Finite Group Databasebeta

← C3×#68986 #11793895

Subgroups — C3×#68986 #11793895

Order 1152.

613 conjugacy classes of subgroups.

The subgroup lattice has 509 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C211yesmaximal, characteristic
2C2×C3×#823C211yesmaximal, characteristic, complemented
3C3×#5129C211yesmaximal, characteristic, complemented
4C2×C3×#822C211yesmaximal, characteristic, complemented
5C3×#4966C211yesmaximal, characteristic, complemented
6C2×C3×#809C211yesmaximal, characteristic, complemented
7C32×#343C211yesmaximal, characteristic, complemented
8C3×#2051—31nomaximal
9#68986C311yesmaximal, characteristic, direct product factor
10C2×C3×#235C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C3×#908—22no—
18C3×#908—22no—
19C2×C3×D24—21no—
20C2×C3×#204—21no—
21C3×#823—22no—
22C3×#822—22no—
23C3×(C2×D3)⋊C8—22no—
24C3×#810—21no—
25C3×#809—21no—
26C3×#809—22no—
27C2×C3×AGL(1,ℤ/8)—31no—
28C2×#908C2×C311yescharacteristic
29C2×C3×#108—31no—
30C3×#417—31no—
31C2×C3×#102—31no—
32C2×C3×#100—31no—
33C3×#408—31no—
34C2×#823C2×C311yescharacteristic, complemented
35#5129C2×C311yescharacteristic, complemented
36C2×#822C2×C311yescharacteristic, complemented
37#4966C2×C311yescharacteristic, complemented
38C2×#809C2×C311yescharacteristic, complemented
39C3×#343—21no—
40C3×#343D311yescharacteristic, complemented
41C3×#343C2×C311yescharacteristic, complemented
42C23×C3×D3—21no—
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C2×C3×#67—21no—
46C3×#235—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12D411yescharacteristic
56C2×C3×D12D412yes—
57C2×C3×C4×D3—21no—
58C2×C3×Dic6D411yescharacteristic
59C32×M16—21no—
60C32×M16—21no—
61C32×M16—21no—
62C32×M16D412yes—
63C2×C32×C8—21no—
64C2×C32×C8—21no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67C3×#208—21no—
68C3×#208—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8D412yes—
73C3×D24—24no—
74C3×#204—24no—
75#2051—31noSylow
76C2×C3×#41—31no—
77C22×C3×D4—31no—
78C2×#235C22×C311yescharacteristic
79C22×D12C22×C311yescharacteristic
80C3×AGL(1,ℤ/8)—62no—
81C3×AGL(1,ℤ/8)—62no—
82C2×C3×SD16—61no—
83C2×C3×D8—61no—
84C2×C3×M16—21no—
85C2×C3×M16—21no—
86C2×C3×M16—31no—
87C2×C3×M16C2×D311yescharacteristic
88C2×C3×M16C2×D311yescharacteristic
89C2×C3×M16C22×C311yescharacteristic
90C2×C3×M16C22×C311yescharacteristic
91C22×C3×C8—31no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×C3×C4⋊C4C22×C311yescharacteristic
95C2×#208C22×C311yescharacteristic
96C22×C3⋊C8C22×C311yescharacteristic
97#908—22no—
98#908—22no—
99C2×D24—21no—
100C2×#204—21no—
101C3×#108—62no—
102C3×#103—61no—
103C3×#102—62no—
104C3×#102—61no—
105C3×#100—62no—
106C3×C22⋊C8—62no—
107#823—22no—
108#822—22no—
109(C2×D3)⋊C8—22no—
110#810—21no—
111#809—21no—
112#809—22no—
113C23×C32#4111yescharacteristic
114C22×C3×D3—21no—
115C22×C3×D3—22no—
116C22×C3×D3—41no—
117C22×C3×D3—41no—
118C22×C3×D3—81no—
119C22×C3×D3—81no—
120C2×C32×C4—41no—
121C2×C32×C4—81no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C3×#67—41no—
129C3×#67—41no—
130C2×C3×Dic3—21no—
131C3×D12—22no—
132C3×D12—21no—
133C3×D12—22no—
134C3×D12—21no—
135C3×D12—41no—
136C3×D12—41no—
137C3×C4×D3—41no—
138C3×C4×D3—41no—
139C3×Dic6—21no—
140C3×Dic6—21no—
141C32×C8—22no—
142C32×C8—41no—
143C3×C3⋊C8—22no—
144C3×C3⋊C8—41no—
145C2×AGL(1,ℤ/8)—31no—
146C2×#108—31no—
147#417—31no—
148C2×#102—31no—
149C2×#100—31no—
150#408—31no—
151#343C3×D311yescharacteristic, complemented
152C24×C3—61no—
153C23×D3—21no—
154C3×#41—61no—
155C3×#41—61no—
156C3×#41—61no—
157C3×#41—61no—
158C2×C3×Q8—31no—
159C2×C3×D4—32no—
