Finite Group Databasebeta

← #13126833

Subgroups — #13126833

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#11719316C211yesmaximal, characteristic, complemented
2#11719303C211yesmaximal, characteristic, complemented
3C13×#466C211yesmaximal, characteristic, complemented
4#11718819C211yesmaximal, characteristic, complemented
5#11718814C211yesmaximal, characteristic, complemented
6#11718772C211yesmaximal, characteristic, complemented
7C2×#88056C211yesmaximal, characteristic, complemented
8#11718701C211yesmaximal, characteristic, complemented
9#11718694C211yesmaximal, characteristic, complemented
10#11718545C211yesmaximal, characteristic, complemented
11#11718536C211yesmaximal, characteristic, complemented
12#11718441C211yesmaximal, characteristic, complemented
13#11718432C211yesmaximal, characteristic, complemented
14#11718426C211yesmaximal, characteristic, complemented
15#11718418C211yesmaximal, characteristic, complemented
16C2×#6129—21no—
17C2×#6129C2211yescharacteristic
18C22×Dic26C2211yescharacteristic
19C2×C13×D8C2211yescharacteristic
20C22×C8×C13C2211yescharacteristic
21C13×#121C2211yescharacteristic
22C13×#121C2211yescharacteristic
23#88193—21no—
24#88192C2211yescharacteristic
25#88190C2211yescharacteristic
26#88189—21no—
27D4×Dic13—21no—
28D4×Dic13C2211yescharacteristic
29C2×#6105C2211yescharacteristic
30C2×#6105C2211yescharacteristic
31C4×C22⋊D13C2211yescharacteristic
32C2×C4⋊Dic13C2211yescharacteristic
33C2×#6094C2211yescharacteristic
34#88151C2211yescharacteristic
35C4⋊C4×D13C2211yescharacteristic
36#88142C2211yescharacteristic
37#88141C2211yescharacteristic
38#88139—21no—
39#88137—21no—
40#88132—21no—
41#88132—21no—
42C13×#107C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×#102C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47C22⋊#1055C2211yescharacteristic
48#88060C2211yescharacteristic
49#88056C2211yescharacteristic
50#88056C2211yescharacteristic
51#88056C2211yescharacteristic
52#88056C2211yescharacteristic
53#88055C2211yescharacteristic
54#88054C2211yescharacteristic
55#88050C2211yescharacteristic
56#88050C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×D4×C13—21no—
60C2×D4×C13—21no—
61C2×D4×C13C2311yescharacteristic
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C2×C22⋊D13D411yescharacteristic
67C22×Dic13—21no—
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71#6129—22no—
72#6129—41no—
73#6129—44no—
74C2×C4×D13—21no—
75C2×C4×D13C2311yescharacteristic
76C2×Dic26—22no—
77C2×Dic26—21no—
78C2×Dic26—21no—
79C2×Dic26—41no—
80C2×Dic26C2311yescharacteristic
81C2×Dic26C2311yescharacteristic
82C13×D8—41no—
83C2×C8×C13—41no—
84C2×C8×C13C2311yescharacteristic
85C2×C8×C13C2311yescharacteristic
86C13×C4⋊C4C2311yescharacteristic
87C13×C4⋊C4C2311yescharacteristic
88C13×C22⋊C4—21no—
89C13×C22⋊C4—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13—21no—
92C22⋊Dic13—21no—
93C22⋊Dic13—21no—
94C22⋊Dic13D411yescharacteristic
95#6105—22no—
96#6105—41no—
97#6103—21no—
98#6103D411yescharacteristic
99C4⋊Dic13—21no—
100C4⋊Dic13—21no—
101C4⋊Dic13C2311yescharacteristic
102C4⋊Dic13C2311yescharacteristic
103#6101—21no—
104#6101—21no—
105#6101—21no—
106#6101D411yescharacteristic
107C4×Dic13—21no—
108C4×Dic13C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111#6094—41no—
112#3308—131nomaximal, Sylow
113C23×C13—21no—
114C23×C13—21no—
115C23×C13C2×D411yescharacteristic
116C22×D13C2×D411yescharacteristic
117D4×C13—21no—
118D4×C13—21no—
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×C13C2×D411yescharacteristic
128C2×C4×C13C2411yescharacteristic
129C22⋊D13—22no—
130C22⋊D13—42no—
131C22⋊D13—42no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—42no—
137C2×Dic13—42no—
138C2×Dic13—42no—
139C2×Dic13—42no—
140C2×Dic13C2×D411yescharacteristic
141C2×Dic13C2×D411yescharacteristic
142C2×Dic13C2×D411yescharacteristic
143C4×D13—21no—
144C4×D13—21no—
145C4×D13—42no—
146Dic26—21no—
147Dic26—21no—
148Dic26—21no—
149Dic26—42no—
150Dic26—42no—
