Finite Group Databasebeta

← C3×#33063 #10651670

Subgroups — C3×#33063 #10651670

Order 768.

772 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#489C211yesmaximal, characteristic, complemented
2C3×#3079C211yesmaximal, characteristic, complemented
3C3×#3040C211yesmaximal, characteristic
4C3×#2875C211yesmaximal, characteristic, complemented
5C3×#1997C211yesmaximal, characteristic, complemented
6C3×#1967C211yesmaximal, characteristic, complemented
7C3×#1931C212yesmaximal, complemented
8C3×#1930C212yesmaximal, complemented
9C3×#1908C212yesmaximal, complemented
10C3×#1907C212yesmaximal
11C3×#1838C211yesmaximal, characteristic, complemented
12#33063C311yesmaximal, characteristic, direct product factor, Sylow
13C2×C3×#137C2211yescharacteristic
14C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
15C2×C3×#131C2212yes—
16C2×C3×C4⋊Q8C2211yescharacteristic
17C2×C3×#124C2211yescharacteristic
18C3×C4×#41C2211yescharacteristic
19C3×#489—21no—
20C3×#489—21no—
21C3×#489—22no—
22C3×#477—21no—
23C3×#476—21no—
24C3×#475—21no—
25C3×#474—21no—
26C3×#464—21no—
27C3×#464—21no—
28C3×#463—21no—
29C3×#463—21no—
30C3×#428C2212yes—
31C3×#423C2211yescharacteristic
32C3×#423C2211yescharacteristic
33C3×#419C2211yescharacteristic
34C3×#418C2211yescharacteristic
35C3×#417C2212yes—
36C2×C3×#103C2212yes—
37C2×C3×#102C2212yes—
38C2×C3×#101C2212yes—
39C2×C3×#100C2212yes—
40C3×#405—22no—
41C3×#405C2212yes—
42C3×C4×M16—21no—
43C3×C4×M16C2211yescharacteristic
44C2×C3×#97—21no—
45C2×C3×#97C2211yescharacteristic
46C3×#343C2212yes—
47C3×#343C2212yes—
48C3×#341C2212yes—
49C3×#341C2212yes—
50C2×#489C2×C311yescharacteristic, complemented
51#3079C2×C311yescharacteristic, complemented
52#3040C2×C311yescharacteristic
53#2875C2×C311yescharacteristic, complemented
54#1997C2×C311yescharacteristic, complemented
55#1967C2×C311yescharacteristic, complemented
56#1931C2×C312yescomplemented
57#1930C2×C312yescomplemented
58#1908C2×C312yescomplemented
59#1907C2×C312yes—
60#1838C2×C311yescharacteristic, complemented
61C2×C3×#41C2311yescharacteristic
62C22×C3×Q8—21no—
63C22×C3×Q8C2311yescharacteristic
64C22×C3×D4C2311yescharacteristic
65C3×#137—24no—
66C3×AGL(1,ℤ/8)—24no—
67C2×C3×Q16—21no—
68C2×C3×SD16—21no—
69C2×C3×SD16—21no—
70C2×C3×D8—21no—
71C3×#131—24no—
72C3×#131—24no—
73C2×C3×M16—22no—
74C2×C3×M16C2311yescharacteristic
75C2×C3×M16C2311yescharacteristic
76C2×C3×M16C2312yes—
77C2×C3×M16C2312yes—
78C22×C3×C8—22no—
79C22×C3×C8C2312yes—
80C3×C4⋊Q8—21no—
81C3×C4⋊Q8—21no—
82C3×C4⋊Q8—21no—
83C3×C4⋊Q8—21no—
84C3×#124—21no—
85C3×#124—21no—
86C3×#124—21no—
87C3×#124—21no—
88C3×C4×Q8D411yescharacteristic
89C3×C4×Q8D411yescharacteristic
90C3×C4×D4—21no—
91C3×C4×D4—21no—
92C3×C4×D4D411yescharacteristic
93C3×C4×D4D411yescharacteristic
94C3×#117—21no—
95C3×#117C2311yescharacteristic
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4C2312yes—
