Finite Group Databasebeta

← C22×C3⋊(#120⋊C3) #11923410

Subgroups — C22×C3⋊(#120⋊C3) #11923410

Order 1152.

1743 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 1743 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C22×C3×C22⋊A4C211yesmaximal, characteristic, complemented
2C2×C3⋊(#120⋊C3)C216yesmaximal, direct product factor
3C22×#953C311yesmaximal, characteristic, complemented
4C22×#120⋊C3—31nomaximal
5C2×C3×C22⋊A4C2213yescomplemented
6C22×D3×A4—41nomaximal
7C3⋊(#120⋊C3)C2214yesdirect product factor
8C26×C3C2×C311yescharacteristic, complemented
9C22×C22⋊A4—21no—
10C22×C22⋊A4D311yescharacteristic, complemented
11C23×#67—31no—
12C2×#953—36no—
13C2×#953C2×C316yescomplemented
14C22×#217—31no—
15C2×#120⋊C3—36no—
16C3×C22⋊A4C2311yescharacteristic, complemented
17C22×C3×A4—41no—
18C22×C3×A4—82no—
19C2×D3×A4—46no—
20C22×#120—31noSylow
21C25×C3—31no—
22C25×C3—33no—
23C25×C3—62no—
24C25×C3—66no—
25C25×C3C22×C313yescomplemented
26C24×D3A411yescharacteristic, complemented
27C2×C22⋊A4—23no—
28C2×C22⋊A4C2×D313yescomplemented
29C23×A4—121no—
30C22×#67—36no—
31C22×#67—36no—
32C22×#67—62no—
33C22×#67—66no—
34C23×Dic3—31no—
35#953—38no—
36#953—312no—
37#953C22×C314yescomplemented
38C2×#217—36no—
39C2×#217—36no—
40#120⋊C3—34no—
41C22×C3×D3—161no—
42C2×C3×A4—43no—
43C2×C3×A4—86no—
44D3×A4—44no—
45C26C3×D311yescharacteristic, complemented
46C23×D4—91no—
47C2×#120—36no—
48C2×#120—96no—
49C22×C22⋊C4—91no—
50C24×C3—22no—
51C24×C3—36no—
52C24×C3—32no—
53C24×C3—33no—
54C24×C3—33no—
55C24×C3—32no—
56C24×C3—33no—
57C24×C3—66no—
58C24×C3—66no—
59C24×C3—66no—
60C24×C3—66no—
61C24×C3—62no—
62C24×C3—66no—
63C24×C3—612no—
64C24×C3—66no—
65C24×C3—612no—
66C24×C3—66no—
67C24×C3—62no—
68C24×C3—64no—
69C24×C3—612no—
70C24×C3—612no—
71C24×C3C2×A411yescharacteristic
72C24×C3C23×C311yescharacteristic, complemented
73C23×D3—61no—
74C23×D3—63no—
75C23×D3C2×A416yescomplemented
76C22⋊A4—21no—
77C22⋊A4C22×D311yescharacteristic, complemented
78C22×A4—41no—
79C22×A4—82no—
80C22×A4—84no—
81C22×A4—81no—
82C22×A4—126no—
83C2×#67—34no—
84C2×#67—312no—
85C2×#67—612no—
86C2×#67—612no—
87C2×#67—612no—
88C2×#67—612no—
89C22×Dic3—36no—
90C22×Dic3—63no—
91C22×Dic3—61no—
92#217—312no—
93#217—34no—
94C22×C32—161no—
95C2×C3×D3—166no—
96C3×A4—41no—
97C3×A4—82no—
98C25—31no—
99C25—33no—
100C25—31no—
101C25—62no—
102C25—66no—
103C25C2×C3×D313yescomplemented
104C22×D4—96no—
105C22×D4—96no—
106C22×D4—182no—
107C22×D4—186no—
108C23×C4—91no—
109#120—34no—
110#120—98no—
111#120—912no—
112C2×C22⋊C4—96no—
113C2×C22⋊C4—96no—
114C23×C3—26no—
115C23×C3—33no—
116C23×C3—31no—
117C23×C3—36no—
118C23×C3—36no—
119C23×C3—36no—
120C23×C3—36no—
121C23×C3—33no—
122C23×C3—31no—
123C23×C3—62no—
124C23×C3—66no—
125C23×C3—66no—
126C23×C3—66no—
127C23×C3—612no—
128C23×C3—66no—
129C23×C3—66no—
130C23×C3—612no—
131C23×C3—66no—
132C23×C3—66no—
133C23×C3—612no—
134C23×C3—612no—
135C23×C3—66no—
136C23×C3—66no—
137C23×C3—66no—
138C23×C3—66no—
139C23×C3—612no—
140C23×C3—612no—
141C23×C3—624no—
142C23×C3—624no—
143C23×C3—612no—
144C23×C3—612no—
145C23×C3—62no—
146C23×C3—481no—
147C23×C3C22×A413yes—
148C22×D3—41no—
149C22×D3—66no—
150C22×D3—66no—
151C22×D3—123no—
152C22×D3—122no—
153C22×D3C22×A414yescomplemented
154C2×A4—43no—
155C2×A4—86no—
156C2×A4—812no—
157C2×A4—83no—
158C2×A4—124no—
159#67—68no—
160#67—624no—
161C2×Dic3—34no—
162C2×Dic3—66no—
163C2×Dic3—66no—
164C2×C32—163no—
165C3×D3—164no—
166C24—22no—
167C24—36no—
168C24—32no—
169C24—33no—
170C24—33no—
171C24—32no—
172C24—33no—
173C24—36no—
