Finite Group Databasebeta

← #13127318

Subgroups — #13127318

Order 1664.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719435C211yesmaximal, characteristic, complemented
2#11719263C211yesmaximal, characteristic
3C13×#474C211yesmaximal, characteristic, complemented
4#11718741C211yesmaximal, characteristic, complemented
5#11718679C211yesmaximal, characteristic, complemented
6#11718549C211yesmaximal, characteristic, complemented
7#11718545C211yesmaximal, characteristic, complemented
8#11718542C211yesmaximal, characteristic, complemented
9D13×#107C211yesmaximal, characteristic, complemented
10#11718497C211yesmaximal, characteristic, complemented
11#11718490C211yesmaximal, characteristic, complemented
12#11718441C211yesmaximal, characteristic, complemented
13#11718439C211yesmaximal, characteristic, complemented
14#11718438C211yesmaximal, characteristic, complemented
15#11718435C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8C2211yescharacteristic
17C4×D4×C13C2211yescharacteristic
18#88200—21no—
19#88200—21no—
20#88192C2211yescharacteristic
21#88192C2211yescharacteristic
22C2×#6105C2211yescharacteristic
23#88183—21no—
24C4×C22⋊D13—21no—
25C2×#6094C2211yescharacteristic
26C2×C8×D13C2211yescharacteristic
27#88151C2211yescharacteristic
28#88151C2211yescharacteristic
29#88147—21no—
30#88146C2211yescharacteristic
31C4⋊C4×D13C2211yescharacteristic
32C4⋊C4×D13C2211yescharacteristic
33C4⋊C4×D13C2211yescharacteristic
34#88144—21no—
35#88138—21no—
36#88133—21no—
37C4×D52C2211yescharacteristic
38#88124C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×#107C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×C4⋊C8C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×#102C2211yescharacteristic
45#88072C2211yescharacteristic
46#88060C2211yescharacteristic
47#88060C2211yescharacteristic
48#88058C2211yescharacteristic
49#88057C2211yescharacteristic
50#88056C2211yescharacteristic
51#88056C2211yescharacteristic
52#88050C2211yescharacteristic
53#88048C2211yescharacteristic
54#88048C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C2×C22⋊D13—21no—
63C2×C22⋊D13—21no—
64C2×D52D411yescharacteristic
65C2×C4×D13—21no—
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×C4×D13C2311yescharacteristic
69C2×C4×D13C2311yescharacteristic
70C2×Dic26C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C13×C4⋊C4—21no—
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C22⋊C4—21no—
78C42×C13C2311yescharacteristic
79C22⋊Dic13—21no—
80C22⋊Dic13—21no—
81#6105—22no—
82#6103—21no—
83#6103—21no—
84#6103—21no—
85#6103D411yescharacteristic
86#6103D411yescharacteristic
87C4⋊Dic13—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13D411yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103#6094—22no—
104C8×D13—22no—
105#3346—131nomaximal, Sylow
106C23×C13—21no—
107C22×D13C2×D411yescharacteristic
108C22×D13C2×D411yescharacteristic
109Q8×C13—81no—
110D4×C13—21no—
111D4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—81no—
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2411yescharacteristic
119C22⋊D13—42no—
120C22⋊D13—81no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13C2×D411yescharacteristic
126C2×Dic13C2×D411yescharacteristic
127D52—22no—
128C4×D13—21no—
129C4×D13—21no—
130C4×D13—21no—
131C4×D13—21no—
132C4×D13—81no—
133C4×D13—81no—
134C4×D13—81no—
135Dic26—21no—
136Dic26—21no—
137C8×C13—21no—
138C8×C13—21no—
139#1055—21no—
140#1055#4112yes—
141#554—131no—
142#553—131no—
143#501—131no—
144#485—131no—
145#484—131no—
146#481—131no—
147#480—131no—
148#479—131no—
149#474D1311yescharacteristic, complemented
150#468—131no—
151#465—131no—
152#440—131no—
153#435—131no—
154#428—131no—
155C2×#107—131no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13C22×D411yescharacteristic
160C2×D13—21no—
161C2×D13—21no—
162C2×D13—21no—
163C2×D13—21no—
164C2×D13—21no—
