Finite Group Databasebeta

← #13127368

Subgroups — #13127368

Order 1664.

336 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719247C211yesmaximal, characteristic
2#11719246C211yesmaximal, characteristic
3C13×#435C211yesmaximal, characteristic
4#11718798C211yesmaximal, characteristic, complemented
5#11718782C211yesmaximal, characteristic, complemented
6#11718777C211yesmaximal, characteristic, complemented
7#11718767C211yesmaximal, characteristic, complemented
8#11718511C211yesmaximal, characteristic, complemented
9#11718490C211yesmaximal, characteristic, complemented
10#11718384C211yesmaximal, characteristic, complemented
11#11718384C211yesmaximal, characteristic, complemented
12#11718384C211yesmaximal, characteristic, complemented
13#11718383C211yesmaximal, characteristic, complemented
14#11718377C211yesmaximal, characteristic, complemented
15#11718363C211yesmaximal, characteristic, complemented
16C2×C13×M16C2211yescharacteristic
17C22×C8×C13C2211yescharacteristic
18C4×D4×C13C2211yescharacteristic
19#88190—21no—
20#88189—21no—
21#88180C2211yescharacteristic
22#88180C2211yescharacteristic
23#88180C2211yescharacteristic
24C2×C4⋊Dic13C2211yescharacteristic
25#88178C2211yescharacteristic
26#88178C2211yescharacteristic
27#88178C2211yescharacteristic
28#88178C2211yescharacteristic
29C2×Dic52C2211yescharacteristic
30#88143—21no—
31#88141—21no—
32#88133—21no—
33#88133—21no—
34#88133—21no—
35#88131—21no—
36#88124C2211yescharacteristic
37#88123C2211yescharacteristic
38C4×Dic26C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×C4⋊C8C2211yescharacteristic
41C13×C22⋊C8C2211yescharacteristic
42C13×C22⋊C8C2211yescharacteristic
43C13×#97C2211yescharacteristic
44#88058C2211yescharacteristic
45#88058C2211yescharacteristic
46#88058C2211yescharacteristic
47#88058C2211yescharacteristic
48#88058C2211yescharacteristic
49#88057C2211yescharacteristic
50#88057C2211yescharacteristic
51#88057C2211yescharacteristic
52#88057C2211yescharacteristic
53#88056C2211yescharacteristic
54#88056C2211yescharacteristic
55#88056C2211yescharacteristic
56#88056C2211yescharacteristic
57#88056C2211yescharacteristic
58#88056C2211yescharacteristic
59C2×D4×C13D411yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C22×Dic13—21no—
63C2×Dic26—21no—
64C2×Dic26C2311yescharacteristic
65C2×Dic26C2311yescharacteristic
66C13×M16—22no—
67C2×C8×C13—22no—
68C2×C8×C13C2311yescharacteristic
69C2×C8×C13C2311yescharacteristic
70C2×C8×C13C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C13×C4⋊C4D411yescharacteristic
73C13×C22⋊C4D411yescharacteristic
74C13×C22⋊C4D411yescharacteristic
75C42×C13C2311yescharacteristic
76C22⋊Dic13—21no—
77C22⋊Dic13—21no—
78C22⋊Dic13—21no—
79C22⋊Dic13—21no—
80C22⋊Dic13—21no—
81C22⋊Dic13—21no—
82C22⋊Dic13—21no—
83C4⋊Dic13—21no—
84C4⋊Dic13—21no—
85C4⋊Dic13C2311yescharacteristic
86C4⋊Dic13C2311yescharacteristic
87C4⋊Dic13C2311yescharacteristic
88C4⋊Dic13C2311yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
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—
102C4×Dic13—21no—
103C4×Dic13—21no—
104Dic52—22no—
105#3349—131nomaximal, Sylow
106C23×C13C2×D411yescharacteristic
107C23×C13C2×D411yescharacteristic
108D4×C13—41no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13C2×D411yescharacteristic
114C2×C4×C13C2×D411yescharacteristic
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2411yescharacteristic
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—42no—
127Dic26—21no—
128Dic26—21no—
129Dic26—21no—
130Dic26—21no—
131Dic26—42no—
132C8×C13—21no—
133C8×C13—21no—
134C8×C13—21no—
135C8×C13#4112yes—
136#556—131no—
137#552—131no—
138#501—131no—
139#485—131no—
140#485—131no—
141#485—131no—
142#484—131no—
143#479—131no—
144#477—131no—
145#470—131no—
146#467—131no—
147#441—131no—
148#435D1311yescharacteristic
149#428—131no—
