Finite Group Databasebeta

← C3×C4×#836 #11783800

Subgroups — C3×C4×#836 #11783800

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×Q8C211yesmaximal, characteristic
2C2×C3×#836C212yesmaximal
3C3×C4×#208C212yesmaximal
4C3×#4530C212yesmaximal
5C3×C4×#101—31nomaximal
6C4×#836C311yesmaximal, characteristic, direct product factor
7C22×C32×Q8C2211yescharacteristic
8C32×C4×Q8—22no—
9C32×C4×Q8—22no—
10C2×C32×C4⋊C4C412yes—
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C42C412yes—
13C2×C32×C42C2211yescharacteristic
14C2×C3×#208C2214yes—
15C3×#836C418yesdirect product factor
16C3×#803—22no—
17C3×C4×C3⋊C8—22no—
18C2×C3×C4×Q8—21no—
19C2×C3×C4×Q8D311yescharacteristic
20C2×C3×C4×Q8C2×C311yescharacteristic
21C2×C3×#101—32no—
22C3×C4×M16—32no—
23C2×#836C2×C312yes—
24C4×#208C2×C312yes—
25C3×#343—32no—
26#4530C2×C312yes—
27C2×C32×Q8—22no—
28C2×C32×Q8—22no—
29C2×C32×Q8C2×C414yes—
30C22×C32×C4C2×C412yes—
31C22×C32×C4C2×C411yescharacteristic
32C22×C32×C4C2×C412yes—
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C32×C4⋊C4—24no—
36C32×C4⋊C4—22no—
37C32×C42—22no—
38C32×C42—22no—
39C32×C42D412yes—
40C32×C42D412yes—
41C3×#208—24no—
42C3×#208C2×C418yes—
43C2×C3×C3⋊C8—24no—
44C4×#101—31noSylow
45C22×C3×Q8—21no—
46C22×C3×Q8C2×D311yescharacteristic
47C22×C3×Q8C22×C311yescharacteristic
48C2×C3×M16—34no—
49C3×C4×Q8—24no—
50C3×C4×Q8—24no—
51C3×C4×Q8—22no—
52C3×C4×Q8—22no—
53C3×C4×Q8—22no—
54C3×C4×Q8—22no—
55C2×C3×C4⋊C4—22no—
56C2×C3×C4⋊C4—21no—
57C2×C3×C4⋊C4Dic312yes—
58C2×C3×C4⋊C4C3×C412yes—
59C2×C3×C4⋊C4C2×D311yescharacteristic
60C2×C3×C4⋊C4C22×C311yescharacteristic
61C2×C3×C42—22no—
62C2×C3×C42—21no—
63C2×C3×C42Dic312yes—
64C2×C3×C42C3×C412yes—
65C2×C3×C42C2×D311yescharacteristic
66C2×C3×C42C22×C311yescharacteristic
67C2×#208C22×C314yes—
68C3×#101—38no—
69C3×#97—62no—
70C3×C4×C8—62no—
71#836C3×C418yesdirect product factor
72#803—22no—
73C4×C3⋊C8—22no—
74C23×C32C22×C411yescharacteristic
75C32×Q8—28no—
76C2×C32×C4—22no—
77C2×C32×C4—22no—
78C2×C32×C4—22no—
79C2×C32×C4—22no—
80C2×C32×C4—41no—
81C2×C32×C4—42no—
82C2×C32×C4C4214yes—
83C2×C32×C4C22⋊C411yescharacteristic
84C2×C32×C4C22⋊C412yes—
85C2×C32×C4C22⋊C411yescharacteristic
86C2×C32×C4C22×C412yes—
87C2×C32×C4C2×D412yes—
88C2×C32×C4#4112yes—
89C3×C3⋊C8—28no—
90C2×C4×Q8C3×D311yescharacteristic
91C2×#101—32no—
92C4×M16—32no—
93#343—32no—
94C2×C3×Q8—24no—
95C2×C3×Q8—24no—
96C2×C3×Q8—22no—
97C2×C3×Q8—22no—
98C2×C3×Q8—22no—
99C2×C3×Q8—22no—
100C2×C3×Q8—24no—
101C2×C3×Q8C4×D314yes—
102C2×C3×Q8C2×C3×C414yes—
103C22×C3×C4—21no—
104C22×C3×C4—22no—
105C22×C3×C4—22no—
106C22×C3×C4—21no—
107C22×C3×C4—21no—
