Finite Group Databasebeta

← #13126996

Subgroups — #13126996

Order 1664.

414 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#11719534C211yesmaximal, characteristic, complemented
2#11719321C211yesmaximal, characteristic, complemented
3C13×#449C211yesmaximal, characteristic, complemented
4#11718894C211yesmaximal, characteristic, complemented
5#11718835C211yesmaximal, characteristic, complemented
6#11718826C211yesmaximal, characteristic, complemented
7#11718817C211yesmaximal, characteristic, complemented
8#11718813C211yesmaximal, characteristic, complemented
9#11718699C211yesmaximal, characteristic, complemented
10#11718476C211yesmaximal, characteristic, complemented
11#11718456C211yesmaximal, characteristic, complemented
12#11718431C211yesmaximal, characteristic, complemented
13#11718420C211yesmaximal, characteristic, complemented
14#11718398C211yesmaximal, characteristic, complemented
15#11718391C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×D4×D13C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic, complemented
19C2×C13×D8C2211yescharacteristic
20C13×#121C2211yescharacteristic, complemented
21#88201C2211yescharacteristic
22#88200C2211yescharacteristic
23#88193—21no—
24#88193—21no—
25#88192C2211yescharacteristic
26#88191—21no—
27#88190—21no—
28D4×Dic13C2211yescharacteristic
29D4×Dic13C2211yescharacteristic, complemented
30C2×#6104C2211yescharacteristic
31#88184C2211yescharacteristic
32#88183—21no—
33C4×C22⋊D13C2211yescharacteristic
34C2×#6103—21no—
35#88180C2211yescharacteristic, complemented
36C22×#1055C2211yescharacteristic, complemented
37C2×#6094C2211yescharacteristic
38#88146C2211yescharacteristic
39#88142C2211yescharacteristic, complemented
40#88139—21no—
41#88131—21no—
42C13×#103C2211yescharacteristic, complemented
43C13×#102C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic, complemented
45#88075C2211yescharacteristic, complemented
46#88075C2211yescharacteristic, complemented
47#88072C2211yescharacteristic
48#88072C2211yescharacteristic
49#88072C2211yescharacteristic, complemented
50#88061C2211yescharacteristic
51#88061C2211yescharacteristic
52#88060C2211yescharacteristic
53#88058C2211yescharacteristic, complemented
54#88057C2211yescharacteristic, complemented
55#88055C2211yescharacteristic, complemented
56#88054C2211yescharacteristic, complemented
57#88049C2211yescharacteristic
58#88047C2211yescharacteristic, complemented
59C23×D13—21no—
60C13×#41—22no—
61C13×#41—41no—
62C2×Q8×C13C2311yescharacteristic
63C2×D4×C13—21no—
64C2×D4×C13—21no—
65C2×D4×C13C2311yescharacteristic
66C2×D4×C13C2311yescharacteristic
67C22×C4×C13—21no—
68C22×C4×C13C2311yescharacteristic
69C2×C22⋊D13—21no—
70C2×C22⋊D13—21no—
71C2×C22⋊D13—21no—
72C2×C22⋊D13D411yescharacteristic
73C22×Dic13—21no—
74C22×Dic13—21no—
75D4×D13—22no—
76D4×D13—41no—
77C2×D52C2311yescharacteristic
78C2×C4×D13C2311yescharacteristic
79C2×Dic26—21no—
80C13×SD16—41no—
81C13×D8—22no—
82C2×C8×C13C2311yescharacteristic
83C2×C8×C13C2311yescharacteristic
84C13×C4⋊C4C2311yescharacteristic
85C13×C22⋊C4—21no—
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88C22⋊Dic13—21no—
89C22⋊Dic13—21no—
90C22⋊Dic13D411yescharacteristic
91#6104—41no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103—21no—
96#6103—21no—
97#6103D411yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99C4⋊Dic13C2311yescharacteristic
100C4⋊Dic13C2311yescharacteristic
101#6101—21no—
102#6101—21no—
103#6101D411yescharacteristic
104C4×Dic13—21no—
105C4×Dic13—21no—
106C4×Dic13C2311yescharacteristic
107C2×#1055—41no—
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110#6094—41no—
111#3319—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13—21no—
114C23×C13C2×D411yescharacteristic
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—21no—
125D4×C13—42no—
126D4×C13—81no—
127D4×C13#4112yes—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—42no—
133C2×C4×C13C2×D411yescharacteristic
134C2×C4×C13C2411yescharacteristic
135C22⋊D13—41no—
136C22⋊D13—42no—
137C22⋊D13—81no—
138C22⋊D13—81no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—42no—
143C2×Dic13—81no—
144C2×Dic13C2×D411yescharacteristic
145C2×Dic13C2×D411yescharacteristic
146C2×Dic13C2×D411yescharacteristic
147D52—21no—
148D52—21no—
149C4×D13—21no—
150C4×D13—21no—
151Dic26—81no—
152C8×C13—21no—
153C8×C13—21no—
154#1055—21no—
155#1055—21no—
156#555—131no—
157#546—131no—
158#489—131no—
159#485—131no—
160#482—131no—
161#474—131no—
162#468—131no—
163#466—131no—
164#463—131no—
165#449D1311yescharacteristic, complemented
166#447—131no—
167#442—131no—
168#435—131no—
169#418—131no—
170#416—131no—
