Finite Group Databasebeta

← C3×#79442 #11888021

Subgroups — C3×#79442 #11888021

Order 1152.

839 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5551C211yesmaximal, characteristic
2C3×#5542C211yesmaximal, characteristic, complemented
3C32×C8×D4C211yesmaximal, characteristic, complemented
4C3×#5116C212yesmaximal, complemented
5C3×#5113C212yesmaximal, complemented
6C3×#4849C211yesmaximal, characteristic, complemented
7C3×#4846C211yesmaximal, characteristic, complemented
8C3×#4733C212yesmaximal, complemented
9C3×#4723C212yesmaximal, complemented
10C3×C4×#204C211yesmaximal, characteristic, complemented
11C3×#4681C211yesmaximal, characteristic, complemented
12C3×#3302—31nomaximal
13#79442C311yesmaximal, characteristic, direct product factor
14C2×C3×#235C2212yes—
15C22×C32×C8C2212yes—
16C32×C4×D4C2211yescharacteristic
17C3×#938—21no—
18C3×#936—21no—
19C3×#926C2212yes—
20C3×#924C2212yes—
21C3×#924C2212yes—
22C2×C3×Dic12C2212yes—
23C2×C3×#204C2211yescharacteristic
24C3×D3×C4⋊C4—21no—
25C3×#887—21no—
26C3×#883—22no—
27C3×#879—22no—
28C3×C4×D12C2211yescharacteristic
29C3×#869C2211yescharacteristic
30C3×#869C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32C32×C4⋊C8C2211yescharacteristic
33C32×C22⋊C8C2212yes—
34C32×C4×C8C2211yescharacteristic
35C3×#821C2211yescharacteristic
36C3×#821C2212yes—
37C3×#818C2212yes—
38C3×#817C2211yescharacteristic
39C3×#816C2212yes—
40C3×#816C2212yes—
41C3×#816C2211yescharacteristic
42C3×#816C2212yes—
43C3×#556—31no—
44C3×#547—31no—
45#5551C2×C311yescharacteristic
46#5542C2×C311yescharacteristic, complemented
47C3×#487—31no—
48C3×#485—32no—
49C3×#474—31no—
50C3×#467—32no—
51C3×#462—31no—
52C3×#452—32no—
53C3×C4×SD16—31no—
54C3×C8×D4—21no—
55C3×C8×D4D311yescharacteristic, complemented
56C3×C8×D4C2×C311yescharacteristic, complemented
57C3×#416—32no—
58#5116C2×C312yescomplemented
59#5113C2×C312yescomplemented
60#4849C2×C311yescharacteristic, complemented
61#4846C2×C311yescharacteristic, complemented
62#4733C2×C312yescomplemented
63#4723C2×C312yescomplemented
64C4×#204C2×C311yescharacteristic, complemented
65#4681C2×C311yescharacteristic, complemented
66C2×C32×D4D411yescharacteristic
67C22×C32×C4C2312yes—
68C2×C3×#67—22no—
69C3×#235—24no—
70C3×#235—42no—
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3—21no—
74C2×C3×Dic6—21no—
75C2×C3×Dic6C2311yescharacteristic
76C2×C3×Dic6C2312yes—
77C2×C32×C8—42no—
78C2×C32×C8C2311yescharacteristic
79C2×C32×C8C2312yes—
80C2×C32×C8C2311yescharacteristic
81C32×C4⋊C4D411yescharacteristic
82C32×C22⋊C4D412yes—
83C32×C42C2311yescharacteristic
84C3×#217—22no—
85C3×#217—22no—
86C3×#217—22no—
87C3×(C2×D3)⋊C4—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×Dic3⋊C4—21no—
95C3×Dic3⋊C4—22no—
96C3×Dic3⋊C4—22no—
97C3×C4×Dic3—22no—
98C3×C4×Dic3—21no—
99C3×Dic12—42no—
100C3×#204—22no—
101#3302—31noSylow
102C2×C3×#41—32no—
103C2×#235C22×C312yes—
104C2×C3×Q16—32no—
105C2×C3×SD16—31no—
106C22×C3×C8—22no—
107C22×C3×C8C2×D312yes—
108C22×C3×C8C22×C312yes—
109C3×C4⋊Q8—31no—
110C3×C4⋊Q8—31no—
111C3×#126—62no—
112C3×#124—61no—
113C3×#123—62no—
114C3×C22⋊Q8—32no—
115C3×C22⋊Q8—32no—
116C3×#121—61no—
117C3×C4×Q8—31no—
118C3×C4×Q8—61no—
