Finite Group Databasebeta

← C4×#3805 #10594875

Subgroups — C4×#3805 #10594875

Order 576.

674 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3805C211yesmaximal, characteristic
2C2×C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C3×C4×#67C212yesmaximal, complemented
4#67⋊Dic3C212yesmaximal, complemented
5#63957C211yesmaximal, characteristic, complemented
6C4×#627C211yesmaximal, characteristic, complemented
7#63902C211yesmaximal, characteristic, complemented
8C4×#625C211yesmaximal, characteristic, complemented
9#63878C212yesmaximal, complemented
10C4×D3×Dic3C212yesmaximal, complemented
11#63838C211yesmaximal, characteristic, complemented
12C4×#237—32nomaximal
13C22×C32×C4C2211yescharacteristic
14C22×C3⋊Dic3C2211yescharacteristic
15C22×C3⋊Dic3C2211yescharacteristic
16C2×C3×#67C2212yes—
17C2×C3×C4×D3C2212yes—
18C2×#627C2211yescharacteristic
19C2×#625C2211yescharacteristic
20#3805C418yesdirect product factor
21C2×D3×Dic3C2212yes—
22C2×D3×Dic3C2212yes—
23C4×C3⋊Dic3C2211yescharacteristic
24C4×C3⋊Dic3C2211yescharacteristic
25C4×C3⋊Dic3C2211yescharacteristic
26C4×C3⋊Dic3C2211yescharacteristic
27C3×#217C2212yes—
28C3×(C2×D3)⋊C4C2212yes—
29C3×Dic3⋊C4C2212yes—
30C3×C4×Dic3C2212yes—
31#3724C2211yescharacteristic
32#3724C2211yescharacteristic
33Dic3⋊Dic3C2212yes—
34(C2×D3)⋊Dic3C2212yes—
35Dic32C2212yes—
36Dic32C2212yes—
37C2×#237—32no—
38C3×C4×D4—32no—
39D4×Dic3—32no—
40C4×#67—32no—
41C4×#67D312yescomplemented
42C2×C4×Dic3—32no—
43C2×C4×Dic3—32no—
44C2×C4×Dic3—61no—
45#892—32no—
46#887—32no—
47#67⋊C4—32no—
48#67⋊C4—32no—
49#877—32no—
50#877—32no—
51C42×D3—32no—
52C4×Dic6—32no—
53C23×C32C2311yescharacteristic
54C22×C3×D3C2312yes—
55C2×C32×C4—22no—
56C2×C32×C4C2311yescharacteristic
57C2×C32×C4C2311yescharacteristic
58C2×C3⋊Dic3—22no—
59C2×C3⋊Dic3C2×C414yescomplemented
60C2×C3⋊Dic3C2311yescharacteristic
61C2×C3⋊Dic3C2311yescharacteristic
62C2×C3⋊Dic3C2311yescharacteristic
63C2×C3⋊Dic3C2311yescharacteristic
64C3×#67C2×C418yescomplemented
65C2×C3×Dic3C2312yes—
66C2×C3×Dic3C2312yes—
67C2×C3×Dic3C2312yes—
68C3×C4×D3—24no—
69#627C2×C414yescomplemented
70#625C2×C414yescomplemented
71D3×Dic3—24no—
72D3×Dic3C2×C418yescomplemented
73C4×#41—91noSylow
74C2×C3×D4—32no—
75C22×C3×C4—21no—
76C22×C3×C4—32no—
77C22×C3×C4C2×D312yes—
78C2×#67—32no—
79C2×#67C2×D312yes—
80C22×Dic3—32no—
81C22×Dic3—32no—
82C22×Dic3—32no—
83C22×Dic3—32no—
84C22×Dic3—61no—
85C22×Dic3—61no—
86#237—316no—
