Finite Group Databasebeta

← C3×#71552 #11773872

Subgroups — C3×#71552 #11773872

Order 1152.

833 conjugacy classes of subgroups.

The subgroup lattice has 371 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4⋊C4C211yesmaximal, characteristic
2C3×#5207C212yesmaximal
3C3×#4528C214yesmaximal, complemented
4C3×#1463—31nomaximal
5#71552C311yesmaximal, characteristic, direct product factor
6C23×C32×C4C411yescharacteristic
7C23×C32×C4C411yescharacteristic
8C23×C32×C4C2211yescharacteristic
9C2×C32×C4⋊C4—22no—
10C2×C32×C4⋊C4—22no—
11C2×C32×C4⋊C4C412yes—
12C2×C32×C4⋊C4C2212yes—
13C2×C3×#208—22no—
14C3×#830—22no—
15C3×#830C2214yes—
16C22×C3×C4⋊C4—21no—
17C22×C3×C4⋊C4D311yescharacteristic
18C22×C3×C4⋊C4C2×C311yescharacteristic
19C3×#407—32no—
20#5207C2×C312yes—
21C3×#324—34no—
22#4528C2×C314yescomplemented
23C24×C32C2×C411yescharacteristic
24C22×C32×C4—21no—
25C22×C32×C4—21no—
26C22×C32×C4—24no—
27C22×C32×C4—21no—
28C22×C32×C4—21no—
29C22×C32×C4—42no—
30C22×C32×C4—42no—
31C22×C32×C4C2×C412yes—
32C22×C32×C4C2×C412yes—
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4D412yes—
35C22×C32×C4D412yes—
36C22×C32×C4C2311yescharacteristic
37C32×C4⋊C4—24no—
38C32×C4⋊C4—24no—
39C3×#208—44no—
40C2×C3×C3⋊C8—24no—
41#1463—31noSylow
42C23×C3×C4—21no—
43C23×C3×C4—21no—
44C23×C3×C4—21no—
45C23×C3×C4Dic311yescharacteristic
46C23×C3×C4Dic311yescharacteristic
47C23×C3×C4C3×C411yescharacteristic
48C23×C3×C4C3×C411yescharacteristic
49C23×C3×C4C2×D311yescharacteristic
50C23×C3×C4C22×C311yescharacteristic
51C2×C3×M16—62no—
52C2×C3×C4⋊C4—24no—
53C2×C3×C4⋊C4—24no—
54C2×C3×C4⋊C4—22no—
55C2×C3×C4⋊C4—22no—
56C2×C3×C4⋊C4—22no—
57C2×C3×C4⋊C4—22no—
58C2×C3×C4⋊C4—22no—
59C2×C3×C4⋊C4—22no—
60C2×C3×C4⋊C4Dic312yes—
61C2×C3×C4⋊C4C3×C412yes—
62C2×C3×C4⋊C4C2×D312yes—
63C2×C3×C4⋊C4C22×C312yes—
64C2×#208—22no—
65C3×C22⋊C8—34no—
66C3×C22⋊C8—62no—
67#830—22no—
68#830C22×C314yes—
69C23×C32—22no—
70C23×C32—22no—
71C23×C32—22no—
72C23×C32C22⋊C411yescharacteristic
73C23×C32C22⋊C411yescharacteristic
74C23×C32C22×C411yescharacteristic
75C2×C32×C4—24no—
76C2×C32×C4—24no—
77C2×C32×C4—22no—
78C2×C32×C4—22no—
79C2×C32×C4—22no—
80C2×C32×C4—24no—
81C2×C32×C4—41no—
82C2×C32×C4—42no—
83C2×C32×C4—41no—
84C2×C32×C4—42no—
85C2×C32×C4—42no—
86C2×C32×C4—42no—
87C2×C32×C4C22⋊C412yes—
88C2×C32×C4M1614yescomplemented
89C2×C32×C4C2×D412yes—
90C3×C3⋊C8—44no—
91C22×C4⋊C4C3×D311yescharacteristic
92#407—32no—
93#324—34no—
94C24×C3—21no—
95C24×C3C2×Dic311yescharacteristic
96C24×C3C2×C3×C411yescharacteristic
97C22×C3×C4—22no—
98C22×C3×C4—22no—
99C22×C3×C4—28no—
100C22×C3×C4—21no—
101C22×C3×C4—21no—
102C22×C3×C4—21no—
103C22×C3×C4—21no—
104C22×C3×C4—24no—
105C22×C3×C4—24no—
106C22×C3×C4—22no—
107C22×C3×C4—22no—
108C22×C3×C4—21no—
109C22×C3×C4—21no—
110C22×C3×C4—21no—
111C22×C3×C4—21no—
112C22×C3×C4—22no—
113C22×C3×C4—22no—
114C22×C3×C4—21no—
