Finite Group Databasebeta

← C3×#82492 #11808766

Subgroups — C3×#82492 #11808766

Order 1152.

1285 conjugacy classes of subgroups.

The subgroup lattice has 433 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×Q8C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic
3C3×#5231C212yesmaximal, complemented
4C3×#4992C212yesmaximal, complemented
5C3×#4991C212yesmaximal
6C3×#4986C212yesmaximal, complemented
7C3×C4×(C2×D3)⋊C4C214yesmaximal, complemented
8C3×#4932C211yesmaximal, characteristic, complemented
9C3×#2398—31nomaximal
10#82492C311yesmaximal, characteristic, direct product factor
11C22×C32×Q8C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3C2212yes—
14C32×C4×Q8—24no—
15C2×C32×C4⋊C4C2212yes—
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C42C2212yes—
18C2×C32×C42C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2214yes—
20C2×C3×(C2×D3)⋊C4C2214yes—
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2212yes—
24C3×C4×D12—24no—
25C3×C3⋊#95C2212yes—
26C3×C3⋊#95C2212yes—
27C3×C3⋊#95C2214yes—
28C3×C3⋊#95C2214yes—
29C2×C3×C4×Q8—21no—
30C2×C3×C4×Q8D311yescharacteristic, complemented
31C2×C3×C4×Q8C2×C311yescharacteristic, complemented
32C2×C3×C4×D4—31no—
33C2×C4×D12C2×C311yescharacteristic
34C3×#400—32no—
35C3×#397—32no—
36C3×#394—32no—
37C3×#393—32no—
38C3×C4×C22⋊C4—34no—
39C3×#376—31no—
40#5231C2×C312yescomplemented
41#4992C2×C312yescomplemented
42#4991C2×C312yes—
43#4986C2×C312yescomplemented
44C4×(C2×D3)⋊C4C2×C314yescomplemented
45#4932C2×C311yescharacteristic, complemented
46C23×C3×D3C2312yes—
47C2×C32×Q8—22no—
48C2×C32×Q8—24no—
49C22×C32×C4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3×Dic3C2314yes—
55C22×C3×Dic3C2312yes—
56C2×C3×D12—24no—
57C2×C3×D12—22no—
58C2×C3×C4×D3—24no—
59C2×C3×C4×D3—28no—
60C32×C4⋊C4—24no—
61C32×C4⋊C4—22no—
62C32×C42—24no—
63C32×C42D414yes—
64C3×(C2×D3)⋊C4—28no—
65C3×(C2×D3)⋊C4—24no—
66C3×(C2×D3)⋊C4—28no—
67C3×C4⋊Dic3—22no—
68C3×C4×Dic3—24no—
69#2398—31noSylow
70C22×C3×Q8—21no—
71C22×C3×Q8C2×D311yescharacteristic
72C22×C3×Q8C22×C311yescharacteristic
73C22×C3×D4—31no—
74C23×C3×C4—32no—
75C22×D12C22×C311yescharacteristic
76C22×C4×D3C22×C312yes—
77C3×C4×Q8—28no—
78C3×C4×Q8—24no—
79C3×C4×Q8—24no—
80C3×C4×D4—64no—
81C2×C3×C4⋊C4—22no—
82C2×C3×C4⋊C4—21no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4C2×D312yes—
85C2×C3×C4⋊C4C2×D311yescharacteristic
86C2×C3×C4⋊C4C22×C312yes—
87C2×C3×C4⋊C4C22×C311yescharacteristic
88C2×C3×C22⋊C4—34no—
89C2×C3×C22⋊C4—34no—
90C2×C3×C22⋊C4—32no—
