Finite Group Databasebeta

← #13126821

Subgroups — #13126821

Order 1664.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#547C211yesmaximal, characteristic, complemented
2#11719257C211yesmaximal, characteristic, complemented
3#11718752C211yesmaximal, characteristic, complemented
4#11718750C211yesmaximal, characteristic, complemented
5#11718703C211yesmaximal, characteristic, complemented
6#11718701C211yesmaximal, characteristic, complemented
7#11718699C211yesmaximal, characteristic, complemented
8#11718698C211yesmaximal, characteristic, complemented
9#11718679C211yesmaximal, characteristic, complemented
10#11718677C211yesmaximal, characteristic, complemented
11#11718672C211yesmaximal, characteristic, complemented
12#11718631C211yesmaximal, characteristic, complemented
13C2×#88050C211yesmaximal, characteristic, complemented
14#11718628C211yesmaximal, characteristic, complemented
15#11718627C211yesmaximal, characteristic, complemented
16C2×C13×#41—21no—
17C2×#6127C2211yescharacteristic
18C22×Dic26C2211yescharacteristic
19C13×C4⋊Q8C2211yescharacteristic
20C13×#123—21no—
21C13×#123—21no—
22C13×C22⋊Q8—21no—
23C13×#121C2211yescharacteristic
24C13×#121C2211yescharacteristic
25C4×D4×C13C2211yescharacteristic
26C4×D4×C13C2211yescharacteristic
27C2×C13×C4⋊C4C2211yescharacteristic
28C2×C13×C4⋊C4C2211yescharacteristic
29#88193—21no—
30C2×#6105C2211yescharacteristic
31C2×#6105C2211yescharacteristic
32C2×#6104C2211yescharacteristic
33#88184C2211yescharacteristic
34#88178C2211yescharacteristic
35C2×#6099C2211yescharacteristic
36C22×#1055C2211yescharacteristic
37#88150—21no—
38#88139—21no—
39#88135—21no—
40#88129C2211yescharacteristic
41C4×Dic26C2211yescharacteristic
42#88072C2211yescharacteristic
43C22⋊#1055C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88050C2211yescharacteristic
46#88050C2211yescharacteristic
47#88050C2211yescharacteristic
48#88050C2211yescharacteristic
49#88050C2211yescharacteristic
50#88050C2211yescharacteristic
51#88049C2211yescharacteristic
52#88049C2211yescharacteristic
53#88049C2211yescharacteristic
54#88047C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57C4⋊#1055C2211yescharacteristic
58#88043C2211yescharacteristic
59C13×#41—44no—
60C2×Q8×C13—21no—
61C2×D4×C13—21no—
62C2×D4×C13—21no—
63C2×D4×C13D411yescharacteristic
64C2×D4×C13C2311yescharacteristic
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13C2311yescharacteristic
69C22×C4×C13C2311yescharacteristic
70C2×C22⋊D13—21no—
71C2×C22⋊D13—21no—
72C22×Dic13—21no—
73#6127—22no—
74#6127—41no—
75C2×D52C2311yescharacteristic
76C2×C4×D13—21no—
77C2×Dic26—22no—
78C2×Dic26—21no—
79C2×Dic26—41no—
80C2×Dic26C2311yescharacteristic
81C2×Dic26C2311yescharacteristic
82C13×C4⋊C4—21no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4D411yescharacteristic
86C13×C4⋊C4C2311yescharacteristic
87C13×C4⋊C4C2311yescharacteristic
88C13×C4⋊C4C2311yescharacteristic
89C13×C22⋊C4—21no—
90C13×C22⋊C4—21no—
91C13×C22⋊C4—21no—
92C13×C22⋊C4D411yescharacteristic
93C13×C22⋊C4D411yescharacteristic
94C42×C13C2311yescharacteristic
95C22⋊Dic13—21no—
96#6105—22no—
97#6105—41no—
98#6104—41no—
99#6103—21no—
100#6103—21no—
101#6103—21no—
102C4⋊Dic13C2311yescharacteristic
103#6101—21no—
104#6101—21no—
105C4×Dic13—21no—
106#6099—41no—
107C2×#1055—41no—
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111C2×#1055C2311yescharacteristic
112#3308—131nomaximal, Sylow
113C23×C13—21no—
114C23×C13C2×D411yescharacteristic
115C23×C13C2×D411yescharacteristic
116C22×D13—21no—
117Q8×C13—42no—
118D4×C13—22no—
119D4×C13—21no—
120D4×C13—21no—
121D4×C13—42no—
122D4×C13—42no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13C2×D411yescharacteristic
134C2×C4×C13C2×D411yescharacteristic
135C2×C4×C13C2×D411yescharacteristic
136C2×C4×C13C2×D411yescharacteristic
137C2×C4×C13C2411yescharacteristic
138C22⋊D13—42no—
139C22⋊D13—42no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—42no—
144D52—21no—
145D52—21no—
146C4×D13—42no—
147Dic26—21no—
148Dic26—21no—
149Dic26—21no—
150Dic26—42no—
151Dic26#4112yescomplemented
152#1055—21no—
153#1055—21no—
154#1055—21no—
155#1055—21no—
156#548—131no—
157#547D1311yescharacteristic, complemented
158#489—131no—
159#484—131no—
160#480—131no—
161#477—131no—
162#468—131no—
163#466—131no—
164#463—131no—
165#449—131no—
166#448—131no—
167#440—131no—
