Finite Group Databasebeta

← #13125684

Subgroups — #13125684

Order 1664.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719510C211yesmaximal, characteristic, complemented
2#11719313C211yesmaximal, characteristic, complemented
3C13×#447C211yesmaximal, characteristic, complemented
4#11718879C211yesmaximal, characteristic, complemented
5#11718820C211yesmaximal, characteristic, complemented
6#11718819C211yesmaximal, characteristic, complemented
7#11718819C211yesmaximal, characteristic, complemented
8#11718818C211yesmaximal, characteristic, complemented
9#11718696C211yesmaximal, characteristic, complemented
10#11718441C211yesmaximal, characteristic, complemented
11#11718439C211yesmaximal, characteristic, complemented
12#11718438C211yesmaximal, characteristic, complemented
13#11718435C211yesmaximal, characteristic, complemented
14#11718388C211yesmaximal, characteristic, complemented
15#11718384C211yesmaximal, characteristic, complemented
16C22×D4×C13C2211yescharacteristic
17C2×#6129C2211yescharacteristic, complemented
18C2×#6127C2211yescharacteristic
19C2×C13×D8C2211yescharacteristic
20C2×C13×D8C2211yescharacteristic
21C13×#121C2211yescharacteristic
22#88207—21no—
23#88207—21no—
24#88194—21no—
25#88193—21no—
26#88192—21no—
27#88192C2211yescharacteristic
28#88192C2211yescharacteristic
29#88192C2211yescharacteristic
30#88192C2211yescharacteristic
31#88192C2211yescharacteristic, complemented
32#88190—21no—
33C2×#6105C2211yescharacteristic
34C2×#6105C2211yescharacteristic
35#88180C2211yescharacteristic
36#88178C2211yescharacteristic
37C2×#6094C2211yescharacteristic, complemented
38C2×C8×D13C2211yescharacteristic, complemented
39#88151C2211yescharacteristic, complemented
40C4⋊C4×D13C2211yescharacteristic, complemented
41#88138—21no—
42#88132—21no—
43C13×#102C2211yescharacteristic
44C13×#102C2211yescharacteristic
45C13×C22⋊C8C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88072C2211yescharacteristic, complemented
49#88072C2211yescharacteristic, complemented
50C22⋊#1055C2211yescharacteristic
51#88060C2211yescharacteristic, complemented
52#88060C2211yescharacteristic, complemented
53#88058C2211yescharacteristic, complemented
54#88057C2211yescharacteristic, complemented
55#88056C2211yescharacteristic, complemented
56#88056C2211yescharacteristic, complemented
57#88048C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C24×C13—21no—
60C2×D4×C13—21no—
61C2×D4×C13—21no—
62C2×D4×C13—41no—
63C2×D4×C13—41no—
64C2×D4×C13C2311yescharacteristic
65C2×D4×C13C2311yescharacteristic
66C2×D4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C2×C22⋊D13—21no—
69C2×C22⋊D13—21no—
70C2×C22⋊D13—21no—
71C2×C22⋊D13—21no—
72C2×C22⋊D13—21no—
73C2×C22⋊D13—21no—
74C2×C22⋊D13D411yescharacteristic
75C2×C22⋊D13D411yescharacteristic
76C22×Dic13—21no—
77#6129—41no—
78#6129—41no—
79#6127—41no—
80#6127—41no—
81C2×D52D411yescharacteristic
82C2×C4×D13—21no—
83C2×C4×D13C2311yescharacteristic
84C2×C4×D13C2311yescharacteristic
85C2×Dic26D411yescharacteristic
86C2×Dic26C2311yescharacteristic
87C13×D8—41no—
88C13×D8—41no—
89C2×C8×C13C2311yescharacteristic
90C2×C8×C13C2311yescharacteristic
91C13×C4⋊C4C2311yescharacteristic
92C13×C22⋊C4—21no—
93C22⋊Dic13—21no—
94C22⋊Dic13—21no—
95C22⋊Dic13—21no—
