Finite Group Databasebeta

← C2×C4×#3718 #11859949

Subgroups — C2×C4×#3718 #11859949

Order 1152.

1057 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×Dic6C212yesmaximal
2C22×#3718C211yesmaximal, characteristic
3C2×C4×C3⋊(C3⋊C8)C211yesmaximal, characteristic
4C2×#63576C211yesmaximal, characteristic
5C2×#63565C212yesmaximal
6C4×#3718C218yesmaximal, direct product factor
7C2×C4×#216—32nomaximal
8C22×C3×Dic6C2212yes—
9C2×C32×C42C2211yescharacteristic
10C22×C3⋊(C3⋊C8)C2211yescharacteristic
11C22×C3⋊(C3⋊C8)C2211yescharacteristic
12C2×C3×C4⋊Dic3C2212yes—
13C2×C3×Dic3⋊C4—22no—
14C2×C3×C4×Dic3—22no—
15C3×C4×Dic6—24no—
16C3×C4×Dic6C2218yes—
17C2×#3718C418yesdirect product factor
18C2×#3718C2214yes—
19C4×C3⋊(C3⋊C8)C2214yes—
20#63576C2214yes—
21#63565C2218yes—
22C2×C3×C4×Q8—32no—
23C22×#216—32no—
24C2×C4×Dic6D312yes—
25C2×#835—32no—
26C4×#216—316no—
27C2×#810—32no—
28C2×#807—32no—
29C2×C4×C3⋊C8—32no—
30C2×C4×C3⋊C8—61no—
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C22×C3×Dic3—22no—
35C22×C3×Dic3—22no—
36C2×C3×Dic6—22no—
37C2×C3×Dic6—24no—
38C2×C3×Dic6C2×C418yes—
39C2×C3×Dic6C2314yes—
40C32×C42D412yes—
41C32×C42C2312yes—
42C2×C3⋊(C3⋊C8)—22no—
43C2×C3⋊(C3⋊C8)C2×C414yes—
44C2×C3⋊(C3⋊C8)C2312yes—
45C2×C3⋊(C3⋊C8)C2312yes—
46C3×C4⋊Dic3—22no—
47C3×C4⋊Dic3C2314yes—
48C3×Dic3⋊C4—28no—
49C3×C4×Dic3—28no—
50#3718C2×C4116yesdirect product factor
51C2×C4×Q16—91noSylow
52C22×C3×Q8—32no—
53C22×Dic6C2×D312yes—
54C3×C4×Q8—38no—
55C3×C4×Q8—64no—
56C2×C3×C4⋊C4—32no—
57C2×C3×C4⋊C4—62no—
58C2×C3×C42—21no—
59C2×C3×C42—62no—
60C2×C3×C42C2×D312yes—
61C2×#216—316no—
62C2×#216—38no—
63C2×C4⋊Dic3C2×D312yes—
64C2×Dic3⋊C4—22no—
65C2×C4×Dic3—22no—
66C22×C3⋊C8—32no—
67C22×C3⋊C8—32no—
68C22×C3⋊C8—61no—
69C22×C3⋊C8—61no—
70C4×Dic6—24no—
71C4×Dic6C2×D318yes—
72#835—38no—
73#810—38no—
74#807—38no—
75C4×C3⋊C8—38no—
76C4×C3⋊C8—64no—
77C23×C32C2×D411yescharacteristic
78C2×C32×C4—22no—
79C2×C32×C4Q1614yescomplemented
80C2×C32×C4C22×C412yes—
81C2×C32×C4C2×D412yes—
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D412yes—
84C2×C32×C4#4112yes—
85C2×C32×C4C2411yescharacteristic
86C2×C3×Dic3—28no—
87C2×C3×Dic3—24no—
88C2×C3×Dic3—24no—
89C2×C3×Dic3—44no—
90C3×Dic6—28no—
91C3×Dic6—24no—
92C3×Dic6C22×C418yes—
93C3⋊(C3⋊C8)—22no—
94C3⋊(C3⋊C8)C22×C414yes—
95C22×Q16—91no—
96C2×C4×Q8—32no—
97C4×Q16—98no—
98C2×#107—91no—
