Finite Group Databasebeta

← #13125675

Subgroups — #13125675

Order 1664.

418 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719533C211yesmaximal, characteristic, complemented
2#11719311C211yesmaximal, characteristic, complemented
3C13×#449C211yesmaximal, characteristic, complemented
4#11718900C211yesmaximal, characteristic, complemented
5#11718835C211yesmaximal, characteristic, complemented
6#11718834C211yesmaximal, characteristic, complemented
7#11718820C211yesmaximal, characteristic, complemented
8#11718819C211yesmaximal, characteristic, complemented
9#11718696C211yesmaximal, characteristic, complemented
10#11718477C211yesmaximal, characteristic, complemented
11#11718476C211yesmaximal, characteristic, complemented
12#11718445C211yesmaximal, characteristic, complemented
13#11718441C211yesmaximal, characteristic, complemented
14#11718387C211yesmaximal, characteristic, complemented
15#11718384C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×#6129C2211yescharacteristic
18C22×C4×D13C2211yescharacteristic
19C2×C13×SD16C2211yescharacteristic, complemented
20C2×C13×D8C2211yescharacteristic, complemented
21C13×#121C2211yescharacteristic
22#88200C2211yescharacteristic
23#88200C2211yescharacteristic
24C2×#6107C2211yescharacteristic, complemented
25#88192C2211yescharacteristic
26#88192C2211yescharacteristic
27#88192C2211yescharacteristic
28#88191—21no—
29#88191—21no—
30#88189—21no—
31D4×Dic13—21no—
32C2×#6105C2211yescharacteristic, complemented
33C4×C22⋊D13—21no—
34C4×C22⋊D13—21no—
35#88180C2211yescharacteristic
36#88178C2211yescharacteristic
37C2×#6094C2211yescharacteristic
38C2×#6094C2211yescharacteristic
39#88151C2211yescharacteristic
40#88146C2211yescharacteristic
41#88137—21no—
42#88135—21no—
43C13×#103C2211yescharacteristic, complemented
44C13×#102C2211yescharacteristic, complemented
45C13×C22⋊C8C2211yescharacteristic
46#88075C2211yescharacteristic, complemented
47#88072C2211yescharacteristic, complemented
48#88072C2211yescharacteristic, complemented
49#88072C2211yescharacteristic, complemented
50C22⋊#1055C2211yescharacteristic
51#88060C2211yescharacteristic
52#88060C2211yescharacteristic
53#88058C2211yescharacteristic, complemented
54#88057C2211yescharacteristic, complemented
55#88056C2211yescharacteristic, complemented
56#88056C2211yescharacteristic, complemented
57#88048C2211yescharacteristic, complemented
58#88047C2211yescharacteristic, complemented
59C23×D13D411yescharacteristic
60C13×#41—41no—
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⋊D13—21no—
73C22×Dic13—21no—
74C22×Dic13D411yescharacteristic
75#6129—41no—
76#6129—41no—
77C2×C4×D13—41no—
78C2×C4×D13—41no—
79C2×C4×D13D411yescharacteristic
80C2×C4×D13D411yescharacteristic
81C2×C4×D13C2311yescharacteristic
82C2×C4×D13C2311yescharacteristic
83C2×Dic26C2311yescharacteristic
84C13×SD16—41no—
85C13×D8—41no—
86C2×C8×C13C2311yescharacteristic
87C2×C8×C13C2311yescharacteristic
88C13×C4⋊C4C2311yescharacteristic
89C13×C22⋊C4—21no—
90C22⋊Dic13—21no—
91C22⋊Dic13—21no—
92C22⋊Dic13—21no—
93C22⋊Dic13—21no—
94C22⋊Dic13—21no—
95#6107—41no—
96#6105—41no—
97#6103—21no—
98#6103—21no—
99#6103—21no—
100#6103—21no—
101C4⋊Dic13—21no—
102C4⋊Dic13C2311yescharacteristic
103C4⋊Dic13C2311yescharacteristic
