Finite Group Databasebeta

← C4×C3⋊(#120⋊C3) #11921356

Subgroups — C4×C3⋊(#120⋊C3) #11921356

Order 1152.

529 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 529 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×C22⋊A4C211yesmaximal, characteristic, complemented
2C2×C3⋊(#120⋊C3)C211yesmaximal, characteristic
3C3⋊(#379⋊C3)C211yesmaximal, characteristic, complemented
4C4×#953C311yesmaximal, characteristic, complemented
5C4×#120⋊C3—31nomaximal
6C2×C3×C22⋊A4C2211yescharacteristic
7C4×D3×A4—41nomaximal
8C3⋊(#120⋊C3)C412yesdirect product factor
9C24×C3×C4C2×C311yescharacteristic, complemented
10C4×C22⋊A4—21no—
11C4×C22⋊A4D311yescharacteristic, complemented
12C2×#953C2×C311yescharacteristic
13C2×C4×#67—31no—
14C2×#120⋊C3—31no—
15#5247C2×C311yescharacteristic, complemented
16#5213—31no—
17#5210—31no—
18C4×#217—31no—
19#379⋊C3—31no—
20C3×C22⋊A4C2×C411yescharacteristic, complemented
21C2×D3×A4—41no—
22C3×C4×A4—41no—
23C3×C4×A4—82no—
24Dic3×A4—41no—
25C4×#120—31noSylow
26C25×C3C22×C311yescharacteristic
27C2×C22⋊A4—21no—
28C2×C22⋊A4C2×D311yescharacteristic
29C23×C3×C4—31no—
30C23×C3×C4—31no—
31C23×C3×C4—62no—
32C23×C3×C4—62no—
33C22×#67—31no—
34C22×C4×D3A411yescharacteristic, complemented
35C2×C4×A4—121no—
36#953—32no—
37#953C3×C412yescomplemented
38C2×#217—31no—
39C2×#217—31no—
40C2×#217—31no—
41C4×#67—62no—
42C4×#67—62no—
43C2×(C2×D3)⋊C4—31no—
44C2×Dic3⋊C4—31no—
45C2×C4×Dic3—31no—
46#120⋊C3—32no—
47C3⋊#95—32no—
48C2×C3×A4—41no—
49C2×C3×A4—82no—
50D3×A4—42no—
51C3×C4×D3—161no—
52C24×C4C3×D311yescharacteristic, complemented
53C2×#120—31no—
54C2×C4×D4—91no—
55#386—91no—
56#385—91no—
57#379—31no—
58C4×C22⋊C4—91no—
59C24×C3—31no—
60C24×C3—31no—
61C24×C3—62no—
62C24×C3—62no—
63C24×C3C2×C3×C411yescharacteristic, complemented
64C23×D3C2×A411yescharacteristic
65C22⋊A4—21no—
66C22⋊A4C4×D311yescharacteristic, complemented
67C22×A4—121no—
68C22×C3×C4—22no—
69C22×C3×C4—32no—
70C22×C3×C4—32no—
71C22×C3×C4—31no—
72C22×C3×C4—62no—
73C22×C3×C4—62no—
74C22×C3×C4—64no—
75C22×C3×C4—62no—
76C22×C3×C4—62no—
77C22×C3×C4—64no—
78C22×C3×C4—62no—
79C22×C3×C4—62no—
80C22×C3×C4C2×A411yescharacteristic
81C2×#67—32no—
82C2×#67—32no—
83C2×#67—62no—
84C2×#67—62no—
85C22×Dic3—31no—
86C22×Dic3—31no—
87C22×Dic3C2×A411yescharacteristic
88C2×C4×D3—61no—
89C2×C4×D3—61no—
90C4×A4—41no—
91C4×A4—82no—
92C4×A4—84no—
93C4×A4—81no—
94C4×A4—121no—
95#217—32no—
96#217—32no—
97#217—62no—
98#217—62no—
99(C2×D3)⋊C4—62no—
100Dic3⋊C4—62no—
101C4×Dic3—61no—
102C4×Dic3—61no—
103C2×C3×D3—161no—
104C3×A4—41no—
105C3×A4—82no—
106C32×C4—161no—
107C3×Dic3—161no—
108C25C2×C3×D311yescharacteristic
109C22×D4—91no—
110C23×C4—31no—
111C23×C4—31no—
112C23×C4—31no—
113C23×C4—62no—
114C23×C4—62no—
115#120—32no—
116#120—92no—
117C4×D4—182no—
118C4×D4—182no—
119C2×C4⋊C4—91no—
120C2×C22⋊C4—91no—
121C2×C22⋊C4—91no—
122C2×C22⋊C4—91no—
123C2×C22⋊C4—91no—
124C2×C42—91no—
125#95—92no—
126C23×C3—22no—
127C23×C3—32no—
128C23×C3—32no—
129C23×C3—31no—
130C23×C3—31no—
131C23×C3—62no—
132C23×C3—62no—
133C23×C3—62no—
134C23×C3—62no—
135C23×C3—62no—
136C23×C3—64no—
137C23×C3—62no—
138C23×C3—62no—
139C23×C3—64no—
140C23×C3C22×A411yescharacteristic
141C22×D3—61no—
142C22×D3—61no—
143C22×D3C4×A412yescomplemented
144C2×A4—41no—
145C2×A4—82no—
146C2×A4—84no—
147C2×A4—81no—
148C2×A4—122no—
149C2×C3×C4—31no—
150C2×C3×C4—31no—
151C2×C3×C4—32no—
152C2×C3×C4—62no—
153C2×C3×C4—64no—
154C2×C3×C4—62no—
155C2×C3×C4—64no—
156C2×C3×C4—62no—
157C2×C3×C4—62no—
158C2×C3×C4—62no—
159C2×C3×C4—481no—
160#67—64no—
161#67—64no—
