Finite Group Databasebeta

← C3×#81795 #11898356

Subgroups — C3×#81795 #11898356

Order 1152.

781 conjugacy classes of subgroups.

The subgroup lattice has 371 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5732C212yesmaximal, complemented
2C32×#494C211yesmaximal, characteristic, complemented
3C3×#5191C212yesmaximal
4C3×#5185C214yesmaximal, complemented
5C3×Dic3×Q16C212yesmaximal, complemented
6C3×#5083C212yesmaximal, complemented
7C3×C4×D24C211yesmaximal, characteristic
8C3×C8×Dic6C211yesmaximal, characteristic, complemented
9C3×#3393—31nomaximal
10#81795C311yesmaximal, characteristic, direct product factor
11C2×C32×Q16C2212yes—
12C2×C32×Q16C2212yes—
13C32×C4⋊Q8C2212yes—
14C3×#947C2214yes—
15C3×Q8×Dic3C2214yes—
16C2×C3×#215C2214yes—
17C2×C3×D24C2211yescharacteristic
18C3×#898—24no—
19C3×#897—22no—
20C3×#892—22no—
21C3×C4×D12C2212yes—
22C3×C4×Dic6C2211yescharacteristic
23C32×C4×C8C2211yescharacteristic
24C3×#835C2214yes—
25C3×#821C2212yes—
26C3×#818C2211yescharacteristic
27C3×Dic3⋊C8C2212yes—
28C3×C8×Dic3C2212yes—
29C3×C4⋊(C3⋊C8)C2211yescharacteristic
30C3×#556—32no—
31#5732C2×C312yescomplemented
32C3×#495—32no—
33C3×#494—21no—
34C3×#494D311yescharacteristic, complemented
35C3×#494C2×C311yescharacteristic, complemented
36C3×#464—34no—
37C3×#461—32no—
38C3×C8×Q8—31no—
39C3×C4×Q16—32no—
40C3×C4×D8—31no—
41#5191C2×C312yes—
42#5185C2×C314yescomplemented
43Dic3×Q16C2×C312yescomplemented
44#5083C2×C312yescomplemented
45C4×D24C2×C311yescharacteristic
46C8×Dic6C2×C311yescharacteristic, complemented
47C2×C32×Q8C2314yes—
48C2×C3×D12C2312yes—
49C2×C3×C4×D3—22no—
50C2×C3×Dic6D411yescharacteristic
51C32×Q16—24no—
52C32×Q16—42no—
53C2×C32×C8C2311yescharacteristic
54C2×C32×C8C2311yescharacteristic
55C32×C4⋊C4—22no—
56C32×C4⋊C4—22no—
57C32×C42C2311yescharacteristic
58C3×#215—44no—
59C3×(C2×D3)⋊C4—22no—
60C3×(C2×D3)⋊C4—24no—
61C3×(C2×D3)⋊C4—24no—
62C3×C4⋊Dic3—24no—
63C3×C4⋊Dic3D411yescharacteristic
64C3×C4⋊Dic3C2312yes—
65C3×Dic3⋊C4D412yes—
66C3×C4×Dic3—24no—
67C3×C4×Dic3C2312yes—
68C2×C3×C3⋊C8C2312yes—
69C3×D24—22no—
70#3393—31noSylow
71C2×C3×Q16—22no—
72C2×C3×Q16—22no—
73C2×C3×Q16C2×D312yes—
74C2×C3×Q16C2×D312yes—
75C2×C3×Q16C22×C312yes—
76C2×C3×Q16C22×C312yes—
77C2×C3×SD16—34no—
78C2×C3×D8—31no—
79C3×C4⋊Q8—22no—
80C3×C4⋊Q8C2×D312yes—
81C3×C4⋊Q8C22×C312yes—
82C3×#126—64no—
83C3×#124—34no—
84C3×C22⋊Q8—62no—
85C3×C4×Q8—31no—
86C3×C4×Q8—34no—
87C3×C4×D4—32no—
88C3×#117—62no—
89#947C22×C314yes—
90Q8×Dic3C22×C314yes—
91C2×#215C22×C314yes—
92C2×D24C22×C311yescharacteristic
93#898—24no—
94#897—22no—
95#892—22no—
96C4×D12C22×C312yes—
97C4×Dic6C22×C311yescharacteristic
98C3×#107—31no—
99C3×C4⋊C8—32no—
100C3×C4⋊C8—31no—
101C3×#103—34no—
102C3×#102—32no—
103C3×C4×C8—21no—
104C3×C4×C8—32no—
105C3×C4×C8C2×D311yescharacteristic
106C3×C4×C8C22×C311yescharacteristic
107#835C22×C314yes—
108#821C22×C312yes—
109#818C22×C311yescharacteristic
110Dic3⋊C8C22×C312yes—
111C8×Dic3C22×C312yes—
112C4⋊(C3⋊C8)C22×C311yescharacteristic
113C22×C3×D3—22no—
114C32×Q8—24no—
115C32×Q8—24no—
