Finite Group Databasebeta

← #13126827

Subgroups — #13126827

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×#548C211yesmaximal, characteristic, complemented
2#11719260C211yesmaximal, characteristic, complemented
3#11718899C211yesmaximal, characteristic, complemented
4#11718893C211yesmaximal, characteristic, complemented
5#11718888C211yesmaximal, characteristic, complemented
6C2×#88075C211yesmaximal, characteristic, complemented
7#11718718C211yesmaximal, characteristic, complemented
8#11718716C211yesmaximal, characteristic, complemented
9#11718710C211yesmaximal, characteristic, complemented
10#11718705C211yesmaximal, characteristic, complemented
11#11718699C211yesmaximal, characteristic, complemented
12#11718694C211yesmaximal, characteristic, complemented
13#11718687C211yesmaximal, characteristic, complemented
14#11718682C211yesmaximal, characteristic, complemented
15#11718672C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C22×Q8×C13C2211yescharacteristic
18C2×#6129—21no—
19C13×#124—21no—
20C13×#124C2211yescharacteristic
21C13×C22⋊Q8—21no—
22C13×C22⋊Q8C2211yescharacteristic
23C13×#121—21no—
24C13×#121C2211yescharacteristic
25C4×Q8×C13C2211yescharacteristic
26C4×D4×C13—21no—
27C4×D4×C13C2211yescharacteristic
28C2×#6106C2211yescharacteristic
29C2×#6106C2211yescharacteristic
30C2×#6104C2211yescharacteristic
31#88184C2211yescharacteristic
32#88184C2211yescharacteristic
33C2×C4⋊Dic13C2211yescharacteristic
34C2×C4⋊Dic13C2211yescharacteristic
35C2×#6099C2211yescharacteristic
36C22×#1055C2211yescharacteristic
37#88151—21no—
38#88140—21no—
39#88140—21no—
40C4×D52C2211yescharacteristic
41#88123C2211yescharacteristic
42#88075C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47#88075C2211yescharacteristic
48#88072C2211yescharacteristic
49#88072C2211yescharacteristic
50#88072C2211yescharacteristic
51C22⋊#1055C2211yescharacteristic
52C22⋊#1055C2211yescharacteristic
53#88049C2211yescharacteristic
54#88047C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57C4⋊#1055C2211yescharacteristic
58#88043C2211yescharacteristic
59C13×#41—22no—
60C13×#41—41no—
61C2×Q8×C13—21no—
62C2×Q8×C13—22no—
63C2×Q8×C13—41no—
64C2×Q8×C13C2311yescharacteristic
65C2×Q8×C13C2311yescharacteristic
66C2×D4×C13—21no—
67C2×D4×C13—21no—
68C2×D4×C13D411yescharacteristic
69C2×D4×C13C2311yescharacteristic
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13C2311yescharacteristic
73C22×C4×C13C2311yescharacteristic
74C2×C22⋊D13—21no—
75C2×C22⋊D13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78#6129—44no—
79C2×D52C2311yescharacteristic
80C2×C4×D13—21no—
81C2×Dic26—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4D411yescharacteristic
85C13×C4⋊C4C2311yescharacteristic
86C13×C22⋊C4—21no—
87C13×C22⋊C4—21no—
88C13×C22⋊C4—21no—
89C13×C22⋊C4—21no—
90C13×C22⋊C4D411yescharacteristic
91C13×C22⋊C4D411yescharacteristic
92C42×C13—21no—
93C42×C13C2311yescharacteristic
94#6106—22no—
95#6106—41no—
96#6104—41no—
97#6103—21no—
98#6103—21no—
99#6103—21no—
100C4⋊Dic13—21no—
101C4⋊Dic13—21no—
102C4⋊Dic13—21no—
103C4⋊Dic13C2311yescharacteristic
104C4⋊Dic13C2311yescharacteristic
105C4⋊Dic13C2311yescharacteristic
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—21no—
118Q8×C13—21no—
119Q8×C13—21no—
120Q8×C13—42no—
121Q8×C13#4112yescomplemented
122D4×C13—22no—
123D4×C13—21no—
124D4×C13—21no—
125D4×C13—42no—
126D4×C13—42no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13C2×D411yescharacteristic
137C2×C4×C13C2×D411yescharacteristic
138C2×C4×C13C2×D411yescharacteristic
