Finite Group Databasebeta

← #16846889

Subgroups — #16846889

Order 3968.

278 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 63 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#14521675C211yesmaximal, characteristic, complemented
2C2×#11758394C211yesmaximal, characteristic
3C2×#11758394C211yesmaximal, characteristic
4C2×#11758394C211yesmaximal, characteristic
5#14520816C211yesmaximal, characteristic, complemented
6#14520815C211yesmaximal, characteristic, complemented
7C31×#342C211yesmaximal, characteristic, complemented
8C22×C22⋊D31C2211yescharacteristic
9C2×C22⋊C4×C31C2211yescharacteristic
10C2×C22⋊C4×C31C2211yescharacteristic
11C2×C22⋊C4×C31C2211yescharacteristic
12C2×C22⋊Dic31C2211yescharacteristic
13C2×C22⋊Dic31C2211yescharacteristic
14C2×C22⋊Dic31C2211yescharacteristic
15#11758501—22no—
16#11758455—22no—
17#11758455—22no—
18#11758394—22no—
19#11758394—22no—
20#11758394—22no—
21C24×C31C2311yescharacteristic
22C23×D31Q811yescharacteristic, complemented
23C22×C4×C31—21no—
24C22×C4×C31—21no—
25C22×C4×C31—21no—
26C2×C22⋊D31—21no—
27C2×C22⋊D31—21no—
28C2×C22⋊D31—21no—
29C2×C22⋊D31—21no—
30C2×C22⋊D31—21no—
31C2×C22⋊D31—21no—
32C22×Dic31—21no—
33C22×Dic31—21no—
34C22×Dic31—21no—
35C22×Dic31Q811yescharacteristic, complemented
36C2×Dic62—22no—
37C22⋊C4×C31—21no—
38C22⋊C4×C31—21no—
39C22⋊C4×C31—21no—
40C22⋊C4×C31—21no—
41C22⋊C4×C31—21no—
42C22⋊C4×C31D412yes—
43C22⋊Dic31—21no—
44C22⋊Dic31—21no—
45C22⋊Dic31—21no—
46C22⋊Dic31—21no—
47C22⋊Dic31D412yes—
48C22⋊Dic31D412yes—
49C4⋊Dic31—22no—
50Dic31⋊C4—24no—
51C23×C31—81no—
52C23×C31C2×D411yescharacteristic
53C23×C31C2×D411yescharacteristic
54C23×C31C2×D411yescharacteristic
55C23×C31C2×Q811yescharacteristic
56C23×C31#4111yescharacteristic
57C23×C31#4111yescharacteristic
58C23×C31#4111yescharacteristic
59C22×D31—21no—
60C22×D31—21no—
61C22×D31—21no—
62C22×D31—81no—
63C2×C4×C31—22no—
64C2×C4×C31—41no—
65C2×C4×C31—41no—
66C2×C4×C31—81no—
67C2×C4×C31—81no—
68C2×C4×C31—81no—
69C22⋊D31—41no—
70C22⋊D31—41no—
71C22⋊D31—41no—
72C22⋊D31—41no—
73C2×Dic31—22no—
74C2×Dic31—22no—
75C2×Dic31—21no—
76C2×Dic31—21no—
77C2×Dic31—21no—
78C2×Dic31—41no—
79C2×Dic31—81no—
80C2×Dic31—81no—
81C2×Dic31—81no—
82Dic62—82no—
83#2032—311nomaximal, Sylow
84C22×C31—41no—
85C22×C31—41no—
86C22×C31—41no—
87C22×C31—41no—
88C22×C31—41no—
89C22×C31—41no—
90C22×C31—41no—
91C22×C31#12011yescharacteristic
92C22×C31C22⋊Q811yescharacteristic
93C22×C31C22⋊Q811yescharacteristic
94C22×C31C22⋊Q811yescharacteristic
95C22×C31#12411yescharacteristic
96C22×C31#12411yescharacteristic
97C22×C31#12411yescharacteristic
98C2×D31—41no—
99C2×D31—81no—
100C2×D31—81no—
101C2×D31—81no—
102C4×C31—42no—
103C4×C31—81no—
104C4×C31—81no—
105Dic31—42no—
106Dic31—42no—
107Dic31—41no—
108Dic31—81no—
109#543—311no—
110C2×#99—311no—
111C2×#99—311no—
112C2×#99—311no—
