Finite Group Databasebeta

← #13126879

Subgroups — #13126879

Order 1664.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719381C211yesmaximal, characteristic
2#11719289C211yesmaximal, characteristic, complemented
3C13×#464C211yesmaximal, characteristic, complemented
4#11718850C211yesmaximal, characteristic, complemented
5#11718848C211yesmaximal, characteristic, complemented
6#11718832C211yesmaximal, characteristic, complemented
7#11718830C211yesmaximal, characteristic, complemented
8#11718716C211yesmaximal, characteristic, complemented
9#11718687C211yesmaximal, characteristic, complemented
10#11718503C211yesmaximal, characteristic, complemented
11#11718497C211yesmaximal, characteristic, complemented
12#11718476C211yesmaximal, characteristic, complemented
13#11718465C211yesmaximal, characteristic, complemented
14#11718440C211yesmaximal, characteristic, complemented
15#11718431C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic
17C2×D4×D13C2211yescharacteristic
18C2×C13×Q16C2211yescharacteristic, complemented
19C2×C13×SD16C2211yescharacteristic
20C13×#124C2211yescharacteristic
21C4×Q8×C13C2211yescharacteristic, complemented
22#88200C2211yescharacteristic
23#88200C2211yescharacteristic
24#88200C2211yescharacteristic, complemented
25C2×#6106C2211yescharacteristic
26#88192C2211yescharacteristic
27C2×#6094C2211yescharacteristic
28C2×C8×D13C2211yescharacteristic, complemented
29#88152—21no—
30#88152—21no—
31#88146C2211yescharacteristic
32#88146C2211yescharacteristic, complemented
33#88138—21no—
34#88137—21no—
35#88136—21no—
36C22⋊C4×D13—21no—
37#88129—21no—
38C4×D52C2211yescharacteristic
39C4×D52C2211yescharacteristic
40#88123C2211yescharacteristic, complemented
41C4×Dic26—21no—
42C13×C4⋊C8C2211yescharacteristic, complemented
43C13×#103C2211yescharacteristic, complemented
44C13×#102C2211yescharacteristic
45#88075C2211yescharacteristic, complemented
46#88075C2211yescharacteristic, complemented
47#88075C2211yescharacteristic, complemented
48#88072C2211yescharacteristic
49#88072C2211yescharacteristic
50#88061C2211yescharacteristic
51#88061C2211yescharacteristic
52#88060C2211yescharacteristic
53#88060C2211yescharacteristic, complemented
54#88057C2211yescharacteristic, complemented
55#88057C2211yescharacteristic, complemented
56#88049C2211yescharacteristic
57#88047C2211yescharacteristic, complemented
58#88043C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13C2311yescharacteristic
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65#6131—22no—
66#6131—41no—
67D4×D13—22no—
68D4×D13—41no—
69C2×D52—21no—
70C2×D52D411yescharacteristic
71C2×D52C2311yescharacteristic
72C2×C4×D13—21no—
73C2×C4×D13—21no—
74C2×C4×D13C2311yescharacteristic
75C2×C4×D13C2311yescharacteristic
76C2×Dic26—21no—
77C13×Q16—41no—
78C13×SD16—41no—
79C2×C8×C13C2311yescharacteristic
80C2×C8×C13C2311yescharacteristic
81C13×C4⋊C4—21no—
82C13×C4⋊C4C2311yescharacteristic
83C13×C22⋊C4—21no—
84C13×C22⋊C4—21no—
85C42×C13—21no—
86C42×C13C2311yescharacteristic
87C22⋊Dic13—21no—
88#6106—22no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103D411yescharacteristic
96#6103D411yescharacteristic
97C4⋊Dic13—21no—