116C2×C32×C4—24no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2411yescharacteristic
120C2×C3×Dic3—22no—
121C2×C3×Dic3C2×D412yes—
122C2×C3×Dic3C2×D412yes—
123C3×D12—22no—
124C3×D12—22no—
125C3×C4×D3—44no—
126C3×Dic6—22no—
127C32×C8—21no—
128C32×C8#4112yes—
129C3×C3⋊C8—22no—
130#556—32no—
131#495—32no—
132#494C3×D311yescharacteristic, complemented
133#464—34no—
134#461—32no—
135C8×Q8—31no—
136C4×Q16—32no—
137C4×D8—31no—
138C2×C3×Q8—24no—
139C2×C3×Q8—31no—
140C2×C3×Q8C22×D314yes—
141C2×C3×Q8C23×C314yes—
142C2×C3×D4—32no—
143C22×C3×C4—62no—
144C2×D12C23×C312yes—
145C2×C4×D3—22no—
146C2×Dic6C3×D411yescharacteristic
147C3×Q16—24no—
148C3×Q16—24no—
149C3×Q16—44no—
150C3×Q16—42no—
151C3×Q16—42no—
152C3×Q16—44no—
153C3×SD16—124no—
154C3×D8—62no—
155C2×C3×C8—21no—
156C2×C3×C8—21no—
157C2×C3×C8—32no—
158C2×C3×C8C22×D311yescharacteristic
159C2×C3×C8C22×D311yescharacteristic
160C2×C3×C8C23×C311yescharacteristic
161C2×C3×C8C23×C311yescharacteristic
162C3×C4⋊C4—22no—
163C3×C4⋊C4—22no—
164C3×C4⋊C4—22no—
165C3×C4⋊C4—22no—
166C3×C4⋊C4—32no—
167C3×C4⋊C4—31no—
168C3×C4⋊C4—32no—
169C3×C4⋊C4—42no—
170C3×C4⋊C4—42no—
171C3×C4⋊C4—64no—
172C3×C22⋊C4—64no—
173C3×C22⋊C4—64no—
174C3×C22⋊C4—62no—
175C3×C42—21no—
176C3×C42—32no—
177C3×C42—64no—
178C3×C42C22×D311yescharacteristic
179C3×C42C23×C311yescharacteristic
180#215—44no—
181(C2×D3)⋊C4—22no—
182(C2×D3)⋊C4—24no—
183(C2×D3)⋊C4—24no—
184C4⋊Dic3—24no—
185C4⋊Dic3C3×D411yescharacteristic
186C4⋊Dic3C23×C312yes—
187Dic3⋊C4C3×D412yes—
188C4×Dic3—24no—
189C4×Dic3C23×C312yes—
190C2×C3⋊C8C23×C312yes—
191D24—22no—
192C22×C32C22×D411yescharacteristic
193C2×C3×D3—42no—
194C2×C3×D3—42no—
195C2×C3×D3—42no—
196C32×C4—21no—
197C32×C4—44no—
198C32×C4#13512yes—
199C32×C4C2×#4111yescharacteristic
200C32×C4H(5,𝔽2)11yescharacteristic
201C3×Dic3—22no—
202C3×Dic3—22no—
203C3×Dic3—42no—
204C2×Q16C2×C3×D312yes—
205C2×Q16C2×C3×D312yes—
206C2×SD16—34no—
207C2×D8—31no—
208C4⋊Q8C2×C3×D312yes—
209#126—64no—
210#124—34no—
211C22⋊Q8—62no—
212C4×Q8—31no—
213C4×Q8—34no—
214C4×D4—32no—
215#117—62no—
216#107—31no—
217C4⋊C8—32no—
218C4⋊C8—31no—
219#103—34no—
220#102—32no—
221C4×C8—32no—
222C4×C8C2×C3×D311yescharacteristic
223C23×C3—62no—
224C22×D3—22no—
225C3×Q8—24no—
226C3×Q8—24no—
227C3×Q8—24no—
228C3×Q8—24no—
229C3×Q8—44no—
230C3×Q8—44no—
231C3×Q8—62no—
232C3×D4—62no—
233C3×D4—62no—
234C2×C3×C4—24no—
235C2×C3×C4—24no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—32no—
240C2×C3×C4—32no—
241C2×C3×C4—44no—
242C2×C3×C4—62no—
243C2×C3×C4—124no—
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4C2×C3×D411yescharacteristic
247C2×C3×C4C2×C3×D411yescharacteristic
248C2×C3×C4C23×D311yescharacteristic
249C2×C3×C4C24×C311yescharacteristic
250C2×Dic3—22no—
251C2×Dic3C2×C3×D412yes—
252C2×Dic3C2×C3×D412yes—
253D12—22no—
254D12—22no—
255C4×D3—44no—
256Dic6—22no—
257C3×C8—22no—
258C3×C8—21no—
259C3×C8—21no—
260C3×C8—22no—
261C3×C8—62no—
262C3×C8#23712yes—
263C3×C8C3×#4112yes—
264C3⋊C8—22no—
265C2×C32#55011yescharacteristic
266C2×C32C2×#13511yescharacteristic
267C2×C32#57811yescharacteristic
268C3×D3—82no—
269C2×Q8—31no—
270C2×Q8C22×C3×D314yes—
