Finite Group Databasebeta

← C2×C3×#4530 #11783394

Subgroups — C2×C3×#4530 #11783394

Order 1152.

1073 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4⋊C4C211yesmaximal, characteristic
2C22×C3×#208C212yesmaximal
3C3×#4530C214yesmaximal, direct product factor
4C2×C3×#343—31nomaximal
5C2×#4530C311yesmaximal, characteristic, direct product factor
6C23×C32×C4C412yes—
7C23×C32×C4C2211yescharacteristic
8C2×C32×C4⋊C4—22no—
9C2×C32×C4⋊C4—22no—
10C2×C32×C4⋊C4C412yes—
11C2×C32×C4⋊C4C2212yes—
12C2×C3×#208—24no—
13C2×C3×#208—22no—
14C2×C3×#208C418yescomplemented
15C2×C3×#208C2214yes—
16C22×C3×C3⋊C8—22no—
17C22×C3×M16—32no—
18C22×C3×C4⋊C4—21no—
19C22×C3×C4⋊C4D311yescharacteristic
20C22×C3×C4⋊C4C2×C311yescharacteristic
21C22×#208C2×C312yes—
22C3×#343—34no—
23#4530C2×C314yesdirect product factor
24C24×C32C2×C411yescharacteristic
25C22×C32×C4—22no—
26C22×C32×C4—22no—
27C22×C32×C4—44no—
28C22×C32×C4C2×C414yes—
29C22×C32×C4C2×C411yescharacteristic
30C22×C32×C4C2×C414yes—
31C22×C32×C4D412yes—
32C22×C32×C4D412yes—
33C22×C32×C4D412yes—
34C22×C32×C4Q812yes—
35C22×C32×C4C2311yescharacteristic
36C32×C4⋊C4—24no—
37C32×C4⋊C4—24no—
38C3×#208—28no—
39C3×#208—24no—
40C3×#208C2×C418yescomplemented
41C2×C3×C3⋊C8—28no—
42C2×C3×C3⋊C8—24no—
43C2×#343—31noSylow
44C23×C3×C4—22no—
45C23×C3×C4—21no—
46C23×C3×C4Dic312yes—
47C23×C3×C4C3×C412yes—
48C23×C3×C4C2×D311yescharacteristic
49C23×C3×C4C22×C311yescharacteristic
50C2×C3×M16—38no—
51C2×C3×M16—34no—
52C2×C3×M16—64no—
53C2×C3×M16—62no—
54C22×C3×C8—62no—
55C2×C3×C4⋊C4—24no—
56C2×C3×C4⋊C4—24no—
57C2×C3×C4⋊C4—22no—
58C2×C3×C4⋊C4—22no—
59C2×C3×C4⋊C4—22no—
60C2×C3×C4⋊C4—22no—
61C2×C3×C4⋊C4—22no—
62C2×C3×C4⋊C4—22no—
63C2×C3×C4⋊C4Dic312yes—
64C2×C3×C4⋊C4C3×C412yes—
65C2×C3×C4⋊C4C2×D312yes—
66C2×C3×C4⋊C4C22×C312yes—
67C2×#208—24no—
68C2×#208—22no—
69C2×#208C3×C418yescomplemented
70C2×#208C22×C314yes—
71C22×C3⋊C8—22no—
72C23×C32—22no—
73C23×C32—22no—
74C23×C32C4212yes—
75C23×C32C22⋊C411yescharacteristic
76C23×C32C22⋊C411yescharacteristic
77C23×C32C4⋊C412yes—
78C23×C32C22×C411yescharacteristic
79C2×C32×C4—24no—
80C2×C32×C4—44no—
81C2×C32×C4—44no—
82C2×C32×C4—44no—
83C2×C32×C4C4212yes—
84C2×C32×C4C22⋊C414yes—
85C2×C32×C4C22⋊C414yes—
86C2×C32×C4C22⋊C412yes—
87C2×C32×C4C4⋊C414yes—
88C2×C32×C4C4⋊C414yes—
89C2×C32×C4C4⋊C412yes—
90C2×C32×C4C22×C412yes—
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D412yes—
93C2×C32×C4C2×Q811yescharacteristic
94C3×C3⋊C8—28no—
95C22×M16—32no—
96C22×C4⋊C4C3×D311yescharacteristic
97#343—34no—
98C24×C3—21no—