87C2×C4×D3—32no—
88C2×C4×D3—32no—
89C2×C4×D3C2×D312yes—
90C2×Dic6—32no—
91C3×C4⋊C4—32no—
92C3×C22⋊C4—32no—
93C3×C22⋊C4—32no—
94C3×C42—32no—
95#217—32no—
96#217C2×D312yes—
97(C2×D3)⋊C4—32no—
98(C2×D3)⋊C4C2×D312yes—
99C4⋊Dic3—32no—
100Dic3⋊C4—32no—
101Dic3⋊C4—32no—
102Dic3⋊C4—32no—
103Dic3⋊C4C2×D312yes—
104C4×Dic3—32no—
105C4×Dic3—32no—
106C4×Dic3—32no—
107C4×Dic3—32no—
108C4×Dic3—32no—
109C4×Dic3—32no—
110C4×Dic3—32no—
111C4×Dic3—32no—
112C4×Dic3—61no—
113C4×Dic3—61no—
114C4×Dic3—61no—
115C4×Dic3—61no—
116C4×Dic3C2×D312yes—
117C22×C32—21no—
118C22×C32—21no—
119C22×C32C22×C412yes—
120C22×C32C2411yescharacteristic
121C2×C3×D3—22no—
122C2×C3×D3—22no—
123C2×C3×D3C22×C414yes—
124C32×C4—21no—
125C32×C4#4112yescomplemented
126C3⋊Dic3—21no—
127C3⋊Dic3C22×C412yes—
128C3⋊Dic3C22×C412yes—
129C3⋊Dic3#4112yescomplemented
130C3×Dic3—22no—
131C3×Dic3—22no—
132C3×Dic3C22×C414yes—
133C2×#41—91no—
134C4×Q8—91no—
135C4×Q8—91no—
136C4×D4—32no—
137C4×D4—91no—
138C4×D4—92no—
139C4×D4—91no—
140#117—91no—
141#117—92no—
142C2×C42—92no—
143C2×C42—91no—
144C23×C3—21no—
145C23×C3—32no—
146C23×C3C22×D312yes—
147C22×D3C22×D312yes—
148C3×D4—38no—
149C2×C3×C4—24no—
150C2×C3×C4—24no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—32no—
154C2×C3×C4—32no—
155C2×C3×C4—32no—
156C2×C3×C4—64no—
157C2×C3×C4C22×D312yes—
158C2×C3×C4C22×D312yes—
159#67—38no—
160#67C4×D318yescomplemented
161C2×Dic3—38no—
162C2×Dic3—32no—
163C2×Dic3—32no—
164C2×Dic3—32no—
165C2×Dic3—38no—
166C2×Dic3—32no—
167C2×Dic3—64no—
168C2×Dic3—61no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171C2×Dic3—61no—
172C2×Dic3—64no—
173C2×Dic3—64no—
174C2×Dic3—64no—
175C2×Dic3C22×D312yes—
176C2×Dic3C22×D312yes—
177C2×Dic3C22×D312yes—
178C4×D3—24no—
179C4×D3—38no—
180C4×D3—64no—
181Dic6—38no—
182C2×C32—22no—
183C2×C32C23×C411yescharacteristic
184C2×C32C2×#4111yescharacteristic
185C2×C32C2×#4111yescharacteristic
186C3×D3—24no—
187#41—98no—
188C2×Q8—91no—
189C2×D4—32no—
190C2×D4—91no—
191C22×C4—32no—
192C22×C4—92no—
193C22×C4—92no—
194C22×C4—91no—
195C22×C4—91no—
196C22×C4D3211yescharacteristic
197C4⋊C4—32no—
198C4⋊C4—91no—
199C4⋊C4—91no—
200C4⋊C4—92no—
201C22⋊C4—32no—
202C22⋊C4—32no—
203C22⋊C4—92no—
204C42—32no—
205C42—92no—
206C42—92no—
207C42—91no—
208C42—91no—
209C42—91no—
210C42—91no—
211C22×C3—22no—
212C22×C3—22no—
213C22×C3—22no—
214C22×C3—22no—
215C22×C3—21no—
216C22×C3—22no—
217C22×C3—34no—
218C22×C3—62no—
