Finite Group Databasebeta

← #82611⋊C3 #11921287

Subgroups — #82611⋊C3 #11921287

Order 1152.

343 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 343 conjugacy classes of subgroups — too many to draw. Only its 31 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
1C2×C3×#120⋊C3C211yesmaximal, characteristic, complemented
2C2×C3⋊(#120⋊C3)C211yesmaximal, characteristic, complemented
3C3⋊(#379⋊C3)C211yesmaximal, characteristic, complemented
4#82611C311yesmaximal, characteristic, complemented
5#2812⋊C3—31nomaximal
6C2×C3×C22⋊A4C2211yescharacteristic
7A4×#67—41nomaximal
8C3×#120⋊C3—21no—
9C3⋊(#120⋊C3)—21no—
10C2×C3×#120C2×C311yescharacteristic, complemented
11C2×#953C2×C311yescharacteristic, complemented
12C2×#120⋊C3—21no—
13C2×#120⋊C3—31no—
14C2×#120⋊C3D311yescharacteristic, complemented
15#5247C2×C311yescharacteristic, complemented
16#5223—31no—
17#5222—31no—
18#4959—31no—
19#4952—31no—
20#379⋊C3—31no—
21C3×C22⋊A4D411yescharacteristic, complemented
22C22×C3×A4—41no—
23C2×D3×A4—41no—
24Dic3×A4—41no—
25#2812—31noSylow
26C25×C3C22×C311yescharacteristic
27C2×C22⋊A4—21no—
28C2×C22⋊A4C2×D311yescharacteristic
29C22×C3×D4—31no—
30C22×#67—31no—
31C22×#67A411yescharacteristic, complemented
32D4×A4—121no—
33C3×#120—21no—
34C3×#120—61no—
35C2×C3×C22⋊C4—31no—
36#953—21no—
37#953—61no—
38C2×#217—31no—
39C2×#217—31no—
40C2×#217—31no—
41C2×#217—31no—
42C2×(C2×D3)⋊C4—31no—
43C2×Dic3⋊C4—31no—
44#120⋊C3—22no—
45#120⋊C3—21no—
46#120⋊C3—61no—
47C3⋊#95—31no—
48C3⋊#95—31no—
49C2×C3×A4—41no—
50C2×C3×A4—81no—
51C2×C3×A4—161no—
52D3×A4—81no—
53C3×#67—161no—
54C2×#120—31no—
55C2×#120C3×D311yescharacteristic, complemented
56#397—91no—
57#394—91no—
58#394—91no—
59#392—91no—
60#379—31no—
61C24×C3—31no—
62C24×C3—31no—
63C24×C3—121no—
64C24×C3—121no—
65C24×C3C3×D411yescharacteristic, complemented
66C24×C3C2×A411yescharacteristic
67C23×D3C2×A411yescharacteristic
68C22⋊A4—21no—
69C22⋊A4#6711yescharacteristic, complemented
70C22×A4—41no—
71C22×A4—81no—
72C22×A4—121no—
73C2×C3×D4—61no—
74C2×C3×D4—61no—
75C2×C3×D4—121no—
76C2×C3×D4—121no—
77C22×C3×C4—31no—
78C2×#67—61no—
79C2×#67—61no—
80C2×#67—121no—
81C2×#67—121no—
82C2×#67—121no—
83C22×Dic3—31no—
84C22×Dic3—31no—
85C22×Dic3C2×A411yescharacteristic
86C4×A4—121no—
87C3×C22⋊C4—61no—
88C3×C22⋊C4—61no—
89#217—61no—
90#217—61no—
91#217—121no—
92#217—121no—
93#217—121no—
94(C2×D3)⋊C4—121no—
95Dic3⋊C4—121no—
96C22×C32—161no—
97C2×C3×D3—161no—
98C3×A4—41no—
99C3×A4—161no—
100C3×Dic3—161no—
101C25C2×C3×D311yescharacteristic
102C22×D4—31no—
103C22×D4—31no—
104C22×D4—91no—
105#120—21no—
106#120—61no—
107#120—61no—
108#120—181no—
109C2×C4⋊C4—91no—
110C2×C22⋊C4—31no—
111C2×C22⋊C4—91no—
112C2×C22⋊C4—91no—
113C2×C22⋊C4—91no—
114C2×C22⋊C4—91no—
115C2×C22⋊C4—91no—
116#95—91no—
117#95—91no—
118C23×C3—21no—
119C23×C3—31no—
120C23×C3—31no—
121C23×C3—41no—
122C23×C3—61no—
123C23×C3—61no—
124C23×C3—61no—
125C23×C3—61no—
126C23×C3—61no—
127C23×C3—61no—
128C23×C3—61no—
129C23×C3—61no—
130C23×C3—121no—
131C23×C3—121no—
132C23×C3—121no—
133C23×C3—121no—
134C23×C3—121no—
135C23×C3—121no—
136C23×C3—123no—
137C23×C3C22×A411yescharacteristic
138C22×D3—21no—
139C22×D3—61no—
140C22×D3—61no—
141C2×A4—41no—
142C2×A4—81no—
143C2×A4—82no—
144C2×A4—81no—
145C2×A4—161no—
146C2×A4—162no—
147C2×A4—241no—
148C3×D4—122no—
149C3×D4—122no—
150C3×D4—481no—
151C2×C3×C4—61no—
152C2×C3×C4—61no—
153C2×C3×C4—61no—
154#67—41no—
