Finite Group Databasebeta

← C3×#79447 #11887510

Subgroups — C3×#79447 #11887510

Order 1152.

907 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5555C211yesmaximal, characteristic
2C3×D4×Dic6C211yesmaximal, characteristic, complemented
3C32×C8×D4C211yesmaximal, characteristic, complemented
4C3×#5114C212yesmaximal, complemented
5C2×C3×#816C212yesmaximal, complemented
6C3×#4851C211yesmaximal, characteristic, complemented
7C3×#4841C211yesmaximal, characteristic, complemented
8C3×#4738C212yesmaximal, complemented
9C3×#4721C212yesmaximal, complemented
10C3×C4×#204C211yesmaximal, characteristic, complemented
11C3×#4681C211yesmaximal, characteristic, complemented
12C3×#3298—31nomaximal
13#79447C311yesmaximal, characteristic, direct product factor
14C2×C3×#237—21no—
15C22×C3×Dic6C2212yes—
16C22×C32×C8C2212yes—
17C32×C4×D4C2211yescharacteristic
18C3×D4×Dic3—21no—
19C3×#930C2212yes—
20C2×C3×C4⋊Dic3C2212yes—
21C3×#924C2212yes—
22C2×C3×#204C2211yescharacteristic
23C2×C3×#204C2212yes—
24C3×#897—21no—
25C3×#888—21no—
26C3×#886—22no—
27C3×#878—22no—
28C3×C4×D12C2211yescharacteristic
29C3×#869C2211yescharacteristic
30C3×#869C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32C32×C4⋊C8C2211yescharacteristic
33C32×C22⋊C8C2212yes—
34C32×C4×C8C2211yescharacteristic
35C3×#821C2211yescharacteristic
36C3×#817C2211yescharacteristic
37C3×#817C2212yes—
38C3×#816C2212yes—
39C3×#816C2212yes—
40C3×#816C2211yescharacteristic
41C3×#816C2212yes—
42C3×#816C2212yes—
43C3×D4×Q8—31no—
44C3×#547—31no—
45#5555C2×C311yescharacteristic
46D4×Dic6C2×C311yescharacteristic, complemented
47C3×#487—31no—
48C3×#483—32no—
49C3×#475—31no—
50C3×#465—32no—
51C3×#461—31no—
52C3×#448—32no—
53C3×C4×SD16—31no—
54C3×C8×D4—21no—
55C3×C8×D4D311yescharacteristic, complemented
56C3×C8×D4C2×C311yescharacteristic, complemented
57C2×C3×#103—32no—
58#5114C2×C312yescomplemented
59C2×#816C2×C312yescomplemented
60#4851C2×C311yescharacteristic, complemented
61#4841C2×C311yescharacteristic, complemented
62#4738C2×C312yescomplemented
63#4721C2×C312yescomplemented
64C4×#204C2×C311yescharacteristic, complemented
65#4681C2×C311yescharacteristic, complemented
66C2×C32×D4D411yescharacteristic
67C22×C32×C4C2312yes—
68C2×C3×#67—22no—
69C22×C3×Dic3—22no—
70C22×C3×Dic3—22no—
71C3×#237—44no—
72C2×C3×D12C2311yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×Dic6—24no—
75C2×C3×Dic6—22no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6—42no—
78C2×C3×Dic6C2312yes—
79C2×C3×Dic6C2311yescharacteristic
80C2×C32×C8—42no—
81C2×C32×C8C2311yescharacteristic
82C2×C32×C8C2312yes—
83C2×C32×C8C2311yescharacteristic
84C32×C4⋊C4D411yescharacteristic
85C32×C22⋊C4D412yes—
86C32×C42C2311yescharacteristic
87C3×#217—22no—
88C3×(C2×D3)⋊C4—21no—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—22no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4⋊Dic3C2312yes—
97C3×Dic3⋊C4—21no—
98C3×Dic3⋊C4—22no—
99C3×C4×Dic3—21no—
100C3×#204—22no—
101C3×#204—42no—
102#3298—31noSylow
103C2×C3×#41—61no—
104C22×C3×Q8—32no—
105C2×#237—21no—
106C22×Dic6C22×C312yes—
107C2×C3×SD16—31no—