119C3×C4×D4—21no—
120C3×C4×D4—31no—
121C3×C4×D4C2×D311yescharacteristic
122C3×C4×D4C22×C311yescharacteristic
123C3×#117—32no—
124C2×C3×C4⋊C4—61no—
125#938—21no—
126#936—21no—
127#926C22×C312yes—
128#924C22×C312yes—
129#924C22×C312yes—
130C2×Dic12C22×C312yes—
131C2×#204C22×C311yescharacteristic
132D3×C4⋊C4—21no—
133#887—21no—
134#883—22no—
135#879—22no—
136C4×D12C22×C311yescharacteristic
137#869C22×C311yescharacteristic
138#869C22×C311yescharacteristic
139C4×Dic6C22×C311yescharacteristic
140C3×#107—32no—
141C3×#106—31no—
142C3×C4⋊C8—21no—
143C3×C4⋊C8C2×D311yescharacteristic
144C3×C4⋊C8C22×C311yescharacteristic
145C3×#103—32no—
146C3×#103—32no—
147C3×#103—31no—
148C3×#103—32no—
149C3×#102—31no—
150C3×#102—32no—
151C3×C22⋊C8—22no—
152C3×C22⋊C8C2×D312yes—
153C3×C22⋊C8C22×C312yes—
154C3×C4×C8—21no—
155C3×C4×C8C2×D311yescharacteristic
156C3×C4×C8C22×C311yescharacteristic
157#821C22×C311yescharacteristic
158#821C22×C312yes—
159#818C22×C312yes—
160#817C22×C311yescharacteristic
161#816C22×C312yes—
162#816C22×C312yes—
163#816C22×C311yescharacteristic
164#816C22×C312yes—
165C23×C32C2×D412yes—
166C22×C3×D3—21no—
167C32×D4—22no—
168C2×C32×C4—22no—
169C2×C32×C4—22no—
170C2×C32×C4C2×D412yes—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C3×#67—44no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C3×D12—21no—
181C3×D12#4112yes—
182C3×C4×D3—44no—
183C3×C4×D3—42no—
184C3×Dic6—21no—
185C3×Dic6—22no—
186C3×Dic6—21no—
187C3×Dic6—22no—
188C3×Dic6—42no—
189C32×C8—21no—
190C32×C8—21no—
191C32×C8—22no—
192#556—31no—
193#547—31no—
194#487—31no—
195#485—32no—
196#474—31no—
197#467—32no—
198#462—31no—
199#452—32no—
200C4×SD16—31no—
201C8×D4C3×D311yescharacteristic, complemented
202#416—32no—
203C3×#41—64no—
204C3×#41—122no—
205C2×C3×Q8—32no—
206C2×C3×Q8—31no—
207C2×C3×Q8—61no—
208C2×C3×D4—21no—
209C2×C3×D4—31no—
210C2×C3×D4—62no—
211C2×C3×D4D1211yescharacteristic
212C2×C3×D4C3×D411yescharacteristic
213C22×C3×C4—22no—
214C22×C3×C4—61no—
215C22×C3×C4—62no—
216C22×C3×C4C22×D312yes—
217C22×C3×C4C23×C312yes—
218C2×#67—22no—
219#235—24no—
220#235—42no—
221C2×D12C23×C311yescharacteristic
222C2×C4×D3—21no—
223C2×C4×D3—22no—
224C2×Dic6—21no—
225C2×Dic6C23×C312yes—
226C2×Dic6C23×C311yescharacteristic
227C3×Q16—122no—
228C3×SD16—62no—
229C2×C3×C8—21no—
230C2×C3×C8—21no—
231C2×C3×C8—22no—
232C2×C3×C8—42no—
233C2×C3×C8—42no—
234C2×C3×C8—44no—
235C2×C3×C8C22×D311yescharacteristic
236C2×C3×C8C22×D311yescharacteristic
237C2×C3×C8C22×D312yes—
238C2×C3×C8C23×C311yescharacteristic
239C2×C3×C8C23×C311yescharacteristic
240C2×C3×C8C23×C312yes—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—32no—
244C3×C4⋊C4—31no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4—62no—
248C3×C4⋊C4—61no—
249C3×C4⋊C4—61no—
250C3×C4⋊C4—61no—
251C3×C4⋊C4D1211yescharacteristic
252C3×C4⋊C4C3×D411yescharacteristic
253C3×C22⋊C4—22no—
254C3×C22⋊C4—62no—
255C3×C22⋊C4—62no—
256C3×C22⋊C4—62no—
257C3×C22⋊C4—61no—
258C3×C22⋊C4D1212yes—
259C3×C22⋊C4C3×D412yes—
260C3×C42—21no—
261C3×C42—62no—
262C3×C42—61no—
263C3×C42C22×D311yescharacteristic
264C3×C42C23×C311yescharacteristic
265#217—22no—
266#217—22no—
267#217—22no—
268(C2×D3)⋊C4—21no—
269C4⋊Dic3—21no—
