Finite Group Databasebeta

← C3×#70836 #11775175

Subgroups — C3×#70836 #11775175

Order 1152.

511 conjugacy classes of subgroups.

The subgroup lattice has 343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5470C211yesmaximal, characteristic
2C32×#432C211yesmaximal, characteristic
3C3×#4932C211yesmaximal, characteristic
4C3×#4467C214yesmaximal
5C3×#1506—31nomaximal
6#70836C311yesmaximal, characteristic, direct product factor
7C2×C32×C42C2211yescharacteristic
8C3×#926—21no—
9C3×#924—21no—
10C3×#924C2212yes—
11C2×C3×C4×Dic3—21no—
12C3×#870—21no—
13C3×#869C411yescharacteristic, complemented
14C3×#869C411yescharacteristic, complemented
15C3×C4×Dic6—21no—
16C3×C4×Dic6C412yescomplemented
17C32×C4⋊C8—21no—
18C32×C22⋊C8C2212yes—
19C32×#97—21no—
20C3×C3⋊#95—21no—
21C3×C3⋊#95C2212yes—
22C3×#533—31no—
23#5470C2×C311yescharacteristic
24C3×#432—21no—
25C3×#432D311yescharacteristic
26C3×#432C2×C311yescharacteristic
27C3×#376—31no—
28#4932C2×C311yescharacteristic
29C3×#328—34no—
30#4467C2×C314yes—
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C22×C3×Dic3—22no—
35C2×C3×Dic6—21no—
36C2×C3×Dic6C2×C412yes—
37C2×C32×C8—22no—
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—24no—
50C3×C4×Dic3—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—21no—
61C2×C3×C42—61no—
62C2×C3×C42C2×D311yescharacteristic
63C2×C3×C42C22×C311yescharacteristic
64#926—21no—
65#924—21no—
66#924C22×C312yes—
67C2×C4×Dic3—21no—
68#870—21no—
69#869C3×C411yescharacteristic, complemented
70#869C3×C411yescharacteristic, complemented
71C4×Dic6—21no—
72C4×Dic6C3×C412yescomplemented
73C3×C4⋊C8—22no—
74C3×C4⋊C8—21no—
75C3×C4⋊C8—21no—
76C3×C22⋊C8—22no—
77C3×C22⋊C8C2×D312yes—
78C3×C22⋊C8C22×C312yes—
79C3×#97—22no—
80C3×#97—21no—
81C3×#97—21no—
82C3×#95—32no—
83C3×#95—61no—
84C3⋊#95—21no—
85C3⋊#95C22×C312yes—
86C23×C32C2×D411yescharacteristic
87C2×C32×C4—22no—
88C2×C32×C4—22no—
89C2×C32×C4—41no—
90C2×C32×C4C22⋊C411yescharacteristic
91C2×C32×C4C22⋊C411yescharacteristic
92C2×C32×C4C22⋊C411yescharacteristic
93C2×C32×C4C22⋊C411yescharacteristic
94C2×C32×C4C22×C411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C3×Dic3—24no—
97C2×C3×Dic3—22no—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—42no—
100C2×C3×Dic3—42no—
101C3×Dic6—42no—
102C3×Dic6—42no—
103C32×C8—42no—
104#533—31no—
105#432C3×D311yescharacteristic
106#376—31no—
107#328—34no—
108C2×C3×Q8—32no—
109C2×C3×Q8—61no—
110C22×C3×C4—21no—
111C22×C3×C4—21no—
112C22×C3×C4—21no—
113C22×C3×C4—62no—
114C22×C3×C4D1211yescharacteristic
115C22×C3×C4D1211yescharacteristic
116C22×C3×C4C3×D411yescharacteristic
117C22×C3×C4C3×D411yescharacteristic
118C22×C3×C4C22×D311yescharacteristic
119C22×C3×C4C23×C311yescharacteristic
120C22×Dic3—22no—
121C2×Dic6—21no—
122C2×Dic6C2×C3×C412yes—
123C2×C3×C8—24no—
124C2×C3×C8—22no—
125C2×C3×C8—22no—
126C3×C4⋊C4—32no—
127C3×C4⋊C4—62no—
128C3×C4⋊C4—61no—
129C3×C4⋊C4—61no—
130C3×C4⋊C4—61no—
131C3×C4⋊C4—62no—
132C3×C22⋊C4—62no—
133C3×C42—21no—
134C3×C42—21no—
135C3×C42—21no—
136C3×C42—21no—
137C3×C42—64no—
138C3×C42—62no—
139C3×C42C4×D311yescharacteristic
140C3×C42C4×D311yescharacteristic
141C3×C42#6711yescharacteristic
142C3×C42#6711yescharacteristic
143C3×C42C2×C3×C411yescharacteristic
144C3×C42C2×C3×C411yescharacteristic
145C3×C42C3×D411yescharacteristic
146C3×C42C3×D411yescharacteristic
147#217—22no—
148C4⋊Dic3—21no—
149C4⋊Dic3—21no—
150C4⋊Dic3—21no—
151C4⋊Dic3C2×C3×C412yes—
152Dic3⋊C4—22no—
153Dic3⋊C4—22no—
154C4×Dic3—24no—
155C4×Dic3—22no—
156C22×C32—21no—
157C22×C32—21no—
158C22×C32C2×C22⋊C411yescharacteristic
159C22×C32#13712yes—
160C32×C4—21no—
161C32×C4—21no—
162C32×C4—21no—
163C32×C4—21no—
164C32×C4—21no—
165C32×C4#10412yes—
166C3×Dic3—44no—
167C3×Dic3—42no—
168C3×Dic3—42no—
169C4⋊Q8—31no—
170C4⋊Q8—31no—
171#125—61no—
172C22⋊Q8—32no—
173C22⋊Q8—61no—
174C4×Q8—32no—
175C4×Q8—61no—
176#117—61no—
177C2×C42—61no—
178C2×C42C2×C3×D311yescharacteristic
179C4⋊C8—21no—
