Finite Group Databasebeta

← #16857794

Subgroups — #16857794

Order 3968.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521756C211yesmaximal, characteristic, complemented
2#14521695C211yesmaximal, characteristic
3#14521409C211yesmaximal, characteristic, complemented
4#14521385C211yesmaximal, characteristic, complemented
5#14521363C211yesmaximal, characteristic, complemented
6#14521330C211yesmaximal, characteristic, complemented
7#14521295C211yesmaximal, characteristic, complemented
8#14521290C211yesmaximal, characteristic, complemented
9#14521272C211yesmaximal, characteristic, complemented
10#14521213C211yesmaximal, characteristic, complemented
11#14521202C211yesmaximal, characteristic, complemented
12#14521151C211yesmaximal, characteristic, complemented
13#14521051C211yesmaximal, characteristic, complemented
14C2×#11758409C211yesmaximal, characteristic, complemented
15C31×#435C211yesmaximal, characteristic, complemented
16C2×#92495C2211yescharacteristic
17C22×D124C2211yescharacteristic
18C2×M16×C31C2211yescharacteristic, complemented
19C22×C8×C31C2211yescharacteristic
20C4×D4×C31C2211yescharacteristic
21#11758514—21no—
22D4×Dic31—21no—
23#11758507C2211yescharacteristic
24C2×C4⋊Dic31C2211yescharacteristic
25C2×C4⋊Dic31C2211yescharacteristic, complemented
26#11758501C2211yescharacteristic
27#11758501C2211yescharacteristic
28#11758501C2211yescharacteristic, complemented
29C2×Dic124C2211yescharacteristic, complemented
30C2×#92470C2211yescharacteristic
31C2×#92470C2211yescharacteristic
32#11758471—21no—
33#11758467—21no—
34#11758461—21no—
35C22⋊C4×D31—21no—
36#11758455—21no—
37#11758455—21no—
38#11758452C2211yescharacteristic
39C4×D124C2211yescharacteristic
40#11758446C2211yescharacteristic, complemented
41C4×Dic62C2211yescharacteristic, complemented
42C31×C4⋊C8C2211yescharacteristic, complemented
43C31×C22⋊C8C2211yescharacteristic
44C31×C22⋊C8C2211yescharacteristic, complemented
45C31×#97C2211yescharacteristic, complemented
46#11758409C2211yescharacteristic
47#11758409C2211yescharacteristic
48#11758409C2211yescharacteristic
49#11758409C2211yescharacteristic
50#11758409C2211yescharacteristic
51#11758409C2211yescharacteristic
52#11758406C2211yescharacteristic, complemented
53#11758406C2211yescharacteristic, complemented
54#11758406C2211yescharacteristic, complemented
55#11758404C2211yescharacteristic, complemented
56#11758404C2211yescharacteristic, complemented
57#11758404C2211yescharacteristic, complemented
58#11758404C2211yescharacteristic, complemented
59C23×D31—21no—
60C2×D4×C31D411yescharacteristic
61C22×C4×C31C2311yescharacteristic
62C22×C4×C31C2311yescharacteristic
63C2×C22⋊D31—21no—
64C2×C22⋊D31—21no—
65C22×Dic31—21no—
66C22×Dic31—21no—
67#92495—22no—
68#92495—41no—
69C2×D124—22no—
70C2×D124—21no—
71C2×D124—41no—
72C2×D124C2311yescharacteristic
73C2×D124C2311yescharacteristic
74C2×C4×D31—21no—
75C2×C4×D31—21no—
76C2×Dic62—21no—
77C2×Dic62C2311yescharacteristic
78C2×Dic62C2311yescharacteristic
79M16×C31—41no—
80C2×C8×C31—41no—
81C2×C8×C31C2311yescharacteristic
82C2×C8×C31C2311yescharacteristic
83C2×C8×C31C2311yescharacteristic
84C2×C8×C31C2311yescharacteristic
85C4⋊C4×C31D411yescharacteristic
86C22⋊C4×C31D411yescharacteristic
87C22⋊C4×C31D411yescharacteristic
88C42×C31C2311yescharacteristic
89C22⋊Dic31—21no—
90C22⋊Dic31—21no—
91C22⋊Dic31—21no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4—21no—