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×C3×C42—21no—
101C2×C3×C42C2311yescharacteristic
102C3×#107—22no—
103C3×#106—22no—
104C3×C4⋊C8—21no—
105C3×C4⋊C8—21no—
106C3×C4⋊C8—21no—
107C3×C4⋊C8—21no—
108C3×#103—22no—
109C3×#103—22no—
110C3×#103—22no—
111C3×#103—21no—
112C3×#103—21no—
113C3×#102—22no—
114C3×#102—22no—
115C3×#102—22no—
116C3×#102—21no—
117C3×#102—21no—
118C3×#101—24no—
119C3×#100—24no—
120C3×#97—22no—
121C3×#97—21no—
122C3×#97D411yescharacteristic
123C3×#97D411yescharacteristic
124C3×#97D412yes—
125C3×C4×C8—22no—
126C3×C4×C8—21no—
127C2×#137C22×C311yescharacteristic
128C2×AGL(1,ℤ/8)C22×C311yescharacteristic
129C2×#131C22×C312yes—
130C2×C4⋊Q8C22×C311yescharacteristic
131C2×#124C22×C311yescharacteristic
132C4×#41C22×C311yescharacteristic
133#489—21no—
134#489—21no—
135#489—22no—
136#477—21no—
137#476—21no—
138#475—21no—
139#474—21no—
140#464—21no—
141#464—21no—
142#463—21no—
143#463—21no—
144#428C22×C312yes—
145#423C22×C311yescharacteristic
146#423C22×C311yescharacteristic
147#419C22×C311yescharacteristic
148#418C22×C311yescharacteristic
149#417C22×C312yes—
150C2×#103C22×C312yes—
151C2×#102C22×C312yes—
152C2×#101C22×C312yes—
153C2×#100C22×C312yes—
154#405—22no—
155#405C22×C312yes—
156C4×M16—21no—
157C4×M16C22×C311yescharacteristic
158C2×#97—21no—
159C2×#97C22×C311yescharacteristic
160#343C22×C312yes—
161#343C22×C312yes—
162#341C22×C312yes—
163#341C22×C312yes—
164C24×C3—21no—
165C3×#41—22no—
166C3×#41#4114yes—
167C2×C3×Q8—21no—
168C2×C3×Q8—21no—
169C2×C3×Q8—22no—
170C2×C3×Q8—22no—
171C2×C3×Q8—41no—
172C2×C3×Q8—41no—
173C2×C3×Q8—82no—
174C2×C3×Q8C2×D411yescharacteristic
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—22no—
179C2×C3×D4—22no—
180C2×C3×D4C2×D411yescharacteristic
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—22no—
186C22×C3×C4#4111yescharacteristic
187C22×C3×C4#4111yescharacteristic
188C22×C3×C4C2411yescharacteristic
189C3×Q16—42no—
190C3×SD16—42no—
191C3×SD16—42no—
192C3×D8—42no—
193C3×M16—28no—
194C3×M16—22no—
195C3×M16—22no—
196C3×M16—22no—
197C3×M16—22no—
198C3×M16—22no—
199C3×M16#4114yes—
200C2×C3×C8—28no—
201C2×C3×C8—22no—
202C2×C3×C8—22no—
203C2×C3×C8—22no—
204C2×C3×C8—21no—
205C2×C3×C8—22no—
206C2×C3×C8—21no—
207C2×C3×C8C2×D412yes—
208C2×C3×C8C2×D412yes—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—22no—
212C3×C4⋊C4—22no—
213C3×C4⋊C4—41no—
214C3×C4⋊C4—41no—
215C3×C4⋊C4C2×D411yescharacteristic
216C3×C4⋊C4C2×D411yescharacteristic
217C3×C22⋊C4—21no—
218C3×C22⋊C4—21no—
219C3×C22⋊C4—21no—
220C3×C22⋊C4—41no—
221C3×C22⋊C4—41no—
222C3×C22⋊C4—41no—
223C3×C22⋊C4—41no—
224C3×C42—21no—
225C3×C42—21no—
226C3×C42—21no—
227C3×C42C2×D411yescharacteristic
228C3×C42C2×D411yescharacteristic
229C3×C42C2×D411yescharacteristic
230C3×C42C2×D411yescharacteristic
231C2×#41C23×C311yescharacteristic
232C22×Q8—21no—
233C22×Q8C23×C311yescharacteristic
