Finite Group Databasebeta

← #13127376

Subgroups — #13127376

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#11719346C211yesmaximal, characteristic, complemented
2#11719323C211yesmaximal, characteristic
3C13×#468C211yesmaximal, characteristic, complemented
4#11718832C211yesmaximal, characteristic, complemented
5#11718825C211yesmaximal, characteristic, complemented
6#11718788C211yesmaximal, characteristic, complemented
7#11718782C211yesmaximal, characteristic, complemented
8#11718704C211yesmaximal, characteristic, complemented
9#11718696C211yesmaximal, characteristic, complemented
10#11718541C211yesmaximal, characteristic, complemented
11#11718537C211yesmaximal, characteristic, complemented
12#11718476C211yesmaximal, characteristic, complemented
13#11718457C211yesmaximal, characteristic, complemented
14#11718445C211yesmaximal, characteristic, complemented
15#11718422C211yesmaximal, characteristic, complemented
16C2×C13×SD16C2211yescharacteristic
17C2×C13×M16C2211yescharacteristic
18C13×C22⋊Q8C2211yescharacteristic
19C13×#121C2211yescharacteristic
20#88200C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22#88193—21no—
23#88192C2211yescharacteristic
24D4×Dic13—21no—
25D4×Dic13C2211yescharacteristic
26C4×C22⋊D13C2211yescharacteristic
27#88180C2211yescharacteristic
28C2×C4⋊Dic13C2211yescharacteristic
29C2×C8×D13C2211yescharacteristic
30#88152—21no—
31#88146C2211yescharacteristic
32#88146C2211yescharacteristic
33#88144C2211yescharacteristic
34#88142C2211yescharacteristic
35#88141—21no—
36#88140—21no—
37#88139—21no—
38#88133—21no—
39#88133—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#88055C2211yescharacteristic
54#88054C2211yescharacteristic
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×D13C2311yescharacteristic
68C2×Dic26—21no—
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#6103—21no—
85#6103D411yescharacteristic
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#6101D411yescharacteristic
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C8×D13—22no—
105#3350—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—42no—
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—81no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—81no—
128C2×Dic13—81no—
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132C4×D13—21no—
133C4×D13—21no—
134Dic26—42no—
135C8×C13—21no—
136C8×C13#4112yes—
137#1055—21no—
138#1055—21no—
139#556—131no—
140#553—131no—
141#501—131no—
142#485—131no—
143#483—131no—
144#482—131no—
145#482—131no—
146#479—131no—
147#476—131no—
148#468D1311yescharacteristic, complemented
149#465—131no—
150#440—131no—
151#435—131no—
152#428—131no—
153#427—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×M16C2×D1311yescharacteristic
179C22×C8—131no—
180C4⋊Q8—131no—
181#126—261no—
182#126—261no—
183#126—261no—
184#125—131no—
185#124—261no—
186#123—261no—
187C22⋊Q8—131no—
188C22⋊Q8C2×D1311yescharacteristic
189#121—131no—
190#121—261no—
191#121C2×D1311yescharacteristic
192C4×Q8—131no—
193C4×Q8—261no—
194C4×D4—131no—
195C4×D4—131no—
196C4×D4—261no—
197#117—131no—
198#117—131no—
199#117—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—
219#97—131no—
220C2×C13—41no—
221C2×C13—81no—
222C2×C13#54711yescharacteristic
223C2×C13#57511yescharacteristic
224C2×C13#57711yescharacteristic
225D13—41no—
226C2×Q8—261no—
227C2×Q8C22×D1311yescharacteristic
228C2×D4—21no—
229C2×D4—131no—
230C2×D4—261no—
231C2×D4C22×D1311yescharacteristic
232C22×C4—131no—
233C22×C4—261no—
234C22×C4—261no—
235C22×C4C22×D1311yescharacteristic
236SD16—22no—
237M16—22no—
238C2×C8—131no—
239C2×C8—131no—
240C2×C8—262no—
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⋊C4C22×D1311yescharacteristic
256C4⋊C4C22×D1311yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—131no—
260C22⋊C4—131no—
261C22⋊C4—261no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C42—131no—
268C42—261no—
269C42—261no—
270C42—261no—
271C42—261no—
272C13#335011yescharacteristic, complemented, Sylow
273C23—21no—
274C23—131no—
275C23D4×D1311yescharacteristic
276Q8—21no—
277Q8—21no—
278Q8—522no—
279D4—21no—
280D4—21no—
281D4—42no—
282D4—521no—
283D4—1041no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—131no—
290C2×C4—131no—
291C2×C4—131no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
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#1171947811yescharacteristic
334C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#468C2
socleC22×C13C22×D4
prime radical#11719323C2
hypercenter#468D13
hypocenterC13#3350
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. #11719346C2semidirect
3. C13×#468C2semidirect
4. #11718832C2semidirect
5. #11718825C2semidirect
6. #11718788C2semidirect
7. #11718782C2semidirect
8. #11718704C2semidirect
9. #11718696C2semidirect
10. #11718541C2semidirect
11. #11718537C2semidirect
12. #11718476C2semidirect
13. #11718457C2semidirect
14. #11718445C2semidirect
15. #11718422C2semidirect
148. #468D13semidirect
272. C13#3350semidirect

Maximal subgroups

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

subgroupindex
#117193462
#117193232
C13×#4682
#117188322
#117188252
#117187882
#117187822
#117187042
#117186962
#117185412
#117185372
#117184762
#117184572
#117184452
#117184222
#335013