Finite Group Databasebeta

← C3×#70787 #11774047

Subgroups — C3×#70787 #11774047

Order 1152.

467 conjugacy classes of subgroups.

The subgroup lattice has 327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#870C211yesmaximal, characteristic
2C32×#431C211yesmaximal, characteristic
3C3×#4926C211yesmaximal, characteristic
4C3×#4469C214yesmaximal
5C3×#1470—31nomaximal
6#70787C311yesmaximal, characteristic, direct product factor
7C2×C32×C42C2211yescharacteristic
8C2×C3×C4⋊Dic3C411yescharacteristic
9C2×C3×C4⋊Dic3C411yescharacteristic
10C2×C3×Dic3⋊C4C412yes—
11C2×C3×Dic3⋊C4C2212yes—
12C3×#870—21no—
13C3×#870—21no—
14C3×#870—21no—
15C3×#870—21no—
16C32×C4⋊C8—21no—
17C32×C22⋊C8C2212yes—
18C32×C4×C8—21no—
19C3×#830C2212yes—
20C3×C4⋊(C3⋊C8)—21no—
21C3×#803—21no—
22C2×C3×#125—31no—
23C2×#870C2×C311yescharacteristic
24C3×#432—31no—
25C3×#431—21no—
26C3×#431D311yescharacteristic
27C3×#431C2×C311yescharacteristic
28#4926C2×C311yescharacteristic
29C3×#324—34no—
30#4469C2×C314yes—
31C22×C32×C4C2×C411yescharacteristic
32C22×C32×C4C2×C411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C22×C3×Dic3C2×C412yes—
35C22×C3×Dic3C2×C412yes—
36C2×C32×C8—22no—
37C32×C42D411yescharacteristic
38C32×C42D411yescharacteristic
39C32×C42D411yescharacteristic
40C32×C42D411yescharacteristic
41C3×C4⋊Dic3—21no—
42C3×C4⋊Dic3—21no—
43C3×C4⋊Dic3—21no—
44C3×C4⋊Dic3—21no—
45C3×Dic3⋊C4—22no—
46C3×Dic3⋊C4—22no—
47C3×Dic3⋊C4—22no—
48C3×Dic3⋊C4—22no—
49C2×C3×C3⋊C8—22no—
50#1470—31noSylow
51C3×#125—61no—
52C3×#125—61no—
53C3×#125—61no—
54C3×#125—61no—
55C2×C3×C4⋊C4—32no—
56C2×C3×C4⋊C4—31no—
57C2×C3×C4⋊C4—31no—
58C2×C3×C4⋊C4—32no—
59C2×C3×C42—21no—
60C2×C3×C42C2×D311yescharacteristic
61C2×C3×C42C22×C311yescharacteristic
62C2×C4⋊Dic3C3×C411yescharacteristic
63C2×C4⋊Dic3C3×C411yescharacteristic
64C2×Dic3⋊C4C3×C412yes—
65C2×Dic3⋊C4C22×C312yes—
66#870—21no—
67#870—21no—
68#870—21no—
69#870—21no—
70C3×C4⋊C8—22no—
71C3×C4⋊C8—21no—
72C3×C4⋊C8—21no—
73C3×C4⋊C8—61no—
74C3×C22⋊C8—22no—
75C3×C22⋊C8—32no—
76C3×C22⋊C8C2×D312yes—
77C3×C22⋊C8C22×C312yes—
78C3×#97—61no—
79C3×C4×C8—22no—
80C3×C4×C8—21no—
81C3×C4×C8—21no—
82#830C22×C312yes—
83C4⋊(C3⋊C8)—21no—
84#803—21no—
85C23×C32C22×C411yescharacteristic
86C2×C32×C4—22no—
87C2×C32×C4—22no—
88C2×C32×C4—41no—
89C2×C32×C4C22⋊C411yescharacteristic
90C2×C32×C4C22⋊C411yescharacteristic
91C2×C32×C4C22⋊C411yescharacteristic
92C2×C32×C4C22⋊C411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C3×Dic3—22no—
96C2×C3×Dic3—22no—
97C2×C3×Dic3—24no—
98C2×C3×Dic3—42no—
99C32×C8—42no—
100C3×C3⋊C8—42no—
101C2×#125—31no—
102#432—31no—
103#431C3×D311yescharacteristic
104#324—34no—
105C22×C3×C4—21no—
106C22×C3×C4—21no—
