Finite Group Databasebeta

← #16845939

Subgroups — #16845939

Order 3968.

302 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 97 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#14521532C211yesmaximal, characteristic
2#14521091C211yesmaximal, characteristic, complemented
3#14521050C211yesmaximal, characteristic
4#14520919C211yesmaximal, characteristic, complemented
5#14520817C211yesmaximal, characteristic, complemented
6#14520809C211yesmaximal, characteristic, complemented
7C2×C31×#104C211yesmaximal, characteristic
8C2×#41×C31C2211yescharacteristic
9C2×M16×C31C2211yescharacteristic
10C2×C42×C31C2211yescharacteristic
11Q8×Dic31—21no—
12D4×Dic31—21no—
13D4×Dic31—22no—
14#11758503—21no—
15#11758503C2211yescharacteristic
16C2×C4⋊Dic31—21no—
17C2×C4⋊Dic31—22no—
18C2×C4⋊Dic31C2211yescharacteristic
19C2×C4⋊Dic31C2211yescharacteristic
20C2×#92474C2211yescharacteristic
21C31×#104C414yescomplemented
22#11758423—21no—
23#11758420—21no—
24#11758406—21no—
25#11758405—21no—
26#41×C31—21no—
27#41×C31—21no—
28#41×C31C2×C412yes—
29#41×C31Q812yes—
30C2×Q8×C31D411yescharacteristic
31C2×D4×C31—21no—
32C2×D4×C31D411yescharacteristic
33C22×C4×C31—21no—
34C22×C4×C31—21no—
35C22×C4×C31C2311yescharacteristic
36C22×Dic31—22no—
37C22×Dic31—21no—
38C22×Dic31D412yes—
39M16×C31—21no—
40M16×C31C2×C412yescomplemented
41C2×C8×C31—21no—
42C42×C31—21no—
43C42×C31C2×C412yescomplemented
44C22⋊Dic31—22no—
45C22⋊Dic31—21no—
46C4⋊Dic31—22no—
47C4⋊Dic31—21no—
48C4⋊Dic31—21no—
49C4⋊Dic31—21no—
50C4⋊Dic31—21no—
51C4⋊Dic31—44no—
52C4⋊Dic31D411yescharacteristic
53C4⋊Dic31D411yescharacteristic
54C4×Dic31—22no—
55C4×Dic31—21no—
56#92474—21no—
57#92474—21no—
58C2×C31⋊C8—21no—
59C23×C31—21no—
60C23×C31C2×D411yescharacteristic
61Q8×C31—21no—
62Q8×C31C4⋊C412yescomplemented
63D4×C31—22no—
64D4×C31—22no—
65D4×C31—21no—
66D4×C31C4⋊C412yescomplemented
67C2×C4×C31—22no—
68C2×C4×C31—22no—
69C2×C4×C31—22no—
70C2×C4×C31—21no—
71C2×C4×C31—22no—
72C2×C4×C31—22no—
73C2×C4×C31C22×C411yescharacteristic
74C2×C4×C31C2×D411yescharacteristic
75C2×C4×C31C2×D411yescharacteristic
76C2×C4×C31C2×Q811yescharacteristic
77C2×C4×C31#4111yescharacteristic
78C2×C4×C31#4111yescharacteristic
79C2×Dic31—21no—
80C2×Dic31—22no—
81C2×Dic31—21no—
82C2×Dic31—42no—
83C2×Dic31—42no—
84C2×Dic31—41no—
85C2×Dic31—82no—
86C8×C31—22no—
87C31⋊C8—41no—
88#1859—311nomaximal, Sylow
89C22×C31—21no—
90C22×C31—21no—
91C22×C31—22no—
92C22×C31—41no—
93C22×C31—41no—
94C22×C31C4×D411yescharacteristic
95C22×C31#12011yescharacteristic
96C22×C31C22⋊Q811yescharacteristic
97C4×C31—24no—
98C4×C31—22no—
99C4×C31C2×C4⋊C411yescharacteristic
100C4×C31C4×D411yescharacteristic
101C4×C31C22⋊Q811yescharacteristic
102C4×C31#12311yescharacteristic
103Dic31—42no—
104Dic31—41no—
105Dic31—41no—
106Dic31—81no—
107#520—311no—
108#428—311no—
109C2×#104D3111yescharacteristic
110#417—311no—
111#384—311no—
112#343—311no—
113#339—311no—
114C2×C31—21no—
115C2×C31—21no—
116C2×C31—42no—
117C2×C31#38511yescharacteristic