94(C2×D31)⋊C4—21no—
95(C2×D31)⋊C4—21no—
96C4⋊Dic31—21no—
97C4⋊Dic31—21no—
98C4⋊Dic31—21no—
99C4⋊Dic31C2311yescharacteristic
100C4⋊Dic31C2311yescharacteristic
101C4⋊Dic31C2311yescharacteristic
102C4⋊Dic31C2311yescharacteristic
103Dic31⋊C4—21no—
104Dic31⋊C4—21no—
105Dic31⋊C4—21no—
106Dic31⋊C4—21no—
107C4×Dic31—21no—
108Dic124—41no—
109#92470—22no—
110#92470—41no—
111C23×C31C2×D411yescharacteristic
112C23×C31C2×D411yescharacteristic
113C22×D31—21no—
114C22×D31—21no—
115C22×D31—42no—
116C22×D31—42no—
117C22×D31—81no—
118D4×C31—22no—
119C2×C4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31C2×D411yescharacteristic
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2411yescharacteristic
128C22⋊D31—42no—
129C22⋊D31—81no—
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31—21no—
133C2×Dic31—21no—
134C2×Dic31—21no—
135C2×Dic31—21no—
136C2×Dic31—81no—
137C2×Dic31—81no—
138D124—21no—
139D124—21no—
140D124—21no—
141D124—42no—
142D124#4112yes—
143C4×D31—42no—
144C4×D31—81no—
145Dic62—21no—
146Dic62—21no—
147Dic62—21no—
148Dic62—21no—
149Dic62—81no—
150C8×C31—21no—
151C8×C31—21no—
152C8×C31—21no—
153C8×C31—21no—
154#3314—311nomaximal, Sylow
155C22×C31—21no—
156C22×C31—21no—
157C22×C31—21no—
158C22×C31—21no—
159C22×C31—21no—
160C22×C31#13712yes—
161C22×C31C22×D411yescharacteristic
162C2×D31—22no—
163C2×D31—41no—
164C2×D31—41no—
165C2×D31—41no—
166C2×D31—41no—
167C2×D31—41no—
168C2×D31—84no—
169C4×C31—21no—
170C4×C31—21no—
171C4×C31—21no—
172C4×C31—21no—
173C4×C31C2×#4111yescharacteristic
174C4×C31H(5,𝔽2)11yescharacteristic
175Dic31—41no—
176Dic31—41no—
177Dic31—41no—
178Dic31—41no—
179Dic31—41no—
180Dic31—41no—
181#554—311no—
182#546—311no—
183#489—311no—
184#484—311no—
185#480—311no—
186#474—311no—
187#468—311no—
188#467—311no—
189#464—311no—
190#452—311no—
191#450—311no—
192#440—311no—
193#435D3111yescharacteristic, complemented
194#417—311no—
195C2×#102—311no—
196C2×C31—22no—
197C2×C31—41no—
198C2×C31#54611yescharacteristic
199C2×C31C2×#13711yescharacteristic
200C2×C31#57611yescharacteristic
201D31—42no—
202D31—81no—
203C2×#41—311no—
204C22×D4—311no—
205C2×Q16—311no—
206C2×SD16—311no—
207C2×SD16—311no—
208C2×M16C2×D3111yescharacteristic, complemented
209C22×C8C2×D3111yescharacteristic
210C4⋊Q8—311no—
211#125—621no—
212#124—311no—
213#123—621no—
214C22⋊Q8—311no—
215C22⋊Q8—311no—
216C22⋊Q8—311no—
217C22⋊Q8—621no—
218C22⋊Q8—621no—
219#121—311no—
220#121—621no—
221#120—621no—
222C4×Q8—311no—
223C4×D4—311no—
224C4×D4—621no—
225C4×D4C2×D3111yescharacteristic
226C2×C4⋊C4—311no—
227C2×C4⋊C4—311no—
228C2×C22⋊C4—621no—
229#107—311no—
230#107—311no—
231#107—311no—
232C4⋊C8C2×D3111yescharacteristic, complemented
233#103—311no—
234#103—311no—
235#103—311no—
236#103—311no—
237#102—311no—
238#102—311no—
239#102—311no—
240#102—311no—
241#102—311no—
242#102—311no—
243C22⋊C8C2×D3111yescharacteristic
244C22⋊C8C2×D3111yescharacteristic, complemented
245#97C2×D3111yescharacteristic, complemented
246C31#331411yescharacteristic, complemented, Sylow
247C24—621no—
248#41—622no—
249#41—1241no—
250C2×Q8—311no—
251C2×Q8—311no—
252C2×Q8—621no—
253C2×D4—311no—
254C2×D4—311no—
255C2×D4—622no—
256C2×D4—621no—
257C2×D4—621no—
258C2×D4—621no—
259C2×D4—1241no—
260C2×D4D12411yescharacteristic
261C22×C4—621no—
262C22×C4—621no—
263C22×C4—621no—
264C22×C4—621no—
265C22×C4C22×D3111yescharacteristic
266C22×C4C22×D3111yescharacteristic
