Finite Group Databasebeta

← #16846724

Subgroups — #16846724

Order 3968.

478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758526C211yesmaximal, characteristic, complemented
2C2×#11758517C211yesmaximal, characteristic, complemented
3C2×#11758425C211yesmaximal, characteristic, complemented
4#14521053C211yesmaximal, characteristic, complemented
5C2×#11758421C211yesmaximal, characteristic, complemented
6#14520808C211yesmaximal, characteristic, complemented
7C31×#535C211yesmaximal, characteristic, complemented
8C2×#41×C31C2211yescharacteristic
9C22×D4×C31C2211yescharacteristic
10C22×C22⋊D31—22no—
11C22×D124C2211yescharacteristic
12C31×#127—21no—
13C31×#124—21no—
14C31×#121—22no—
15C31×#120—22no—
16C31×#117C2211yescharacteristic
17#11758526—22no—
18#11758526—22no—
19C2×#92481—21no—
20#11758517—22no—
21#11758517—22no—
22C2×#92479—21no—
23C2×C4×Dic31C2211yescharacteristic
24C2×#92474C2211yescharacteristic
25C2×#92474C2211yescharacteristic
26#11758425—22no—
27#11758421—22no—
28#11758397—22no—
29C24×C31D412yes—
30C23×D31—21no—
31#41×C31—21no—
32#41×C31—21no—
33#41×C31—21no—
34#41×C31—21no—
35C2×Q8×C31D411yescharacteristic, complemented
36C2×D4×C31—21no—
37C2×D4×C31—24no—
38C2×D4×C31—21no—
39C2×D4×C31—21no—
40C2×D4×C31—21no—
41C2×D4×C31—21no—
42C2×D4×C31—21no—
43C2×D4×C31—21no—
44C2×D4×C31D411yescharacteristic, complemented
45C22×C4×C31—21no—
46C22×C4×C31C2311yescharacteristic
47C2×C22⋊D31—28no—
48C2×C22⋊D31—48no—
49C22×Dic31—21no—
50C2×D124—21no—
51C2×D124—21no—
52C2×D124—21no—
53C2×D124—21no—
54C2×D124—21no—
55C2×D124D412yescomplemented
56C4⋊C4×C31D412yescomplemented
57C22⋊C4×C31—24no—
58C22⋊C4×C31—21no—
59C42×C31—21no—
60#92481—24no—
61#92479—24no—
62C4×Dic31—21no—
63C4×Dic31D412yescomplemented
64#92474—21no—
65#92474—21no—
66#92474—21no—
67#92474D412yescomplemented
68C2×C31⋊C8—21no—
69C2×C31⋊C8—21no—
70C23×C31—22no—
71C23×C31—22no—
72C23×C31—21no—
73C23×C31—22no—
74C23×C31—44no—
75C23×C31C2×D411yescharacteristic
76C22×D31—22no—
77C22×D31—44no—
78C22×D31—41no—
79C22×D31—41no—
80Q8×C31—21no—
81Q8×C31—21no—
82D4×C31—21no—
83D4×C31—21no—
84D4×C31—41no—
85D4×C31—41no—
86D4×C31—41no—
87D4×C31—41no—
88D4×C31—41no—
89D4×C31—41no—
90D4×C31—84no—
91C2×C4×C31—22no—
92C2×C4×C31—21no—
93C2×C4×C31—41no—
94C2×C4×C31—41no—
95C2×C4×C31C2×D411yescharacteristic
96C2×C4×C31C2×D411yescharacteristic
97C2×C4×C31C2×D411yescharacteristic
98C2×C4×C31C2×D411yescharacteristic
99C2×C4×C31C2×D411yescharacteristic
100C2×C4×C31#4111yescharacteristic
101C22⋊D31—416no—
102C2×Dic31—24no—
103C2×Dic31—22no—
104D124—22no—
105D124—22no—
106D124—41no—
107D124—41no—
108C31⋊C8—22no—
109C31⋊C8—41no—
110#2002—311nomaximal, Sylow
111C22×C31—22no—
112C22×C31—44no—
113C22×C31—41no—
114C22×C31—42no—
115C22×C31—42no—
116C22×C31—44no—
117C22×C31—82no—
118C22×C31#12011yescharacteristic
119C22×C31#12011yescharacteristic
120C22×C31#12111yescharacteristic
121C2×D31—44no—
122C2×D31—42no—
123C2×D31—82no—
124C2×D31—82no—
125C4×C31—41no—
126C4×C31—42no—
127C4×C31#12011yescharacteristic
128C4×C31#12111yescharacteristic
129C4×C31#12111yescharacteristic
130C4×C31#12711yescharacteristic
131Dic31—24no—
132C2×AGL(1,ℤ/8)—311no—
133#535D3111yescharacteristic, complemented
134C2×#127—311no—
135C2×#104—311no—
136#418—311no—
137C2×#100—311no—
138#339—311no—
