Finite Group Databasebeta

← #82601⋊C3 #11921286

Subgroups — #82601⋊C3 #11921286

Order 1152.

527 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 527 conjugacy classes of subgroups — too many to draw. Only its 32 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
1Dic3×C22⋊A4C211yesmaximal, characteristic, complemented
2C2×C3×#120⋊C3C211yesmaximal, characteristic, complemented
3C2×C3⋊(#120⋊C3)C211yesmaximal, characteristic, complemented
4#82601C311yesmaximal, characteristic, complemented
5C4⋊(#120⋊C3)—31nomaximal
6C2×C3×C22⋊A4C2211yescharacteristic
7A4×#67—41nomaximal
8C3×#120⋊C3—21no—
9C3⋊(#120⋊C3)—21no—
10C24×Dic3C2×C311yescharacteristic, complemented
11C4×C22⋊A4—31no—
12C2×C3×#120C2×C311yescharacteristic, complemented
13C2×#953C2×C311yescharacteristic, complemented
14C2×#939—31no—
15C2×#120⋊C3—21no—
16C2×#120⋊C3—31no—
17C2×#120⋊C3D311yescharacteristic, complemented
18#5220—31no—
19#4958—31no—
20#4942—31no—
21C3×C22⋊A4D411yescharacteristic, complemented
22C22×C3×A4—41no—
23C2×D3×A4—41no—
24Dic3×A4—41no—
25Dic3×A4—82no—
26#2847—31noSylow
27C25×C3C22×C311yescharacteristic
28C2×C22⋊A4—21no—
29C2×C22⋊A4C2×D311yescharacteristic
30C22×C3×D4—31no—
31C22×#67—31no—
32C22×#67A411yescharacteristic, complemented
33C23×Dic3—31no—
34C23×Dic3—31no—
35C23×Dic3—62no—
36C23×Dic3—62no—
37D4×A4—121no—
38C3×#120—21no—
39C3×#120—61no—
40C2×C3×C22⋊C4—31no—
41#953—21no—
42#953—61no—
43C2×#217—31no—
44C2×#217—31no—
45#939—62no—
46#939—62no—
47C2×(C2×D3)⋊C4—31no—
48C2×Dic3⋊C4—31no—
49#120⋊C3—22no—
50#120⋊C3—21no—
51#120⋊C3—61no—
52C3⋊#95—32no—
53C2×C3×A4—41no—
54C2×C3×A4—82no—
55C2×C3×A4—81no—
56D3×A4—81no—
57C3×#67—161no—
58C24×C4—31no—
59C2×#121—91no—
60C2×#120—31no—
61C2×#120C3×D311yescharacteristic, complemented
62#386—91no—
63#386—91no—
64#380—91no—
65C24×C3—31no—
66C24×C3—31no—
67C24×C3—62no—
68C24×C3—62no—
69C24×C3C3×D411yescharacteristic, complemented
70C24×C3C2×A411yescharacteristic
71C23×D3C2×A411yescharacteristic
72C22⋊A4—21no—
73C22⋊A4#6711yescharacteristic, complemented
74C22×A4—41no—
75C22×A4—81no—
76C22×A4—121no—
77C2×C3×D4—61no—
78C2×C3×D4—61no—
79C2×C3×D4—62no—
80C2×C3×D4—62no—
81C22×C3×C4—31no—
82C2×#67—61no—
83C2×#67—61no—
84C2×#67—61no—
85C2×#67—61no—
86C2×#67—62no—
87C2×#67—62no—
88C22×Dic3—22no—
89C22×Dic3—32no—
90C22×Dic3—32no—
91C22×Dic3—31no—
92C22×Dic3—31no—
93C22×Dic3—62no—
94C22×Dic3—62no—
95C22×Dic3—64no—
96C22×Dic3—62no—
97C22×Dic3—62no—
98C22×Dic3—64no—
99C22×Dic3—62no—
