Finite Group Databasebeta

← #16846025

Subgroups — #16846025

Order 3968.

456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 107 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×#11758515C211yesmaximal, characteristic
2C2×C4⋊C4×D31C211yesmaximal, characteristic, complemented
3C2×#11758420C211yesmaximal, characteristic, complemented
4C2×(C2×D31)⋊C8C211yesmaximal, characteristic, complemented
5#14520812C211yesmaximal, characteristic, complemented
6#14520811C211yesmaximal, characteristic, complemented
7C2×C31×#102C211yesmaximal, characteristic, complemented
8C22×D4×C31C2211yescharacteristic
9C22×C22⋊D31—21no—
10C22×C4×D31—21no—
11C22×C4×D31C2211yescharacteristic
12C22×C8×C31C2211yescharacteristic
13C2×C4⋊C4×C31C2211yescharacteristic
14C2×C22⋊Dic31—21no—
15#11758515—22no—
16#11758515C414yescomplemented
17C2×C4⋊Dic31C2211yescharacteristic
18C2×C4⋊Dic31C2211yescharacteristic
19C2×Dic31⋊C4—21no—
20C22×C31⋊C8C2211yescharacteristic
21C4⋊C4×D31—22no—
22C4⋊C4×D31—22no—
23C31×#102—22no—
24#11758420—22no—
25(C2×D31)⋊C8—22no—
26C24×C31—21no—
27C23×D31D411yescharacteristic
28C2×D4×C31—21no—
29C2×D4×C31—21no—
30C2×D4×C31—21no—
31C2×D4×C31—21no—
32C2×D4×C31—21no—
33C2×D4×C31C2×C412yescomplemented
34C22×C4×C31—21no—
35C22×C4×C31C2311yescharacteristic
36C2×C22⋊D31—24no—
37C2×C22⋊D31—42no—
38C2×C22⋊D31—42no—
39C22×Dic31—21no—
40C22×Dic31—21no—
41C22×Dic31D411yescharacteristic
42C2×C4×D31—21no—
43C2×C4×D31—21no—
44C2×C4×D31—21no—
45C2×C4×D31—21no—
46C2×C4×D31—24no—
47C2×C4×D31—42no—
48C2×C4×D31—42no—
49C2×C4×D31C2×C412yes—
50C2×C4×D31D412yes—
51C2×C8×C31—21no—
52C2×C8×C31—21no—
53C2×C8×C31—21no—
54C4⋊C4×C31—21no—
55C4⋊C4×C31D412yescomplemented
56C22⋊Dic31—24no—
57C4⋊Dic31—21no—
58C4⋊Dic31—21no—
59C4⋊Dic31C2×C412yescomplemented
60C4⋊Dic31D412yescomplemented
61Dic31⋊C4—24no—
62C2×C31⋊C8—21no—
63C2×C31⋊C8—21no—
64C2×C31⋊C8—21no—
65C23×C31—22no—
66C23×C31—41no—
67C23×C31—41no—
68C23×C31—41no—
69C23×C31—41no—
70C23×C31—41no—
71C23×C31—41no—
72C23×C31C2×D411yescharacteristic
73C22×D31—21no—
74C22×D31—21no—
75C22×D31—21no—
76C22×D31—21no—
77C22×D31C22⋊C412yes—
78C22×D31D812yes—
79C22×D31SD1612yes—
80D4×C31—22no—
81D4×C31—22no—
82D4×C31—41no—
83D4×C31—41no—
84C2×C4×C31—22no—
85C2×C4×C31—41no—
86C2×C4×C31—41no—
87C2×C4×C31C22×C411yescharacteristic
88C2×C4×C31C2×D411yescharacteristic
89C2×C4×C31C2×D411yescharacteristic
90C2×C4×C31C2×D411yescharacteristic
91C2×C4×C31#4111yescharacteristic
92C2×C4×C31#4111yescharacteristic
93C22⋊D31—48no—
94C2×Dic31—21no—
95C2×Dic31—21no—
96C2×Dic31—22no—
97C2×Dic31—22no—
98C2×Dic31—41no—
99C2×Dic31—41no—
100C2×Dic31—41no—
101C2×Dic31—41no—
102C2×Dic31C22⋊C412yes—
103C4×D31—22no—
104C4×D31—22no—
105C4×D31—22no—
106C4×D31—22no—
107C4×D31—48no—
108C8×C31—41no—
109C31⋊C8—41no—
110#1874—311nomaximal, Sylow
111C22×C31—42no—
112C22×C31—42no—
113C22×C31—42no—
114C22×C31—81no—
115C22×C31—81no—
116C22×C31—81no—
117C22×C31—81no—
118C22×C31C2×C22⋊C411yescharacteristic
119C22×C31#12011yescharacteristic
120C22×C31#12311yescharacteristic
121C22×C31C2×D811yescharacteristic
122C22×C31C2×SD1611yescharacteristic
123C22×C31AGL(1,ℤ/8)11yescharacteristic
124C22×C31#13711yescharacteristic
125C2×D31—22no—
126C2×D31—22no—
127C2×D31—22no—
128C2×D31—22no—
129C2×D31—22no—
130C2×D31—22no—
131C2×D31#10214yescomplemented
132C4×C31—42no—
133C4×C31C4×D411yescharacteristic
134C4×C31C4×D411yescharacteristic
135C4×C31#12111yescharacteristic
136C4×C31#12111yescharacteristic
137Dic31—22no—
138Dic31—42no—
139Dic31—42no—
140C2×#121—311no—
141C22×C4⋊C4—311no—
142C2×#102—311no—
143C2×#102D3111yescharacteristic, complemented
144C2×C22⋊C8—311no—
145#340—311no—
146#340—311no—
147C2×C31—82no—
148C2×C31#38611yescharacteristic
149C2×C31C2×#10211yescharacteristic
150C2×C31#41711yescharacteristic
