Finite Group Databasebeta

← #13126921

Subgroups — #13126921

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
1#11719511C211yesmaximal, characteristic
2#11719340C211yesmaximal, characteristic, complemented
3C13×#450C211yesmaximal, characteristic, complemented
4C2×#88072C211yesmaximal, characteristic, complemented
5#11718835C211yesmaximal, characteristic, complemented
6#11718834C211yesmaximal, characteristic, complemented
7#11718827C211yesmaximal, characteristic, complemented
8#11718825C211yesmaximal, characteristic, complemented
9#11718712C211yesmaximal, characteristic, complemented
10#11718435C211yesmaximal, characteristic, complemented
11#11718432C211yesmaximal, characteristic, complemented
12#11718426C211yesmaximal, characteristic, complemented
13#11718420C211yesmaximal, characteristic, complemented
14#11718391C211yesmaximal, characteristic, complemented
15#11718383C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C2×#6129C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic
19C2×C13×SD16C2211yescharacteristic
20C13×C22⋊Q8C2211yescharacteristic
21#88207—21no—
22C2×C22⋊Dic13—21no—
23#88200C2211yescharacteristic, complemented
24Q8×Dic13C2211yescharacteristic, complemented
25C2×#6107C2211yescharacteristic, complemented
26#88193—21no—
27#88192C2211yescharacteristic
28#88190C2211yescharacteristic
29#88189—21no—
30D4×Dic13C2211yescharacteristic
31C4×C22⋊D13C2211yescharacteristic
32C2×C4⋊Dic13C2211yescharacteristic
33#88178C2211yescharacteristic
34C22×#1055C2211yescharacteristic
35C2×#6094C2211yescharacteristic, complemented
36#88151—21no—
37C4⋊C4×D13C2211yescharacteristic, complemented
38#88143—21no—
39#88142C2211yescharacteristic, complemented
40#88135—21no—
41#88132—21no—
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45#88075C2211yescharacteristic, complemented
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88072C2211yescharacteristic
49#88072C2211yescharacteristic
50#88060C2211yescharacteristic, complemented
51#88058C2211yescharacteristic, complemented
52#88058C2211yescharacteristic, complemented
53#88056C2211yescharacteristic, complemented
54#88056C2211yescharacteristic, complemented
55#88055C2211yescharacteristic, complemented
56#88054C2211yescharacteristic, complemented
57#88050C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C24×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13—22no—
62C2×D4×C13—21no—
63C2×D4×C13—41no—
64C2×D4×C13C2311yescharacteristic
65C2×D4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C2×C22⋊D13D411yescharacteristic
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—21no—
73#6129—22no—
74#6129—41no—
75C2×C4×D13—21no—
76C2×C4×D13C2311yescharacteristic
77C2×Dic26—21no—
78C2×Dic26C2311yescharacteristic
79C13×SD16—22no—
80C13×SD16—41no—
81C2×C8×C13C2311yescharacteristic
82C2×C8×C13C2311yescharacteristic
83C13×C4⋊C4—21no—
84C13×C4⋊C4C2311yescharacteristic
85C13×C22⋊C4—21no—
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88C22⋊Dic13—21no—
89C22⋊Dic13—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13D411yescharacteristic
92#6107—41no—
93#6103—21no—
94#6103D411yescharacteristic
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99C4⋊Dic13C2311yescharacteristic
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101—21no—
104#6101D411yescharacteristic
105C4×Dic13—21no—
106C4×Dic13C2311yescharacteristic
107C2×#1055—41no—
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110#6094—41no—
111#3314—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—42no—
115C23×C13—42no—
116C23×C13—81no—
117C23×C13C2×D411yescharacteristic
118C22×D13C2×D411yescharacteristic
119Q8×C13—21no—
120Q8×C13—21no—
121D4×C13—21no—
122D4×C13—21no—
123D4×C13—21no—
124D4×C13—42no—
125D4×C13#4112yes—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13C2×D411yescharacteristic
131C2×C4×C13C2411yescharacteristic
132C22⋊D13—22no—
133C22⋊D13—42no—
134C22⋊D13—81no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—42no—
140C2×Dic13—81no—
141C2×Dic13—81no—
142C2×Dic13C2×D411yescharacteristic
143C2×Dic13C2×D411yescharacteristic
144C2×Dic13C2×D411yescharacteristic
145C4×D13—21no—
146C4×D13—21no—
147C4×D13—81no—
148Dic26—21no—
149Dic26—21no—
150Dic26—81no—
151C8×C13—21no—
152C8×C13—21no—
153#1055—21no—
154#1055—21no—
155#554—131no—
156#546—131no—
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#450D1311yescharacteristic, complemented
166#440—131no—
167#435—131no—
168#417—131no—