180C22⋊C8C2×C3×D312yes—
181#97—21no—
182#95—32no—
183#95—61no—
184C23×C3—21no—
185C23×C3C2×D1211yescharacteristic
186C23×C3C2×C3×D411yescharacteristic
187C3×Q8—122no—
188C3×Q8—122no—
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—22no—
192C2×C3×C4—22no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—42no—
200C2×C3×C4—42no—
201C2×C3×C4—41no—
202C2×C3×C4—41no—
203C2×C3×C4—42no—
204C2×C3×C4—64no—
205C2×C3×C4—62no—
206C2×C3×C4—62no—
207C2×C3×C4—122no—
208C2×C3×C4—122no—
209C2×C3×C4(C2×D3)⋊C411yescharacteristic
210C2×C3×C4(C2×D3)⋊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×C22⋊C411yescharacteristic
216C2×C3×C4C3×C22⋊C411yescharacteristic
217C2×C3×C4C2×C4×D311yescharacteristic
218C2×C3×C4C2×#6711yescharacteristic
219C2×C3×C4C22×C3×C411yescharacteristic
220C2×C3×C4C2×C3×D411yescharacteristic
221C2×Dic3—24no—
222C2×Dic3—22no—
223C2×Dic3—22no—
224C2×Dic3—42no—
225C2×Dic3—42no—
226Dic6—42no—
227Dic6—42no—
228C3×C8—44no—
229C3×C8—42no—
230C3×C8—42no—
231C2×C32—22no—
232C2×C32#41011yescharacteristic
233C2×C32#41911yescharacteristic
234C2×C32C2×#10411yescharacteristic
235C2×Q8—32no—
236C2×Q8—61no—
237C22×C4—62no—
238C22×C4C3×D1211yescharacteristic
239C22×C4C3×D1211yescharacteristic
240C22×C4C22×C3×D311yescharacteristic
241C2×C8—22no—
242C4⋊C4—32no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4—62no—
246C4⋊C4—61no—
247C4⋊C4—62no—
248C22⋊C4—62no—
249C42—64no—
250C42—62no—
251C42C3×C4×D311yescharacteristic
252C42C3×C4×D311yescharacteristic
253C42C3×#6711yescharacteristic
254C42C3×#6711yescharacteristic
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—22no—
260C22×C3—21no—
261C22×C3—41no—
262C22×C3—41no—
263C22×C3#90912yes—
264C22×C3C2×(C2×D3)⋊C411yescharacteristic
265C22×C3C2×C3×C22⋊C411yescharacteristic
266C22×C3C3×#13712yes—
267C3×C4—22no—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—22no—
279C3×C4—41no—
280C3×C4—41no—
281C3×C4—41no—
282C3×C4—41no—
283C3×C4—124no—
284C3×C4—122no—
285C3×C4—122no—
286C3×C4#82512yes—
287C3×C4C3×#10412yes—
288Dic3—44no—
289Dic3—42no—
290Dic3—42no—
291C32#150611yescharacteristic, complemented, Sylow
292C23C2×C3×D1211yescharacteristic
293Q8—122no—
294Q8—122no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—41no—
298C2×C4—64no—
299C2×C4—62no—
300C2×C4—62no—
301C2×C4—122no—
302C2×C4—122no—
303C2×C4C3×(C2×D3)⋊C411yescharacteristic
304C2×C4C3×(C2×D3)⋊C411yescharacteristic
305C2×C4C3×(C2×D3)⋊C411yescharacteristic
306C2×C4C3×(C2×D3)⋊C411yescharacteristic
307C2×C4C2×C3×C4×D311yescharacteristic
308C2×C4C2×C3×#6711yescharacteristic
309C8—42no—
310C2×C3—22no—
311C2×C3—22no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—42no—
316C2×C3#500611yescharacteristic
317C2×C3#512011yescharacteristic
318C2×C3C2×#82511yescharacteristic
319C2×C3C3×#41011yescharacteristic
320C2×C3C3×#41911yescharacteristic
321C2×C3C2×C3×#10411yescharacteristic
322C22—21no—
323C22—21no—
324C22C3×#90912yes—
325C22C2×C3×(C2×D3)⋊C411yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—124no—
332C4—122no—
333C4—122no—
334C4C3×#82512yes—
335C3—21no—
336C3#7083611yescharacteristic, direct product factor
337C3C3×#150611yescharacteristic, complemented
338C2—22no—
339C2C3×#500611yescharacteristic
340C2C3×#512011yescharacteristic
341C2C2×C3×#82511yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#432C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C2×D4
cosocleC22×C3×C4C23×C3
hypercenterC3×#432D3
hypocenterC3C3×#1506
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#432

Complements

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

NH ≅ G/Ntype
6. #70836C3direct (N × H)
13. C3×#869C4semidirect
14. C3×#869C4semidirect
16. C3×C4×Dic6C4semidirect
69. #869C3×C4semidirect
70. #869C3×C4semidirect
72. C4×Dic6C3×C4semidirect
291. C32#1506semidirect
336. C3#70836direct (N × H)
337. 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×#4322
C3×#49322
C3×#44672
C3×#15063
#708363