174C24—66no—
175C24—66no—
176C24—66no—
177C24—66no—
178C24—62no—
179C24—66no—
180C24—612no—
181C24—66no—
182C24—612no—
183C24—66no—
184C24—62no—
185C24—64no—
186C24—612no—
187C24—612no—
188C24—181no—
189C24—183no—
190C24D3×A411yescharacteristic
191C24C22×C3×D311yescharacteristic, complemented
192C2×D4—94no—
193C2×D4—912no—
194C2×D4—1812no—
195C2×D4—1812no—
196C2×D4—1812no—
197C2×D4—1812no—
198C22×C4—96no—
199C22×C4—183no—
200C22×C4—181no—
201C22⋊C4—912no—
202C22⋊C4—94no—
203C22×C3—22no—
204C22×C3—33no—
205C22×C3—32no—
206C22×C3—33no—
207C22×C3—33no—
208C22×C3—32no—
209C22×C3—36no—
210C22×C3—62no—
211C22×C3—66no—
212C22×C3—612no—
213C22×C3—66no—
214C22×C3—612no—
215C22×C3—66no—
216C22×C3—66no—
217C22×C3—62no—
218C22×C3—66no—
219C22×C3—612no—
220C22×C3—64no—
221C22×C3—612no—
222C22×C3—66no—
223C22×C3—66no—
224C22×C3—161no—
225C22×C3—321no—
226C22×C3—486no—
227C22×C3#120⋊C311yescharacteristic, complemented
228C22×C3C23×A411yescharacteristic
229C2×D3—46no—
230C2×D3—64no—
231C2×D3—126no—
232A4—41no—
233A4—82no—
234A4—84no—
235A4—81no—
236Dic3—64no—
237C32—161noSylow
238C23—26no—
239C23—33no—
240C23—31no—
241C23—36no—
242C23—36no—
243C23—36no—
244C23—36no—
245C23—31no—
246C23—33no—
247C23—34no—
248C23—62no—
249C23—66no—
250C23—66no—
251C23—66no—
252C23—612no—
253C23—66no—
254C23—66no—
255C23—612no—
256C23—66no—
257C23—66no—
258C23—612no—
259C23—612no—
260C23—66no—
261C23—66no—
262C23—66no—
263C23—66no—
264C23—612no—
265C23—612no—
266C23—624no—
267C23—624no—
268C23—612no—
269C23—612no—
270C23—62no—
271C23—121no—
272C23—186no—
273C23—186no—
274C23—363no—
275C23—362no—
276C23C2×D3×A413yes—
277D4—188no—
278D4—1824no—
279C2×C4—94no—
280C2×C4—186no—
281C2×C4—186no—
282C2×C3—31no—
283C2×C3—33no—
284C2×C3—62no—
285C2×C3—66no—
286C2×C3—163no—
287C2×C3—323no—
288C2×C3—484no—
289C2×C3C2×#120⋊C313yescomplemented
290D3—44no—
291C22—22no—
292C22—33no—
293C22—32no—
294C22—33no—
295C22—33no—
296C22—32no—
297C22—36no—
298C22—62no—
299C22—66no—
300C22—612no—
301C22—66no—
302C22—612no—
303C22—66no—
304C22—66no—
305C22—62no—
306C22—66no—
307C22—612no—
308C22—64no—
309C22—612no—
310C22—66no—
311C22—66no—
312C22—126no—
313C22—184no—
314C22—366no—
315C22C3⋊(#120⋊C3)11yescharacteristic, direct product factor
316C22C22×D3×A411yescharacteristic
317C4—184no—
318C3—161no—
319C3—321no—
320C3C22×#120⋊C311yescharacteristic, complemented
321C2—31no—
322C2—33no—
323C2—62no—
324C2—66no—
325C2—124no—
326C2C2×C3⋊(#120⋊C3)13yesdirect product factor
subgroupG/H
center, hypercenterC22C3⋊(#120⋊C3)
commutator, cosocle, hypocenterC24×C3C23×C3
FrattiniC22C22×D3×A4
FittingC26×C3C2×C3
socleC24×C3C2×A4
LCSG ▷ C24×C3
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊A4C2semidirect
2. C2×C3⋊(#120⋊C3)C2direct (N × H)
3. C22×#953C3semidirect
5. C2×C3×C22⋊A4C22semidirect
7. C3⋊(#120⋊C3)C22direct (N × H)
8. C26×C3C2×C3semidirect
10. C22×C22⋊A4D3semidirect
13. C2×#953C2×C3semidirect
16. C3×C22⋊A4C23semidirect
25. C25×C3C22×C3semidirect
26. C24×D3A4semidirect
28. C2×C22⋊A4C2×D3semidirect
37. #953C22×C3semidirect
45. C26C3×D3semidirect
72. C24×C3C23×C3semidirect
75. C23×D3C2×A4semidirect
77. C22⋊A4C22×D3semidirect
103. C25C2×C3×D3semidirect
153. C22×D3C22×A4semidirect
191. C24C22×C3×D3semidirect
227. C22×C3#120⋊C3semidirect
289. C2×C3C2×#120⋊C3semidirect
315. C22C3⋊(#120⋊C3)direct (N × H)
320. C3C22×#120⋊C3semidirect
326. C2C2×C3⋊(#120⋊C3)direct (N × H)

Maximal subgroups

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

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