Finite Group Databasebeta

← #16846123

Subgroups — #16846123

Order 3968.

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

normal subgroups only

This group has 386 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×#11758463C211yesmaximal, characteristic
2#14521522C211yesmaximal, characteristic
3C2×#11758394C211yesmaximal, characteristic
4#14520910C211yesmaximal, characteristic, complemented
5#14520910C211yesmaximal, characteristic, complemented
6#14520815C211yesmaximal, characteristic, complemented
7C31×#342C211yesmaximal, characteristic, complemented
8C22×C22⋊D31C2211yescharacteristic
9C23×Dic31C2211yescharacteristic
10C2×C22⋊C4×C31C2211yescharacteristic
11C2×C22⋊C4×C31C2211yescharacteristic
12C2×C22⋊C4×C31C2211yescharacteristic
13C2×C22⋊Dic31C2211yescharacteristic
14C2×C22⋊Dic31C2211yescharacteristic
15C4×C22⋊D31—22no—
16C2×(C2×D31)⋊C4—21no—
17C2×C4⋊Dic31—21no—
18#11758463—22no—
19#11758463C414yescomplemented
20(C22⋊D31)⋊C4—22no—
21C22⋊C4×D31—21no—
22#11758454—21no—
23C31⋊#95—22no—
24C31⋊#95—22no—
25#11758394—22no—
26C24×C31C2311yescharacteristic
27C23×D31D411yescharacteristic
28C22×C4×C31—21no—
29C22×C4×C31—21no—
30C22×C4×C31D412yes—
31C2×C22⋊D31—21no—
32C2×C22⋊D31—21no—
33C2×C22⋊D31—21no—
34C2×C22⋊D31—21no—
35C2×C22⋊D31C2×C412yes—
36C2×C22⋊D31D412yes—
37C22×Dic31—21no—
38C22×Dic31—21no—
39C22×Dic31—21no—
40C22×Dic31—21no—
41C22×Dic31—21no—
42C22×Dic31—21no—
43C22×Dic31—21no—
44C22×Dic31C2×C412yescomplemented
45C22×Dic31D411yescharacteristic
46C22×Dic31D412yes—
47C2×C4×D31—22no—
48C22⋊C4×C31—21no—
49C22⋊C4×C31—21no—
50C22⋊C4×C31—21no—
51C22⋊C4×C31—21no—
52C22⋊C4×C31—21no—
53C22⋊C4×C31C2×C412yescomplemented
54C22⋊Dic31—21no—
55C22⋊Dic31—21no—
56C22⋊Dic31—21no—
57C22⋊Dic31—21no—
58(C2×D31)⋊C4—22no—
59(C2×D31)⋊C4—24no—
60C4⋊Dic31—24no—
61Dic31⋊C4—22no—
62C4×Dic31—22no—
63C23×C31—42no—
64C23×C31C22×C411yescharacteristic
65C23×C31C2×D411yescharacteristic
66C23×C31C2×D411yescharacteristic
67C23×C31C2×D411yescharacteristic
68C23×C31C2×D411yescharacteristic
69C23×C31#4111yescharacteristic
70C23×C31#4111yescharacteristic
71C22×D31—21no—
72C22×D31—21no—
73C22×D31—42no—
74C22×D31C22⋊C412yes—
75C2×C4×C31—22no—
76C2×C4×C31—22no—
77C2×C4×C31—42no—
78C2×C4×C31—42no—
79C2×C4×C31—42no—
80C2×C4×C31—41no—
81C22⋊D31—22no—
82C22⋊D31—22no—
83C22⋊D31—22no—
84C22⋊D31—22no—
85C2×Dic31—21no—
86C2×Dic31—21no—
87C2×Dic31—22no—
88C2×Dic31—22no—
89C2×Dic31—22no—
90C2×Dic31—22no—
91C2×Dic31—41no—
92C2×Dic31—41no—
93C2×Dic31—41no—
94C2×Dic31—41no—
95C2×Dic31—42no—
96C2×Dic31—42no—
97C2×Dic31—41no—
98C2×Dic31C22⋊C412yes—
99C4×D31—82no—
100#1890—311nomaximal, Sylow
101C22×C31—22no—
102C22×C31—22no—
103C22×C31—22no—
104C22×C31—41no—
105C22×C31—41no—
106C22×C31—41no—
107C22×C31—41no—
108C22×C31C2×C22⋊C411yescharacteristic
109C22×C31C4×D411yescharacteristic
110C22×C31C4×D411yescharacteristic
111C22×C31#12011yescharacteristic
112C22×C31#12111yescharacteristic
113C22×C31#12111yescharacteristic
114C22×C31#12311yescharacteristic
115C2×D31—22no—
116C2×D31—42no—
117C2×D31—42no—
118C2×D31—81no—
119C4×C31—42no—
120C4×C31—42no—
121C4×C31—81no—
122Dic31—22no—
123Dic31—42no—
124Dic31—42no—
125Dic31—81no—
126C2×#123—311no—
127#518—311no—
128C2×#99—311no—
129#381—311no—
