—
187#117—131no—
188#117—131no—
189#117—261no—
190C2×C42—131no—
191#107—131no—
192#107—131no—
193#107—131no—
194#107—131no—
195#106—131no—
196#106—131no—
197#106—131no—
198#106—131no—
199C4⋊C8—131no—
200C4⋊C8—131no—
201#103—131no—
202#103—131no—
203#103C2×D1311yescharacteristic
204#103C2×D1311yescharacteristic
205#102—131no—
206#102—131no—
207#102C2×D1311yescharacteristic
208#102C2×D1311yescharacteristic
209C22⋊C8—131no—
210C22⋊C8—131no—
211C4×C8—131no—
212C4×C8C2×D1311yescharacteristic
213C2×C13—81no—
214C2×C13#53611yescharacteristic
215C2×C13C2×#13511yescharacteristic
216C2×C13#57511yescharacteristic
217D13—41no—
218C2×Q8—261no—
219C2×Q8—261no—
220C2×Q8C22×D1311yescharacteristic
221C2×D4—261no—
222C2×D4C22×D1311yescharacteristic
223C22×C4—131no—
224C22×C4—131no—
225C22×C4—131no—
226C22×C4—261no—
227C2×C8—131no—
228C2×C8—131no—
229C2×C8C22×D1311yescharacteristic
230C2×C8C22×D1311yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—131no—
234C4⋊C4—131no—
235C4⋊C4—131no—
236C4⋊C4—131no—
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⋊C4C22×D1311yescharacteristic
246C4⋊C4C22×D1311yescharacteristic
247C22⋊C4—21no—
248C22⋊C4—21no—
249C22⋊C4—261no—
250C22⋊C4—261no—
251C22⋊C4—261no—
252C22⋊C4—261no—
253C22⋊C4—261no—
254C42—131no—
255C42—131no—
256C42—131no—
257C42—261no—
258C42—261no—
259C42—261no—
260C42C22×D1311yescharacteristic
261C13#323311yescharacteristic, complemented, Sylow
262C23—21no—
263C23—131no—
264Q8—21no—
265Q8—21no—
266Q8—522no—
267Q8—522no—
268D4—21no—
269D4—21no—
270D4—522no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—131no—
275C2×C4—131no—
276C2×C4—131no—
277C2×C4—262no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—521no—
285C2×C4—522no—
286C2×C4D4×D1311yescharacteristic
287C2×C4D4×D1311yescharacteristic
288C2×C4C23×D1311yescharacteristic
289C8—21no—
290C8—21no—
291C8—261no—
292C8—261no—
293C22—41no—
294C22—41no—
295C22—41no—
296C22—261no—
297C22—261no—
298C22—261no—
299C22C2×D4×D1311yescharacteristic
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—132no—
306C4—261no—
307C4—261no—
308C4—521no—
309C4—521no—
310C4—521no—
311C4—521no—
312C4#8825711yescharacteristic
313C4#8825711yescharacteristic
314C2—81no—
315C2—521no—
316C2#1171938011yescharacteristic
317C2D13×#13511yescharacteristic
318C2#1171947311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#488C2
socleC22×C13C22×D4
prime radical#88192C22
hypercenter#488D13
hypocenterC13#3233
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #11719393C2semidirect
3. C13×#488C2semidirect
4. #11718725C2semidirect
5. #11718717C2semidirect
6. #11718476C2semidirect
7. #11718475C2semidirect
8. #11718455C2semidirect
9. #11718452C2semidirect
12. #11718422C2semidirect
13. #11718420C2semidirect
14. #11718346C2semidirect
15. #11718344C2semidirect
139. #488D13semidirect
261. C13#3233semidirect

Maximal subgroups

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

subgroupindex
#117193932
#117193852
C13×#4882
#117187252
#117187172
#117184762
#117184752
#117184552
#117184522
#117184452
#117184402
#117184222
#117184202
#117183462
#117183442
#323313