Finite Group Databasebeta

← C3×#79256 #11868018

Subgroups — C3×#79256 #11868018

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5748C212yesmaximal, complemented
2C2×C3×#904C211yesmaximal, characteristic, complemented
3C2×C3×#901C211yesmaximal, characteristic, complemented
4C2×C32×#108C211yesmaximal, characteristic, complemented
5C3×#5132C212yesmaximal, complemented
6C3×#4898C214yesmaximal, complemented
7C3×#4897C212yesmaximal, complemented
8C3×#4896C212yesmaximal, complemented
9C3×#3067—31nomaximal
10#79256C311yesmaximal, characteristic, direct product factor
11C2×C3×#235C2211yescharacteristic
12C2×C3×#235C2212yes—
13C2×C32×M16C2212yes—
14C22×C32×C8C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C3×#909—22no—
17C3×#909C2214yes—
18C3×#908—22no—
19C3×#908C2214yes—
20C2×C3×Dic12C2211yescharacteristic, complemented
21C3×#904—24no—
22C3×#904—21no—
23C3×#904—21no—
24C3×#904—21no—
25C3×#904—21no—
26C2×C3×D24C2211yescharacteristic, complemented
27C2×C3×#204C2212yescomplemented
28C3×#901—21no—
29C3×#901—21no—
30C3×#901C2212yes—
31C3×#901C2212yes—
32C2×C3×ΓL(1,𝔽25)—21no—
33C2×C3×D3×C8—21no—
34C32×#108C2212yescomplemented
35C32×#108C2212yescomplemented
36C3×#824C2214yescomplemented
37C3×#823C2214yescomplemented
38C3×#575—32no—
39C2×C3×#135—31no—
40C2×C3×#131—31no—
41#5748C2×C312yescomplemented
42C2×#904C2×C311yescharacteristic, complemented
43C2×#901C2×C311yescharacteristic, complemented
44C3×#473—32no—
45C3×#472—32no—
46C3×#471—34no—
47C2×C3×#108—21no—
48C2×C3×#108D311yescharacteristic, complemented
49C2×C3×#108C2×C311yescharacteristic, complemented
50C3×#413—32no—
51#5132C2×C312yescomplemented
52#4898C2×C314yescomplemented
53#4897C2×C312yescomplemented
54#4896C2×C312yescomplemented
55C22×C32×C4C2311yescharacteristic
56C2×C3×#67—21no—
57C2×C3×#67—22no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—22no—
61C3×#235—22no—
62C3×#235—22no—
63C3×#235—22no—
64C3×#235D412yes—
65C3×#235C2312yes—
66C2×C3×D12D411yescharacteristic
67C2×C3×D12C2312yes—
68C2×C3×C4×D3—21no—
69C2×C3×C4×D3—22no—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6C2312yes—
72C32×M16—22no—
73C32×M16C2314yes—
74C2×C32×C8—22no—
75C2×C32×C8D411yescharacteristic
76C2×C32×C8D411yescharacteristic
77C2×C32×C8D411yescharacteristic
78C2×C32×C8D411yescharacteristic
79C2×C32×C8C2311yescharacteristic
80C2×C32×C8C2311yescharacteristic
81C3×#208—21no—
82C3×#208C2312yes—
83C2×C3×C3⋊C8—21no—
84C3×Dic12—24no—
85C3×Dic12—21no—
86C3×Dic12—21no—
87C3×D24—24no—
88C3×D24—21no—
89C3×D24—21no—
90C3×#204—24no—
91C3×#204—24no—
92C3×#204—22no—
93C3×#204—22no—
94C3×ΓL(1,𝔽25)—22no—
95C3×ΓL(1,𝔽25)—22no—
96C3×D3×C8—22no—
97C3×D3×C8—22no—
98#3067—31noSylow
99C2×C3×#41—31no—
100C2×C3×#41—32no—
101C2×#235C22×C311yescharacteristic
102C2×#235C22×C312yes—
103C3×#137—34no—
104C3×#137—62no—
105C3×AGL(1,ℤ/8)—34no—
106C3×AGL(1,ℤ/8)—62no—
107C3×#135—64no—
108C3×#135—61no—
109C3×#135—61no—
110C3×#135—61no—
111C3×#135—61no—
112C2×C3×Q16—31no—
113C2×C3×SD16—32no—
114C2×C3×D8—31no—
115C3×#131—32no—
116C3×#131—32no—
117C3×#131—61no—
118C3×#131—61no—
119C2×C3×M16—22no—
120C2×C3×M16—31no—
121C2×C3×M16—61no—
