Finite Group Databasebeta

← #16857554

Subgroups — #16857554

Order 3968.

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#14521746C211yesmaximal, characteristic, complemented
2#14521687C211yesmaximal, characteristic, complemented
3#14521405C211yesmaximal, characteristic, complemented
4#14521383C211yesmaximal, characteristic, complemented
5#14521374C211yesmaximal, characteristic, complemented
6#14521351C211yesmaximal, characteristic, complemented
7#14521283C211yesmaximal, characteristic, complemented
8#14521275C211yesmaximal, characteristic, complemented
9#14521266C211yesmaximal, characteristic, complemented
10#14521181C211yesmaximal, characteristic, complemented
11D8×Dic31C211yesmaximal, characteristic, complemented
12(C22⋊D31)⋊C8C211yesmaximal, characteristic, complemented
13#14521045C211yesmaximal, characteristic, complemented
14#102×D31C211yesmaximal, characteristic, complemented
15C31×#449C211yesmaximal, characteristic, complemented
16C2×#41×C31C2211yescharacteristic
17C2×D4×D31C2211yescharacteristic
18C2×SD16×C31C2211yescharacteristic, complemented
19C2×D8×C31C2211yescharacteristic
20C31×#121C2211yescharacteristic, complemented
21#11758524C2211yescharacteristic
22#11758523C2211yescharacteristic
23#11758516—21no—
24#11758515—21no—
25#11758515C2211yescharacteristic
26#11758514—21no—
27#11758512—21no—
28D4×Dic31C2211yescharacteristic
29D4×Dic31C2211yescharacteristic, complemented
30C2×#92479C2211yescharacteristic
31#11758507C2211yescharacteristic
32#11758506—21no—
33C4×C22⋊D31C2211yescharacteristic
34C2×(C2×D31)⋊C4—21no—
35#11758503C2211yescharacteristic, complemented
36C22×C31⋊C8C2211yescharacteristic, complemented
37C2×C8×D31C2211yescharacteristic
38C4⋊C4×D31C2211yescharacteristic
39#11758467C2211yescharacteristic, complemented
40(C22⋊D31)⋊C4—21no—
41#11758456—21no—
42C31×#103C2211yescharacteristic, complemented
43C31×#102C2211yescharacteristic
44C31×C22⋊C8C2211yescharacteristic, complemented
45#11758423C2211yescharacteristic, complemented
46#11758423C2211yescharacteristic, complemented
47#11758420C2211yescharacteristic
48#11758420C2211yescharacteristic
49#11758420C2211yescharacteristic, complemented
50#11758409C2211yescharacteristic
51#11758409C2211yescharacteristic
52(C2×D31)⋊C8C2211yescharacteristic
53#11758406C2211yescharacteristic, complemented
54#11758405C2211yescharacteristic, complemented
55Dic31⋊C8C2211yescharacteristic, complemented
56C8×Dic31C2211yescharacteristic, complemented
57#11758397C2211yescharacteristic
58#11758395C2211yescharacteristic, complemented
59C23×D31—21no—
60#41×C31—22no—
61#41×C31—41no—
62C2×Q8×C31C2311yescharacteristic
63C2×D4×C31—21no—
64C2×D4×C31—21no—
65C2×D4×C31C2311yescharacteristic
66C2×D4×C31C2311yescharacteristic
67C22×C4×C31—21no—
68C22×C4×C31C2311yescharacteristic
69C2×C22⋊D31—21no—
70C2×C22⋊D31—21no—
71C2×C22⋊D31—21no—
72C2×C22⋊D31D411yescharacteristic
73C22×Dic31—21no—
74C22×Dic31—21no—
75D4×D31—22no—
76D4×D31—41no—
77C2×D124C2311yescharacteristic
78C2×C4×D31—21no—
79C2×C4×D31C2311yescharacteristic
80SD16×C31—41no—
81D8×C31—22no—
82C2×C8×C31C2311yescharacteristic
83C2×C8×C31C2311yescharacteristic
84C4⋊C4×C31C2311yescharacteristic
85C22⋊C4×C31—21no—
86C22⋊Dic31—21no—
87C22⋊Dic31—21no—
88C22⋊Dic31—21no—
89C22⋊Dic31—21no—
90C22⋊Dic31D411yescharacteristic
91#92479—41no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4—21no—