219C22×C3—62no—
220C22×C3C2×C4×D314yes—
221C22×C3C23×D312yes—
222C2×D3—22no—
223C2×D3—22no—
224C2×D3C2×C4×D314yes—
225C3×C4—22no—
226C3×C4—22no—
227C3×C4—22no—
228C3×C4—34no—
229C3×C4—62no—
230C3×C4—62no—
231C3×C4#23714yescomplemented
232Dic3—22no—
233Dic3—22no—
234Dic3—34no—
235Dic3—34no—
236Dic3—34no—
237Dic3—62no—
238Dic3—62no—
239Dic3—62no—
240Dic3—62no—
241Dic3—62no—
242Dic3C2×C4×D314yes—
243C32C4×#4111yescharacteristic, complemented, Sylow
244C23—32no—
245C23C2×D3211yescharacteristic
246Q8—94no—
247D4—38no—
248D4—94no—
249C2×C4—22no—
250C2×C4—32no—
251C2×C4—32no—
252C2×C4—32no—
253C2×C4—64no—
254C2×C4—98no—
255C2×C4—91no—
256C2×C4—91no—
257C2×C4—91no—
258C2×C4—94no—
259C2×C4—91no—
260C2×C4—184no—
261C2×C4—182no—
262C2×C4C2×D3211yescharacteristic
263C2×C4C2×D3211yescharacteristic
264C2×C3—24no—
265C2×C3—24no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—64no—
270C2×C3C22×C4×D312yes—
271C2×C3C2×#23712yes—
272C2×C3D3×#4112yes—
273D3—24no—
274C22—21no—
275C22—21no—
276C22—34no—
277C22—62no—
278C22—62no—
279C22C4×D3212yes—
280C22C22×D3211yescharacteristic
281C4—21no—
282C4—34no—
283C4—62no—
284C4—62no—
285C4—92no—
286C4—92no—
287C4—92no—
288C4—181no—
289C4#380512yesdirect product factor
290C3—21no—
291C3C4×#23712yescomplemented
292C2—22no—
293C2—64no—
294C2C2×C4×D3211yescharacteristic
295C2#6430611yescharacteristic
296C2C2×#380511yescharacteristic
subgroupG/H
centerC2×C4C2×D32
commutatorC2×C32C23×C4
FrattiniC22C22×D32
FittingC22×C32×C4C22
socle, cosocleC22×C32C24
prime radicalC2×#3805C2
hypercenterC22×C4D32
hypocenterC32C4×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C3⋊Dic3C2semidirect
3. C3×C4×#67C2semidirect
4. #67⋊Dic3C2semidirect
5. #63957C2semidirect
6. C4×#627C2semidirect
7. #63902C2semidirect
8. C4×#625C2semidirect
9. #63878C2semidirect
10. C4×D3×Dic3C2semidirect
11. #63838C2semidirect
20. #3805C4direct (N × H)
41. C4×#67D3semidirect
59. C2×C3⋊Dic3C2×C4semidirect
64. C3×#67C2×C4semidirect
69. #627C2×C4semidirect
70. #625C2×C4semidirect
72. D3×Dic3C2×C4semidirect
125. C32×C4#41semidirect
129. C3⋊Dic3#41semidirect
160. #67C4×D3semidirect
231. C3×C4#237semidirect
243. C32C4×#41semidirect
289. C4#3805direct (N × H)
291. C3C4×#237semidirect

Maximal subgroups

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

subgroupindex
C2×#38052
C2×C4×C3⋊Dic32
C3×C4×#672
#67⋊Dic32
#639572
C4×#6272
#639022
C4×#6252
#638782
C4×D3×Dic32
#638382
C4×#2373