104C4⋊Dic13C2311yescharacteristic
105#6101—21no—
106#6101—21no—
107#6101—21no—
108C4×Dic13—21no—
109C4×Dic13—21no—
110C2×#1055C2311yescharacteristic
111C2×#1055C2311yescharacteristic
112#6094—41no—
113#6094—41no—
114#3197—131nomaximal, Sylow
115C23×C13—21no—
116C23×C13—21no—
117C23×C13C2×D411yescharacteristic
118C22×D13—41no—
119C22×D13—41no—
120C22×D13—41no—
121C22×D13C2×D411yescharacteristic
122C22×D13C2×D411yescharacteristic
123Q8×C13—21no—
124Q8×C13—21no—
125D4×C13—21no—
126D4×C13—21no—
127D4×C13—21no—
128D4×C13—21no—
129D4×C13—42no—
130D4×C13—42no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—42no—
136C2×C4×C13C2×D411yescharacteristic
137C2×C4×C13C2411yescharacteristic
138C22⋊D13—42no—
139C22⋊D13—42no—
140C22⋊D13—42no—
141C22⋊D13—42no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—41no—
147C2×Dic13—42no—
148C2×Dic13C2×D411yescharacteristic
149C2×Dic13C2×D411yescharacteristic
150C4×D13—21no—
151C4×D13—21no—
152C4×D13—21no—
153C4×D13—21no—
154C4×D13—41no—
155C4×D13—41no—
156Dic26—21no—
157Dic26—21no—
158C8×C13—21no—
159C8×C13—21no—
160#1055—21no—
161#1055—21no—
162#525—131no—
163#525—131no—
164#485—131no—
165#485—131no—
166#482—131no—
167#482—131no—
168#470—131no—
169#469—131no—
170#468—131no—
171#468—131no—
172#452—131no—
173#452—131no—
174#449—131no—
175#449D1311yescharacteristic, complemented
176#407—131no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13C22×D411yescharacteristic
187C2×D13—21no—
188C2×D13—21no—
189C2×D13—21no—
190C2×D13—21no—
191C2×D13—21no—
192C2×D13—21no—
193C2×D13—44no—
194C4×C13—21no—
195C4×C13—41no—
196C4×C13—41no—
197C4×C13H(5,𝔽2)11yescharacteristic
198C4×C13H(5,𝔽2)11yescharacteristic
199Dic13—21no—
200Dic13—21no—
201Dic13—41no—
202Dic13—41no—
203Dic13—41no—
204Dic13—41no—
205C2×#41—131no—
206C2×#41C2×D1311yescharacteristic
207C23×C4—131no—
208C2×Q16—131no—
209C2×SD16—131no—
210C2×SD16C2×D1311yescharacteristic, complemented
211C2×D8C2×D1311yescharacteristic, complemented
212C2×M16—131no—
213C2×M16—131no—
214#123—261no—
215#123—261no—
216C22⋊Q8—131no—
217C22⋊Q8—131no—
218C22⋊Q8—131no—
219C22⋊Q8—131no—
220#121—131no—
221#121—131no—
222#121—131no—
223#121C2×D1311yescharacteristic
224#120—261no—
225#120—261no—
226C4×D4—261no—
227C4×D4—261no—
228C4×D4—261no—
229C4×D4—261no—
230#117—131no—
231#117—131no—
232#107—131no—
233#107—131no—
234#106—131no—
235#106—131no—
236#103—131no—
237#103—131no—
238#103—131no—
239#103C2×D1311yescharacteristic, complemented
240#102—131no—
241#102—131no—
242#102—131no—
243#102C2×D1311yescharacteristic, complemented
244C22⋊C8—131no—
245C22⋊C8—131no—
246C22⋊C8—131no—
247C22⋊C8C2×D1311yescharacteristic
248C2×C13—41no—
249C2×C13—81no—
250C2×C13—81no—
251C2×C13#53411yescharacteristic
252C2×C13#57511yescharacteristic
253C2×C13#57511yescharacteristic
254D13—41no—
255D13—41no—
256C24—131no—
257#41—41no—
258#41—41no—
259#41—521no—
260#41—521no—
261C2×Q8—131no—
262C2×Q8C22×D1311yescharacteristic
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—261no—
266C2×D4—261no—
267C2×D4—261no—
268C2×D4—261no—
269C2×D4C22×D1311yescharacteristic
270C2×D4C22×D1311yescharacteristic
271C22×C4—21no—
272C22×C4—131no—
273C22×C4—131no—
274C22×C4—131no—
275C22×C4—131no—
276C22×C4—131no—
277C22×C4—261no—