270C4⋊Dic3—21no—
271C4⋊Dic3—21no—
272C4⋊Dic3C23×C311yescharacteristic
273C4⋊Dic3C23×C312yes—
274C4⋊Dic3C23×C311yescharacteristic
275Dic3⋊C4—21no—
276Dic3⋊C4—22no—
277Dic3⋊C4—22no—
278C4×Dic3—21no—
279C4×Dic3—22no—
280Dic12—42no—
281#204—22no—
282C22×C32—22no—
283C22×C32—22no—
284C22×C32—22no—
285C22×C32C22×D411yescharacteristic
286C2×C3×D3—22no—
287C2×C3×D3—41no—
288C2×C3×D3—41no—
289C32×C4—22no—
290C32×C4—21no—
291C32×C4#13512yes—
292C32×C4C2×#4111yescharacteristic
293C32×C4H(5,𝔽2)11yescharacteristic
294C3×Dic3—42no—
295C3×Dic3—41no—
296C3×Dic3—42no—
297C3×Dic3—41no—
298C3×Dic3—41no—
299C2×#41—32no—
300C2×Q16—32no—
301C2×SD16—31no—
302C22×C8C2×C3×D312yes—
303C4⋊Q8—31no—
304C4⋊Q8—31no—
305#126—62no—
306#124—61no—
307#123—62no—
308C22⋊Q8—32no—
309C22⋊Q8—32no—
310#121—61no—
311C4×Q8—31no—
312C4×Q8—61no—
313C4×D4—31no—
314C4×D4C2×C3×D311yescharacteristic
315#117—32no—
316C2×C4⋊C4—61no—
317#107—32no—
318#106—31no—
319C4⋊C8C2×C3×D311yescharacteristic
320#103—32no—
321#103—32no—
322#103—31no—
323#103—32no—
324#102—31no—
325#102—32no—
326C22⋊C8C2×C3×D312yes—
327C4×C8C2×C3×D311yescharacteristic
328C23×C3—22no—
329C23×C3—61no—
330C23×C3C2×D1212yes—
331C23×C3C2×C3×D412yes—
332C22×D3—21no—
333C3×Q8—61no—
334C3×Q8—62no—
335C3×Q8—61no—
336C3×Q8—62no—
337C3×Q8—122no—
338C3×D4—24no—
339C3×D4—22no—
340C3×D4—22no—
341C3×D4—32no—
342C3×D4—61no—
343C3×D4—124no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—22no—
352C2×C3×C4—42no—
353C2×C3×C4—42no—
354C2×C3×C4—61no—
355C2×C3×C4—62no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
358C2×C3×C4—62no—
359C2×C3×C4—124no—
360C2×C3×C4—122no—
361C2×C3×C4C2×D1212yes—
362C2×C3×C4C2×D1211yescharacteristic
363C2×C3×C4C2×D1211yescharacteristic
364C2×C3×C4C2×C3×D412yes—
365C2×C3×C4C2×C3×D411yescharacteristic
366C2×C3×C4C2×C3×D411yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368C2×C3×C4C24×C311yescharacteristic
369#67—44no—
370C2×Dic3—21no—
371C2×Dic3—21no—
372C2×Dic3—22no—
373C2×Dic3—21no—
374C2×Dic3—22no—
375D12—21no—
376D12C3×#4112yes—
377C4×D3—44no—
378C4×D3—42no—
379Dic6—21no—
380Dic6—22no—
381Dic6—21no—
382Dic6—22no—
383Dic6—42no—
384C3×C8—22no—
385C3×C8—21no—
386C3×C8—22no—
387C3×C8—21no—
388C3×C8—21no—
389C3×C8—22no—
390C3×C8—21no—
391C3×C8—41no—
392C3×C8—42no—
393C2×C32—42no—
394C2×C32#54611yescharacteristic
395C2×C32C2×#13511yescharacteristic
396C2×C32#57811yescharacteristic
397C3×D3—42no—
398#41—64no—
399#41—122no—
400C2×Q8—32no—
401C2×Q8—31no—
402C2×Q8—61no—
403C2×D4—31no—
404C2×D4—62no—
405C2×D4C3×D1211yescharacteristic
406C22×C4—61no—
407C22×C4—62no—
408C22×C4C22×C3×D312yes—
409Q16—122no—
410SD16—62no—
411C2×C8—42no—
412C2×C8C22×C3×D311yescharacteristic
413C2×C8C22×C3×D311yescharacteristic
414C2×C8C22×C3×D312yes—
415C4⋊C4—31no—
416C4⋊C4—32no—
417C4⋊C4—31no—
418C4⋊C4—61no—
419C4⋊C4—62no—
420C4⋊C4—61no—
421C4⋊C4—62no—
422C4⋊C4—61no—
423C4⋊C4—61no—
424C4⋊C4C3×D1211yescharacteristic
425C22⋊C4—62no—
426C22⋊C4—62no—
427C22⋊C4—62no—
428C22⋊C4—61no—
429C22⋊C4C3×D1212yes—
430C42—62no—
431C42—61no—
432C42C22×C3×D311yescharacteristic
433C22×C3—24no—
434C22×C3—22no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—22no—
438C22×C3—22no—
439C22×C3—22no—
