Finite Group Databasebeta

← #16857732

Subgroups — #16857732

Order 3968.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521739C211yesmaximal, characteristic, complemented
2#14521413C211yesmaximal, characteristic, complemented
3#14521370C211yesmaximal, characteristic, complemented
4#14521360C211yesmaximal, characteristic, complemented
5#14521349C211yesmaximal, characteristic, complemented
6#14521293C211yesmaximal, characteristic, complemented
7#14521276C211yesmaximal, characteristic, complemented
8#14521246C211yesmaximal, characteristic, complemented
9#14521200C211yesmaximal, characteristic, complemented
10#14521200C211yesmaximal, characteristic, complemented
11#14521149C211yesmaximal, characteristic, complemented
12#14521121C211yesmaximal, characteristic, complemented
13#14521054C211yesmaximal, characteristic, complemented
14C2×#11758420C211yesmaximal, characteristic, complemented
15D42×C31C211yesmaximal, characteristic
16C22×D4×C31—21no—
17C22×D4×C31C2211yescharacteristic
18C22×D4×C31C2211yescharacteristic
19C31×#127C2211yescharacteristic
20C31×#121—21no—
21C31×#121C2211yescharacteristic
22C31×#121C2211yescharacteristic
23C31×#120—21no—
24C31×#120—21no—
25C4×D4×C31C2211yescharacteristic
26C4×D4×C31C2211yescharacteristic
27#11758512—21no—
28C2×#92480C2211yescharacteristic
29C2×#92480C2211yescharacteristic, complemented
30C2×#92480C2211yescharacteristic, complemented
31#11758503C2211yescharacteristic, complemented
32C2×C4⋊Dic31C2211yescharacteristic, complemented
33#11758501C2211yescharacteristic, complemented
34#11758501C2211yescharacteristic, complemented
35C2×#92474C2211yescharacteristic, complemented
36C22×C31⋊C8C2211yescharacteristic, complemented
37#11758466—21no—
38#11758456—21no—
39#11758454—21no—
40#11758447C2211yescharacteristic, complemented
41C4×Dic62C2211yescharacteristic, complemented
42#11758420C2211yescharacteristic
43#11758420C2211yescharacteristic
44#11758420C2211yescharacteristic
45#11758420C2211yescharacteristic, complemented
46#11758420C2211yescharacteristic, complemented
47#11758420C2211yescharacteristic, complemented
48#11758420C2211yescharacteristic, complemented
49#11758420C2211yescharacteristic, complemented
50#11758420C2211yescharacteristic, complemented
51C22⋊(C31⋊C8)C2211yescharacteristic, complemented
52C22⋊(C31⋊C8)C2211yescharacteristic, complemented
53#11758398C2211yescharacteristic, complemented
54#11758396C2211yescharacteristic, complemented
55#11758395C2211yescharacteristic, complemented
56#11758395C2211yescharacteristic, complemented
57C4⋊(C31⋊C8)C2211yescharacteristic, complemented
58#11758391C2211yescharacteristic, complemented
59C24×C31—21no—
60C24×C31—21no—
61C2×D4×C31—22no—
62C2×D4×C31—22no—
63C2×D4×C31—21no—
64C2×D4×C31—21no—
65C2×D4×C31—21no—
66C2×D4×C31—21no—
67C2×D4×C31—21no—
68C2×D4×C31—21no—
69C2×D4×C31—41no—
70C2×D4×C31—41no—
71C2×D4×C31—44no—
72C2×D4×C31D411yescharacteristic
73C2×D4×C31C2311yescharacteristic
74C2×D4×C31C2311yescharacteristic
75C2×D4×C31C2311yescharacteristic
76C22×C4×C31—21no—
77C22×C4×C31C2311yescharacteristic
78C22×C4×C31C2311yescharacteristic
79C22×Dic31—21no—
80C2×Dic62C2311yescharacteristic
81C4⋊C4×C31D411yescharacteristic
82C4⋊C4×C31C2311yescharacteristic
83C22⋊C4×C31—21no—
84C22⋊C4×C31—21no—
85C22⋊C4×C31—21no—
86C22⋊C4×C31D411yescharacteristic
87C22⋊C4×C31D411yescharacteristic
88C42×C31C2311yescharacteristic
89C22⋊Dic31—21no—
90C22⋊Dic31—21no—
91C22⋊Dic31—21no—
92#92480—22no—
