Finite Group Databasebeta

← #13127657

Subgroups — #13127657

Order 1664.

346 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#556C211yesmaximal, characteristic, complemented
2#11719284C211yesmaximal, characteristic, complemented
3#11718744C211yesmaximal, characteristic, complemented
4#11718743C211yesmaximal, characteristic, complemented
5#11718718C211yesmaximal, characteristic
6#11718718C211yesmaximal, characteristic
7#11718717C211yesmaximal, characteristic, complemented
8#11718716C211yesmaximal, characteristic, complemented
9#11718687C211yesmaximal, characteristic, complemented
10C4×#6106C211yesmaximal, characteristic, complemented
11#11718685C211yesmaximal, characteristic, complemented
12#11718683C211yesmaximal, characteristic, complemented
13#11718681C211yesmaximal, characteristic, complemented
14#11718675C211yesmaximal, characteristic
15#11718670C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8C2211yescharacteristic
17C13×#126—21no—
18C13×#126—21no—
19C13×#124C2211yescharacteristic
20C13×#124C2211yescharacteristic
21C13×C22⋊Q8—21no—
22C4×Q8×C13C2211yescharacteristic
23C4×Q8×C13C2211yescharacteristic
24C4×Q8×C13C2211yescharacteristic
25C4×D4×C13C2211yescharacteristic
26C13×#117—21no—
27#88200—21no—
28C2×#6106C2211yescharacteristic
29C2×#6106C2211yescharacteristic
30C2×#6104C2211yescharacteristic
31#88150—21no—
32#88150—21no—
33C4⋊C4×D13—21no—
34C4×D52C2211yescharacteristic
35C4×D52C2211yescharacteristic
36C4×D52C2211yescharacteristic
37#88124C2211yescharacteristic
38#88124C2211yescharacteristic
39#88123C2211yescharacteristic
40#88075C2211yescharacteristic
41#88075C2211yescharacteristic
42#88075C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88072C2211yescharacteristic
49#88049C2211yescharacteristic
50#88048C2211yescharacteristic
51#88048C2211yescharacteristic
52#88047C2211yescharacteristic
53C4⋊#1055C2211yescharacteristic
54C4⋊#1055C2211yescharacteristic
55C4⋊#1055C2211yescharacteristic
56#88043C2211yescharacteristic
57#88043C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13D411yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13—21no—
64C2×D52C2311yescharacteristic
65C2×C4×D13—21no—
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×Dic26—21no—
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4D411yescharacteristic
74C13×C4⋊C4D411yescharacteristic
75C13×C4⋊C4D411yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C22⋊C4—21no—
78C13×C22⋊C4—21no—
79C13×C22⋊C4—21no—
80C13×C22⋊C4—21no—
81C13×C22⋊C4—21no—
82C42×C13—21no—
83C42×C13—21no—
84C42×C13C2311yescharacteristic
85C42×C13C2311yescharacteristic
86C42×C13C2311yescharacteristic
87#6106—22no—
88#6106—22no—
89#6104—22no—
90#6103—21no—
91#6103—21no—
92#6103—21no—
93C4⋊Dic13—21no—
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101—21no—
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#3376—131nomaximal, Sylow
106C23×C13—21no—
107C22×D13—21no—
108Q8×C13—21no—
109Q8×C13—21no—
110Q8×C13—21no—
111Q8×C13—21no—
112Q8×C13—41no—
113D4×C13—21no—
114D4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—42no—
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2411yescharacteristic
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129D52—21no—
130D52#4112yes—
131C4×D13—42no—
132C4×D13—81no—
133C4×D13—81no—
134Dic26—81no—
135#1055—21no—
136#1055—21no—
137#1055—21no—
138#1055—21no—
139#556D1311yescharacteristic, complemented
140#554—131no—
141#491—131no—
142#489—131no—
143#488—131no—
144#479—131no—
145#478—131no—
146#475—131no—
147#463—131no—
148#463—131no—
149#461—131no—
150#446—131no—
151#442—131no—
152#440—131no—
153C4×SD16—131no—
154C22×C13—41no—
155C22×C13—41no—
156C22×C13—41no—
157C22×C13C22×D411yescharacteristic
158C2×D13—22no—
159C2×D13—41no—
160C2×D13—41no—
161C4×C13—21no—
