Finite Group Databasebeta

← #16857709

Subgroups — #16857709

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#14521707C211yesmaximal, characteristic, complemented
2#14521704C211yesmaximal, characteristic, complemented
3#14521408C211yesmaximal, characteristic, complemented
4#14521383C211yesmaximal, characteristic, complemented
5#14521361C211yesmaximal, characteristic, complemented
6#14521345C211yesmaximal, characteristic, complemented
7#14521292C211yesmaximal, characteristic, complemented
8#14521282C211yesmaximal, characteristic, complemented
9#14521191C211yesmaximal, characteristic, complemented
10#14521186C211yesmaximal, characteristic, complemented
11#14521149C211yesmaximal, characteristic, complemented
12#14521119C211yesmaximal, characteristic, complemented
13#14521047C211yesmaximal, characteristic, complemented
14#103×D31C211yesmaximal, characteristic, complemented
15C31×#463C211yesmaximal, characteristic, complemented
16C2×Q8×D31C2211yescharacteristic
17C2×#92497C2211yescharacteristic
18C2×#92495—21no—
19C2×SD16×C31C2211yescharacteristic
20C2×D8×C31C2211yescharacteristic
21C31×#124C2211yescharacteristic
22C4×D4×C31C2211yescharacteristic
23#11758523C2211yescharacteristic
24#11758515C2211yescharacteristic
25#11758515C2211yescharacteristic
26#11758515C2211yescharacteristic
27C2×#92480C2211yescharacteristic
28#11758501—21no—
29C2×#92469C2211yescharacteristic
30C2×C8×D31C2211yescharacteristic
31C4⋊C4×D31C2211yescharacteristic
32C4⋊C4×D31C2211yescharacteristic
33#11758462—21no—
34#11758461—21no—
35#11758460—21no—
36#11758460—21no—
37(C22⋊D31)⋊C4—21no—
38#11758455—21no—
39C4×D124C2211yescharacteristic
40#11758446C2211yescharacteristic
41C4×Dic62C2211yescharacteristic
42C31×C4⋊C8C2211yescharacteristic
43C31×#103C2211yescharacteristic
44C31×#102C2211yescharacteristic
45#11758423C2211yescharacteristic
46#11758423C2211yescharacteristic
47#11758420C2211yescharacteristic
48#11758420C2211yescharacteristic
49#11758420C2211yescharacteristic
50(C2×D31)⋊C8C2211yescharacteristic
51(C2×D31)⋊C8C2211yescharacteristic
52#11758406C2211yescharacteristic
53#11758406C2211yescharacteristic
54#11758404C2211yescharacteristic
55#11758404C2211yescharacteristic
56#11758398C2211yescharacteristic
57#11758395C2211yescharacteristic
58#11758391C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C2×D4×C31C2311yescharacteristic
61C2×D4×C31C2311yescharacteristic
62C22×C4×C31—21no—
63C2×C22⋊D31—21no—
64C2×C22⋊D31—21no—
65C2×C22⋊D31—21no—
66C2×C22⋊D31—21no—
67C22×Dic31—21no—
68Q8×D31—22no—
69Q8×D31—41no—
70#92497—22no—
71#92497—41no—
72#92495—44no—
73C2×D124D411yescharacteristic
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—41no—
83D8×C31—41no—
84C2×C8×C31C2311yescharacteristic
85C2×C8×C31C2311yescharacteristic
86C4⋊C4×C31C2311yescharacteristic
87C22⋊C4×C31—21no—
88C22⋊C4×C31—21no—
89C22⋊C4×C31—21no—
90C42×C31C2311yescharacteristic
91C22⋊Dic31—21no—
92C22⋊Dic31—21no—
93C22⋊Dic31—21no—
94#92480—22no—
95(C2×D31)⋊C4—21no—
96(C2×D31)⋊C4D411yescharacteristic
97(C2×D31)⋊C4D411yescharacteristic
98C4⋊Dic31—21no—
99C4⋊Dic31D411yescharacteristic
100C4⋊Dic31C2311yescharacteristic
101C4⋊Dic31C2311yescharacteristic
102C4⋊Dic31C2311yescharacteristic
103Dic31⋊C4—21no—
104Dic31⋊C4—21no—
105Dic31⋊C4—21no—
106Dic31⋊C4—21no—
107C4×Dic31—21no—
108C2×C31⋊C8C2311yescharacteristic
109C2×C31⋊C8C2311yescharacteristic
110#92469—41no—
111C8×D31—41no—
112C23×C31—21no—
113C23×C31—21no—
114C22×D31C2×D411yescharacteristic
115C22×D31C2×D411yescharacteristic
116Q8×C31—21no—
117Q8×C31—21no—
118D4×C31—21no—
119D4×C31—21no—
120D4×C31—21no—
121D4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31—42no—
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2×D411yescharacteristic
127C2×C4×C31C2411yescharacteristic
128C22⋊D31—42no—
129C22⋊D31—42no—
130C22⋊D31—42no—
131C22⋊D31—42no—
132C2×Dic31—21no—
133C2×Dic31—21no—
134C2×Dic31—21no—
135C2×Dic31—21no—
136C2×Dic31—42no—
137C2×Dic31C2×D411yescharacteristic
138C2×Dic31C2×D411yescharacteristic
