Finite Group Databasebeta

← C3×#76349 #11824477

Subgroups — C3×#76349 #11824477

Order 1152.

1481 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic
2C2×C3×#888C211yesmaximal, characteristic, complemented
3C2×C3×#878C214yesmaximal, complemented
4C32×#390C211yesmaximal, characteristic
5C3×#5221C211yesmaximal, characteristic
6C3×#4975C211yesmaximal, characteristic, complemented
7C3×#4949C214yesmaximal, complemented
8C3×#4935C211yesmaximal, characteristic, complemented
9C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
10C3×#2542—31nomaximal
11#76349C311yesmaximal, characteristic, direct product factor
12C22×C32×D4C2211yescharacteristic
13C23×C3×Dic3C2212yes—
14C22×C3×Dic6C2212yes—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C22⋊C4C2214yes—
17C2×C32×C42C2211yescharacteristic
18C2×C3×#217C2212yes—
19C2×C3×#217C2214yes—
20C3×D4×Dic3—24no—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2214yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×Dic3⋊C4C2214yes—
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C3×#888—24no—
30C3×#878—216no—
31C3×C3⋊#95C2212yes—
32C2×C3×C4⋊Q8—31no—
33C2×C3×C22⋊Q8—34no—
34C2×C3×C4×D4—31no—
35C2×D4×Dic3C2×C311yescharacteristic
36C2×#888C2×C311yescharacteristic, complemented
37C2×#878C2×C314yescomplemented
38C3×#399—34no—
39C3×#390—21no—
40C3×#390—31no—
41C3×#390D311yescharacteristic
42C3×#390C2×C311yescharacteristic
43C3×#384—31no—
44C3×#384—31no—
45C3×C4×C4⋊C4—31no—
46#5221C2×C311yescharacteristic
47#4975C2×C311yescharacteristic, complemented
48#4949C2×C314yescomplemented
49#4935C2×C311yescharacteristic, complemented
50C4×Dic3⋊C4C2×C311yescharacteristic, complemented
51C24×C32C2312yes—
52C2×C32×D4—22no—
53C2×C32×D4—22no—
54C2×C32×D4Q814yescomplemented
55C22×C32×C4C2312yes—
56C22×C32×C4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C3×Dic3—28no—
59C22×C3×Dic3—24no—
60C22×C3×Dic3C2312yes—
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2311yescharacteristic
64C22×C3×Dic3C2311yescharacteristic
65C2×C3×Dic6—28no—
66C2×C3×Dic6—24no—
67C32×C4⋊C4—22no—
68C32×C22⋊C4—28no—
69C32×C42—22no—
70C3×#217—28no—
71C3×#217—24no—
72C3×C4⋊Dic3—28no—
73C3×C4⋊Dic3—22no—
74C3×C4⋊Dic3—22no—
75C3×Dic3⋊C4—28no—
76C3×Dic3⋊C4—24no—
77C3×Dic3⋊C4D418yescomplemented
78C3×C4×Dic3—22no—
79C3×C4×Dic3D414yes—
80#2542—31noSylow
81C22×C3×Q8—32no—
82C22×C3×D4—21no—
83C22×C3×D4C2×D311yescharacteristic
84C22×C3×D4C22×C311yescharacteristic
85C23×C3×C4—32no—
86C23×Dic3C22×C312yes—
87C22×Dic6C22×C312yes—
88C3×C4⋊Q8—64no—
89C3×C22⋊Q8—616no—
90C3×C4×D4—64no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—32no—
93C2×C3×C4⋊C4—34no—
94C2×C3×C4⋊C4—32no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—34no—
98C2×C3×C4⋊C4C2×D311yescharacteristic
99C2×C3×C4⋊C4C22×C311yescharacteristic
100C2×C3×C22⋊C4—24no—
101C2×C3×C22⋊C4—34no—
102C2×C3×C22⋊C4—32no—
103C2×C3×C22⋊C4C2×D314yes—
104C2×C3×C22⋊C4C22×C314yes—
105C2×C3×C42—21no—
106C2×C3×C42—31no—
107C2×C3×C42—31no—
108C2×C3×C42C2×D311yescharacteristic
