Finite Group Databasebeta

← #13125927

Subgroups — #13125927

Order 1664.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719420C211yesmaximal, characteristic, complemented
2#11719266C211yesmaximal, characteristic, complemented
3C13×#459C211yesmaximal, characteristic, complemented
4#11718819C211yesmaximal, characteristic, complemented
5#11718817C211yesmaximal, characteristic, complemented
6#11718816C211yesmaximal, characteristic, complemented
7#11718815C211yesmaximal, characteristic, complemented
8#11718736C211yesmaximal, characteristic, complemented
9#11718677C211yesmaximal, characteristic, complemented
10#11718506C211yesmaximal, characteristic, complemented
11#11718501C211yesmaximal, characteristic, complemented
12#11718444C211yesmaximal, characteristic, complemented
13#11718437C211yesmaximal, characteristic, complemented
14#11718426C211yesmaximal, characteristic, complemented
15#11718421C211yesmaximal, characteristic, complemented
16C2×#6129C2211yescharacteristic
17C2×D4×D13C2211yescharacteristic
18C2×C13×D8C2211yescharacteristic
19C2×C13×D8C2211yescharacteristic, complemented
20C13×#127C2211yescharacteristic
21C4×D4×C13C2211yescharacteristic, complemented
22#88194C2211yescharacteristic
23#88193—21no—
24#88193—21no—
25#88192C2211yescharacteristic
26#88191—21no—
27#88191—21no—
28#88190C2211yescharacteristic
29#88190C2211yescharacteristic, complemented
30C2×#6105C2211yescharacteristic
31C2×#6105C2211yescharacteristic, complemented
32C2×#6105C2211yescharacteristic, complemented
33C2×#6104C2211yescharacteristic
34#88183—21no—
35#88178—21no—
36C2×Dic52C2211yescharacteristic, complemented
37C2×#6095C2211yescharacteristic
38#88151C2211yescharacteristic
39#88142C2211yescharacteristic, complemented
40#88139—21no—
41#88133—21no—
42#88129C2211yescharacteristic
43#88126C2211yescharacteristic
44C4×Dic26C2211yescharacteristic, complemented
45C13×C4⋊C8C2211yescharacteristic, complemented
46C13×#102C2211yescharacteristic
47C13×#102C2211yescharacteristic, complemented
48#88072C2211yescharacteristic
49#88072C2211yescharacteristic, complemented
50#88061C2211yescharacteristic
51#88060C2211yescharacteristic
52#88060C2211yescharacteristic
53#88056C2211yescharacteristic, complemented
54#88055C2211yescharacteristic, complemented
55C8×Dic13C2211yescharacteristic, complemented
56#88050C2211yescharacteristic, complemented
57#88049C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic, complemented
59C23×D13—21no—
60C2×D4×C13—21no—
61C2×D4×C13—21no—
62C2×D4×C13C2311yescharacteristic
63C2×D4×C13C2311yescharacteristic
64C2×D4×C13C2311yescharacteristic
65C22×C4×C13—21no—
66C2×C22⋊D13—21no—
67C2×C22⋊D13—21no—
68C2×C22⋊D13—21no—
69C2×C22⋊D13—21no—
70C2×C22⋊D13—21no—
71C22×Dic13—21no—
72#6129—41no—
73#6129—41no—
74D4×D13—41no—
75D4×D13—41no—
76C2×D52C2311yescharacteristic
77C2×C4×D13C2311yescharacteristic
78C2×Dic26—21no—
79C2×Dic26C2311yescharacteristic
80C2×Dic26C2311yescharacteristic
81C13×D8—41no—
82C13×D8—41no—
83C2×C8×C13C2311yescharacteristic
84C2×C8×C13C2311yescharacteristic
85C13×C4⋊C4C2311yescharacteristic
86C13×C22⋊C4—21no—
87C42×C13C2311yescharacteristic
88C22⋊Dic13—21no—
89C22⋊Dic13—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13—21no—
92C22⋊Dic13—21no—
93#6105—41no—
94#6105—41no—
95#6105—41no—
96#6104—41no—
97#6103—21no—
98#6103—21no—
