Finite Group Databasebeta

← #13125050

Subgroups — #13125050

Order 1664.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#520C211yesmaximal, characteristic
2#11719223C211yesmaximal, characteristic, complemented
3#11718900C211yesmaximal, characteristic
4#11718900C211yesmaximal, characteristic
5#11718692C211yesmaximal, characteristic, complemented
6#11718691C211yesmaximal, characteristic, complemented
7C4×#6107C211yesmaximal, characteristic, complemented
8#11718683C211yesmaximal, characteristic, complemented
9#11718680C211yesmaximal, characteristic, complemented
10#11718679C211yesmaximal, characteristic, complemented
11C4×#6105C211yesmaximal, characteristic, complemented
12#11718670C211yesmaximal, characteristic, complemented
13#11718661C211yesmaximal, characteristic, complemented
14#11718632C211yesmaximal, characteristic, complemented
15#11718631C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C4×Q8×C13C2211yescharacteristic
18C4×Q8×C13C2211yescharacteristic
19C4×D4×C13—21no—
20C4×D4×C13—21no—
21C4×D4×C13C2211yescharacteristic
22C4×D4×C13C2211yescharacteristic
23C13×#117—21no—
24C13×#117C2211yescharacteristic
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4C2211yescharacteristic
27C2×#6107C2211yescharacteristic
28C2×#6107C2211yescharacteristic
29C2×#6105C2211yescharacteristic
30C2×#6105C2211yescharacteristic
31#88178C2211yescharacteristic
32#88178C2211yescharacteristic
33#88143—21no—
34#88143—21no—
35#88133—21no—
36#88133—21no—
37#88124C2211yescharacteristic
38#88123C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C4×Dic26C2211yescharacteristic
41#88075C2211yescharacteristic
42#88075C2211yescharacteristic
43#88072C2211yescharacteristic
44#88072C2211yescharacteristic
45C22⋊#1055C2211yescharacteristic
46C22⋊#1055C2211yescharacteristic
47#88050C2211yescharacteristic
48#88050C2211yescharacteristic
49#88050C2211yescharacteristic
50#88050C2211yescharacteristic
51#88048C2211yescharacteristic
52#88048C2211yescharacteristic
53#88047C2211yescharacteristic
54#88047C2211yescharacteristic
55C4⋊#1055C2211yescharacteristic
56C4⋊#1055C2211yescharacteristic
57#88043C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C13×#41—22no—
60C13×#41—22no—
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13—21no—
63C2×D4×C13C2311yescharacteristic
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13C2311yescharacteristic
69C2×Dic26C2311yescharacteristic
70C2×Dic26C2311yescharacteristic
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4D411yescharacteristic
75C13×C4⋊C4D411yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C22⋊C4—21no—
79C13×C22⋊C4—21no—
80C13×C22⋊C4D411yescharacteristic
81C13×C22⋊C4D411yescharacteristic
82C42×C13—21no—
83C42×C13—21no—
84C42×C13C2311yescharacteristic
85C42×C13C2311yescharacteristic
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88#6107—22no—
89#6107—22no—
90#6105—22no—
91#6105—22no—
92C4⋊Dic13—21no—
93C4⋊Dic13—21no—
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101—21no—
101#6101—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108#3120—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13C2×D411yescharacteristic
111Q8×C13—21no—
112Q8×C13#4112yes—
113D4×C13—24no—
114D4×C13—21no—
115D4×C13#4112yes—
116C2×C4×C13—24no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—81no—
123C2×C4×C13—81no—
124C2×C4×C13—81no—
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2×D411yescharacteristic
128C2×C4×C13C2×D411yescharacteristic
129C2×C4×C13C2×D411yescharacteristic
130C2×C4×C13C2411yescharacteristic
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135Dic26—21no—
136Dic26—21no—
137Dic26—21no—
138Dic26—21no—
139#1055—21no—
140#1055—21no—
141#1055—21no—
142#1055—21no—
143#541—131no—
144#520D1311yescharacteristic
145#484—131no—
146#483—131no—
147#479—131no—
148#478—131no—
149#462—131no—
150#461—131no—
