Finite Group Databasebeta

← #13126828

Subgroups — #13126828

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
1#11719536C211yesmaximal, characteristic, complemented
2#11719212C211yesmaximal, characteristic, complemented
3C13×#417C211yesmaximal, characteristic, complemented
4#11718899C211yesmaximal, characteristic, complemented
5#11718795C211yesmaximal, characteristic, complemented
6#11718788C211yesmaximal, characteristic, complemented
7#11718631C211yesmaximal, characteristic, complemented
8#11718478C211yesmaximal, characteristic, complemented
9#11718467C211yesmaximal, characteristic, complemented
10D13×#103C211yesmaximal, characteristic, complemented
11#11718455C211yesmaximal, characteristic, complemented
12#11718448C211yesmaximal, characteristic, complemented
13#11718436C211yesmaximal, characteristic, complemented
14#11718435C211yesmaximal, characteristic, complemented
15#11718426C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×Q8×D13C2211yescharacteristic
18C2×#6127—21no—
19C2×C13×M16C2211yescharacteristic
20C2×C13×C4⋊C4C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22C2×#6106C2211yescharacteristic
23#88192—21no—
24#88192C2211yescharacteristic
25#88190—21no—
26#88190C2211yescharacteristic
27C2×#6104C2211yescharacteristic
28#88184C2211yescharacteristic
29#88183—21no—
30C4×C22⋊D13—21no—
31C4×C22⋊D13C2211yescharacteristic
32#88178—21no—
33#88178C2211yescharacteristic
34C2×#6095C2211yescharacteristic
35C2×C8×D13C2211yescharacteristic
36#88150—21no—
37#88149C2211yescharacteristic
38#88148—21no—
39#88147C2211yescharacteristic
40C4⋊C4×D13C2211yescharacteristic
41#88142C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#102C2211yescharacteristic
45C13×#102C2211yescharacteristic
46#88075C2211yescharacteristic
47#88072C2211yescharacteristic
48C22⋊#1055C2211yescharacteristic
49#88061C2211yescharacteristic
50#88060C2211yescharacteristic
51#88058C2211yescharacteristic
52#88056C2211yescharacteristic
53#88055C2211yescharacteristic
54#88054C2211yescharacteristic
55#88050C2211yescharacteristic
56#88050C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C13×#41—22no—
60C13×#41—41no—
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13—21no—
63C2×D4×C13C2311yescharacteristic
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13C2311yescharacteristic
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C2×C22⋊D13D411yescharacteristic
70Q8×D13—22no—
71Q8×D13—41no—
72#6127—44no—
73C2×D52—21no—
74C2×D52C2311yescharacteristic
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C2×C4×D13—21no—
78C2×C4×D13C2311yescharacteristic
79C2×Dic26—21no—
80C2×Dic26—21no—
81C2×Dic26C2311yescharacteristic
82C13×M16—41no—
83C2×C8×C13C2311yescharacteristic
84C2×C8×C13C2311yescharacteristic
85C13×C4⋊C4—21no—
86C13×C4⋊C4C2311yescharacteristic
87C13×C4⋊C4C2311yescharacteristic
88C22⋊Dic13—21no—
89C22⋊Dic13—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13—21no—
92C22⋊Dic13D411yescharacteristic
93#6106—22no—
94#6104—41no—
95#6103—21no—
96#6103—21no—
97#6103—21no—
98#6103D411yescharacteristic
99C4⋊Dic13—21no—
100C4⋊Dic13C2311yescharacteristic
101C4⋊Dic13C2311yescharacteristic
102#6101—21no—
103#6101—21no—
104#6101—21no—
105#6101D411yescharacteristic
106C4×Dic13—21no—
107C4×Dic13C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110#6095—41no—
111C8×D13—41no—
112#3308—131nomaximal, Sylow
113C23×C13—21no—
114C23×C13C2×D411yescharacteristic
115C22×D13—21no—
116C22×D13C2×D411yescharacteristic
117Q8×C13—21no—
118Q8×C13#4112yescomplemented
119D4×C13—21no—
120D4×C13—21no—
121D4×C13—42no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13C2×D411yescharacteristic
130C2×C4×C13C2411yescharacteristic
131C22⋊D13—22no—
132C22⋊D13—42no—
133C22⋊D13—42no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13C2×D411yescharacteristic
138C2×Dic13C2×D411yescharacteristic
139C2×Dic13C2×D411yescharacteristic
140D52—21no—
141D52—21no—
142D52—42no—
143C4×D13—21no—
144C4×D13—21no—
145C4×D13—42no—
146C4×D13—42no—
147C4×D13—42no—
148Dic26—21no—
149Dic26—21no—
150Dic26—42no—
151Dic26—42no—
152C8×C13—21no—
153C8×C13—21no—
154#1055—21no—
155#1055—21no—
156#548—131no—
157#547—131no—
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#417D1311yescharacteristic, complemented
170C2×#103—131no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13C22×D411yescharacteristic