94(C2×D31)⋊C4—21no—
95(C2×D31)⋊C4—21no—
96(C2×D31)⋊C4D411yescharacteristic
97C4⋊Dic31—21no—
98C4⋊Dic31C2311yescharacteristic
99C4⋊Dic31C2311yescharacteristic
100C4⋊Dic31C2311yescharacteristic
101Dic31⋊C4—21no—
102Dic31⋊C4—21no—
103Dic31⋊C4—21no—
104Dic31⋊C4D411yescharacteristic
105C4×Dic31—21no—
106C4×Dic31C2311yescharacteristic
107C2×C31⋊C8—41no—
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110C8×D31—41no—
111C23×C31—21no—
112C23×C31—21no—
113C23×C31C2×D411yescharacteristic
114C22×D31—21no—
115C22×D31—42no—
116C22×D31—42no—
117C22×D31—81no—
118C22×D31C2×D411yescharacteristic
119Q8×C31—21no—
120Q8×C31—21no—
121D4×C31—21no—
122D4×C31—21no—
123D4×C31—21no—
124D4×C31—42no—
125D4×C31—81no—
126D4×C31#4112yes—
127C2×C4×C31—21no—
128C2×C4×C31—21no—
129C2×C4×C31—21no—
130C2×C4×C31—21no—
131C2×C4×C31—42no—
132C2×C4×C31C2×D411yescharacteristic
133C2×C4×C31C2411yescharacteristic
134C22⋊D31—22no—
135C22⋊D31—42no—
136C22⋊D31—42no—
137C22⋊D31—81no—
138C2×Dic31—21no—
139C2×Dic31—21no—
140C2×Dic31—21no—
141C2×Dic31—81no—
142C2×Dic31—81no—
143C2×Dic31C2×D411yescharacteristic
144C2×Dic31C2×D411yescharacteristic
145C2×Dic31C2×D411yescharacteristic
146D124—21no—
147D124—21no—
148C4×D31—21no—
149C4×D31—21no—
150C4×D31—81no—
151C8×C31—21no—
152C8×C31—21no—
153C31⋊C8—21no—
154C31⋊C8—21no—
155#3297—311nomaximal, Sylow
156C22×C31—22no—
157C22×C31—21no—
158C22×C31—21no—
159C22×C31—21no—
160C22×C31—41no—
161C22×C31—41no—
162C22×C31—41no—
163C22×C31—41no—
164C22×C31—41no—
165C22×C31C22×D411yescharacteristic
166C2×D31—21no—
167C2×D31—21no—
168C2×D31—41no—
169C2×D31—41no—
170C2×D31—41no—
171C2×D31—84no—
172C2×D31#13512yes—
173C4×C31—21no—
174C4×C31—41no—
175C4×C31—41no—
176C4×C31C2×#4111yescharacteristic
177C4×C31H(5,𝔽2)11yescharacteristic
178Dic31—21no—
179Dic31—21no—
180Dic31—21no—
181Dic31—41no—
182Dic31—41no—
183Dic31—41no—
184#553—311no—
185#546—311no—
186#488—311no—
187#484—311no—
188#482—311no—
189#478—311no—
190#466—311no—
191#465—311no—
192#463—311no—
193#449D3111yescharacteristic, complemented
194#447—311no—
195C4×D8—311no—
196C8×D4—311no—
197#416—311no—
198C2×#102—311no—
199C2×C31—42no—
200C2×C31—41no—
201C2×C31—81no—
202C2×C31#54611yescharacteristic
203C2×C31C2×#13511yescharacteristic
204C2×C31#57611yescharacteristic
205D31—22no—
206D31—81no—
207C2×#41C2×D3111yescharacteristic
208C22×D4—311no—
209C2×SD16C2×D3111yescharacteristic, complemented
210C2×D8—311no—
211C2×D8C2×D3111yescharacteristic
212C22×C8—311no—
213C22×C8—311no—
214#126—621no—
215#125—311no—
216#124—311no—
217#123—621no—
218#123—621no—
219C22⋊Q8—311no—
220#121—311no—
221#121—311no—
222#121—621no—
223#121—621no—
224#121C2×D3111yescharacteristic, complemented
225#120—621no—
226C4×D4—311no—
227C4×D4—311no—
228C4×D4—311no—
229C4×D4—621no—
230#117—311no—
231C2×C4⋊C4—311no—
232C2×C22⋊C4—621no—
233#107—311no—
234#107—311no—
235#106—311no—
236C4⋊C8—311no—
237#103—311no—
238#103—311no—
239#103C2×D3111yescharacteristic, complemented
240#102—311no—
241#102—311no—
242#102—311no—
243#102—311no—
244#102—311no—
245#102—311no—
246#102C2×D3111yescharacteristic
247C22⋊C8—311no—
248C22⋊C8C2×D3111yescharacteristic, complemented
249C4×C8—311no—
250C31#329711yescharacteristic, complemented, Sylow
251C24—621no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D3111yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—311no—
258C2×D4—311no—
259C2×D4—621no—
