Finite Group Databasebeta

← #16846227

Subgroups — #16846227

Order 3968.

312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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×#11758486C211yesmaximal, characteristic
2C2×#11758484C211yesmaximal, characteristic
3#14521048C211yesmaximal, characteristic
4C2×#11758398C211yesmaximal, characteristic, complemented
5C2×#11758412C211yesmaximal, characteristic, complemented
6#14520813C211yesmaximal, characteristic, complemented
7C31×#343C211yesmaximal, characteristic, complemented
8C2×#92495C2211yescharacteristic
9C22×Dic62C2211yescharacteristic
10C2×M16×C31C2211yescharacteristic
11C2×M16×C31C2211yescharacteristic
12C2×C4⋊C4×C31C2211yescharacteristic
13C2×#92474C2211yescharacteristic
14C22×C31⋊C8C2211yescharacteristic
15#11758486—22no—
16#11758486C414yescomplemented
17#11758484—22no—
18#11758484—22no—
19C2×Dic124—21no—
20C2×#92470—21no—
21C2×#92469—21no—
22C2×C8×D31—21no—
23#11758412—22no—
24#11758398—21no—
25#11758398—21no—
26#11758398—21no—
27#11758397—21no—
28C22×C4×C31—21no—
29C22×C4×C31C2311yescharacteristic
30C2×C22⋊D31—21no—
31C22×Dic31—21no—
32#92495—21no—
33#92495—21no—
34#92495C2×C412yes—
35#92495D412yes—
36C2×D124D411yescharacteristic
37C2×C4×D31—21no—
38C2×Dic62—21no—
39C2×Dic62—21no—
40C2×Dic62—21no—
41C2×Dic62—21no—
42C2×Dic62—21no—
43C2×Dic62C2×C412yes—
44C2×Dic62D411yescharacteristic
45M16×C31—21no—
46M16×C31—21no—
47M16×C31C2×C412yes—
48M16×C31D412yes—
49C2×C8×C31—21no—
50C2×C8×C31—21no—
51C4⋊C4×C31—21no—
52C4⋊C4×C31—21no—
53#92474—21no—
54#92474—21no—
55C2×C31⋊C8—21no—
56C2×C31⋊C8—21no—
57C2×C31⋊C8—21no—
58C2×C31⋊C8D411yescharacteristic
59C2×C31⋊C8D411yescharacteristic
60Dic124—24no—
61#92470—24no—
62#92469—24no—
63C8×D31—24no—
64C23×C31#4111yescharacteristic
65C22×D31—21no—
66C2×C4×C31—41no—
67C2×C4×C31—81no—
68C2×C4×C31C22×C411yescharacteristic
69C2×C4×C31C2×D411yescharacteristic
70C2×C4×C31C2×D411yescharacteristic
71C2×C4×C31C2×D411yescharacteristic
72C2×C4×C31C2×D411yescharacteristic
73C2×C4×C31#4111yescharacteristic
74C22⋊D31—22no—
75C22⋊D31—22no—
76C2×Dic31—21no—
77C2×Dic31—22no—
78C2×Dic31—41no—
79C2×Dic31—41no—
80D124—21no—
81D124C22⋊C412yes—
82C4×D31—22no—
83C4×D31—22no—
84Dic62—21no—
85Dic62—22no—
86Dic62—22no—
87Dic62—41no—
88Dic62—41no—
89Dic62C22⋊C412yes—
90C8×C31—22no—
91C8×C31—22no—
92C31⋊C8—21no—
93C31⋊C8—21no—
94C31⋊C8—41no—
95#1908—311nomaximal, Sylow
96C22×C31—21no—
97C22×C31—21no—
98C22×C31C4×D411yescharacteristic
99C22×C31#12111yescharacteristic
100C22×C31#12311yescharacteristic
101C2×D31—22no—
102C2×D31—41no—
103C2×D31—41no—
104C4×C31—81no—
105C4×C31C2×C22⋊C411yescharacteristic
106C4×C31C4×D411yescharacteristic
107C4×C31#12011yescharacteristic
108C4×C31#12111yescharacteristic
109Dic31—22no—
110Dic31—42no—
111C2×#137—311no—
112C2×#131—311no—
113#417—311no—
114C2×#103—311no—
115C2×#101—311no—
116#343D3111yescharacteristic, complemented