115C22×C3×C4—22no—
116C22×C3×C4—22no—
117C22×C3×C4—21no—
118C22×C3×C4—42no—
119C22×C3×C4—42no—
120C22×C3×C4—44no—
121C22×C3×C4—44no—
122C22×C3×C4—42no—
123C22×C3×C4—42no—
124C22×C3×C4C2×Dic312yes—
125C22×C3×C4C2×Dic312yes—
126C22×C3×C4C2×Dic311yescharacteristic
127C22×C3×C4#6712yes—
128C22×C3×C4#6712yes—
129C22×C3×C4C2×C3×C412yes—
130C22×C3×C4C2×C3×C412yes—
131C22×C3×C4C2×C3×C411yescharacteristic
132C22×C3×C4C3×D412yes—
133C22×C3×C4C3×D412yes—
134C22×C3×C4C22×D311yescharacteristic
135C22×C3×C4C23×C311yescharacteristic
136C3×M16—124no—
137C2×C3×C8—64no—
138C3×C4⋊C4—28no—
139C3×C4⋊C4—28no—
140C3×C4⋊C4—24no—
141C3×C4⋊C4—24no—
142C3×C4⋊C4—24no—
143C3×C4⋊C4—24no—
144#208—44no—
145C2×C3⋊C8—24no—
146C22×C32—28no—
147C22×C32—21no—
148C22×C32—21no—
149C22×C32—21no—
150C22×C32—21no—
151C22×C32—21no—
152C22×C32—21no—
153C22×C32#9912yes—
154C22×C32#10112yes—
155C22×C32C2×C22⋊C411yescharacteristic
156C22×C32C2×M1612yes—
157C32×C4—24no—
158C32×C4—22no—
159C32×C4—22no—
160C32×C4—42no—
161C23×C4C3×Dic311yescharacteristic
162C23×C4C3×Dic311yescharacteristic
163C23×C4C2×C3×D311yescharacteristic
164C2×M16—62no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4C3×Dic312yes—
168C2×C4⋊C4C2×C3×D312yes—
169C22⋊C8—34no—
170C22⋊C8—62no—
171C23×C3—24no—
172C23×C3—24no—
173C23×C3—24no—
174C23×C3—22no—
175C23×C3—22no—
176C23×C3—22no—
177C23×C3—22no—
178C23×C3—22no—
179C23×C3—22no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3—21no—
183C23×C3#21711yescharacteristic
184C23×C3#21711yescharacteristic
185C23×C3C3×C22⋊C411yescharacteristic
186C23×C3C3×C22⋊C411yescharacteristic
187C23×C3C22×Dic311yescharacteristic
188C23×C3C22×C3×C411yescharacteristic
189C2×C3×C4—24no—
190C2×C3×C4—28no—
191C2×C3×C4—28no—
192C2×C3×C4—24no—
193C2×C3×C4—24no—
194C2×C3×C4—24no—
195C2×C3×C4—24no—
196C2×C3×C4—24no—
197C2×C3×C4—24no—
198C2×C3×C4—24no—
199C2×C3×C4—22no—
200C2×C3×C4—22no—
201C2×C3×C4—22no—
202C2×C3×C4—22no—
203C2×C3×C4—24no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—24no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—44no—
210C2×C3×C4—41no—
211C2×C3×C4—42no—
212C2×C3×C4—41no—
213C2×C3×C4—42no—
214C2×C3×C4—41no—
215C2×C3×C4—41no—
216C2×C3×C4—42no—
217C2×C3×C4—44no—
218C2×C3×C4—42no—
219C2×C3×C4—44no—
220C2×C3×C4—42no—
221C2×C3×C4—42no—
222C2×C3×C4—44no—
223C2×C3×C4—44no—
224C2×C3×C4—42no—
225C2×C3×C4—42no—
226C2×C3×C4—42no—
227C2×C3×C4—42no—
228C2×C3×C4#20814yescomplemented
229C2×C3×C4#21712yes—
230C2×C3×C4C3×C22⋊C412yes—
231C2×C3×C4C3×M1614yescomplemented
232C2×C3×C4C2×#6712yes—
233C2×C3×C4C2×C3×D412yes—
234C3×C8—124no—
235C3⋊C8—44no—
236C2×C32—22no—
237C2×C32—22no—
238C2×C32—22no—
239C2×C32#40711yescharacteristic
240C2×C32C2×#9911yescharacteristic
241C2×C32C2×#10111yescharacteristic
242C24C2×C3×Dic311yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—24no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4C2×C3×Dic312yes—
