Finite Group Databasebeta

← #13126917

Subgroups — #13126917

Order 1664.

410 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×#546C211yesmaximal, characteristic
2#11719248C211yesmaximal, characteristic, complemented
3#11718900C211yesmaximal, characteristic, complemented
4#11718893C211yesmaximal, characteristic, complemented
5#11718879C211yesmaximal, characteristic, complemented
6C2×#88072C211yesmaximal, characteristic, complemented
7#11718716C211yesmaximal, characteristic, complemented
8#11718715C211yesmaximal, characteristic, complemented
9#11718712C211yesmaximal, characteristic, complemented
10#11718705C211yesmaximal, characteristic, complemented
11#11718703C211yesmaximal, characteristic, complemented
12#11718694C211yesmaximal, characteristic, complemented
13#11718679C211yesmaximal, characteristic, complemented
14#11718672C211yesmaximal, characteristic, complemented
15#11718668C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C22×D4×C13C2211yescharacteristic
18C13×#124C2211yescharacteristic
19C13×#123—21no—
20C13×C22⋊Q8C2211yescharacteristic
21C13×#121—21no—
22C13×#121C2211yescharacteristic
23C13×#120—21no—
24C4×D4×C13C2211yescharacteristic
25C4×D4×C13C2211yescharacteristic
26C2×C13×C22⋊C4—21no—
27C2×#6107C2211yescharacteristic, complemented
28D4×Dic13—21no—
29C2×#6105C2211yescharacteristic
30C2×#6105C2211yescharacteristic
31C2×C4⋊Dic13C2211yescharacteristic
32C2×C4⋊Dic13C2211yescharacteristic, complemented
33#88178C2211yescharacteristic
34#88178C2211yescharacteristic, complemented
35C2×#6099C2211yescharacteristic, complemented
36C22×#1055C2211yescharacteristic
37#88144—21no—
38#88132—21no—
39#88132—21no—
40#88123C2211yescharacteristic, complemented
41C4×Dic26C2211yescharacteristic, complemented
42#88075C2211yescharacteristic, complemented
43#88075C2211yescharacteristic, complemented
44#88075C2211yescharacteristic, complemented
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88072C2211yescharacteristic
49#88072C2211yescharacteristic
50#88072C2211yescharacteristic
51C22⋊#1055C2211yescharacteristic
52C22⋊#1055C2211yescharacteristic, complemented
53#88050C2211yescharacteristic, complemented
54#88047C2211yescharacteristic, complemented
55#88047C2211yescharacteristic, complemented
56#88047C2211yescharacteristic, complemented
57C4⋊#1055C2211yescharacteristic, complemented
58#88043C2211yescharacteristic, complemented
59C24×C13—21no—
60C13×#41—22no—
61C13×#41—41no—
62C2×Q8×C13C2311yescharacteristic
63C2×D4×C13—22no—
64C2×D4×C13—21no—
65C2×D4×C13—21no—
66C2×D4×C13—21no—
67C2×D4×C13—41no—
68C2×D4×C13D411yescharacteristic
69C2×D4×C13C2311yescharacteristic
70C2×D4×C13C2311yescharacteristic
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13C2311yescharacteristic
74C22×C4×C13C2311yescharacteristic
75C22×Dic13—21no—
76C22×Dic13—21no—
77C2×Dic26—21no—
78C2×Dic26C2311yescharacteristic
79C13×C4⋊C4—21no—
80C13×C4⋊C4D411yescharacteristic
81C13×C4⋊C4C2311yescharacteristic
82C13×C22⋊C4—21no—
83C13×C22⋊C4—21no—
84C13×C22⋊C4—21no—
85C13×C22⋊C4—21no—
86C13×C22⋊C4—21no—
87C13×C22⋊C4D411yescharacteristic
88C13×C22⋊C4D411yescharacteristic
89C42×C13C2311yescharacteristic
90C22⋊Dic13—21no—
91C22⋊Dic13—21no—
92#6107—41no—
93#6105—22no—
94#6105—41no—
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13C2311yescharacteristic
99C4⋊Dic13C2311yescharacteristic
100C4⋊Dic13C2311yescharacteristic
101#6101—21no—
102#6101—21no—
103#6101—21no—
104C4×Dic13—21no—
105#6099—41no—
106C2×#1055—41no—
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111#3314—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—42no—
115C23×C13—42no—
116C23×C13—81no—
117C23×C13C2×D411yescharacteristic
118C23×C13C2×D411yescharacteristic
119Q8×C13—21no—
120Q8×C13—21no—
121D4×C13—22no—
122D4×C13—21no—
123D4×C13—21no—
124D4×C13—21no—
125D4×C13—42no—
126D4×C13—42no—
127D4×C13—81no—
128D4×C13#4112yes—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—42no—
136C2×C4×C13—81no—
137C2×C4×C13C2×D411yescharacteristic
138C2×C4×C13C2×D411yescharacteristic
139C2×C4×C13C2×D411yescharacteristic
140C2×C4×C13C2×D411yescharacteristic
141C2×C4×C13C2411yescharacteristic
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—81no—
147C2×Dic13—81no—
148Dic26—21no—
149Dic26—21no—
150Dic26—81no—
151#1055—21no—
152#1055—21no—
153#1055—21no—
154#1055—21no—
155#554—131no—
156#546D1311yescharacteristic
157#489—131no—
158#484—131no—
159#480—131no—
160#474—131no—
161#468—131no—
162#467—131no—
163#464—131no—
164#452—131no—
165#450—131no—
166#440—131no—
167#435—131no—