122C2×C3×M16C2×D312yes—
123C2×C3×M16C22×C312yes—
124C22×C3×C8—21no—
125C22×C3×C8—61no—
126C22×C3×C8C2×D311yescharacteristic
127C22×C3×C8C22×C311yescharacteristic
128C2×#208C22×C311yescharacteristic
129#909—22no—
130#909C22×C314yes—
131#908—22no—
132#908C22×C314yes—
133C2×Dic12C22×C311yescharacteristic, complemented
134#904—24no—
135#904—21no—
136#904—21no—
137#904—21no—
138#904—21no—
139C2×D24C22×C311yescharacteristic, complemented
140C2×#204C22×C312yescomplemented
141#901—21no—
142#901—21no—
143#901C22×C312yes—
144#901C22×C312yes—
145C2×ΓL(1,𝔽25)—21no—
146C2×D3×C8—21no—
147C3×#108—22no—
148C3×#108—22no—
149C3×#108C2×D312yescomplemented
150C3×#108C2×D312yescomplemented
151C3×#108C22×C312yescomplemented
152C3×#108C22×C312yescomplemented
153C3×#101—34no—
154C3×#100—34no—
155#824C22×C314yescomplemented
156#823C22×C314yescomplemented
157C23×C32#4111yescharacteristic
158C22×C3×D3—21no—
159C22×C3×D3—22no—
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4#4111yescharacteristic
165C2×C32×C4C2411yescharacteristic
166C3×#67—22no—
167C3×#67—22no—
168C3×#67—42no—
169C3×#67—42no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—22no—
172C3×D12—21no—
173C3×D12—22no—
174C3×D12—22no—
175C3×D12C2×D412yes—
176C3×C4×D3—22no—
177C3×C4×D3—22no—
178C3×C4×D3—42no—
179C3×C4×D3—42no—
180C3×Dic6—21no—
181C3×Dic6—22no—
182C3×Dic6—22no—
183C3×Dic6C2×D412yes—
184C32×C8—24no—
185C32×C8C2×D411yescharacteristic
186C32×C8C2×D411yescharacteristic
187C32×C8C2×D411yescharacteristic
188C32×C8C2×D411yescharacteristic
189C3×C3⋊C8—22no—
190#575—32no—
191C2×#135—31no—
192C2×#131—31no—
193#473—32no—
194#472—32no—
195#471—34no—
196C2×#108C3×D311yescharacteristic, complemented
197#413—32no—
198C3×#41—32no—
199C3×#41—32no—
200C3×#41—61no—
201C3×#41—61no—
202C3×#41—62no—
203C3×#41—62no—
204C3×#41—62no—
205C3×#41—62no—
206C2×C3×Q8—31no—
207C2×C3×Q8—32no—
208C2×C3×D4—31no—
209C2×C3×D4—32no—
210C2×C3×D4—61no—
211C2×C3×D4—62no—
212C22×C3×C4—21no—
213C22×C3×C4—61no—
214C22×C3×C4—62no—
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C23×C311yescharacteristic
217C2×#67—21no—
218C2×#67—22no—
219#235—21no—
220#235—21no—
221#235—22no—
222#235—22no—
223#235—22no—
224#235—22no—
225#235C3×D412yes—
226#235C23×C312yes—
227C2×D12C3×D411yescharacteristic
228C2×D12C23×C312yes—
229C2×C4×D3—21no—
230C2×C4×D3—22no—
231C2×Dic6C3×D411yescharacteristic
232C2×Dic6C23×C312yes—
233C3×Q16—64no—
234C3×Q16—61no—
235C3×Q16—61no—
236C3×SD16—64no—
237C3×SD16—64no—
238C3×SD16—62no—
239C3×SD16—62no—
240C3×D8—64no—
241C3×D8—61no—
242C3×D8—61no—
243C3×M16—22no—
244C3×M16—22no—
245C3×M16—24no—
246C3×M16—32no—
247C3×M16—42no—
248C3×M16—61no—
249C3×M16—62no—
250C3×M16—62no—
251C3×M16C22×D314yes—
252C3×M16C23×C314yes—
253C2×C3×C8—22no—
254C2×C3×C8—22no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8—42no—
262C2×C3×C8—61no—
263C2×C3×C8—62no—
264C2×C3×C8—62no—
265C2×C3×C8D1211yescharacteristic
266C2×C3×C8D1211yescharacteristic
267C2×C3×C8D1211yescharacteristic
268C2×C3×C8D1211yescharacteristic
269C2×C3×C8C3×D411yescharacteristic
270C2×C3×C8C3×D411yescharacteristic
271C2×C3×C8C3×D411yescharacteristic