93#92480—41no—
94#92480—41no—
95C4⋊Dic31—21no—
96C4⋊Dic31C2311yescharacteristic
97C4⋊Dic31C2311yescharacteristic
98C4⋊Dic31C2311yescharacteristic
99Dic31⋊C4—21no—
100Dic31⋊C4—21no—
101Dic31⋊C4—21no—
102Dic31⋊C4—21no—
103Dic31⋊C4—21no—
104C4×Dic31—21no—
105C4×Dic31—21no—
106#92474—41no—
107C2×C31⋊C8—41no—
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110C2×C31⋊C8C2311yescharacteristic
111C2×C31⋊C8C2311yescharacteristic
112C23×C31—21no—
113C23×C31—21no—
114C23×C31—21no—
115C23×C31—42no—
116C23×C31—42no—
117C23×C31—42no—
118C23×C31—42no—
119C23×C31—81no—
120C23×C31—81no—
121C23×C31C2×D411yescharacteristic
122C23×C31C2×D411yescharacteristic
123D4×C31—22no—
124D4×C31—21no—
125D4×C31—21no—
126D4×C31—21no—
127D4×C31—21no—
128D4×C31—21no—
129D4×C31—42no—
130D4×C31—42no—
131D4×C31—42no—
132D4×C31—42no—
133D4×C31—42no—
134D4×C31—81no—
135D4×C31#4112yes—
136C2×C4×C31—21no—
137C2×C4×C31—21no—
138C2×C4×C31—21no—
139C2×C4×C31—21no—
140C2×C4×C31—21no—
141C2×C4×C31—42no—
142C2×C4×C31C2×D411yescharacteristic
143C2×C4×C31C2×D411yescharacteristic
144C2×C4×C31C2×D411yescharacteristic
145C2×C4×C31C2×D411yescharacteristic
146C2×C4×C31C2411yescharacteristic
147C2×Dic31—21no—
148C2×Dic31—21no—
149C2×Dic31—21no—
150C2×Dic31—21no—
151C2×Dic31—42no—
152Dic62—21no—
153Dic62—21no—
154C31⋊C8—21no—
155C31⋊C8—21no—
156C31⋊C8—21no—
157C31⋊C8—21no—
158#3310—311nomaximal, Sylow
159C22×C31—21no—
160C22×C31—21no—
161C22×C31—21no—
162C22×C31—22no—
163C22×C31—21no—
164C22×C31—21no—
165C22×C31—41no—
166C22×C31—41no—
167C22×C31—41no—
168C22×C31—41no—
169C22×C31—41no—
170C22×C31—41no—
171C22×C31—41no—
172C22×C31—41no—
173C22×C31—84no—
174C22×C31—84no—
175C22×C31AGL(1,ℤ/8)12yes—
176C22×C31C22×D411yescharacteristic
177C4×C31—21no—
178C4×C31—21no—
179C4×C31—21no—
180C4×C31—21no—
181C4×C31—41no—
182C4×C31C2×#4111yescharacteristic
183C4×C31H(5,𝔽2)11yescharacteristic
184Dic31—41no—
185Dic31—41no—
186Dic31—41no—
187Dic31—41no—
188#552—311no—
189D42D3111yescharacteristic
190#490—311no—
191#482—311no—
192#480—311no—
193#478—311no—
194#468—311no—
195#465—311no—
196#460—311no—
197#450—311no—
198#450—311no—
199#440—311no—
200#435—311no—
201#418—311no—
202C2×#102—311no—
203C2×C31—22no—
204C2×C31—41no—
205C2×C31—42no—
206C2×C31—81no—
207C2×C31—81no—
208C2×C31#54611yescharacteristic
209C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
210C2×C31#57711yescharacteristic
211C22×D4—21no—
212C22×D4C2×D3111yescharacteristic
213C22×D4C2×D3111yescharacteristic
214C2×SD16—311no—
215C2×SD16—311no—
216C2×SD16—311no—
217C2×M16—311no—
218C22×C8—311no—
219#127C2×D3111yescharacteristic
220#126—621no—
221#125—311no—
222#125—621no—
223#123—621no—
224C22⋊Q8—311no—
225C22⋊Q8—311no—
226#121—21no—
227#121C2×D3111yescharacteristic
228#121C2×D3111yescharacteristic
229#120—21no—
230#120—21no—
231C4×Q8—311no—
232C4×D4C2×D3111yescharacteristic
233C4×D4C2×D3111yescharacteristic
234#117—311no—
235#117—621no—
236C2×C4⋊C4—311no—
237#107—311no—
238#107—311no—
239#106—311no—
240C4⋊C8—311no—
241#103—311no—
242#102—311no—
243#102—311no—
244#102—311no—
245#102—311no—
246#102—311no—
247#102—311no—
248#102—311no—
249#102—311no—
250#102—311no—
251C22⋊C8—311no—
252C22⋊C8—311no—
253#97—311no—
254C31#331011yescharacteristic, complemented, Sylow
255C24—21no—
256C24—21no—
257C2×Q8—311no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—44no—
269C2×D4C22⋊D3111yescharacteristic
270C2×D4C22×D3111yescharacteristic
271C2×D4C22×D3111yescharacteristic