96C22⋊Dic13—21no—
97C22⋊Dic13—21no—
98C22⋊Dic13—21no—
99C22⋊Dic13—21no—
100#6105—41no—
101#6105—41no—
102#6103—21no—
103C4⋊Dic13—21no—
104C4⋊Dic13C2311yescharacteristic
105C4⋊Dic13C2311yescharacteristic
106C4⋊Dic13C2311yescharacteristic
107#6101—21no—
108#6101—21no—
109C4×Dic13—21no—
110C2×#1055C2311yescharacteristic
111C2×#1055C2311yescharacteristic
112#6094—41no—
113C8×D13—41no—
114#3198—131nomaximal, Sylow
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13—42no—
119C23×C13—81no—
120C23×C13—81no—
121C23×C13C2×D411yescharacteristic
122C22×D13C2×D411yescharacteristic
123C22×D13C2×D411yescharacteristic
124D4×C13—21no—
125D4×C13—21no—
126D4×C13—21no—
127D4×C13—21no—
128D4×C13—21no—
129D4×C13—21no—
130D4×C13—42no—
131D4×C13—81no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13C2×D411yescharacteristic
136C2×C4×C13C2411yescharacteristic
137C22⋊D13—41no—
138C22⋊D13—41no—
139C22⋊D13—42no—
140C22⋊D13—81no—
141C22⋊D13—81no—
142C22⋊D13—81no—
143C22⋊D13—81no—
144C22⋊D13—81no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—42no—
150C2×Dic13C2×D411yescharacteristic
151C2×Dic13C2×D411yescharacteristic
152D52—41no—
153C4×D13—21no—
154C4×D13—21no—
155C4×D13—21no—
156C4×D13—21no—
157C4×D13—81no—
158Dic26—21no—
159Dic26—21no—
160Dic26—41no—
161C8×C13—21no—
162C8×C13—21no—
163#1055—21no—
164#1055—21no—
165#537—131no—
166#535—131no—
167#485—131no—
168#482—131no—
169#481—131no—
170#480—131no—
171#469—131no—
172#468—131no—
173#466—131no—
174#465—131no—
175#450—131no—
176#449—131no—
177#449—131no—
178#447D1311yescharacteristic, complemented
179#408—131no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13—84no—
193C22×C13C22×D411yescharacteristic
194C2×D13—21no—
195C2×D13—21no—
196C2×D13—21no—
197C2×D13—21no—
198C2×D13—21no—
199C2×D13—21no—
200C4×C13—21no—
201C4×C13—41no—
202C4×C13H(5,𝔽2)11yescharacteristic
203C4×C13H(5,𝔽2)11yescharacteristic
204Dic13—21no—
205Dic13—21no—
206Dic13—41no—
207Dic13—41no—
208Dic13—41no—
209Dic13—41no—
210C2×#41—131no—
211C2×#41—131no—
212C22×D4C2×D1311yescharacteristic
213C2×SD16—131no—
214C2×SD16—131no—
215C2×D8C2×D1311yescharacteristic
216C2×D8C2×D1311yescharacteristic
217C2×M16—131no—
218C22×C8—131no—
219#127—261no—
220#124—261no—
221C22⋊Q8—131no—
222C22⋊Q8—131no—
223C22⋊Q8—261no—
224#121—131no—
225#121—131no—
226#121—131no—
227#121—131no—
228#121—131no—
229#121—261no—
230#121—261no—
231#121—261no—
232#121C2×D1311yescharacteristic
233#120—261no—
234#120—261no—
235#117—131no—
236C2×C4⋊C4—131no—
237#107—131no—
238#107—131no—
239#106—131no—
240#106—131no—
241#103—131no—
242#103—131no—
243#102—131no—
244#102—131no—
245#102—131no—
246#102—131no—
247#102C2×D1311yescharacteristic
248#102C2×D1311yescharacteristic
249C22⋊C8—131no—
250C22⋊C8—131no—
251C22⋊C8—131no—
252C22⋊C8C2×D1311yescharacteristic
253C2×C13—41no—
254C2×C13—81no—
255C2×C13—81no—
256C2×C13—81no—
257C2×C13#53411yescharacteristic
258C2×C13#57611yescharacteristic
259C2×C13#57711yescharacteristic
260D13—41no—
261D13—41no—
262C24—21no—
263#41—521no—
264#41—521no—
265#41—521no—
266#41—521no—
267C2×Q8—131no—
268C2×Q8—131no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—131no—
274C2×D4—131no—
275C2×D4—131no—
276C2×D4—261no—
277C2×D4—261no—
278C2×D4—261no—
279C2×D4—261no—
280C2×D4—261no—
