Finite Group Databasebeta

← #16846063

Subgroups — #16846063

Order 3968.

374 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#92480C211yesmaximal, characteristic
2C2×#11758464C211yesmaximal, characteristic, complemented
3C2×#11758404C211yesmaximal, characteristic, complemented
4#14520952C211yesmaximal, characteristic
5#14520811C211yesmaximal, characteristic, complemented
6#14520803C211yesmaximal, characteristic, complemented
7C2×C31×#102C211yesmaximal, characteristic
8C22×D4×C31C2211yescharacteristic
9C22×Dic62C2211yescharacteristic
10C22×C8×C31C2211yescharacteristic
11C2×C4⋊C4×C31C2211yescharacteristic
12C2×C22⋊Dic31—21no—
13C2×C22⋊Dic31—21no—
14C2×#92480—22no—
15C2×#92480—22no—
16C2×#92480C414yescomplemented
17C2×C4⋊Dic31C2211yescharacteristic
18C2×Dic31⋊C4—21no—
19C2×C4×Dic31—21no—
20C2×C4×Dic31C2211yescharacteristic
21C22×C31⋊C8C2211yescharacteristic
22#11758464—22no—
23#11758464—22no—
24C31×#102—22no—
25#11758404—22no—
26C24×C31—21no—
27C2×D4×C31—21no—
28C2×D4×C31—21no—
29C2×D4×C31—21no—
30C2×D4×C31—21no—
31C2×D4×C31—21no—
32C2×D4×C31C2×C412yes—
33C22×C4×C31—21no—
34C22×C4×C31C2311yescharacteristic
35C22×Dic31—21no—
36C22×Dic31—21no—
37C22×Dic31D411yescharacteristic
38C22×Dic31D411yescharacteristic
39C2×Dic62—21no—
40C2×Dic62—21no—
41C2×Dic62—21no—
42C2×Dic62C2×C412yes—
43C2×Dic62D412yes—
44C2×Dic62D412yes—
45C2×C8×C31—21no—
46C2×C8×C31—21no—
47C2×C8×C31—21no—
48C4⋊C4×C31—21no—
49C4⋊C4×C31D412yes—
50C22⋊Dic31—42no—
51C22⋊Dic31—42no—
52#92480—28no—
53C4⋊Dic31—21no—
54C4⋊Dic31—21no—
55Dic31⋊C4—24no—
56C4×Dic31—24no—
57C4×Dic31—21no—
58C4×Dic31—21no—
59C2×C31⋊C8—21no—
60C2×C31⋊C8—21no—
61C2×C31⋊C8C2×C412yes—
62C23×C31—22no—
63C23×C31—41no—
64C23×C31—41no—
65C23×C31—41no—
66C23×C31—41no—
67C23×C31—41no—
68C23×C31—41no—
69C23×C31C2×D411yescharacteristic
70D4×C31—22no—
71D4×C31—22no—
72D4×C31—41no—
73D4×C31—41no—
74C2×C4×C31—22no—
75C2×C4×C31—41no—
76C2×C4×C31—41no—
77C2×C4×C31C22×C411yescharacteristic
78C2×C4×C31C2×D411yescharacteristic
79C2×C4×C31C2×D411yescharacteristic
80C2×C4×C31C2×D411yescharacteristic
81C2×C4×C31#4111yescharacteristic
82C2×C4×C31#4111yescharacteristic
83C2×Dic31—22no—
84C2×Dic31—21no—
85C2×Dic31—22no—
86C2×Dic31—22no—
87C2×Dic31—21no—
88C2×Dic31—21no—
89C2×Dic31—21no—
90C2×Dic31—21no—
91C2×Dic31—41no—
92C2×Dic31—41no—
93C2×Dic31—41no—
94C2×Dic31SD1612yescomplemented
95Dic62—22no—
96Dic62—22no—
97Dic62—22no—
98Dic62C22⋊C414yescomplemented
99C8×C31—41no—
100C31⋊C8—22no—
101#1880—311nomaximal, Sylow
102C22×C31—42no—
103C22×C31—42no—
104C22×C31—42no—
105C22×C31—81no—
106C22×C31—81no—
107C22×C31—81no—
108C22×C31—81no—
109C22×C31C4×D411yescharacteristic
110C22×C31#12011yescharacteristic
111C22×C31#12111yescharacteristic
112C22×C31C2×SD1611yescharacteristic
113C22×C31#13511yescharacteristic
114C22×C31AGL(1,ℤ/8)11yescharacteristic
115C22×C31#13711yescharacteristic
116C4×C31—42no—
117C4×C31C2×C22⋊C411yescharacteristic
118C4×C31C4×D411yescharacteristic
119C4×C31#12111yescharacteristic
120C4×C31#12311yescharacteristic
121Dic31—24no—
122Dic31—22no—
123Dic31—41no—
124Dic31—81no—
125C22×SD16—311no—
126C2×C4×Q8—311no—
127C2×#103—311no—
128C2×#102D3111yescharacteristic
129#390—311no—
130#340—311no—
131#336—311no—
132C2×C31—82no—
133C2×C31#38611yescharacteristic
134C2×C31C4×SD1611yescharacteristic
