Finite Group Databasebeta

← #13126247

Subgroups — #13126247

Order 1664.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#542C211yesmaximal, characteristic, complemented
2#11719240C211yesmaximal, characteristic, complemented
3#11718748C211yesmaximal, characteristic, complemented
4#11718745C211yesmaximal, characteristic, complemented
5#11718718C211yesmaximal, characteristic, complemented
6#11718718C211yesmaximal, characteristic, complemented
7#11718710C211yesmaximal, characteristic, complemented
8#11718709C211yesmaximal, characteristic, complemented
9#11718700C211yesmaximal, characteristic, complemented
10#11718699C211yesmaximal, characteristic, complemented
11#11718688C211yesmaximal, characteristic, complemented
12#11718683C211yesmaximal, characteristic, complemented
13#11718676C211yesmaximal, characteristic, complemented
14#11718670C211yesmaximal, characteristic, complemented
15#11718660C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8C2211yescharacteristic
17C13×#126—21no—
18C13×#124—21no—
19C13×#124C2211yescharacteristic
20C13×#123—21no—
21C13×C22⋊Q8—21no—
22C13×C22⋊Q8C2211yescharacteristic
23C13×#121C2211yescharacteristic
24C4×Q8×C13C2211yescharacteristic
25C4×D4×C13C2211yescharacteristic
26C13×#117C2211yescharacteristic
27C2×#6106C2211yescharacteristic
28C2×#6106C2211yescharacteristic
29C2×#6104C2211yescharacteristic
30C2×#6104C2211yescharacteristic
31#88184C2211yescharacteristic
32#88184C2211yescharacteristic
33C2×#6099C2211yescharacteristic
34C22×#1055C2211yescharacteristic
35#88148—21no—
36#88148—21no—
37#88138—21no—
38#88138—21no—
39#88128C2211yescharacteristic
40C4×D52C2211yescharacteristic
41C4×D52C2211yescharacteristic
42#88124C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47#88049C2211yescharacteristic
48#88049C2211yescharacteristic
49#88049C2211yescharacteristic
50#88049C2211yescharacteristic
51#88048C2211yescharacteristic
52#88048C2211yescharacteristic
53#88047C2211yescharacteristic
54#88047C2211yescharacteristic
55C4⋊#1055C2211yescharacteristic
56C4⋊#1055C2211yescharacteristic
57C4⋊#1055C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13—21no—
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13—21no—
64C22×C4×C13C2311yescharacteristic
65C2×C22⋊D13—21no—
66C2×C22⋊D13—21no—
67C2×D52—21no—
68C2×D52—21no—
69C2×D52C2311yescharacteristic
70C2×D52C2311yescharacteristic
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4D411yescharacteristic
77C13×C4⋊C4D411yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C22⋊C4—21no—
81C13×C22⋊C4—21no—
82C13×C22⋊C4—21no—
83C13×C22⋊C4—21no—
84C13×C22⋊C4—21no—
85C13×C22⋊C4D411yescharacteristic
86C13×C22⋊C4D411yescharacteristic
87C42×C13—21no—
88C42×C13C2311yescharacteristic
89C42×C13C2311yescharacteristic
90#6106—41no—
91#6106—41no—
92#6104—41no—
93#6104—41no—
94#6103—21no—
95#6103—21no—
96#6103—21no—
97#6103—21no—
98C4⋊Dic13C2311yescharacteristic
99C4⋊Dic13C2311yescharacteristic
100#6101—21no—
101#6101—21no—
102#6099—41no—
103C2×#1055—41no—
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108#3257—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13C2×D411yescharacteristic
111C22×D13—21no—
112C22×D13—21no—
113Q8×C13—21no—
114Q8×C13—21no—
115Q8×C13—81no—
116D4×C13—21no—
117D4×C13—21no—
118D4×C13—81no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
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
131C22⋊D13—81no—
132C22⋊D13—81no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135D52—21no—
136D52—21no—
137D52—21no—
138D52—21no—
139D52—81no—
140D52—81no—
141C4×D13—81no—
142C4×D13—81no—
143#1055—21no—
144#1055—21no—
145#1055—21no—
146#1055—21no—
147#542D1311yescharacteristic, complemented
148#540—131no—
149#479—131no—
150#478—131no—
151#476—131no—
152#474—131no—
153#469—131no—
154#468—131no—
155#466—131no—
156#465—131no—
157#463—131no—
158#463—131no—
159#460—131no—
160#459—131no—
161#424—131no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13C22×D411yescharacteristic
169C2×D13—41no—
170C2×D13—41no—
171C2×D13—41no—
