Finite Group Databasebeta

← #16857699

Subgroups — #16857699

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#14521711C211yesmaximal, characteristic, complemented
2#14521702C211yesmaximal, characteristic, complemented
3#14521411C211yesmaximal, characteristic, complemented
4#14521386C211yesmaximal, characteristic, complemented
5#14521364C211yesmaximal, characteristic, complemented
6#14521296C211yesmaximal, characteristic, complemented
7#14521286C211yesmaximal, characteristic, complemented
8#14521265C211yesmaximal, characteristic, complemented
9#14521197C211yesmaximal, characteristic, complemented
10#14521189C211yesmaximal, characteristic, complemented
11#14521147C211yesmaximal, characteristic, complemented
12#14521119C211yesmaximal, characteristic, complemented
13#14521049C211yesmaximal, characteristic, complemented
14#103×D31C211yesmaximal, characteristic, complemented
15C31×#477C211yesmaximal, characteristic, complemented
16C2×#92499—21no—
17C2×#92499C2211yescharacteristic
18C2×Q8×D31C2211yescharacteristic
19C31×C4⋊Q8C2211yescharacteristic
20C4×Q8×C31C2211yescharacteristic
21#11758523—21no—
22C2×#92481C2211yescharacteristic
23C2×D248C2211yescharacteristic
24C2×#92470C2211yescharacteristic
25C2×#92469C2211yescharacteristic
26C2×C8×D31C2211yescharacteristic
27#11758474—21no—
28#11758474C2211yescharacteristic
29#11758472—21no—
30#11758472C2211yescharacteristic
31#11758472C2211yescharacteristic
32#11758472C2211yescharacteristic
33#11758471—21no—
34#11758471—21no—
35C4⋊C4×D31C2211yescharacteristic
36C4⋊C4×D31C2211yescharacteristic
37#11758452—21no—
38#11758452C2211yescharacteristic
39C4×D124—21no—
40C4×D124C2211yescharacteristic
41C4×D124C2211yescharacteristic
42C31×#107C2211yescharacteristic
43C31×#107C2211yescharacteristic
44C31×C4⋊C8C2211yescharacteristic
45C31×#103C2211yescharacteristic
46C31×#103C2211yescharacteristic
47#11758423C2211yescharacteristic
48#11758409C2211yescharacteristic
49(C2×D31)⋊C8C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic
51#11758404C2211yescharacteristic
52#11758398C2211yescharacteristic
53#11758398C2211yescharacteristic
54#11758397C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758397C2211yescharacteristic
57#11758395C2211yescharacteristic
58#11758391C2211yescharacteristic
59C2×Q8×C31—21no—
60C2×Q8×C31C2311yescharacteristic
61#92499—22no—
62#92499—41no—
63#92499—44no—
64Q8×D31—22no—
65Q8×D31—41no—
66C2×D124—21no—
67C2×D124—21no—
68C2×D124—21no—
69C2×D124—21no—
70C2×D124D411yescharacteristic
71C2×D124C2311yescharacteristic
72C2×D124C2311yescharacteristic
73C2×C4×D31—21no—
74C2×C4×D31—21no—
75C2×C4×D31—21no—
76C2×C4×D31—21no—
77C2×C4×D31—21no—
78C2×C4×D31C2311yescharacteristic
79C2×C4×D31C2311yescharacteristic
80C2×Dic62—21no—
81C2×Dic62C2311yescharacteristic
82C2×C8×C31C2311yescharacteristic
83C2×C8×C31C2311yescharacteristic
84C4⋊C4×C31—21no—
85C4⋊C4×C31—21no—
86C4⋊C4×C31C2311yescharacteristic
