Finite Group Databasebeta

← #16858798

Subgroups — #16858798

Order 3968.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521784C211yesmaximal, characteristic, complemented
2#14521781C211yesmaximal, characteristic, complemented
3#14521439C211yesmaximal, characteristic, complemented
4#14521435C211yesmaximal, characteristic, complemented
5#14521434C211yesmaximal, characteristic, complemented
6#14521273C211yesmaximal, characteristic, complemented
7#14521267C211yesmaximal, characteristic, complemented
8#14521266C211yesmaximal, characteristic, complemented
9#14521245C211yesmaximal, characteristic, complemented
10#14521243C211yesmaximal, characteristic, complemented
11#14521178C211yesmaximal, characteristic, complemented
12#14521152C211yesmaximal, characteristic, complemented
13#14521147C211yesmaximal, characteristic, complemented
14#14521129C211yesmaximal, characteristic, complemented
15C31×#464C211yesmaximal, characteristic, complemented
16C2×Q16×C31C2211yescharacteristic
17C2×SD16×C31C2211yescharacteristic
18C31×#124C2211yescharacteristic
19C4×Q8×C31C2211yescharacteristic
20#11758524C2211yescharacteristic
21#11758524C2211yescharacteristic
22#11758524C2211yescharacteristic
23Q8×Dic31C2211yescharacteristic
24C2×#92481C2211yescharacteristic
25C2×#92481C2211yescharacteristic
26C2×#92481C2211yescharacteristic
27#11758517C2211yescharacteristic
28D4×Dic31C2211yescharacteristic
29C2×#92479C2211yescharacteristic
30C2×#92479C2211yescharacteristic
31C2×D248C2211yescharacteristic
32C2×D248C2211yescharacteristic
33#11758471—21no—
34#11758471—21no—
35#11758470C2211yescharacteristic
36#11758470C2211yescharacteristic
37#11758463—21no—
38#11758462—21no—
39#11758460—21no—
40(C22⋊D31)⋊C4—21no—
41#11758452—21no—
42#11758451C2211yescharacteristic
43C4×D124—21no—
44C4×D124C2211yescharacteristic
45C4×Dic62C2211yescharacteristic
46C31×C4⋊C8C2211yescharacteristic
47C31×#103C2211yescharacteristic
48C31×#102C2211yescharacteristic
49#11758423C2211yescharacteristic
50#11758409C2211yescharacteristic
51#11758409C2211yescharacteristic
52#11758403C2211yescharacteristic
53Dic31⋊C8C2211yescharacteristic
54Dic31⋊C8C2211yescharacteristic
55C8×Dic31C2211yescharacteristic
56#11758397C2211yescharacteristic
57#11758395C2211yescharacteristic
58#11758391C2211yescharacteristic
59C2×Q8×C31C2311yescharacteristic
60C2×Q8×C31C2311yescharacteristic
61C2×D4×C31C2311yescharacteristic
62C2×C22⋊D31—21no—
63C2×C22⋊D31—21no—
64C22×Dic31—21no—
65C2×D124—21no—
66C2×D124—21no—
67C2×D124C2311yescharacteristic
68C2×D124C2311yescharacteristic
69C2×D124C2311yescharacteristic
70C2×C4×D31—21no—
71C2×C4×D31—21no—
72C2×C4×D31—21no—
73C2×Dic62D411yescharacteristic
74Q16×C31—41no—
75SD16×C31—41no—
76C2×C8×C31C2311yescharacteristic
77C2×C8×C31C2311yescharacteristic
78C4⋊C4×C31—21no—
79C4⋊C4×C31C2311yescharacteristic
80C22⋊C4×C31—21no—
81C22⋊C4×C31—21no—
82C42×C31—21no—
83C42×C31C2311yescharacteristic
84C22⋊Dic31—21no—
85#92481—22no—
86#92481—22no—
87#92481—41no—
88#92479—22no—