91C2×C3×C42—22no—
92C2×C3×C42—21no—
93C2×C3×C42—32no—
94C2×C3×C42C2×D312yes—
95C2×C3×C42C2×D311yescharacteristic
96C2×C3×C42C22×C312yes—
97C2×C3×C42C22×C311yescharacteristic
98C2×(C2×D3)⋊C4C22×C314yes—
99C2×(C2×D3)⋊C4C22×C314yes—
100C2×(C2×D3)⋊C4C22×C312yes—
101C2×C4⋊Dic3C22×C311yescharacteristic
102C2×C4×Dic3C22×C312yes—
103C4×D12—24no—
104C3×#95—32no—
105C3×#95—32no—
106C3×#95—34no—
107C3×#95—34no—
108C3⋊#95C22×C312yes—
109C3⋊#95C22×C312yes—
110C3⋊#95C22×C314yes—
111C3⋊#95C22×C314yes—
112C23×C32C2411yescharacteristic
113C22×C3×D3—22no—
114C22×C3×D3—24no—
115C22×C3×D3—24no—
116C22×C3×D3—22no—
117C22×C3×D3#4114yes—
118C32×Q8—28no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4—24no—
125C2×C32×C4C2×D412yes—
126C2×C32×C4C2×D412yes—
127C2×C32×C4C2×D412yes—
128C2×C32×C4#4114yes—
129C2×C32×C4#4114yes—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—24no—
132C2×C3×Dic3—24no—
133C2×C3×Dic3—24no—
134C2×C3×Dic3—24no—
135C3×D12—28no—
136C3×C4×D3—48no—
137C2×C4×Q8C3×D311yescharacteristic, complemented
138C2×C4×D4—31no—
139#400—32no—
140#397—32no—
141#394—32no—
142#393—32no—
143C4×C22⋊C4—34no—
144#376—31no—
145C24×C3—32no—
146C23×D3C23×C312yes—
147C2×C3×Q8—24no—
148C2×C3×Q8—28no—
149C2×C3×Q8—24no—
150C2×C3×Q8—22no—
151C2×C3×Q8—22no—
152C2×C3×Q8—24no—
153C2×C3×D4—64no—
154C2×C3×D4—62no—
155C22×C3×C4—21no—
156C22×C3×C4—22no—
157C22×C3×C4—21no—
158C22×C3×C4—22no—
159C22×C3×C4—21no—
160C22×C3×C4—34no—
161C22×C3×C4—32no—
162C22×C3×C4—68no—
163C22×C3×C4—64no—
164C22×C3×C4C22×D312yes—
165C22×C3×C4C22×D312yes—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C23×C312yes—
170C22×C3×C4C23×C311yescharacteristic
171C22×C3×C4C23×C311yescharacteristic
172C22×C3×C4C23×C312yes—
173C22×C3×C4C23×C311yescharacteristic
174C22×Dic3C23×C314yes—
175C22×Dic3C23×C312yes—
176C2×D12—24no—
177C2×D12—22no—
178C2×C4×D3—24no—
179C2×C4×D3—28no—
180C3×C4⋊C4—28no—
181C3×C4⋊C4—24no—
182C3×C4⋊C4—24no—
183C3×C4⋊C4—22no—
184C3×C4⋊C4—24no—
185C3×C4⋊C4—22no—
186C3×C4⋊C4—62no—
187C3×C22⋊C4—68no—
188C3×C22⋊C4—68no—
189C3×C22⋊C4—64no—
190C3×C42—28no—
191C3×C42—24no—
192C3×C42—24no—
193C3×C42—24no—
194C3×C42—64no—
195C3×C42#6714yes—
196C3×C42C3×D414yes—
197(C2×D3)⋊C4—28no—
198(C2×D3)⋊C4—24no—
199(C2×D3)⋊C4—28no—
200C4⋊Dic3—22no—
201C4×Dic3—24no—
202C22×C32C22×D411yescharacteristic
203C22×C32C2×#4112yes—
204C22×C32C2×#4112yes—
205C22×C32C2×#4112yes—
206C2×C3×D3—24no—
207C2×C3×D3—28no—
208C2×C3×D3—42no—
209C2×C3×D3—42no—
210C2×C3×D3—44no—
211C32×C4—22no—
212C32×C4—24no—
