Finite Group Databasebeta

← C3×#69433 #11775169

Subgroups — C3×#69433 #11775169

Order 1152.

545 conjugacy classes of subgroups.

The subgroup lattice has 347 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5470C211yesmaximal, characteristic
2C32×#376C211yesmaximal, characteristic
3C3×#4926C211yesmaximal, characteristic
4C3×#4452C214yesmaximal
5C3×#1506—31nomaximal
6#69433C311yesmaximal, characteristic, direct product factor
7C2×C32×C42—21no—
8C2×C32×C42C2211yescharacteristic
9C3×#926—21no—
10C3×#924—21no—
11C3×#924C2212yes—
12C3×#870—21no—
13C3×#869C411yescharacteristic, complemented
14C3×#869C411yescharacteristic, complemented
15C3×C4×Dic6—21no—
16C3×C4×Dic6C412yescomplemented
17C32×#95—21no—
18C32×#95C2212yes—
19C3×#830C2212yes—
20C3×C4⋊(C3⋊C8)—21no—
21C3×#803—21no—
22C3×#533—31no—
23#5470C2×C311yescharacteristic
24C3×#432—31no—
25C3×#376—21no—
26C3×#376D311yescharacteristic
27C3×#376C2×C311yescharacteristic
28#4926C2×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×C42—24no—
38C32×C42C2×C411yescharacteristic
39C32×C42C2×C411yescharacteristic
40C32×C42D411yescharacteristic
41C32×C42D411yescharacteristic
42C3×#217—22no—
43C3×C4⋊Dic3—21no—
44C3×C4⋊Dic3—21no—
45C3×C4⋊Dic3—21no—
46C3×C4⋊Dic3C2×C412yes—
47C3×Dic3⋊C4—22no—
48C3×Dic3⋊C4—22no—
49C3×C4×Dic3—22no—
50C2×C3×C3⋊C8—22no—
51#1506—31noSylow
52C3×C4⋊Q8—31no—
53C3×C4⋊Q8—31no—
54C3×#125—61no—
55C3×C22⋊Q8—32no—
56C3×C22⋊Q8—61no—
57C3×C4×Q8—32no—
58C3×C4×Q8—61no—
59C3×#117—61no—
60C2×C3×C42—22no—
61C2×C3×C42—21no—
62C2×C3×C42—21no—
63C2×C3×C42—21no—
64C2×C3×C42C2×D311yescharacteristic
65C2×C3×C42C22×C311yescharacteristic
66#926—21no—
67#924—21no—
68#924C22×C312yes—
69#870—21no—
70#869C3×C411yescharacteristic, complemented
71#869C3×C411yescharacteristic, complemented
72C4×Dic6—21no—
73C4×Dic6C3×C412yescomplemented
74C3×C4⋊C8—61no—
75C3×C22⋊C8—32no—
76C3×#97—61no—
77C3×#95—22no—
78C3×#95—21no—
79C3×#95—21no—
80C3×#95—22no—
81C3×#95C2×D312yes—
82C3×#95C22×C312yes—
83#830C22×C312yes—
84C4⋊(C3⋊C8)—21no—
85#803—21no—
86C23×C32C2×D411yescharacteristic
87C2×C32×C4—22no—
88C2×C32×C4—24no—
89C2×C32×C4—22no—
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×C4C22×C411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C3×Dic3—22no—
100C2×C3×Dic3—22no—
101C3×Dic6—42no—
102C3×Dic6—42no—
103C3×C3⋊C8—42no—
104#533—31no—
105#432—31no—
106#376C3×D311yescharacteristic
107#328—34no—
108C2×C3×Q8—32no—
109C2×C3×Q8—61no—
110C22×C3×C4—24no—
111C22×C3×C4—22no—
112C22×C3×C4—22no—
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4—21no—
116C22×C3×C4#6711yescharacteristic
117C22×C3×C4#6711yescharacteristic
118C22×C3×C4C3×D411yescharacteristic
119C22×C3×C4C3×D411yescharacteristic
