Finite Group Databasebeta

← #16855064

Subgroups — #16855064

Order 3968.

724 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 145 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
1#14521885C211yesmaximal, characteristic, complemented
2#14521849C212yesmaximal, complemented
3#14521595C211yesmaximal, characteristic, complemented
4#14521234C212yesmaximal, complemented
5#14521229C212yesmaximal, complemented
6#14521224C212yesmaximal, complemented
7#14521219C212yesmaximal, complemented
8C2×#11758413C212yesmaximal, complemented
9C31×#413C211yesmaximal, characteristic, complemented
10C2×#41×C31C2211yescharacteristic
11#11758567—22no—
12#11758566—22no—
13#41×D31—24no—
14#11758564C2212yes—
15#11758561—22no—
16#11758561C2212yes—
17C2×#92495—22no—
18C2×#92495C2212yes—
19C2×#92495C2211yescharacteristic, complemented
20C2×M16×C31C2212yescomplemented
21#11758524C2211yescharacteristic, complemented
22#11758521C2211yescharacteristic, complemented
23#11758517C2211yescharacteristic, complemented
24#11758516—22no—
25#11758513C2211yescharacteristic, complemented
26C4×C22⋊D31—22no—
27C2×C4×Dic31C2211yescharacteristic, complemented
28#11758486—22no—
29#11758486C2214yescomplemented
30#11758485—22no—
31#11758485C2214yescomplemented
32#11758481—24no—
33C31×#101C2212yescomplemented
34C31×#100C2212yescomplemented
35#11758413C2214yescomplemented
36#11758413C2214yescomplemented
37#41×C31—22no—
38#41×C31—22no—
39C2×Q8×C31C2311yescharacteristic
40C2×D4×C31D412yes—
41C2×D4×C31C2311yescharacteristic
42C22×C4×C31D412yes—
43C22×C4×C31C2311yescharacteristic
44C2×C22⋊D31—24no—
45C2×C22⋊D31—22no—
46C2×C22⋊D31—22no—
47C2×C22⋊D31—21no—
48C22×Dic31—21no—
49#92499—24no—
50Q8×D31—24no—
51#92497—28no—
52#92497—24no—
53D4×D31—28no—
54D4×D31—24no—
55#92495—24no—
56#92495—24no—
57#92495—22no—
58#92495—24no—
59#92495—22no—
60#92495—22no—
61#92495—22no—
62#92495D414yescomplemented
63#92495C2314yes—
64C2×D124—22no—
65C2×D124D412yescomplemented
66C2×D124C2311yescharacteristic
67C2×C4×D31—24no—
68C2×C4×D31—22no—
69C2×C4×D31—21no—
70C2×Dic62—22no—
71C2×Dic62D412yescomplemented
72C2×Dic62C2311yescharacteristic
73M16×C31—22no—
74M16×C31C2314yes—
75C2×C8×C31—22no—
76C22⋊Dic31—22no—
77(C2×D31)⋊C4—22no—
78Dic31⋊C4—22no—
79C4×Dic31—21no—
80C4×Dic31C2311yescharacteristic
81C4×Dic31C2311yescharacteristic
82Dic124—24no—
83D248—24no—
84#92470—24no—
85#92470—24no—
86C23×C31C2×D412yes—
87C23×C31C2×D411yescharacteristic
88C22×D31—24no—
89C22×D31—22no—
90C22×D31—21no—
91Q8×C31—22no—
92D4×C31—24no—
93D4×C31—22no—
94C2×C4×C31—22no—
95C2×C4×C31—22no—
96C2×C4×C31C2×D412yes—
97C2×C4×C31C2×D411yescharacteristic
98C2×C4×C31C2×D412yes—
99C2×C4×C31C2×D412yes—
100C2×C4×C31C2411yescharacteristic
101C22⋊D31—28no—
102C22⋊D31—24no—
103C22⋊D31—24no—
104C22⋊D31—44no—
105C22⋊D31—42no—
106C2×Dic31—24no—
107C2×Dic31—22no—
108C2×Dic31—21no—
109C2×Dic31—21no—
110C2×Dic31—21no—
111C2×Dic31—42no—
112D124—24no—
113D124—22no—
114D124—22no—
115D124C2×D414yes—
116C4×D31—28no—
117C4×D31—24no—
118C4×D31—24no—
119C4×D31—41no—
120C4×D31—41no—
121Dic62—24no—
122Dic62—22no—
123Dic62—22no—
124Dic62C2×D414yes—
125C8×C31—24no—
126#3018—311nomaximal, Sylow
127C22×C31—22no—
128C22×C31—41no—
129C22×C31—42no—
130C22×C31#12012yes—
131C22×C31C22×D411yescharacteristic
132C2×D31—24no—
133C2×D31—42no—
134C2×D31—41no—
135C2×D31—82no—
136C2×D31—84no—
137C4×C31—22no—
138C4×C31#12011yescharacteristic
139C4×C31#12011yescharacteristic
140C4×C31C22×D412yes—
141Dic31—22no—
142Dic31—24no—
143Dic31—41no—
144Dic31—41no—
145#585—311no—
146#575—312no—
147#532—311no—
148#456—312no—
149#455—312no—
150#454—312no—
151#453—312no—
152C2×#104—312no—
153#413D3111yescharacteristic, complemented
154C2×C31—21no—
155C2×C31—22no—
156C2×C31—42no—