139C2×C31—21no—
140C2×C31—21no—
141C2×C31—81no—
142C2×C31—82no—
143C2×C31#39211yescharacteristic
144C2×C31#45312yes—
145D31—82no—
146C2×#41C2×D3111yescharacteristic
147C22×D4—311no—
148C22×D4—622no—
149C22×D4C2×D3111yescharacteristic
150AGL(1,ℤ/8)—622no—
151AGL(1,ℤ/8)—622no—
152C2×SD16—621no—
153C2×D8—621no—
154C2×M16—311no—
155C2×M16—311no—
156#127—21no—
157#127—622no—
158#127—622no—
159#124—21no—
160#121—22no—
161#120—22no—
162#117C2×D3111yescharacteristic
163C2×C42—311no—
164#104—622no—
165#102—622no—
166#100—622no—
167C31#200211yescharacteristic, complemented, Sylow
168C24—621no—
169C24C22⋊D3112yes—
170#41—21no—
171#41—21no—
172#41—21no—
173#41—21no—
174C2×Q8C22⋊D3111yescharacteristic, complemented
175C2×D4—21no—
176C2×D4—24no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—312no—
184C2×D4—628no—
185C2×D4—621no—
186C2×D4—621no—
187C2×D4—621no—
188C2×D4—621no—
189C2×D4—621no—
190C2×D4—1248no—
191C2×D4C22⋊D3111yescharacteristic, complemented
192C22×C4—21no—
193C22×C4—621no—
194C22×C4C22×D3111yescharacteristic
195SD16—624no—
196D8—624no—
197M16—312no—
198M16—621no—
199M16—621no—
200M16—621no—
201C2×C8—621no—
202C2×C8—621no—
203C4⋊C4C22⋊D3112yescomplemented
204C22⋊C4—24no—
205C22⋊C4—21no—
206C42—21no—
207C42—312no—
208C42—621no—
209C23—22no—
210C23—22no—
211C23—21no—
212C23—22no—
213C23—44no—
214C23—622no—
215C23—1244no—
216C23—1241no—
217C23—1241no—
218C23C2×C22⋊D3111yescharacteristic
219Q8—21no—
220Q8—21no—
221D4—21no—
222D4—21no—
223D4—41no—
224D4—41no—
225D4—41no—
226D4—41no—
227D4—41no—
228D4—41no—
229D4—84no—
230D4—622no—
231D4—622no—
232D4—12416no—
233D4—1241no—
234D4—1241no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—624no—
240C2×C4—622no—
241C2×C4D4×D3111yescharacteristic
242C2×C4D4×D3111yescharacteristic
243C2×C4D4×D3111yescharacteristic
244C2×C4#9249711yescharacteristic
245C2×C4C2×C22⋊D3111yescharacteristic
246C2×C4C2×C22⋊D3111yescharacteristic
247C8—622no—
248C8—1241no—
249C22—22no—
250C22—44no—
251C22—41no—
252C22—42no—
253C22—42no—
254C22—44no—
255C22—82no—
256C22—1244no—
257C22—1242no—
258C22—2482no—
259C22—2482no—
260C22#1175851411yescharacteristic
261C22#1175851611yescharacteristic
262C22#1175853011yescharacteristic
263C4—41no—
264C4—42no—
265C4—624no—
266C4#1175851411yescharacteristic
267C4#1175851511yescharacteristic
268C4#1175851611yescharacteristic
269C4#1175851711yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—81no—
274C2—2482no—
275C2#1452095711yescharacteristic
276C2#1452121712yes—
subgroupG/H
centerC22#11758530
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#535C2
socleC22×C31#120
hypercenter#535D31
hypocenterC31#2002
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#11758526C2semidirect
2. C2×#11758517C2semidirect
3. C2×#11758425C2semidirect
4. #14521053C2semidirect
5. C2×#11758421C2semidirect
6. #14520808C2semidirect
7. C31×#535C2semidirect
35. C2×Q8×C31D4semidirect
44. C2×D4×C31D4semidirect
55. C2×D124D4semidirect
56. C4⋊C4×C31D4semidirect
63. C4×Dic31D4semidirect
67. #92474D4semidirect
133. #535D31semidirect
167. C31#2002semidirect
174. C2×Q8C22⋊D31semidirect
191. C2×D4C22⋊D31semidirect
203. C4⋊C4C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117585262
C2×#117585172
C2×#117584252
#145210532
C2×#117584212
#145208082
C31×#5352
#200231