Finite Group Databasebeta

← C3×#71624 #11773831

Subgroups — C3×#71624 #11773831

Order 1152.

645 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×Q8C211yesmaximal, characteristic
2C3×#4925C212yesmaximal
3C3×#4528C214yesmaximal
4C3×#1461—31nomaximal
5#71624C311yesmaximal, characteristic, direct product factor
6C22×C32×Q8C411yescharacteristic
7C32×C4×Q8—22no—
8C32×C4×Q8—22no—
9C2×C32×C4⋊C4C411yescharacteristic
10C2×C32×C4⋊C4C2212yes—
11C2×C32×C42C412yes—
12C2×C32×C42C2211yescharacteristic
13C3×#830C2214yes—
14C3×C4⋊(C3⋊C8)—22no—
15C3×C4×C3⋊C8—22no—
16C2×C3×C4×Q8—21no—
17C2×C3×C4×Q8D311yescharacteristic
18C2×C3×C4×Q8C2×C311yescharacteristic
19C3×#431—32no—
20#4925C2×C312yes—
21C3×#324—34no—
22#4528C2×C314yes—
23C2×C32×Q8—22no—
24C2×C32×Q8—22no—
25C2×C32×Q8C814yescomplemented
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4C2×C412yes—
28C22×C32×C4C2×C412yes—
29C22×C32×C4C2×C411yescharacteristic
30C22×C32×C4C2311yescharacteristic
31C32×C4⋊C4—22no—
32C32×C4⋊C4—24no—
33C32×C42—22no—
34C32×C42—22no—
35C32×C42D412yes—
36C32×C42D412yes—
37C2×C3×C3⋊C8—24no—
38#1461—31noSylow
39C22×C3×Q8—21no—
40C22×C3×Q8Dic311yescharacteristic
41C22×C3×Q8C3×C411yescharacteristic
42C3×C4×Q8—24no—
43C3×C4×Q8—24no—
44C3×C4×Q8—22no—
45C3×C4×Q8—22no—
46C3×C4×Q8—22no—
47C3×C4×Q8—22no—
48C2×C3×C4⋊C4—21no—
49C2×C3×C4⋊C4—22no—
50C2×C3×C4⋊C4Dic311yescharacteristic
51C2×C3×C4⋊C4C3×C411yescharacteristic
52C2×C3×C4⋊C4C2×D312yes—
53C2×C3×C4⋊C4C22×C312yes—
54C2×C3×C42—22no—
55C2×C3×C42—21no—
56C2×C3×C42Dic312yes—
57C2×C3×C42C3×C412yes—
58C2×C3×C42C2×D311yescharacteristic
59C2×C3×C42C22×C311yescharacteristic
60C3×C4⋊C8—62no—
61C3×C22⋊C8—34no—
62C3×C4×C8—62no—
63#830C22×C314yes—
64C4⋊(C3⋊C8)—22no—
65C4×C3⋊C8—22no—
66C23×C32C22×C411yescharacteristic
67C32×Q8—28no—
68C2×C32×C4—22no—
69C2×C32×C4—22no—
70C2×C32×C4—22no—
71C2×C32×C4—22no—
72C2×C32×C4—41no—
73C2×C32×C4—42no—
74C2×C32×C4C22⋊C411yescharacteristic
75C2×C32×C4C22⋊C412yes—
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C2×C814yes—
78C2×C32×C4C2×C812yes—
79C2×C32×C4M1612yes—
80C2×C32×C4C2×D412yes—
81C3×C3⋊C8—44no—
82C2×C4×Q8C3×D311yescharacteristic
83#431—32no—
84#324—34no—
85C2×C3×Q8—24no—
86C2×C3×Q8—24no—
87C2×C3×Q8—22no—
88C2×C3×Q8—22no—
89C2×C3×Q8—22no—
90C2×C3×Q8—22no—
91C2×C3×Q8—24no—
92C2×C3×Q8C3⋊C814yescomplemented
93C2×C3×Q8C3×C814yescomplemented
94C22×C3×C4—21no—
95C22×C3×C4—22no—
96C22×C3×C4—21no—
97C22×C3×C4—22no—
98C22×C3×C4—21no—
99C22×C3×C4C2×Dic312yes—
100C22×C3×C4C2×Dic311yescharacteristic
101C22×C3×C4C2×Dic312yes—