160C2×C3×D4—31no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4—61no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C2×C3×D4—61no—
167C22×C3×C4—22no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—61no—
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C23×C311yescharacteristic
174C2×#67—21no—
175#235—21no—
176#235—21no—
177#235—21no—
178#235—21no—
179C2×D12—21no—
180C2×D12—21no—
181C2×D12—21no—
182C2×D12—21no—
183C2×D12—21no—
184C2×D12C3×D411yescharacteristic
185C2×D12C3×D412yes—
186C2×C4×D3—21no—
187C2×Dic6C3×D411yescharacteristic
188C3×SD16—64no—
189C3×D8—64no—
190C3×M16—21no—
191C3×M16—21no—
192C3×M16—22no—
193C3×M16—21no—
194C3×M16—21no—
195C3×M16—21no—
196C3×M16—21no—
197C3×M16—22no—
198C3×M16—41no—
199C3×M16—41no—
200C3×M16—61no—
201C3×M16—61no—
202C3×M16D1212yes—
203C3×M16C3×D412yes—
204C2×C3×C8—21no—
205C2×C3×C8—21no—
206C2×C3×C8—21no—
207C2×C3×C8—21no—
208C2×C3×C8—32no—
209C2×C3×C8—41no—
210C2×C3×C8—41no—
211C2×C3×C8—61no—
212C2×C3×C8—61no—
213C2×C3×C8—61no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—41no—
219C3×C4⋊C4—41no—
220#208—21no—
221#208—21no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8C3×D412yes—
226D24—24no—
227#204—24no—
228C22×C32—21no—
229C22×C32—21no—
230C22×C32#12111yescharacteristic
231C22×C32#12311yescharacteristic
232C22×C32#12411yescharacteristic
233C2×C3×D3—41no—
234C2×C3×D3—42no—
235C2×C3×D3—41no—
236C2×C3×D3—41no—
237C2×C3×D3—82no—
238C2×C3×D3—81no—
239C2×C3×D3—81no—
240C2×C3×D3—82no—
241C32×C4—81no—
242C32×C4#12011yescharacteristic
243C32×C4#12111yescharacteristic
244C32×C4#12111yescharacteristic
245C32×C4#12311yescharacteristic
246C3×Dic3—41no—
247C2×#41—31no—
248C22×D4—31no—
249AGL(1,ℤ/8)—62no—
250AGL(1,ℤ/8)—62no—
251C2×SD16—61no—
252C2×D8—61no—
253C2×M16—31no—
254C2×M16C2×C3×D311yescharacteristic
255C2×M16C2×C3×D311yescharacteristic
256C22×C8—31no—
257C2×C4⋊C4C2×C3×D311yescharacteristic
258#108—62no—
259#103—61no—
260#102—62no—
261#102—61no—
262#100—62no—
263C22⋊C8—62no—
264C23×C3—21no—
265C23×C3—61no—
266C23×C3—62no—
267C23×C3—121no—
268C23×C3—121no—
269C23×C3—241no—
270C23×C3—241no—
271C23×C3#23511yescharacteristic
272C23×C3C3×#4111yescharacteristic
273C22×D3—21no—
274C22×D3—22no—
275C22×D3—41no—
276C22×D3—41no—
277C22×D3—81no—
278C22×D3—81no—
279C3×Q8—61no—
280C3×Q8—61no—
281C3×D4—61no—
282C3×D4—62no—
283C3×D4—62no—
284C3×D4—61no—
285C3×D4—121no—
286C3×D4—121no—
287C3×D4—121no—
288C3×D4—121no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—42no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—61no—
299C2×C3×C4—81no—
300C2×C3×C4—81no—
301C2×C3×C4—82no—
302C2×C3×C4—121no—
303C2×C3×C4—121no—
304C2×C3×C4C2×D1211yescharacteristic
305C2×C3×C4#23511yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4#23911yescharacteristic
310C2×C3×C4C2×C3×D411yescharacteristic
311C2×C3×C4C2×C3×D411yescharacteristic
312C2×C3×C4C2×C3×D411yescharacteristic
313C2×C3×C4C2×C3×D411yescharacteristic
314C2×C3×C4C3×#4111yescharacteristic
315C2×C3×C4C3×#4111yescharacteristic
316#67—41no—
317#67—41no—
318C2×Dic3—21no—
319D12—22no—
320D12—21no—
321D12—22no—
322D12—21no—
323D12—41no—
324D12—41no—
325C4×D3—41no—
326C4×D3—41no—
327Dic6—21no—
328Dic6—21no—
329C3×C8—22no—
330C3×C8—22no—
331C3×C8—42no—
332C3×C8—42no—
333C3×C8—41no—
334C3×C8—41no—
335C3×C8—62no—
336C3×C8—121no—
337C3⋊C8—22no—
338C3⋊C8—41no—
339C2×C32—21no—
340C2×C32—21no—
341C2×C32#39411yescharacteristic
342C2×C32#47111yescharacteristic
343C2×C32#47211yescharacteristic
344C3×D3—81no—
345C3×D3—82no—
346C24—61no—
347#41—61no—
348#41—61no—
349#41—61no—
350#41—61no—
351C2×Q8—31no—
352C2×D4—32no—