99C2×#103—92no—
100C2×C4×C8—91no—
101C2×C3×Q8—38no—
102C2×C3×Q8—34no—
103C2×C3×Q8—64no—
104C2×C3×Q8—62no—
105C22×C3×C4—21no—
106C22×C3×C4—21no—
107C22×C3×C4—21no—
108C22×C3×C4—62no—
109C22×C3×C4—62no—
110C22×C3×C4#6712yes—
111C22×C3×C4#6712yes—
112C22×C3×C4C22×D312yes—
113C22×Dic3—22no—
114C22×Dic3—22no—
115C2×Dic6—24no—
116C2×Dic6—22no—
117C2×Dic6C4×D318yes—
118C2×Dic6C22×D314yes—
119C3×C4⋊C4—34no—
120C3×C4⋊C4—68no—
121C3×C4⋊C4—62no—
122C3×C42—22no—
123C3×C42—22no—
124C3×C42—68no—
125C3×C42#6714yes—
126C3×C42C22×D314yes—
127#216—332no—
128C4⋊Dic3—22no—
129C4⋊Dic3C22×D314yes—
130Dic3⋊C4—28no—
131C4×Dic3—28no—
132C2×C3⋊C8—38no—
133C2×C3⋊C8—34no—
134C2×C3⋊C8—34no—
135C2×C3⋊C8—62no—
136C2×C3⋊C8—62no—
137C2×C3⋊C8—64no—
138C2×C3⋊C8—64no—
139C2×C3⋊C8—64no—
140C22×C32C4×D412yes—
141C22×C32C2×Q1612yes—
142C22×C32#13512yes—
143C22×C32C22×D411yescharacteristic
144C32×C4—22no—
145C32×C4C4×D412yes—
146C32×C4C2×Q1614yescomplemented
147C32×C4C23×C411yescharacteristic
148C32×C4C2×#4111yescharacteristic
149C3×Dic3—28no—
150C3×Dic3—44no—
151C22×Q8—32no—
152C2×Q16—98no—
153C2×Q16—94no—
154C22×C8—91no—
155C22×C8—91no—
156C4×Q8—38no—
157C4×Q8—64no—
158C2×C4⋊C4—32no—
159C2×C4⋊C4—62no—
160C2×C42—62no—
161C2×C42D3211yescharacteristic
162#107—94no—
163#103—98no—
164C4×C8—94no—
165C23×C3—21no—
166C23×C3C2×#6712yes—
167C3×Q8—38no—
168C3×Q8—68no—
169C3×Q8—64no—
170C2×C3×C4—24no—
171C2×C3×C4—24no—
172C2×C3×C4—21no—
173C2×C3×C4—24no—
174C2×C3×C4—22no—
175C2×C3×C4—22no—
176C2×C3×C4—22no—
177C2×C3×C4—22no—
178C2×C3×C4—21no—
179C2×C3×C4—68no—
180C2×C3×C4—64no—
181C2×C3×C4—64no—
182C2×C3×C4—124no—
183C2×C3×C4#21618yescomplemented
184C2×C3×C4C2×C4×D314yes—
185C2×C3×C4#23514yes—
186C2×C3×C4C2×#6714yes—
187C2×C3×C4C2×#6712yes—
188C2×C3×C4C2×#6714yes—
189C2×C3×C4C23×D312yes—
190C2×Dic3—28no—
191C2×Dic3—24no—
192C2×Dic3—24no—
193C2×Dic3—44no—
194Dic6—28no—
195Dic6—24no—
196Dic6C2×C4×D318yes—
197C3⋊C8—38no—
198C3⋊C8—64no—
199C3⋊C8—64no—
200C3⋊C8—64no—
201C2×C32C4×Q1614yescomplemented
202C2×C32C2×C4×D411yescharacteristic
203C2×C32C22×Q1611yescharacteristic
204C2×C32C2×#13511yescharacteristic
205C2×Q8—34no—
206C2×Q8—38no—
207C2×Q8—64no—
208C2×Q8—62no—
209C22×C4—62no—
210C22×C4—62no—
211C22×C4#62511yescharacteristic
212C22×C4#62511yescharacteristic
213C22×C4C2×D3211yescharacteristic
214Q16—916no—
215C2×C8—92no—