108C2×C3×SD16—32no—
109C22×C3×C8—22no—
110C22×C3×C8C2×D312yes—
111C22×C3×C8C22×C312yes—
112C3×C4⋊Q8—31no—
113C3×C4⋊Q8—31no—
114C3×C4⋊Q8—61no—
115C3×#123—62no—
116C3×C22⋊Q8—32no—
117C3×C22⋊Q8—61no—
118C3×C22⋊Q8—62no—
119C3×#121—32no—
120C3×C4×Q8—31no—
121C3×C4×D4—21no—
122C3×C4×D4—31no—
123C3×C4×D4—61no—
124C3×C4×D4C2×D311yescharacteristic
125C3×C4×D4C22×C311yescharacteristic
126C2×C3×C4⋊C4—32no—
127D4×Dic3—21no—
128#930C22×C312yes—
129C2×C4⋊Dic3C22×C312yes—
130#924C22×C312yes—
131C2×#204C22×C311yescharacteristic
132C2×#204C22×C312yes—
133#897—21no—
134#888—21no—
135#886—22no—
136#878—22no—
137C4×D12C22×C311yescharacteristic
138#869C22×C311yescharacteristic
139#869C22×C311yescharacteristic
140C4×Dic6C22×C311yescharacteristic
141C3×#106—31no—
142C3×#106—32no—
143C3×C4⋊C8—21no—
144C3×C4⋊C8C2×D311yescharacteristic
145C3×C4⋊C8C22×C311yescharacteristic
146C3×#103—31no—
147C3×#103—32no—
148C3×#103—32no—
149C3×#103—32no—
150C3×#103—32no—
151C3×#102—31no—
152C3×C22⋊C8—22no—
153C3×C22⋊C8C2×D312yes—
154C3×C22⋊C8C22×C312yes—
155C3×C4×C8—21no—
156C3×C4×C8C2×D311yescharacteristic
157C3×C4×C8C22×C311yescharacteristic
158#821C22×C311yescharacteristic
159#817C22×C311yescharacteristic
160#817C22×C312yes—
161#816C22×C312yes—
162#816C22×C312yes—
163#816C22×C311yescharacteristic
164#816C22×C312yes—
165#816C22×C312yes—
166C23×C32C2×D412yes—
167C22×C3×D3—21no—
168C32×D4SD1614yescomplemented
169C2×C32×C4—22no—
170C2×C32×C4—22no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D412yes—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C3×#67—44no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—44no—
182C2×C3×Dic3—44no—
183C3×D12—21no—
184C3×D12—21no—
185C3×C4×D3—42no—
186C3×Dic6—21no—
187C3×Dic6—22no—
188C3×Dic6—22no—
189C3×Dic6—44no—
190C3×Dic6—42no—
191C3×Dic6#4112yescomplemented
192C32×C8—21no—
193C32×C8—21no—
194C32×C8—22no—
195D4×Q8—31no—
196#547—31no—
197#487—31no—
198#483—32no—
199#475—31no—
200#465—32no—
201#461—31no—
202#448—32no—
203C4×SD16—31no—
204C8×D4C3×D311yescharacteristic, complemented
205C2×#103—32no—
206C3×#41—124no—
207C2×C3×Q8—31no—
208C2×C3×Q8—32no—
209C2×C3×Q8—64no—
210C2×C3×Q8—61no—
211C2×C3×Q8—62no—
212C2×C3×Q8—122no—
213C2×C3×D4—21no—
214C2×C3×D4—31no—
215C2×C3×D4—62no—
216C2×C3×D4D1211yescharacteristic
217C2×C3×D4C3×D411yescharacteristic
218C22×C3×C4—22no—
219C22×C3×C4—62no—
220C22×C3×C4—62no—
221C22×C3×C4—61no—
222C22×C3×C4C22×D312yes—
223C22×C3×C4C23×C312yes—
224C2×#67—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227#237—44no—
228C2×D12C23×C311yescharacteristic
229C2×C4×D3—21no—
230C2×Dic6—24no—
231C2×Dic6—21no—
232C2×Dic6—22no—
233C2×Dic6—42no—
234C2×Dic6C23×C312yes—
235C2×Dic6C23×C311yescharacteristic
236C3×SD16—62no—
237C3×SD16—122no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—22no—
241C2×C3×C8—42no—
242C2×C3×C8—42no—
243C2×C3×C8—44no—
244C2×C3×C8C22×D311yescharacteristic
245C2×C3×C8C22×D311yescharacteristic
246C2×C3×C8C22×D312yes—
247C2×C3×C8C23×C311yescharacteristic
248C2×C3×C8C23×C311yescharacteristic
249C2×C3×C8C23×C312yes—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—31no—
