Finite Group Databasebeta

← C3×#74334 #11824480

Subgroups — C3×#74334 #11824480

Order 1152.

1445 conjugacy classes of subgroups.

The subgroup lattice has 487 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#896C214yesmaximal, complemented
2C2×C3×#893C211yesmaximal, characteristic
3C2×C3×#888C211yesmaximal, characteristic, complemented
4C32×#384C211yesmaximal, characteristic, complemented
5C3×#4993C214yesmaximal, complemented
6C3×#4988C211yesmaximal, characteristic
7C3×#4975C211yesmaximal, characteristic, complemented
8C3×#4939C211yesmaximal, characteristic
9C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
10C3×#2542—31nomaximal
11#74334C311yesmaximal, characteristic, direct product factor
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3C2212yes—
14C22×C3×Dic6C2212yes—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C4⋊C4C2214yes—
18C2×C32×C42C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2212yes—
20C2×C3×(C2×D3)⋊C4C2214yes—
21C2×C3×(C2×D3)⋊C4C2214yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×Dic3⋊C4C2214yes—
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C3×#896—216no—
29C3×#893—24no—
30C3×#888—24no—
31C3×C3⋊#95C2212yes—
32C2×C3×C4⋊Q8—31no—
33C2×C3×C22⋊Q8—34no—
34C2×C3×C4×D4—31no—
35C2×#896C2×C314yescomplemented
36C2×#893C2×C311yescharacteristic
37C2×#888C2×C311yescharacteristic, complemented
38C3×#399—34no—
39C3×#390—31no—
40C3×#390—31no—
41C3×#384—21no—
42C3×#384—31no—
43C3×#384D311yescharacteristic, complemented
44C3×#384C2×C311yescharacteristic, complemented
45C3×C4×C4⋊C4—31no—
46#4993C2×C314yescomplemented
47#4988C2×C311yescharacteristic
48#4975C2×C311yescharacteristic, complemented
49#4939C2×C311yescharacteristic
50C4×Dic3⋊C4C2×C311yescharacteristic, complemented
51C23×C3×D3C2312yes—
52C22×C32×C4C2312yes—
53C22×C32×C4C2312yes—
54C22×C32×C4C2312yes—
55C22×C32×C4C2311yescharacteristic
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2311yescharacteristic
59C22×C3×Dic3C2311yescharacteristic
60C2×C3×D12—22no—
61C2×C3×D12—22no—
62C2×C3×D12Q814yescomplemented
63C2×C3×C4×D3—24no—
64C2×C3×C4×D3—28no—
65C2×C3×Dic6—24no—
66C2×C3×Dic6—28no—
67C32×C4⋊C4—22no—
68C32×C4⋊C4—22no—
69C32×C4⋊C4—28no—
70C32×C42—22no—
71C3×(C2×D3)⋊C4—28no—
72C3×(C2×D3)⋊C4—24no—
73C3×(C2×D3)⋊C4—28no—
74C3×C4⋊Dic3—22no—
75C3×Dic3⋊C4—24no—
76C3×Dic3⋊C4—28no—
77C3×Dic3⋊C4D418yescomplemented
78C3×C4×Dic3—22no—
79C3×C4×Dic3D414yes—
80#2542—31noSylow
81C22×C3×Q8—32no—
82C22×C3×D4—31no—
83C23×C3×C4—32no—
84C22×D12C22×C311yescharacteristic
85C22×C4×D3C22×C312yes—
86C22×Dic6C22×C312yes—
87C3×C4⋊Q8—64no—
88C3×C22⋊Q8—616no—
89C3×C4×D4—64no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4—24no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4—32no—
94C2×C3×C4⋊C4—34no—
95C2×C3×C4⋊C4—32no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4C2×D311yescharacteristic
98C2×C3×C4⋊C4C2×D311yescharacteristic
99C2×C3×C4⋊C4C2×D314yes—
100C2×C3×C4⋊C4C22×C311yescharacteristic
101C2×C3×C4⋊C4C22×C311yescharacteristic
102C2×C3×C4⋊C4C22×C314yes—
103C2×C3×C22⋊C4—34no—
104C2×C3×C22⋊C4—34no—
105C2×C3×C22⋊C4—32no—
106C2×C3×C42—21no—
107C2×C3×C42—31no—
108C2×C3×C42—31no—
109C2×C3×C42C2×D311yescharacteristic
110C2×C3×C42C22×C311yescharacteristic
111C2×(C2×D3)⋊C4C22×C314yes—
112C2×(C2×D3)⋊C4C22×C314yes—
113C2×(C2×D3)⋊C4C22×C312yes—
114C2×C4⋊Dic3C22×C311yescharacteristic
115C2×Dic3⋊C4C22×C314yes—
116C2×Dic3⋊C4C22×C312yes—
117C2×Dic3⋊C4C22×C312yes—
118C2×C4×Dic3C22×C311yescharacteristic
119C2×C4×Dic3C22×C311yescharacteristic
120#896—216no—
121#893—24no—
122#888—24no—
123C3×#95—32no—
124C3⋊#95C22×C312yes—
125C23×C32C2411yescharacteristic
126C22×C3×D3—24no—
127C22×C3×D3—22no—
128C22×C3×D3—22no—
