Finite Group Databasebeta

← #16857703

Subgroups — #16857703

Order 3968.

420 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#14521706C211yesmaximal, characteristic, complemented
2#14521700C211yesmaximal, characteristic, complemented
3#14521407C211yesmaximal, characteristic, complemented
4#14521384C211yesmaximal, characteristic, complemented
5#14521361C211yesmaximal, characteristic, complemented
6#14521342C211yesmaximal, characteristic, complemented
7#14521295C211yesmaximal, characteristic, complemented
8#14521284C211yesmaximal, characteristic, complemented
9#14521263C211yesmaximal, characteristic, complemented
10#14521194C211yesmaximal, characteristic, complemented
11#14521189C211yesmaximal, characteristic, complemented
12#14521152C211yesmaximal, characteristic, complemented
13#14521118C211yesmaximal, characteristic, complemented
14#103×D31C211yesmaximal, characteristic, complemented
15C31×#417C211yesmaximal, characteristic, complemented
16C2×#41×C31C2211yescharacteristic
17C2×Q8×D31C2211yescharacteristic
18C2×#92495—21no—
19C2×M16×C31C2211yescharacteristic
20C2×C4⋊C4×C31C2211yescharacteristic
21Q8×Dic31C2211yescharacteristic
22C2×#92481C2211yescharacteristic
23#11758515—21no—
24#11758515C2211yescharacteristic
25#11758513—21no—
26#11758513C2211yescharacteristic
27C2×#92479C2211yescharacteristic
28#11758507C2211yescharacteristic
29#11758506—21no—
30C4×C22⋊D31—21no—
31C4×C22⋊D31C2211yescharacteristic
32#11758501—21no—
33#11758501C2211yescharacteristic
34C2×#92470C2211yescharacteristic
35C2×C8×D31C2211yescharacteristic
36#11758473—21no—
37#11758472C2211yescharacteristic
38#11758471—21no—
39#11758470C2211yescharacteristic
40C4⋊C4×D31C2211yescharacteristic
41#11758465C2211yescharacteristic
42C31×#103C2211yescharacteristic
43C31×#103C2211yescharacteristic
44C31×#102C2211yescharacteristic
45C31×#102C2211yescharacteristic
46#11758423C2211yescharacteristic
47#11758420C2211yescharacteristic
48C22⋊(C31⋊C8)C2211yescharacteristic
49#11758409C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic
51#11758406C2211yescharacteristic
52#11758404C2211yescharacteristic
53#11758403C2211yescharacteristic
54Dic31⋊C8C2211yescharacteristic
55#11758398C2211yescharacteristic
56#11758398C2211yescharacteristic
57#11758395C2211yescharacteristic
58#11758395C2211yescharacteristic
59#41×C31—22no—
60#41×C31—41no—
61C2×Q8×C31C2311yescharacteristic
62C2×D4×C31—21no—
63C2×D4×C31C2311yescharacteristic
64C22×C4×C31—21no—
65C22×C4×C31—21no—
66C22×C4×C31C2311yescharacteristic
67C2×C22⋊D31—21no—
68C2×C22⋊D31—21no—
69C2×C22⋊D31D411yescharacteristic
70Q8×D31—22no—
71Q8×D31—41no—
72#92495—44no—
73C2×D124—21no—
74C2×D124C2311yescharacteristic
75C2×C4×D31—21no—
76C2×C4×D31—21no—
77C2×C4×D31—21no—
78C2×C4×D31C2311yescharacteristic
79C2×Dic62—21no—
80C2×Dic62—21no—
81C2×Dic62C2311yescharacteristic
82M16×C31—41no—
83C2×C8×C31C2311yescharacteristic
84C2×C8×C31C2311yescharacteristic
85C4⋊C4×C31—21no—
86C4⋊C4×C31C2311yescharacteristic
87C4⋊C4×C31C2311yescharacteristic
88C22⋊Dic31—21no—
89C22⋊Dic31—21no—
90C22⋊Dic31—21no—
91C22⋊Dic31—21no—