99#6103—21no—
100#6103D411yescharacteristic
101#6103D411yescharacteristic
102C4⋊Dic13—21no—
103C4⋊Dic13C2311yescharacteristic
104#6101—21no—
105#6101—21no—
106#6101D411yescharacteristic
107#6101D411yescharacteristic
108C4×Dic13—21no—
109C4×Dic13C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111C2×#1055C2311yescharacteristic
112Dic52—41no—
113#6095—41no—
114#3224—131nomaximal, Sylow
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C22×D13—21no—
119C22×D13—42no—
120C22×D13—81no—
121C22×D13—81no—
122C22×D13C2×D411yescharacteristic
123D4×C13—21no—
124D4×C13—21no—
125D4×C13—21no—
126D4×C13—21no—
127D4×C13—21no—
128D4×C13—21no—
129D4×C13—81no—
130D4×C13—81no—
131C2×C4×C13—21no—
132C2×C4×C13—81no—
133C2×C4×C13C2×D411yescharacteristic
134C2×C4×C13C2×D411yescharacteristic
135C2×C4×C13C2411yescharacteristic
136C22⋊D13—42no—
137C22⋊D13—42no—
138C22⋊D13—81no—
139C22⋊D13—81no—
140C22⋊D13—81no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—42no—
145C2×Dic13C2×D411yescharacteristic
146C2×Dic13C2×D411yescharacteristic
147C2×Dic13C2×D411yescharacteristic
148D52—21no—
149D52—21no—
150C4×D13—21no—
151C4×D13—21no—
152Dic26—21no—
153Dic26—21no—
154Dic26—21no—
155Dic26—21no—
156Dic26—81no—
157C8×C13—21no—
158C8×C13—21no—
159#1055—21no—
160#1055—21no—
161#542—131no—
162#535—131no—
163#496—131no—
164#495—131no—
165#489—131no—
166#486—131no—
167#464—131no—
168#463—131no—
169#460—131no—
170#459D1311yescharacteristic, complemented
171#452—131no—
172#450—131no—
173#449—131no—
174#447—131no—
175#433—131no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13C22×D411yescharacteristic
186C2×D13—21no—
187C2×D13—21no—
188C2×D13—21no—
189C2×D13—41no—
190C2×D13—41no—
191C2×D13—41no—
192C2×D13—84no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—41no—
196C4×C13H(5,𝔽2)11yescharacteristic
197C4×C13H(5,𝔽2)11yescharacteristic
198Dic13—21no—
199Dic13—21no—
200Dic13—21no—
201Dic13—41no—
202Dic13—41no—
203Dic13—41no—
204C2×#41—131no—
205C22×D4—131no—
206C2×Q16—131no—
207C2×SD16—131no—
208C2×SD16—131no—
209C2×SD16—131no—
210C2×SD16—131no—
211C2×D8—131no—
212C2×D8C2×D1311yescharacteristic
213C2×D8C2×D1311yescharacteristic, complemented
214C4⋊Q8—131no—
215#127—131no—
216#127C2×D1311yescharacteristic
217#126—261no—
218#124—131no—
219#124—131no—
220#124—131no—
221#124—261no—
222#123—261no—
223C22⋊Q8—131no—
224C22⋊Q8—261no—
225#121—131no—
226#121—261no—
227#121—261no—
228#120—261no—
229#120—261no—
230C4×Q8—131no—
231C4×D4C2×D1311yescharacteristic, complemented
232#117—131no—
233C4⋊C8—131no—
234C4⋊C8C2×D1311yescharacteristic, complemented
235#103—131no—
236#103—131no—
237#102—131no—
238#102—131no—
239#102—131no—
240#102—131no—
241#102C2×D1311yescharacteristic
242#102C2×D1311yescharacteristic, complemented
243C22⋊C8—131no—
244C22⋊C8—131no—
245#97—131no—
246C4×C8—131no—
247C2×C13—81no—
248C2×C13—81no—
249C2×C13—81no—
250C2×C13#53511yescharacteristic
251C2×C13#57611yescharacteristic
252C2×C13#57711yescharacteristic
253D13—41no—
254D13—81no—
255C24—261no—
256#41—521no—
257#41—521no—
258C2×Q8—131no—
259C2×Q8—131no—
260C2×Q8—261no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—131no—
264C2×D4—261no—
265C2×D4—261no—
266C2×D4—261no—
267C2×D4—261no—
268C2×D4—261no—
269C2×D4—521no—
270C2×D4—521no—
271C2×D4C22×D1311yescharacteristic
272C2×D4C22×D1311yescharacteristic
