Finite Group Databasebeta

← C3×#82347 #11808740

Subgroups — C3×#82347 #11808740

Order 1152.

1893 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C214yesmaximal, complemented
3C2×C3×C4×D12C211yesmaximal, characteristic, complemented
4C3×#5223C212yesmaximal, complemented
5C3×#4993C212yesmaximal, complemented
6C3×#4960C212yesmaximal, complemented
7C3×#4949C212yesmaximal, complemented
8C3×#4932C211yesmaximal, characteristic, complemented
9C3×#2397—31nomaximal
10#82347C311yesmaximal, characteristic, direct product factor
11C22×C32×D4C2211yescharacteristic
12C23×C32×C4C2212yes—
13C22×C3×#67C2214yes—
14C22×C3×D12C2211yescharacteristic
15C22×C3×C4×D3C2212yes—
16C32×C4×D4—24no—
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C32×C22⋊C4C2212yes—
19C2×C32×C42C2211yescharacteristic
20C2×C3×#217C2214yes—
21C3×C4×#67—216no—
22C2×C3×(C2×D3)⋊C4C2214yes—
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2214yes—
26C2×C3×C4×Dic3C2212yes—
27C3×C4×D12—24no—
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2212yes—
30C2×C3×C4×D4—21no—
31C2×C3×C4×D4—34no—
32C2×C3×C4×D4—31no—
33C2×C3×C4×D4D311yescharacteristic, complemented
34C2×C3×C4×D4C2×C311yescharacteristic, complemented
35C2×C4×#67C2×C314yescomplemented
36C2×C4×D12C2×C311yescharacteristic, complemented
37C3×#399—32no—
38C3×#399—32no—
39C3×#392—32no—
40C3×#392—32no—
41C3×#376—31no—
42#5223C2×C312yescomplemented
43#4993C2×C312yescomplemented
44#4960C2×C312yescomplemented
45#4949C2×C312yescomplemented
46#4932C2×C311yescharacteristic, complemented
47C24×C32C2312yes—
48C23×C3×D3C2312yes—
49C2×C32×D4—24no—
50C2×C32×D4—22no—
51C22×C32×C4—24no—
52C22×C32×C4—28no—
53C22×C32×C4C2312yes—
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C2×C3×#67—28no—
58C2×C3×#67—28no—
59C2×C3×#67—28no—
60C22×C3×Dic3C2312yes—
61C22×C3×Dic3C2314yes—
62C2×C3×D12—24no—
63C2×C3×D12—22no—
64C2×C3×C4×D3—28no—
65C2×C3×C4×D3—24no—
66C32×C4⋊C4—22no—
67C32×C22⋊C4—24no—
68C32×C42D414yescomplemented
69C3×#217—28no—
70C3×(C2×D3)⋊C4—24no—
71C3×(C2×D3)⋊C4—28no—
72C3×C4⋊Dic3—22no—
73C3×Dic3⋊C4—28no—
74C3×C4×Dic3D418yescomplemented
75#2397—31noSylow
76C22×C3×D4—21no—
77C22×C3×D4—34no—
78C22×C3×D4—31no—
79C22×C3×D4C2×D311yescharacteristic
80C22×C3×D4C22×C311yescharacteristic
81C23×C3×C4—22no—
82C23×C3×C4—32no—
83C23×C3×C4C2×D312yes—
84C23×C3×C4C22×C312yes—
85C22×#67C22×C314yes—
86C22×D12C22×C311yescharacteristic
87C22×C4×D3C22×C312yes—
88C3×C4×D4—28no—
89C3×C4×D4—24no—
90C3×C4×D4—24no—
91C3×C4×D4—616no—
92C3×C4×D4—64no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4—34no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4C2×D311yescharacteristic
97C2×C3×C4⋊C4C22×C311yescharacteristic
98C2×C3×C22⋊C4—22no—
99C2×C3×C22⋊C4—34no—
100C2×C3×C22⋊C4—34no—
101C2×C3×C22⋊C4—32no—
102C2×C3×C22⋊C4C2×D312yes—
103C2×C3×C22⋊C4C22×C312yes—
104C2×C3×C42—21no—
105C2×C3×C42—32no—
106C2×C3×C42C2×D311yescharacteristic