92C22⋊Dic31D411yescharacteristic
93#92481—22no—
94#92479—41no—
95(C2×D31)⋊C4—21no—
96(C2×D31)⋊C4—21no—
97(C2×D31)⋊C4—21no—
98(C2×D31)⋊C4D411yescharacteristic
99C4⋊Dic31—21no—
100C4⋊Dic31C2311yescharacteristic
101C4⋊Dic31C2311yescharacteristic
102Dic31⋊C4—21no—
103Dic31⋊C4—21no—
104Dic31⋊C4—21no—
105Dic31⋊C4D411yescharacteristic
106C4×Dic31—21no—
107C4×Dic31C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110#92470—41no—
111C8×D31—41no—
112C23×C31—21no—
113C23×C31C2×D411yescharacteristic
114C22×D31—21no—
115C22×D31C2×D411yescharacteristic
116Q8×C31—21no—
117Q8×C31#4112yescomplemented
118D4×C31—21no—
119D4×C31—21no—
120D4×C31—42no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—21no—
125C2×C4×C31—21no—
126C2×C4×C31—42no—
127C2×C4×C31—42no—
128C2×C4×C31C2×D411yescharacteristic
129C2×C4×C31C2411yescharacteristic
130C22⋊D31—22no—
131C22⋊D31—42no—
132C22⋊D31—42no—
133C2×Dic31—21no—
134C2×Dic31—21no—
135C2×Dic31—21no—
136C2×Dic31C2×D411yescharacteristic
137C2×Dic31C2×D411yescharacteristic
138C2×Dic31C2×D411yescharacteristic
139D124—21no—
140D124—21no—
141D124—42no—
142C4×D31—21no—
143C4×D31—21no—
144C4×D31—42no—
145C4×D31—42no—
146C4×D31—42no—
147Dic62—21no—
148Dic62—21no—
149Dic62—42no—
150Dic62—42no—
151C8×C31—21no—
152C8×C31—21no—
153C31⋊C8—21no—
154C31⋊C8—21no—
155#3308—311nomaximal, Sylow
156C22×C31—21no—
157C22×C31—21no—
158C22×C31—21no—
159C22×C31—41no—
160C22×C31—41no—
161C22×C31—41no—
162C22×C31C22×D411yescharacteristic
163C2×D31—21no—
164C2×D31—21no—
165C2×D31—41no—
166C2×D31—41no—
167C2×D31—41no—
168C2×D31AGL(1,ℤ/8)12yes—
169C4×C31—22no—
170C4×C31—21no—
171C4×C31—41no—
172C4×C31—41no—
173C4×C31C2×#4111yescharacteristic
174C4×C31H(5,𝔽2)11yescharacteristic
175Dic31—21no—
176Dic31—21no—
177Dic31—21no—
178Dic31—41no—
179Dic31—41no—
180Dic31—41no—
181#548—311no—
182#547—311no—
183#489—311no—
184#484—311no—
185#480—311no—
186#477—311no—
187#468—311no—
188#466—311no—
189#463—311no—
190#449—311no—
191#448—311no—
192#440—311no—
193#435—311no—
194#417D3111yescharacteristic, complemented
195C2×#103—311no—
196C2×C31—41no—
197C2×C31—81no—
198C2×C31#54611yescharacteristic
199C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
200C2×C31#57811yescharacteristic
201D31—22no—
202D31—81no—
203C2×#41—621no—
204C2×#41C2×D3111yescharacteristic
205C22×Q8—311no—
206C2×SD16—311no—
207C2×SD16—311no—
208C2×D8—311no—
209C2×M16C2×D3111yescharacteristic
210C22×C8—311no—
211C4⋊Q8—311no—
212#124—311no—
213#124—621no—
214#123—621no—
215#123—621no—
216C22⋊Q8—311no—
217C22⋊Q8—621no—
218C22⋊Q8—621no—
219#121—311no—
220#121—311no—
221#121—311no—
222#121—621no—
223C4×Q8—311no—
224C4×D4—311no—
225C4×D4—311no—
226C4×D4—621no—
227C2×C4⋊C4—311no—
228C2×C4⋊C4C2×D3111yescharacteristic
229#107—311no—
230#107—311no—
231#107—311no—
232C4⋊C8—311no—
233#103—311no—
234#103—311no—
235#103—311no—
236#103—311no—
237#103C2×D3111yescharacteristic
238#103C2×D3111yescharacteristic
239#102—311no—
240#102—311no—
241#102C2×D3111yescharacteristic
242#102C2×D3111yescharacteristic
243C22⋊C8—311no—
244C22⋊C8—311no—
245#97—311no—