89#92479—41no—
90(C2×D31)⋊C4—21no—
91(C2×D31)⋊C4—21no—
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—
99C4⋊Dic31—21no—
100C4⋊Dic31D411yescharacteristic
101C4⋊Dic31C2311yescharacteristic
102Dic31⋊C4D411yescharacteristic
103Dic31⋊C4D411yescharacteristic
104C4×Dic31—21no—
105C4×Dic31C2311yescharacteristic
106C4×Dic31C2311yescharacteristic
107C2×C31⋊C8C2311yescharacteristic
108C2×C31⋊C8C2311yescharacteristic
109D248—41no—
110D248—41no—
111C23×C31—21no—
112C22×D31—21no—
113C22×D31—21no—
114C22×D31—21no—
115Q8×C31—21no—
116Q8×C31—21no—
117Q8×C31—21no—
118Q8×C31—21no—
119D4×C31—21no—
120D4×C31—21no—
121C2×C4×C31—21no—
122C2×C4×C31—21no—
123C2×C4×C31—21no—
124C2×C4×C31C2×D411yescharacteristic
125C2×C4×C31C2×D411yescharacteristic
126C2×C4×C31C2411yescharacteristic
127C22⋊D31—42no—
128C22⋊D31—81no—
129C2×Dic31—21no—
130C2×Dic31—81no—
131C2×Dic31C2×D411yescharacteristic
132C2×Dic31C2×D411yescharacteristic
133C2×Dic31C2×D411yescharacteristic
134C2×Dic31C2×D411yescharacteristic
135D124—21no—
136D124—21no—
137D124—21no—
138D124—21no—
139D124—21no—
140D124—21no—
141D124—42no—
142D124—81no—
143C4×D31—81no—
144C4×D31—81no—
145C4×D31—81no—
146Dic62—41no—
147C8×C31—21no—
148C8×C31—21no—
149C31⋊C8—21no—
150C31⋊C8#4112yes—
151#3403—311nomaximal, Sylow
152C22×C31—41no—
153C22×C31—41no—
154C22×C31—41no—
155C22×C31C22×D411yescharacteristic
156C2×D31—41no—
157C2×D31—41no—
158C2×D31—41no—
159C2×D31—41no—
160C2×D31—41no—
161C2×D31—41no—
162C2×D31—41no—
163C2×D31—41no—
164C2×D31—41no—
165C4×C31—21no—
166C4×C31—21no—
167C4×C31—41no—
168C4×C31—41no—
169C4×C31—41no—
170C4×C31C2×#4111yescharacteristic
171C4×C31H(5,𝔽2)11yescharacteristic
172Dic31—21no—
173Dic31—21no—
174Dic31—21no—
175Dic31—21no—
176Dic31—41no—
177#559—311no—
178#559—311no—
179#496—311no—
180#496—311no—
181#495—311no—
182#464—311no—
183#464D3111yescharacteristic, complemented
184#463—311no—
185#463—311no—
186#459—311no—
187#459—311no—
188#446—311no—
189#440—311no—
190#440—311no—
191C4×D8—311no—
192C2×C31—81no—
193C2×C31#55011yescharacteristic
194C2×C31#57511yescharacteristic
195C2×C31#57611yescharacteristic
196D31—81no—
197D31—81no—
198D31—81no—
199C2×Q16C2×D3111yescharacteristic
200C2×SD16—311no—
201C2×SD16—311no—
202C2×SD16—311no—
203C2×SD16C2×D3111yescharacteristic
204C2×D8—311no—
205C2×D8—311no—
206C2×D8—311no—
207C2×D8—311no—
208#127—311no—
209#127—311no—
210#124—311no—
211#124—311no—
212#124—311no—
213#124—621no—
214#124—621no—
215#124C2×D3111yescharacteristic
216#123—621no—
217#123—621no—
218#123—621no—
219#123—621no—
220C4×Q8—311no—
221C4×Q8—311no—
222C4×Q8C2×D3111yescharacteristic
223C4×D4—311no—
224C4×D4—311no—
225C4×D4—311no—
226C4×D4—311no—
227C4×D4—621no—
228C4×D4—621no—
229#107—311no—
230C4⋊C8—311no—
231C4⋊C8—311no—
232C4⋊C8C2×D3111yescharacteristic
233#103—311no—
234#103C2×D3111yescharacteristic
235#102—311no—
236#102—311no—
237#102—311no—
238#102C2×D3111yescharacteristic
239#97—311no—
240#97—311no—
241C4×C8—311no—
242C31#340311yescharacteristic, complemented, Sylow