100C22×Dic3—62no—
101C22×Dic3C2×A411yescharacteristic
102C4×A4—121no—
103C4×A4—242no—
104C3×C22⋊C4—61no—
105C3×C22⋊C4—61no—
106#217—62no—
107#217—61no—
108#217—61no—
109(C2×D3)⋊C4—62no—
110Dic3⋊C4—61no—
111Dic3⋊C4—61no—
112C22×C32—161no—
113C2×C3×D3—161no—
114C3×A4—41no—
115C3×A4—82no—
116C3×Dic3—161no—
117C25C2×C3×D311yescharacteristic
118C22×D4—31no—
119C22×D4—31no—
120C22×D4—91no—
121C23×C4—91no—
122C23×C4—91no—
123C23×C4—182no—
124C23×C4—182no—
125#121—182no—
126#121—182no—
127#120—21no—
128#120—61no—
129#120—61no—
130#120—181no—
131C2×C4⋊C4—91no—
132C2×C22⋊C4—31no—
133C2×C22⋊C4—91no—
134C2×C22⋊C4—91no—
135C2×C22⋊C4—91no—
136#95—92no—
137C23×C3—22no—
138C23×C3—21no—
139C23×C3—32no—
140C23×C3—32no—
141C23×C3—31no—
142C23×C3—31no—
143C23×C3—62no—
144C23×C3—62no—
145C23×C3—61no—
146C23×C3—62no—
147C23×C3—62no—
148C23×C3—62no—
149C23×C3—64no—
150C23×C3—61no—
151C23×C3—62no—
152C23×C3—62no—
153C23×C3—64no—
154C23×C3C22×A411yescharacteristic
155C22×D3—21no—
156C22×D3—61no—
157C22×D3—61no—
158C2×A4—41no—
159C2×A4—82no—
160C2×A4—81no—
161C2×A4—82no—
162C2×A4—81no—
163C2×A4—162no—
164C2×A4—241no—
165C3×D4—122no—
166C3×D4—122no—
167C3×D4—481no—
168C2×C3×C4—61no—
169C2×C3×C4—61no—
170C2×C3×C4—61no—
171#67—41no—
172#67—121no—
173#67—122no—
174#67—122no—
175C2×Dic3—31no—
176C2×Dic3—31no—
177C2×Dic3—32no—
178C2×Dic3—62no—
179C2×Dic3—64no—
180C2×Dic3—62no—
181C2×Dic3—64no—
182C2×Dic3—62no—
183C2×Dic3—62no—
184C2×Dic3—62no—
185C2×Dic3—61no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×C32—161no—
189C2×C32—321no—
190C3×D3—321no—
191C24—31no—
192C24—31no—
193C24—31no—
194C24—62no—
195C24—62no—
196C24C3×#6711yescharacteristic, complemented
197C24D3×A411yescharacteristic
198C2×D4—61no—
199C2×D4—61no—
200C2×D4—62no—
201C2×D4—62no—
202C2×D4—181no—
203C2×D4—181no—
204C2×D4—181no—
205C2×D4—181no—
206C2×D4—182no—
207C2×D4—182no—
208C22×C4—31no—
209C22×C4—31no—
210C22×C4—62no—
211C22×C4—92no—
212C22×C4—92no—
213C22×C4—91no—
214C22×C4—91no—
215C22×C4—182no—
216C22×C4—182no—
217C22×C4—184no—
218C22×C4—182no—
219C22×C4—182no—
220C22×C4—184no—
221C22×C4—182no—
222C22×C4—182no—
223C4⋊C4—181no—
224C4⋊C4—181no—
225C22⋊C4—61no—
226C22⋊C4—61no—
227C22⋊C4—182no—
228C22⋊C4—182no—
229C22⋊C4—181no—
230C22⋊C4—181no—
231C22×C3—22no—
232C22×C3—31no—
233C22×C3—31no—
234C22×C3—32no—
235C22×C3—32no—
236C22×C3—41no—
237C22×C3—62no—
238C22×C3—62no—
239C22×C3—62no—
240C22×C3—64no—
241C22×C3—62no—
242C22×C3—62no—
243C22×C3—62no—
244C22×C3—64no—
