Finite Group Databasebeta

← #13126692

Subgroups — #13126692

Order 1664.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719335C211yesmaximal, characteristic, complemented
2#11719323C211yesmaximal, characteristic, complemented
3C13×#465C211yesmaximal, characteristic, complemented
4#11718833C211yesmaximal, characteristic, complemented
5#11718826C211yesmaximal, characteristic, complemented
6C2×#88061C211yesmaximal, characteristic, complemented
7C8×C22⋊D13C211yesmaximal, characteristic, complemented
8#11718705C211yesmaximal, characteristic, complemented
9#11718697C211yesmaximal, characteristic, complemented
10#11718532C211yesmaximal, characteristic, complemented
11#11718527C211yesmaximal, characteristic, complemented
12#11718465C211yesmaximal, characteristic, complemented
13#11718461C211yesmaximal, characteristic, complemented
14#11718436C211yesmaximal, characteristic, complemented
15#11718417C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic
17C22×D52C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic, complemented
19C22×C8×C13C2211yescharacteristic
20C13×C22⋊Q8C2211yescharacteristic
21C13×#121C2211yescharacteristic
22#88201C2211yescharacteristic
23#88193—21no—
24#88192C2211yescharacteristic, complemented
25D4×Dic13—21no—
26D4×Dic13C2211yescharacteristic, complemented
27C2×#6104C2211yescharacteristic
28C2×#6104C2211yescharacteristic
29C4×C22⋊D13C2211yescharacteristic
30C2×C4⋊Dic13C2211yescharacteristic
31C2×C8×D13C2211yescharacteristic, complemented
32#88149—21no—
33#88149C2211yescharacteristic
34#88148—21no—
35#88147C2211yescharacteristic
36#88146C2211yescharacteristic, complemented
37#88144C2211yescharacteristic, complemented
38#88140—21no—
39#88136—21no—
40C22⋊C4×D13—21no—
41#88133—21no—
42C13×#106C2211yescharacteristic, complemented
43C13×#103C2211yescharacteristic, complemented
44C13×#102C2211yescharacteristic, complemented
45#88075C2211yescharacteristic, complemented
46#88075C2211yescharacteristic, complemented
47C22⋊#1055C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88061C2211yescharacteristic
51#88061C2211yescharacteristic
52#88060C2211yescharacteristic, complemented
53#88054C2211yescharacteristic, complemented
54C8×Dic13C2211yescharacteristic, complemented
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic
57#88047C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13—21no—
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C2×C22⋊D13—21no—
65C2×C22⋊D13D411yescharacteristic
66C22×Dic13—21no—
67C22×Dic13—21no—
68#6131—22no—
69#6131—41no—
70C2×D52—22no—
71C2×D52—21no—
72C2×D52—21no—
73C2×D52—21no—
74C2×D52—41no—
75C2×D52C2311yescharacteristic
76C2×D52C2311yescharacteristic
77C2×C4×D13—21no—
78C2×C4×D13—21no—
79C2×C4×D13C2311yescharacteristic
80C13×SD16—41no—
81C2×C8×C13—41no—
82C2×C8×C13C2311yescharacteristic
83C2×C8×C13C2311yescharacteristic
84C13×C4⋊C4—21no—
85C13×C4⋊C4C2311yescharacteristic
86C13×C4⋊C4C2311yescharacteristic
87C13×C22⋊C4—21no—
88C13×C22⋊C4—21no—
89C22⋊Dic13—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13D411yescharacteristic
92#6104—22no—
93#6104—41no—
94#6103—21no—
95#6103—21no—
96#6103—21no—
97#6103—21no—
98#6103—21no—
99#6103D411yescharacteristic