162C2×Dic3—32no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165C2×Dic3—61no—
166C2×Dic3—61no—
167C2×Dic3—62no—
168C4×D3—41no—
169C4×D3—121no—
170C2×C32—161no—
171C3×D3—162no—
172C24—31no—
173C24—31no—
174C24—31no—
175C24—62no—
176C24—62no—
177C24C3×C4×D311yescharacteristic, complemented
178C2×D4—92no—
179C2×D4—92no—
180C2×D4—182no—
181C2×D4—182no—
182C22×C4—22no—
183C22×C4—32no—
184C22×C4—32no—
185C22×C4—31no—
186C22×C4—31no—
187C22×C4—62no—
188C22×C4—62no—
189C22×C4—64no—
190C22×C4—62no—
191C22×C4—62no—
192C22×C4—64no—
193C22×C4—62no—
194C22×C4—62no—
195C22×C4—91no—
196C22×C4—91no—
197C22×C4—181no—
198C22×C4—181no—
199C22×C4D3×A411yescharacteristic
200C4⋊C4—182no—
201C22⋊C4—92no—
202C22⋊C4—92no—
203C22⋊C4—182no—
204C22⋊C4—182no—
205C22⋊C4—182no—
206C42—181no—
207C42—181no—
208C22×C3—22no—
209C22×C3—31no—
210C22×C3—31no—
211C22×C3—32no—
212C22×C3—32no—
213C22×C3—62no—
214C22×C3—62no—
215C22×C3—62no—
216C22×C3—64no—
217C22×C3—62no—
218C22×C3—62no—
219C22×C3—62no—
220C22×C3—64no—
221C22×C3—62no—
222C22×C3—481no—
223C22×C3C2×C4×A411yescharacteristic
224C2×D3—41no—
225C2×D3—62no—
226C2×D3—121no—
227A4—41no—
228A4—82no—
229A4—84no—
230A4—81no—
231C3×C4—31no—
232C3×C4—62no—
233C3×C4—161no—
234C3×C4—321no—
235C3×C4—481no—
236C3×C4#120⋊C311yescharacteristic, complemented
237Dic3—41no—
238Dic3—62no—
239Dic3—121no—
240C32—161noSylow
241C23—22no—
242C23—32no—
243C23—32no—
244C23—31no—
245C23—31no—
246C23—32no—
247C23—62no—
248C23—62no—
249C23—62no—
250C23—62no—
251C23—62no—
252C23—64no—
253C23—62no—
254C23—62no—
255C23—64no—
256C23—181no—
257C23—181no—
258C23C2×D3×A411yescharacteristic
259D4—184no—
260D4—184no—
261C2×C4—31no—
262C2×C4—31no—
263C2×C4—32no—
264C2×C4—62no—
265C2×C4—64no—
266C2×C4—62no—
267C2×C4—64no—
268C2×C4—62no—
269C2×C4—62no—
270C2×C4—62no—
271C2×C4—92no—
272C2×C4—121no—
273C2×C4—181no—
274C2×C4—181no—
275C2×C4—181no—
276C2×C4—181no—
277C2×C4—182no—
278C2×C4—361no—
279C2×C3—31no—
280C2×C3—31no—
281C2×C3—62no—
282C2×C3—62no—
283C2×C3—161no—
284C2×C3—321no—
285C2×C3—482no—
286C2×C3C2×#120⋊C311yescharacteristic
287D3—42no—
288C22—22no—
289C22—31no—
290C22—31no—
291C22—32no—
292C22—32no—
293C22—62no—
294C22—62no—
295C22—62no—
296C22—64no—
297C22—62no—
298C22—62no—
299C22—62no—
300C22—64no—
301C22—62no—
302C22—121no—
303C22—182no—
304C22—361no—
305C22C4×D3×A411yescharacteristic
306C4—31no—
307C4—62no—
308C4—121no—
309C4—182no—
310C4—361no—
311C4C3⋊(#120⋊C3)11yescharacteristic, direct product factor
312C3—161no—
313C3—321no—
314C3C4×#120⋊C311yescharacteristic, complemented
315C2—31no—
316C2—31no—
317C2—62no—
318C2—62no—
319C2—122no—
320C2C2×C3⋊(#120⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC4C3⋊(#120⋊C3)
commutator, hypocenterC24×C3C2×C3×C4
FrattiniC23C2×D3×A4
FittingC24×C3×C4C2×C3
socleC23×C3C22×A4
prime radicalC2×C3⋊(#120⋊C3)C2
cosocleC25×C3C22×C3
LCSG ▷ C24×C3
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C3×C4×C22⋊A4C2semidirect
3. C3⋊(#379⋊C3)C2semidirect
4. C4×#953C3semidirect
8. C3⋊(#120⋊C3)C4direct (N × H)
9. C24×C3×C4C2×C3semidirect
11. C4×C22⋊A4D3semidirect
15. #5247C2×C3semidirect
20. C3×C22⋊A4C2×C4semidirect
34. C22×C4×D3A4semidirect
37. #953C3×C4semidirect
52. C24×C4C3×D3semidirect
63. C24×C3C2×C3×C4semidirect
66. C22⋊A4C4×D3semidirect
143. C22×D3C4×A4semidirect
177. C24C3×C4×D3semidirect
236. C3×C4#120⋊C3semidirect
311. C4C3⋊(#120⋊C3)direct (N × H)
314. C3C4×#120⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3×C4×C22⋊A42
C2×C3⋊(#120⋊C3)2
C3⋊(#379⋊C3)2
C4×#9533
C4×#120⋊C33
C4×D3×A44