251C22×C4C2×C3×Dic312yes—
252C22×C4C2×C3×Dic311yescharacteristic
253C22×C4C3×#6712yes—
254C22×C4C3×#6712yes—
255C22×C4C22×C3×D311yescharacteristic
256M16—124no—
257C2×C8—64no—
258C4⋊C4—24no—
259C4⋊C4—24no—
260C22×C3—22no—
261C22×C3—22no—
262C22×C3—22no—
263C22×C3—22no—
264C22×C3—216no—
265C22×C3—28no—
266C22×C3—28no—
267C22×C3—22no—
268C22×C3—22no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—21no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—22no—
282C22×C3—21no—
283C22×C3—22no—
284C22×C3—22no—
285C22×C3#83412yes—
286C22×C3#83612yes—
287C22×C3C3×#9912yes—
288C22×C3C3×#10112yes—
289C22×C3C2×#20812yes—
290C22×C3C2×#21711yescharacteristic
291C22×C3C2×C3×C22⋊C411yescharacteristic
292C22×C3C2×C3×M1612yes—
293C3×C4—28no—
294C3×C4—24no—
295C3×C4—22no—
296C3×C4—22no—
297C3×C4—24no—
298C3×C4—22no—
299C3×C4—22no—
300C3×C4—42no—
301C3×C4—42no—
302C3×C4—44no—
303C3×C4—42no—
304C3×C4—42no—
305C32#146311yescharacteristic, complemented, Sylow
306C23—22no—
307C23—22no—
308C23—22no—
309C23C3×#21711yescharacteristic
310C23C3×#21711yescharacteristic
311C23C22×C3×Dic311yescharacteristic
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4C3×#20814yescomplemented
325C2×C4C3×#21712yes—
326C2×C4C2×C3×#6712yes—
327C8—124no—
328C2×C3—24no—
329C2×C3—24no—
330C2×C3—24no—
331C2×C3—22no—
332C2×C3—22no—
333C2×C3—22no—
334C2×C3—22no—
335C2×C3—22no—
336C2×C3—22no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3#520711yescharacteristic
341C2×C3C2×#83411yescharacteristic
342C2×C3C2×#83611yescharacteristic
343C2×C3C3×#40711yescharacteristic
344C2×C3C2×C3×#9911yescharacteristic
345C2×C3C2×C3×#10111yescharacteristic
346C22—28no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22C3×#83412yes—
354C22C3×#83612yes—
355C22C2×C3×#20812yes—
356C22C2×C3×#21711yescharacteristic
357C4—24no—
358C4—22no—
359C4—22no—
360C4—42no—
361C3—21no—
362C3#7155211yescharacteristic, direct product factor
363C3C3×#146311yescharacteristic, complemented
364C2—22no—
365C2—22no—
366C2—22no—
367C2C3×#520711yescharacteristic
368C2C2×C3×#83411yescharacteristic
369C2C2×C3×#83611yescharacteristic
subgroupG/H
centerC22×C3C2×#217
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC22×C32×C4⋊C4C2
socleC22×C32C2×C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC22×C3×C4⋊C4D3
hypocenterC3C3×#1463
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C22×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#4528C2semidirect
5. #71552C3direct (N × H)
22. #4528C2×C3semidirect
88. C2×C32×C4M16semidirect
228. C2×C3×C4#208semidirect
231. C2×C3×C4C3×M16semidirect
305. C32#1463semidirect
324. C2×C4C3×#208semidirect
362. C3#71552direct (N × H)
363. C3C3×#1463semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C4⋊C42
C3×#52072
C3×#45282
C3×#14633
#715523