245C22×C3—62no—
246C22×C3—121no—
247C22×C3—121no—
248C22×C3—161no—
249C22×C3—321no—
250C22×C3—481no—
251C22×C3D4×A411yescharacteristic
252C2×D3—41no—
253C2×D3—121no—
254C2×D3—121no—
255A4—41no—
256A4—82no—
257A4—81no—
258A4—162no—
259C3×C4—121no—
260C3×C4—481no—
261Dic3—31no—
262Dic3—62no—
263Dic3—121no—
264Dic3#120⋊C311yescharacteristic, complemented
265C32—161noSylow
266C23—22no—
267C23—21no—
268C23—32no—
269C23—32no—
270C23—31no—
271C23—31no—
272C23—62no—
273C23—62no—
274C23—61no—
275C23—62no—
276C23—62no—
277C23—62no—
278C23—64no—
279C23—61no—
280C23—62no—
281C23—62no—
282C23—64no—
283C23—61no—
284C23—181no—
285C23—181no—
286C23C2×D3×A411yescharacteristic
287D4—121no—
288D4—122no—
289D4—122no—
290D4—361no—
291D4—362no—
292D4—362no—
293C2×C4—61no—
294C2×C4—61no—
295C2×C4—61no—
296C2×C4—91no—
297C2×C4—91no—
298C2×C4—92no—
299C2×C4—182no—
300C2×C4—182no—
301C2×C4—184no—
302C2×C4—182no—
303C2×C4—184no—
304C2×C4—182no—
305C2×C4—182no—
306C2×C4—181no—
307C2×C4—181no—
308C2×C4—181no—
309C2×C3—31no—
310C2×C3—31no—
311C2×C3—62no—
312C2×C3—62no—
313C2×C3—81no—
314C2×C3—161no—
315C2×C3—321no—
316C2×C3—322no—
317C2×C3—321no—
318C2×C3—961no—
319C2×C3C2×#120⋊C311yescharacteristic
320D3—81no—
321C22—22no—
322C22—31no—
323C22—31no—
324C22—32no—
325C22—32no—
326C22—41no—
327C22—62no—
328C22—62no—
329C22—62no—
330C22—64no—
331C22—62no—
332C22—62no—
333C22—62no—
334C22—64no—
335C22—62no—
336C22—121no—
337C22—121no—
338C22—121no—
339C22—361no—
340C22—361no—
341C22A4×#6711yescharacteristic
342C4—31no—
343C4—91no—
344C4—121no—
345C4—182no—
346C4—361no—
347C3—161no—
348C3—321no—
349C3C4⋊(#120⋊C3)11yescharacteristic, complemented
350C2—31no—
351C2—31no—
352C2—62no—
353C2—62no—
354C2—81no—
355C2—241no—
356C2D3×#120⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#120⋊C3
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. Dic3×C22⋊A4C2semidirect
2. C2×C3×#120⋊C3C2semidirect
3. C2×C3⋊(#120⋊C3)C2semidirect
4. #82601C3semidirect
10. C24×Dic3C2×C3semidirect
12. C2×C3×#120C2×C3semidirect
13. C2×#953C2×C3semidirect
17. C2×#120⋊C3D3semidirect
21. C3×C22⋊A4D4semidirect
32. C22×#67A4semidirect
61. C2×#120C3×D3semidirect
69. C24×C3C3×D4semidirect
73. C22⋊A4#67semidirect
196. C24C3×#67semidirect
264. Dic3#120⋊C3semidirect
349. C3C4⋊(#120⋊C3)semidirect

Maximal subgroups

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

subgroupindex
Dic3×C22⋊A42
C2×C3×#120⋊C32
C2×C3⋊(#120⋊C3)2
#826013
C4⋊(#120⋊C3)3
A4×#674