Finite Group Databasebeta

← C3×#69471 #11775076

Subgroups — C3×#69471 #11775076

Order 1152.

577 conjugacy classes of subgroups.

The subgroup lattice has 367 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5470C211yesmaximal, characteristic
2C32×C4×C4⋊C4C211yesmaximal, characteristic
3C3×#4925C211yesmaximal, characteristic
4C3×#4452C214yesmaximal
5C3×#1503—31nomaximal
6#69471C311yesmaximal, characteristic, direct product factor
7C2×C32×C4⋊C4—21no—
8C2×C32×C42—21no—
9C2×C32×C42C2211yescharacteristic
10C3×#926—21no—
11C3×#924—21no—
12C3×#924C2212yes—
13C3×#870—21no—
14C3×#869C411yescharacteristic, complemented
15C3×#869C411yescharacteristic, complemented
16C3×C4×Dic6—21no—
17C3×C4×Dic6C412yescomplemented
18C32×#95C2212yes—
19C3×#830C2212yes—
20C3×C4⋊(C3⋊C8)—21no—
21C3×C4×C3⋊C8—21no—
22C3×#533—31no—
23#5470C2×C311yescharacteristic
24C3×#431—31no—
25C3×C4×C4⋊C4—21no—
26C3×C4×C4⋊C4D311yescharacteristic
27C3×C4×C4⋊C4C2×C311yescharacteristic
28#4925C2×C311yescharacteristic
29C3×#328—34no—
30#4452C2×C314yes—
31C22×C32×C4—22no—
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C2×C3×Dic6—21no—
36C2×C3×Dic6C2×C412yes—
37C32×C4⋊C4—24no—
38C32×C42—42no—
39C32×C42C2×C411yescharacteristic
40C32×C42C2×C411yescharacteristic
41C32×C42D411yescharacteristic
42C32×C42D411yescharacteristic
43C3×#217—22no—
44C3×C4⋊Dic3—21no—
45C3×C4⋊Dic3—21no—
46C3×C4⋊Dic3—21no—
47C3×C4⋊Dic3C2×C412yes—
48C3×Dic3⋊C4—22no—
49C3×Dic3⋊C4—22no—
50C3×C4×Dic3—22no—
51C2×C3×C3⋊C8—22no—
52#1503—31noSylow
53C3×C4⋊Q8—31no—
54C3×C4⋊Q8—31no—
55C3×#125—61no—
56C3×C22⋊Q8—32no—
57C3×C22⋊Q8—61no—
58C3×C4×Q8—32no—
59C3×C4×Q8—61no—
60C3×#117—61no—
61C2×C3×C4⋊C4—22no—
62C2×C3×C4⋊C4—21no—
63C2×C3×C4⋊C4—21no—
64C2×C3×C42—22no—
65C2×C3×C42—21no—
66C2×C3×C42—21no—
67C2×C3×C42—21no—
68C2×C3×C42C2×D311yescharacteristic
69C2×C3×C42C22×C311yescharacteristic
70#926—21no—
71#924—21no—
72#924C22×C312yes—
73#870—21no—
74#869C3×C411yescharacteristic, complemented
75#869C3×C411yescharacteristic, complemented
76C4×Dic6—21no—
77C4×Dic6C3×C412yescomplemented
78C3×C4⋊C8—61no—
79C3×C22⋊C8—32no—
80C3×C4×C8—61no—
81C3×#95—22no—
82C3×#95C2×D312yes—
83C3×#95C22×C312yes—
84#830C22×C312yes—
85C4⋊(C3⋊C8)—21no—
86C4×C3⋊C8—21no—
87C23×C32C2×D411yescharacteristic
88C2×C32×C4—22no—
89C2×C32×C4—24no—
90C2×C32×C4—41no—
91C2×C32×C4—42no—
92C2×C32×C4—42no—
93C2×C32×C4C22⋊C411yescharacteristic
94C2×C32×C4C22⋊C411yescharacteristic
95C2×C32×C4C22⋊C411yescharacteristic
96C2×C32×C4C22⋊C411yescharacteristic
97C2×C32×C4SD1612yes—
98C2×C32×C4Q1612yes—
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C3×Dic3—22no—
102C2×C3×Dic3—22no—
103C3×Dic6—42no—
104C3×Dic6—42no—
105C3×C3⋊C8—42no—
106#533—31no—
107#431—31no—
108C4×C4⋊C4C3×D311yescharacteristic
109#328—34no—
110C2×C3×Q8—32no—
111C2×C3×Q8—61no—
112C22×C3×C4—24no—
113C22×C3×C4—22no—
114C22×C3×C4—22no—
115C22×C3×C4—21no—
116C22×C3×C4—21no—
117C22×C3×C4—21no—
118C22×C3×C4#6711yescharacteristic
119C22×C3×C4#6711yescharacteristic