243C2×Q8—311no—
244C2×Q8C22×D3111yescharacteristic
245C2×Q8C22×D3111yescharacteristic
246C2×D4—311no—
247C2×D4—311no—
248C2×D4—311no—
249C2×D4—621no—
250C2×D4—621no—
251C2×D4—621no—
252C2×D4—621no—
253C2×D4C22×D3111yescharacteristic
254C22×C4—621no—
255C22×C4—621no—
256C22×C4—621no—
257C22×C4—621no—
258Q16—41no—
259SD16—41no—
260SD16—622no—
261SD16—622no—
262SD16—1241no—
263D8—622no—
264D8—1241no—
265D8—1241no—
266D8—1241no—
267C2×C8—311no—
268C2×C8—311no—
269C2×C8C22×D3111yescharacteristic
270C2×C8C22×D3111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—311no—
273C4⋊C4—311no—
274C4⋊C4—311no—
275C4⋊C4—311no—
276C4⋊C4—621no—
277C4⋊C4C22×D3111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—621no—
281C22⋊C4—621no—
282C22⋊C4—621no—
283C22⋊C4—621no—
284C22⋊C4—621no—
285C22⋊C4—621no—
286C22⋊C4—621no—
287C22⋊C4—621no—
288C22⋊C4—621no—
289C22⋊C4—621no—
290C42—21no—
291C42—311no—
292C42—311no—
293C42—621no—
294C42C22×D3111yescharacteristic
295C23—21no—
296C23—621no—
297C23—621no—
298C23—621no—
299Q8—21no—
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—1241no—
304D4—21no—
305D4—21no—
306D4—621no—
307D4—621no—
308D4—621no—
309D4—621no—
310D4—621no—
311D4—621no—
312D4—1242no—
313D4—1242no—
314D4—2481no—
315D4—2481no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—311no—
320C2×C4—311no—
321C2×C4—311no—
322C2×C4—311no—
323C2×C4—621no—
324C2×C4—2481no—
325C2×C4—2481no—
326C2×C4—2481no—
327C2×C4—2481no—
328C2×C4D4×D3111yescharacteristic
329C2×C4D4×D3111yescharacteristic
330C2×C4C23×D3111yescharacteristic
331C8—21no—
332C8—21no—
333C8—312no—
334C8—621no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—1241no—
339C22—1241no—
340C22—1241no—
341C22—1241no—
342C22—1241no—
343C22—1241no—
344C22—1241no—
345C22—1241no—
346C22—1241no—
347C22C2×D4×D3111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—621no—
354C4—621no—
355C4—621no—
356C4—621no—
357C4—1241no—
358C4#1175856111yescharacteristic
359C4#41×D3111yescharacteristic
360C2—81no—
361C2—2481no—
362C2—2481no—
363C2—2481no—
364C2#1452171711yescharacteristic
365C2#1452184811yescharacteristic
366C2#1452185111yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#464C2
socleC22×C31C22×D4
hypercenter#464D31
hypocenterC31#3403
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #14521784C2semidirect
2. #14521781C2semidirect
3. #14521439C2semidirect
4. #14521435C2semidirect
5. #14521434C2semidirect
6. #14521273C2semidirect
7. #14521267C2semidirect
8. #14521266C2semidirect
9. #14521245C2semidirect
10. #14521243C2semidirect
11. #14521178C2semidirect
12. #14521152C2semidirect
13. #14521147C2semidirect
14. #14521129C2semidirect
15. C31×#464C2semidirect
183. #464D31semidirect
242. C31#3403semidirect

Maximal subgroups

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

subgroupindex
#145217842
#145217812
#145214392
#145214352
#145214342
#145212732
#145212672
#145212662
#145212452
#145212432
#145211782
#145211522
#145211472
#145211292
C31×#4642
#340331