130#381—311no—
131#342—311no—
132#342D3111yescharacteristic, complemented
133C2×C31—21no—
134C2×C31—21no—
135C2×C31—21no—
136C2×C31—21no—
137C2×C31—21no—
138C2×C31—21no—
139C2×C31#38611yescharacteristic
140C2×C31#45812yes—
141D31—42no—
142C22×D4—311no—
143C23×C4—311no—
144#123—314no—
145#123—622no—
146C4×D4—622no—
147C4×D4—622no—
148#117—621no—
149C2×C4⋊C4—621no—
150C2×C22⋊C4—311no—
151C2×C22⋊C4—311no—
152C2×C22⋊C4—621no—
153C2×C22⋊C4—621no—
154C2×C22⋊C4C2×D3111yescharacteristic
155C2×C22⋊C4C2×D3111yescharacteristic
156C2×C22⋊C4C2×D3111yescharacteristic
157#99—622no—
158#95—622no—
159#95—622no—
160C31#189011yescharacteristic, complemented, Sylow
161C24—311no—
162C24C22×D3111yescharacteristic
163C2×D4—312no—
164C2×D4—312no—
165C2×D4—621no—
166C2×D4—621no—
167C2×D4—621no—
168C2×D4—621no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—311no—
172C22×C4—312no—
173C22×C4—312no—
174C22×C4—622no—
175C22×C4—621no—
176C22×C4—621no—
177C22×C4—621no—
178C22×C4—621no—
179C22×C4—621no—
180C22×C4—621no—
181C22×C4—621no—
182C22×C4D12412yes—
183C4⋊C4—624no—
184C4⋊C4—622no—
185C22⋊C4—21no—
186C22⋊C4—21no—
187C22⋊C4—21no—
188C22⋊C4—21no—
189C22⋊C4—21no—
190C22⋊C4—624no—
191C22⋊C4—622no—
192C22⋊C4—621no—
193C22⋊C4—621no—
194C22⋊C4—621no—
195C22⋊C4—621no—
196C22⋊C4C4×D3112yescomplemented
197C42—622no—
198C23—42no—
199C23—312no—
200C23—621no—
201C23—621no—
202C23—1242no—
203C23C2×C4×D3111yescharacteristic
204C23C2×D12411yescharacteristic
205C23#9249511yescharacteristic
206C23D4×D3111yescharacteristic
207C23D4×D3111yescharacteristic
208C23D4×D3111yescharacteristic
209C23#9249911yescharacteristic
210D4—622no—
211D4—622no—
212D4—622no—
213D4—622no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—41no—
220C2×C4—312no—
221C2×C4—621no—
222C2×C4—621no—
223C2×C4—622no—
224C2×C4—622no—
225C2×C4—622no—
226C2×C4—622no—
227C2×C4—1241no—
228C2×C4—1241no—
229C2×C4—1241no—
230C2×C4—1241no—
231C2×C4—1242no—
232C2×C4—1242no—
233C2×C4—1241no—
234C2×C4—2482no—
235C22—22no—
236C22—22no—
237C22—22no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—622no—
243C22—1242no—
244C22—1242no—
245C22—2481no—
246C22C4×D12411yescharacteristic
247C22C22⋊C4×D3111yescharacteristic
248C22#1175845911yescharacteristic
249C22#1175846111yescharacteristic
250C22#1175847011yescharacteristic
251C22#1175847111yescharacteristic
252C22#1175847211yescharacteristic
253C4—42no—
254C4—42no—
255C4—81no—
256C4—622no—
257C4—1242no—
258C4—1242no—
259C4—2481no—
260C2—21no—
261C2—21no—
262C2—21no—
263C2—21no—
264C2—21no—
265C2—21no—
266C2—1242no—
267C2#1452092711yescharacteristic
268C2#1452124012yes—
subgroupG/H
centerC22#11758459
commutatorC23×C31C22×C4
FrattiniC24C22×D31
FittingC31×#342C2
socleC22×C31#120
prime radicalC22×C22⋊D31C22
cosocleC24×C31C23
hypercenter#342D31
hypocenterC31#1890
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
4. #14520910C2semidirect
5. #14520910C2semidirect
6. #14520815C2semidirect
7. C31×#342C2semidirect
19. #11758463C4semidirect
44. C22×Dic31C2×C4semidirect
53. C22⋊C4×C31C2×C4semidirect
132. #342D31semidirect
160. C31#1890semidirect
196. C22⋊C4C4×D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117584632
#145215222
C2×#117583942
#145209102
#145208152
C31×#3422
#189031