87C4⋊C4×C31C2311yescharacteristic
88C4⋊C4×C31C2311yescharacteristic
89C42×C31—21no—
90C42×C31C2311yescharacteristic
91#92481—22no—
92(C2×D31)⋊C4—21no—
93(C2×D31)⋊C4—21no—
94(C2×D31)⋊C4—21no—
95(C2×D31)⋊C4—21no—
96(C2×D31)⋊C4—21no—
97(C2×D31)⋊C4—21no—
98(C2×D31)⋊C4—21no—
99(C2×D31)⋊C4D411yescharacteristic
100(C2×D31)⋊C4D411yescharacteristic
101C4⋊Dic31—21no—
102C4⋊Dic31D411yescharacteristic
103C4⋊Dic31C2311yescharacteristic
104Dic31⋊C4—21no—
105Dic31⋊C4—21no—
106C2×C31⋊C8C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108D248—41no—
109#92470—41no—
110#92469—41no—
111C8×D31—41no—
112C22×D31—21no—
113C22×D31—21no—
114C22×D31C2×D411yescharacteristic
115C22×D31C2×D411yescharacteristic
116Q8×C31—21no—
117Q8×C31—42no—
118Q8×C31#4112yescomplemented
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×C31C2411yescharacteristic
126C2×Dic31—21no—
127C2×Dic31—21no—
128C2×Dic31C2×D411yescharacteristic
129C2×Dic31C2×D411yescharacteristic
130D124—22no—
131D124—21no—
132D124—21no—
133D124—21no—
134D124—21no—
135D124—42no—
136D124—42no—
137D124—42no—
138D124—42no—
139C4×D31—21no—
140C4×D31—21no—
141C4×D31—21no—
142C4×D31—21no—
143C4×D31—42no—
144C4×D31—42no—
145C4×D31—42no—
146C4×D31—42no—
147C4×D31—42no—
148Dic62—21no—
149Dic62—21no—
150Dic62—42no—
151C8×C31—21no—
152C8×C31—21no—
153C31⋊C8—21no—
154C31⋊C8—21no—
155#3308—311nomaximal, Sylow
156C22×C31C22×D411yescharacteristic
157C2×D31—21no—
158C2×D31—21no—
159C2×D31—21no—
160C2×D31—21no—
161C2×D31—21no—
162C2×D31—41no—
163C2×D31—41no—
164C2×D31—41no—
165C2×D31—41no—
166C2×D31—41no—
167C2×D31—41no—
168C2×D31AGL(1,ℤ/8)12yes—
169C4×C31—22no—
170C4×C31—21no—
171C4×C31—21no—
172C4×C31—41no—
173C4×C31—41no—
174C4×C31—41no—
175C4×C31C2×#4111yescharacteristic
176C4×C31H(5,𝔽2)11yescharacteristic
177Dic31—21no—
178Dic31—21no—
179Dic31—41no—
180Dic31—41no—
181#548—311no—
182#547—311no—
183#489—311no—
184#484—311no—
185#480—311no—
186#477D3111yescharacteristic, complemented
187#468—311no—
188#466—311no—
189#463—311no—
190#449—311no—
191#448—311no—
192#440—311no—
193#435—311no—
194#417—311no—
195C2×#103—311no—
196C2×C31#54611yescharacteristic
197C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
198C2×C31#57811yescharacteristic
199D31—22no—
200D31—41no—
201D31—81no—
202D31—81no—
203C2×#41—311no—
204C2×#41—621no—
205C22×Q8—311no—
206C2×SD16—311no—
207C2×SD16—311no—
208C2×D8—311no—
209C2×M16—311no—
210C22×C8—311no—
211C4⋊Q8C2×D3111yescharacteristic
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×Q8C2×D3111yescharacteristic
224C4×D4—311no—
225C4×D4—311no—
226C4×D4—621no—
227C2×C4⋊C4—311no—
228C2×C4⋊C4—311no—
229#107—311no—
230#107C2×D3111yescharacteristic
231#107C2×D3111yescharacteristic
232C4⋊C8C2×D3111yescharacteristic
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#102—311no—
242#102—311no—
243C22⋊C8—311no—
244C22⋊C8—311no—
245#97—311no—
246C31#330811yescharacteristic, complemented, Sylow
247#41—622no—
248#41—1241no—