120C22×C3×C4C3×D411yescharacteristic
121C22×C3×C4C3×D411yescharacteristic
122C22×C3×C4C22×D311yescharacteristic
123C22×C3×C4C23×C311yescharacteristic
124C2×Dic6—21no—
125C2×Dic6C2×C3×C412yes—
126C2×C3×C8—62no—
127C3×C4⋊C4—28no—
128C3×C4⋊C4—24no—
129C3×C4⋊C4—24no—
130C3×C4⋊C4—32no—
131C3×C4⋊C4—62no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—62no—
136C3×C22⋊C4—62no—
137C3×C42—21no—
138C3×C42—21no—
139C3×C42—21no—
140C3×C42—21no—
141C3×C42—44no—
142C3×C42—42no—
143C3×C42—42no—
144C3×C42—62no—
145C3×C42C4×D311yescharacteristic
146C3×C42C4×D311yescharacteristic
147C3×C42D1211yescharacteristic
148C3×C42D1211yescharacteristic
149C3×C42C2×C3×C411yescharacteristic
150C3×C42C2×C3×C411yescharacteristic
151C3×C42C3×D411yescharacteristic
152C3×C42C3×D411yescharacteristic
153#217—22no—
154C4⋊Dic3—21no—
155C4⋊Dic3—21no—
156C4⋊Dic3—21no—
157C4⋊Dic3C2×C3×C412yes—
158Dic3⋊C4—22no—
159Dic3⋊C4—22no—
160C4×Dic3—22no—
161C2×C3⋊C8—22no—
162C22×C32—21no—
163C22×C32—21no—
164C22×C32C2×C22⋊C411yescharacteristic
165C22×C32C2×SD1611yescharacteristic
166C22×C32C2×Q1611yescharacteristic
167C32×C4—21no—
168C32×C4—21no—
169C32×C4—21no—
170C32×C4—44no—
171C32×C4#10312yes—
172C32×C4#10312yes—
173C32×C4#10412yes—
174C3×Dic3—42no—
175C3×Dic3—42no—
176C4⋊Q8—31no—
177C4⋊Q8—31no—
178#125—61no—
179C22⋊Q8—32no—
180C22⋊Q8—61no—
181C4×Q8—32no—
182C4×Q8—61no—
183#117—61no—
184C2×C4⋊C4—21no—
185C2×C42—21no—
186C2×C42C2×C3×D311yescharacteristic
187C4⋊C8—61no—
188C22⋊C8—32no—
189C4×C8—61no—
190#95C2×C3×D312yes—
191C23×C3—21no—
192C23×C3C2×#6711yescharacteristic
193C23×C3C2×C3×D411yescharacteristic
194C3×Q8—122no—
195C3×Q8—122no—
196C2×C3×C4—24no—
197C2×C3×C4—22no—
198C2×C3×C4—22no—
199C2×C3×C4—28no—
200C2×C3×C4—24no—
201C2×C3×C4—24no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—41no—
211C2×C3×C4—41no—
212C2×C3×C4—44no—
213C2×C3×C4—42no—
214C2×C3×C4—44no—
215C2×C3×C4—42no—
216C2×C3×C4—42no—
217C2×C3×C4—42no—
218C2×C3×C4—42no—
219C2×C3×C4—62no—
220C2×C3×C4—62no—
221C2×C3×C4(C2×D3)⋊C411yescharacteristic
222C2×C3×C4(C2×D3)⋊C411yescharacteristic
223C2×C3×C4(C2×D3)⋊C411yescharacteristic
224C2×C3×C4(C2×D3)⋊C411yescharacteristic
225C2×C3×C4#21412yes—
226C2×C3×C4#21612yes—
227C2×C3×C4C3×C22⋊C411yescharacteristic
228C2×C3×C4C3×C22⋊C411yescharacteristic
229C2×C3×C4C3×C22⋊C411yescharacteristic
230C2×C3×C4C3×C22⋊C411yescharacteristic
231C2×C3×C4C3×SD1612yes—
232C2×C3×C4C3×Q1612yes—
233C2×C3×C4C2×C4×D311yescharacteristic
234C2×C3×C4C2×D1211yescharacteristic
235C2×C3×C4C22×C3×C411yescharacteristic
236C2×C3×C4C2×C3×D411yescharacteristic
237C2×Dic3—22no—
238C2×Dic3—22no—
239Dic6—42no—
240Dic6—42no—
241C3×C8—122no—
242C3⋊C8—42no—
243C2×C32—21no—
244C2×C32—21no—
245C2×C32#41011yescharacteristic
246C2×C32C2×#10311yescharacteristic
247C2×C32C2×#10411yescharacteristic
248C2×Q8—32no—
249C2×Q8—61no—
250C22×C4—22no—
251C22×C4C3×#6711yescharacteristic
252C22×C4C3×#6711yescharacteristic
253C22×C4C22×C3×D311yescharacteristic
254C2×C8—62no—