151#452—131no—
152#452—131no—
153#441—131no—
154#440—131no—
155C4×Q16—131no—
156C4×SD16—131no—
157#433—131no—
158C22×C13—21no—
159C22×C13—22no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13C22×D411yescharacteristic
165C4×C13—21no—
166C4×C13—22no—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13C2×#4111yescharacteristic
174C4×C13C2×#4111yescharacteristic
175Dic13—41no—
176Dic13—41no—
177Dic13—41no—
178Dic13—41no—
179C2×#41C2×D1311yescharacteristic
180C2×Q16—131no—
181C2×Q16—131no—
182C2×SD16—131no—
183C2×SD16—131no—
184C4⋊Q8—131no—
185#126—261no—
186#126—261no—
187#125—131no—
188#125—261no—
189#125—261no—
190C22⋊Q8—131no—
191C22⋊Q8—131no—
192C4×Q8—131no—
193C4×Q8—131no—
194C4×Q8C2×D1311yescharacteristic
195C4×Q8C2×D1311yescharacteristic
196C4×D4—21no—
197C4×D4—21no—
198C4×D4C2×D1311yescharacteristic
199C4×D4C2×D1311yescharacteristic
200#117—21no—
201#117C2×D1311yescharacteristic
202C2×C4⋊C4—21no—
203C2×C4⋊C4C2×D1311yescharacteristic
204#107—131no—
205#107—131no—
206#106—131no—
207#106—131no—
208C4⋊C8—131no—
209C4⋊C8—131no—
210#103—131no—
211#103—131no—
212#103—131no—
213#103—131no—
214#103—131no—
215#103—131no—
216#102—131no—
217#102—131no—
218C22⋊C8—131no—
219C22⋊C8—131no—
220#97—131no—
221C4×C8—131no—
222C2×C13—41no—
223C2×C13—42no—
224C2×C13#52511yescharacteristic
225C2×C13#57711yescharacteristic
226C2×C13#57811yescharacteristic
227#41—22no—
228#41—22no—
229C2×Q8—131no—
230C2×Q8—131no—
231C2×Q8C22×D1311yescharacteristic
232C2×D4—21no—
233C2×D4C22×D1311yescharacteristic
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4C22×D1311yescharacteristic
239Q16—262no—
240Q16—262no—
241SD16—262no—
242SD16—262no—
243C2×C8—131no—
244C2×C8—131no—
245C2×C8—131no—
246C2×C8—131no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
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
263C4⋊C4C22×D1311yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4C22⋊D1311yescharacteristic
269C22⋊C4C22⋊D1311yescharacteristic
270C42—21no—
271C42—21no—
272C42—261no—
273C42—261no—
274C42C22×D1311yescharacteristic
275C42C22×D1311yescharacteristic
276C13#312011yescharacteristic, complemented, Sylow
277C23—21no—
278C23C2×C22⋊D1311yescharacteristic
279Q8—21no—
280Q8—261no—
281Q8—261no—
282Q8—261no—
283Q8—261no—
284Q8#612712yes—
285D4—24no—
286D4—21no—
287D4#612712yes—
288C2×C4—24no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4C2×C22⋊D1311yescharacteristic
302C2×C4C2×C22⋊D1311yescharacteristic
303C2×C4C2×C22⋊D1311yescharacteristic
304C2×C4C2×C22⋊D1311yescharacteristic
305C2×C4C2×C22⋊D1311yescharacteristic
306C2×C4C23×D1311yescharacteristic
307C8—261no—
308C8—261no—
309C8—261no—
310C8—261no—
311C22—21no—
312C22—22no—
313C22—21no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22C22×C22⋊D1311yescharacteristic
318C4—21no—
319C4—22no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—521no—
327C4—521no—
328C4—521no—
329C4—521no—
330C4C2×#612711yescharacteristic
331C4C2×#612711yescharacteristic
332C2—41no—
333C2—42no—
334C2#1171949611yescharacteristic
335C2#1171954111yescharacteristic
336C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#520C2
socleC22×C13C22×D4
prime radicalC2×C13×#41C22
hypercenter#520D13
hypocenterC13#3120
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
2. #11719223C2semidirect
5. #11718692C2semidirect
6. #11718691C2semidirect
7. C4×#6107C2semidirect
8. #11718683C2semidirect
9. #11718680C2semidirect
10. #11718679C2semidirect
11. C4×#6105C2semidirect
12. #11718670C2semidirect
13. #11718661C2semidirect
14. #11718632C2semidirect
15. #11718631C2semidirect
276. C13#3120semidirect

Maximal subgroups

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

subgroupindex
C13×#5202
#117192232
#117189002
#117186922
#117186912
C4×#61072
#117186832
#117186802
#117186792
C4×#61052
#117186702
#117186612
#117186322
#117186312
#312013