234C22×D4C23×C311yescharacteristic
235#137—24no—
236AGL(1,ℤ/8)—24no—
237C2×Q16—21no—
238C2×SD16—21no—
239C2×SD16—21no—
240C2×D8—21no—
241#131—24no—
242#131—24no—
243C2×M16—22no—
244C2×M16C23×C311yescharacteristic
245C2×M16C23×C311yescharacteristic
246C2×M16C23×C312yes—
247C2×M16C23×C312yes—
248C22×C8—22no—
249C22×C8C23×C312yes—
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254#124—21no—
255#124—21no—
256#124—21no—
257#124—21no—
258C4×Q8C3×D411yescharacteristic
259C4×Q8C3×D411yescharacteristic
260C4×D4—21no—
261C4×D4—21no—
262C4×D4C3×D411yescharacteristic
263C4×D4C3×D411yescharacteristic
264#117—21no—
265#117C23×C311yescharacteristic
266C2×C4⋊C4—21no—
267C2×C4⋊C4C23×C312yes—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C42—21no—
271C2×C42C23×C311yescharacteristic
272#107—22no—
273#106—22no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278#103—22no—
279#103—22no—
280#103—22no—
281#103—21no—
282#103—21no—
283#102—22no—
284#102—22no—
285#102—22no—
286#102—21no—
287#102—21no—
288#101—24no—
289#100—24no—
290#97—22no—
291#97—21no—
292#97C3×D411yescharacteristic
293#97C3×D411yescharacteristic
294#97C3×D412yes—
295C4×C8—22no—
296C4×C8—21no—
297C23×C3—21no—
298C23×C3—41no—
299C23×C3—42no—
300C23×C3—81no—
301C23×C3—81no—
302C23×C3C2×#4111yescharacteristic
303C3×Q8—21no—
304C3×Q8—42no—
305C3×Q8—41no—
306C3×Q8—41no—
307C3×Q8—82no—
308C3×Q8—82no—
309C3×Q8#12412yes—
310C3×D4—24no—
311C3×D4—21no—
312C3×D4—42no—
313C3×D4—41no—
314C3×D4—41no—
315C3×D4#12412yes—
316C2×C3×C4—21no—
317C2×C3×C4—24no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—42no—
324C2×C3×C4—42no—
325C2×C3×C4—81no—
326C2×C3×C4—81no—
327C2×C3×C4—82no—
328C2×C3×C4#12111yescharacteristic
329C2×C3×C4#12111yescharacteristic
330C2×C3×C4#12111yescharacteristic
331C2×C3×C4#12111yescharacteristic
332C2×C3×C4C22×D411yescharacteristic
333C2×C3×C4C22×D411yescharacteristic
334C2×C3×C4C2×#4112yes—
335C2×C3×C4C2×#4112yes—
336C3×C8—22no—
337C3×C8—24no—
338C3×C8—22no—
339C3×C8—41no—
340C3×C8—41no—
341C3×C8—42no—
342C24—21no—
343#41—22no—
344#41C3×#4114yes—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—41no—
350C2×Q8—41no—
351C2×Q8—82no—
352C2×Q8C2×C3×D411yescharacteristic
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4C2×C3×D411yescharacteristic
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4C3×#4111yescharacteristic
365C22×C4C3×#4111yescharacteristic
366C22×C4C24×C311yescharacteristic
367Q16—42no—
368SD16—42no—
369SD16—42no—
370D8—42no—
371M16—28no—
372M16—22no—
373M16—22no—
374M16—22no—
375M16—22no—
376M16—22no—
377M16C3×#4114yes—
378C2×C8—28no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—21no—
383C2×C8—22no—
384C2×C8—21no—
385C2×C8C2×C3×D412yes—
386C2×C8C2×C3×D412yes—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4C2×C3×D411yescharacteristic
394C4⋊C4C2×C3×D411yescharacteristic
395C22⋊C4—21no—