129C22×C3×D3—24no—
130C22×C3×D3C2×Q814yes—
131C2×C32×C4—22no—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4—24no—
135C2×C32×C4—24no—
136C2×C32×C4—22no—
137C2×C32×C4C2×D414yes—
138C2×C32×C4C2×D412yes—
139C2×C32×C4C2×Q812yes—
140C2×C32×C4#4112yes—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—24no—
146C2×C3×Dic3C2×D412yes—
147C2×C3×Dic3C2×D414yes—
148C2×C3×Dic3C2×D412yes—
149C2×C3×Dic3C2×D414yes—
150C3×D12—28no—
151C3×C4×D3—48no—
152C3×Dic6—48no—
153C2×C4⋊Q8—31no—
154C2×C22⋊Q8—34no—
155C2×C4×D4—31no—
156#399—34no—
157#390—31no—
158#390—31no—
159#384—31no—
160#384C3×D311yescharacteristic, complemented
161C4×C4⋊C4—31no—
162C24×C3—32no—
163C23×D3C23×C312yes—
164C2×C3×Q8—68no—
165C2×C3×Q8—64no—
166C2×C3×D4—34no—
167C2×C3×D4—62no—
168C2×C3×D4—62no—
169C22×C3×C4—22no—
170C22×C3×C4—21no—
171C22×C3×C4—22no—
172C22×C3×C4—22no—
173C22×C3×C4—31no—
174C22×C3×C4—31no—
175C22×C3×C4—32no—
176C22×C3×C4—32no—
177C22×C3×C4—64no—
178C22×C3×C4—68no—
179C22×C3×C4C22×D312yes—
180C22×C3×C4C22×D312yes—
181C22×C3×C4C22×D312yes—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C23×C312yes—
184C22×C3×C4C23×C312yes—
185C22×C3×C4C23×C312yes—
186C22×C3×C4C23×C311yescharacteristic
187C22×Dic3C23×C312yes—
188C22×Dic3C23×C311yescharacteristic
189C22×Dic3C23×C312yes—
190C22×Dic3C23×C311yescharacteristic
191C2×D12—22no—
192C2×D12—22no—
193C2×D12C3×Q814yescomplemented
194C2×C4×D3—24no—
195C2×C4×D3—28no—
196C2×Dic6—24no—
197C2×Dic6—28no—
198C3×C4⋊C4—22no—
199C3×C4⋊C4—28no—
200C3×C4⋊C4—22no—
201C3×C4⋊C4—22no—
202C3×C4⋊C4—22no—
203C3×C4⋊C4—28no—
204C3×C4⋊C4—38no—
205C3×C4⋊C4—42no—
206C3×C4⋊C4—48no—
207C3×C4⋊C4—42no—
208C3×C4⋊C4—68no—
209C3×C4⋊C4—64no—
210C3×C4⋊C4—62no—
211C3×C22⋊C4—64no—
212C3×C22⋊C4—68no—
213C3×C22⋊C4—68no—
214C3×C42—24no—
215C3×C42—22no—
216C3×C42—22no—
217C3×C42—34no—
218C3×C42—62no—
219(C2×D3)⋊C4—28no—
220(C2×D3)⋊C4—24no—
221(C2×D3)⋊C4—28no—
222C4⋊Dic3—22no—
223Dic3⋊C4—24no—
224Dic3⋊C4—28no—
225Dic3⋊C4C3×D418yescomplemented
226C4×Dic3—22no—
227C4×Dic3C3×D414yes—
228C22×C32C22×D411yescharacteristic
229C22×C32C22×D412yes—
230C22×C32C22×Q811yescharacteristic
231C22×C32C2×#4111yescharacteristic
232C22×C322−1+412yes—
233C2×C3×D3—24no—
234C2×C3×D3—28no—
235C2×C3×D3—42no—
236C2×C3×D3—42no—
237C2×C3×D3—44no—
238C32×C4—24no—
239C32×C4—42no—
240C32×C4—42no—
241C32×C4C22⋊Q814yescomplemented
242C3×Dic3—22no—
243C3×Dic3—24no—
244C3×Dic3—42no—
245C3×Dic3#12714yes—
246C22×Q8—32no—
247C22×D4—31no—
248C23×C4—32no—
249C4⋊Q8—64no—
250C22⋊Q8—616no—
251C4×D4—64no—
252C2×C4⋊C4—32no—
253C2×C4⋊C4—34no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4—32no—
256C2×C4⋊C4C2×C3×D311yescharacteristic
257C2×C4⋊C4C2×C3×D314yes—
258C2×C4⋊C4C2×C3×D311yescharacteristic
259C2×C22⋊C4—32no—
260C2×C22⋊C4—34no—
261C2×C22⋊C4—34no—
262C2×C42—31no—
263C2×C42—31no—
264C2×C42C2×C3×D311yescharacteristic
265#95—32no—
266C23×C3—21no—
267C23×C3—34no—
268C23×C3—62no—
269C23×C3—64no—
270C23×C3—62no—
271C23×C3—64no—
272C23×C3C23×D311yescharacteristic
273C23×C3C24×C311yescharacteristic
274C22×D3—24no—
275C22×D3—22no—
276C22×D3—22no—
277C22×D3—24no—
278C22×D3C2×C3×Q814yes—
279C3×Q8—128no—
280C3×D4—68no—
281C2×C3×C4—24no—
282C2×C3×C4—24no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—24no—
289C2×C3×C4—24no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—24no—
293C2×C3×C4—24no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—24no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—32no—
300C2×C3×C4—34no—
301C2×C3×C4—32no—
302C2×C3×C4—34no—
303C2×C3×C4—42no—
304C2×C3×C4—44no—
305C2×C3×C4—44no—
306C2×C3×C4—42no—
307C2×C3×C4—62no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—64no—
311C2×C3×C4—62no—
312C2×C3×C4—128no—
313C2×C3×C4#23512yes—