98C4⋊Dic13D411yescharacteristic
99C4⋊Dic13C2311yescharacteristic
100C4⋊Dic13C2311yescharacteristic
101C4⋊Dic13C2311yescharacteristic
102#6101—21no—
103#6101—21no—
104#6101—21no—
105C4×Dic13—21no—
106C4×Dic13—21no—
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109#6094—41no—
110C8×D13—41no—
111#3311—131nomaximal, Sylow
112C23×C13—21no—
113C22×D13—21no—
114C22×D13—42no—
115C22×D13—42no—
116C22×D13—81no—
117C22×D13C2×D411yescharacteristic
118C22×D13C2×D411yescharacteristic
119Q8×C13—21no—
120Q8×C13—21no—
121Q8×C13—21no—
122Q8×C13—21no—
123D4×C13—21no—
124D4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13C2×D411yescharacteristic
129C2×C4×C13C2×D411yescharacteristic
130C2×C4×C13C2411yescharacteristic
131C22⋊D13—42no—
132C22⋊D13—81no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13C2×D411yescharacteristic
137C2×Dic13C2×D411yescharacteristic
138D52—21no—
139D52—41no—
140D52—42no—
141D52#4112yes—
142C4×D13—21no—
143C4×D13—21no—
144C4×D13—21no—
145C4×D13—21no—
146C4×D13—42no—
147C4×D13—81no—
148Dic26—42no—
149C8×C13—21no—
150C8×C13—21no—
151#1055—21no—
152#1055—21no—
153#556—131no—
154#546—131no—
155#489—131no—
156#485—131no—
157#482—131no—
158#476—131no—
159#470—131no—
160#465—131no—
161#464D1311yescharacteristic, complemented
162#452—131no—
163#450—131no—
164#440—131no—
165#435—131no—
166#418—131no—
167#416—131no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13C22×D411yescharacteristic
172C2×D13—21no—
173C2×D13—21no—
174C2×D13—22no—
175C2×D13—21no—
176C2×D13—21no—
177C2×D13—21no—
178C2×D13—21no—
179C2×D13—41no—
180C2×D13—41no—
181C2×D13—84no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—41no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13C2×#4111yescharacteristic
188C4×C13H(5,𝔽2)11yescharacteristic
189Dic13—21no—
190Dic13—21no—
191Dic13—41no—
192Dic13—41no—
193Dic13—41no—
194C2×#41—131no—
195C22×D4—131no—
196C2×Q16C2×D1311yescharacteristic, complemented
197C2×SD16—131no—
198C2×SD16C2×D1311yescharacteristic
199C2×M16—131no—
200C22×C8—131no—
201C4⋊Q8—131no—
202#126—261no—
203#126—261no—
204#124—261no—
205#124C2×D1311yescharacteristic
206#123—261no—
207C22⋊Q8—131no—
208C22⋊Q8—131no—
209C22⋊Q8—131no—
210#121—131no—
211#121—261no—
212#120—261no—
213C4×Q8—261no—
214C4×Q8C2×D1311yescharacteristic, complemented
215C4×D4—131no—
216C4×D4—131no—
217#117—131no—
218#117—131no—
219C2×C22⋊C4—261no—
220#107—131no—
221#106—131no—
222#106—131no—
223C4⋊C8C2×D1311yescharacteristic, complemented
224#103—131no—
225#103—131no—
226#103—131no—
227#103C2×D1311yescharacteristic, complemented
228#102—131no—
229#102—131no—
230#102—131no—
231#102—131no—
232#102—131no—
233#102C2×D1311yescharacteristic
234C22⋊C8—131no—
235C22⋊C8—131no—
236#97—131no—
237C2×C13—81no—
238C2×C13#54611yescharacteristic
239C2×C13#57511yescharacteristic
240C2×C13#57711yescharacteristic
241D13—41no—
242D13—41no—
243D13—42no—
244C24—261no—
245#41—262no—
246#41—521no—
247C2×Q8—261no—
248C2×Q8C22×D1311yescharacteristic
249C2×Q8C22×D1311yescharacteristic
250C2×D4—131no—
251C2×D4—131no—
252C2×D4—261no—
253C2×D4—261no—
254C2×D4—262no—
255C2×D4—261no—
256C2×D4—521no—
257C2×D4C22×D1311yescharacteristic
258C22×C4—131no—
259C22×C4—131no—