178C2×D13—21no—
179C2×D13—21no—
180C2×D13—41no—
181C2×D13—41no—
182C2×D13—41no—
183C2×D13AGL(1,ℤ/8)12yes—
184C4×C13—22no—
185C4×C13—21no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13C2×#4111yescharacteristic
189C4×C13H(5,𝔽2)11yescharacteristic
190Dic13—21no—
191Dic13—21no—
192Dic13—21no—
193Dic13—41no—
194Dic13—41no—
195Dic13—41no—
196C2×#41—261no—
197C2×#41C2×D1311yescharacteristic
198C22×Q8—131no—
199C2×SD16—131no—
200C2×SD16—131no—
201C2×D8—131no—
202C2×M16C2×D1311yescharacteristic
203C22×C8—131no—
204C4⋊Q8—131no—
205#124—131no—
206#124—261no—
207#123—261no—
208#123—261no—
209C22⋊Q8—131no—
210C22⋊Q8—261no—
211C22⋊Q8—261no—
212#121—131no—
213#121—131no—
214#121—131no—
215#121—261no—
216C4×Q8—131no—
217C4×D4—131no—
218C4×D4—131no—
219C4×D4—261no—
220C2×C4⋊C4—131no—
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#103C2×D1311yescharacteristic
231#103C2×D1311yescharacteristic
232#102—131no—
233#102—131no—
234#102C2×D1311yescharacteristic
235#102C2×D1311yescharacteristic
236C22⋊C8—131no—
237C22⋊C8—131no—
238#97—131no—
239C2×C13—41no—
240C2×C13—81no—
241C2×C13#54611yescharacteristic
242C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
243C2×C13#57811yescharacteristic
244D13—22no—
245D13—81no—
246#41—22no—
247#41—41no—
248#41—524no—
249C2×Q8—131no—
250C2×Q8—261no—
251C2×Q8—261no—
252C2×Q8—262no—
253C2×Q8—521no—
254C2×Q8C22×D1311yescharacteristic
255C2×D4—21no—
256C2×D4—131no—
257C2×D4—131no—
258C2×D4—261no—
259C2×D4—261no—
260C2×D4—261no—
261C2×D4C22×D1311yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—131no—
265C22×C4—261no—
266C22×C4—261no—
267C22×C4—261no—
268C22×C4C22×D1311yescharacteristic
269SD16—262no—
270SD16—521no—
271D8—521no—
272M16—41no—
273C2×C8—131no—
274C2×C8—131no—
275C2×C8—521no—
276C2×C8C22×D1311yescharacteristic
277C2×C8C22×D1311yescharacteristic
278C4⋊C4—21no—
279C4⋊C4—131no—
280C4⋊C4—131no—
281C4⋊C4—131no—
282C4⋊C4—261no—
283C4⋊C4—261no—
284C4⋊C4—261no—
285C4⋊C4—261no—
286C4⋊C4C22×D1311yescharacteristic
287C4⋊C4C22×D1311yescharacteristic
288C22⋊C4—131no—
289C22⋊C4—131no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C22⋊C4—261no—
294C22⋊C4—261no—
295C22⋊C4—261no—
296C22⋊C4—261no—
297C42—131no—
298C42—261no—
299C13#330811yescharacteristic, complemented, Sylow
300C23—21no—
301C23—131no—
302C23—261no—
303C23D4×D1311yescharacteristic
304Q8—21no—
305Q8—261no—
306Q8—261no—
307Q8—522no—
308Q8—522no—
309Q8#612712yescomplemented
310D4—21no—
311D4—21no—
312D4—42no—
313D4—262no—
314D4—261no—
315D4—261no—
316D4—522no—
317D4—522no—
318D4—522no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—131no—
327C2×C4—131no—
328C2×C4—131no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—261no—
332C2×C4—261no—
333C2×C4—261no—
334C2×C4—522no—
335C2×C4—522no—
336C2×C4—522no—
337C2×C4D4×D1311yescharacteristic
338C2×C4C23×D1311yescharacteristic
339C8—21no—
340C8—21no—
341C8—261no—
342C8—261no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—132no—
350C22—261no—
351C22—261no—
352C22—521no—
353C22—521no—
354C22—521no—
355C22C2×D4×D1311yescharacteristic
356C4—21no—
357C4—22no—
358C4—41no—
359C4—41no—
360C4—261no—
361C4—261no—
362C4—261no—
363C4—521no—
364C4—521no—
365C4—521no—
366C4C2×#612711yescharacteristic
367C4#8825111yescharacteristic
368C2—41no—
369C2—81no—
370C2—262no—
371C2—1041no—
372C2#1171919511yescharacteristic
373C2D13×AGL(1,ℤ/8)11yescharacteristic
374C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#417C2
socleC22×C13C22×D4
hypercenter#417D13
hypocenterC13#3308
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #11719536C2semidirect
2. #11719212C2semidirect
3. C13×#417C2semidirect
4. #11718899C2semidirect
5. #11718795C2semidirect
6. #11718788C2semidirect
7. #11718631C2semidirect
8. #11718478C2semidirect
9. #11718467C2semidirect
10. D13×#103C2semidirect
11. #11718455C2semidirect
12. #11718448C2semidirect
13. #11718436C2semidirect
14. #11718435C2semidirect
15. #11718426C2semidirect
118. Q8×C13#41semidirect
169. #417D13semidirect
299. C13#3308semidirect
309. Q8#6127semidirect

Maximal subgroups

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

subgroupindex
#117195362
#117192122
C13×#4172
#117188992
#117187952
#117187882
#117186312
#117184782
#117184672
D13×#1032
#117184552
#117184482
#117184362
#117184352
#117184262
#330813