Finite Group Databasebeta

← #16846727

Subgroups — #16846727

Order 3968.

478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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×#11758509C211yesmaximal, characteristic, complemented
2#14521618C211yesmaximal, characteristic, complemented
3C2×#11758517C211yesmaximal, characteristic, complemented
4C2×#11758413C211yesmaximal, characteristic, complemented
5C2×#11758411C211yesmaximal, characteristic, complemented
6#14520808C211yesmaximal, characteristic, complemented
7C31×#418C211yesmaximal, characteristic, complemented
8C22×D4×C31C2211yescharacteristic
9C22×C22⋊D31—22no—
10C2×#92495C2211yescharacteristic
11C22×D124C2211yescharacteristic
12C2×M16×C31C2211yescharacteristic
13C31×#117C2211yescharacteristic
14#11758517—22no—
15#11758517—22no—
16C2×#92480—21no—
17#11758509—22no—
18#11758509—22no—
19C2×#92479—21no—
20C2×C4×Dic31C2211yescharacteristic
21C2×#92474C2211yescharacteristic
22#11758472—22no—
23#11758459—22no—
24#11758452—21no—
25#11758451—21no—
26C31×#102—22no—
27#11758413—22no—
28#11758411—22no—
29C24×C31—21no—
30C23×D31D412yes—
31C2×D4×C31—21no—
32C2×D4×C31—21no—
33C2×D4×C31—21no—
34C2×D4×C31—21no—
35C2×D4×C31—21no—
36C2×D4×C31D412yescomplemented
37C22×C4×C31C2311yescharacteristic
38C2×C22⋊D31—28no—
39C2×C22⋊D31—21no—
40C2×C22⋊D31—48no—
41C22×Dic31—21no—
42#92495—21no—
43#92495—21no—
44#92495—21no—
45#92495—21no—
46C2×D124—21no—
47C2×D124—21no—
48C2×D124—21no—
49C2×D124—21no—
50C2×D124—21no—
51C2×D124—21no—
52C2×D124—24no—
53C2×D124D411yescharacteristic, complemented
54C2×C4×D31—21no—
55C2×Dic62D411yescharacteristic, complemented
56M16×C31—21no—
57M16×C31—21no—
58C2×C8×C31—21no—
59C4⋊C4×C31D412yescomplemented
60C22⋊C4×C31—21no—
61C42×C31—21no—
62#92480—24no—
63#92479—24no—
64(C2×D31)⋊C4—24no—
65C4×Dic31—21no—
66C4×Dic31D412yescomplemented
67#92474—21no—
68#92474D412yescomplemented
69C2×C31⋊C8—21no—
70C23×C31—22no—
71C23×C31—44no—
72C23×C31—41no—
73C23×C31—41no—
74C23×C31C2×D411yescharacteristic
75C22×D31—22no—
76C22×D31—21no—
77C22×D31—22no—
78C22×D31—22no—
79C22×D31—44no—
80D4×C31—22no—
81D4×C31—22no—
82D4×C31—41no—
83D4×C31—41no—
84C2×C4×C31—22no—
85C2×C4×C31C2×D411yescharacteristic
86C2×C4×C31C2×D411yescharacteristic
87C2×C4×C31C2×D411yescharacteristic
88C2×C4×C31C2×D411yescharacteristic
89C2×C4×C31C2×D411yescharacteristic
90C2×C4×C31#4111yescharacteristic
91C22⋊D31—416no—
92C22⋊D31—41no—
93C22⋊D31—41no—
94C2×Dic31—24no—
95C2×Dic31—22no—
96C2×Dic31—21no—
97D124—21no—
98D124—21no—
99D124—41no—
100D124—41no—
101D124—41no—
102D124—41no—
103D124—84no—
104C4×D31—41no—
105C4×D31—41no—
106Dic62—21no—
107Dic62—21no—
108C8×C31—41no—
109C31⋊C8—22no—
110#2002—311nomaximal, Sylow
111C22×C31—22no—
112C22×C31—44no—
113C22×C31—42no—
114C22×C31—82no—
115C22×C31—82no—
116C22×C31#12011yescharacteristic
117C22×C31#12011yescharacteristic
118C22×C31#12111yescharacteristic
119C2×D31—44no—
120C2×D31—41no—
121C2×D31—42no—
122C2×D31—42no—
123C2×D31—44no—
124C2×D31—82no—
125C4×C31—42no—
126C4×C31#12011yescharacteristic
127C4×C31#12111yescharacteristic
128C4×C31#12111yescharacteristic
129C4×C31#12711yescharacteristic
130Dic31—24no—
131Dic31—41no—
132C2×AGL(1,ℤ/8)—311no—
133#535—311no—
134C2×#127—311no—
