Finite Group Databasebeta

← #16857707

Subgroups — #16857707

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#14521704C211yesmaximal, characteristic, complemented
3#14521409C211yesmaximal, characteristic, complemented
4#14521386C211yesmaximal, characteristic, complemented
5#14521364C211yesmaximal, characteristic, complemented
6#14521344C211yesmaximal, characteristic, complemented
7#14521294C211yesmaximal, characteristic, complemented
8#14521284C211yesmaximal, characteristic, complemented
9#14521264C211yesmaximal, characteristic, complemented
10#14521193C211yesmaximal, characteristic, complemented
11#14521186C211yesmaximal, characteristic, complemented
12#14521122C211yesmaximal, characteristic, complemented
13#14521049C211yesmaximal, characteristic, complemented
14#103×D31C211yesmaximal, characteristic, complemented
15C31×#440C211yesmaximal, characteristic, complemented
16C2×#92499C2211yescharacteristic
17C2×Q8×D31C2211yescharacteristic
18C2×#92495—21no—
19C2×SD16×C31C2211yescharacteristic
20C4×Q8×C31C2211yescharacteristic
21C4×D4×C31C2211yescharacteristic
22#11758515C2211yescharacteristic
23#11758515C2211yescharacteristic
24C2×#92480C2211yescharacteristic
25C2×#92479C2211yescharacteristic
26#11758501—21no—
27C2×#92469C2211yescharacteristic
28C2×C8×D31C2211yescharacteristic
29#11758474—21no—
30#11758474C2211yescharacteristic
31#11758472—21no—
32#11758472C2211yescharacteristic
33C4⋊C4×D31C2211yescharacteristic
34C4⋊C4×D31C2211yescharacteristic
35#11758460—21no—
36#11758460—21no—
37#11758452—21no—
38#11758452C2211yescharacteristic
39C4×D124—21no—
40C4×D124C2211yescharacteristic
41#11758446C2211yescharacteristic
42C31×#107C2211yescharacteristic
43C31×#103C2211yescharacteristic
44C31×#102C2211yescharacteristic
45C31×#97C2211yescharacteristic
46#11758423C2211yescharacteristic
47#11758423C2211yescharacteristic
48#11758409C2211yescharacteristic
49#11758409C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic
51(C2×D31)⋊C8C2211yescharacteristic
52#11758404C2211yescharacteristic
53#11758404C2211yescharacteristic
54#11758398C2211yescharacteristic
55#11758397C2211yescharacteristic
56#11758395C2211yescharacteristic
57#11758395C2211yescharacteristic
58C4⋊(C31⋊C8)C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C2×D4×C31C2311yescharacteristic
61C22×C4×C31—21no—
62C2×C22⋊D31—21no—
63C2×C22⋊D31—21no—
64#92499—22no—
65#92499—41no—
66Q8×D31—22no—
67Q8×D31—41no—
68#92495—44no—
69C2×D124—21no—
70C2×D124—21no—
71C2×D124D411yescharacteristic
72C2×D124C2311yescharacteristic
73C2×C4×D31—21no—
74C2×C4×D31—21no—
75C2×C4×D31—21no—
76C2×C4×D31—21no—
77C2×C4×D31C2311yescharacteristic
78C2×C4×D31C2311yescharacteristic
79C2×Dic62—21no—
80C2×Dic62—21no—
81C2×Dic62C2311yescharacteristic
82SD16×C31—22no—
83C2×C8×C31C2311yescharacteristic
84C2×C8×C31C2311yescharacteristic
85C4⋊C4×C31—21no—
86C4⋊C4×C31C2311yescharacteristic
87C4⋊C4×C31C2311yescharacteristic
88C22⋊C4×C31—21no—
89C42×C31—21no—
90C42×C31C2311yescharacteristic
91C22⋊Dic31—21no—
92C22⋊Dic31—21no—
93#92480—41no—
94#92479—41no—
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⋊Dic31—21no—
103C4⋊Dic31D411yescharacteristic
104C4⋊Dic31C2311yescharacteristic
105C4⋊Dic31C2311yescharacteristic
106Dic31⋊C4—21no—
107Dic31⋊C4—21no—
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110#92469—41no—
111C8×D31—41no—
112C23×C31—21no—
113C22×D31—21no—
114C22×D31C2×D411yescharacteristic
115C22×D31C2×D411yescharacteristic
116Q8×C31—21no—
117Q8×C31#4112yescomplemented
118D4×C31—21no—
119D4×C31—21no—
120C2×C4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—42no—
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2411yescharacteristic
127C22⋊D31—42no—
128C22⋊D31—42no—
129C2×Dic31—21no—
130C2×Dic31—21no—
131C2×Dic31—21no—
132C2×Dic31C2×D411yescharacteristic
133C2×Dic31C2×D411yescharacteristic
134D124—22no—
135D124—21no—
136D124—21no—
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—