113#342—311no—
114#342—311no—
115#342D3111yescharacteristic, complemented
116C2×C31—21no—
117C2×C31—21no—
118C2×C31—21no—
119C2×C31—21no—
120C2×C31—21no—
121C2×C31—21no—
122C2×C31—21no—
123C2×C31#39311yescharacteristic
124D31—81no—
125C22×D4—311no—
126C22⋊Q8—622no—
127C22⋊Q8—622no—
128C22⋊Q8—622no—
129C2×C22⋊C4—311no—
130C2×C22⋊C4—311no—
131C2×C22⋊C4—311no—
132C2×C22⋊C4C2×D3111yescharacteristic
133C2×C22⋊C4C2×D3111yescharacteristic
134C2×C22⋊C4C2×D3111yescharacteristic
135#99—622no—
136#99—622no—
137#99—622no—
138C31#203211yescharacteristic, complemented, Sylow
139C24—311no—
140C24C22×D3111yescharacteristic
141C2×Q8—622no—
142C2×D4—621no—
143C2×D4—621no—
144C2×D4—621no—
145C2×D4—621no—
146C2×D4—621no—
147C2×D4—621no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—311no—
152C22×C4—621no—
153C22×C4—621no—
154C22×C4—621no—
155C4⋊C4—624no—
156C4⋊C4—622no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—312no—
163C22⋊C4—312no—
164C22⋊C4—621no—
165C22⋊C4—621no—
166C22⋊C4—621no—
167C22⋊C4—621no—
168C22⋊C4D12412yes—
169C23—81no—
170C23—621no—
171C23—621no—
172C23—621no—
173C23—2481no—
174C23C2×D12411yescharacteristic
175C23#9249511yescharacteristic
176C23#9249511yescharacteristic
177C23D4×D3111yescharacteristic
178C23D4×D3111yescharacteristic
179C23#9249711yescharacteristic
180C23Q8×D3111yescharacteristic
181Q8—2482no—
182D4—1241no—
183D4—1241no—
184D4—1241no—
185D4—1241no—
186C2×C4—22no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—81no—
190C2×C4—81no—
191C2×C4—81no—
192C2×C4—622no—
193C2×C4—622no—
194C2×C4—621no—
195C2×C4—621no—
196C2×C4—621no—
197C2×C4—1241no—
198C2×C4—2481no—
199C2×C4—2481no—
200C2×C4—2481no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—1241no—
209C22—2481no—
210C22—2481no—
211C22—2481no—
212C22#1175845211yescharacteristic
213C22#1175845911yescharacteristic
214C22#1175846211yescharacteristic
215C22#1175846211yescharacteristic
216C22#1175847311yescharacteristic
217C22#1175847311yescharacteristic
218C22#1175847411yescharacteristic
219C4—42no—
220C4—81no—
221C4—81no—
222C4—1242no—
223C4—1242no—
224C4—1241no—
225C4—2481no—
226C2—21no—
227C2—21no—
228C2—21no—
229C2—21no—
230C2—21no—
231C2—21no—
232C2—21no—
233C2—2481no—
234C2#1452096211yescharacteristic
subgroupG/H
centerC2#14520962
commutator, cosocleC24×C31C23
FrattiniC24C22×D31
FittingC31×#342C2
socleC2×C31#393
prime radicalC22×C22⋊D31C22
hypercenter#342D31
hypocenterC31#2032
LCSG ▷ C24×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #14521675C2semidirect
5. #14520816C2semidirect
6. #14520815C2semidirect
7. C31×#342C2semidirect
22. C23×D31Q8semidirect
35. C22×Dic31Q8semidirect
115. #342D31semidirect
138. C31#2032semidirect

Maximal subgroups

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

subgroupindex
#145216752
C2×#117583942
#145208162
#145208152
C31×#3422
#203231