213C32×C4—22no—
214C32×C4—42no—
215C32×C4#12414yes—
216C3×Dic3—42no—
217C3×Dic3—44no—
218C22×Q8C2×C3×D311yescharacteristic
219C22×D4—31no—
220C23×C4—32no—
221C4×Q8—24no—
222C4×D4—64no—
223C2×C4⋊C4—31no—
224C2×C4⋊C4C2×C3×D312yes—
225C2×C4⋊C4C2×C3×D311yescharacteristic
226C2×C22⋊C4—32no—
227C2×C22⋊C4—34no—
228C2×C22⋊C4—34no—
229C2×C42—32no—
230C2×C42C2×C3×D312yes—
231C2×C42C2×C3×D311yescharacteristic
232#95—32no—
233#95—32no—
234#95—34no—
235#95—34no—
236C23×C3—21no—
237C23×C3—34no—
238C23×C3—64no—
239C23×C3—64no—
240C23×C3—62no—
241C23×C3—62no—
242C23×C3C23×D311yescharacteristic
243C23×C3C24×C311yescharacteristic
244C22×D3—22no—
245C22×D3—24no—
246C22×D3—24no—
247C22×D3—22no—
248C22×D3C3×#4114yes—
249C3×Q8—216no—
250C3×Q8—28no—
251C3×Q8—28no—
252C3×D4—68no—
253C2×C3×C4—24no—
254C2×C3×C4—24no—
255C2×C3×C4—24no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—24no—
265C2×C3×C4—24no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—24no—
269C2×C3×C4—24no—
270C2×C3×C4—24no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—42no—
275C2×C3×C4—44no—
276C2×C3×C4—64no—
277C2×C3×C4—64no—
278C2×C3×C4—64no—
279C2×C3×C4—64no—
280C2×C3×C4—62no—
281C2×C3×C4—128no—
282C2×C3×C4#23514yes—
283C2×C3×C4#23914yes—
284C2×C3×C4C2×#6712yes—
285C2×C3×C4C2×#6712yes—
286C2×C3×C4C2×#6712yes—
287C2×C3×C4C2×C3×D412yes—
288C2×C3×C4C2×C3×D412yes—
289C2×C3×C4C2×C3×D412yes—
290C2×C3×C4C3×#4114yes—
291C2×C3×C4C3×#4114yes—
292C2×Dic3—22no—
293C2×Dic3—24no—
294C2×Dic3—24no—
295C2×Dic3—24no—
296C2×Dic3—24no—
297D12—28no—
298C4×D3—48no—
299C2×C32#52511yescharacteristic
300C2×C32#52511yescharacteristic
301C2×C32C2×#12411yescharacteristic
302C2×C32#52914yes—
303C3×D3—44no—
304C24—32no—
305C2×Q8—24no—
306C2×Q8—22no—
307C2×D4—64no—
308C2×D4—62no—
309C22×C4—34no—
310C22×C4—32no—
311C22×C4—68no—
312C22×C4—64no—
313C22×C4C22×C3×D312yes—
314C22×C4C22×C3×D312yes—
315C22×C4C22×C3×D311yescharacteristic
316C22×C4C22×C3×D311yescharacteristic
317C22×C4C22×C3×D311yescharacteristic
318C4⋊C4—24no—
319C4⋊C4—22no—
320C4⋊C4—62no—
321C22⋊C4—68no—
322C22⋊C4—68no—
323C22⋊C4—64no—
324C42—24no—
325C42—64no—
326C42C3×#6714yes—
327C22×C3—22no—
328C22×C3—22no—
329C22×C3—22no—
330C22×C3—21no—
331C22×C3—64no—
332C22×C3—68no—
333C22×C3—122no—
334C22×C3—122no—
335C22×C3—124no—
336C22×C3C2×#23512yes—
337C22×C3C2×#23912yes—
338C22×C3D3×#4112yes—
339C22×C3C22×#6711yescharacteristic
340C22×C3C22×C3×D411yescharacteristic
341C22×C3C2×C3×#4112yes—
342C22×C3C2×C3×#4112yes—
343C22×C3C2×C3×#4112yes—