281C2×D4—261no—
282C2×D4C22×D1311yescharacteristic
283C2×D4C22×D1311yescharacteristic
284C2×D4C22×D1311yescharacteristic
285C22×C4—131no—
286C22×C4—131no—
287C22×C4—261no—
288C22×C4—261no—
289C22×C4C22×D1311yescharacteristic
290SD16—521no—
291SD16—521no—
292D8—41no—
293D8—41no—
294M16—521no—
295C2×C8—131no—
296C2×C8—131no—
297C2×C8—521no—
298C2×C8C22×D1311yescharacteristic
299C2×C8C22×D1311yescharacteristic
300C4⋊C4—131no—
301C4⋊C4—131no—
302C4⋊C4—131no—
303C4⋊C4—261no—
304C4⋊C4—261no—
305C4⋊C4—261no—
306C4⋊C4C22×D1311yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—261no—
309C22⋊C4—261no—
310C22⋊C4—261no—
311C22⋊C4—261no—
312C22⋊C4—261no—
313C22⋊C4—261no—
314C22⋊C4—261no—
315C22⋊C4—261no—
316C42—261no—
317C13#319811yescharacteristic, complemented, Sylow
318C23—21no—
319C23—21no—
320C23—21no—
321C23—42no—
322C23—81no—
323C23—81no—
324C23—131no—
325C23—131no—
326C23D4×D1311yescharacteristic
327Q8—261no—
328Q8—261no—
329Q8—521no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—42no—
337D4—81no—
338D4—521no—
339D4—521no—
340D4—521no—
341D4—522no—
342D4—1041no—
343D4—1041no—
344D4—1041no—
345D4—1041no—
346D4—1041no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—131no—
351C2×C4—131no—
352C2×C4—261no—
353C2×C4—261no—
354C2×C4—261no—
355C2×C4—261no—
356C2×C4—261no—
357C2×C4—261no—
358C2×C4—261no—
359C2×C4—261no—
360C2×C4—522no—
361C2×C4—1041no—
362C2×C4D4×D1311yescharacteristic
363C2×C4C23×D1311yescharacteristic
364C8—21no—
365C8—21no—
366C8—261no—
367C8—261no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—84no—
381C22—261no—
382C22—261no—
383C22—261no—
384C22—261no—
385C22—261no—
386C22—261no—
387C22C2×D4×D1311yescharacteristic
388C4—21no—
389C4—41no—
390C4—261no—
391C4—261no—
392C4—521no—
393C4—521no—
394C4—521no—
395C4—521no—
396C4#8825111yescharacteristic
397C4#8825111yescharacteristic
398C2—41no—
399C2—81no—
400C2—81no—
401C2—81no—
402C2—521no—
403C2—521no—
404C2#1171929411yescharacteristic
405C2#1171946211yescharacteristic
406C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#447C2
socleC22×C13C22×D4
hypercenter#447D13
hypocenterC13#3198
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #11719510C2semidirect
2. #11719313C2semidirect
3. C13×#447C2semidirect
4. #11718879C2semidirect
5. #11718820C2semidirect
6. #11718819C2semidirect
7. #11718819C2semidirect
8. #11718818C2semidirect
9. #11718696C2semidirect
10. #11718441C2semidirect
11. #11718439C2semidirect
12. #11718438C2semidirect
13. #11718435C2semidirect
14. #11718388C2semidirect
15. #11718384C2semidirect
17. C2×#6129C22semidirect
31. #88192C22semidirect
37. C2×#6094C22semidirect
38. C2×C8×D13C22semidirect
39. #88151C22semidirect
40. C4⋊C4×D13C22semidirect
48. #88072C22semidirect
49. #88072C22semidirect
51. #88060C22semidirect
52. #88060C22semidirect
53. #88058C22semidirect
54. #88057C22semidirect
55. #88056C22semidirect
56. #88056C22semidirect
57. #88048C22semidirect
58. #88047C22semidirect
178. #447D13semidirect
317. C13#3198semidirect

Maximal subgroups

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

subgroupindex
#117195102
#117193132
C13×#4472
#117188792
#117188202
#117188192
#117188182
#117186962
#117184412
#117184392
#117184382
#117184352
#117183882
#117183842
#319813