139C2×C4×C13C2×D411yescharacteristic
140C2×C4×C13C2411yescharacteristic
141C22⋊D13—42no—
142C22⋊D13—42no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—42no—
147C2×Dic13—42no—
148D52—21no—
149D52—21no—
150C4×D13—42no—
151Dic26—42no—
152#1055—21no—
153#1055—21no—
154#1055—21no—
155#1055—21no—
156#548D1311yescharacteristic, complemented
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#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—22no—
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13C2×#4111yescharacteristic
192C4×C13H(5,𝔽2)11yescharacteristic
193Dic13—41no—
194Dic13—41no—
195Dic13—41no—
196C2×#41—261no—
197C2×#41C2×D1311yescharacteristic
198C22×Q8C2×D1311yescharacteristic
199C2×SD16—131no—
200C2×SD16—131no—
201C2×D8—131no—
202C2×M16—131no—
203C22×C8—131no—
204C4⋊Q8—131no—
205#124—21no—
206#124C2×D1311yescharacteristic
207#123—261no—
208#123—261no—
209C22⋊Q8—21no—
210C22⋊Q8—261no—
211C22⋊Q8C2×D1311yescharacteristic
212#121—21no—
213#121—131no—
214#121—131no—
215#121C2×D1311yescharacteristic
216C4×Q8C2×D1311yescharacteristic
217C4×D4—21no—
218C4×D4—131no—
219C4×D4C2×D1311yescharacteristic
220C2×C4⋊C4—131no—
221C2×C4⋊C4—131no—
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—22no—
247#41—41no—
248#41—524no—
249C2×Q8—21no—
250C2×Q8—22no—
251C2×Q8—41no—
252C2×Q8—261no—
253C2×Q8C22×D1311yescharacteristic
254C2×Q8C22×D1311yescharacteristic
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—261no—
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—131no—
281C4⋊C4—131no—
282C4⋊C4—131no—
283C4⋊C4—261no—
284C4⋊C4—261no—
285C4⋊C4—261no—
286C4⋊C4C22⋊D1311yescharacteristic
287C4⋊C4C22×D1311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—261no—
293C22⋊C4—261no—
294C22⋊C4—261no—
295C22⋊C4C22⋊D1311yescharacteristic
296C22⋊C4C22⋊D1311yescharacteristic
297C42—21no—
298C42C22×D1311yescharacteristic
299C13#330811yescharacteristic, complemented, Sylow
300C23—21no—
301C23—261no—
302C23C2×C22⋊D1311yescharacteristic
303C23C2×C22⋊D1311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—522no—
309Q8#612912yescomplemented
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—261no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—522no—
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#8820312yes—
355C22C22×C22⋊D1311yescharacteristic
356C4—21no—
357C4—21no—
358C4—22no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—521no—
364C4—521no—
365C4—521no—
366C4C2×#612911yescharacteristic
367C4#8825111yescharacteristic
368C2—22no—
369C2—41no—
370C2—81no—
371C2—1041no—
372C2#1171951111yescharacteristic
373C2C2×#8820311yescharacteristic
374C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#548C2
socleC22×C13C22×D4
hypercenter#548D13
hypocenterC13#3308
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C13×#548C2semidirect
2. #11719260C2semidirect
3. #11718899C2semidirect
4. #11718893C2semidirect
5. #11718888C2semidirect
6. C2×#88075C2semidirect
7. #11718718C2semidirect
8. #11718716C2semidirect
9. #11718710C2semidirect
10. #11718705C2semidirect
11. #11718699C2semidirect
12. #11718694C2semidirect
13. #11718687C2semidirect
14. #11718682C2semidirect
15. #11718672C2semidirect
121. Q8×C13#41semidirect
156. #548D13semidirect
299. C13#3308semidirect
309. Q8#6129semidirect

Maximal subgroups

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

subgroupindex
C13×#5482
#117192602
#117188992
#117188932
#117188882
C2×#880752
#117187182
#117187162
#117187102
#117187052
#117186992
#117186942
#117186872
#117186822
#117186722
#330813