252C3×C4⋊C4—31no—
253C3×C4⋊C4—32no—
254C3×C4⋊C4—61no—
255C3×C4⋊C4—62no—
256C3×C4⋊C4—62no—
257C3×C4⋊C4—61no—
258C3×C4⋊C4—61no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4D1211yescharacteristic
261C3×C4⋊C4C3×D411yescharacteristic
262C3×C22⋊C4—22no—
263C3×C22⋊C4—62no—
264C3×C22⋊C4—61no—
265C3×C22⋊C4—62no—
266C3×C22⋊C4D1212yes—
267C3×C22⋊C4C3×D412yes—
268C3×C42—21no—
269C3×C42—61no—
270C3×C42C22×D311yescharacteristic
271C3×C42C23×C311yescharacteristic
272#217—22no—
273(C2×D3)⋊C4—21no—
274(C2×D3)⋊C4—22no—
275C4⋊Dic3—21no—
276C4⋊Dic3—21no—
277C4⋊Dic3—21no—
278C4⋊Dic3—22no—
279C4⋊Dic3C23×C312yes—
280C4⋊Dic3C23×C311yescharacteristic
281C4⋊Dic3C23×C311yescharacteristic
282Dic3⋊C4—21no—
283Dic3⋊C4—22no—
284C4×Dic3—21no—
285#204—22no—
286#204—42no—
287C22×C32—22no—
288C22×C32—22no—
289C22×C32C2×SD1614yes—
290C22×C32C22×D411yescharacteristic
291C2×C3×D3—41no—
292C2×C3×D3—41no—
293C2×C3×D3—41no—
294C32×C4—22no—
295C32×C4—21no—
296C32×C4C2×SD1612yes—
297C32×C4C2×#4111yescharacteristic
298C32×C4H(5,𝔽2)11yescharacteristic
299C3×Dic3—22no—
300C3×Dic3—42no—
301C3×Dic3—42no—
302C3×Dic3—41no—
303C3×Dic3—41no—
304C2×#41—61no—
305C22×Q8—32no—
306C2×SD16—31no—
307C2×SD16—32no—
308C22×C8C2×C3×D312yes—
309C4⋊Q8—31no—
310C4⋊Q8—31no—
311C4⋊Q8—61no—
312#123—62no—
313C22⋊Q8—32no—
314C22⋊Q8—61no—
315C22⋊Q8—62no—
316#121—32no—
317C4×Q8—31no—
318C4×D4—31no—
319C4×D4—61no—
320C4×D4C2×C3×D311yescharacteristic
321C2×C4⋊C4—32no—
322#106—31no—
323#106—32no—
324C4⋊C8C2×C3×D311yescharacteristic
325#103—31no—
326#103—32no—
327#103—32no—
328#103—32no—
329#103—32no—
330#102—31no—
331C22⋊C8C2×C3×D312yes—
332C4×C8C2×C3×D311yescharacteristic
333C23×C3—22no—
334C23×C3—61no—
335C23×C3C2×D1212yes—
336C23×C3C2×C3×D412yes—
337C22×D3—21no—
338C3×Q8—32no—
339C3×Q8—61no—
340C3×Q8—62no—
341C3×Q8—62no—
342C3×Q8—124no—
343C3×Q8—122no—
344C3×D4—24no—
345C3×D4—61no—
346C3×D4—61no—
347C3×D4—124no—
348C3×D4#20414yescomplemented
349C3×D4C3×SD1614yescomplemented
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—22no—
358C2×C3×C4—42no—
359C2×C3×C4—42no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—124no—
366C2×C3×C4—124no—
367C2×C3×C4—122no—
368C2×C3×C4C2×D1211yescharacteristic
369C2×C3×C4C2×D1212yes—
370C2×C3×C4C2×D1211yescharacteristic
371C2×C3×C4C2×C3×D411yescharacteristic
372C2×C3×C4C2×C3×D412yes—
373C2×C3×C4C2×C3×D411yescharacteristic
374C2×C3×C4C23×D311yescharacteristic
375C2×C3×C4C24×C311yescharacteristic
376#67—44no—
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—21no—
382C2×Dic3—44no—
383C2×Dic3—44no—
384D12—21no—
385D12—21no—
386C4×D3—42no—
387Dic6—21no—
388Dic6—22no—
389Dic6—22no—
390Dic6—44no—
391Dic6—42no—
392Dic6C3×#4112yescomplemented
393C3×C8—22no—
394C3×C8—21no—
395C3×C8—22no—
396C3×C8—21no—
397C3×C8—21no—
398C3×C8—22no—
399C3×C8—21no—
400C3×C8—41no—
401C3×C8—42no—
402C2×C32—24no—
403C2×C32#54611yescharacteristic
404C2×C32C22×SD1611yescharacteristic
405C2×C32#57811yescharacteristic
406C3×D3—81no—
407#41—124no—
408C2×Q8—31no—
409C2×Q8—32no—
410C2×Q8—64no—
411C2×Q8—61no—
412C2×Q8—62no—
413C2×Q8—122no—
414C2×D4—31no—