109C2×C3×C42C22×C311yescharacteristic
110C2×#217C22×C312yes—
111C2×#217C22×C314yes—
112D4×Dic3—24no—
113C2×C4⋊Dic3C22×C314yes—
114C2×C4⋊Dic3C22×C311yescharacteristic
115C2×C4⋊Dic3C22×C311yescharacteristic
116C2×Dic3⋊C4C22×C312yes—
117C2×Dic3⋊C4C22×C314yes—
118C2×Dic3⋊C4C22×C312yes—
119C2×C4×Dic3C22×C311yescharacteristic
120C2×C4×Dic3C22×C311yescharacteristic
121#888—24no—
122#878—216no—
123C3×#95—32no—
124C3⋊#95C22×C312yes—
125C23×C32—24no—
126C23×C32—22no—
127C23×C32—22no—
128C23×C32—24no—
129C23×C32C2×Q814yes—
130C23×C32C2411yescharacteristic
131C32×D4—28no—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4—24no—
135C2×C32×C4—22no—
136C2×C32×C4C2×D414yes—
137C2×C32×C4C2×D412yes—
138C2×C32×C4C2×Q812yes—
139C2×C32×C4#4112yes—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—24no—
145C2×C3×Dic3—24no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—48no—
148C2×C3×Dic3C2×D412yes—
149C2×C3×Dic3C2×D414yes—
150C2×C3×Dic3C2×D412yes—
151C2×C3×Dic3C2×D414yes—
152C3×Dic6—48no—
153C2×C4⋊Q8—31no—
154C2×C22⋊Q8—34no—
155C2×C4×D4—31no—
156#399—34no—
157#390—31no—
158#390C3×D311yescharacteristic
159#384—31no—
160#384—31no—
161C4×C4⋊C4—31no—
162C24×C3—22no—
163C24×C3C22×D312yes—
164C24×C3C23×C312yes—
165C2×C3×Q8—68no—
166C2×C3×Q8—64no—
167C2×C3×D4—22no—
168C2×C3×D4—22no—
169C2×C3×D4—22no—
170C2×C3×D4—22no—
171C2×C3×D4—24no—
172C2×C3×D4—42no—
173C2×C3×D4—42no—
174C2×C3×D4Dic614yescomplemented
175C2×C3×D4C3×Q814yescomplemented
176C22×C3×C4—21no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—31no—
180C22×C3×C4—31no—
181C22×C3×C4—32no—
182C22×C3×C4—32no—
183C22×C3×C4—32no—
184C22×C3×C4—64no—
185C22×C3×C4—68no—
186C22×C3×C4C22×D312yes—
187C22×C3×C4C22×D312yes—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C23×C312yes—
190C22×C3×C4C23×C312yes—
191C22×C3×C4C23×C311yescharacteristic
192C22×Dic3—28no—
193C22×Dic3—24no—
194C22×Dic3C23×C312yes—
195C22×Dic3C23×C312yes—
196C22×Dic3C23×C311yescharacteristic
197C22×Dic3C23×C312yes—
198C22×Dic3C23×C311yescharacteristic
199C2×Dic6—28no—
200C2×Dic6—24no—
201C3×C4⋊C4—22no—
202C3×C4⋊C4—22no—
203C3×C4⋊C4—38no—
204C3×C4⋊C4—42no—
205C3×C4⋊C4—68no—
206C3×C4⋊C4—64no—
207C3×C4⋊C4—62no—
208C3×C4⋊C4—68no—
209C3×C4⋊C4—62no—
210C3×C22⋊C4—28no—
211C3×C22⋊C4—28no—
212C3×C22⋊C4—48no—
213C3×C22⋊C4—64no—
214C3×C22⋊C4—68no—
215C3×C42—22no—
216C3×C42—22no—
217C3×C42—34no—
218C3×C42—42no—
219C3×C42—62no—
220#217—28no—
221#217—24no—
222C4⋊Dic3—28no—
223C4⋊Dic3—22no—
224C4⋊Dic3—22no—
225Dic3⋊C4—28no—
226Dic3⋊C4—24no—
227Dic3⋊C4C3×D418yescomplemented
228C4×Dic3—22no—
229C4×Dic3C3×D414yes—
230C22×C32—24no—
231C22×C32—28no—
232C22×C32—42no—
233C22×C32—42no—
234C22×C32—44no—
235C22×C32C22×D411yescharacteristic
236C22×C32C22×D412yes—
237C22×C32C22×Q811yescharacteristic
238C22×C32C2×#4111yescharacteristic
239C22×C322−1+412yes—
240C32×C4—24no—
241C32×C4—42no—
242C32×C4C22⋊Q814yescomplemented
243C3×Dic3—22no—
244C3×Dic3—24no—
245C3×Dic3—42no—
246C3×Dic3—42no—
247C3×Dic3#12714yes—
248C22×Q8—32no—