108C22×C3×C4C2×Dic312yes—
109C22×C3×C4C2×Dic311yescharacteristic
110C22×C3×C4C2×Dic312yes—
111C22×C3×C4C2×Dic311yescharacteristic
112C22×C3×C4C2×C3×C412yes—
113C22×C3×C4C2×C3×C411yescharacteristic
114C22×C3×C4C2×C3×C412yes—
115C22×C3×C4C2×C3×C411yescharacteristic
116C22×C3×C4C22×D311yescharacteristic
117C22×C3×C4C23×C311yescharacteristic
118C3×M16—38no—
119C3×M16—64no—
120C2×C3×C8—64no—
121C3×C4⋊C4—28no—
122C3×C4⋊C4—24no—
123C3×C4⋊C4—24no—
124C3×C4⋊C4—24no—
125C3×C4⋊C4—22no—
126C3×C4⋊C4—22no—
127C3×C42—24no—
128C3×C42—24no—
129C3×C42—22no—
130C3×C42—22no—
131C3×C42—22no—
132C3×C42—22no—
133C3×C42—22no—
134C3×C42—22no—
135C3×C42#6712yes—
136C3×C42#6712yes—
137C3×C42C3×D412yes—
138C3×C42C3×D412yes—
139#208—24no—
140#208C2×C3×C418yes—
141C2×C3⋊C8—24no—
142C22×C32—21no—
143C22×C32—21no—
144C22×C32C2×C4211yescharacteristic
145C22×C32C2×C22⋊C411yescharacteristic
146C22×C32#11711yescharacteristic
147C32×C4—24no—
148C32×C4—21no—
149C32×C4—22no—
150C32×C4—42no—
151C32×C4#10112yescomplemented
152C32×C4C4×D414yes—
153C22×Q8C2×C3×D311yescharacteristic
154C2×M16—34no—
155C4×Q8—22no—
156C4×Q8—22no—
157C2×C4⋊C4C3×Dic312yes—
158C2×C4⋊C4C2×C3×D311yescharacteristic
159C2×C42C3×Dic312yes—
160C2×C42C2×C3×D311yescharacteristic
161#101—38no—
162#97—62no—
163C4×C8—62no—
164C23×C3—21no—
165C23×C3C22×Dic311yescharacteristic
166C23×C3C22×C3×C411yescharacteristic
167C3×Q8—216no—
168C3×Q8—28no—
169C3×Q8—28no—
170C2×C3×C4—24no—
171C2×C3×C4—24no—
172C2×C3×C4—24no—
173C2×C3×C4—22no—
174C2×C3×C4—22no—
175C2×C3×C4—22no—
176C2×C3×C4—22no—
177C2×C3×C4—22no—
178C2×C3×C4—22no—
179C2×C3×C4—24no—
180C2×C3×C4—22no—
181C2×C3×C4—22no—
182C2×C3×C4—24no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—22no—
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—22no—
189C2×C3×C4—41no—
190C2×C3×C4—41no—
191C2×C3×C4—42no—
192C2×C3×C4—44no—
193C2×C3×C4—42no—
194C2×C3×C4—42no—
195C2×C3×C4C4×Dic314yes—
196C2×C3×C4#21711yescharacteristic
197C2×C3×C4#21712yes—
198C2×C3×C4#21711yescharacteristic
199C2×C3×C4C3×C4214yes—
200C2×C3×C4C3×C22⋊C411yescharacteristic
201C2×C3×C4C3×C22⋊C412yes—
202C2×C3×C4C3×C22⋊C411yescharacteristic
203C2×C3×C4C2×C4×D312yes—
204C2×C3×C4#23512yes—
205C2×C3×C4C2×#6712yes—
206C2×C3×C4C22×C3×C412yes—
207C2×C3×C4C2×C3×D412yes—
208C2×C3×C4C3×#4112yes—
209C3×C8—68no—
210C3⋊C8—28no—
211C2×C32—21no—
212C2×C32—21no—
213C2×C32C4×C22⋊C411yescharacteristic
214C2×C32C2×#10111yescharacteristic
215C2×C32#41311yescharacteristic
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8C3×C4×D314yes—
219C22×C4C2×C3×Dic312yes—
220C22×C4C2×C3×Dic311yescharacteristic
221C22×C4C2×C3×Dic312yes—