155#67—121no—
156#67—122no—
157#67—122no—
158C2×Dic3—61no—
159C2×Dic3—61no—
160C2×Dic3—61no—
161C2×Dic3—61no—
162C2×Dic3—61no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165C2×C32—161no—
166C2×C32—321no—
167C3×D3—321no—
168C24—31no—
169C24—31no—
170C24—31no—
171C24—121no—
172C24—121no—
173C24C3×#6711yescharacteristic, complemented
174C24D3×A411yescharacteristic
175C2×D4—61no—
176C2×D4—61no—
177C2×D4—121no—
178C2×D4—121no—
179C2×D4—181no—
180C2×D4—181no—
181C2×D4—361no—
182C2×D4—361no—
183C2×D4—361no—
184C22×C4—31no—
185C22×C4—31no—
186C22×C4—91no—
187C22×C4—91no—
188C4⋊C4—361no—
189C22⋊C4—61no—
190C22⋊C4—61no—
191C22⋊C4—181no—
192C22⋊C4—181no—
193C22⋊C4—361no—
194C22⋊C4—361no—
195C22⋊C4—361no—
196C22⋊C4—361no—
197C22×C3—31no—
198C22×C3—31no—
199C22×C3—41no—
200C22×C3—41no—
201C22×C3—61no—
202C22×C3—61no—
203C22×C3—61no—
204C22×C3—61no—
205C22×C3—61no—
206C22×C3—61no—
207C22×C3—121no—
208C22×C3—121no—
209C22×C3—121no—
210C22×C3—121no—
211C22×C3—121no—
212C22×C3—121no—
213C22×C3—121no—
214C22×C3—123no—
215C22×C3—121no—
216C22×C3—161no—
217C22×C3—321no—
218C22×C3—481no—
219C22×C3D4×A411yescharacteristic
220C2×D3—41no—
221C2×D3—121no—
222C2×D3—121no—
223A4—41no—
224A4—81no—
225A4—161no—
226A4—162no—
227C3×C4—121no—
228C3×C4—481no—
229Dic3—41no—
230Dic3—121no—
231Dic3—121no—
232C32—161noSylow
233C23—21no—
234C23—31no—
235C23—31no—
236C23—41no—
237C23—61no—
238C23—61no—
239C23—61no—
240C23—61no—
241C23—61no—
242C23—61no—
243C23—61no—
244C23—61no—
245C23—61no—
246C23—121no—
247C23—121no—
248C23—121no—
249C23—121no—
250C23—121no—
251C23—121no—
252C23—123no—
253C23—181no—
254C23—181no—
255C23C2×D3×A411yescharacteristic
256D4—121no—
257D4—122no—
258D4—122no—
259D4—361no—
260D4—362no—
261D4—362no—
262C2×C4—61no—
263C2×C4—61no—
264C2×C4—61no—
265C2×C4—181no—
266C2×C4—181no—
267C2×C4—181no—
268C2×C4—181no—
269C2×C4—181no—
270C2×C4—181no—
271C2×C4—181no—
272C2×C3—31no—
273C2×C3—31no—
274C2×C3—81no—
275C2×C3—121no—
276C2×C3—121no—
277C2×C3—161no—
278C2×C3—321no—
279C2×C3—322no—
280C2×C3—321no—
281C2×C3—961no—
282C2×C3#545011yescharacteristic
283D3—81no—
284C22—31no—
285C22—31no—
286C22—41no—
287C22—41no—
288C22—61no—
289C22—61no—
290C22—61no—
291C22—61no—
292C22—61no—
293C22—61no—
294C22—121no—
295C22—121no—
296C22—121no—
297C22—121no—
298C22—121no—
299C22—121no—
300C22—121no—
301C22—123no—
302C22—121no—
303C22—121no—
304C22—361no—
305C22—361no—
306C22A4×#6711yescharacteristic
307C4—121no—
308C4—121no—
309C4—361no—
310C4—361no—
311C3—161no—
312C3—321no—
313C3#2812⋊C311yescharacteristic, complemented
314C2—31no—
315C2—31no—
316C2—81no—
317C2—121no—
318C2—121no—
319C2—241no—
320C2C3⋊#545011yescharacteristic
subgroupG/H
center, hypercenterC2C3⋊#5450
commutator, cosocleC25×C3C22×C3
FrattiniC23C2×D3×A4
FittingC2×C3×#120C2×C3
socleC23×C3C22×A4
hypocenterC24×C3C3×D4
LCSG ▷ C25×C3 ▷ C24×C3
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×#120⋊C3C2semidirect
2. C2×C3⋊(#120⋊C3)C2semidirect
3. C3⋊(#379⋊C3)C2semidirect
4. #82611C3semidirect
10. C2×C3×#120C2×C3semidirect
11. C2×#953C2×C3semidirect
14. C2×#120⋊C3D3semidirect
15. #5247C2×C3semidirect
21. C3×C22⋊A4D4semidirect
31. C22×#67A4semidirect
55. C2×#120C3×D3semidirect
65. C24×C3C3×D4semidirect
69. C22⋊A4#67semidirect
173. C24C3×#67semidirect
313. C3#2812⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#120⋊C32
C2×C3⋊(#120⋊C3)2
C3⋊(#379⋊C3)2
#826113
#2812⋊C33
A4×#674