344C2×D3—24no—
345C2×D3—28no—
346C2×D3—42no—
347C2×D3—42no—
348C2×D3—44no—
349C3×C4—28no—
350C3×C4—24no—
351C3×C4—24no—
352C3×C4—22no—
353C3×C4—22no—
354C3×C4—22no—
355C3×C4—22no—
356C3×C4—24no—
357C3×C4—24no—
358C3×C4—42no—
359C3×C4—44no—
360C3×C4—42no—
361C3×C4—42no—
362C3×C4—122no—
363C3×C4—124no—
364C3×C4#94714yes—
365C3×C4C3×#12414yes—
366Dic3—42no—
367Dic3—44no—
368C32#239811yescharacteristic, complemented, Sylow
369C23—34no—
370C23—64no—
371C23—64no—
372C23—62no—
373C23—62no—
374C23C23×C3×D311yescharacteristic
375Q8—28no—
376D4—68no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—24no—
382C2×C4—22no—
383C2×C4—64no—
384C2×C4—64no—
385C2×C4—64no—
386C2×C4—64no—
387C2×C4—62no—
388C2×C4—128no—
389C2×C4C3×#23514yes—
390C2×C4C3×#23914yes—
391C2×C4C2×C3×#6712yes—
392C2×C4C2×C3×#6712yes—
393C2×C4C2×C3×#6712yes—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—24no—
398C2×C3—124no—
399C2×C3#558014yes—
400C2×C3#579111yescharacteristic
401C2×C3C2×#94711yescharacteristic
402C2×C3#582811yescharacteristic
403C2×C3C3×#52511yescharacteristic
404C2×C3C3×#52511yescharacteristic
405C2×C3C2×C3×#12411yescharacteristic
406C2×C3C3×#52914yes—
407D3—44no—
408C22—64no—
409C22—68no—
410C22—122no—
411C22—122no—
412C22—124no—
413C22C2×C3×#23512yes—
414C22C2×C3×#23912yes—
415C22C3×D3×#4112yes—
416C22C22×C3×#6711yescharacteristic
417C4—24no—
418C4—22no—
419C4—22no—
420C4—42no—
421C4—122no—
422C4—124no—
423C4C3×#94714yes—
424C3—21no—
425C3#8249211yescharacteristic, direct product factor
426C3C3×#239811yescharacteristic, complemented
427C2—124no—
428C2C3×#558014yes—
429C2C3×#579111yescharacteristic
430C2C2×C3×#94711yescharacteristic
431C2C3×#582811yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×C4×Q8C2
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C3×C4×Q8D3
hypocenterC3C3×#2398
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×Q8C2semidirect
3. C3×#5231C2semidirect
4. C3×#4992C2semidirect
6. C3×#4986C2semidirect
7. C3×C4×(C2×D3)⋊C4C2semidirect
8. C3×#4932C2semidirect
10. #82492C3direct (N × H)
30. C2×C3×C4×Q8D3semidirect
31. C2×C3×C4×Q8C2×C3semidirect
40. #5231C2×C3semidirect
41. #4992C2×C3semidirect
43. #4986C2×C3semidirect
44. C4×(C2×D3)⋊C4C2×C3semidirect
45. #4932C2×C3semidirect
137. C2×C4×Q8C3×D3semidirect
368. C32#2398semidirect
425. C3#82492direct (N × H)
426. C3C3×#2398semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×Q82
C2×C3×C4×D122
C3×#52312
C3×#49922
C3×#49912
C3×#49862
C3×C4×(C2×D3)⋊C42
C3×#49322
C3×#23983
#824923