216C2×C8—94no—
217C2×C8—92no—
218C2×C8—182no—
219C4⋊C4—34no—
220C4⋊C4—62no—
221C4⋊C4—68no—
222C42—68no—
223C42#62512yes—
224C42C2×D3212yes—
225C22×C3—21no—
226C22×C3—22no—
227C22×C3—22no—
228C22×C3—22no—
229C22×C3C4×#6714yes—
230C22×C3C2×#21614yes—
231C22×C3#95014yes—
232C22×C3C22×#6712yes—
233C3×C4—24no—
234C3×C4—24no—
235C3×C4—21no—
236C3×C4—21no—
237C3×C4—24no—
238C3×C4—22no—
239C3×C4—68no—
240C3×C4—124no—
241C3×C4C4×#6714yes—
242C3×C4C2×#21618yescomplemented
243C3×C4C22×C4×D312yes—
244C3×C4C2×#23512yes—
245Dic3—28no—
246Dic3—44no—
247C32C2×C4×Q1611yescharacteristic, complemented, Sylow
248C23C2×#62511yescharacteristic
249Q8—38no—
250Q8—64no—
251Q8—68no—
252C2×C4—22no—
253C2×C4—64no—
254C2×C4—68no—
255C2×C4—64no—
256C2×C4—124no—
257C2×C4#371814yesdirect product factor
258C2×C4#379812yes—
259C2×C4C4×D3212yes—
260C2×C4C2×#62512yes—
261C2×C4C2×#62512yes—
262C2×C4C2×#62511yescharacteristic
263C2×C4C22×D3211yescharacteristic
264C8—94no—
265C8—182no—
266C2×C3—24no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3C4×#21618yescomplemented
271C2×C3C2×C4×#6712yes—
272C2×C3C22×#21612yes—
273C2×C3C2×#95012yes—
274C22#6382212yes—
275C22C2×#371812yes—
276C22C4×#62512yes—
277C22C22×#62511yescharacteristic
278C4—22no—
279C4—68no—
280C4—124no—
281C4C2×#371814yesdirect product factor
282C4C4×#62512yes—
283C4C2×#379811yescharacteristic
284C4C2×C4×D3211yescharacteristic
285C3—21no—
286C3C2×C4×#21612yescomplemented
287C2C4×#371814yesdirect product factor
288C2C2×#6382211yescharacteristic
289C2C22×#371811yescharacteristic
290C2C2×C4×#62511yescharacteristic
subgroupG/H
centerC22×C4#625
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socle, prime radicalC23×C32C2×D4
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32C2×C4×Q16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
6. C4×#3718C2direct (N × H)
17. C2×#3718C4direct (N × H)
50. #3718C2×C4direct (N × H)
79. C2×C32×C4Q16semidirect
146. C32×C4C2×Q16semidirect
183. C2×C3×C4#216semidirect
201. C2×C32C4×Q16semidirect
242. C3×C4C2×#216semidirect
247. C32C2×C4×Q16semidirect
257. C2×C4#3718direct (N × H)
270. C2×C3C4×#216semidirect
281. C4C2×#3718direct (N × H)
286. C3C2×C4×#216semidirect
287. C2C4×#3718direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×Dic62
C22×#37182
C2×C4×C3⋊(C3⋊C8)2
C2×#635762
C2×#635652
C4×#37182
C2×C4×#2163