249C22×D4C2×C3×D311yescharacteristic
250C23×C4—32no—
251C4⋊Q8—64no—
252C22⋊Q8—616no—
253C4×D4—64no—
254C2×C4⋊C4—32no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—34no—
257C2×C4⋊C4—34no—
258C2×C4⋊C4—31no—
259C2×C4⋊C4—32no—
260C2×C4⋊C4C2×C3×D311yescharacteristic
261C2×C22⋊C4—32no—
262C2×C22⋊C4—34no—
263C2×C22⋊C4C2×C3×D314yes—
264C2×C42—31no—
265C2×C42—31no—
266C2×C42C2×C3×D311yescharacteristic
267#95—32no—
268C23×C3—24no—
269C23×C3—22no—
270C23×C3—22no—
271C23×C3—24no—
272C23×C3—24no—
273C23×C3—22no—
274C23×C3—22no—
275C23×C3—24no—
276C23×C3—21no—
277C23×C3—24no—
278C23×C3—44no—
279C23×C3—42no—
280C23×C3—42no—
281C23×C3—44no—
282C23×C3C2×Dic614yes—
283C23×C3C2×C3×Q814yes—
284C23×C3C23×D311yescharacteristic
285C23×C3C24×C311yescharacteristic
286C3×Q8—128no—
287C3×D4—28no—
288C3×D4—28no—
289C3×D4—48no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—24no—
295C2×C3×C4—22no—
296C2×C3×C4—24no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—24no—
301C2×C3×C4—22no—
302C2×C3×C4—32no—
303C2×C3×C4—34no—
304C2×C3×C4—32no—
305C2×C3×C4—34no—
306C2×C3×C4—42no—
307C2×C3×C4—42no—
308C2×C3×C4—44no—
309C2×C3×C4—42no—
310C2×C3×C4—62no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—64no—
315C2×C3×C4—64no—
316C2×C3×C4—62no—
317C2×C3×C4—128no—
318C2×C3×C4C2×Dic612yes—
319C2×C3×C4D3×D414yes—
320C2×C3×C4D3×D412yes—
321C2×C3×C4#23712yes—
322C2×C3×C4C2×C3×D414yes—
323C2×C3×C4C2×C3×D412yes—
324C2×C3×C4C2×C3×Q812yes—
325C2×C3×C4C3×#4112yes—
326C2×Dic3—22no—
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—24no—
331C2×Dic3—24no—
332C2×Dic3—22no—
333C2×Dic3—48no—
334C2×Dic3C2×C3×D412yes—
335C2×Dic3C2×C3×D414yes—
336C2×Dic3C2×C3×D412yes—
337C2×Dic3C2×C3×D414yes—
338Dic6—48no—
339C2×C32—44no—
340C2×C32C2×C22⋊Q811yescharacteristic
341C2×C32C2×#12711yescharacteristic
342C2×C32#53611yescharacteristic
343C2×C32#54712yes—
344C2×C32D4×Q812yes—
345C24C22×C3×D312yes—
346C2×Q8—68no—
347C2×Q8—64no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4C3×Dic614yescomplemented
351C22×C4—31no—
352C22×C4—31no—
353C22×C4—32no—
354C22×C4—32no—
355C22×C4—32no—
356C22×C4—64no—
357C22×C4—68no—
358C22×C4C22×C3×D312yes—
359C22×C4C22×C3×D312yes—
360C22×C4C22×C3×D311yescharacteristic
361C4⋊C4—22no—
362C4⋊C4—38no—
363C4⋊C4—68no—
364C4⋊C4—64no—
365C4⋊C4—62no—
366C4⋊C4—68no—
367C4⋊C4—62no—
368C22⋊C4—28no—
369C22⋊C4—64no—
370C22⋊C4—68no—
371C42—22no—
372C42—34no—
373C42—62no—
374C22×C3—24no—
375C22×C3—28no—
376C22×C3—24no—
377C22×C3—28no—
378C22×C3—21no—
379C22×C3—22no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—22no—
383C22×C3—44no—
384C22×C3—48no—
385C22×C3—42no—
386C22×C3—42no—
387C22×C3—42no—
388C22×C3—42no—
389C22×C3—44no—
390C22×C3—44no—
391C22×C3—84no—
392C22×C3—82no—
393C22×C3—82no—
394C22×C3C22×Dic611yescharacteristic
395C22×C3C2×D3×D411yescharacteristic
396C22×C3C2×D3×D412yes—
397C22×C3C2×#23711yescharacteristic
398C22×C3#101012yes—
399C22×C3C22×C3×D411yescharacteristic
400C22×C3C22×C3×D412yes—
401C22×C3C22×C3×Q811yescharacteristic