151C2×C31#44711yescharacteristic
152C2×C31#44811yescharacteristic
153C2×C31#48011yescharacteristic
154C2×C31#48111yescharacteristic
155D31—24no—
156C22×D4—621no—
157C22×D4C2×D3111yescharacteristic
158C23×C4—311no—
159C23×C4—621no—
160C22×C8—311no—
161C22×C8C2×D3111yescharacteristic
162#121—314no—
163#121—622no—
164C2×C4⋊C4—311no—
165C2×C4⋊C4—311no—
166C2×C4⋊C4—622no—
167C2×C4⋊C4—621no—
168C2×C4⋊C4—622no—
169C2×C4⋊C4C2×D3111yescharacteristic
170C2×C22⋊C4—621no—
171#102—22no—
172#102—622no—
173C22⋊C8—622no—
174C31#187411yescharacteristic, complemented, Sylow
175C24—21no—
176C24—311no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—624no—
183C2×D4—1242no—
184C2×D4—1242no—
185C2×D4C4×D3112yescomplemented
186C22×C4—21no—
187C22×C4—311no—
188C22×C4—312no—
189C22×C4—312no—
190C22×C4—624no—
191C22×C4—621no—
192C22×C4—621no—
193C22×C4—621no—
194C22×C4—621no—
195C22×C4—621no—
196C22×C4—621no—
197C22×C4—1242no—
198C22×C4—1242no—
199C22×C4C22×D3111yescharacteristic
200C2×C8—21no—
201C2×C8—21no—
202C2×C8—21no—
203C2×C8—621no—
204C2×C8—621no—
205C2×C8—621no—
206C4⋊C4—21no—
207C4⋊C4—312no—
208C4⋊C4—312no—
209C4⋊C4—624no—
210C4⋊C4—621no—
211C4⋊C4—621no—
212C4⋊C4C22⋊D3112yescomplemented
213C22⋊C4—624no—
214C23—22no—
215C23—41no—
216C23—41no—
217C23—41no—
218C23—41no—
219C23—41no—
220C23—41no—
221C23—312no—
222C23—312no—
223C23—312no—
224C23—621no—
225C23—621no—
226C23—621no—
227C23—621no—
228C23D4×D3111yescharacteristic
229D4—22no—
230D4—22no—
231D4—41no—
232D4—41no—
233D4—1248no—
234C2×C4—22no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—312no—
238C2×C4—621no—
239C2×C4—621no—
240C2×C4—622no—
241C2×C4—622no—
242C2×C4—622no—
243C2×C4—622no—
244C2×C4—622no—
245C2×C4—622no—
246C2×C4—1248no—
247C2×C4—1241no—
248C2×C4—1241no—
249C2×C4—1241no—
250C2×C4—1241no—
251C2×C4C2×C4×D3111yescharacteristic
252C2×C4#9249511yescharacteristic
253C2×C4D4×D3111yescharacteristic
254C2×C4D4×D3111yescharacteristic
255C2×C4#9249711yescharacteristic
256C2×C4C2×C22⋊D3111yescharacteristic
257C8—41no—
258C8—1241no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—81no—
263C22—81no—
264C22—81no—
265C22—81no—
266C22—314no—
267C22—622no—
268C22—622no—
269C22—622no—
270C22—622no—
271C22—622no—
272C22—622no—
273C22C22⋊C4×D3111yescharacteristic
274C22#1175846011yescharacteristic
275C22D8×D3111yescharacteristic
276C22#1175848811yescharacteristic
277C22SD16×D3111yescharacteristic
278C22#1175849211yescharacteristic
279C22#1175851411yescharacteristic
280C4—42no—
281C4—622no—
282C4—1242no—
283C4—1242no—
284C4(C22⋊D31)⋊C411yescharacteristic
285C4#1175846111yescharacteristic
286C4C4×C22⋊D3111yescharacteristic
287C4#1175851511yescharacteristic
288C2—82no—
289C2—624no—
290C2#1452092511yescharacteristic
291C2#102×D3111yescharacteristic
292C2#1452104711yescharacteristic
293C2#1452118111yescharacteristic
294C2#1452118611yescharacteristic
295C2#1452136111yescharacteristic
296C2#1452136611yescharacteristic
subgroupG/H
centerC23D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×#102C2
socleC23×C31C2×D4
prime radicalC2×#11758515C2
cosocleC22×C4×C31C23
hypercenterC2×#102D31
hypocenterC31#1874
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D31C2semidirect
3. C2×#11758420C2semidirect
4. C2×(C2×D31)⋊C8C2semidirect
5. #14520812C2semidirect
6. #14520811C2semidirect
7. C2×C31×#102C2semidirect
16. #11758515C4semidirect
33. C2×D4×C31C2×C4semidirect
55. C4⋊C4×C31D4semidirect
59. C4⋊Dic31C2×C4semidirect
60. C4⋊Dic31D4semidirect
131. C2×D31#102semidirect
143. C2×#102D31semidirect
174. C31#1874semidirect
185. C2×D4C4×D31semidirect
212. C4⋊C4C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117585152
C2×C4⋊C4×D312
C2×#117584202
C2×(C2×D31)⋊C82
#145208122
#145208112
C2×C31×#1022
#187431