314C2×C3×C4D3×D414yes—
315C2×C3×C4D3×D412yes—
316C2×C3×C4D3×Q812yes—
317C2×C3×C4C2×C3×D414yes—
318C2×C3×C4C2×C3×D412yes—
319C2×C3×C4C2×C3×Q812yes—
320C2×C3×C4C3×#4112yes—
321C2×Dic3—22no—
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3—22no—
325C2×Dic3—24no—
326C2×Dic3C2×C3×D412yes—
327C2×Dic3C2×C3×D414yes—
328C2×Dic3C2×C3×D412yes—
329C2×Dic3C2×C3×D414yes—
330D12—28no—
331C4×D3—48no—
332Dic6—48no—
333C2×C32C2×C22⋊Q811yescharacteristic
334C2×C32C2×#12711yescharacteristic
335C2×C32#53611yescharacteristic
336C2×C32#54712yes—
337C2×C32D4×Q812yes—
338C3×D3—44no—
339C24—32no—
340C2×Q8—68no—
341C2×Q8—64no—
342C2×D4—34no—
343C2×D4—62no—
344C2×D4—62no—
345C22×C4—31no—
346C22×C4—31no—
347C22×C4—32no—
348C22×C4—32no—
349C22×C4—64no—
350C22×C4—68no—
351C22×C4C22×C3×D312yes—
352C22×C4C22×C3×D312yes—
353C22×C4C22×C3×D312yes—
354C22×C4C22×C3×D311yescharacteristic
355C4⋊C4—22no—
356C4⋊C4—28no—
357C4⋊C4—22no—
358C4⋊C4—38no—
359C4⋊C4—68no—
360C4⋊C4—64no—
361C4⋊C4—62no—
362C22⋊C4—64no—
363C22⋊C4—68no—
364C22⋊C4—68no—
365C42—22no—
366C42—34no—
367C42—62no—
368C22×C3—21no—
369C22×C3—22no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—22no—
373C22×C3—68no—
374C22×C3—64no—
375C22×C3—122no—
376C22×C3—122no—
377C22×C3—124no—
378C22×C3C2×#23511yescharacteristic
379C22×C3C2×D3×D411yescharacteristic
380C22×C3C2×D3×D412yes—
381C22×C3C2×D3×Q811yescharacteristic
382C22×C3#100712yes—
383C22×C3C22×C3×D411yescharacteristic
384C22×C3C22×C3×D412yes—
385C22×C3C22×C3×Q811yescharacteristic
386C22×C3C2×C3×#4111yescharacteristic
387C22×C3C3×2−1+412yes—
388C2×D3—24no—
389C2×D3—28no—
390C2×D3—42no—
391C2×D3—42no—
392C2×D3—44no—
393C3×C4—28no—
394C3×C4—24no—
395C3×C4—24no—
396C3×C4—24no—
397C3×C4—34no—
398C3×C4—42no—
399C3×C4—42no—
400C3×C4—42no—
401C3×C4—42no—
402C3×C4—62no—
403C3×C4—64no—
404C3×C4—82no—
405C3×C4—82no—
406C3×C4—122no—
407C3×C4#89614yescomplemented
408C3×C4C3×C22⋊Q814yescomplemented
409Dic3—22no—
410Dic3—24no—
411Dic3—42no—
412Dic3C3×#12714yes—
413C32#254211yescharacteristic, complemented, Sylow
414C23—34no—
415C23—62no—
416C23—64no—
417C23—62no—
418C23—64no—
419C23C23×C3×D311yescharacteristic
420Q8—128no—
421D4—68no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—22no—
428C2×C4—32no—
429C2×C4—34no—
430C2×C4—32no—
431C2×C4—34no—
432C2×C4—62no—
433C2×C4—62no—
434C2×C4—62no—
435C2×C4—64no—
436C2×C4—62no—
437C2×C4—128no—
438C2×C4C3×#23512yes—
439C2×C4C3×D3×D414yes—
440C2×C4C3×D3×D412yes—
441C2×C4C3×D3×Q812yes—
442C2×C3—22no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—22no—
447C2×C3—124no—
448C2×C3#550712yes—
449C2×C3C2×#89611yescharacteristic
450C2×C3D3×#12711yescharacteristic
451C2×C3#572411yescharacteristic
452C2×C3#572712yes—
453C2×C3C2×C3×C22⋊Q811yescharacteristic
454C2×C3C2×C3×#12711yescharacteristic
455C2×C3C3×#53611yescharacteristic
456C2×C3C3×#54712yes—
457C2×C3C3×D4×Q812yes—
458D3—44no—
459C22—64no—
460C22—68no—
461C22—124no—
462C22—122no—
463C22—122no—
464C22C2×C3×#23511yescharacteristic
465C22C2×C3×D3×D412yes—
466C22C2×C3×D3×D411yescharacteristic
467C22C2×C3×D3×Q811yescharacteristic
468C22C3×#100712yes—
469C4—24no—
470C4—34no—
471C4—42no—
472C4—42no—
473C4—64no—
474C4—62no—
475C4—122no—
476C4C3×#89614yescomplemented
477C3—21no—
478C3#7433411yescharacteristic, direct product factor
479C3C3×#254211yescharacteristic, complemented
480C2—124no—
481C2C3×#550712yes—
482C2C2×C3×#89611yescharacteristic
483C2C3×D3×#12711yescharacteristic
484C2C3×#572411yescharacteristic
485C2C3×#572712yes—
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#384C2
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC3×#384D3
hypocenterC3C3×#2542
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#384