117#341—311no—
118C2×C31—21no—
119C2×C31—21no—
120C2×C31#38611yescharacteristic
121C2×C31#47111yescharacteristic
122C2×C31#47311yescharacteristic
123D31—42no—
124C2×#41—311no—
125C22×Q8—311no—
126#137—314no—
127#137—622no—
128C2×Q16—621no—
129C2×SD16—621no—
130#131—622no—
131#131—622no—
132C2×M16—311no—
133C2×M16—621no—
134C2×M16C2×D3111yescharacteristic
135C2×M16C2×D3111yescharacteristic
136C22×C8—311no—
137C22×C8—621no—
138C2×C4⋊C4C2×D3111yescharacteristic
139#103—621no—
140#103—621no—
141#103—621no—
142#102—621no—
143#101—622no—
144C31#190811yescharacteristic, complemented, Sylow
145#41—312no—
146#41—312no—
147#41—621no—
148#41—621no—
149C2×Q8—312no—
150C2×Q8—311no—
151C2×Q8—621no—
152C2×Q8—621no—
153C2×Q8—621no—
154C2×Q8—621no—
155C2×Q8—621no—
156C2×D4—311no—
157C2×D4—621no—
158C22×C4—21no—
159C22×C4—621no—
160C22×C4—621no—
161C22×C4C22×D3111yescharacteristic
162Q16—624no—
163SD16—624no—
164M16—21no—
165M16—21no—
166M16—624no—
167M16—621no—
168M16—621no—
169M16C4×D3112yes—
170M16D12412yes—
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—311no—
174C2×C8—311no—
175C2×C8—624no—
176C2×C8—621no—
177C2×C8—621no—
178C2×C8—621no—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C23—621no—
182C23#9249511yescharacteristic
183Q8—312no—
184Q8—621no—
185Q8—622no—
186Q8—622no—
187Q8—1241no—
188Q8—1241no—
189D4—312no—
190D4—622no—
191D4—622no—
192D4—621no—
193C2×C4—41no—
194C2×C4—81no—
195C2×C4—621no—
196C2×C4—622no—
197C2×C4—622no—
198C2×C4—622no—
199C2×C4—1241no—
200C2×C4—1241no—
201C2×C4C2×C4×D3111yescharacteristic
202C2×C4C2×D12411yescharacteristic
203C2×C4D4×D3111yescharacteristic
204C2×C4D4×D3111yescharacteristic
205C2×C4D4×D3111yescharacteristic
206C2×C4#9249911yescharacteristic
207C8—22no—
208C8—22no—
209C8—621no—
210C8—621no—
211C8—1241no—
212C22—21no—
213C22—21no—
214C22—622no—
215C22—1241no—
216C22—1241no—
217C22C4×D12411yescharacteristic
218C22#1175846111yescharacteristic
219C22#1175847111yescharacteristic
220C4—81no—
221C4—622no—
222C4—1242no—
223C4C22⋊C4×D3111yescharacteristic
224C4#1175845911yescharacteristic
225C4#1175847011yescharacteristic
226C4#1175847211yescharacteristic
227C2—21no—
228C2—21no—
229C2—1242no—
230C2#1452092711yescharacteristic
231C2#1452131111yescharacteristic
232C2#1452132311yescharacteristic
subgroupG/H
centerC22#11758461
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#343C2
socleC22×C31#121
prime radicalC2×#92495C22
cosocleC22×C4×C31C23
hypercenter#343D31
hypocenterC31#1908
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
4. C2×#11758398C2semidirect
5. C2×#11758412C2semidirect
6. #14520813C2semidirect
7. C31×#343C2semidirect
16. #11758486C4semidirect
116. #343D31semidirect
144. C31#1908semidirect

Maximal subgroups

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

subgroupindex
C2×#117584862
C2×#117584842
#145210482
C2×#117583982
C2×#117584122
#145208132
C31×#3432
#190831