99C24×C3C2×Dic311yescharacteristic
100C24×C3C2×C3×C411yescharacteristic
101C22×C3×C4—24no—
102C22×C3×C4—24no—
103C22×C3×C4—22no—
104C22×C3×C4—22no—
105C22×C3×C4—22no—
106C22×C3×C4—22no—
107C22×C3×C4—22no—
108C22×C3×C4—24no—
109C22×C3×C4—22no—
110C22×C3×C4—21no—
111C22×C3×C4—24no—
112C22×C3×C4—22no—
113C22×C3×C4—22no—
114C22×C3×C4—21no—
115C22×C3×C4—48no—
116C22×C3×C4—44no—
117C22×C3×C4—44no—
118C22×C3×C4Dic612yes—
119C22×C3×C4C4×D314yes—
120C22×C3×C4D1212yes—
121C22×C3×C4C2×Dic314yes—
122C22×C3×C4C2×Dic311yescharacteristic
123C22×C3×C4#6712yes—
124C22×C3×C4#6712yes—
125C22×C3×C4C2×C3×C414yes—
126C22×C3×C4C2×C3×C414yes—
127C22×C3×C4C2×C3×C411yescharacteristic
128C22×C3×C4C3×D412yes—
129C22×C3×C4C3×D412yes—
130C22×C3×C4C3×D412yes—
131C22×C3×C4C3×Q812yes—
132C22×C3×C4C22×D311yescharacteristic
133C22×C3×C4C23×C311yescharacteristic
134C3×M16—38no—
135C3×M16—68no—
136C3×M16—64no—
137C2×C3×C8—68no—
138C2×C3×C8—64no—
139C3×C4⋊C4—28no—
140C3×C4⋊C4—28no—
141C3×C4⋊C4—24no—
142C3×C4⋊C4—24no—
143C3×C4⋊C4—24no—
144C3×C4⋊C4—24no—
145#208—28no—
146#208—24no—
147#208C2×C3×C418yescomplemented
148C2×C3⋊C8—28no—
149C2×C3⋊C8—24no—
150C22×C32—24no—
151C22×C32—24no—
152C22×C32—21no—
153C22×C32—21no—
154C22×C32—21no—
155C22×C32—21no—
156C22×C32#9512yes—
157C22×C32#9512yes—
158C22×C32#10012yes—
159C22×C32#10112yes—
160C22×C32C2×C4211yescharacteristic
161C22×C32C2×C22⋊C411yescharacteristic
162C22×C32C2×C4⋊C411yescharacteristic
163C32×C4—44no—
164C32×C4#9514yes—
165C32×C4C2×C22⋊C412yes—
166C32×C4C2×C4⋊C412yes—
167C23×C4C3×Dic312yes—
168C23×C4C2×C3×D311yescharacteristic
169C2×M16—38no—
170C2×M16—34no—
171C2×M16—64no—
172C2×M16—62no—
173C22×C8—62no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4C3×Dic312yes—
177C2×C4⋊C4C2×C3×D312yes—
178C23×C3—24no—
179C23×C3—24no—
180C23×C3—22no—
181C23×C3—22no—
182C23×C3—22no—
183C23×C3—22no—
184C23×C3—22no—
185C23×C3—22no—
186C23×C3—21no—
187C23×C3—21no—
188C23×C3—21no—
189C23×C3C4×Dic312yes—
190C23×C3C4⋊Dic312yes—
191C23×C3#21711yescharacteristic
192C23×C3#21711yescharacteristic
193C23×C3C3×C4212yes—
194C23×C3C3×C22⋊C411yescharacteristic
195C23×C3C3×C22⋊C411yescharacteristic
196C23×C3C3×C4⋊C412yes—
197C23×C3C22×Dic311yescharacteristic
198C23×C3C22×C3×C411yescharacteristic
199C2×C3×C4—28no—
200C2×C3×C4—24no—
201C2×C3×C4—24no—
202C2×C3×C4—22no—
203C2×C3×C4—24no—
204C2×C3×C4—24no—
205C2×C3×C4—22no—
206C2×C3×C4—24no—
207C2×C3×C4—24no—
208C2×C3×C4—22no—
209C2×C3×C4—21no—
210C2×C3×C4—22no—
211C2×C3×C4—21no—
212C2×C3×C4—22no—