415C2×D4—62no—
416C2×D4C3×D1211yescharacteristic
417C22×C4—62no—
418C22×C4—62no—
419C22×C4—61no—
420C22×C4C22×C3×D312yes—
421SD16—62no—
422SD16—122no—
423C2×C8—42no—
424C2×C8C22×C3×D311yescharacteristic
425C2×C8C22×C3×D311yescharacteristic
426C2×C8C22×C3×D312yes—
427C4⋊C4—31no—
428C4⋊C4—31no—
429C4⋊C4—32no—
430C4⋊C4—62no—
431C4⋊C4—61no—
432C4⋊C4—61no—
433C4⋊C4—62no—
434C4⋊C4—61no—
435C4⋊C4—61no—
436C4⋊C4C3×D1211yescharacteristic
437C22⋊C4—62no—
438C22⋊C4—61no—
439C22⋊C4—62no—
440C22⋊C4C3×D1212yes—
441C42—61no—
442C42C22×C3×D311yescharacteristic
443C22×C3—22no—
444C22×C3—22no—
445C22×C3—22no—
446C22×C3—22no—
447C22×C3—24no—
448C22×C3—21no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—121no—
452C22×C3—121no—
453C22×C3—121no—
454C22×C3C2×#20414yes—
455C22×C3C2×C3×SD1614yes—
456C22×C3C22×D1211yescharacteristic
457C22×C3C22×C3×D411yescharacteristic
458C2×D3—41no—
459C2×D3—41no—
460C2×D3—41no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—22no—
464C3×C4—22no—
465C3×C4—22no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—42no—
469C3×C4—41no—
470C3×C4—62no—
471C3×C4—121no—
472C3×C4—122no—
473C3×C4—121no—
474C3×C4—122no—
475C3×C4C2×#20412yes—
476C3×C4C2×C3×SD1612yes—
477C3×C4#100411yescharacteristic
478C3×C4D3×#4111yescharacteristic
479C3×C4C2×C3×#4111yescharacteristic
480C3×C4C3×H(5,𝔽2)11yescharacteristic
481Dic3—22no—
482Dic3—42no—
483Dic3—41no—
484Dic3—41no—
485Dic3—42no—
486C32#329811yescharacteristic, complemented, Sylow
487C23—61no—
488C23C2×C3×D1212yes—
489Q8—32no—
490Q8—61no—
491Q8—62no—
492Q8—62no—
493Q8—124no—
494Q8—122no—
495D4—61no—
496D4—61no—
497D4—124no—
498D4C3×#20414yescomplemented
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—61no—
502C2×C4—61no—
503C2×C4—61no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—124no—
507C2×C4—124no—
508C2×C4—122no—
509C2×C4C2×C3×D1211yescharacteristic
510C2×C4C2×C3×D1212yes—
511C2×C4C2×C3×D1211yescharacteristic
512C2×C4C23×C3×D311yescharacteristic
513C8—21no—
514C8—22no—
515C8—21no—
516C2×C3—24no—
517C2×C3—24no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—44no—
522C2×C3—241no—
523C2×C3#555411yescharacteristic
524C2×C3C22×#20411yescharacteristic
525C2×C3#575311yescharacteristic
526C2×C3C3×#54611yescharacteristic
527C2×C3C22×C3×SD1611yescharacteristic
528C2×C3C3×#57811yescharacteristic
529D3—81no—
530C22—22no—
531C22—22no—
532C22—121no—
533C22—121no—
534C22—121no—
535C22C2×C3×#20414yes—
536C22C22×C3×D1211yescharacteristic
537C4—21no—
538C4—22no—
539C4—62no—
540C4—121no—
541C4—122no—
542C4—121no—
543C4—122no—
544C4C2×C3×#20412yes—
545C4C3×#100411yescharacteristic
546C4C3×D3×#4111yescharacteristic
547C3—21no—
548C3#7944711yescharacteristic, direct product factor
549C3C3×#329811yescharacteristic, complemented
550C2—24no—
551C2—241no—
552C2C3×#555411yescharacteristic
553C2C22×C3×#20411yescharacteristic
554C2C3×#575311yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C8×D4C2
socleC22×C32C22×D4
prime radicalC3×#5555C2
hypercenterC3×C8×D4D3
hypocenterC3C3×#3298
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×C8×D4