260C2×D4—622no—
261C2×D4—621no—
262C2×D4—621no—
263C2×D4—1241no—
264C2×D4C22×D3111yescharacteristic
265C2×D4C22×D3111yescharacteristic
266C22×C4—21no—
267C22×C4—311no—
268C22×C4—621no—
269C22×C4—621no—
270C22×C4—621no—
271C22×C4C22×D3111yescharacteristic
272SD16—41no—
273D8—22no—
274D8—1241no—
275C2×C8—311no—
276C2×C8—311no—
277C2×C8—1241no—
278C2×C8—1241no—
279C2×C8C22×D3111yescharacteristic
280C2×C8C22×D3111yescharacteristic
281C4⋊C4—311no—
282C4⋊C4—311no—
283C4⋊C4—311no—
284C4⋊C4—311no—
285C4⋊C4—621no—
286C4⋊C4—621no—
287C4⋊C4—621no—
288C4⋊C4—621no—
289C4⋊C4C22×D3111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—311no—
292C22⋊C4—311no—
293C22⋊C4—621no—
294C22⋊C4—621no—
295C22⋊C4—621no—
296C22⋊C4—621no—
297C22⋊C4—621no—
298C22⋊C4—621no—
299C22⋊C4—621no—
300C22⋊C4—621no—
301C42—311no—
302C42—621no—
303C23—21no—
304C23—21no—
305C23—311no—
306C23—621no—
307C23—1242no—
308C23—1242no—
309C23—2481no—
310C23D4×D3111yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—81no—
318D4—622no—
319D4—621no—
320D4—621no—
321D4—1242no—
322D4—1242no—
323D4—2481no—
324D4#9249712yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—311no—
331C2×C4—311no—
332C2×C4—311no—
333C2×C4—621no—
334C2×C4—621no—
335C2×C4—621no—
336C2×C4—621no—
337C2×C4—621no—
338C2×C4—2481no—
339C2×C4—2481no—
340C2×C4—2481no—
341C2×C4D4×D3111yescharacteristic
342C2×C4C23×D3111yescharacteristic
343C8—21no—
344C8—21no—
345C8—621no—
346C8—621no—
347C22—21no—
348C22—22no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—312no—
357C22—621no—
358C22—621no—
359C22—1241no—
360C22—1241no—
361C22—1241no—
362C22—2484no—
363C22C2×D4×D3111yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—621no—
368C4—621no—
369C4—621no—
370C4—1241no—
371C4—1241no—
372C4—1241no—
373C4C2×#9249711yescharacteristic
374C4#1175856111yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—622no—
379C2—2481no—
380C2#1452168611yescharacteristic
381C2#135×D3111yescharacteristic
382C2#1452185311yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#449C2
socleC22×C31C22×D4
hypercenter#449D31
hypocenterC31#3297
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #14521746C2semidirect
2. #14521687C2semidirect
3. #14521405C2semidirect
4. #14521383C2semidirect
5. #14521374C2semidirect
6. #14521351C2semidirect
7. #14521283C2semidirect
8. #14521275C2semidirect
9. #14521266C2semidirect
10. #14521181C2semidirect
11. D8×Dic31C2semidirect
12. (C22⋊D31)⋊C8C2semidirect
13. #14521045C2semidirect
14. #102×D31C2semidirect
15. C31×#449C2semidirect
18. C2×SD16×C31C22semidirect
20. C31×#121C22semidirect
29. D4×Dic31C22semidirect
35. #11758503C22semidirect
36. C22×C31⋊C8C22semidirect
39. #11758467C22semidirect
42. C31×#103C22semidirect
44. C31×C22⋊C8C22semidirect
45. #11758423C22semidirect
46. #11758423C22semidirect
49. #11758420C22semidirect
53. #11758406C22semidirect
54. #11758405C22semidirect
55. Dic31⋊C8C22semidirect
56. C8×Dic31C22semidirect
58. #11758395C22semidirect
193. #449D31semidirect
209. C2×SD16C2×D31semidirect
224. #121C2×D31semidirect
239. #103C2×D31semidirect
248. C22⋊C8C2×D31semidirect
250. C31#3297semidirect

Maximal subgroups

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

subgroupindex
#145217462
#145216872
#145214052
#145213832
#145213742
#145213512
#145212832
#145212752
#145212662
#145211812
D8×Dic312
(C22⋊D31)⋊C82
#145210452
#102×D312
C31×#4492
#329731