255C4⋊C4—24no—
256C4⋊C4—32no—
257C4⋊C4—61no—
258C4⋊C4—61no—
259C4⋊C4—62no—
260C4⋊C4—61no—
261C4⋊C4—62no—
262C22⋊C4—62no—
263C42—42no—
264C42—62no—
265C42C3×C4×D311yescharacteristic
266C42C3×C4×D311yescharacteristic
267C42C3×D1211yescharacteristic
268C42C3×D1211yescharacteristic
269C22×C3—22no—
270C22×C3—22no—
271C22×C3—21no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3C2×(C2×D3)⋊C411yescharacteristic
279C22×C3C2×#21411yescharacteristic
280C22×C3C2×#21611yescharacteristic
281C22×C3C2×C3×C22⋊C411yescharacteristic
282C22×C3C2×C3×SD1611yescharacteristic
283C22×C3C2×C3×Q1611yescharacteristic
284C3×C4—22no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—22no—
292C3×C4—22no—
293C3×C4—22no—
294C3×C4—41no—
295C3×C4—41no—
296C3×C4—48no—
297C3×C4—44no—
298C3×C4—44no—
299C3×C4—122no—
300C3×C4—122no—
301C3×C4#80512yes—
302C3×C4#81012yes—
303C3×C4#81012yes—
304C3×C4C3×#10312yes—
305C3×C4C3×#10312yes—
306C3×C4C3×#10412yes—
307Dic3—42no—
308Dic3—42no—
309C32#150311yescharacteristic, complemented, Sylow
310C23C2×C3×#6711yescharacteristic
311Q8—122no—
312Q8—122no—
313C2×C4—22no—
314C2×C4—24no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—62no—
319C2×C4—62no—
320C2×C4C3×(C2×D3)⋊C411yescharacteristic
321C2×C4C3×(C2×D3)⋊C411yescharacteristic
322C2×C4C3×(C2×D3)⋊C411yescharacteristic
323C2×C4C3×(C2×D3)⋊C411yescharacteristic
324C2×C4C3×#21412yes—
325C2×C4C3×#21612yes—
326C2×C4C2×C3×C4×D311yescharacteristic
327C2×C4C2×C3×D1211yescharacteristic
328C8—122no—
329C2×C3—22no—
330C2×C3—22no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3C2×#80511yescharacteristic
339C2×C3C2×#81011yescharacteristic
340C2×C3#500611yescharacteristic
341C2×C3C3×#41011yescharacteristic
342C2×C3C2×C3×#10311yescharacteristic
343C2×C3C2×C3×#10411yescharacteristic
344C22—21no—
345C22—21no—
346C22C2×C3×(C2×D3)⋊C411yescharacteristic
347C22C2×C3×#21411yescharacteristic
348C22C2×C3×#21611yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—44no—
353C4—122no—
354C4—122no—
355C4C3×#80512yes—
356C4C3×#81012yes—
357C4C3×#81012yes—
358C3—21no—
359C3#6947111yescharacteristic, direct product factor
360C3C3×#150311yescharacteristic, complemented
361C2—21no—
362C2—21no—
363C2C2×C3×#80511yescharacteristic
364C2C2×C3×#81011yescharacteristic
365C2C3×#500611yescharacteristic
subgroupG/H
centerC2×C3×C4(C2×D3)⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×C4×C4⋊C4C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C2×D4
cosocleC22×C3×C4C23×C3
hypercenterC3×C4×C4⋊C4D3
hypocenterC3C3×#1503
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. #69471C3direct (N × H)
14. C3×#869C4semidirect
15. C3×#869C4semidirect
17. C3×C4×Dic6C4semidirect
74. #869C3×C4semidirect
75. #869C3×C4semidirect
77. C4×Dic6C3×C4semidirect
309. C32#1503semidirect
359. C3#69471direct (N × H)
360. C3C3×#1503semidirect

Maximal subgroups

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

subgroupindex
C3×#54702
C32×C4×C4⋊C42
C3×#49252
C3×#44522
C3×#15033
#694713