Finite Group Databasebeta

← #16846168

Subgroups — #16846168

Order 3968.

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

normal subgroups only

This group has 378 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
2C2×#11758454C211yesmaximal, characteristic, complemented
3C2×#11758394C211yesmaximal, characteristic
4C2×#11758394C211yesmaximal, characteristic
5#14520910C211yesmaximal, characteristic, complemented
6#14520816C211yesmaximal, 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
15C2×(C2×D31)⋊C4C412yescomplemented
16C2×C4⋊Dic31C412yescomplemented
17C2×Dic31⋊C4—21no—
18C2×C4×Dic31—21no—
19#11758463—22no—
20#11758463—21no—
21#11758463—21no—
22#11758454—22no—
23#11758454—22no—
24C31⋊#95—22no—
25#11758394—22no—
26#11758394—22no—
27C24×C31C2311yescharacteristic
28C23×D31C2×C411yescharacteristic
29C22×C4×C31—21no—
30C22×C4×C31—21no—
31C22×C4×C31C2×C412yes—
32C2×C22⋊D31—21no—
33C2×C22⋊D31—21no—
34C2×C22⋊D31—21no—
35C2×C22⋊D31—21no—
36C2×C22⋊D31—21no—
37C2×C22⋊D31—21no—
38C22×Dic31—21no—
39C22×Dic31—21no—
40C22×Dic31—21no—
41C22×Dic31—21no—
42C22×Dic31—21no—
43C22×Dic31—21no—
44C22×Dic31C2×C411yescharacteristic
45C22×Dic31C2×C412yes—
46C22×Dic31D412yes—
47C22×Dic31D411yescharacteristic
48C22×Dic31D411yescharacteristic
49C22⋊C4×C31—21no—
50C22⋊C4×C31—21no—
51C22⋊C4×C31—21no—
52C22⋊C4×C31—21no—
53C22⋊C4×C31—21no—
54C22⋊C4×C31D412yes—
55C22⋊Dic31—21no—
56C22⋊Dic31—21no—
57C22⋊Dic31—21no—
58C22⋊Dic31D412yes—
59(C2×D31)⋊C4—22no—
60(C2×D31)⋊C4—22no—
61C4⋊Dic31—22no—
62C4⋊Dic31—22no—
63Dic31⋊C4—24no—
64C4×Dic31—24no—
65C23×C31—42no—
66C23×C31C22×C411yescharacteristic
67C23×C31C2×D411yescharacteristic
68C23×C31C2×D411yescharacteristic
69C23×C31C2×D411yescharacteristic
70C23×C31C2×D411yescharacteristic
71C23×C31#4111yescharacteristic
72C23×C31#4111yescharacteristic
73C22×D31—21no—
74C22×D31—21no—
75C22×D31—21no—
76C22×D31—42no—
77C2×C4×C31—22no—
78C2×C4×C31—22no—
79C2×C4×C31—42no—
80C2×C4×C31—42no—
81C2×C4×C31—42no—
82C2×C4×C31—41no—
83C22⋊D31—41no—
84C22⋊D31—41no—
85C22⋊D31—41no—
86C22⋊D31—41no—
87C2×Dic31—22no—
88C2×Dic31—22no—
89C2×Dic31—21no—
90C2×Dic31—21no—
91C2×Dic31—22no—
92C2×Dic31—22no—
93C2×Dic31—21no—
94C2×Dic31—21no—
95C2×Dic31—21no—
96C2×Dic31—21no—
97C2×Dic31—21no—
98C2×Dic31—22no—
99C2×Dic31—42no—
100C2×Dic31—42no—
101C2×Dic31—41no—
102C2×Dic31C22⋊C412yes—
103C2×Dic31C22⋊C412yes—
104#1899—311nomaximal, Sylow
105C22×C31—22no—
106C22×C31—22no—
107C22×C31—22no—
108C22×C31—41no—
109C22×C31—41no—
110C22×C31—41no—
111C22×C31—41no—
112C22×C31C2×C22⋊C411yescharacteristic
113C22×C31C4×D411yescharacteristic
114C22×C31C4×D411yescharacteristic
115C22×C31#12011yescharacteristic
116C22×C31#12111yescharacteristic
117C22×C31#12111yescharacteristic
118C22×C31#12311yescharacteristic
119C2×D31—41no—
120C2×D31—42no—
121C2×D31—81no—
122C2×D31—81no—
123C4×C31—42no—
124C4×C31—42no—
125C4×C31—81no—
126Dic31—22no—
127Dic31—22no—
128Dic31—42no—
129Dic31—41no—
130Dic31—81no—
131C2×#123—311no—
132C2×#117—311no—
133C2×#99—311no—
134C2×#99—311no—
135#381—311no—
136#342—311no—
137#342D3111yescharacteristic, complemented
138C2×C31—21no—
139C2×C31—21no—