260C22×C4—261no—
261C22×C4—261no—
262Q16—41no—
263SD16—41no—
264SD16—262no—
265M16—521no—
266C2×C8—131no—
267C2×C8—131no—
268C2×C8—521no—
269C2×C8C22×D1311yescharacteristic
270C2×C8C22×D1311yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—131no—
273C4⋊C4—131no—
274C4⋊C4—131no—
275C4⋊C4—131no—
276C4⋊C4—261no—
277C4⋊C4—261no—
278C4⋊C4—261no—
279C4⋊C4—261no—
280C4⋊C4C22×D1311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—131no—
284C22⋊C4—131no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C22⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C42—21no—
293C42—261no—
294C42—261no—
295C42C22×D1311yescharacteristic
296C13#331111yescharacteristic, complemented, Sylow
297C23—21no—
298C23—131no—
299C23—131no—
300C23—261no—
301C23—522no—
302C23—522no—
303C23—1041no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—522no—
309D4—21no—
310D4—21no—
311D4—132no—
312D4—261no—
313D4—521no—
314D4—522no—
315D4—522no—
316D4—1041no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—131no—
321C2×C4—131no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—261no—
329C2×C4—522no—
330C2×C4—1041no—
331C2×C4D4×D1311yescharacteristic
332C2×C4D4×D1311yescharacteristic
333C2×C4C23×D1311yescharacteristic
334C8—21no—
335C8—21no—
336C8—261no—
337C8—261no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—261no—
342C22—261no—
343C22—261no—
344C22—261no—
345C22—261no—
346C22—261no—
347C22—262no—
348C22—521no—
349C22—521no—
350C22—1044no—
351C22C2×D4×D1311yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—261no—
358C4—261no—
359C4—521no—
360C4—521no—
361C4—521no—
362C4#8825111yescharacteristic
363C4#41×D1311yescharacteristic
364C2—81no—
365C2—521no—
366C2—521no—
367C2—522no—
368C2#1171931711yescharacteristic
369C2#1171947511yescharacteristic
370C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#464C2
socleC22×C13C22×D4
prime radical#11719381C2
hypercenter#464D13
hypocenterC13#3311
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. #11719289C2semidirect
3. C13×#464C2semidirect
4. #11718850C2semidirect
5. #11718848C2semidirect
6. #11718832C2semidirect
7. #11718830C2semidirect
8. #11718716C2semidirect
9. #11718687C2semidirect
10. #11718503C2semidirect
11. #11718497C2semidirect
12. #11718476C2semidirect
13. #11718465C2semidirect
14. #11718440C2semidirect
15. #11718431C2semidirect
18. C2×C13×Q16C22semidirect
21. C4×Q8×C13C22semidirect
24. #88200C22semidirect
28. C2×C8×D13C22semidirect
32. #88146C22semidirect
40. #88123C22semidirect
42. C13×C4⋊C8C22semidirect
43. C13×#103C22semidirect
45. #88075C22semidirect
46. #88075C22semidirect
47. #88075C22semidirect
53. #88060C22semidirect
54. #88057C22semidirect
55. #88057C22semidirect
57. #88047C22semidirect
58. #88043C22semidirect
161. #464D13semidirect
196. C2×Q16C2×D13semidirect
214. C4×Q8C2×D13semidirect
223. C4⋊C8C2×D13semidirect
227. #103C2×D13semidirect
296. C13#3311semidirect

Maximal subgroups

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

subgroupindex
#117193812
#117192892
C13×#4642
#117188502
#117188482
#117188322
#117188302
#117187162
#117186872
#117185032
#117184972
#117184762
#117184652
#117184402
#117184312
#331113