396C22⋊C4—21no—
397C22⋊C4—21no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C42—21no—
403C42—21no—
404C42—21no—
405C42C2×C3×D411yescharacteristic
406C42C2×C3×D411yescharacteristic
407C42C2×C3×D411yescharacteristic
408C42C2×C3×D411yescharacteristic
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—22no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—81no—
415C22×C3—81no—
416C22×C3—81no—
417C22×C3—162no—
418C22×C3C2×#12111yescharacteristic
419C22×C3#52912yes—
420C3×C4—22no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—41no—
426C3×C4—41no—
427C3×C4—81no—
428C3×C4—82no—
429C3×C4#52512yes—
430C3×C4C2×#12411yescharacteristic
431C3×C4#53211yescharacteristic
432C23—21no—
433C23—41no—
434C23—42no—
435C23—81no—
436C23—81no—
437C23C2×C3×#4111yescharacteristic
438Q8—21no—
439Q8—42no—
440Q8—41no—
441Q8—41no—
442Q8—82no—
443Q8—82no—
444Q8C3×#12412yes—
445D4—24no—
446D4—21no—
447D4—42no—
448D4—41no—
449D4—41no—
450D4C3×#12412yes—
451C2×C4—21no—
452C2×C4—24no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4—82no—
463C2×C4C3×#12111yescharacteristic
464C2×C4C3×#12111yescharacteristic
465C2×C4C3×#12111yescharacteristic
466C2×C4C3×#12111yescharacteristic
467C2×C4C22×C3×D411yescharacteristic
468C2×C4C22×C3×D411yescharacteristic
469C2×C4C2×C3×#4112yes—
470C2×C4C2×C3×#4112yes—
471C8—22no—
472C8—24no—
473C8—22no—
474C8—41no—
475C8—41no—
476C8—42no—
477C2×C3—22no—
478C2×C3—42no—
479C2×C3—161no—
480C2×C3#285011yescharacteristic
481C2×C3#306811yescharacteristic
482C2×C3#306911yescharacteristic
483C22—21no—
484C22—21no—
485C22—22no—
486C22—41no—
487C22—41no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22—162no—
492C22C2×C3×#12111yescharacteristic
493C22C3×#52912yes—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—22no—
499C4—41no—
500C4—41no—
501C4—82no—
502C4—81no—
503C4C3×#52512yes—
504C4C2×C3×#12411yescharacteristic
505C4C3×#53211yescharacteristic
506C3#3306311yescharacteristic, direct product factor, Sylow
507C2—22no—
508C2—42no—
509C2—161no—
510C2C3×#285011yescharacteristic
511C2C3×#306811yescharacteristic
512C2C3×#306911yescharacteristic
subgroupG/H
center, socleC22×C3C2×#121
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#489C2semidirect
2. C3×#3079C2semidirect
4. C3×#2875C2semidirect
5. C3×#1997C2semidirect
6. C3×#1967C2semidirect
7. C3×#1931C2semidirect
8. C3×#1930C2semidirect
9. C3×#1908C2semidirect
11. C3×#1838C2semidirect
12. #33063C3direct (N × H)
50. C2×#489C2×C3semidirect
51. #3079C2×C3semidirect
53. #2875C2×C3semidirect
54. #1997C2×C3semidirect
55. #1967C2×C3semidirect
56. #1931C2×C3semidirect
57. #1930C2×C3semidirect
58. #1908C2×C3semidirect
60. #1838C2×C3semidirect
506. C3#33063direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4892
C3×#30792
C3×#30402
C3×#28752
C3×#19972
C3×#19672
C3×#19312
C3×#19302
C3×#19082
C3×#19072
C3×#18382
#330633