Finite Group Databasebeta

← C3×#67626 #11771227

Subgroups — C3×#67626 #11771227

Order 1152.

517 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#380C211yesmaximal, characteristic
2C3×#5207C211yesmaximal, characteristic
3C3×#5207C211yesmaximal, characteristic
4C3×#1305—31nomaximal
5#67626C311yesmaximal, characteristic, direct product factor
6C23×C32×C4C2211yescharacteristic
7C2×C32×C4⋊C4—21no—
8C2×C32×C22⋊C4C412yes—
9C2×C3×#208—21no—
10C2×C3×#208C412yescomplemented
11C32×#95—21no—
12C3×#830—21no—
13C3×#830—21no—
14C3×#830—21no—
15C3×#830C412yescomplemented
16C3×#407—31no—
17C3×#407—31no—
18C3×#380—21no—
19C3×#380D311yescharacteristic
20C3×#380C2×C311yescharacteristic
21#5207C2×C311yescharacteristic
22#5207C2×C311yescharacteristic
23C24×C32C2×C411yescharacteristic
24C22×C32×C4—22no—
25C22×C32×C4—42no—
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4D411yescharacteristic
29C22×C32×C4D411yescharacteristic
30C22×C32×C4D411yescharacteristic
31C22×C32×C4Q811yescharacteristic
32C32×C4⋊C4—42no—
33C32×C22⋊C4—42no—
34C3×#208—42no—
35C3×#208—42no—
36C2×C3×C3⋊C8—22no—
37C2×C3×C3⋊C8—22no—
38#1305—31noSylow
39C23×C3×C4—21no—
40C23×C3×C4C2×D311yescharacteristic
41C23×C3×C4C22×C311yescharacteristic
42C2×C3×M16—32no—
43C2×C3×M16—61no—
44C2×C3×C4⋊C4—22no—
45C2×C3×C4⋊C4—21no—
46C2×C3×C4⋊C4—21no—
47C2×C3×C22⋊C4—22no—
48C2×C3×C22⋊C4Dic312yes—
49C2×C3×C22⋊C4C3×C412yes—
50C2×#208—21no—
51C2×#208C3×C412yescomplemented
52C3×C22⋊C8—32no—
53C3×C22⋊C8—61no—
54C3×C22⋊C8—61no—
55C3×C22⋊C8—61no—
56C3×#95—22no—
57C3×#95—21no—
58C3×#95—21no—
59#830—21no—
60#830—21no—
61#830—21no—
62#830C3×C412yescomplemented
63C23×C32—21no—
64C23×C32—21no—
65C23×C32—41no—
66C23×C32—41no—
67C23×C32C4211yescharacteristic
68C23×C32C22⋊C411yescharacteristic
69C23×C32C4⋊C411yescharacteristic
70C2×C32×C4—22no—
71C2×C32×C4—22no—
72C2×C32×C4—22no—
73C2×C32×C4—41no—
74C2×C32×C4—41no—
75C2×C32×C4—41no—
76C2×C32×C4—42no—
77C2×C32×C4—42no—
78C2×C32×C4—42no—
79C2×C32×C4C22⋊C411yescharacteristic
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C4⋊C411yescharacteristic
82C2×C32×C4C4⋊C411yescharacteristic
83C3×C3⋊C8—42no—
84C3×C3⋊C8—42no—
85#407—31no—
86#407—31no—
87#380C3×D311yescharacteristic
88C24×C3—21no—
89C24×C3C2×Dic311yescharacteristic
90C24×C3C2×C3×C411yescharacteristic
91C22×C3×C4—24no—
92C22×C3×C4—22no—
93C22×C3×C4—22no—
94C22×C3×C4—21no—
95C22×C3×C4—21no—
96C22×C3×C4—21no—
97C22×C3×C4—21no—
98C22×C3×C4—21no—
99C22×C3×C4—21no—
100C22×C3×C4—42no—
101C22×C3×C4—42no—
102C22×C3×C4—44no—
103C22×C3×C4Dic611yescharacteristic
104C22×C3×C4C4×D311yescharacteristic
105C22×C3×C4C4×D311yescharacteristic
106C22×C3×C4D1211yescharacteristic
107C22×C3×C4#6711yescharacteristic
108C22×C3×C4#6711yescharacteristic
109C22×C3×C4C2×C3×C411yescharacteristic