213C2×C3×C4—48no—
214C2×C3×C4—44no—
215C2×C3×C4—44no—
216C2×C3×C4—48no—
217C2×C3×C4—48no—
218C2×C3×C4—44no—
219C2×C3×C4—44no—
220C2×C3×C4—44no—
221C2×C3×C4—44no—
222C2×C3×C4C4×Dic312yes—
223C2×C3×C4Dic3⋊C414yes—
224C2×C3×C4Dic3⋊C414yes—
225C2×C3×C4C4⋊Dic312yes—
226C2×C3×C4(C2×D3)⋊C414yes—
227C2×C3×C4(C2×D3)⋊C414yes—
228C2×C3×C4#21712yes—
229C2×C3×C4C3×C4212yes—
230C2×C3×C4C3×C22⋊C414yes—
231C2×C3×C4C3×C22⋊C414yes—
232C2×C3×C4C3×C22⋊C412yes—
233C2×C3×C4C3×C4⋊C414yes—
234C2×C3×C4C3×C4⋊C414yes—
235C2×C3×C4C3×C4⋊C412yes—
236C2×C3×C4C2×Dic611yescharacteristic
237C2×C3×C4C2×C4×D312yes—
238C2×C3×C4C2×D1211yescharacteristic
239C2×C3×C4C2×#6712yes—
240C2×C3×C4C22×C3×C412yes—
241C2×C3×C4C2×C3×D411yescharacteristic
242C2×C3×C4C2×C3×D412yes—
243C2×C3×C4C2×C3×Q811yescharacteristic
244C3×C8—68no—
245C3⋊C8—28no—
246C2×C32—22no—
247C2×C32—21no—
248C2×C32—21no—
249C2×C32#34314yescomplemented
250C2×C32C2×#9511yescharacteristic
251C2×C32C2×#10011yescharacteristic
252C2×C32C2×#10111yescharacteristic
253C24C2×C3×Dic311yescharacteristic
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—44no—
257C22×C4C3×Dic612yes—
258C22×C4C3×C4×D314yes—
259C22×C4C3×D1212yes—
260C22×C4C2×C3×Dic314yes—
261C22×C4C2×C3×Dic311yescharacteristic
262C22×C4C3×#6712yes—
263C22×C4C3×#6712yes—
264C22×C4C22×C3×D311yescharacteristic
265M16—38no—
266M16—68no—
267M16—64no—
268C2×C8—68no—
269C2×C8—64no—
270C4⋊C4—24no—
271C4⋊C4—24no—
272C22×C3—22no—
273C22×C3—22no—
274C22×C3—22no—
275C22×C3—22no—
276C22×C3—28no—
277C22×C3—28no—
278C22×C3—21no—
279C22×C3—21no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—21no—
284C22×C3—21no—
285C22×C3—21no—
286C22×C3—24no—
287C22×C3—24no—
288C22×C3—24no—
289C22×C3—24no—
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—22no—
294C22×C3—22no—
295C22×C3—22no—
296C22×C3—22no—
297C22×C3C3⋊#9512yes—
298C22×C3C3⋊#9512yes—
299C22×C3#83312yes—
300C22×C3#83612yes—
301C22×C3C3×#9512yes—
302C22×C3C3×#9512yes—
303C22×C3C3×#10012yes—
304C22×C3C3×#10112yes—
305C22×C3C2×C4×Dic311yescharacteristic
306C22×C3C2×C4⋊Dic311yescharacteristic
307C22×C3C2×#21711yescharacteristic
308C22×C3C2×C3×C4211yescharacteristic
309C22×C3C2×C3×C22⋊C411yescharacteristic
310C22×C3C2×C3×C4⋊C411yescharacteristic
311C3×C4—22no—
312C3×C4—22no—
313C3×C4—24no—
314C3×C4—48no—
315C3×C4—44no—
316C3×C4—44no—
317C3×C4C3⋊#9514yes—
318C3×C4C3×#9514yes—
319C3×C4C2×Dic3⋊C412yes—
320C3×C4C2×(C2×D3)⋊C412yes—
321C3×C4C2×C3×C22⋊C412yes—
322C3×C4C2×C3×C4⋊C412yes—
323C32C2×#34311yescharacteristic, complemented, Sylow