135C2×#104—311no—
136#418D3111yescharacteristic, complemented
137C2×#100—311no—
138#339—311no—
139C2×C31—21no—
140C2×C31—21no—
141C2×C31—82no—
142C2×C31#39211yescharacteristic
143C2×C31#45312yes—
144D31—81no—
145D31—82no—
146C2×#41—311no—
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×M16C2×D3111yescharacteristic
156#127—621no—
157#127—622no—
158#127—622no—
159#124—621no—
160#121—622no—
161#120—622no—
162#117C2×D3111yescharacteristic
163C2×C42—311no—
164#104—622no—
165#102—22no—
166#100—622no—
167C31#200211yescharacteristic, complemented, Sylow
168C24—21no—
169C24—312no—
170#41—621no—
171#41—621no—
172#41—621no—
173#41—621no—
174C2×Q8—311no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—311no—
181C2×D4—624no—
182C2×D4—628no—
183C2×D4—621no—
184C2×D4—621no—
185C2×D4—621no—
186C2×D4—621no—
187C2×D4—621no—
188C2×D4—621no—
189C2×D4—621no—
190C2×D4—1248no—
191C2×D4D12412yescomplemented
192C22×C4—621no—
193C22×C4—621no—
194C22×C4C22×D3111yescharacteristic
195SD16—624no—
196D8—624no—
197M16—21no—
198M16—21no—
199M16—312no—
200M16—621no—
201C2×C8—21no—
202C2×C8—621no—
203C4⋊C4C22⋊D3112yescomplemented
204C22⋊C4—21no—
205C22⋊C4—624no—
206C42—21no—
207C42—312no—
208C42—621no—
209C23—22no—
210C23—44no—
211C23—41no—
212C23—41no—
213C23—622no—
214C23—622no—
215C23—621no—
216C23—622no—
217C23—1244no—
218C23D4×D3111yescharacteristic
219Q8—621no—
220Q8—621no—
221D4—22no—
222D4—22no—
223D4—41no—
224D4—41no—
225D4—621no—
226D4—621no—
227D4—12416no—
228D4—1241no—
229D4—1241no—
230D4—1241no—
231D4—1241no—
232D4—1241no—
233D4—1241no—
234D4—2484no—
235C2×C4—22no—
236C2×C4—624no—
237C2×C4—622no—
238C2×C4—621no—
239C2×C4—1241no—
240C2×C4—1241no—
241C2×C4C2×D12411yescharacteristic
242C2×C4#9249511yescharacteristic
243C2×C4D4×D3111yescharacteristic
244C2×C4D4×D3111yescharacteristic
245C2×C4D4×D3111yescharacteristic
246C2×C4C2×C22⋊D3111yescharacteristic
247C8—41no—
248C8—622no—
249C22—22no—
250C22—44no—
251C22—42no—
252C22—82no—
253C22—82no—
254C22—1244no—
255C22—1241no—
256C22—1242no—
257C22—1242no—
258C22—1244no—
259C22—2482no—
260C22#1175845911yescharacteristic
261C22#1175846111yescharacteristic
262C22#1175851411yescharacteristic
263C4—42no—
264C4—624no—
265C4—1241no—
266C4#1175845911yescharacteristic
267C4#1175846111yescharacteristic
268C4#1175850711yescharacteristic
269C4#1175851711yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—2482no—
274C2—2481no—
275C2#1452095811yescharacteristic
276C2#1452121512yes—
subgroupG/H
centerC22#11758514
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#418C2
socleC22×C31#120
hypercenter#418D31
hypocenterC31#2002
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#11758509C2semidirect
2. #14521618C2semidirect
3. C2×#11758517C2semidirect
4. C2×#11758413C2semidirect
5. C2×#11758411C2semidirect
6. #14520808C2semidirect
7. C31×#418C2semidirect
36. C2×D4×C31D4semidirect
53. C2×D124D4semidirect
55. C2×Dic62D4semidirect
59. C4⋊C4×C31D4semidirect
66. C4×Dic31D4semidirect
68. #92474D4semidirect
136. #418D31semidirect
167. C31#2002semidirect
191. C2×D4D124semidirect
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×#117585092
#145216182
C2×#117585172
C2×#117584132
C2×#117584112
#145208082
C31×#4182
#200231