165C2×D13#13712yes—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13C2×#4111yescharacteristic
172C4×C132−1+411yescharacteristic
173Dic13—21no—
174Dic13—21no—
175Dic13—41no—
176Dic13—41no—
177Dic13—41no—
178Dic13—41no—
179C2×SD16—131no—
180C2×M16—131no—
181C22×C8—131no—
182C4⋊Q8C2×D1311yescharacteristic
183#126—261no—
184#125—131no—
185#125—261no—
186#123—261no—
187C22⋊Q8—131no—
188C22⋊Q8—131no—
189C22⋊Q8—261no—
190C22⋊Q8—261no—
191#121—131no—
192#121—131no—
193#121—261no—
194C4×Q8—131no—
195C4×D4—131no—
196C4×D4—261no—
197C4×D4—261no—
198C4×D4C2×D1311yescharacteristic
199#117—131no—
200C2×C4⋊C4—131no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4—131no—
203#107—131no—
204#107—131no—
205#107—131no—
206#107—131no—
207#107C2×D1311yescharacteristic
208#107C2×D1311yescharacteristic
209#106—131no—
210#106—131no—
211#106—131no—
212C4⋊C8C2×D1311yescharacteristic
213#103—131no—
214#103—131no—
215#103—131no—
216#102—131no—
217#102C2×D1311yescharacteristic
218#102C2×D1311yescharacteristic
219C22⋊C8—131no—
220C22⋊C8—131no—
221#97—131no—
222C2×C13—81no—
223C2×C13#54711yescharacteristic
224C2×C13C2×#13711yescharacteristic
225C2×C13#57611yescharacteristic
226D13—22no—
227D13—41no—
228C2×Q8—21no—
229C2×Q8—131no—
230C2×D4—131no—
231C2×D4—261no—
232C2×D4—261no—
233C2×D4C22×D1311yescharacteristic
234C22×C4—21no—
235C22×C4—131no—
236C22×C4—131no—
237C22×C4—261no—
238C22×C4—261no—
239C22×C4—261no—
240SD16—262no—
241M16—262no—
242C2×C8—131no—
243C2×C8—131no—
244C2×C8—262no—
245C2×C8C22×D1311yescharacteristic
246C2×C8C22×D1311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—131no—
249C4⋊C4—131no—
250C4⋊C4—131no—
251C4⋊C4—131no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4C22×D1311yescharacteristic
261C4⋊C4C22×D1311yescharacteristic
262C4⋊C4C22×D1311yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—131no—
265C22⋊C4—131no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C42—261no—
272C42—261no—
273C42C22×D1311yescharacteristic
274C13#334611yescharacteristic, complemented, Sylow
275C23—21no—
276C23—131no—
277C23—131no—
278Q8—81no—
279Q8—261no—
280Q8—261no—
281D4—21no—
282D4—21no—
283D4—262no—
284D4—522no—
285D4—1041no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—81no—
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—261no—
299C2×C4—261no—
300C2×C4—1041no—
301C2×C4—1041no—
302C2×C4—1041no—
303C2×C4D4×D1311yescharacteristic
304C2×C4D4×D1311yescharacteristic
305C2×C4C23×D1311yescharacteristic
306C8—21no—
307C8—21no—
308C8—132no—
309C8—261no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22—132no—
314C22—261no—
315C22—261no—
316C22—261no—
317C22—261no—
318C22—261no—
319C22C2×D4×D1311yescharacteristic
320C4—21no—
321C4—21no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—261no—
326C4—261no—
327C4—521no—
328C4—521no—
329C4—521no—
330C4—521no—
331C4#8825411yescharacteristic
332C4#41×D1311yescharacteristic
333C2—81no—
334C2—262no—
335C2—521no—
336C2#1171933611yescharacteristic
337C2#1171946211yescharacteristic
338C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#474C2
socleC22×C13C22×D4
prime radical#11719263C2
hypercenter#474D13
hypocenterC13#3346
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #11719435C2semidirect
3. C13×#474C2semidirect
4. #11718741C2semidirect
5. #11718679C2semidirect
6. #11718549C2semidirect
7. #11718545C2semidirect
8. #11718542C2semidirect
9. D13×#107C2semidirect
10. #11718497C2semidirect
11. #11718490C2semidirect
12. #11718441C2semidirect
13. #11718439C2semidirect
14. #11718438C2semidirect
15. #11718435C2semidirect
149. #474D13semidirect
274. C13#3346semidirect

Maximal subgroups

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

subgroupindex
#117194352
#117192632
C13×#4742
#117187412
#117186792
#117185492
#117185452
#117185422
D13×#1072
#117184972
#117184902
#117184412
#117184392
#117184382
#117184352
#334613