440C22×C3—21no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—62no—
444C22×C3—121no—
445C22×C3—121no—
446C22×C3C22×D1211yescharacteristic
447C22×C3C22×C3×D411yescharacteristic
448C2×D3—22no—
449C2×D3—41no—
450C2×D3—41no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—22no—
454C3×C4—22no—
455C3×C4—22no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—42no—
459C3×C4—41no—
460C3×C4—121no—
461C3×C4—122no—
462C3×C4—121no—
463C3×C4—122no—
464C3×C4—121no—
465C3×C4#90412yes—
466C3×C4C3×#13512yes—
467C3×C4#100411yescharacteristic
468C3×C4D3×#4111yescharacteristic
469C3×C4C2×C3×#4111yescharacteristic
470C3×C4C3×H(5,𝔽2)11yescharacteristic
471Dic3—42no—
472Dic3—41no—
473Dic3—41no—
474Dic3—42no—
475Dic3—41no—
476C32#330211yescharacteristic, complemented, Sylow
477C23—61no—
478C23C2×C3×D1212yes—
479Q8—61no—
480Q8—62no—
481Q8—61no—
482Q8—62no—
483Q8—122no—
484D4—22no—
485D4—32no—
486D4—61no—
487D4—124no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—61no—
491C2×C4—62no—
492C2×C4—61no—
493C2×C4—61no—
494C2×C4—62no—
495C2×C4—124no—
496C2×C4—122no—
497C2×C4C2×C3×D1212yes—
498C2×C4C2×C3×D1211yescharacteristic
499C2×C4C2×C3×D1211yescharacteristic
500C2×C4C23×C3×D311yescharacteristic
501C8—21no—
502C8—22no—
503C8—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—44no—
508C2×C3—42no—
509C2×C3—42no—
510C2×C3—122no—
511C2×C3#555411yescharacteristic
512C2×C3C2×#90411yescharacteristic
513C2×C3#575311yescharacteristic
514C2×C3C3×#54611yescharacteristic
515C2×C3C2×C3×#13511yescharacteristic
516C2×C3C3×#57811yescharacteristic
517D3—42no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—62no—
522C22—121no—
523C22—121no—
524C22C22×C3×D1211yescharacteristic
525C4—21no—
526C4—22no—
527C4—121no—
528C4—122no—
529C4—121no—
530C4—121no—
531C4—122no—
532C4C3×#90412yes—
533C4C3×#100411yescharacteristic
534C4C3×D3×#4111yescharacteristic
535C3—21no—
536C3#7944211yescharacteristic, direct product factor
537C3C3×#330211yescharacteristic, complemented
538C2—42no—
539C2—122no—
540C2C3×#555411yescharacteristic
541C2C2×C3×#90411yescharacteristic
542C2C3×#575311yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C8×D4C2
socleC22×C32C22×D4
prime radicalC3×#5551C2
hypercenterC3×C8×D4D3
hypocenterC3C3×#3302
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×#5542C2semidirect
3. C32×C8×D4C2semidirect
4. C3×#5116C2semidirect
5. C3×#5113C2semidirect
6. C3×#4849C2semidirect
7. C3×#4846C2semidirect
8. C3×#4733C2semidirect
9. C3×#4723C2semidirect
10. C3×C4×#204C2semidirect
11. C3×#4681C2semidirect
13. #79442C3direct (N × H)
46. #5542C2×C3semidirect
55. C3×C8×D4D3semidirect
56. C3×C8×D4C2×C3semidirect
58. #5116C2×C3semidirect
59. #5113C2×C3semidirect
60. #4849C2×C3semidirect
61. #4846C2×C3semidirect
62. #4733C2×C3semidirect
63. #4723C2×C3semidirect
64. C4×#204C2×C3semidirect
65. #4681C2×C3semidirect
201. C8×D4C3×D3semidirect
476. C32#3302semidirect
536. C3#79442direct (N × H)
537. C3C3×#3302semidirect

Maximal subgroups

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

subgroupindex
C3×#55512
C3×#55422
C32×C8×D42
C3×#51162
C3×#51132
C3×#48492
C3×#48462
C3×#47332
C3×#47232
C3×C4×#2042
C3×#46812
C3×#33023
#794423