102C22×C3×C4C2×Dic311yescharacteristic
103C22×C3×C4C2×C3×C411yescharacteristic
104C22×C3×C4C2×C3×C412yes—
105C22×C3×C4C2×C3×C412yes—
106C22×C3×C4C2×C3×C411yescharacteristic
107C22×C3×C4C22×D311yescharacteristic
108C22×C3×C4C23×C311yescharacteristic
109C2×C3×C8—64no—
110C3×C4⋊C4—24no—
111C3×C4⋊C4—28no—
112C3×C4⋊C4—22no—
113C3×C4⋊C4—22no—
114C3×C4⋊C4—24no—
115C3×C4⋊C4—24no—
116C3×C42—24no—
117C3×C42—24no—
118C3×C42—22no—
119C3×C42—22no—
120C3×C42—22no—
121C3×C42—22no—
122C3×C42—22no—
123C3×C42—22no—
124C3×C42#6712yes—
125C3×C42#6712yes—
126C3×C42C3×D412yes—
127C3×C42C3×D412yes—
128C2×C3⋊C8—24no—
129C22×C32—21no—
130C22×C32—21no—
131C22×C32C2×C22⋊C411yescharacteristic
132C22×C32C22×C811yescharacteristic
133C22×C32C2×M1611yescharacteristic
134C32×C4—24no—
135C32×C4—21no—
136C32×C4—22no—
137C32×C4—42no—
138C32×C4C22⋊C814yes—
139C32×C4#10112yes—
140C22×Q8C3×Dic311yescharacteristic
141C4×Q8—22no—
142C4×Q8—22no—
143C2×C4⋊C4C3×Dic311yescharacteristic
144C2×C4⋊C4C2×C3×D312yes—
145C2×C42C3×Dic312yes—
146C2×C42C2×C3×D311yescharacteristic
147C4⋊C8—62no—
148C22⋊C8—34no—
149C4×C8—62no—
150C23×C3—21no—
151C23×C3C22×Dic311yescharacteristic
152C23×C3C22×C3×C411yescharacteristic
153C3×Q8—216no—
154C3×Q8—28no—
155C3×Q8—28no—
156C2×C3×C4—24no—
157C2×C3×C4—24no—
158C2×C3×C4—24no—
159C2×C3×C4—22no—
160C2×C3×C4—22no—
161C2×C3×C4—22no—
162C2×C3×C4—22no—
163C2×C3×C4—22no—
164C2×C3×C4—22no—
165C2×C3×C4—24no—
166C2×C3×C4—22no—
167C2×C3×C4—22no—
168C2×C3×C4—24no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—22no—
174C2×C3×C4—22no—
175C2×C3×C4—41no—
176C2×C3×C4—41no—
177C2×C3×C4—42no—
178C2×C3×C4—44no—
179C2×C3×C4—42no—
180C2×C3×C4—42no—
181C2×C3×C4C2×C3⋊C814yes—
182C2×C3×C4C2×C3⋊C812yes—
183C2×C3×C4#20812yes—
184C2×C3×C4#21711yescharacteristic
185C2×C3×C4#21712yes—
186C2×C3×C4#21711yescharacteristic
187C2×C3×C4C3×C22⋊C411yescharacteristic
188C2×C3×C4C3×C22⋊C412yes—
189C2×C3×C4C3×C22⋊C411yescharacteristic
190C2×C3×C4C2×C3×C814yes—
191C2×C3×C4C2×C3×C812yes—
192C2×C3×C4C3×M1612yes—
193C2×C3×C4C2×#6712yes—
194C2×C3×C4C2×C3×D412yes—
195C3×C8—124no—
196C3⋊C8—44no—
197C2×C32—21no—
198C2×C32—21no—
199C2×C32C2×C22⋊C811yescharacteristic
200C2×C32#41011yescharacteristic
201C2×C32C2×#10111yescharacteristic
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8C3×C3⋊C814yescomplemented
205C22×C4C2×C3×Dic312yes—
206C22×C4C2×C3×Dic311yescharacteristic
207C22×C4C2×C3×Dic312yes—
208C22×C4C2×C3×Dic311yescharacteristic
209C22×C4C22×C3×D311yescharacteristic
210C2×C8—64no—
211C4⋊C4—22no—
212C4⋊C4—24no—
213C42—22no—
214C42—22no—