271C2×D4—32no—
272C22×C4—62no—
273Q16—24no—
274Q16—42no—
275SD16—124no—
276D8—62no—
277C2×C8—32no—
278C2×C8C22×C3×D311yescharacteristic
279C2×C8C22×C3×D311yescharacteristic
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—31no—
283C4⋊C4—32no—
284C4⋊C4—32no—
285C4⋊C4—64no—
286C22⋊C4—64no—
287C22⋊C4—64no—
288C22⋊C4—62no—
289C42—32no—
290C42—64no—
291C42C22×C3×D311yescharacteristic
292C22×C3—21no—
293C22×C3—122no—
294C22×C3—122no—
295C22×C3—122no—
296C22×C3C2×D3×D411yescharacteristic
297C22×C3C22×C3×D411yescharacteristic
298C2×D3—42no—
299C2×D3—42no—
300C2×D3—42no—
301C3×C4—22no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—22no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—44no—
308C3×C4—44no—
309C3×C4—62no—
310C3×C4—62no—
311C3×C4—84no—
312C3×C4—122no—
313C3×C4#91912yes—
314C3×C4C3×#13512yes—
315C3×C4C2×#23711yescharacteristic
316C3×C4#100411yescharacteristic
317C3×C4C2×C3×#4111yescharacteristic
318C3×C4C3×H(5,𝔽2)11yescharacteristic
319Dic3—22no—
320Dic3—22no—
321Dic3—42no—
322C32#339311yescharacteristic, complemented, Sylow
323C23—62no—
324Q8—24no—
325Q8—24no—
326Q8—62no—
327D4—62no—
328D4—62no—
329C2×C4—24no—
330C2×C4—32no—
331C2×C4—32no—
332C2×C4—62no—
333C2×C4—124no—
334C2×C4C3×D3×D411yescharacteristic
335C2×C4C3×D3×D411yescharacteristic
336C2×C4C23×C3×D311yescharacteristic
337C8—21no—
338C8—62no—
339C8C3×#23712yes—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3—21no—
343C2×C3—242no—
344C2×C3#571811yescharacteristic
345C2×C3C2×#91911yescharacteristic
346C2×C3#576611yescharacteristic
347C2×C3C3×#55011yescharacteristic
348C2×C3C2×C3×#13511yescharacteristic
349C2×C3C3×#57811yescharacteristic
350D3—82no—
351C22—122no—
352C22—122no—
353C22—122no—
354C22C2×C3×D3×D411yescharacteristic
355C4—21no—
356C4—44no—
357C4—62no—
358C4—62no—
359C4—122no—
360C4C3×#91912yes—
361C4C2×C3×#23711yescharacteristic
362C4C3×#100411yescharacteristic
363C3—21no—
364C3#8179511yescharacteristic, direct product factor
365C3C3×#339311yescharacteristic, complemented
366C2—242no—
367C2C3×#571811yescharacteristic
368C2C2×C3×#91911yescharacteristic
369C2C3×#576611yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#494C2
socleC22×C32C22×D4
prime radicalC2×C3×D24C22
hypercenterC3×#494D3
hypocenterC3C3×#3393
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#494

Complements

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

NH ≅ G/Ntype
1. C3×#5732C2semidirect
2. C32×#494C2semidirect
4. C3×#5185C2semidirect
5. C3×Dic3×Q16C2semidirect
6. C3×#5083C2semidirect
8. C3×C8×Dic6C2semidirect
10. #81795C3direct (N × H)
31. #5732C2×C3semidirect
34. C3×#494D3semidirect
35. C3×#494C2×C3semidirect
42. #5185C2×C3semidirect
43. Dic3×Q16C2×C3semidirect
44. #5083C2×C3semidirect
46. C8×Dic6C2×C3semidirect
132. #494C3×D3semidirect
322. C32#3393semidirect
364. C3#81795direct (N × H)
365. C3C3×#3393semidirect

Maximal subgroups

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

subgroupindex
C3×#57322
C32×#4942
C3×#51912
C3×#51852
C3×Dic3×Q162
C3×#50832
C3×C4×D242
C3×C8×Dic62
C3×#33933
#817953