Finite Group Databasebeta

← #13127402

Subgroups — #13127402

Order 1664.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719347C211yesmaximal, characteristic, complemented
2#11719319C211yesmaximal, characteristic
3C13×#468C211yesmaximal, characteristic, complemented
4#11718835C211yesmaximal, characteristic, complemented
5SD16×Dic13C211yesmaximal, characteristic, complemented
6#11718789C211yesmaximal, characteristic, complemented
7#11718782C211yesmaximal, characteristic, complemented
8#11718706C211yesmaximal, characteristic, complemented
9#11718695C211yesmaximal, characteristic, complemented
10#11718542C211yesmaximal, characteristic, complemented
11#11718539C211yesmaximal, characteristic, complemented
12#11718466C211yesmaximal, characteristic, complemented
13#11718457C211yesmaximal, characteristic, complemented
14#11718445C211yesmaximal, characteristic, complemented
15#11718424C211yesmaximal, characteristic, complemented
16C2×C13×SD16C2211yescharacteristic
17C2×C13×M16C2211yescharacteristic
18C13×C22⋊Q8C2211yescharacteristic
19C13×#121C2211yescharacteristic
20#88200C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22#88192—21no—
23#88192C2211yescharacteristic
24#88189—21no—
25D4×Dic13C2211yescharacteristic
26C4×C22⋊D13C2211yescharacteristic
27#88180C2211yescharacteristic
28C2×C4⋊Dic13C2211yescharacteristic
29C2×#6094C2211yescharacteristic
30#88152—21no—
31#88146C2211yescharacteristic
32C4⋊C4×D13C2211yescharacteristic
33#88144—21no—
34#88144C2211yescharacteristic
35#88144C2211yescharacteristic
36#88140—21no—
37#88135—21no—
38#88133—21no—
39#88131—21no—
40C13×#107C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#102C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47C22⋊#1055C2211yescharacteristic
48#88060C2211yescharacteristic
49#88058C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88057C2211yescharacteristic
53#88054C2211yescharacteristic
54C8×Dic13C2211yescharacteristic
55#88048C2211yescharacteristic
56#88048C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13—21no—
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13—21no—
64C2×C22⋊D13D411yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67C2×C4×D13—21no—
68C2×C4×D13C2311yescharacteristic
69C13×SD16—22no—
70C13×M16—22no—
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C13×C4⋊C4—21no—
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C22⋊C4—21no—
77C13×C22⋊C4—21no—
78C22⋊Dic13—21no—
79C22⋊Dic13—21no—
80C22⋊Dic13—21no—
81C22⋊Dic13D411yescharacteristic
82#6103—21no—
83#6103—21no—
84#6103D411yescharacteristic
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101D411yescharacteristic
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104#6094—22no—
105#3351—131nomaximal, Sylow
106C23×C13—21no—
107C23×C13C2×D411yescharacteristic
108C22×D13C2×D411yescharacteristic
109Q8×C13—21no—
110Q8×C13—21no—
111D4×C13—21no—
112D4×C13—21no—
113D4×C13—81no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2411yescharacteristic
121C22⋊D13—41no—
122C22⋊D13—42no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—42no—
128C2×Dic13—81no—
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132C4×D13—21no—
133C4×D13—21no—
134C4×D13—81no—
135C8×C13—21no—
136C8×C13#4112yes—
137#1055—21no—
138#1055—21no—
139#553—131no—
140#552—131no—
141#499—131no—
142#485—131no—
143#483—131no—
144#482—131no—
145#481—131no—
146#479—131no—
147#478—131no—
148#468—131no—
149#468D1311yescharacteristic, complemented
150C4×SD16—131no—
151#436—131no—
152#428—131no—
153#428—131no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13C22×D411yescharacteristic
161C2×D13—21no—
162C2×D13—21no—
163C2×D13—21no—
164C4×C13—21no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13C2×#4111yescharacteristic