272C2×C3×C8C3×D411yescharacteristic
273C2×C3×C8C22×D311yescharacteristic
274C2×C3×C8C22×D311yescharacteristic
275C2×C3×C8C23×C311yescharacteristic
276C2×C3×C8C23×C311yescharacteristic
277#208—21no—
278#208C23×C312yes—
279C2×C3⋊C8—21no—
280Dic12—24no—
281Dic12—21no—
282Dic12—21no—
283D24—24no—
284D24—21no—
285D24—21no—
286#204—24no—
287#204—24no—
288#204—22no—
289#204—22no—
290ΓL(1,𝔽25)—22no—
291ΓL(1,𝔽25)—22no—
292D3×C8—22no—
293D3×C8—22no—
294C22×C32—41no—
295C22×C32#12111yescharacteristic
296C22×C32#12111yescharacteristic
297C22×C32C2×#4111yescharacteristic
298C2×C3×D3—22no—
299C2×C3×D3—42no—
300C2×C3×D3—42no—
301C2×C3×D3—82no—
302C32×C4#12111yescharacteristic
303C32×C4#12111yescharacteristic
304C32×C4C22×D411yescharacteristic
305C32×C4C22×D411yescharacteristic
306C3×Dic3—22no—
307C3×Dic3—42no—
308C2×#41—31no—
309C2×#41—32no—
310#137—34no—
311#137—62no—
312AGL(1,ℤ/8)—34no—
313AGL(1,ℤ/8)—62no—
314#135—64no—
315#135—61no—
316#135—61no—
317#135—61no—
318#135—61no—
319C2×Q16—31no—
320C2×SD16—32no—
321C2×D8—31no—
322#131—32no—
323#131—32no—
324#131—61no—
325#131—61no—
326C2×M16—31no—
327C2×M16—61no—
328C2×M16C2×C3×D312yes—
329C22×C8—61no—
330C22×C8C2×C3×D311yescharacteristic
331#108C2×C3×D312yescomplemented
332#108C2×C3×D312yescomplemented
333#101—34no—
334#100—34no—
335C23×C3—21no—
336C23×C3—61no—
337C23×C3—62no—
338C23×C3#23911yescharacteristic
339C23×C3C3×#4111yescharacteristic
340C22×D3—21no—
341C22×D3—22no—
342C3×Q8—32no—
343C3×Q8—61no—
344C3×Q8—62no—
345C3×Q8—62no—
346C3×D4—32no—
347C3×D4—62no—
348C3×D4—62no—
349C3×D4—61no—
350C3×D4—62no—
351C3×D4—62no—
352C3×D4—122no—
353C3×D4—122no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—61no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—122no—
365C2×C3×C4—122no—
366C2×C3×C4C2×D1211yescharacteristic
367C2×C3×C4C2×D1211yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4#23911yescharacteristic
371C2×C3×C4C2×C3×D411yescharacteristic
372C2×C3×C4C2×C3×D411yescharacteristic
373C2×C3×C4C2×C3×D411yescharacteristic
374C2×C3×C4C2×C3×D411yescharacteristic
375C2×C3×C4C3×#4111yescharacteristic
376C2×C3×C4C23×D311yescharacteristic
377C2×C3×C4C24×C311yescharacteristic
378#67—22no—
379#67—22no—
380#67—42no—
381#67—42no—
382C2×Dic3—21no—
383C2×Dic3—22no—
384D12—21no—
385D12—22no—
386D12—22no—
387D12C2×C3×D412yes—
388C4×D3—22no—
389C4×D3—22no—
390C4×D3—42no—
391C4×D3—42no—
392Dic6—21no—
393Dic6—22no—
394Dic6—22no—
395Dic6C2×C3×D412yes—
396C3×C8—24no—
397C3×C8—24no—
398C3×C8—21no—
399C3×C8—21no—
400C3×C8—21no—
401C3×C8—21no—
402C3×C8—44no—
403C3×C8—62no—
404C3×C8C2×D1211yescharacteristic
405C3×C8C2×D1211yescharacteristic
406C3×C8C2×D1211yescharacteristic
407C3×C8C2×D1211yescharacteristic
408C3×C8C2×C3×D411yescharacteristic
409C3×C8C2×C3×D411yescharacteristic
410C3×C8C2×C3×D411yescharacteristic
411C3×C8C2×C3×D411yescharacteristic
412C3⋊C8—22no—
413C2×C32—21no—
414C2×C32—21no—
415C2×C32—21no—
416C2×C32C2×#12111yescharacteristic
417C3×D3—42no—
418C3×D3—82no—
419#41—32no—
420#41—32no—
421#41—61no—
422#41—61no—
423#41—62no—
424#41—62no—
425#41—62no—
426#41—62no—
427C2×Q8—32no—
428C2×Q8—31no—
429C2×D4—32no—
430C2×D4—31no—