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—41no—
157C22×C31—41no—
158C22×C31—41no—
159C22×C31C22×D411yescharacteristic
160C2×D31—21no—
161C2×D31—21no—
162C2×D31—21no—
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—21no—
172C4×C31—41no—
173C4×C31—41no—
174C4×C31C2×#4111yescharacteristic
175C4×C31H(5,𝔽2)11yescharacteristic
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#440D3111yescharacteristic, complemented
193#435—311no—
194#417—311no—
195C2×#103—311no—
196C2×C31—81no—
197C2×C31#54611yescharacteristic
198C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
199C2×C31#57811yescharacteristic
200D31—22no—
201D31—41no—
202D31—81no—
203C2×#41—311no—
204C2×#41—621no—
205C22×Q8—311no—
206C2×SD16—311no—
207C2×SD16C2×D3111yescharacteristic
208C2×D8—311no—
209C2×M16—311no—
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×Q8C2×D3111yescharacteristic
224C4×D4—311no—
225C4×D4—621no—
226C4×D4C2×D3111yescharacteristic
227C2×C4⋊C4—311no—
228C2×C4⋊C4—311no—
229#107—311no—
230#107—311no—
231#107C2×D3111yescharacteristic
232C4⋊C8—311no—
233#103—311no—
234#103—311no—
235#103—311no—
236#103—311no—
237#103—311no—
238#103C2×D3111yescharacteristic
239#102—311no—
240#102—311no—
241#102—311no—
242#102C2×D3111yescharacteristic
243C22⋊C8—311no—
244C22⋊C8—311no—
245#97C2×D3111yescharacteristic
246C31#330811yescharacteristic, complemented, Sylow
247#41—622no—
248#41—1244no—
249#41—1241no—
250C2×Q8—311no—
251C2×Q8—621no—
252C2×Q8—621no—
253C2×Q8—622no—
254C2×Q8—1241no—
255C2×Q8C22×D3111yescharacteristic
256C2×D4—311no—
257C2×D4—311no—
258C2×D4—621no—
259C2×D4—621no—
260C2×D4—621no—
261C2×D4—621no—
262C2×D4C22×D3111yescharacteristic
263C22×C4—21no—
264C22×C4—311no—
265C22×C4—311no—
266C22×C4—621no—
267C22×C4—621no—
268C22×C4—621no—
269C22×C4—621no—
270SD16—22no—
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—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—21no—
290C22⋊C4—311no—
291C22⋊C4—311no—
292C22⋊C4—621no—
293C22⋊C4—621no—
294C22⋊C4—621no—
295C22⋊C4—621no—
296C22⋊C4—621no—
297C22⋊C4—621no—
298C42—21no—
299C42C22×D3111yescharacteristic
300C23—21no—
301C23—311no—
302C23—311no—
303C23—621no—
304Q8—21no—
305Q8—621no—
306Q8—621no—
307Q8—1242no—
308Q8—1242no—
309Q8#9249512yescomplemented
310D4—21no—
311D4—21no—
312D4—622no—
313D4—621no—
314D4—621no—
315D4—1242no—
316D4—1242no—
317D4—1242no—
318D4—1242no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
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—621no—
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—41no—
344C22—41no—
345C22—41no—
346C22—312no—
347C22—621no—
348C22—621no—
349C22—621no—
350C22—621no—
351C22—621no—
352C22—1241no—
353C22—1241no—
354C22—1241no—
355C22C2×D4×D3111yescharacteristic
356C4—21no—
357C4—22no—
358C4—21no—
359C4—41no—
360C4—41no—
361C4—621no—
362C4—621no—
363C4—1241no—
364C4—1241no—
365C4—1241no—
366C4C2×#9249511yescharacteristic
367C4#1175856611yescharacteristic
368C2—81no—
369C2—622no—
370C2—1241no—
371C2—2481no—
372C2#1452169511yescharacteristic
373C2AGL(1,ℤ/8)×D3111yescharacteristic
374C2#1452186511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#440C2
socleC22×C31C22×D4
hypercenter#440D31
hypocenterC31#3308
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #14521711C2semidirect
2. #14521704C2semidirect
3. #14521409C2semidirect
4. #14521386C2semidirect
5. #14521364C2semidirect
6. #14521344C2semidirect
7. #14521294C2semidirect
8. #14521284C2semidirect
9. #14521264C2semidirect
10. #14521193C2semidirect
11. #14521186C2semidirect
12. #14521122C2semidirect
13. #14521049C2semidirect
14. #103×D31C2semidirect
15. C31×#440C2semidirect
117. Q8×C31#41semidirect
192. #440D31semidirect
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
#145217112
#145217042
#145214092
#145213862
#145213642
#145213442
#145212942
#145212842
#145212642
#145211932
#145211862
#145211222
#145210492
#103×D312
C31×#4402
#330831