110C22×C3×C4C2×C3×C411yescharacteristic
111C22×C3×C4C3×D411yescharacteristic
112C22×C3×C4C3×D411yescharacteristic
113C22×C3×C4C3×D411yescharacteristic
114C22×C3×C4C3×Q811yescharacteristic
115C3×M16—122no—
116C3×M16—122no—
117C2×C3×C8—62no—
118C2×C3×C8—62no—
119C3×C4⋊C4—44no—
120C3×C4⋊C4—42no—
121C3×C4⋊C4—42no—
122C3×C22⋊C4—44no—
123C3×C22⋊C4—42no—
124C3×C22⋊C4—42no—
125#208—42no—
126#208—42no—
127C2×C3⋊C8—22no—
128C2×C3⋊C8—22no—
129C22×C32—21no—
130C22×C32—21no—
131C22×C32—21no—
132C22×C32—21no—
133C22×C32—21no—
134C22×C32—21no—
135C22×C32—21no—
136C22×C32—21no—
137C22×C32—42no—
138C22×C32—42no—
139C22×C32#9511yescharacteristic
140C22×C32#10011yescharacteristic
141C22×C32#10111yescharacteristic
142C32×C4—21no—
143C32×C4—21no—
144C32×C4—21no—
145C32×C4—82no—
146C32×C4#9912yes—
147C23×C4C2×C3×D311yescharacteristic
148C2×M16—32no—
149C2×M16—61no—
150C2×C4⋊C4—21no—
151C2×C22⋊C4C3×Dic312yes—
152C22⋊C8—32no—
153C22⋊C8—61no—
154C22⋊C8—61no—
155C22⋊C8—61no—
156#95—21no—
157C23×C3—22no—
158C23×C3—22no—
159C23×C3—21no—
160C23×C3—21no—
161C23×C3—21no—
162C23×C3—21no—
163C23×C3—21no—
164C23×C3—21no—
165C23×C3—21no—
166C23×C3—41no—
167C23×C3—41no—
168C23×C3—41no—
169C23×C3—41no—
170C23×C3—42no—
171C23×C3—42no—
172C23×C3C4×Dic311yescharacteristic
173C23×C3C4⋊Dic311yescharacteristic
174C23×C3#21711yescharacteristic
175C23×C3C3×C4211yescharacteristic
176C23×C3C3×C22⋊C411yescharacteristic
177C23×C3C3×C4⋊C411yescharacteristic
178C2×C3×C4—24no—
179C2×C3×C4—22no—
180C2×C3×C4—22no—
181C2×C3×C4—22no—
182C2×C3×C4—22no—
183C2×C3×C4—22no—
184C2×C3×C4—22no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—42no—
190C2×C3×C4—42no—
191C2×C3×C4—41no—
192C2×C3×C4—41no—
193C2×C3×C4—41no—
194C2×C3×C4—41no—
195C2×C3×C4—41no—
196C2×C3×C4—41no—
197C2×C3×C4—42no—
198C2×C3×C4—42no—
199C2×C3×C4—42no—
200C2×C3×C4—44no—
201C2×C3×C4—44no—
202C2×C3×C4—42no—
203C2×C3×C4—42no—
204C2×C3×C4—44no—
205C2×C3×C4—42no—
206C2×C3×C4—42no—
207C2×C3×C4—42no—
208C2×C3×C4—42no—
209C2×C3×C4Dic3⋊C411yescharacteristic
210C2×C3×C4Dic3⋊C411yescharacteristic
211C2×C3×C4(C2×D3)⋊C411yescharacteristic
212C2×C3×C4(C2×D3)⋊C411yescharacteristic
213C2×C3×C4C3×C22⋊C411yescharacteristic
214C2×C3×C4C3×C22⋊C411yescharacteristic
215C2×C3×C4C3×C4⋊C411yescharacteristic
216C2×C3×C4C3×C4⋊C411yescharacteristic
217C3×C8—122no—
218C3×C8—122no—
219C3⋊C8—42no—
220C3⋊C8—42no—
221C2×C32—21no—
222C2×C32—21no—
223C2×C32—41no—
224C2×C32—41no—
225C2×C32#34211yescharacteristic
226C2×C32#34311yescharacteristic
227C2×C32#34411yescharacteristic
228C24C2×C3×Dic311yescharacteristic
229C22×C4—22no—
230C22×C4—42no—
231C22×C4C3×Dic611yescharacteristic
232C22×C4C3×C4×D311yescharacteristic
233C22×C4C3×C4×D311yescharacteristic
234C22×C4C3×D1211yescharacteristic
235C22×C4C3×#6711yescharacteristic