273C2×D4C22×D1311yescharacteristic
274C22×C4—21no—
275C22×C4—131no—
276C22×C4—261no—
277Q16—521no—
278SD16—521no—
279SD16—521no—
280SD16—521no—
281SD16—521no—
282D8—41no—
283D8—41no—
284D8—521no—
285C2×C8—131no—
286C2×C8—131no—
287C2×C8C22×D1311yescharacteristic
288C2×C8C22×D1311yescharacteristic
289C4⋊C4—131no—
290C4⋊C4—131no—
291C4⋊C4—131no—
292C4⋊C4—261no—
293C4⋊C4—261no—
294C4⋊C4—261no—
295C4⋊C4C22×D1311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—131no—
298C22⋊C4—131no—
299C22⋊C4—261no—
300C22⋊C4—261no—
301C22⋊C4—261no—
302C22⋊C4—261no—
303C22⋊C4—261no—
304C22⋊C4—261no—
305C22⋊C4—261no—
306C22⋊C4—261no—
307C42—131no—
308C42—261no—
309C42C22×D1311yescharacteristic
310C13#322411yescharacteristic, complemented, Sylow
311C23—21no—
312C23—21no—
313C23—21no—
314C23—131no—
315C23—261no—
316C23—522no—
317C23—1041no—
318C23—1041no—
319Q8—261no—
320Q8—261no—
321Q8—261no—
322Q8—261no—
323Q8—1041no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—81no—
331D4—81no—
332D4—261no—
333D4—261no—
334D4—522no—
335D4—522no—
336D4—1041no—
337D4—1041no—
338D4—1041no—
339C2×C4—21no—
340C2×C4—81no—
341C2×C4—131no—
342C2×C4—131no—
343C2×C4—131no—
344C2×C4—261no—
345C2×C4—261no—
346C2×C4—261no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—522no—
350C2×C4D4×D1311yescharacteristic
351C2×C4D4×D1311yescharacteristic
352C2×C4C23×D1311yescharacteristic
353C8—21no—
354C8—21no—
355C8—261no—
356C8—261no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—261no—
367C22—261no—
368C22—261no—
369C22—521no—
370C22—521no—
371C22—521no—
372C22—1044no—
373C22C2×D4×D1311yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—261no—
378C4—261no—
379C4—261no—
380C4—521no—
381C4—521no—
382C4—521no—
383C4#8825111yescharacteristic
384C4#8825611yescharacteristic
385C2—81no—
386C2—81no—
387C2—81no—
388C2—521no—
389C2—1041no—
390C2#1171931211yescharacteristic
391C2#1171946211yescharacteristic
392C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#459C2
socleC22×C13C22×D4
hypercenter#459D13
hypocenterC13#3224
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #11719420C2semidirect
2. #11719266C2semidirect
3. C13×#459C2semidirect
4. #11718819C2semidirect
5. #11718817C2semidirect
6. #11718816C2semidirect
7. #11718815C2semidirect
8. #11718736C2semidirect
9. #11718677C2semidirect
10. #11718506C2semidirect
11. #11718501C2semidirect
12. #11718444C2semidirect
13. #11718437C2semidirect
14. #11718426C2semidirect
15. #11718421C2semidirect
19. C2×C13×D8C22semidirect
21. C4×D4×C13C22semidirect
29. #88190C22semidirect
31. C2×#6105C22semidirect
32. C2×#6105C22semidirect
36. C2×Dic52C22semidirect
39. #88142C22semidirect
44. C4×Dic26C22semidirect
45. C13×C4⋊C8C22semidirect
47. C13×#102C22semidirect
49. #88072C22semidirect
53. #88056C22semidirect
54. #88055C22semidirect
55. C8×Dic13C22semidirect
56. #88050C22semidirect
58. C4⋊#1055C22semidirect
170. #459D13semidirect
213. C2×D8C2×D13semidirect
231. C4×D4C2×D13semidirect
234. C4⋊C8C2×D13semidirect
242. #102C2×D13semidirect
310. C13#3224semidirect

Maximal subgroups

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

subgroupindex
#117194202
#117192662
C13×#4592
#117188192
#117188172
#117188162
#117188152
#117187362
#117186772
#117185062
#117185012
#117184442
#117184372
#117184262
#117184212
#322413