120C22×C3×C4C22×D311yescharacteristic
121C22×C3×C4C23×C311yescharacteristic
122C2×Dic6—21no—
123C2×Dic6C2×C3×C412yes—
124C2×C3×C8—62no—
125C3×C4⋊C4—32no—
126C3×C4⋊C4—62no—
127C3×C4⋊C4—61no—
128C3×C4⋊C4—61no—
129C3×C4⋊C4—61no—
130C3×C4⋊C4—62no—
131C3×C22⋊C4—62no—
132C3×C42—28no—
133C3×C42—24no—
134C3×C42—24no—
135C3×C42—21no—
136C3×C42—21no—
137C3×C42—21no—
138C3×C42—21no—
139C3×C42—62no—
140C3×C42C4×D311yescharacteristic
141C3×C42C4×D311yescharacteristic
142C3×C42D1211yescharacteristic
143C3×C42D1211yescharacteristic
144C3×C42C2×C3×C411yescharacteristic
145C3×C42C2×C3×C411yescharacteristic
146C3×C42C3×D411yescharacteristic
147C3×C42C3×D411yescharacteristic
148#217—22no—
149C4⋊Dic3—21no—
150C4⋊Dic3—21no—
151C4⋊Dic3—21no—
152C4⋊Dic3C2×C3×C412yes—
153Dic3⋊C4—22no—
154Dic3⋊C4—22no—
155C4×Dic3—22no—
156C2×C3⋊C8—22no—
157C22×C32—21no—
158C22×C32—21no—
159C22×C32C2×C22⋊C411yescharacteristic
160C22×C32#13712yes—
161C32×C4—21no—
162C32×C4—21no—
163C32×C4—21no—
164C32×C4—21no—
165C32×C4—21no—
166C32×C4—44no—
167C32×C4#10412yes—
168C3×Dic3—42no—
169C3×Dic3—42no—
170C4⋊Q8—31no—
171C4⋊Q8—31no—
172#125—61no—
173C22⋊Q8—32no—
174C22⋊Q8—61no—
175C4×Q8—32no—
176C4×Q8—61no—
177#117—61no—
178C2×C42—21no—
179C2×C42C2×C3×D311yescharacteristic
180C4⋊C8—61no—
181C22⋊C8—32no—
182#97—61no—
183#95—21no—
184#95C2×C3×D312yes—
185C23×C3—21no—
186C23×C3C2×#6711yescharacteristic
187C23×C3C2×C3×D411yescharacteristic
188C3×Q8—122no—
189C3×Q8—122no—
190C2×C3×C4—24no—
191C2×C3×C4—22no—
192C2×C3×C4—22no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—28no—
196C2×C3×C4—24no—
197C2×C3×C4—24no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—42no—
205C2×C3×C4—41no—
206C2×C3×C4—41no—
207C2×C3×C4—42no—
208C2×C3×C4—44no—
209C2×C3×C4—42no—
210C2×C3×C4—42no—
211C2×C3×C4—44no—
212C2×C3×C4—42no—
213C2×C3×C4—42no—
214C2×C3×C4—62no—
215C2×C3×C4—62no—
216C2×C3×C4(C2×D3)⋊C411yescharacteristic
217C2×C3×C4(C2×D3)⋊C411yescharacteristic
218C2×C3×C4(C2×D3)⋊C411yescharacteristic
219C2×C3×C4(C2×D3)⋊C411yescharacteristic
220C2×C3×C4C3×C22⋊C411yescharacteristic
221C2×C3×C4C3×C22⋊C411yescharacteristic
222C2×C3×C4C3×C22⋊C411yescharacteristic
223C2×C3×C4C3×C22⋊C411yescharacteristic
224C2×C3×C4C2×C4×D311yescharacteristic
225C2×C3×C4C2×D1211yescharacteristic
226C2×C3×C4C22×C3×C411yescharacteristic
227C2×C3×C4C2×C3×D411yescharacteristic
228C2×Dic3—22no—
229C2×Dic3—22no—
230Dic6—42no—
231Dic6—42no—
232C3×C8—122no—
233C3⋊C8—42no—
234C2×C32—22no—
235C2×C32#41011yescharacteristic
236C2×C32#41911yescharacteristic
237C2×C32C2×#10411yescharacteristic
238C2×Q8—32no—
239C2×Q8—61no—
240C22×C4—22no—
241C22×C4C3×#6711yescharacteristic
242C22×C4C3×#6711yescharacteristic
243C22×C4C22×C3×D311yescharacteristic
244C2×C8—62no—