236C22×C4C3×#6711yescharacteristic
237M16—122no—
238M16—122no—
239C2×C8—62no—
240C2×C8—62no—
241C4⋊C4—42no—
242C22⋊C4—42no—
243C22×C3—22no—
244C22×C3—22no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—22no—
250C22×C3—22no—
251C22×C3—21no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—44no—
271C22×C3—44no—
272C22×C3—42no—
273C22×C3—42no—
274C22×C3—42no—
275C22×C3—42no—
276C22×C3C3⋊#9511yescharacteristic
277C22×C3#83311yescharacteristic
278C22×C3#83611yescharacteristic
279C22×C3C3×#9511yescharacteristic
280C22×C3C3×#10011yescharacteristic
281C22×C3C3×#10111yescharacteristic
282C3×C4—22no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—22no—
290C3×C4—41no—
291C3×C4—41no—
292C3×C4—84no—
293C3×C4—82no—
294C3×C4—82no—
295C3×C4#80612yes—
296C3×C4C3×#9912yes—
297C32#130511yescharacteristic, complemented, Sylow
298C23—21no—
299C23—21no—
300C23—41no—
301C23—41no—
302C23C3×C4×Dic311yescharacteristic
303C23C3×C4⋊Dic311yescharacteristic
304C23C3×#21711yescharacteristic
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4C3×Dic3⋊C411yescharacteristic
315C2×C4C3×Dic3⋊C411yescharacteristic
316C2×C4C3×(C2×D3)⋊C411yescharacteristic
317C2×C4C3×(C2×D3)⋊C411yescharacteristic
318C8—122no—
319C8—122no—
320C2×C3—22no—
321C2×C3—22no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—42no—
330C2×C3—42no—
331C2×C3—41no—
332C2×C3—41no—
333C2×C3—41no—
334C2×C3—41no—
335C2×C3#452711yescharacteristic
336C2×C3#453011yescharacteristic
337C2×C3#453311yescharacteristic
338C2×C3C3×#34211yescharacteristic
339C2×C3C3×#34311yescharacteristic
340C2×C3C3×#34411yescharacteristic
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—42no—
350C22—42no—
351C22C3×C3⋊#9511yescharacteristic
352C22C3×#83311yescharacteristic
353C22C3×#83611yescharacteristic
354C4—21no—
355C4—21no—
356C4—21no—
357C4—82no—
358C4C3×#80612yes—
359C3—21no—
360C3#6762611yescharacteristic, direct product factor
361C3C3×#130511yescharacteristic, complemented
362C2—21no—
363C2—21no—
364C2—41no—
365C2—41no—
366C2C3×#452711yescharacteristic
367C2C3×#453011yescharacteristic
368C2C3×#453311yescharacteristic
subgroupG/H
centerC22×C3C3⋊#95
commutatorC23×C3C3×C42
FrattiniC23×C4C2×C3×D3
FittingC32×#380C2
socleC22×C32#95
prime radicalC24×C32C2×C4
cosocleC23×C3×C4C22×C3
hypercenterC3×#380D3
hypocenterC3C3×#1305
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#380

Complements

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

NH ≅ G/Ntype
5. #67626C3direct (N × H)
10. C2×C3×#208C4semidirect
15. C3×#830C4semidirect
51. C2×#208C3×C4semidirect
62. #830C3×C4semidirect
297. C32#1305semidirect
360. C3#67626direct (N × H)
361. C3C3×#1305semidirect

Maximal subgroups

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

subgroupindex
C32×#3802
C3×#52072
C3×#13053
#676263