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13C2×#4111yescharacteristic
171C4×C132−1+411yescharacteristic
172Dic13—41no—
173Dic13—41no—
174Dic13—41no—
175C2×SD16—131no—
176C2×SD16—131no—
177C2×D8—131no—
178C4⋊Q8—131no—
179C4⋊Q8C2×D1311yescharacteristic
180#126—21no—
181#126—21no—
182#125—131no—
183#125—131no—
184#124C2×D1311yescharacteristic
185#124C2×D1311yescharacteristic
186C22⋊Q8—21no—
187C22⋊Q8—261no—
188C22⋊Q8—261no—
189C22⋊Q8—261no—
190C4×Q8C2×D1311yescharacteristic
191C4×Q8C2×D1311yescharacteristic
192C4×Q8C2×D1311yescharacteristic
193C4×D4—131no—
194C4×D4—131no—
195C4×D4—131no—
196C4×D4C2×D1311yescharacteristic
197#117—21no—
198C2×C4⋊C4—261no—
199#107—131no—
200#106—131no—
201#106—131no—
202C4⋊C8—131no—
203C4⋊C8—131no—
204C4⋊C8—131no—
205#103—131no—
206#103—131no—
207#103—131no—
208#103—131no—
209#103—131no—
210#103—131no—
211#102—131no—
212#102—131no—
213#102—131no—
214#102—131no—
215#97—131no—
216#97—131no—
217C4×C8—131no—
218C2×C13—81no—
219C2×C13#54811yescharacteristic
220C2×C13#57511yescharacteristic
221C2×C13#57711yescharacteristic
222D13—42no—
223C2×Q8—261no—
224C2×Q8C22⋊D1311yescharacteristic
225C2×Q8C22×D1311yescharacteristic
226C2×Q8C22×D1311yescharacteristic
227C2×D4—131no—
228C2×D4C22×D1311yescharacteristic
229C22×C4—21no—
230C22×C4—261no—
231C22×C4—261no—
232C22×C4—261no—
233SD16—262no—
234SD16—262no—
235D8—262no—
236C2×C8—131no—
237C2×C8—131no—
238C2×C8—131no—
239C2×C8—131no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—131no—
245C4⋊C4—131no—
246C4⋊C4—131no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4C22⋊D1311yescharacteristic
253C4⋊C4C22⋊D1311yescharacteristic
254C4⋊C4C22⋊D1311yescharacteristic
255C4⋊C4C22×D1311yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—261no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C42—21no—
265C42—21no—
266C42C22×D1311yescharacteristic
267C42C22×D1311yescharacteristic
268C42C22×D1311yescharacteristic
269C13#337611yescharacteristic, complemented, Sylow
270C23—21no—
271C23—261no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—21no—
276Q8—41no—
277Q8—1041no—
278D4—21no—
279D4—21no—
280D4—132no—
281D4—261no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—42no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—522no—
290C2×C4—1041no—
291C2×C4—1041no—
292C2×C4C2×C22⋊D1311yescharacteristic
293C2×C4C2×C22⋊D1311yescharacteristic
294C2×C4C2×C22⋊D1311yescharacteristic
295C2×C4C2×C22⋊D1311yescharacteristic
296C2×C4C2×C22⋊D1311yescharacteristic
297C2×C4C2×C22⋊D1311yescharacteristic
298C2×C4C23×D1311yescharacteristic
299C8—261no—
300C8—261no—
301C8—261no—
302C8—261no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—262no—
307C22—521no—
308C22—521no—
309C22C22×C22⋊D1311yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—521no—
320C4—521no—
321C4—521no—
322C4#41×D1311yescharacteristic
323C4#8825711yescharacteristic
324C2—81no—
325C2—522no—
326C2#1171952711yescharacteristic
327C2#1171953611yescharacteristic
328C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#556C2
socleC22×C13C22×D4
prime radicalC2×#6104C22
hypercenter#556D13
hypocenterC13#3376
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. C13×#556C2semidirect
2. #11719284C2semidirect
3. #11718744C2semidirect
4. #11718743C2semidirect
7. #11718717C2semidirect
8. #11718716C2semidirect
9. #11718687C2semidirect
10. C4×#6106C2semidirect
11. #11718685C2semidirect
12. #11718683C2semidirect
13. #11718681C2semidirect
15. #11718670C2semidirect
139. #556D13semidirect
269. C13#3376semidirect

Maximal subgroups

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

subgroupindex
C13×#5562
#117192842
#117187442
#117187432
#117187182
#117187172
#117187162
#117186872
C4×#61062
#117186852
#117186832
#117186812
#117186752
#117186702
#337613