278C22×C4—521no—
279C22×C4—521no—
280C22×C4C22×D1311yescharacteristic
281Q16—521no—
282SD16—41no—
283SD16—521no—
284D8—41no—
285M16—521no—
286M16—521no—
287C2×C8—131no—
288C2×C8—131no—
289C2×C8C22×D1311yescharacteristic
290C2×C8C22×D1311yescharacteristic
291C4⋊C4—131no—
292C4⋊C4—131no—
293C4⋊C4—131no—
294C4⋊C4—261no—
295C4⋊C4—261no—
296C4⋊C4—261no—
297C4⋊C4—261no—
298C4⋊C4C22×D1311yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—261no—
301C22⋊C4—261no—
302C22⋊C4—261no—
303C22⋊C4—261no—
304C22⋊C4—261no—
305C22⋊C4—261no—
306C22⋊C4—261no—
307C22⋊C4—261no—
308C22⋊C4—261no—
309C42—261no—
310C42—261no—
311C13#319711yescharacteristic, complemented, Sylow
312C23—21no—
313C23—21no—
314C23—131no—
315C23—131no—
316C23—521no—
317C23—521no—
318C23—521no—
319C23D4×D1311yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—261no—
323Q8—261no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—42no—
330D4—522no—
331D4—522no—
332D4—522no—
333D4—522no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—131no—
340C2×C4—131no—
341C2×C4—261no—
342C2×C4—261no—
343C2×C4—261no—
344C2×C4—261no—
345C2×C4—261no—
346C2×C4—261no—
347C2×C4—261no—
348C2×C4—261no—
349C2×C4—521no—
350C2×C4—521no—
351C2×C4—521no—
352C2×C4—522no—
353C2×C4D4×D1311yescharacteristic
354C2×C4C23×D1311yescharacteristic
355C8—21no—
356C8—21no—
357C8—261no—
358C8—261no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—261no—
369C22—261no—
370C22—261no—
371C22—261no—
372C22—261no—
373C22—261no—
374C22—524no—
375C22C2×D4×D1311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—261no—
380C4—261no—
381C4—521no—
382C4—521no—
383C4—521no—
384C4—521no—
385C4#8825111yescharacteristic
386C4#8825111yescharacteristic
387C2—41no—
388C2—81no—
389C2—81no—
390C2—521no—
391C2—521no—
392C2#1171929411yescharacteristic
393C2#1171947311yescharacteristic
394C2#1171947811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#449C2
socleC22×C13C22×D4
hypercenter#449D13
hypocenterC13#3197
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. #11719533C2semidirect
2. #11719311C2semidirect
3. C13×#449C2semidirect
4. #11718900C2semidirect
5. #11718835C2semidirect
6. #11718834C2semidirect
7. #11718820C2semidirect
8. #11718819C2semidirect
9. #11718696C2semidirect
10. #11718477C2semidirect
11. #11718476C2semidirect
12. #11718445C2semidirect
13. #11718441C2semidirect
14. #11718387C2semidirect
15. #11718384C2semidirect
19. C2×C13×SD16C22semidirect
20. C2×C13×D8C22semidirect
24. C2×#6107C22semidirect
32. C2×#6105C22semidirect
43. C13×#103C22semidirect
44. C13×#102C22semidirect
46. #88075C22semidirect
47. #88072C22semidirect
48. #88072C22semidirect
49. #88072C22semidirect
53. #88058C22semidirect
54. #88057C22semidirect
55. #88056C22semidirect
56. #88056C22semidirect
57. #88048C22semidirect
58. #88047C22semidirect
175. #449D13semidirect
210. C2×SD16C2×D13semidirect
211. C2×D8C2×D13semidirect
239. #103C2×D13semidirect
243. #102C2×D13semidirect
311. C13#3197semidirect

Maximal subgroups

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

subgroupindex
#117195332
#117193112
C13×#4492
#117189002
#117188352
#117188342
#117188202
#117188192
#117186962
#117184772
#117184762
#117184452
#117184412
#117183872
#117183842
#319713