107C22×C3×C4—21no—
108C22×C3×C4—32no—
109C22×C3×C4—32no—
110C22×C3×C4C4×D311yescharacteristic
111C22×C3×C4C4×D311yescharacteristic
112C22×C3×C4C2×C3×C411yescharacteristic
113C22×C3×C4C2×C3×C411yescharacteristic
114C22×C3×C4C22×D311yescharacteristic
115C22×C3×C4C23×C311yescharacteristic
116C22×Dic3C2×C3×C412yes—
117C22×Dic3C2×C3×C412yes—
118C2×C3×C8—24no—
119C2×C3×C8—22no—
120C2×C3×C8—22no—
121C2×C3×C8—62no—
122C3×C4⋊C4—62no—
123C3×C4⋊C4—62no—
124C3×C4⋊C4—61no—
125C3×C4⋊C4—61no—
126C3×C4⋊C4—61no—
127C3×C4⋊C4—61no—
128C3×C4⋊C4—62no—
129C3×C4⋊C4—62no—
130C3×C42—21no—
131C3×C42—21no—
132C3×C42—21no—
133C3×C42—21no—
134C3×C42D1211yescharacteristic
135C3×C42D1211yescharacteristic
136C3×C42#6711yescharacteristic
137C3×C42#6711yescharacteristic
138C3×C42C3×D411yescharacteristic
139C3×C42C3×D411yescharacteristic
140C3×C42C3×D411yescharacteristic
141C3×C42C3×D411yescharacteristic
142C4⋊Dic3—21no—
143C4⋊Dic3—21no—
144C4⋊Dic3—21no—
145C4⋊Dic3—21no—
146Dic3⋊C4—22no—
147Dic3⋊C4—22no—
148Dic3⋊C4—22no—
149Dic3⋊C4—22no—
150C2×C3⋊C8—22no—
151C22×C32—21no—
152C22×C32—21no—
153C22×C32C2×C22⋊C411yescharacteristic
154C22×C32#13112yes—
155C32×C4—21no—
156C32×C4—21no—
157C32×C4—21no—
158C32×C4—21no—
159C32×C4—21no—
160C32×C4#10112yes—
161C3×Dic3—42no—
162C3×Dic3—42no—
163#125—61no—
164#125—61no—
165#125—61no—
166#125—61no—
167C2×C4⋊C4—32no—
168C2×C4⋊C4—31no—
169C2×C4⋊C4—31no—
170C2×C4⋊C4—32no—
171C2×C42C2×C3×D311yescharacteristic
172C4⋊C8—21no—
173C4⋊C8—61no—
174C22⋊C8—32no—
175C22⋊C8C2×C3×D312yes—
176#97—61no—
177C4×C8—21no—
178C23×C3—21no—
179C23×C3C2×C4×D311yescharacteristic
180C23×C3C22×C3×C411yescharacteristic
181C2×C3×C4—24no—
182C2×C3×C4—22no—
183C2×C3×C4—22no—
184C2×C3×C4—22no—
185C2×C3×C4—22no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—42no—
193C2×C3×C4—41no—
194C2×C3×C4—41no—
195C2×C3×C4—42no—
196C2×C3×C4—64no—
197C2×C3×C4—62no—
198C2×C3×C4—62no—
199C2×C3×C4—122no—
200C2×C3×C4(C2×D3)⋊C411yescharacteristic
201C2×C3×C4(C2×D3)⋊C411yescharacteristic
202C2×C3×C4(C2×D3)⋊C411yescharacteristic
203C2×C3×C4(C2×D3)⋊C411yescharacteristic
204C2×C3×C4C3×C22⋊C411yescharacteristic
205C2×C3×C4C3×C22⋊C411yescharacteristic
206C2×C3×C4C3×C22⋊C411yescharacteristic
207C2×C3×C4C3×C22⋊C411yescharacteristic
208C2×C3×C4C2×D1211yescharacteristic
209C2×C3×C4C2×#6711yescharacteristic
210C2×C3×C4C2×C3×D411yescharacteristic
211C2×C3×C4C2×C3×D411yescharacteristic
212C2×Dic3—22no—
213C2×Dic3—22no—
214C2×Dic3—24no—
215C2×Dic3—42no—
216C3×C8—44no—
217C3×C8—42no—
218C3×C8—42no—
219C3×C8—122no—
220C3⋊C8—42no—
221C2×C32—22no—
222C2×C32#40811yescharacteristic
223C2×C32#41011yescharacteristic
224C2×C32C2×#10111yescharacteristic
225C22×C4—32no—
226C22×C4—32no—
