Finite Group Databasebeta

← #16846846

Subgroups — #16846846

Order 3968.

326 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 87 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×#11758465C211yesmaximal, characteristic, complemented
2C2×#11758409C211yesmaximal, characteristic
3C2×#11758397C211yesmaximal, characteristic
4#14520950C211yesmaximal, characteristic
5#14520811C211yesmaximal, characteristic, complemented
6#14520803C211yesmaximal, characteristic, complemented
7C31×#340C211yesmaximal, characteristic, complemented
8C22×D124C2211yescharacteristic
9C22×Dic62—21no—
10C22×C8×C31C2211yescharacteristic
11C2×C4⋊C4×C31C2211yescharacteristic
12C2×C4⋊C4×C31C2211yescharacteristic
13C2×(C2×D31)⋊C4—21no—
14C2×(C2×D31)⋊C4—21no—
15C2×C4⋊Dic31C2211yescharacteristic
16C2×Dic31⋊C4—21no—
17C2×C4×Dic31C2211yescharacteristic
18C22×C31⋊C8C2211yescharacteristic
19#11758465—22no—
20#11758465—22no—
21#11758409—22no—
22#11758397—22no—
23C23×D31—21no—
24C22×C4×C31—21no—
25C22×C4×C31—21no—
26C22×C4×C31C2311yescharacteristic
27C22×Dic31—21no—
28C22×Dic31D411yescharacteristic
29C22×Dic31D411yescharacteristic
30C2×D124—21no—
31C2×D124—21no—
32C2×D124—21no—
33C2×D124—21no—
34C2×D124—21no—
35C2×D124Q812yescomplemented
36C2×Dic62—24no—
37C2×Dic62—42no—
38C2×Dic62—42no—
39C2×C8×C31—21no—
40C2×C8×C31—21no—
41C2×C8×C31—21no—
42C4⋊C4×C31—21no—
43C4⋊C4×C31—21no—
44C4⋊C4×C31—21no—
45C4⋊C4×C31D412yes—
46(C2×D31)⋊C4—42no—
47(C2×D31)⋊C4—42no—
48C4⋊Dic31—21no—
49C4⋊Dic31D412yes—
50Dic31⋊C4—24no—
51C4×Dic31—21no—
52C4×Dic31—21no—
53C2×C31⋊C8—21no—
54C2×C31⋊C8—21no—
55C2×C31⋊C8—21no—
56C23×C31C2×D411yescharacteristic
57C22×D31—22no—
58C22×D31—41no—
59C22×D31—41no—
60C22×D31—41no—
61C22×D31—41no—
62C22×D31—41no—
63C22×D31—41no—
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×C31C2×D411yescharacteristic
71C2×C4×C31C2×D411yescharacteristic
72C2×C4×C31C2×Q811yescharacteristic
73C2×C4×C31#4111yescharacteristic
74C2×C4×C31#4111yescharacteristic
75C2×C4×C31#4111yescharacteristic
76C2×Dic31—21no—
77C2×Dic31—21no—
78C2×Dic31—21no—
79C2×Dic31—21no—
80C2×Dic31—22no—
81C2×Dic31—41no—
82C2×Dic31—41no—
83C2×Dic31D812yes—
84C2×Dic31SD1612yes—
85D124—22no—
86D124—22no—
87D124—41no—
88D124—41no—
89Dic62—48no—
90C8×C31—41no—
91C31⋊C8—41no—
92#2023—311nomaximal, Sylow
93C22×C31#12011yescharacteristic
94C22×C31C22⋊Q811yescharacteristic
95C22×C31#12411yescharacteristic
96C22×C31C2×D811yescharacteristic
97C22×C31C2×SD1611yescharacteristic
98C22×C31AGL(1,ℤ/8)11yescharacteristic
99C22×C31#13711yescharacteristic
100C2×D31—42no—
101C2×D31—42no—
102C2×D31—42no—
103C2×D31—81no—
104C2×D31—81no—
105C2×D31—81no—
106C2×D31—81no—
107C4×C31—42no—
108C4×C31—81no—
109C4×C31C22⋊Q811yescharacteristic
110C4×C31C22⋊Q811yescharacteristic
111C4×C31#12411yescharacteristic
112C4×C31#12411yescharacteristic
113Dic31—22no—
114Dic31—22no—
115Dic31—42no—
116C2×C4⋊Q8—311no—
117C2×#102—311no—
118C2×#102—311no—
119#390—311no—
120#340—311no—
121#340D3111yescharacteristic, complemented
122#336—311no—
123C2×C31#39311yescharacteristic
124C2×C31#44711yescharacteristic