151Dic26#4112yescomplemented
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#466D1311yescharacteristic, complemented
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—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13AGL(1,ℤ/8)12yes—
180C22×C13C22×D411yescharacteristic
181C2×D13—21no—
182C2×D13—21no—
183C2×D13—21no—
184C4×C13—21no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13C2×#4111yescharacteristic
188C4×C13H(5,𝔽2)11yescharacteristic
189Dic13—22no—
190Dic13—21no—
191Dic13—21no—
192Dic13—21no—
193Dic13—41no—
194Dic13—41no—
195Dic13—41no—
196C2×#41—131no—
197C2×#41—261no—
198C22×Q8—131no—
199C2×SD16—131no—
200C2×SD16—131no—
201C2×D8C2×D1311yescharacteristic
202C2×M16—131no—
203C22×C8C2×D1311yescharacteristic
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—261no—
214#121C2×D1311yescharacteristic
215#121C2×D1311yescharacteristic
216C4×Q8—131no—
217C4×D4—131no—
218C4×D4—131no—
219C4×D4—261no—
220C2×C4⋊C4—131no—
221C2×C4⋊C4—131no—
222#107—131no—
223#107—131no—
224#107C2×D1311yescharacteristic
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#102C2×D1311yescharacteristic
235#102C2×D1311yescharacteristic
236C22⋊C8—131no—
237C22⋊C8—131no—
238#97—131no—
239C2×C13—22no—
240C2×C13—81no—
241C2×C13—81no—
242C2×C13#54611yescharacteristic
243C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
244C2×C13#57811yescharacteristic
245D13—41no—
246#41—262no—
247#41—521no—
248#41—524no—
249C2×Q8—131no—
250C2×Q8—131no—
251C2×Q8—261no—
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—131no—
263C22×C4—261no—
264C22×C4—261no—
265C22×C4—261no—
266C22×C4—261no—
267C22×C4—261no—
268C22×C4C22×D1311yescharacteristic
269SD16—262no—
270SD16—521no—
271D8—41no—
272M16—521no—
273C2×C8—41no—
274C2×C8—131no—
275C2×C8—131no—
276C2×C8C22×D1311yescharacteristic
277C2×C8C22×D1311yescharacteristic
278C4⋊C4—131no—
279C4⋊C4—131no—
280C4⋊C4—131no—
281C4⋊C4—261no—
282C4⋊C4—261no—
283C4⋊C4—261no—
284C4⋊C4—261no—
285C4⋊C4—261no—
286C4⋊C4C22×D1311yescharacteristic
287C4⋊C4C22×D1311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—131no—
291C22⋊C4—131no—
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—21no—
302C23—131no—
303C23D4×D1311yescharacteristic
304Q8—132no—
305Q8—261no—
306Q8—261no—
307Q8—261no—
308Q8—522no—
309Q8—522no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—42no—
316D4—262no—
317D4—522no—
318D4—522no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—131no—
324C2×C4—131no—
325C2×C4—131no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—261no—
332C2×C4—522no—
333C2×C4—522no—
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—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—261no—
352C22—261no—
353C22—261no—
354C22#8816512yes—
355C22C2×D4×D1311yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—261no—
360C4—261no—
361C4—261no—
362C4—262no—
363C4—521no—
364C4—521no—
365C4—521no—
366C4#8825111yescharacteristic
367C4#41×D1311yescharacteristic
368C2—22no—
369C2—81no—
370C2—81no—
371C2—521no—
372C2#1171931511yescharacteristic
373C2C2×#8816511yescharacteristic
374C2#1171947611yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#466C2
socleC22×C13C22×D4
hypercenter#466D13
hypocenterC13#3308
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #11719316C2semidirect
2. #11719303C2semidirect
3. C13×#466C2semidirect
4. #11718819C2semidirect
5. #11718814C2semidirect
6. #11718772C2semidirect
7. C2×#88056C2semidirect
8. #11718701C2semidirect
9. #11718694C2semidirect
10. #11718545C2semidirect
11. #11718536C2semidirect
12. #11718441C2semidirect
13. #11718432C2semidirect
14. #11718426C2semidirect
15. #11718418C2semidirect
151. Dic26#41semidirect
163. #466D13semidirect
299. C13#3308semidirect

Maximal subgroups

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

subgroupindex
#117193162
#117193032
C13×#4662
#117188192
#117188142
#117187722
C2×#880562
#117187012
#117186942
#117185452
#117185362
#117184412
#117184322
#117184262
#117184182
#330813