118C2×C31#45311yescharacteristic
119C2×C31#45611yescharacteristic
120C2×#41C2×D3111yescharacteristic
121C2×M16—311no—
122C2×M16C2×D3111yescharacteristic
123C4×Q8—621no—
124C4×D4—622no—
125C4×D4—621no—
126#117—311no—
127#117—621no—
128C2×C4⋊C4—311no—
129C2×C4⋊C4—311no—
130C2×C4⋊C4—621no—
131C2×C4⋊C4—622no—
132C2×C42C2×D3111yescharacteristic
133#107—621no—
134#106—621no—
135#104Dic3114yescomplemented
136#103—621no—
137#102—621no—
138C31#185911yescharacteristic, complemented, Sylow
139#41—21no—
140#41—21no—
141#41Dic6212yes—
142#41C2×Dic3112yes—
143C2×Q8D12411yescharacteristic
144C2×D4—21no—
145C2×D4D12411yescharacteristic
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—312no—
149C22×C4—622no—
150C22×C4—621no—
151C22×C4C22×D3111yescharacteristic
152M16—21no—
153M16—621no—
154M16—621no—
155M16C2×Dic3112yescomplemented
156C2×C8—21no—
157C2×C8—621no—
158C4⋊C4—311no—
159C4⋊C4—311no—
160C4⋊C4—622no—
161C4⋊C4—621no—
162C4⋊C4—621no—
163C4⋊C4—621no—
164C4⋊C4—621no—
165C4⋊C4—1244no—
166C22⋊C4—622no—
167C22⋊C4—621no—
168C42—21no—
169C42—622no—
170C42—621no—
171C42C2×Dic3112yescomplemented
172C23—21no—
173C23D4×D3111yescharacteristic
174Q8—21no—
175Q8C4⋊Dic3112yescomplemented
176D4—22no—
177D4—22no—
178D4—21no—
179D4C4⋊Dic3112yescomplemented
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—621no—
187C2×C4—621no—
188C2×C4—622no—
189C2×C4—1242no—
190C2×C4—1242no—
191C2×C4—1241no—
192C2×C4—2482no—
193C2×C4C2×Dic6211yescharacteristic
194C2×C4C2×D12411yescharacteristic
195C2×C4D4×D3111yescharacteristic
196C2×C4#9249711yescharacteristic
197C2×C4#9249711yescharacteristic
198C2×C4C22×Dic3111yescharacteristic
199C8—22no—
200C8—1241no—
201C22—21no—
202C22—21no—
203C22—22no—
204C22—41no—
205C22—41no—
206C22#1175845511yescharacteristic
207C22#1175845911yescharacteristic
208C22D4×Dic3111yescharacteristic
209C4—24no—
210C4—22no—
211C4—1242no—
212C4—1241no—
213C4—1241no—
214C4—2481no—
215C4#1175845511yescharacteristic
216C4#1175846311yescharacteristic
217C4C2×C4⋊Dic3111yescharacteristic
218C4D4×Dic3111yescharacteristic
219C2—21no—
220C2—21no—
221C2—42no—
222C2#1452092411yescharacteristic
223C2#1452121811yescharacteristic
224C2#1452123311yescharacteristic
subgroupG/H
centerC22#11758459
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×#104C2
socleC22×C31#120
prime radicalC2×#41×C31C22
cosocleC22×C4×C31C23
hypercenterC2×#104D31
hypocenterC31#1859
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #14521091C2semidirect
4. #14520919C2semidirect
5. #14520817C2semidirect
6. #14520809C2semidirect
21. C31×#104C4semidirect
40. M16×C31C2×C4semidirect
43. C42×C31C2×C4semidirect
62. Q8×C31C4⋊C4semidirect
66. D4×C31C4⋊C4semidirect
135. #104Dic31semidirect
138. C31#1859semidirect
155. M16C2×Dic31semidirect
171. C42C2×Dic31semidirect
175. Q8C4⋊Dic31semidirect
179. D4C4⋊Dic31semidirect

Maximal subgroups

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

subgroupindex
#145215322
#145210912
#145210502
#145209192
#145208172
#145208092
C2×C31×#1042
#185931