267Q16—1241no—
268SD16—622no—
269SD16—1241no—
270M16—41no—
271C2×C8—41no—
272C2×C8C22×D3111yescharacteristic
273C2×C8C22×D3111yescharacteristic
274C2×C8C22×D3111yescharacteristic
275C2×C8C22×D3111yescharacteristic
276C4⋊C4—311no—
277C4⋊C4—311no—
278C4⋊C4—311no—
279C4⋊C4—311no—
280C4⋊C4—621no—
281C4⋊C4—621no—
282C4⋊C4—621no—
283C4⋊C4—621no—
284C4⋊C4—621no—
285C4⋊C4—621no—
286C4⋊C4—621no—
287C4⋊C4D12411yescharacteristic
288C22⋊C4—621no—
289C22⋊C4—621no—
290C22⋊C4—621no—
291C22⋊C4—621no—
292C22⋊C4—621no—
293C22⋊C4—621no—
294C22⋊C4—621no—
295C22⋊C4D12411yescharacteristic
296C22⋊C4D12411yescharacteristic
297C42—621no—
298C42C22×D3111yescharacteristic
299C23—621no—
300C23—621no—
301C23—1242no—
302C23—1242no—
303C23—2481no—
304C23C2×D12411yescharacteristic
305C23C2×D12411yescharacteristic
306Q8—621no—
307Q8—621no—
308Q8—621no—
309Q8—621no—
310Q8—2481no—
311D4—22no—
312D4—312no—
313D4—621no—
314D4—621no—
315D4—621no—
316D4—1242no—
317D4—1242no—
318D4—2481no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—621no—
324C2×C4—621no—
325C2×C4—621no—
326C2×C4—621no—
327C2×C4—621no—
328C2×C4—621no—
329C2×C4—1242no—
330C2×C4—2481no—
331C2×C4—2481no—
332C2×C4—2481no—
333C2×C4C2×D12411yescharacteristic
334C2×C4C2×D12411yescharacteristic
335C2×C4C2×D12411yescharacteristic
336C2×C4C2×D12411yescharacteristic
337C2×C4C23×D3111yescharacteristic
338C8—21no—
339C8—21no—
340C8—21no—
341C8—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—622no—
348C22—1241no—
349C22—1241no—
350C22—1241no—
351C22—1241no—
352C22—1241no—
353C22—2484no—
354C22#1175848612yes—
355C22C22×D12411yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—1241no—
361C4—1241no—
362C4—1241no—
363C4—1241no—
364C4—1241no—
365C4—1241no—
366C4#1175856111yescharacteristic
367C4#41×D3111yescharacteristic
368C2—22no—
369C2—41no—
370C2—1242no—
371C2—2481no—
372C2#1452169411yescharacteristic
373C2C2×#1175848611yescharacteristic
374C2#1452185411yescharacteristic
subgroupG/H
centerC22C22×D124
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#435C2
socleC22×C31C22×D4
prime radical#14521695C2
hypercenter#435D31
hypocenterC31#3314
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #14521756C2semidirect
3. #14521409C2semidirect
4. #14521385C2semidirect
5. #14521363C2semidirect
6. #14521330C2semidirect
7. #14521295C2semidirect
8. #14521290C2semidirect
9. #14521272C2semidirect
10. #14521213C2semidirect
11. #14521202C2semidirect
12. #14521151C2semidirect
13. #14521051C2semidirect
14. C2×#11758409C2semidirect
15. C31×#435C2semidirect
18. C2×M16×C31C22semidirect
25. C2×C4⋊Dic31C22semidirect
28. #11758501C22semidirect
29. C2×Dic124C22semidirect
40. #11758446C22semidirect
41. C4×Dic62C22semidirect
42. C31×C4⋊C8C22semidirect
44. C31×C22⋊C8C22semidirect
45. C31×#97C22semidirect
52. #11758406C22semidirect
53. #11758406C22semidirect
54. #11758406C22semidirect
55. #11758404C22semidirect
56. #11758404C22semidirect
57. #11758404C22semidirect
58. #11758404C22semidirect
193. #435D31semidirect
208. C2×M16C2×D31semidirect
232. C4⋊C8C2×D31semidirect
244. C22⋊C8C2×D31semidirect
245. #97C2×D31semidirect
246. C31#3314semidirect

Maximal subgroups

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

subgroupindex
#145217562
#145216952
#145214092
#145213852
#145213632
#145213302
#145212952
#145212902
#145212722
#145212132
#145212022
#145211512
#145210512
C2×#117584092
C31×#4352
#331431