172C2×D13—41no—
173C2×D13—41no—
174C2×D13—41no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13H(5,𝔽2)11yescharacteristic
184C4×C132−1+411yescharacteristic
185Dic13—41no—
186Dic13—41no—
187C2×SD16—131no—
188C2×SD16—131no—
189C2×D8—131no—
190C2×D8—131no—
191C2×M16—131no—
192C22×C8—131no—
193C4⋊Q8C2×D1311yescharacteristic
194#127—131no—
195#126—21no—
196#125—131no—
197#124—21no—
198#124C2×D1311yescharacteristic
199#123—21no—
200#123—261no—
201#123—261no—
202C22⋊Q8—21no—
203C22⋊Q8C2×D1311yescharacteristic
204#121—131no—
205#121—131no—
206#121—261no—
207#121—261no—
208#121C2×D1311yescharacteristic
209C4×Q8C2×D1311yescharacteristic
210C4×D4—131no—
211C4×D4—131no—
212C4×D4C2×D1311yescharacteristic
213#117C2×D1311yescharacteristic
214#107—131no—
215#107—131no—
216#106—131no—
217#106—131no—
218C4⋊C8—131no—
219C4⋊C8—131no—
220C4⋊C8—131no—
221C4⋊C8—131no—
222#103—131no—
223#103—131no—
224#102—131no—
225#102—131no—
226#102—131no—
227#102—131no—
228#102—131no—
229#102—131no—
230C2×C13—41no—
231C2×C13—81no—
232C2×C13#53711yescharacteristic
233C2×C13#57611yescharacteristic
234C2×C13#57711yescharacteristic
235D13—81no—
236D13—81no—
237C2×Q8—21no—
238C2×Q8C22×D1311yescharacteristic
239C2×D4—21no—
240C2×D4—131no—
241C2×D4—131no—
242C2×D4—261no—
243C2×D4—261no—
244C2×D4—261no—
245C2×D4—261no—
246C2×D4C22×D1311yescharacteristic
247C22×C4—21no—
248C22×C4—261no—
249C22×C4—261no—
250C22×C4C22×D1311yescharacteristic
251SD16—521no—
252SD16—521no—
253D8—521no—
254D8—521no—
255M16—521no—
256C2×C8—131no—
257C2×C8—131no—
258C2×C8—131no—
259C2×C8—131no—
260C2×C8—521no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—131no—
265C4⋊C4—131no—
266C4⋊C4—261no—
267C4⋊C4—261no—
268C4⋊C4C22⋊D1311yescharacteristic
269C4⋊C4C22⋊D1311yescharacteristic
270C4⋊C4C22×D1311yescharacteristic
271C4⋊C4C22×D1311yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—261no—
278C22⋊C4—261no—
279C22⋊C4—261no—
280C22⋊C4—261no—
281C22⋊C4C22⋊D1311yescharacteristic
282C22⋊C4C22⋊D1311yescharacteristic
283C42—21no—
284C42C22×D1311yescharacteristic
285C42C22×D1311yescharacteristic
286C13#325711yescharacteristic, complemented, Sylow
287C23—21no—
288C23—261no—
289C23—261no—
290C23C2×C22⋊D1311yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—81no—
294D4—21no—
295D4—21no—
296D4—81no—
297D4—261no—
298D4—261no—
299D4—261no—
300D4—261no—
301D4—1041no—
302D4—1041no—
303D4—1041no—
304D4—1041no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—1041no—
314C2×C4—1041no—
315C2×C4C2×C22⋊D1311yescharacteristic
316C2×C4C2×C22⋊D1311yescharacteristic
317C2×C4C2×C22⋊D1311yescharacteristic
318C2×C4C2×C22⋊D1311yescharacteristic
319C2×C4C2×C22⋊D1311yescharacteristic
320C2×C4C23×D1311yescharacteristic
321C8—261no—
322C8—261no—
323C8—261no—
324C8—261no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—521no—
332C22—521no—
333C22—521no—
334C22—521no—
335C22—521no—
336C22—521no—
337C22C22×C22⋊D1311yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—521no—
347C4—521no—
348C4#8825611yescharacteristic
349C4#8825711yescharacteristic
350C2—41no—
351C2—81no—
352C2—1041no—
353C2—1041no—
354C2#1171953811yescharacteristic
355C2#1171954011yescharacteristic
356C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#542C2
socleC22×C13C22×D4
hypercenter#542D13
hypocenterC13#3257
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. C13×#542C2semidirect
2. #11719240C2semidirect
3. #11718748C2semidirect
4. #11718745C2semidirect
5. #11718718C2semidirect
6. #11718718C2semidirect
7. #11718710C2semidirect
8. #11718709C2semidirect
9. #11718700C2semidirect
10. #11718699C2semidirect
11. #11718688C2semidirect
12. #11718683C2semidirect
13. #11718676C2semidirect
14. #11718670C2semidirect
15. #11718660C2semidirect
147. #542D13semidirect
286. C13#3257semidirect

Maximal subgroups

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

subgroupindex
C13×#5422
#117192402
#117187482
#117187452
#117187182
#117187102
#117187092
#117187002
#117186992
#117186882
#117186832
#117186762
#117186702
#117186602
#325713