139D124—22no—
140C4×D31—21no—
141C4×D31—21no—
142C4×D31—21no—
143C4×D31—21no—
144C4×D31—42no—
145C4×D31—42no—
146C4×D31—42no—
147Dic62—21no—
148Dic62—42no—
149Dic62—42no—
150Dic62#4112yescomplemented
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×C31—41no—
160C22×C31—41no—
161C22×C31—41no—
162C22×C31C22×D411yescharacteristic
163C2×D31—21no—
164C2×D31—21no—
165C2×D31—21no—
166C2×D31—21no—
167C2×D31—21no—
168C2×D31AGL(1,ℤ/8)12yes—
169C4×C31—21no—
170C4×C31—21no—
171C4×C31—41no—
172C4×C31—41no—
173C4×C31C2×#4111yescharacteristic
174C4×C31H(5,𝔽2)11yescharacteristic
175Dic31—22no—
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#463D3111yescharacteristic, complemented
190#449—311no—
191#448—311no—
192#440—311no—
193#435—311no—
194#417—311no—
195C2×#103—311no—
196C2×C31—81no—
197C2×C31—81no—
198C2×C31#54611yescharacteristic
199C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
200C2×C31#57811yescharacteristic
201D31—22no—
202D31—41no—
203C2×#41—311no—
204C2×#41—621no—
205C22×Q8—311no—
206C2×SD16—311no—
207C2×SD16C2×D3111yescharacteristic
208C2×D8C2×D3111yescharacteristic
209C2×M16—311no—
210C22×C8—311no—
211C4⋊Q8—311no—
212#124—621no—
213#124C2×D3111yescharacteristic
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—621no—
226C4×D4C2×D3111yescharacteristic
227C2×C4⋊C4—311no—
228C2×C4⋊C4—311no—
229#107—311no—
230#107—311no—
231#107—311no—
232C4⋊C8C2×D3111yescharacteristic
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#97—311no—
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—621no—
258C2×D4—621no—
259C2×D4—621no—
260C2×D4—621no—
261C2×D4C22×D3111yescharacteristic
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—41no—
271SD16—622no—
272D8—41no—
273M16—1241no—
274C2×C8—311no—
275C2×C8—311no—
276C2×C8—1241no—
277C2×C8C22×D3111yescharacteristic
278C2×C8C22×D3111yescharacteristic
279C4⋊C4—311no—
280C4⋊C4—311no—
281C4⋊C4—311no—
282C4⋊C4—311no—
283C4⋊C4—621no—
284C4⋊C4—621no—
285C4⋊C4—621no—
286C4⋊C4—621no—
287C4⋊C4—621no—
288C4⋊C4C22×D3111yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—311no—
293C22⋊C4—311no—
294C22⋊C4—621no—
295C22⋊C4—621no—
296C22⋊C4—621no—
297C22⋊C4—621no—
298C42—621no—
299C42C22×D3111yescharacteristic
300C23—21no—
301C23—21no—
302C23—311no—
303C23—311no—
304Q8—21no—
305Q8—21no—
306Q8—312no—
307Q8—621no—
308Q8—1242no—
309Q8—1242no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—622no—
315D4—1242no—
316D4—1242no—
317D4—1242no—
318D4—1242no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—311no—
323C2×C4—311no—
324C2×C4—621no—
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—41no—
347C22—41no—
348C22—41no—
349C22—312no—
350C22—621no—
351C22—621no—
352C22—621no—
353C22—621no—
354C22—621no—
355C22C2×D4×D3111yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—621no—
361C4—621no—
362C4—622no—
363C4—1241no—
364C4—1241no—
365C4—1241no—
366C4#1175856111yescharacteristic
367C4#41×D3111yescharacteristic
368C2—81no—
369C2—81no—
370C2—622no—
371C2—1241no—
372C2#1452169611yescharacteristic
373C2AGL(1,ℤ/8)×D3111yescharacteristic
374C2#1452186311yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#463C2
socleC22×C31C22×D4
hypercenter#463D31
hypocenterC31#3308
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #14521707C2semidirect
2. #14521704C2semidirect
3. #14521408C2semidirect
4. #14521383C2semidirect
5. #14521361C2semidirect
6. #14521345C2semidirect
7. #14521292C2semidirect
8. #14521282C2semidirect
9. #14521191C2semidirect
10. #14521186C2semidirect
11. #14521149C2semidirect
12. #14521119C2semidirect
13. #14521047C2semidirect
14. #103×D31C2semidirect
15. C31×#463C2semidirect
150. Dic62#41semidirect
189. #463D31semidirect
246. C31#3308semidirect

Maximal subgroups

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

subgroupindex
#145217072
#145217042
#145214082
#145213832
#145213612
#145213452
#145212922
#145212822
#145211912
#145211862
#145211492
#145211192
#145210472
#103×D312
C31×#4632
#330831