245C4⋊C4—32no—
246C4⋊C4—61no—
247C4⋊C4—61no—
248C4⋊C4—62no—
249C4⋊C4—61no—
250C4⋊C4—62no—
251C22⋊C4—62no—
252C42—24no—
253C42—62no—
254C42C3×C4×D311yescharacteristic
255C42C3×C4×D311yescharacteristic
256C42C3×D1211yescharacteristic
257C42C3×D1211yescharacteristic
258C22×C3—22no—
259C22×C3—22no—
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—22no—
266C22×C3C2×(C2×D3)⋊C411yescharacteristic
267C22×C3#95112yes—
268C22×C3C2×C3×C22⋊C411yescharacteristic
269C22×C3C3×#13712yes—
270C3×C4—22no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—22no—
282C3×C4—41no—
283C3×C4—41no—
284C3×C4—41no—
285C3×C4—41no—
286C3×C4—48no—
287C3×C4—44no—
288C3×C4—44no—
289C3×C4—122no—
290C3×C4—122no—
291C3×C4#80512yes—
292C3×C4C3×#10412yes—
293Dic3—42no—
294Dic3—42no—
295C32#150611yescharacteristic, complemented, Sylow
296C23C2×C3×#6711yescharacteristic
297Q8—122no—
298Q8—122no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—24no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—62no—
306C2×C4—62no—
307C2×C4C3×(C2×D3)⋊C411yescharacteristic
308C2×C4C3×(C2×D3)⋊C411yescharacteristic
309C2×C4C3×(C2×D3)⋊C411yescharacteristic
310C2×C4C3×(C2×D3)⋊C411yescharacteristic
311C2×C4C2×C3×C4×D311yescharacteristic
312C2×C4C2×C3×D1211yescharacteristic
313C8—122no—
314C2×C3—24no—
315C2×C3—22no—
316C2×C3—22no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3C2×#80511yescharacteristic
321C2×C3#500411yescharacteristic
322C2×C3#500611yescharacteristic
323C2×C3C3×#41011yescharacteristic
324C2×C3C3×#41911yescharacteristic
325C2×C3C2×C3×#10411yescharacteristic
326C22—21no—
327C22—21no—
328C22C2×C3×(C2×D3)⋊C411yescharacteristic
329C22C3×#95112yes—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—44no—
336C4—122no—
337C4—122no—
338C4C3×#80512yes—
339C3—21no—
340C3#6943311yescharacteristic, direct product factor
341C3C3×#150611yescharacteristic, complemented
342C2—22no—
343C2C2×C3×#80511yescharacteristic
344C2C3×#500411yescharacteristic
345C2C3×#500611yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#376C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C2×D4
cosocleC22×C3×C4C23×C3
hypercenterC3×#376D3
hypocenterC3C3×#1506
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#376

Complements

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

NH ≅ G/Ntype
6. #69433C3direct (N × H)
13. C3×#869C4semidirect
14. C3×#869C4semidirect
16. C3×C4×Dic6C4semidirect
70. #869C3×C4semidirect
71. #869C3×C4semidirect
73. C4×Dic6C3×C4semidirect
295. C32#1506semidirect
340. C3#69433direct (N × H)
341. C3C3×#1506semidirect

Maximal subgroups

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

subgroupindex
C3×#54702
C32×#3762
C3×#49262
C3×#44522
C3×#15063
#694333