Complements

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

NH ≅ G/Ntype
2. C3×D4×Dic6C2semidirect
3. C32×C8×D4C2semidirect
4. C3×#5114C2semidirect
5. C2×C3×#816C2semidirect
6. C3×#4851C2semidirect
7. C3×#4841C2semidirect
8. C3×#4738C2semidirect
9. C3×#4721C2semidirect
10. C3×C4×#204C2semidirect
11. C3×#4681C2semidirect
13. #79447C3direct (N × H)
46. D4×Dic6C2×C3semidirect
55. C3×C8×D4D3semidirect
56. C3×C8×D4C2×C3semidirect
58. #5114C2×C3semidirect
59. C2×#816C2×C3semidirect
60. #4851C2×C3semidirect
61. #4841C2×C3semidirect
62. #4738C2×C3semidirect
63. #4721C2×C3semidirect
64. C4×#204C2×C3semidirect
65. #4681C2×C3semidirect
168. C32×D4SD16semidirect
191. C3×Dic6#41semidirect
204. C8×D4C3×D3semidirect
348. C3×D4#204semidirect
349. C3×D4C3×SD16semidirect
392. Dic6C3×#41semidirect
486. C32#3298semidirect
498. D4C3×#204semidirect
548. C3#79447direct (N × H)
549. C3C3×#3298semidirect

Maximal subgroups

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

subgroupindex
C3×#55552
C3×D4×Dic62
C32×C8×D42
C3×#51142
C2×C3×#8162
C3×#48512
C3×#48412
C3×#47382
C3×#47212
C3×C4×#2042
C3×#46812
C3×#32983
#794473