227C22×C4C3×C4×D311yescharacteristic
228C22×C4C3×C4×D311yescharacteristic
229C22×C4C22×C3×D311yescharacteristic
230C2×C8—22no—
231C2×C8—62no—
232C4⋊C4—62no—
233C4⋊C4—62no—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4—61no—
237C4⋊C4—61no—
238C4⋊C4—62no—
239C4⋊C4—62no—
240C42C3×D1211yescharacteristic
241C42C3×D1211yescharacteristic
242C42C3×#6711yescharacteristic
243C42C3×#6711yescharacteristic
244C22×C3—21no—
245C22×C3—21no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—22no—
249C22×C3—21no—
250C22×C3—41no—
251C22×C3—41no—
252C22×C3#90112yes—
253C22×C3C2×(C2×D3)⋊C411yescharacteristic
254C22×C3C2×C3×C22⋊C411yescharacteristic
255C22×C3C3×#13112yes—
256C3×C4—22no—
257C3×C4—22no—
258C3×C4—22no—
259C3×C4—21no—
260C3×C4—21no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—21no—
268C3×C4—21no—
269C3×C4—22no—
270C3×C4—41no—
271C3×C4—41no—
272C3×C4—122no—
273C3×C4—122no—
274C3×C4#82412yes—
275C3×C4C3×#10112yes—
276Dic3—42no—
277Dic3—42no—
278C32#147011yescharacteristic, complemented, Sylow
279C23C2×C3×C4×D311yescharacteristic
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—41no—
283C2×C4—64no—
284C2×C4—62no—
285C2×C4—62no—
286C2×C4—122no—
287C2×C4C3×(C2×D3)⋊C411yescharacteristic
288C2×C4C3×(C2×D3)⋊C411yescharacteristic
289C2×C4C3×(C2×D3)⋊C411yescharacteristic
290C2×C4C3×(C2×D3)⋊C411yescharacteristic
291C2×C4C2×C3×D1211yescharacteristic
292C2×C4C2×C3×#6711yescharacteristic
293C8—42no—
294C8—122no—
295C2×C3—22no—
296C2×C3—22no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—42no—
301C2×C3#500611yescharacteristic
302C2×C3#511011yescharacteristic
303C2×C3C2×#82411yescharacteristic
304C2×C3C3×#40811yescharacteristic
305C2×C3C3×#41011yescharacteristic
306C2×C3C2×C3×#10111yescharacteristic
307C22—21no—
308C22—21no—
309C22C3×#90112yes—
310C22C2×C3×(C2×D3)⋊C411yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—122no—
317C4—122no—
318C4C3×#82412yes—
319C3—21no—
320C3#7078711yescharacteristic, direct product factor
321C3C3×#147011yescharacteristic, complemented
322C2—22no—
323C2C3×#500611yescharacteristic
324C2C3×#511011yescharacteristic
325C2C2×C3×#82411yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#431C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22×C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#431D3
hypocenterC3C3×#1470
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#431

Complements

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

NH ≅ G/Ntype
6. #70787C3direct (N × H)
278. C32#1470semidirect
320. C3#70787direct (N × H)
321. C3C3×#1470semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8702
C32×#4312
C3×#49262
C3×#44692
C3×#14703
#707873