402C22×C3C2×C3×#4111yescharacteristic
403C22×C3C3×2−1+412yes—
404C3×C4—24no—
405C3×C4—24no—
406C3×C4—24no—
407C3×C4—34no—
408C3×C4—44no—
409C3×C4—42no—
410C3×C4—42no—
411C3×C4—62no—
412C3×C4—64no—
413C3×C4—82no—
414C3×C4—122no—
415C3×C4—122no—
416C3×C4#87814yescomplemented
417C3×C4C3×C22⋊Q814yescomplemented
418Dic3—22no—
419Dic3—24no—
420Dic3—42no—
421Dic3—42no—
422Dic3C3×#12714yes—
423C32#254211yescharacteristic, complemented, Sylow
424C23—24no—
425C23—22no—
426C23—22no—
427C23—24no—
428C23C2×C3×Dic614yes—
429C23C23×C3×D311yescharacteristic
430Q8—128no—
431D4—28no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—24no—
435C2×C4—22no—
436C2×C4—32no—
437C2×C4—34no—
438C2×C4—32no—
439C2×C4—34no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—62no—
443C2×C4—62no—
444C2×C4—64no—
445C2×C4—64no—
446C2×C4—62no—
447C2×C4—128no—
448C2×C4C2×C3×Dic612yes—
449C2×C4C3×D3×D414yes—
450C2×C4C3×D3×D412yes—
451C2×C4C3×#23712yes—
452C2×C3—22no—
453C2×C3—22no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—44no—
458C2×C3—44no—
459C2×C3—84no—
460C2×C3C2×#87811yescharacteristic
461C2×C3D4×Dic612yes—
462C2×C3#561112yes—
463C2×C3#567511yescharacteristic
464C2×C3D3×#12711yescharacteristic
465C2×C3C2×C3×C22⋊Q811yescharacteristic
466C2×C3C2×C3×#12711yescharacteristic
467C2×C3C3×#53611yescharacteristic
468C2×C3C3×#54712yes—
469C2×C3C3×D4×Q812yes—
470C22—28no—
471C22—24no—
472C22—44no—
473C22—42no—
474C22—42no—
475C22C22×C3×Dic611yescharacteristic
476C22C2×C3×D3×D412yes—
477C22C2×C3×D3×D411yescharacteristic
478C22C2×C3×#23711yescharacteristic
479C22C3×#101012yes—
480C4—24no—
481C4—34no—
482C4—42no—
483C4—64no—
484C4—62no—
485C4—122no—
486C4—122no—
487C4C3×#87814yescomplemented
488C3—21no—
489C3#7634911yescharacteristic, direct product factor
490C3C3×#254211yescharacteristic, complemented
491C2—44no—
492C2C2×C3×#87811yescharacteristic
493C2C3×D4×Dic612yes—
494C2C3×#561112yes—
495C2C3×#567511yescharacteristic
496C2C3×D3×#12711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#390C2
socleC23×C32C24
prime radicalC22×C32×D4C22
hypercenterC3×#390D3
hypocenterC3C3×#2542
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
2. C2×C3×#888C2semidirect
3. C2×C3×#878C2semidirect
6. C3×#4975C2semidirect
7. C3×#4949C2semidirect
8. C3×#4935C2semidirect
9. C3×C4×Dic3⋊C4C2semidirect
11. #76349C3direct (N × H)
36. C2×#888C2×C3semidirect
37. C2×#878C2×C3semidirect
47. #4975C2×C3semidirect
48. #4949C2×C3semidirect
49. #4935C2×C3semidirect
50. C4×Dic3⋊C4C2×C3semidirect
54. C2×C32×D4Q8semidirect
77. C3×Dic3⋊C4D4semidirect
174. C2×C3×D4Dic6semidirect
175. C2×C3×D4C3×Q8semidirect
227. Dic3⋊C4C3×D4semidirect
242. C32×C4C22⋊Q8semidirect
350. C2×D4C3×Dic6semidirect
416. C3×C4#878semidirect
417. C3×C4C3×C22⋊Q8semidirect
423. C32#2542semidirect
487. C4C3×#878semidirect
489. C3#76349direct (N × H)
490. C3C3×#2542semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
C2×C3×#8882
C2×C3×#8782
C32×#3902
C3×#52212
C3×#49752
C3×#49492
C3×#49352
C3×C4×Dic3⋊C42
C3×#25423
#763493