272C2×D4C22×D3111yescharacteristic
273C22×C4—21no—
274C22×C4—621no—
275C22×C4C22×D3111yescharacteristic
276C22×C4C22×D3111yescharacteristic
277SD16—622no—
278SD16—1241no—
279SD16—1241no—
280M16—1241no—
281C2×C8—311no—
282C2×C8—311no—
283C2×C8—311no—
284C2×C8—311no—
285C2×C8—1241no—
286C4⋊C4—311no—
287C4⋊C4—311no—
288C4⋊C4—311no—
289C4⋊C4—621no—
290C4⋊C4—621no—
291C4⋊C4—621no—
292C4⋊C4—621no—
293C4⋊C4—621no—
294C4⋊C4—621no—
295C4⋊C4C22⋊D3111yescharacteristic
296C4⋊C4C22×D3111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—621no—
301C22⋊C4—621no—
302C22⋊C4—621no—
303C22⋊C4C22⋊D3111yescharacteristic
304C22⋊C4C22⋊D3111yescharacteristic
305C42—621no—
306C42—621no—
307C42C22×D3111yescharacteristic
308C23—21no—
309C23—21no—
310C23—21no—
311C23—42no—
312C23—42no—
313C23—42no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23C2×C22⋊D3111yescharacteristic
318C23C2×C22⋊D3111yescharacteristic
319Q8—621no—
320Q8—621no—
321D4—22no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—42no—
329D4—42no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4#9249712yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—621no—
341C2×C4—621no—
342C2×C4—621no—
343C2×C4—621no—
344C2×C4—1242no—
345C2×C4C2×C22⋊D3111yescharacteristic
346C2×C4C2×C22⋊D3111yescharacteristic
347C2×C4C2×C22⋊D3111yescharacteristic
348C2×C4C2×C22⋊D3111yescharacteristic
349C2×C4C23×D3111yescharacteristic
350C8—621no—
351C8—621no—
352C8—621no—
353C8—621no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—22no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—84no—
370C22#1175850912yes—
371C22C22×C22⋊D3111yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—1241no—
378C4—1241no—
379C4—1241no—
380C4—1241no—
381C4C2×#9249711yescharacteristic
382C4#1175856111yescharacteristic
383C2—22no—
384C2—41no—
385C2—42no—
386C2—81no—
387C2—81no—
388C2#1452169311yescharacteristic
389C2C2×#1175850911yescharacteristic
390C2#1452186011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
Fitting, prime radicalD42×C31C2
socleC22×C31C22×D4
hypercenterD42D31
hypocenterC31#3310
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #14521739C2semidirect
2. #14521413C2semidirect
3. #14521370C2semidirect
4. #14521360C2semidirect
5. #14521349C2semidirect
6. #14521293C2semidirect
7. #14521276C2semidirect
8. #14521246C2semidirect
9. #14521200C2semidirect
10. #14521200C2semidirect
11. #14521149C2semidirect
12. #14521121C2semidirect
13. #14521054C2semidirect
14. C2×#11758420C2semidirect
29. C2×#92480C22semidirect
30. C2×#92480C22semidirect
31. #11758503C22semidirect
32. C2×C4⋊Dic31C22semidirect
33. #11758501C22semidirect
34. #11758501C22semidirect
35. C2×#92474C22semidirect
36. C22×C31⋊C8C22semidirect
40. #11758447C22semidirect
41. C4×Dic62C22semidirect
45. #11758420C22semidirect
46. #11758420C22semidirect
47. #11758420C22semidirect
48. #11758420C22semidirect
49. #11758420C22semidirect
50. #11758420C22semidirect
51. C22⋊(C31⋊C8)C22semidirect
52. C22⋊(C31⋊C8)C22semidirect
53. #11758398C22semidirect
54. #11758396C22semidirect
55. #11758395C22semidirect
56. #11758395C22semidirect
57. C4⋊(C31⋊C8)C22semidirect
58. #11758391C22semidirect
254. C31#3310semidirect

Maximal subgroups

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

subgroupindex
#145217392
#145214132
#145213702
#145213602
#145213492
#145212932
#145212762
#145212462
#145212002
#145211492
#145211212
#145210542
C2×#117584202
D42×C312
#331031