431C2×D4—61no—
432C2×D4—62no—
433C22×C4—61no—
434C22×C4—62no—
435C22×C4C22×C3×D311yescharacteristic
436Q16—64no—
437Q16—61no—
438Q16—61no—
439SD16—64no—
440SD16—64no—
441SD16—62no—
442SD16—62no—
443D8—64no—
444D8—61no—
445D8—61no—
446M16—22no—
447M16—32no—
448M16—61no—
449M16—62no—
450M16—62no—
451M16C22×C3×D314yes—
452C2×C8—22no—
453C2×C8—61no—
454C2×C8—62no—
455C2×C8—62no—
456C2×C8C3×D1211yescharacteristic
457C2×C8C3×D1211yescharacteristic
458C2×C8C3×D1211yescharacteristic
459C2×C8C3×D1211yescharacteristic
460C2×C8C22×C3×D311yescharacteristic
461C2×C8C22×C3×D311yescharacteristic
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—41no—
466C22×C3—41no—
467C22×C3—42no—
468C22×C3—62no—
469C22×C3—122no—
470C22×C3—122no—
471C22×C3—242no—
472C22×C3#89511yescharacteristic
473C22×C3#89511yescharacteristic
474C22×C3C3×#12111yescharacteristic
475C22×C3C3×#12111yescharacteristic
476C22×C3C2×#23911yescharacteristic
477C22×C3C2×C3×#4111yescharacteristic
478C2×D3—22no—
479C2×D3—42no—
480C2×D3—42no—
481C2×D3—82no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—62no—
487C3×C4—122no—
488C3×C4#89511yescharacteristic
489C3×C4#89511yescharacteristic
490C3×C4C3×#12111yescharacteristic
491C3×C4C3×#12111yescharacteristic
492C3×C4C22×D1211yescharacteristic
493C3×C4C2×D3×D411yescharacteristic
494C3×C4C22×C3×D411yescharacteristic
495C3×C4C22×C3×D411yescharacteristic
496Dic3—22no—
497Dic3—42no—
498C32#306711yescharacteristic, complemented, Sylow
499C23—61no—
500C23—62no—
501C23C3×#23911yescharacteristic
502Q8—32no—
503Q8—61no—
504Q8—62no—
505Q8—62no—
506D4—32no—
507D4—62no—
508D4—62no—
509D4—61no—
510D4—62no—
511D4—62no—
512D4—122no—
513D4—122no—
514C2×C4—61no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—122no—
519C2×C4—122no—
520C2×C4C2×C3×D1211yescharacteristic
521C2×C4C2×C3×D1211yescharacteristic
522C2×C4C3×D3×D411yescharacteristic
523C2×C4C3×D3×D411yescharacteristic
524C2×C4C3×#23911yescharacteristic
525C2×C4C23×C3×D311yescharacteristic
526C8—24no—
527C8—62no—
528C8C2×C3×D1211yescharacteristic
529C8C2×C3×D1211yescharacteristic
530C8C2×C3×D1211yescharacteristic
531C8C2×C3×D1211yescharacteristic
532C2×C3—22no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—41no—
541C2×C3—41no—
542C2×C3—122no—
543C2×C3—242no—
544C2×C3C2×#89511yescharacteristic
545C2×C3C2×C3×#12111yescharacteristic
546D3—42no—
547D3—82no—
548C22—41no—
549C22—62no—
550C22—122no—
551C22—122no—
552C22—242no—
553C22C3×#89511yescharacteristic
554C22C3×#89511yescharacteristic
555C22C2×C3×#23911yescharacteristic
556C4—62no—
557C4—122no—
558C4C3×#89511yescharacteristic
559C4C3×#89511yescharacteristic
560C4C22×C3×D1211yescharacteristic
561C4C2×C3×D3×D411yescharacteristic
562C3—21no—
563C3#7925611yescharacteristic, direct product factor
564C3C3×#306711yescharacteristic, complemented
565C2—21no—
566C2—21no—
567C2—21no—
568C2—122no—
569C2—242no—
570C2C2×C3×#89511yescharacteristic
subgroupG/H
centerC3×C4#895
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#108C2
socleC2×C32C2×#121
hypercenterC2×C3×#108D3
hypocenterC3C3×#3067
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#108