140C2×C31—21no—
141C2×C31—21no—
142C2×C31—21no—
143C2×C31—21no—
144C2×C31#38611yescharacteristic
145C2×C31#41012yes—
146D31—81no—
147C22×D4—311no—
148C23×C4—311no—
149#123—622no—
150#123—621no—
151#123—621no—
152#117—622no—
153#117—622no—
154C2×C4⋊C4—312no—
155C2×C4⋊C4—621no—
156C2×C22⋊C4—311no—
157C2×C22⋊C4—312no—
158C2×C22⋊C4—311no—
159C2×C22⋊C4C2×D3111yescharacteristic
160C2×C22⋊C4C2×D3111yescharacteristic
161C2×C22⋊C4C2×D3111yescharacteristic
162C2×C42—621no—
163#99—622no—
164#99—622no—
165#95—622no—
166C31#189911yescharacteristic, complemented, Sylow
167C24—311no—
168C24C22×D3111yescharacteristic
169C2×D4—621no—
170C2×D4—621no—
171C2×D4—621no—
172C2×D4—621no—
173C2×D4—621no—
174C2×D4—621no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—312no—
178C22×C4—312no—
179C22×C4—311no—
180C22×C4—311no—
181C22×C4—311no—
182C22×C4—621no—
183C22×C4—621no—
184C22×C4—621no—
185C22×C4—621no—
186C22×C4—621no—
187C22×C4—621no—
188C22×C4C4×D3112yes—
189C4⋊C4—622no—
190C4⋊C4—622no—
191C4⋊C4—624no—
192C22⋊C4—21no—
193C22⋊C4—21no—
194C22⋊C4—21no—
195C22⋊C4—21no—
196C22⋊C4—21no—
197C22⋊C4—312no—
198C22⋊C4—622no—
199C22⋊C4—622no—
200C22⋊C4—621no—
201C22⋊C4—621no—
202C22⋊C4—621no—
203C22⋊C4D12412yes—
204C42—624no—
205C23—42no—
206C23—621no—
207C23—621no—
208C23—621no—
209C23—1242no—
210C23C2×C4×D3111yescharacteristic
211C23C2×D12411yescharacteristic
212C23#9249511yescharacteristic
213C23D4×D3111yescharacteristic
214C23D4×D3111yescharacteristic
215C23D4×D3111yescharacteristic
216C23#9249911yescharacteristic
217D4—1241no—
218D4—1241no—
219D4—1241no—
220D4—1241no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—312no—
228C2×C4—312no—
229C2×C4—622no—
230C2×C4—621no—
231C2×C4—621no—
232C2×C4—622no—
233C2×C4—622no—
234C2×C4—621no—
235C2×C4—621no—
236C2×C4—622no—
237C2×C4—621no—
238C2×C4—621no—
239C2×C4—622no—
240C2×C4—621no—
241C2×C4—1242no—
242C2×C4—1242no—
243C2×C4—1241no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—1241no—
252C22—1242no—
253C22—2481no—
254C22—2481no—
255C22C4×D12411yescharacteristic
256C22C22⋊C4×D3111yescharacteristic
257C22#1175845911yescharacteristic
258C22#1175846111yescharacteristic
259C22#1175847011yescharacteristic
260C22#1175847111yescharacteristic
261C22#1175847211yescharacteristic
262C4—42no—
263C4—42no—
264C4—81no—
265C4—622no—
266C4—622no—
267C4—1242no—
268C4—1241no—
269C4—2481no—
270C2—21no—
271C2—21no—
272C2—21no—
273C2—21no—
274C2—21no—
275C2—21no—
276C2—2481no—
277C2#1452092711yescharacteristic
278C2#1452102112yes—
subgroupG/H
centerC22C22⋊C4×D31
commutatorC23×C31C22×C4
FrattiniC24C22×D31
FittingC31×#342C2
socleC22×C31C2×C22⋊C4
prime radicalC22×C22⋊D31C22
cosocleC24×C31C23
hypercenter#342D31
hypocenterC31#1899
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#11758454C2semidirect
5. #14520910C2semidirect
6. #14520816C2semidirect
7. C31×#342C2semidirect
15. C2×(C2×D31)⋊C4C4semidirect
16. C2×C4⋊Dic31C4semidirect
137. #342D31semidirect
166. C31#1899semidirect

Maximal subgroups

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

subgroupindex
C2×#117584632
C2×#117584542
C2×#117583942
#145209102
#145208162
C31×#3422
#189931