Finite Group Databasebeta

← #16845902

Subgroups — #16845902

Order 3968.

360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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×C4⋊C4×D31C211yesmaximal, characteristic
2C2×#11758396C211yesmaximal, characteristic, complemented
3C2×(C2×D31)⋊C8C211yesmaximal, characteristic
4#14520906C211yesmaximal, characteristic
5#14520812C211yesmaximal, characteristic, complemented
6#14520811C211yesmaximal, characteristic, complemented
7C2×C31×#106C211yesmaximal, characteristic, complemented
8C22×C4×D31—21no—
9C22×C4×D31C2211yescharacteristic
10C22×C8×C31C2211yescharacteristic
11C2×C4⋊C4×C31C2211yescharacteristic
12C2×C4⋊C4×C31C2211yescharacteristic
13C2×(C2×D31)⋊C4—21no—
14C2×C4⋊Dic31C2211yescharacteristic
15C2×C4⋊Dic31C2211yescharacteristic
16C2×Dic31⋊C4—21no—
17C22×C31⋊C8C2211yescharacteristic
18C4⋊C4×D31—22no—
19C4⋊C4×D31—22no—
20C31×#106—22no—
21C31⋊#95—21no—
22(C2×D31)⋊C8C414yescomplemented
23#11758396—22no—
24C23×D31D411yescharacteristic
25C22×C4×C31—21no—
26C22×C4×C31—21no—
27C22×C4×C31C2311yescharacteristic
28C22×Dic31—21no—
29C22×Dic31—21no—
30C22×Dic31D411yescharacteristic
31C2×C4×D31—21no—
32C2×C4×D31—21no—
33C2×C4×D31—21no—
34C2×C4×D31—21no—
35C2×C4×D31—24no—
36C2×C4×D31—42no—
37C2×C4×D31—42no—
38C2×C4×D31C2×C412yes—
39C2×C4×D31Q812yes—
40C2×C8×C31—21no—
41C2×C8×C31—21no—
42C2×C8×C31C2×C412yescomplemented
43C4⋊C4×C31—21no—
44C4⋊C4×C31—21no—
45C4⋊C4×C31—21no—
46C4⋊C4×C31D412yes—
47(C2×D31)⋊C4—42no—
48C4⋊Dic31—21no—
49C4⋊Dic31—21no—
50C4⋊Dic31—21no—
51C4⋊Dic31D412yes—
52Dic31⋊C4—24no—
53C2×C31⋊C8—21no—
54C2×C31⋊C8—21no—
55C2×C31⋊C8C2×C412yescomplemented
56C23×C31C2×D411yescharacteristic
57C22×D31—21no—
58C22×D31—21no—
59C22×D31—21no—
60C22×D31—21no—
61C22×D31C4⋊C412yes—
62C22×D31SD1612yes—
63C22×D31SD1612yes—
64C2×C4×C31—22no—
65C2×C4×C31—41no—
66C2×C4×C31—41no—
67C2×C4×C31—41no—
68C2×C4×C31—41no—
69C2×C4×C31—41no—
70C2×C4×C31C22×C411yescharacteristic
71C2×C4×C31C2×D411yescharacteristic
72C2×C4×C31C2×D411yescharacteristic
73C2×C4×C31C2×Q811yescharacteristic
74C2×C4×C31#4111yescharacteristic
75C2×C4×C31#4111yescharacteristic
76C2×Dic31—21no—
77C2×Dic31—21no—
78C2×Dic31—22no—
79C2×Dic31—41no—
80C2×Dic31—41no—
81C2×Dic31—41no—
82C2×Dic31—41no—
83C2×Dic31—41no—
84C2×Dic31C4⋊C412yes—
85C4×D31—22no—
86C4×D31—22no—
87C4×D31—22no—
88C4×D31—22no—
89C4×D31—48no—
90C8×C31—22no—
91C31⋊C8—22no—
92#1853—311nomaximal, Sylow
93C22×C31C2×C4⋊C411yescharacteristic
94C22×C31#12011yescharacteristic
95C22×C31#12311yescharacteristic
96C22×C31C2×SD1611yescharacteristic
97C22×C31C2×SD1611yescharacteristic
98C22×C31AGL(1,ℤ/8)11yescharacteristic
99C22×C31#13711yescharacteristic
100C2×D31—22no—
101C2×D31—22no—
102C2×D31—22no—
103C2×D31—22no—
104C2×D31—22no—
105C2×D31—22no—
106C2×D31#10614yescomplemented
107C4×C31—42no—
108C4×C31—81no—
109C4×C31C4×D411yescharacteristic
110C4×C31C4×D411yescharacteristic
111C4×C31C22⋊Q811yescharacteristic
112C4×C31C22⋊Q811yescharacteristic
113Dic31—22no—
114Dic31—42no—
115Dic31—81no—
116C22×C4⋊C4—311no—
117C2×#106—311no—
118C2×#106D3111yescharacteristic, complemented
119C2×C22⋊C8—311no—
120#380—311no—
121#340—311no—
122#340—311no—
123C2×C31#38511yescharacteristic
124C2×C31C2×#10611yescharacteristic
125C2×C31#42811yescharacteristic