Complements

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

NH ≅ G/Ntype
1. C3×#5748C2semidirect
2. C2×C3×#904C2semidirect
3. C2×C3×#901C2semidirect
4. C2×C32×#108C2semidirect
5. C3×#5132C2semidirect
6. C3×#4898C2semidirect
7. C3×#4897C2semidirect
8. C3×#4896C2semidirect
10. #79256C3direct (N × H)
20. C2×C3×Dic12C22semidirect
26. C2×C3×D24C22semidirect
27. C2×C3×#204C22semidirect
34. C32×#108C22semidirect
35. C32×#108C22semidirect
36. C3×#824C22semidirect
37. C3×#823C22semidirect
41. #5748C2×C3semidirect
42. C2×#904C2×C3semidirect
43. C2×#901C2×C3semidirect
48. C2×C3×#108D3semidirect
49. C2×C3×#108C2×C3semidirect
51. #5132C2×C3semidirect
52. #4898C2×C3semidirect
53. #4897C2×C3semidirect
54. #4896C2×C3semidirect
133. C2×Dic12C22×C3semidirect
139. C2×D24C22×C3semidirect
140. C2×#204C22×C3semidirect
149. C3×#108C2×D3semidirect
150. C3×#108C2×D3semidirect
151. C3×#108C22×C3semidirect
152. C3×#108C22×C3semidirect
155. #824C22×C3semidirect
156. #823C22×C3semidirect
196. C2×#108C3×D3semidirect
331. #108C2×C3×D3semidirect
332. #108C2×C3×D3semidirect
498. C32#3067semidirect
563. C3#79256direct (N × H)
564. C3C3×#3067semidirect

Maximal subgroups

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

subgroupindex
C3×#57482
C2×C3×#9042
C2×C3×#9012
C2×C32×#1082
C3×#51322
C3×#48982
C3×#48972
C3×#48962
C3×#30673
#792563