107C2×C3×C42C22×C311yescharacteristic
108C2×#217C22×C314yes—
109C4×#67—216no—
110C2×(C2×D3)⋊C4C22×C314yes—
111C2×(C2×D3)⋊C4C22×C312yes—
112C2×C4⋊Dic3C22×C311yescharacteristic
113C2×Dic3⋊C4C22×C314yes—
114C2×C4×Dic3C22×C312yes—
115C4×D12—24no—
116C3×#95—32no—
117C3×#95—32no—
118C3⋊#95C22×C312yes—
119C3⋊#95C22×C312yes—
120C23×C32—22no—
121C23×C32—22no—
122C23×C32—24no—
123C23×C32—24no—
124C23×C32#4114yes—
125C23×C32C2411yescharacteristic
126C22×C3×D3—22no—
127C22×C3×D3—24no—
128C22×C3×D3—22no—
129C22×C3×D3—24no—
130C22×C3×D3#4114yes—
131C32×D4—28no—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4—22no—
135C2×C32×C4—24no—
136C2×C32×C4—48no—
137C2×C32×C4C2×D414yes—
138C2×C32×C4C2×D412yes—
139C2×C32×C4C2×D412yes—
140C2×C32×C4C2×D412yes—
141C3×#67—232no—
142C2×C3×Dic3—24no—
143C2×C3×Dic3—24no—
144C2×C3×Dic3—24no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3C2×D418yes—
147C3×D12—28no—
148C3×C4×D3—48no—
149C2×C4×D4—34no—
150C2×C4×D4—31no—
151C2×C4×D4C3×D311yescharacteristic, complemented
152#399—32no—
153#399—32no—
154#392—32no—
155#392—32no—
156#376—31no—
157C24×C3—22no—
158C24×C3—32no—
159C24×C3C22×D312yes—
160C24×C3C23×C312yes—
161C23×D3C23×C312yes—
162C2×C3×D4—24no—
163C2×C3×D4—28no—
164C2×C3×D4—24no—
165C2×C3×D4—24no—
166C2×C3×D4—22no—
167C2×C3×D4—22no—
168C2×C3×D4—64no—
169C2×C3×D4—68no—
170C2×C3×D4—68no—
171C2×C3×D4—68no—
172C2×C3×D4—62no—
173C22×C3×C4—28no—
174C22×C3×C4—28no—
175C22×C3×C4—24no—
176C22×C3×C4—28no—
177C22×C3×C4—24no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—22no—
182C22×C3×C4—34no—
183C22×C3×C4—32no—
184C22×C3×C4—48no—
185C22×C3×C4—68no—
186C22×C3×C4—64no—
187C22×C3×C4C22×D312yes—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C23×C312yes—
192C22×C3×C4C23×C311yescharacteristic
193C22×C3×C4C23×C311yescharacteristic
194C22×C3×C4C23×C311yescharacteristic
195C2×#67—28no—
196C2×#67—28no—
197C2×#67—28no—
198C22×Dic3C23×C312yes—
199C22×Dic3C23×C314yes—
200C2×D12—24no—
201C2×D12—22no—
202C2×C4×D3—24no—
203C2×C4×D3—28no—
204C3×C4⋊C4—24no—
205C3×C4⋊C4—22no—
206C3×C4⋊C4—22no—
207C3×C4⋊C4—68no—
208C3×C4⋊C4—62no—
209C3×C22⋊C4—28no—
210C3×C22⋊C4—24no—
211C3×C22⋊C4—24no—
212C3×C22⋊C4—68no—
213C3×C22⋊C4—68no—
214C3×C22⋊C4—64no—
215C3×C42—24no—
216C3×C42—38no—
217C3×C42#6714yescomplemented
218C3×C42C3×D414yescomplemented
219#217—28no—
220(C2×D3)⋊C4—24no—
221(C2×D3)⋊C4—28no—
222C4⋊Dic3—22no—
223Dic3⋊C4—28no—
224C4×Dic3C3×D418yescomplemented
225C22×C32—24no—
226C22×C32—28no—
227C22×C32—44no—
228C22×C32—42no—
229C22×C32—42no—
230C22×C32C22×D412yes—
231C22×C32C22×D411yescharacteristic
232C22×C32C2×#4112yes—
233C22×C32C2×#4112yes—
234C2×C3×D3—24no—
235C2×C3×D3—28no—
236C2×C3×D3—42no—
237C2×C3×D3—44no—
238C2×C3×D3—42no—
239C32×C4—22no—
240C32×C4—22no—
241C32×C4—42no—
242C32×C4#12714yes—
243C3×Dic3—28no—
244C3×Dic3—42no—
245C22×D4—34no—
246C22×D4—31no—
247C22×D4C2×C3×D311yescharacteristic