249#41—1244no—
250C2×Q8—21no—
251C2×Q8—311no—
252C2×Q8—621no—
253C2×Q8—622no—
254C2×Q8—1241no—
255C2×Q8C22×D3111yescharacteristic
256C2×D4—311no—
257C2×D4—311no—
258C2×D4—311no—
259C2×D4—621no—
260C2×D4—621no—
261C2×D4—621no—
262C2×D4—621no—
263C22×C4—311no—
264C22×C4—311no—
265C22×C4—621no—
266C22×C4—621no—
267C22×C4—621no—
268C22×C4—621no—
269C22×C4—621no—
270SD16—622no—
271SD16—1241no—
272D8—1241no—
273M16—1241no—
274C2×C8—311no—
275C2×C8—311no—
276C2×C8—1241no—
277C2×C8C22×D3111yescharacteristic
278C2×C8C22×D3111yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—311no—
282C4⋊C4—311no—
283C4⋊C4—621no—
284C4⋊C4—621no—
285C4⋊C4—621no—
286C4⋊C4C22×D3111yescharacteristic
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—21no—
299C42C22×D3111yescharacteristic
300C23—311no—
301C23—311no—
302C23—621no—
303C23—621no—
304Q8—21no—
305Q8—42no—
306Q8—621no—
307Q8—621no—
308Q8—1242no—
309Q8#9249912yescomplemented
310D4—622no—
311D4—621no—
312D4—621no—
313D4—621no—
314D4—621no—
315D4—1242no—
316D4—1242no—
317D4—1242no—
318D4—1242no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—311no—
324C2×C4—311no—
325C2×C4—621no—
326C2×C4—621no—
327C2×C4—621no—
328C2×C4—621no—
329C2×C4—621no—
330C2×C4—621no—
331C2×C4—1242no—
332C2×C4—1242no—
333C2×C4—1242no—
334C2×C4—1242no—
335C2×C4—1242no—
336C2×C4D4×D3111yescharacteristic
337C2×C4D4×D3111yescharacteristic
338C2×C4C23×D3111yescharacteristic
339C8—21no—
340C8—21no—
341C8—621no—
342C8—621no—
343C22—312no—
344C22—621no—
345C22—621no—
346C22—621no—
347C22—621no—
348C22—621no—
349C22—1241no—
350C22—1241no—
351C22—1241no—
352C22—1241no—
353C22—1241no—
354C22—1241no—
355C22C2×D4×D3111yescharacteristic
356C4—21no—
357C4—22no—
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—621no—
363C4—621no—
364C4—1241no—
365C4—1241no—
366C4C2×#9249911yescharacteristic
367C4#1175856611yescharacteristic
368C2—622no—
369C2—1241no—
370C2—2481no—
371C2—2481no—
372C2#1452169011yescharacteristic
373C2AGL(1,ℤ/8)×D3111yescharacteristic
374C2#1452186211yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#477C2
socleC22×C31C22×D4
hypercenter#477D31
hypocenterC31#3308
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #14521711C2semidirect
2. #14521702C2semidirect
3. #14521411C2semidirect
4. #14521386C2semidirect
5. #14521364C2semidirect
6. #14521296C2semidirect
7. #14521286C2semidirect
8. #14521265C2semidirect
9. #14521197C2semidirect
10. #14521189C2semidirect
11. #14521147C2semidirect
12. #14521119C2semidirect
13. #14521049C2semidirect
14. #103×D31C2semidirect
15. C31×#477C2semidirect
118. Q8×C31#41semidirect
186. #477D31semidirect
246. C31#3308semidirect
309. Q8#92499semidirect

Maximal subgroups

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

subgroupindex
#145217112
#145217022
#145214112
#145213862
#145213642
#145212962
#145212862
#145212652
#145211972
#145211892
#145211472
#145211192
#145210492
#103×D312
C31×#4772
#330831