150#427—131no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13C22×D411yescharacteristic
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—21no—
162C4×C13C2×#4111yescharacteristic
163C4×C132−1+411yescharacteristic
164Dic13—41no—
165Dic13—41no—
166Dic13—41no—
167Dic13—41no—
168Dic13—41no—
169Dic13—41no—
170Dic13—41no—
171Dic13—41no—
172C2×Q16—131no—
173C2×M16C2×D1311yescharacteristic
174C22×C8C2×D1311yescharacteristic
175C4⋊Q8—131no—
176#126—261no—
177#126—261no—
178#126—261no—
179#125—131no—
180#125—261no—
181#124—261no—
182#123—261no—
183C22⋊Q8—131no—
184C22⋊Q8—131no—
185C22⋊Q8—131no—
186C22⋊Q8—131no—
187C4×Q8—131no—
188C4×Q8—131no—
189C4×Q8—261no—
190C4×D4C2×D1311yescharacteristic
191#117—131no—
192#117—131no—
193#117—131no—
194#117—261no—
195C2×C4⋊C4—131no—
196#107—131no—
197#107—131no—
198#107—131no—
199#107—131no—
200#107—131no—
201#106—131no—
202#106—131no—
203#106—131no—
204#106—131no—
205C4⋊C8C2×D1311yescharacteristic
206#103—131no—
207#103—131no—
208#103—131no—
209#103—131no—
210#103—131no—
211#103—131no—
212C22⋊C8C2×D1311yescharacteristic
213C22⋊C8C2×D1311yescharacteristic
214#97C2×D1311yescharacteristic
215C2×C13—41no—
216C2×C13—41no—
217C2×C13#54711yescharacteristic
218C2×C13#57511yescharacteristic
219C2×C13#57811yescharacteristic
220C2×Q8—131no—
221C2×Q8—131no—
222C2×Q8—261no—
223C2×D4D5211yescharacteristic
224C22×C4—261no—
225C22×C4C22×D1311yescharacteristic
226C22×C4C22×D1311yescharacteristic
227Q16—262no—
228M16—22no—
229C2×C8—22no—
230C2×C8C22×D1311yescharacteristic
231C2×C8C22×D1311yescharacteristic
232C2×C8C22×D1311yescharacteristic
233C2×C8C22×D1311yescharacteristic
234C4⋊C4—131no—
235C4⋊C4—131no—
236C4⋊C4—131no—
237C4⋊C4—131no—
238C4⋊C4—131no—
239C4⋊C4—131no—
240C4⋊C4—261no—
241C4⋊C4—261no—
242C4⋊C4—261no—
243C4⋊C4—261no—
244C4⋊C4—261no—
245C4⋊C4—261no—
246C4⋊C4—261no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4D5211yescharacteristic
251C22⋊C4—261no—
252C22⋊C4—261no—
253C22⋊C4—261no—
254C22⋊C4—261no—
255C22⋊C4—261no—
256C22⋊C4—261no—
257C22⋊C4—261no—
258C22⋊C4D5211yescharacteristic
259C22⋊C4D5211yescharacteristic
260C42—261no—
261C42—261no—
262C42—261no—
263C42—261no—
264C42—261no—
265C42C22×D1311yescharacteristic
266C13#334911yescharacteristic, complemented, Sylow
267C23C2×D5211yescharacteristic
268C23C2×D5211yescharacteristic
269Q8—261no—
270Q8—261no—
271Q8—261no—
272Q8—261no—
273Q8—522no—
274D4—41no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—522no—
288C2×C4C2×D5211yescharacteristic
289C2×C4C2×D5211yescharacteristic
290C2×C4C2×D5211yescharacteristic
291C2×C4C2×D5211yescharacteristic
292C2×C4C23×D1311yescharacteristic
293C8—21no—
294C8—21no—
295C8—21no—
296C8#612912yes—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22C22×D5211yescharacteristic
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—521no—
309C4—521no—
310C4—521no—
311C4—521no—
312C4—521no—
313C4—521no—
314C4—521no—
315C4—521no—
316C4C2×#612911yescharacteristic
317C4#8825711yescharacteristic
318C2—41no—
319C2—41no—
320C2#1171926011yescharacteristic
321C2#1171945311yescharacteristic
322C2#1171945811yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#435C2
socleC22×C13C22×D4
prime radicalC2×D4×C13D4
hypercenter#435D13
hypocenterC13#3349
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
4. #11718798C2semidirect
5. #11718782C2semidirect
6. #11718777C2semidirect
7. #11718767C2semidirect
8. #11718511C2semidirect
9. #11718490C2semidirect
10. #11718384C2semidirect
11. #11718384C2semidirect
12. #11718384C2semidirect
13. #11718383C2semidirect
14. #11718377C2semidirect
15. #11718363C2semidirect
266. C13#3349semidirect

Maximal subgroups

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

subgroupindex
#117192472
#117192462
C13×#4352
#117187982
#117187822
#117187772
#117187672
#117185112
#117184902
#117183842
#117183832
#117183772
#117183632
#334913