125C2×C31#44811yescharacteristic
126C2×C31#47411yescharacteristic
127C2×C31#47611yescharacteristic
128C2×C31#48611yescharacteristic
129C2×C31#48911yescharacteristic
130D31—82no—
131C22×Q8—621no—
132C22×D4—311no—
133C22×C8—311no—
134C22×C8C2×D3111yescharacteristic
135C4⋊Q8—622no—
136C4⋊Q8—622no—
137C2×C4⋊C4—311no—
138C2×C4⋊C4—621no—
139C2×C4⋊C4C2×D3111yescharacteristic
140C2×C4⋊C4C2×D3111yescharacteristic
141C2×C22⋊C4—621no—
142C2×C22⋊C4—621no—
143C2×C42—311no—
144#102—622no—
145#102—622no—
146C31#202311yescharacteristic, complemented, Sylow
147C24—621no—
148C2×Q8—624no—
149C2×Q8—1242no—
150C2×Q8—1242no—
151C2×D4—312no—
152C2×D4—621no—
153C2×D4—621no—
154C2×D4—621no—
155C2×D4—621no—
156C2×D4—621no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—311no—
160C22×C4—311no—
161C22×C4—621no—
162C22×C4C22×D3111yescharacteristic
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—621no—
167C2×C8—621no—
168C2×C8—621no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—312no—
173C4⋊C4—624no—
174C4⋊C4—621no—
175C4⋊C4D12412yes—
176C22⋊C4—1242no—
177C22⋊C4—1242no—
178C42—621no—
179C42—621no—
180C23—622no—
181C23—1241no—
182C23—1241no—
183C23—1241no—
184C23—1241no—
185C23—1241no—
186C23—1241no—
187C23D4×D3111yescharacteristic
188Q8—1248no—
189D4—622no—
190D4—622no—
191D4—1241no—
192D4—1241no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—312no—
200C2×C4—312no—
201C2×C4—621no—
202C2×C4—621no—
203C2×C4—621no—
204C2×C4—621no—
205C2×C4—622no—
206C2×C4—1241no—
207C2×C4—1241no—
208C2×C4C2×D12411yescharacteristic
209C2×C4#9249511yescharacteristic
210C2×C4#9249511yescharacteristic
211C2×C4D4×D3111yescharacteristic
212C2×C4#9249711yescharacteristic
213C2×C4Q8×D3111yescharacteristic
214C8—41no—
215C8—1241no—
216C22—1242no—
217C22—1242no—
218C22—1242no—
219C22—2481no—
220C22—2481no—
221C22—2481no—
222C22—2481no—
223C22#1175845911yescharacteristic
224C22#1175846211yescharacteristic
225C22#1175847311yescharacteristic
226C22D8×D3111yescharacteristic
227C22SD16×D3111yescharacteristic
228C22#1175849111yescharacteristic
229C22#1175849511yescharacteristic
230C4—42no—
231C4—81no—
232C4—622no—
233C4—622no—
234C4—1242no—
235C4#1175845211yescharacteristic
236C4#1175846211yescharacteristic
237C4#1175847311yescharacteristic
238C4#1175847411yescharacteristic
239C2—2482no—
240C2#1452096211yescharacteristic
241C2#1452118411yescharacteristic
242C2#1452118911yescharacteristic
243C2#1452132811yescharacteristic
244C2#1452133811yescharacteristic
245C2#1452139411yescharacteristic
246C2#1452141011yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#340C2
socleC23×C31C2×D4
prime radicalC22×D124C22
hypercenter#340D31
hypocenterC31#2023
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
1. C2×#11758465C2semidirect
5. #14520811C2semidirect
6. #14520803C2semidirect
7. C31×#340C2semidirect
35. C2×D124Q8semidirect
121. #340D31semidirect
146. C31#2023semidirect

Maximal subgroups

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

subgroupindex
C2×#117584652
C2×#117584092
C2×#117583972
#145209502
#145208112
#145208032
C31×#3402
#202331