168#417—131no—
169C2×#102—131no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—22no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—84no—
182C22×C13#13712yes—
183C22×C13C22×D411yescharacteristic
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13C2×#4111yescharacteristic
191C4×C13H(5,𝔽2)11yescharacteristic
192Dic13—41no—
193Dic13—41no—
194Dic13—41no—
195Dic13—41no—
196C2×#41C2×D1311yescharacteristic
197C22×D4C2×D1311yescharacteristic
198C2×Q16—131no—
199C2×SD16—131no—
200C2×SD16—131no—
201C2×M16—131no—
202C22×C8—131no—
203C4⋊Q8—131no—
204#125—261no—
205#124C2×D1311yescharacteristic
206#123—21no—
207C22⋊Q8—131no—
208C22⋊Q8—131no—
209C22⋊Q8—261no—
210C22⋊Q8—261no—
211C22⋊Q8C2×D1311yescharacteristic
212#121—21no—
213#121C2×D1311yescharacteristic
214#120—21no—
215C4×Q8—131no—
216C4×D4—261no—
217C4×D4C2×D1311yescharacteristic
218C4×D4C2×D1311yescharacteristic
219C2×C4⋊C4—131no—
220C2×C4⋊C4—131no—
221C2×C22⋊C4—21no—
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#102—131no—
231#102—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—42no—
242C2×C13—81no—
243C2×C13#54611yescharacteristic
244C2×C13C2×#13711yescharacteristic
245C2×C13#57611yescharacteristic
246C24—21no—
247#41—22no—
248#41—41no—
249C2×Q8—131no—
250C2×Q8—261no—
251C2×Q8C22×D1311yescharacteristic
252C2×D4—22no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—41no—
257C2×D4C22⋊D1311yescharacteristic
258C2×D4C22×D1311yescharacteristic
259C2×D4C22×D1311yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—261no—
263C22×C4—261no—
264C22×C4C22×D1311yescharacteristic
265C22×C4C22×D1311yescharacteristic
266Q16—521no—
267SD16—262no—
268SD16—521no—
269M16—521no—
270C2×C8—131no—
271C2×C8—131no—
272C2×C8—131no—
273C2×C8—131no—
274C2×C8—521no—
275C4⋊C4—21no—
276C4⋊C4—131no—
277C4⋊C4—131no—
278C4⋊C4—131no—
279C4⋊C4—261no—
280C4⋊C4—261no—
281C4⋊C4—261no—
282C4⋊C4—261no—
283C4⋊C4—261no—
284C4⋊C4—261no—
285C4⋊C4C22⋊D1311yescharacteristic
286C4⋊C4C22×D1311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—261no—
293C22⋊C4—261no—
294C22⋊C4C22⋊D1311yescharacteristic
295C22⋊C4C22⋊D1311yescharacteristic
296C42—261no—
297C42C22×D1311yescharacteristic
298C13#331411yescharacteristic, complemented, Sylow
299C23—21no—
300C23—21no—
301C23—42no—
302C23—42no—
303C23—81no—
304C23C2×C22⋊D1311yescharacteristic
305C23C2×C22⋊D1311yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—261no—
309Q8—261no—
310Q8—1041no—
311D4—22no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4#612912yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—81no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—1041no—
332C2×C4—1041no—
333C2×C4C2×C22⋊D1311yescharacteristic
334C2×C4C2×C22⋊D1311yescharacteristic
335C2×C4C2×C22⋊D1311yescharacteristic
336C2×C4C2×C22⋊D1311yescharacteristic
337C2×C4C23×D1311yescharacteristic
338C8—261no—
339C8—261no—
340C8—261no—
341C8—261no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—84no—
354C22#8820512yes—
355C22C22×C22⋊D1311yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—521no—
363C4—521no—
364C4—521no—
365C4—521no—
366C4C2×#612911yescharacteristic
367C4#8825111yescharacteristic
368C2—22no—
369C2—41no—
370C2—42no—
371C2—81no—
372C2#1171951111yescharacteristic
373C2C2×#8820511yescharacteristic
374C2#1171954011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
Fitting, prime radicalC13×#546C2
socleC22×C13C22×D4
hypercenter#546D13
hypocenterC13#3314
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
2. #11719248C2semidirect
3. #11718900C2semidirect
4. #11718893C2semidirect
5. #11718879C2semidirect
6. C2×#88072C2semidirect
7. #11718716C2semidirect
8. #11718715C2semidirect
9. #11718712C2semidirect
10. #11718705C2semidirect
11. #11718703C2semidirect
12. #11718694C2semidirect
13. #11718679C2semidirect
14. #11718672C2semidirect
15. #11718668C2semidirect
27. C2×#6107C22semidirect
32. C2×C4⋊Dic13C22semidirect
34. #88178C22semidirect
35. C2×#6099C22semidirect
40. #88123C22semidirect
41. C4×Dic26C22semidirect
42. #88075C22semidirect
43. #88075C22semidirect
44. #88075C22semidirect
52. C22⋊#1055C22semidirect
53. #88050C22semidirect
54. #88047C22semidirect
55. #88047C22semidirect
56. #88047C22semidirect
57. C4⋊#1055C22semidirect
58. #88043C22semidirect
298. C13#3314semidirect

Maximal subgroups

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

subgroupindex
C13×#5462
#117192482
#117189002
#117188932
#117188792
C2×#880722
#117187162
#117187152
#117187122
#117187052
#117187032
#117186942
#117186792
#117186722
#117186682
#331413