168#435—131no—
169#417—131no—
170C2×#103—131no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13AGL(1,ℤ/8)12yes—
180C22×C13C22×D411yescharacteristic
181C2×D13—41no—
182C2×D13—41no—
183C2×D13—41no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13C2×#4111yescharacteristic
192C4×C13H(5,𝔽2)11yescharacteristic
193Dic13—22no—
194Dic13—41no—
195Dic13—41no—
196C2×#41—21no—
197C2×#41—131no—
198C22×Q8—131no—
199C2×SD16—131no—
200C2×SD16—131no—
201C2×D8—131no—
202C2×M16—131no—
203C22×C8—131no—
204C4⋊Q8C2×D1311yescharacteristic
205#124—131no—
206#124—261no—
207#123—21no—
208#123—21no—
209C22⋊Q8—21no—
210C22⋊Q8—131no—
211C22⋊Q8—261no—
212#121—131no—
213#121—261no—
214#121C2×D1311yescharacteristic
215#121C2×D1311yescharacteristic
216C4×Q8—131no—
217C4×D4—261no—
218C4×D4C2×D1311yescharacteristic
219C4×D4C2×D1311yescharacteristic
220C2×C4⋊C4C2×D1311yescharacteristic
221C2×C4⋊C4C2×D1311yescharacteristic
222#107—131no—
223#107—131no—
224#107—131no—
225C4⋊C8—131no—
226#103—131no—
227#103—131no—
228#103—131no—
229#103—131no—
230#103—131no—
231#103—131no—
232#102—131no—
233#102—131no—
234#102—131no—
235#102—131no—
236C22⋊C8—131no—
237C22⋊C8—131no—
238#97—131no—
239C2×C13—22no—
240C2×C13—41no—
241C2×C13—81no—
242C2×C13#54611yescharacteristic
243C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
244C2×C13#57811yescharacteristic
245D13—81no—
246#41—44no—
247#41—262no—
248#41—521no—
249C2×Q8—21no—
250C2×Q8—131no—
251C2×Q8—131no—
252C2×Q8—262no—
253C2×Q8—261no—
254C2×Q8—521no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—131no—
258C2×D4—261no—
259C2×D4—261no—
260C2×D4C22⋊D1311yescharacteristic
261C2×D4C22×D1311yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—261no—
266C22×C4—261no—
267C22×C4C22×D1311yescharacteristic
268C22×C4C22×D1311yescharacteristic
269SD16—262no—
270SD16—521no—
271D8—521no—
272M16—521no—
273C2×C8—131no—
274C2×C8—131no—
275C2×C8—131no—
276C2×C8—131no—
277C2×C8—521no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—131no—
282C4⋊C4—261no—
283C4⋊C4—261no—
284C4⋊C4C22⋊D1311yescharacteristic
285C4⋊C4C22×D1311yescharacteristic
286C4⋊C4C22×D1311yescharacteristic
287C4⋊C4C22×D1311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C22⋊C4—261no—
294C22⋊C4—261no—
295C22⋊C4C22⋊D1311yescharacteristic
296C22⋊C4C22⋊D1311yescharacteristic
297C42—261no—
298C42C22×D1311yescharacteristic
299C13#330811yescharacteristic, complemented, Sylow
300C23—21no—
301C23—261no—
302C23C2×C22⋊D1311yescharacteristic
303C23C2×C22⋊D1311yescharacteristic
304Q8—42no—
305Q8—132no—
306Q8—261no—
307Q8—261no—
308Q8—261no—
309Q8—522no—
310D4—22no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—42no—
315D4—261no—
316D4—261no—
317D4—522no—
318D4—522no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—261no—
332C2×C4—522no—
333C2×C4—522no—
334C2×C4C2×C22⋊D1311yescharacteristic
335C2×C4C2×C22⋊D1311yescharacteristic
336C2×C4C2×C22⋊D1311yescharacteristic
337C2×C4C2×C22⋊D1311yescharacteristic
338C2×C4C23×D1311yescharacteristic
339C8—261no—
340C8—261no—
341C8—261no—
342C8—261no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—521no—
352C22—521no—
353C22—521no—
354C22#8818612yes—
355C22C22×C22⋊D1311yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—262no—
364C4—521no—
365C4—521no—
366C4#41×D1311yescharacteristic
367C4#8825611yescharacteristic
368C2—22no—
369C2—41no—
370C2—81no—
371C2—1041no—
372C2C2×#8818611yescharacteristic
373C2#1171953411yescharacteristic
374C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#547C2
socleC22×C13C22×D4
hypercenter#547D13
hypocenterC13#3308
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C13×#547C2semidirect
2. #11719257C2semidirect
3. #11718752C2semidirect
4. #11718750C2semidirect
5. #11718703C2semidirect
6. #11718701C2semidirect
7. #11718699C2semidirect
8. #11718698C2semidirect
9. #11718679C2semidirect
10. #11718677C2semidirect
11. #11718672C2semidirect
12. #11718631C2semidirect
13. C2×#88050C2semidirect
14. #11718628C2semidirect
15. #11718627C2semidirect
151. Dic26#41semidirect
157. #547D13semidirect
299. C13#3308semidirect

Maximal subgroups

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

subgroupindex
C13×#5472
#117192572
#117187522
#117187502
#117187032
#117187012
#117186992
#117186982
#117186792
#117186772
#117186722
#117186312
C2×#880502
#117186282
#117186272
#330813