246C31#330811yescharacteristic, complemented, Sylow
247#41—22no—
248#41—41no—
249#41—1244no—
250C2×Q8—311no—
251C2×Q8—621no—
252C2×Q8—621no—
253C2×Q8—622no—
254C2×Q8—1241no—
255C2×Q8C22×D3111yescharacteristic
256C2×D4—21no—
257C2×D4—311no—
258C2×D4—311no—
259C2×D4—621no—
260C2×D4—621no—
261C2×D4—621no—
262C2×D4C22×D3111yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—311no—
266C22×C4—621no—
267C22×C4—621no—
268C22×C4—621no—
269C22×C4C22×D3111yescharacteristic
270SD16—622no—
271SD16—1241no—
272D8—1241no—
273M16—41no—
274C2×C8—311no—
275C2×C8—311no—
276C2×C8—1241no—
277C2×C8C22×D3111yescharacteristic
278C2×C8C22×D3111yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—311no—
281C4⋊C4—311no—
282C4⋊C4—311no—
283C4⋊C4—621no—
284C4⋊C4—621no—
285C4⋊C4—621no—
286C4⋊C4—621no—
287C4⋊C4C22×D3111yescharacteristic
288C4⋊C4C22×D3111yescharacteristic
289C22⋊C4—311no—
290C22⋊C4—311no—
291C22⋊C4—621no—
292C22⋊C4—621no—
293C22⋊C4—621no—
294C22⋊C4—621no—
295C22⋊C4—621no—
296C22⋊C4—621no—
297C22⋊C4—621no—
298C42—311no—
299C42—621no—
300C23—21no—
301C23—311no—
302C23—621no—
303C23D4×D3111yescharacteristic
304Q8—21no—
305Q8—621no—
306Q8—621no—
307Q8—1242no—
308Q8—1242no—
309Q8#9249512yescomplemented
310D4—21no—
311D4—21no—
312D4—42no—
313D4—622no—
314D4—621no—
315D4—621no—
316D4—1242no—
317D4—1242no—
318D4—1242no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—311no—
327C2×C4—311no—
328C2×C4—311no—
329C2×C4—621no—
330C2×C4—621no—
331C2×C4—621no—
332C2×C4—621no—
333C2×C4—621no—
334C2×C4—1242no—
335C2×C4—1242no—
336C2×C4—1242no—
337C2×C4D4×D3111yescharacteristic
338C2×C4C23×D3111yescharacteristic
339C8—21no—
340C8—21no—
341C8—621no—
342C8—621no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—312no—
350C22—621no—
351C22—621no—
352C22—1241no—
353C22—1241no—
354C22—1241no—
355C22C2×D4×D3111yescharacteristic
356C4—21no—
357C4—22no—
358C4—41no—
359C4—41no—
360C4—621no—
361C4—621no—
362C4—621no—
363C4—1241no—
364C4—1241no—
365C4—1241no—
366C4C2×#9249511yescharacteristic
367C4#1175856111yescharacteristic
368C2—41no—
369C2—81no—
370C2—622no—
371C2—2481no—
372C2#1452168911yescharacteristic
373C2AGL(1,ℤ/8)×D3111yescharacteristic
374C2#1452186511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#417C2
socleC22×C31C22×D4
hypercenter#417D31
hypocenterC31#3308
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #14521706C2semidirect
2. #14521700C2semidirect
3. #14521407C2semidirect
4. #14521384C2semidirect
5. #14521361C2semidirect
6. #14521342C2semidirect
7. #14521295C2semidirect
8. #14521284C2semidirect
9. #14521263C2semidirect
10. #14521194C2semidirect
11. #14521189C2semidirect
12. #14521152C2semidirect
13. #14521118C2semidirect
14. #103×D31C2semidirect
15. C31×#417C2semidirect
117. Q8×C31#41semidirect
194. #417D31semidirect
246. C31#3308semidirect
309. Q8#92495semidirect

Maximal subgroups

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

subgroupindex
#145217062
#145217002
#145214072
#145213842
#145213612
#145213422
#145212952
#145212842
#145212632
#145211942
#145211892
#145211522
#145211182
#103×D312
C31×#4172
#330831