100C4⋊Dic13—21no—
101C4⋊Dic13—21no—
102C4⋊Dic13C2311yescharacteristic
103C4⋊Dic13C2311yescharacteristic
104#6101—21no—
105#6101D411yescharacteristic
106C4×Dic13—21no—
107C4×Dic13C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C8×D13—41no—
111#3297—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13C2×D411yescharacteristic
114C22×D13—21no—
115C22×D13—21no—
116C22×D13—42no—
117C22×D13—42no—
118C22×D13—81no—
119C22×D13C2×D411yescharacteristic
120Q8×C13—21no—
121Q8×C13—21no—
122D4×C13—21no—
123D4×C13—21no—
124D4×C13—42no—
125C2×C4×C13—21no—
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—81no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—81no—
137C2×Dic13—81no—
138C2×Dic13C2×D411yescharacteristic
139C2×Dic13C2×D411yescharacteristic
140C2×Dic13C2×D411yescharacteristic
141D52—21no—
142D52—21no—
143D52—21no—
144D52—42no—
145D52—42no—
146D52—81no—
147D52#4112yes—
148C4×D13—21no—
149C4×D13—21no—
150C4×D13—42no—
151C4×D13—81no—
152C8×C13—21no—
153C8×C13—21no—
154#1055—21no—
155#1055—21no—
156#553—131no—
157#546—131no—
158#488—131no—
159#484—131no—
160#482—131no—
161#478—131no—
162#466—131no—
163#465D1311yescharacteristic, complemented
164#463—131no—
165#449—131no—
166#447—131no—
167C4×D8—131no—
168C8×D4—131no—
169#416—131no—
170C2×#102—131no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13#13512yes—
177C22×C13C22×D411yescharacteristic
178C2×D13—21no—
179C2×D13—22no—
180C2×D13—21no—
181C2×D13—21no—
182C2×D13—41no—
183C2×D13—41no—
184C2×D13—41no—
185C2×D13—41no—
186C2×D13—41no—
187C2×D13—84no—
188C4×C13—21no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13C2×#4111yescharacteristic
193C4×C13H(5,𝔽2)11yescharacteristic
194Dic13—21no—
195Dic13—21no—
196Dic13—21no—
197Dic13—41no—
198Dic13—41no—
199C2×#41—131no—
200C22×D4—131no—
201C2×SD16C2×D1311yescharacteristic, complemented
202C2×D8—131no—
203C2×D8—131no—
204C22×C8—131no—
205C22×C8C2×D1311yescharacteristic
206#126—261no—
207#125—131no—
208#124—131no—
209#123—261no—
210#123—261no—
211C22⋊Q8C2×D1311yescharacteristic
212#121—131no—
213#121—131no—
214#121—261no—
215#121—261no—
216#121C2×D1311yescharacteristic
217#120—261no—
218C4×D4—131no—
219C4×D4—131no—
220C4×D4—131no—
221C4×D4—261no—
222#117—131no—
223C2×C4⋊C4—131no—
224C2×C22⋊C4—261no—
225#107—131no—
226#107—131no—
227#106C2×D1311yescharacteristic, complemented
228C4⋊C8—131no—
229#103—131no—
230#103—131no—
231#103C2×D1311yescharacteristic, complemented
232#102—131no—
233#102—131no—
234#102—131no—
235#102—131no—
236#102—131no—
237#102—131no—
238#102C2×D1311yescharacteristic, complemented
239C22⋊C8—131no—
240C22⋊C8—131no—
241C4×C8—131no—
242C2×C13—22no—
243C2×C13—81no—
244C2×C13#54611yescharacteristic
245C2×C13C2×#13511yescharacteristic
246C2×C13#57611yescharacteristic
247D13—41no—
248D13—42no—
249D13—81no—
250C24—261no—
251#41—262no—
252#41—521no—
253C2×Q8C22×D1311yescharacteristic
254C2×D4—21no—
255C2×D4—131no—
256C2×D4—131no—
257C2×D4—131no—
258C2×D4—262no—
259C2×D4—261no—
260C2×D4—261no—
261C2×D4—261no—
262C2×D4—261no—
263C2×D4—521no—
264C2×D4C22×D1311yescharacteristic
265C22×C4—131no—
266C22×C4—261no—
267C22×C4—261no—
268C22×C4—261no—
269C22×C4—261no—