171C22×C13—22no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13C22×D411yescharacteristic
181C2×D13—21no—
182C2×D13—21no—
183C2×D13—21no—
184C2×D13—41no—
185C2×D13—41no—
186C2×D13—41no—
187C2×D13—84no—
188C4×C13—21no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13C2×#4111yescharacteristic
192C4×C13H(5,𝔽2)11yescharacteristic
193Dic13—21no—
194Dic13—21no—
195Dic13—21no—
196Dic13—41no—
197Dic13—41no—
198Dic13—41no—
199C2×#41C2×D1311yescharacteristic
200C22×D4—131no—
201C2×SD16C2×D1311yescharacteristic, complemented
202C2×D8—131no—
203C2×D8C2×D1311yescharacteristic
204C2×M16—131no—
205C22×C8—131no—
206C4⋊Q8—131no—
207#124—131no—
208#124—261no—
209#124—261no—
210#123—261no—
211C22⋊Q8—131no—
212#121—131no—
213#121—131no—
214#121—261no—
215#121—261no—
216#121C2×D1311yescharacteristic, complemented
217#120—261no—
218C4×D4—131no—
219C4×D4—131no—
220C4×D4—131no—
221#117—131no—
222#117—131no—
223#117—261no—
224C2×C22⋊C4—261no—
225#107—131no—
226#107—131no—
227#106—131no—
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
239C22⋊C8—131no—
240C22⋊C8C2×D1311yescharacteristic, complemented
241#97—131no—
242C2×C13—42no—
243C2×C13—41no—
244C2×C13—81no—
245C2×C13#54611yescharacteristic
246C2×C13#57511yescharacteristic
247C2×C13#57611yescharacteristic
248D13—41no—
249D13—81no—
250C24—261no—
251#41—22no—
252#41—41no—
253C2×Q8—261no—
254C2×Q8C22×D1311yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—131no—
258C2×D4—131no—
259C2×D4—261no—
260C2×D4—262no—
261C2×D4—261no—
262C2×D4—261no—
263C2×D4—521no—
264C2×D4C22×D1311yescharacteristic
265C2×D4C22×D1311yescharacteristic
266C22×C4—21no—
267C22×C4—131no—
268C22×C4—261no—
269C22×C4—261no—
270C22×C4C22×D1311yescharacteristic
271SD16—41no—
272D8—22no—
273D8—521no—
274M16—521no—
275C2×C8—131no—
276C2×C8—131no—
277C2×C8—521no—
278C2×C8C22×D1311yescharacteristic
279C2×C8C22×D1311yescharacteristic
280C4⋊C4—131no—
281C4⋊C4—131no—
282C4⋊C4—131no—
283C4⋊C4—131no—
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—
296C22⋊C4—261no—
297C22⋊C4—261no—
298C22⋊C4—261no—
299C42—131no—
300C42—261no—
301C42—261no—
302C13#331911yescharacteristic, complemented, Sylow
303C23—21no—
304C23—21no—
305C23—131no—
306C23—261no—
307C23—522no—
308C23—522no—
309C23—1041no—
310C23D4×D1311yescharacteristic
311Q8—21no—
312Q8—21no—
313Q8—1041no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—42no—
318D4—81no—
319D4—261no—
320D4—261no—
321D4—521no—
322D4—522no—
323D4—1041no—
324D4—1041no—
325D4#612912yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—131no—
332C2×C4—131no—
333C2×C4—131no—
334C2×C4—261no—
335C2×C4—261no—
336C2×C4—261no—
337C2×C4—261no—
338C2×C4—261no—
339C2×C4—522no—
340C2×C4—1041no—
341C2×C4D4×D1311yescharacteristic
342C2×C4C23×D1311yescharacteristic
343C8—21no—
344C8—21no—
345C8—261no—
346C8—261no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—261no—
357C22—261no—
358C22—261no—
359C22—521no—
360C22—521no—
361C22—521no—
362C22—1044no—
363C22C2×D4×D1311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—261no—
368C4—261no—
369C4—261no—
370C4—521no—
371C4—521no—
372C4—521no—
373C4C2×#612911yescharacteristic
374C4#8825111yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—521no—
379C2—1041no—
380C2#1171929611yescharacteristic
381C2#1171947311yescharacteristic
382C2#1171947911yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#449C2
socleC22×C13C22×D4
hypercenter#449D13
hypocenterC13#3319
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #11719534C2semidirect
2. #11719321C2semidirect
3. C13×#449C2semidirect
4. #11718894C2semidirect
5. #11718835C2semidirect
6. #11718826C2semidirect
7. #11718817C2semidirect
8. #11718813C2semidirect
9. #11718699C2semidirect
10. #11718476C2semidirect
11. #11718456C2semidirect
12. #11718431C2semidirect
13. #11718420C2semidirect
14. #11718398C2semidirect
15. #11718391C2semidirect
18. C2×C13×SD16C22semidirect
20. C13×#121C22semidirect
29. D4×Dic13C22semidirect
35. #88180C22semidirect
36. C22×#1055C22semidirect
39. #88142C22semidirect
42. C13×#103C22semidirect
44. C13×C22⋊C8C22semidirect
45. #88075C22semidirect
46. #88075C22semidirect
49. #88072C22semidirect
53. #88058C22semidirect
54. #88057C22semidirect
55. #88055C22semidirect
56. #88054C22semidirect
58. #88047C22semidirect
165. #449D13semidirect
201. C2×SD16C2×D13semidirect
216. #121C2×D13semidirect
231. #103C2×D13semidirect
240. C22⋊C8C2×D13semidirect
302. C13#3319semidirect

Maximal subgroups

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

subgroupindex
#117195342
#117193212
C13×#4492
#117188942
#117188352
#117188262
#117188172
#117188132
#117186992
#117184762
#117184562
#117184312
#117184202
#117183982
#117183912
#331913