248C23×C4—32no—
249C23×C4C2×C3×D312yes—
250C4×D4—24no—
251C4×D4—616no—
252C4×D4—64no—
253C2×C4⋊C4—34no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4C2×C3×D311yescharacteristic
256C2×C22⋊C4—34no—
257C2×C22⋊C4—34no—
258C2×C22⋊C4—32no—
259C2×C22⋊C4C2×C3×D312yes—
260C2×C42—32no—
261C2×C42C2×C3×D311yescharacteristic
262#95—32no—
263#95—32no—
264C23×C3—24no—
265C23×C3—24no—
266C23×C3—22no—
267C23×C3—24no—
268C23×C3—24no—
269C23×C3—22no—
270C23×C3—24no—
271C23×C3—22no—
272C23×C3—24no—
273C23×C3—22no—
274C23×C3—21no—
275C23×C3—24no—
276C23×C3—34no—
277C23×C3—44no—
278C23×C3—44no—
279C23×C3—64no—
280C23×C3—64no—
281C23×C3—62no—
282C23×C3—62no—
283C23×C3#23514yes—
284C23×C3C3×#4114yes—
285C23×C3C23×D311yescharacteristic
286C23×C3C24×C311yescharacteristic
287C22×D3—22no—
288C22×D3—24no—
289C22×D3—22no—
290C22×D3—24no—
291C22×D3C3×#4114yes—
292C3×D4—216no—
293C3×D4—28no—
294C3×D4—28no—
295C3×D4—68no—
296C3×D4—632no—
297C2×C3×C4—24no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—24no—
303C2×C3×C4—24no—
304C2×C3×C4—22no—
305C2×C3×C4—24no—
306C2×C3×C4—22no—
307C2×C3×C4—24no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—38no—
312C2×C3×C4—42no—
313C2×C3×C4—44no—
314C2×C3×C4—416no—
315C2×C3×C4—48no—
316C2×C3×C4—48no—
317C2×C3×C4—64no—
318C2×C3×C4—64no—
319C2×C3×C4—64no—
320C2×C3×C4—62no—
321C2×C3×C4—128no—
322C2×C3×C4D3×D414yes—
323C2×C3×C4C2×#6712yes—
324C2×C3×C4C2×#6712yes—
325C2×C3×C4C2×#6712yes—
326C2×C3×C4C2×C3×D414yes—
327C2×C3×C4C2×C3×D412yes—
328C2×C3×C4C2×C3×D412yes—
329C2×C3×C4C2×C3×D412yes—
330#67—232no—
331C2×Dic3—24no—
332C2×Dic3—24no—
333C2×Dic3—24no—
334C2×Dic3—22no—
335C2×Dic3C2×C3×D418yes—
336D12—28no—
337C4×D3—48no—
338C2×C32—44no—
339C2×C32#52511yescharacteristic
340C2×C32#52514yes—
341C2×C32#52511yescharacteristic
342C2×C32C2×#12711yescharacteristic
343C3×D3—44no—
344C24—32no—
345C24C22×C3×D312yes—
346C2×D4—24no—
347C2×D4—22no—
348C2×D4—64no—
349C2×D4—68no—
350C2×D4—68no—
351C2×D4—68no—
352C2×D4—62no—
353C22×C4—28no—
354C22×C4—24no—
355C22×C4—34no—
356C22×C4—32no—
357C22×C4—68no—
358C22×C4—64no—
359C22×C4C22×C3×D312yes—
360C22×C4C22×C3×D311yescharacteristic
361C22×C4C22×C3×D311yescharacteristic
362C22×C4C22×C3×D311yescharacteristic
363C4⋊C4—22no—
364C4⋊C4—68no—
365C4⋊C4—62no—
366C22⋊C4—24no—
367C22⋊C4—68no—
368C22⋊C4—68no—
369C22⋊C4—64no—
370C42—38no—
371C42C3×#6714yescomplemented
372C22×C3—28no—
373C22×C3—24no—
374C22×C3—28no—
375C22×C3—28no—
376C22×C3—24no—
377C22×C3—22no—
378C22×C3—22no—
379C22×C3—22no—
380C22×C3—21no—
381C22×C3—48no—
382C22×C3—44no—
383C22×C3—48no—
384C22×C3—44no—
385C22×C3—44no—
386C22×C3—42no—
387C22×C3—42no—
388C22×C3—44no—
389C22×C3—42no—
390C22×C3—42no—
391C22×C3—68no—
392C22×C3—64no—
393C22×C3—122no—
394C22×C3—124no—
395C22×C3—122no—
396C22×C3C2×#23512yes—
397C22×C3C2×D3×D412yes—
398C22×C3D3×#4112yes—
399C22×C3C22×#6711yescharacteristic
400C22×C3C22×C3×D412yes—