157C2×C31C2×#12011yescharacteristic
158D31—44no—
159D31—81no—
1602−1+4—312no—
1612−1+4—622no—
162H(5,𝔽2)—312no—
163H(5,𝔽2)—622no—
164H(5,𝔽2)—622no—
165C2×#41—312no—
166C2×#41—311no—
167C2×#41—624no—
168C2×#41—622no—
169C2×#41C2×D3111yescharacteristic
170#137—314no—
171#137—622no—
172AGL(1,ℤ/8)—314no—
173AGL(1,ℤ/8)—622no—
174#135—624no—
175C2×M16C2×D3112yescomplemented
176C4⋊Q8—311no—
177#127—311no—
178#124—311no—
179#124—311no—
180#121—622no—
181C4×D4—622no—
182C2×C42—311no—
183#104—314no—
184#104—314no—
185#101C2×D3112yescomplemented
186#100C2×D3112yescomplemented
187C31#301811yescharacteristic, complemented, Sylow
188#41—22no—
189#41—22no—
190#41—314no—
191#41—314no—
192#41—624no—
193#41—624no—
194#41—624no—
195#41—628no—
196#41—624no—
197#41—622no—
198#41—624no—
199#41—622no—
200#41—622no—
201#41—622no—
202C2×Q8—312no—
203C2×Q8—311no—
204C2×Q8—622no—
205C2×Q8—624no—
206C2×Q8C22×D3111yescharacteristic
207C2×D4—312no—
208C2×D4—311no—
209C2×D4—622no—
210C2×D4—624no—
211C2×D4—628no—
212C2×D4—622no—
213C2×D4—624no—
214C2×D4—622no—
215C2×D4—621no—
216C2×D4D12412yes—
217C2×D4C22×D3111yescharacteristic
218C22×C4—624no—
219C22×C4—622no—
220C22×C4—621no—
221C22×C4—621no—
222C22×C4D12412yes—
223C22×C4C22×D3111yescharacteristic
224Q16—624no—
225SD16—624no—
226SD16—624no—
227D8—624no—
228M16—22no—
229M16C22×D3114yes—
230C2×C8—22no—
231C4⋊C4—622no—
232C22⋊C4—622no—
233C22⋊C4—622no—
234C42—311no—
235C42—311no—
236C42—621no—
237C23—624no—
238C23—622no—
239C23—621no—
240C23C2×D12412yes—
241C23C2×D12411yescharacteristic
242Q8—22no—
243Q8—314no—
244Q8—624no—
245Q8—622no—
246Q8—622no—
247D4—24no—
248D4—22no—
249D4—314no—
250D4—624no—
251D4—628no—
252D4—624no—
253D4—624no—
254D4—622no—
255D4—622no—
256D4—1244no—
257D4—1242no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—628no—
261C2×C4—624no—
262C2×C4—622no—
263C2×C4—621no—
264C2×C4—624no—
265C2×C4—624no—
266C2×C4—621no—
267C2×C4—621no—
268C2×C4—1242no—
269C2×C4—1241no—
270C2×C4—1241no—
271C2×C4C2×D12412yes—
272C2×C4C2×D12411yescharacteristic
273C2×C4D4×D3112yes—
274C2×C4D4×D3112yes—
275C2×C4C23×D3111yescharacteristic
276C8—24no—
277C22—22no—
278C22—41no—
279C22—42no—
280C22—624no—
281C22—1242no—
282C22—1241no—
283C22—2482no—
284C22—2484no—
285C22#1175845912yes—
286C22C22×D12411yescharacteristic
287C4—22no—
288C4—622no—
289C4—624no—
290C4—1241no—
291C4—1241no—
292C4#1175845911yescharacteristic
293C4#1175845911yescharacteristic
294C4C2×D4×D3112yes—
295C2—21no—
296C2—22no—
297C2—42no—
298C2—1244no—
299C2—2481no—
300C2C2×#1175845911yescharacteristic
subgroupG/H
centerC4#11758459
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#413C2
socleC2×C31C2×#120
hypercenter#413D31
hypocenterC31#3018
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #14521885C2semidirect
2. #14521849C2semidirect
3. #14521595C2semidirect
4. #14521234C2semidirect
5. #14521229C2semidirect
6. #14521224C2semidirect
7. #14521219C2semidirect
8. C2×#11758413C2semidirect
9. C31×#413C2semidirect
19. C2×#92495C22semidirect
20. C2×M16×C31C22semidirect
21. #11758524C22semidirect
22. #11758521C22semidirect
23. #11758517C22semidirect
25. #11758513C22semidirect
27. C2×C4×Dic31C22semidirect
29. #11758486C22semidirect
31. #11758485C22semidirect
33. C31×#101C22semidirect
34. C31×#100C22semidirect
35. #11758413C22semidirect
36. #11758413C22semidirect
62. #92495D4semidirect
65. C2×D124D4semidirect
71. C2×Dic62D4semidirect
153. #413D31semidirect
175. C2×M16C2×D31semidirect
185. #101C2×D31semidirect
186. #100C2×D31semidirect
187. C31#3018semidirect

Maximal subgroups

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

subgroupindex
#145218852
#145218492
#145215952
#145212342
#145212292
#145212242
#145212192
C2×#117584132
C31×#4132
#301831