169C4×C132−1+411yescharacteristic
170Dic13—21no—
171Dic13—21no—
172Dic13—21no—
173Dic13—41no—
174Dic13—41no—
175Dic13—41no—
176Dic13—41no—
177C2×SD16C2×D1311yescharacteristic
178C2×M16—131no—
179C2×M16C2×D1311yescharacteristic
180#126—261no—
181#126—261no—
182#125—131no—
183#125—131no—
184#125—261no—
185#123—261no—
186#123—261no—
187C22⋊Q8—131no—
188C22⋊Q8C2×D1311yescharacteristic
189#121—131no—
190#121—261no—
191#121C2×D1311yescharacteristic
192C4×Q8—131no—
193C4×D4—131no—
194C4×D4—131no—
195C4×D4—261no—
196#117—131no—
197#117—131no—
198#117—261no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—131no—
201#107—131no—
202#107—131no—
203#107—131no—
204#107C2×D1311yescharacteristic
205#106—131no—
206#106—131no—
207#106—131no—
208#106—131no—
209#106—131no—
210C4⋊C8—131no—
211#103—131no—
212#103—131no—
213#103C2×D1311yescharacteristic
214#102—131no—
215#102—131no—
216#102C2×D1311yescharacteristic
217C22⋊C8—131no—
218C22⋊C8—131no—
219C4×C8—131no—
220C2×C13—41no—
221C2×C13—81no—
222C2×C13#54711yescharacteristic
223C2×C13#57511yescharacteristic
224C2×C13#57711yescharacteristic
225D13—41no—
226C2×Q8C22×D1311yescharacteristic
227C2×D4—21no—
228C2×D4—131no—
229C2×D4—261no—
230C2×D4C22×D1311yescharacteristic
231C22×C4—131no—
232C22×C4—261no—
233C22×C4—261no—
234C22×C4—261no—
235C22×C4C22×D1311yescharacteristic
236SD16—22no—
237M16—22no—
238M16—262no—
239C2×C8—131no—
240C2×C8—131no—
241C2×C8C22×D1311yescharacteristic
242C2×C8C22×D1311yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—131no—
245C4⋊C4—131no—
246C4⋊C4—131no—
247C4⋊C4—131no—
248C4⋊C4—131no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4C22×D1311yescharacteristic
258C4⋊C4C22×D1311yescharacteristic
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—131no—
262C22⋊C4—131no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C42—131no—
269C42—261no—
270C42—261no—
271C42—261no—
272C13#335111yescharacteristic, complemented, Sylow
273C23—21no—
274C23—131no—
275C23D4×D1311yescharacteristic
276Q8—21no—
277Q8—21no—
278D4—21no—
279D4—21no—
280D4—81no—
281D4—521no—
282D4—522no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—131no—
289C2×C4—131no—
290C2×C4—131no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—522no—
298C2×C4—1041no—
299C2×C4—1041no—
300C2×C4D4×D1311yescharacteristic
301C2×C4C23×D1311yescharacteristic
302C8—21no—
303C8—261no—
304C8—261no—
305C8#612912yes—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22—261no—
313C22—261no—
314C22—261no—
315C22C2×D4×D1311yescharacteristic
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—261no—
321C4—261no—
322C4—261no—
323C4—521no—
324C4—521no—
325C4—521no—
326C4—521no—
327C4C2×#612911yescharacteristic
328C4#8825711yescharacteristic
329C2—41no—
330C2—81no—
331C2—521no—
332C2#1171931611yescharacteristic
333C2#1171948011yescharacteristic
334C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#468C2
socleC22×C13C22×D4
prime radical#11719319C2
hypercenter#468D13
hypocenterC13#3351
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #11719347C2semidirect
3. C13×#468C2semidirect
4. #11718835C2semidirect
5. SD16×Dic13C2semidirect
6. #11718789C2semidirect
7. #11718782C2semidirect
8. #11718706C2semidirect
9. #11718695C2semidirect
10. #11718542C2semidirect
11. #11718539C2semidirect
12. #11718466C2semidirect
13. #11718457C2semidirect
14. #11718445C2semidirect
15. #11718424C2semidirect
149. #468D13semidirect
272. C13#3351semidirect

Maximal subgroups

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

subgroupindex
#117193472
#117193192
C13×#4682
#117188352
SD16×Dic132
#117187892
#117187822
#117187062
#117186952
#117185422
#117185392
#117184662
#117184572
#117184452
#117184242
#335113