401C22×C3C22×C3×D411yescharacteristic
402C22×C3C2×C3×#4112yes—
403C22×C3C2×C3×#4112yes—
404C2×D3—24no—
405C2×D3—28no—
406C2×D3—42no—
407C2×D3—44no—
408C2×D3—42no—
409C3×C4—24no—
410C3×C4—22no—
411C3×C4—22no—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—24no—
415C3×C4—42no—
416C3×C4—44no—
417C3×C4—42no—
418C3×C4—42no—
419C3×C4—68no—
420C3×C4—122no—
421C3×C4#94014yes—
422C3×C4C3×#12714yes—
423Dic3—28no—
424Dic3—42no—
425C32#239711yescharacteristic, complemented, Sylow
426C23—22no—
427C23—24no—
428C23—24no—
429C23—22no—
430C23—34no—
431C23—64no—
432C23—64no—
433C23—62no—
434C23—62no—
435C23C3×#23514yes—
436C23C23×C3×D311yescharacteristic
437D4—28no—
438D4—68no—
439D4—632no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—24no—
443C2×C4—22no—
444C2×C4—38no—
445C2×C4—48no—
446C2×C4—64no—
447C2×C4—64no—
448C2×C4—64no—
449C2×C4—62no—
450C2×C4—128no—
451C2×C4C3×D3×D414yes—
452C2×C4C2×C3×#6712yes—
453C2×C4C2×C3×#6712yes—
454C2×C4C2×C3×#6712yes—
455C2×C3—21no—
456C2×C3—24no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—48no—
460C2×C3—44no—
461C2×C3—44no—
462C2×C3—124no—
463C2×C3#554714yes—
464C2×C3#579111yescharacteristic
465C2×C3C2×#94011yescharacteristic
466C2×C3#582811yescharacteristic
467C2×C3C3×#52511yescharacteristic
468C2×C3C3×#52514yes—
469C2×C3C3×#52511yescharacteristic
470C2×C3C2×C3×#12711yescharacteristic
471D3—44no—
472C22—24no—
473C22—28no—
474C22—44no—
475C22—42no—
476C22—42no—
477C22—68no—
478C22—64no—
479C22—122no—
480C22—124no—
481C22—122no—
482C22C2×C3×#23512yes—
483C22C2×C3×D3×D412yes—
484C22C3×D3×#4112yes—
485C22C22×C3×#6711yescharacteristic
486C4—22no—
487C4—22no—
488C4—42no—
489C4—68no—
490C4—122no—
491C4C3×#94014yes—
492C3—21no—
493C3#8234711yescharacteristic, direct product factor
494C3C3×#239711yescharacteristic, complemented
495C2—44no—
496C2—124no—
497C2C3×#554714yes—
498C2C3×#579111yescharacteristic
499C2C2×C3×#94011yescharacteristic
500C2C3×#582811yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×#2397
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
2. C2×C3×C4×#67C2semidirect
3. C2×C3×C4×D12C2semidirect
4. C3×#5223C2semidirect
5. C3×#4993C2semidirect
6. C3×#4960C2semidirect
7. C3×#4949C2semidirect
8. C3×#4932C2semidirect
10. #82347C3direct (N × H)
33. C2×C3×C4×D4D3semidirect
34. C2×C3×C4×D4C2×C3semidirect
35. C2×C4×#67C2×C3semidirect
36. C2×C4×D12C2×C3semidirect
42. #5223C2×C3semidirect
43. #4993C2×C3semidirect
44. #4960C2×C3semidirect
45. #4949C2×C3semidirect
46. #4932C2×C3semidirect
68. C32×C42D4semidirect
74. C3×C4×Dic3D4semidirect
151. C2×C4×D4C3×D3semidirect
217. C3×C42#67semidirect
218. C3×C42C3×D4semidirect
224. C4×Dic3C3×D4semidirect
371. C42C3×#67semidirect
425. C32#2397semidirect
493. C3#82347direct (N × H)
494. C3C3×#2397semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×C4×#672
C2×C3×C4×D122
C3×#52232
C3×#49932
C3×#49602
C3×#49492
C3×#49322
C3×#23973
#823473