Complements

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

NH ≅ G/Ntype
1. C2×C3×#896C2semidirect
3. C2×C3×#888C2semidirect
4. C32×#384C2semidirect
5. C3×#4993C2semidirect
7. C3×#4975C2semidirect
9. C3×C4×Dic3⋊C4C2semidirect
11. #74334C3direct (N × H)
35. C2×#896C2×C3semidirect
37. C2×#888C2×C3semidirect
43. C3×#384D3semidirect
44. C3×#384C2×C3semidirect
46. #4993C2×C3semidirect
48. #4975C2×C3semidirect
50. C4×Dic3⋊C4C2×C3semidirect
62. C2×C3×D12Q8semidirect
77. C3×Dic3⋊C4D4semidirect
160. #384C3×D3semidirect
193. C2×D12C3×Q8semidirect
225. Dic3⋊C4C3×D4semidirect
241. C32×C4C22⋊Q8semidirect
407. C3×C4#896semidirect
408. C3×C4C3×C22⋊Q8semidirect
413. C32#2542semidirect
476. C4C3×#896semidirect
478. C3#74334direct (N × H)
479. C3C3×#2542semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8962
C2×C3×#8932
C2×C3×#8882
C32×#3842
C3×#49932
C3×#49882
C3×#49752
C3×#49392
C3×C4×Dic3⋊C42
C3×#25423
#743343