126C2×C31#44811yescharacteristic
127C2×C31#45011yescharacteristic
128C2×C31#48111yescharacteristic
129C2×C31#48311yescharacteristic
130D31—24no—
131C23×C4—311no—
132C23×C4—621no—
133C22×C8—311no—
134C22×C8C2×D3111yescharacteristic
135C2×C4⋊C4—311no—
136C2×C4⋊C4—311no—
137C2×C4⋊C4—622no—
138C2×C4⋊C4—621no—
139C2×C4⋊C4—622no—
140C2×C4⋊C4C2×D3111yescharacteristic
141C2×C4⋊C4C2×D3111yescharacteristic
142C2×C22⋊C4—621no—
143#106—22no—
144#106—622no—
145C22⋊C8—314no—
146#95—621no—
147C31#185311yescharacteristic, complemented, Sylow
148C24—311no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—311no—
152C22×C4—312no—
153C22×C4—312no—
154C22×C4—624no—
155C22×C4—621no—
156C22×C4—621no—
157C22×C4—621no—
158C22×C4—621no—
159C22×C4—621no—
160C22×C4—621no—
161C22×C4—1242no—
162C22×C4—1242no—
163C22×C4C22×D3111yescharacteristic
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—312no—
167C2×C8—621no—
168C2×C8—621no—
169C2×C8C4×D3112yescomplemented
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—312no—
174C4⋊C4—624no—
175C4⋊C4—621no—
176C4⋊C4—621no—
177C4⋊C4—621no—
178C4⋊C4C22⋊D3112yes—
179C22⋊C4—1242no—
180C23—312no—
181C23—312no—
182C23—312no—
183C23—621no—
184C23—621no—
185C23—621no—
186C23—621no—
187C23D4×D3111yescharacteristic
188C2×C4—22no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—312no—
195C2×C4—621no—
196C2×C4—621no—
197C2×C4—622no—
198C2×C4—622no—
199C2×C4—622no—
200C2×C4—622no—
201C2×C4—622no—
202C2×C4—1248no—
203C2×C4—1241no—
204C2×C4—1241no—
205C2×C4—1241no—
206C2×C4—1241no—
207C2×C4—1241no—
208C2×C4C2×C4×D3111yescharacteristic
209C2×C4#9249511yescharacteristic
210C2×C4D4×D3111yescharacteristic
211C2×C4Q8×D3111yescharacteristic
212C2×C4#9249911yescharacteristic
213C2×C4C2×C22⋊D3111yescharacteristic
214C8—22no—
215C8—622no—
216C22—314no—
217C22—622no—
218C22—622no—
219C22—622no—
220C22—622no—
221C22—622no—
222C22—622no—
223C22C4⋊C4×D3111yescharacteristic
224C22#1175847111yescharacteristic
225C22SD16×D3111yescharacteristic
226C22SD16×D3111yescharacteristic
227C22#1175849111yescharacteristic
228C22#1175849211yescharacteristic
229C22#1175851411yescharacteristic
230C4—42no—
231C4—81no—
232C4—622no—
233C4—1242no—
234C4—2481no—
235C4#1175847011yescharacteristic
236C4#1175847311yescharacteristic
237C4C4×C22⋊D3111yescharacteristic
238C4#1175852311yescharacteristic
239C2—624no—
240C2#1452092011yescharacteristic
241C2#106×D3111yescharacteristic
242C2#1452108811yescharacteristic
243C2#1452118611yescharacteristic
244C2#1452119811yescharacteristic
245C2#1452136911yescharacteristic
246C2#1452138111yescharacteristic
subgroupG/H
centerC23D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×#106C2
socleC23×C31C2×D4
prime radicalC23×D31D4
cosocleC22×C4×C31C23
hypercenterC2×#106D31
hypocenterC31#1853
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×#11758396C2semidirect
5. #14520812C2semidirect
6. #14520811C2semidirect
7. C2×C31×#106C2semidirect
22. (C2×D31)⋊C8C4semidirect
42. C2×C8×C31C2×C4semidirect
55. C2×C31⋊C8C2×C4semidirect
106. C2×D31#106semidirect
118. C2×#106D31semidirect
147. C31#1853semidirect
169. C2×C8C4×D31semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D312
C2×#117583962
C2×(C2×D31)⋊C82
#145209062
#145208122
#145208112
C2×C31×#1062
#185331