324C23—22no—
325C23—22no—
326C23C3×C4×Dic312yes—
327C23C3×C4⋊Dic312yes—
328C23C3×#21711yescharacteristic
329C23C3×#21711yescharacteristic
330C23C22×C3×Dic311yescharacteristic
331C2×C4—24no—
332C2×C4—44no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4C3×C4×Dic312yes—
336C2×C4C3×Dic3⋊C414yes—
337C2×C4C3×Dic3⋊C414yes—
338C2×C4C3×C4⋊Dic312yes—
339C2×C4C3×(C2×D3)⋊C414yes—
340C2×C4C3×(C2×D3)⋊C414yes—
341C2×C4C3×#21712yes—
342C2×C4C2×C3×Dic611yescharacteristic
343C2×C4C2×C3×C4×D312yes—
344C2×C4C2×C3×D1211yescharacteristic
345C2×C4C2×C3×#6712yes—
346C8—68no—
347C2×C3—22no—
348C2×C3—22no—
349C2×C3—24no—
350C2×C3—22no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—22no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—24no—
360C2×C3#453014yesdirect product factor
361C2×C3C3×#34314yescomplemented
362C2×C3C2×C3⋊#9511yescharacteristic
363C2×C3C2×#83311yescharacteristic
364C2×C3C2×#83611yescharacteristic
365C2×C3C2×C3×#9511yescharacteristic
366C2×C3C2×C3×#10011yescharacteristic
367C2×C3C2×C3×#10111yescharacteristic
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—24no—
373C22—24no—
374C22C3×C3⋊#9512yes—
375C22C3×C3⋊#9512yes—
376C22C3×#83312yes—
377C22C3×#83612yes—
378C22C2×C3×C4×Dic311yescharacteristic
379C22C2×C3×C4⋊Dic311yescharacteristic
380C22C2×C3×#21711yescharacteristic
381C4—44no—
382C4C3×C3⋊#9514yes—
383C4C2×C3×Dic3⋊C412yes—
384C4C2×C3×(C2×D3)⋊C412yes—
385C3—21no—
386C3C2×#453011yescharacteristic, direct product factor
387C3C2×C3×#34311yescharacteristic, complemented
388C2—21no—
389C2—21no—
390C2—22no—
391C2C3×#453014yesdirect product factor
392C2C2×C3×C3⋊#9511yescharacteristic
393C2C2×C3×#83311yescharacteristic
394C2C2×C3×#83611yescharacteristic
subgroupG/H
centerC23×C3#217
commutatorC22×C3C2×C3×C42
FrattiniC22×C4C22×C3×D3
FittingC22×C32×C4⋊C4C2
socleC23×C32C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC22×C3×C4⋊C4D3
hypocenterC3C2×C3×#343
LCSG ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C22×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#4530C2direct (N × H)
5. C2×#4530C3direct (N × H)
14. C2×C3×#208C4semidirect
23. #4530C2×C3direct (N × H)
40. C3×#208C2×C4semidirect
69. C2×#208C3×C4semidirect
147. #208C2×C3×C4semidirect
249. C2×C32#343semidirect
323. C32C2×#343semidirect
360. C2×C3#4530direct (N × H)
361. C2×C3C3×#343semidirect
386. C3C2×#4530direct (N × H)
387. C3C2×C3×#343semidirect
391. C2C3×#4530direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C4⋊C42
C22×C3×#2082
C3×#45302
C2×C3×#3433
C2×#45303