135C2×C31#44011yescharacteristic
136C2×C31#44811yescharacteristic
137C2×C31#44911yescharacteristic
138C2×C31#46011yescharacteristic
139C2×C31#46411yescharacteristic
140C22×Q8—311no—
141C22×D4C2×D3111yescharacteristic
142C2×SD16—314no—
143C2×SD16—622no—
144C2×SD16—622no—
145C22×C8—311no—
146C22×C8C2×D3111yescharacteristic
147C4×Q8—622no—
148C4×Q8—622no—
149C2×C4⋊C4—311no—
150C2×C4⋊C4—621no—
151C2×C4⋊C4C2×D3111yescharacteristic
152C2×C22⋊C4—621no—
153C2×C22⋊C4—621no—
154C2×C42—311no—
155C2×C42—621no—
156#103—622no—
157#102—22no—
158C31#188011yescharacteristic, complemented, Sylow
159C24—21no—
160C2×Q8—312no—
161C2×Q8—312no—
162C2×Q8—312no—
163C2×Q8—621no—
164C2×Q8—621no—
165C2×Q8—621no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4C4×D3112yes—
172C22×C4—21no—
173C22×C4—311no—
174C22×C4—311no—
175C22×C4—621no—
176C22×C4—621no—
177C22×C4C22×D3111yescharacteristic
178SD16—628no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—312no—
183C2×C8—621no—
184C2×C8—621no—
185C4⋊C4—21no—
186C4⋊C4—624no—
187C4⋊C4—621no—
188C4⋊C4—621no—
189C4⋊C4C22⋊D3112yes—
190C22⋊C4—1242no—
191C22⋊C4—1242no—
192C42—624no—
193C42—621no—
194C42—621no—
195C23—22no—
196C23—41no—
197C23—41no—
198C23—41no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23D4×D3111yescharacteristic
203Q8—314no—
204Q8—622no—
205Q8—622no—
206Q8—622no—
207D4—22no—
208D4—22no—
209D4—41no—
210D4—41no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—312no—
215C2×C4—622no—
216C2×C4—622no—
217C2×C4—621no—
218C2×C4—621no—
219C2×C4—622no—
220C2×C4—621no—
221C2×C4—621no—
222C2×C4—621no—
223C2×C4—1241no—
224C2×C4—1241no—
225C2×C4—1241no—
226C2×C4C2×C4×D3111yescharacteristic
227C2×C4#9249511yescharacteristic
228C2×C4D4×D3111yescharacteristic
229C2×C4D4×D3111yescharacteristic
230C2×C4#9249711yescharacteristic
231C2×C4C2×C22⋊D3111yescharacteristic
232C8—41no—
233C8—622no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—81no—
238C22—81no—
239C22—81no—
240C22—81no—
241C22(C22⋊D31)⋊C411yescharacteristic
242C22#1175846111yescharacteristic
243C22#1175848811yescharacteristic
244C22#1175848911yescharacteristic
245C22SD16×D3111yescharacteristic
246C22#1175849211yescharacteristic
247C22#1175851411yescharacteristic
248C4—42no—
249C4—624no—
250C4—622no—
251C4—1241no—
252C4—2481no—
253C4C22⋊C4×D3111yescharacteristic
254C4#1175846011yescharacteristic
255C4C4×C22⋊D3111yescharacteristic
256C4#1175851511yescharacteristic
257C2—82no—
258C2#1452092511yescharacteristic
259C2#1452114011yescharacteristic
260C2#1452114611yescharacteristic
261C2#1452118611yescharacteristic
262C2#1452119111yescharacteristic
263C2#1452124811yescharacteristic
264C2#1452127011yescharacteristic
subgroupG/H
centerC23D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×#102C2
socleC23×C31C2×D4
prime radicalC22×D4×C31C22
cosocleC22×C4×C31C23
hypercenterC2×#102D31
hypocenterC31#1880
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#11758464C2semidirect
3. C2×#11758404C2semidirect
5. #14520811C2semidirect
6. #14520803C2semidirect
16. C2×#92480C4semidirect
94. C2×Dic31SD16semidirect
98. Dic62C22⋊C4semidirect
158. C31#1880semidirect

Maximal subgroups

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

subgroupindex
C22×#924802
C2×#117584642
C2×#117584042
#145209522
#145208112
#145208032
C2×C31×#1022
#188031