169C2×#102—131no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—22no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—84no—
179C22×C13#13712yes—
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—21no—
190Dic13—21no—
191Dic13—21no—
192Dic13—41no—
193Dic13—41no—
194Dic13—41no—
195Dic13—41no—
196C2×#41—131no—
197C22×D4C2×D1311yescharacteristic
198C2×Q16—131no—
199C2×SD16C2×D1311yescharacteristic
200C2×SD16C2×D1311yescharacteristic
201C2×M16—131no—
202C22×C8—131no—
203C4⋊Q8—131no—
204#125—261no—
205#124—131no—
206#123—261no—
207C22⋊Q8—131no—
208C22⋊Q8—131no—
209C22⋊Q8—261no—
210C22⋊Q8—261no—
211C22⋊Q8C2×D1311yescharacteristic
212#121—131no—
213#121—261no—
214#120—261no—
215C4×Q8—131no—
216C4×D4—131no—
217C4×D4—131no—
218C4×D4—261no—
219C2×C4⋊C4—131no—
220C2×C4⋊C4—131no—
221C2×C22⋊C4—261no—
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#102C2×D1311yescharacteristic
235#102C2×D1311yescharacteristic
236C22⋊C8—131no—
237C22⋊C8C2×D1311yescharacteristic
238#97—131no—
239C2×C13—22no—
240C2×C13—42no—
241C2×C13—81no—
242C2×C13#54611yescharacteristic
243C2×C13C2×#13711yescharacteristic
244C2×C13#57611yescharacteristic
245D13—41no—
246C24—21no—
247#41—262no—
248#41—521no—
249C2×Q8—131no—
250C2×Q8—261no—
251C2×Q8C22×D1311yescharacteristic
252C2×D4—22no—
253C2×D4—21no—
254C2×D4—41no—
255C2×D4—131no—
256C2×D4—261no—
257C2×D4—261no—
258C2×D4C22×D1311yescharacteristic
259C2×D4C22×D1311yescharacteristic
260C22×C4—131no—
261C22×C4—261no—
262C22×C4—261no—
263C22×C4—261no—
264C22×C4—261no—
265C22×C4C22×D1311yescharacteristic
266Q16—521no—
267SD16—22no—
268SD16—41no—
269M16—521no—
270C2×C8—131no—
271C2×C8—131no—
272C2×C8—521no—
273C2×C8C22×D1311yescharacteristic
274C2×C8C22×D1311yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—131no—
277C4⋊C4—131no—
278C4⋊C4—131no—
279C4⋊C4—131no—
280C4⋊C4—261no—
281C4⋊C4—261no—
282C4⋊C4—261no—
283C4⋊C4—261no—
284C4⋊C4—261no—
285C4⋊C4—261no—
286C4⋊C4C22×D1311yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—131no—
289C22⋊C4—131no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C22⋊C4—261no—
294C22⋊C4—261no—
295C22⋊C4—261no—
296C42—131no—
297C42—261no—
298C13#331411yescharacteristic, complemented, Sylow
299C23—21no—
300C23—21no—
301C23—42no—
302C23—42no—
303C23—81no—
304C23—131no—
305C23D4×D1311yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—261no—
309Q8—261no—
310Q8—1041no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—262no—
316D4—522no—
317D4—1041no—
318D4#612912yes—
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—1041no—
334C2×C4—1041no—
335C2×C4—1041no—
336C2×C4D4×D1311yescharacteristic
337C2×C4C23×D1311yescharacteristic
338C8—21no—
339C8—21no—
340C8—261no—
341C8—261no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—84no—
351C22—261no—
352C22—261no—
353C22—261no—
354C22#8816912yes—
355C22C2×D4×D1311yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—261no—
360C4—261no—
361C4—261no—
362C4—521no—
363C4—521no—
364C4—521no—
365C4—521no—
366C4C2×#612911yescharacteristic
367C4#8825111yescharacteristic
368C2—22no—
369C2—42no—
370C2—81no—
371C2—521no—
372C2#1171929611yescharacteristic
373C2C2×#8816911yescharacteristic
374C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#450C2
socleC22×C13C22×D4
prime radical#11719511C2
hypercenter#450D13
hypocenterC13#3314
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
2. #11719340C2semidirect
3. C13×#450C2semidirect
4. C2×#88072C2semidirect
5. #11718835C2semidirect
6. #11718834C2semidirect
7. #11718827C2semidirect
8. #11718825C2semidirect
9. #11718712C2semidirect
10. #11718435C2semidirect
11. #11718432C2semidirect
12. #11718426C2semidirect
13. #11718420C2semidirect
14. #11718391C2semidirect
15. #11718383C2semidirect
23. #88200C22semidirect
24. Q8×Dic13C22semidirect
25. C2×#6107C22semidirect
35. C2×#6094C22semidirect
37. C4⋊C4×D13C22semidirect
39. #88142C22semidirect
45. #88075C22semidirect
50. #88060C22semidirect
51. #88058C22semidirect
52. #88058C22semidirect
53. #88056C22semidirect
54. #88056C22semidirect
55. #88055C22semidirect
56. #88054C22semidirect
57. #88050C22semidirect
58. #88047C22semidirect
165. #450D13semidirect
298. C13#3314semidirect

Maximal subgroups

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

subgroupindex
#117195112
#117193402
C13×#4502
C2×#880722
#117188352
#117188342
#117188272
#117188252
#117187122
#117184352
#117184322
#117184262
#117184202
#117183912
#117183832
#331413