222C22×C4C2×C3×Dic311yescharacteristic
223C22×C4C22×C3×D311yescharacteristic
224M16—38no—
225M16—64no—
226C2×C8—64no—
227C4⋊C4—24no—
228C4⋊C4—22no—
229C42—22no—
230C42—22no—
231C42C3×#6712yes—
232C42C3×#6712yes—
233C22×C3—22no—
234C22×C3—22no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3C2×C4×Dic311yescharacteristic
243C22×C3#92611yescharacteristic
244C22×C3C2×#21711yescharacteristic
245C22×C3C2×C3×C4211yescharacteristic
246C22×C3C2×C3×C22⋊C411yescharacteristic
247C22×C3C3×#11711yescharacteristic
248C3×C4—28no—
249C3×C4—22no—
250C3×C4—24no—
251C3×C4—21no—
252C3×C4—22no—
253C3×C4—24no—
254C3×C4—21no—
255C3×C4—22no—
256C3×C4—24no—
257C3×C4—22no—
258C3×C4—42no—
259C3×C4—44no—
260C3×C4—42no—
261C3×C4—42no—
262C3×C4#83612yesdirect product factor
263C3×C4C3×#10112yescomplemented
264C3×C4C4×#6714yes—
265C3×C4C3×C4×D414yes—
266C32C4×#10111yescharacteristic, complemented, Sylow
267C23C22×C3×Dic311yescharacteristic
268Q8—28no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4C3×C4×Dic314yes—
276C2×C4C3×#21711yescharacteristic
277C2×C4C3×#21712yes—
278C2×C4C3×#21711yescharacteristic
279C2×C4C2×C3×C4×D312yes—
280C2×C4C3×#23512yes—
281C2×C4C2×C3×#6712yes—
282C8—68no—
283C2×C3—22no—
284C2×C3—22no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—21no—
289C2×C3—21no—
290C2×C3—21no—
291C2×C3—21no—
292C2×C3C4×#21711yescharacteristic
293C2×C3C2×#83611yescharacteristic
294C2×C3#523711yescharacteristic
295C2×C3C3×C4×C22⋊C411yescharacteristic
296C2×C3C2×C3×#10111yescharacteristic
297C2×C3C3×#41311yescharacteristic
298C22—21no—
299C22—21no—
300C22C2×C3×C4×Dic311yescharacteristic
301C22C3×#92611yescharacteristic
302C22C2×C3×#21711yescharacteristic
303C4—24no—
304C4—21no—
305C4—22no—
306C4—42no—
307C4C3×#83612yesdirect product factor
308C4C3×C4×#6714yes—
309C3—21no—
310C3C4×#83611yescharacteristic, direct product factor
311C3C3×C4×#10111yescharacteristic, complemented
312C2—21no—
313C2—21no—
314C2C3×C4×#21711yescharacteristic
315C2C2×C3×#83611yescharacteristic
316C2C3×#523711yescharacteristic
subgroupG/H
centerC2×C3×C4#217
commutatorC22×C3C2×C3×C42
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×C4×#101
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
6. C4×#836C3direct (N × H)
15. C3×#836C4direct (N × H)
71. #836C3×C4direct (N × H)
151. C32×C4#101semidirect
262. C3×C4#836direct (N × H)
263. C3×C4C3×#101semidirect
266. C32C4×#101semidirect
307. C4C3×#836direct (N × H)
310. C3C4×#836direct (N × H)
311. C3C3×C4×#101semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×Q82
C2×C3×#8362
C3×C4×#2082
C3×#45302
C3×C4×#1013
C4×#8363