215C42C3×#6712yes—
216C42C3×#6712yes—
217C22×C3—22no—
218C22×C3—22no—
219C22×C3—21no—
220C22×C3—21no—
221C22×C3—21no—
222C22×C3—21no—
223C22×C3—21no—
224C22×C3—21no—
225C22×C3—21no—
226C22×C3C22×C3⋊C811yescharacteristic
227C22×C3C2×#20811yescharacteristic
228C22×C3C2×#21711yescharacteristic
229C22×C3C2×C3×C22⋊C411yescharacteristic
230C22×C3C22×C3×C811yescharacteristic
231C22×C3C2×C3×M1611yescharacteristic
232C3×C4—28no—
233C3×C4—22no—
234C3×C4—24no—
235C3×C4—21no—
236C3×C4—22no—
237C3×C4—24no—
238C3×C4—22no—
239C3×C4—21no—
240C3×C4—24no—
241C3×C4—22no—
242C3×C4—42no—
243C3×C4—44no—
244C3×C4—42no—
245C3×C4—42no—
246C3×C4#83014yes—
247C3×C4#83612yes—
248C3×C4C3×C22⋊C814yes—
249C3×C4C3×#10112yes—
250C32#146111yescharacteristic, complemented, Sylow
251C23C22×C3×Dic311yescharacteristic
252Q8—28no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4C2×C3×C3⋊C814yes—
260C2×C4C2×C3×C3⋊C812yes—
261C2×C4C3×#20812yes—
262C2×C4C3×#21711yescharacteristic
263C2×C4C3×#21712yes—
264C2×C4C3×#21711yescharacteristic
265C2×C4C2×C3×#6712yes—
266C8—124no—
267C2×C3—22no—
268C2×C3—22no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3C2×#83011yescharacteristic
277C2×C3C2×#83611yescharacteristic
278C2×C3#524011yescharacteristic
279C2×C3C2×C3×C22⋊C811yescharacteristic
280C2×C3C3×#41011yescharacteristic
281C2×C3C2×C3×#10111yescharacteristic
282C22—21no—
283C22—21no—
284C22C22×C3×C3⋊C811yescharacteristic
285C22C2×C3×#20811yescharacteristic
286C22C2×C3×#21711yescharacteristic
287C4—24no—
288C4—21no—
289C4—22no—
290C4—42no—
291C4C3×#83014yes—
292C4C3×#83612yes—
293C3—21no—
294C3#7162411yescharacteristic, direct product factor
295C3C3×#146111yescharacteristic, complemented
296C2—21no—
297C2—21no—
298C2C2×C3×#83011yescharacteristic
299C2C2×C3×#83611yescharacteristic
300C2C3×#524011yescharacteristic
subgroupG/H
centerC2×C3×C4#217
commutatorC22×C3C22×C3×C8
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C4×Q8C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22×C4
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×C4×Q8D3
hypocenterC3C3×#1461
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C2×C3×C4×Q8

Complements

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

NH ≅ G/Ntype
5. #71624C3direct (N × H)
25. C2×C32×Q8C8semidirect
92. C2×C3×Q8C3⋊C8semidirect
93. C2×C3×Q8C3×C8semidirect
204. C2×Q8C3×C3⋊C8semidirect
250. C32#1461semidirect
294. C3#71624direct (N × H)
295. C3C3×#1461semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×Q82
C3×#49252
C3×#45282
C3×#14613
#716243