270C22×C4C22×D1311yescharacteristic
271SD16—41no—
272D8—262no—
273D8—521no—
274C2×C8—41no—
275C2×C8—131no—
276C2×C8—131no—
277C2×C8—521no—
278C2×C8C22×D1311yescharacteristic
279C2×C8C22×D1311yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—131no—
282C4⋊C4—131no—
283C4⋊C4—131no—
284C4⋊C4—261no—
285C4⋊C4—261no—
286C4⋊C4—261no—
287C4⋊C4C22×D1311yescharacteristic
288C4⋊C4C22×D1311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—131no—
292C22⋊C4—131no—
293C22⋊C4—261no—
294C22⋊C4—261no—
295C22⋊C4—261no—
296C22⋊C4—261no—
297C22⋊C4—261no—
298C22⋊C4—261no—
299C22⋊C4—261no—
300C42—131no—
301C42—261no—
302C13#329711yescharacteristic, complemented, Sylow
303C23—21no—
304C23—131no—
305C23—261no—
306C23—261no—
307C23—522no—
308C23—522no—
309C23—1041no—
310C23D4×D1311yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—132no—
317D4—262no—
318D4—261no—
319D4—261no—
320D4—261no—
321D4—522no—
322D4—522no—
323D4—1041no—
324D4—1041no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—131no—
331C2×C4—131no—
332C2×C4—131no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—522no—
338C2×C4—1041no—
339C2×C4—1041no—
340C2×C4—1041no—
341C2×C4D4×D1311yescharacteristic
342C2×C4C23×D1311yescharacteristic
343C8—21no—
344C8—21no—
345C8—261no—
346C8—261no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—261no—
353C22—261no—
354C22—261no—
355C22—262no—
356C22—521no—
357C22—521no—
358C22—521no—
359C22—521no—
360C22—521no—
361C22—1044no—
362C22#8817012yes—
363C22C2×D4×D1311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—261no—
369C4—261no—
370C4—261no—
371C4—521no—
372C4—521no—
373C4#8825111yescharacteristic
374C4#41×D1311yescharacteristic
375C2—22no—
376C2—81no—
377C2—521no—
378C2—522no—
379C2—1041no—
380C2#1171931511yescharacteristic
381C2C2×#8817011yescharacteristic
382C2#1171947411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#465C2
socleC22×C13C22×D4
hypercenter#465D13
hypocenterC13#3297
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #11719335C2semidirect
2. #11719323C2semidirect
3. C13×#465C2semidirect
4. #11718833C2semidirect
5. #11718826C2semidirect
6. C2×#88061C2semidirect
7. C8×C22⋊D13C2semidirect
8. #11718705C2semidirect
9. #11718697C2semidirect
10. #11718532C2semidirect
11. #11718527C2semidirect
12. #11718465C2semidirect
13. #11718461C2semidirect
14. #11718436C2semidirect
15. #11718417C2semidirect
18. C2×C13×SD16C22semidirect
24. #88192C22semidirect
26. D4×Dic13C22semidirect
31. C2×C8×D13C22semidirect
36. #88146C22semidirect
37. #88144C22semidirect
42. C13×#106C22semidirect
43. C13×#103C22semidirect
44. C13×#102C22semidirect
45. #88075C22semidirect
46. #88075C22semidirect
52. #88060C22semidirect
53. #88054C22semidirect
54. C8×Dic13C22semidirect
57. #88047C22semidirect
58. #88047C22semidirect
163. #465D13semidirect
201. C2×SD16C2×D13semidirect
227. #106C2×D13semidirect
231. #103C2×D13semidirect
238. #102C2×D13semidirect
302. C13#3297semidirect

Maximal subgroups

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

subgroupindex
#117193352
#117193232
C13×#4652
#117188332
#117188262
C2×#880612
C8×C22⋊D132
#117187052
#117186972
#117185322
#117185272
#117184652
#117184612
#117184362
#117184172
#329713