353C2×D4—31no—
354C2×D4—61no—
355C2×D4—61no—
356C2×D4—61no—
357C2×D4—61no—
358C2×D4—61no—
359C2×D4—61no—
360C22×C4—21no—
361C22×C4—61no—
362C22×C4C22×C3×D311yescharacteristic
363SD16—64no—
364D8—64no—
365M16—21no—
366M16—21no—
367M16—21no—
368M16—61no—
369M16—61no—
370M16C3×D1212yes—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—32no—
374C2×C8—61no—
375C2×C8—61no—
376C2×C8—61no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—121no—
389C22×C3—122no—
390C22×C3—121no—
391C22×C3—121no—
392C22×C3—242no—
393C22×C3—242no—
394C22×C3—241no—
395C22×C3—241no—
396C22×C3#87511yescharacteristic
397C22×C3#88411yescharacteristic
398C22×C3#89411yescharacteristic
399C22×C3C3×#12111yescharacteristic
400C22×C3C3×#12311yescharacteristic
401C22×C3C3×#12411yescharacteristic
402C2×D3—41no—
403C2×D3—42no—
404C2×D3—41no—
405C2×D3—41no—
406C2×D3—82no—
407C2×D3—81no—
408C2×D3—81no—
409C2×D3—82no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—82no—
415C3×C4—81no—
416C3×C4—81no—
417C3×C4—121no—
418C3×C4#88211yescharacteristic
419C3×C4#88411yescharacteristic
420C3×C4#89411yescharacteristic
421C3×C4#89511yescharacteristic
422C3×C4C3×#12011yescharacteristic
423C3×C4C3×#12111yescharacteristic
424C3×C4C3×#12111yescharacteristic
425C3×C4C3×#12311yescharacteristic
426Dic3—41no—
427C32#205111yescharacteristic, complemented, Sylow
428C23—61no—
429C23—62no—
430C23—121no—
431C23—121no—
432C23—241no—
433C23—241no—
434C23C3×#23511yescharacteristic
435Q8—61no—
436Q8—61no—
437D4—61no—
438D4—62no—
439D4—62no—
440D4—61no—
441D4—121no—
442D4—121no—
443D4—121no—
444D4—121no—
445C2×C4—41no—
446C2×C4—61no—
447C2×C4—81no—
448C2×C4—121no—
449C2×C4—121no—
450C2×C4C2×C3×D1211yescharacteristic
451C2×C4C3×#23511yescharacteristic
452C2×C4C3×D3×D411yescharacteristic
453C2×C4C3×D3×D411yescharacteristic
454C2×C4C3×D3×D411yescharacteristic
455C2×C4C3×#23911yescharacteristic
456C8—22no—
457C8—41no—
458C8—62no—
459C8—121no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—41no—
468C2×C3—41no—
469C2×C3—241no—
470C2×C3—242no—
471C2×C3#467211yescharacteristic
472C2×C3#474911yescharacteristic
473C2×C3#475411yescharacteristic
474C2×C3C3×#39411yescharacteristic
475C2×C3C3×#47111yescharacteristic
476C2×C3C3×#47211yescharacteristic
477D3—81no—
478D3—82no—
479C22—21no—
480C22—21no—
481C22—121no—
482C22—122no—
483C22—121no—
484C22—121no—
485C22—242no—
486C22—242no—
487C22—241no—
488C22—241no—
489C22C3×#87511yescharacteristic
490C22C3×#88411yescharacteristic
491C22C3×#89411yescharacteristic
492C4—81no—
493C4—121no—
494C4C3×#88211yescharacteristic
495C4C3×#88411yescharacteristic
496C4C3×#89411yescharacteristic
497C4C3×#89511yescharacteristic
498C3—21no—
499C3#6898611yescharacteristic, direct product factor
500C3C3×#205111yescharacteristic, complemented
501C2—21no—
502C2—21no—
503C2—241no—
504C2—242no—
505C2C3×#467211yescharacteristic
506C2C3×#474911yescharacteristic
507C2C3×#475411yescharacteristic
subgroupG/H
centerC22×C3#884
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#343C2
socleC22×C32#121
prime radicalC2×C3×#908C2
hypercenterC3×#343D3
hypocenterC3C3×#2051
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#343

Complements

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

NH ≅ G/Ntype
2. C2×C3×#823C2semidirect
3. C3×#5129C2semidirect
4. C2×C3×#822C2semidirect
5. C3×#4966C2semidirect
6. C2×C3×#809C2semidirect
7. C32×#343C2semidirect
9. #68986C3direct (N × H)
34. C2×#823C2×C3semidirect
35. #5129C2×C3semidirect
36. C2×#822C2×C3semidirect
37. #4966C2×C3semidirect
38. C2×#809C2×C3semidirect
40. C3×#343D3semidirect
41. C3×#343C2×C3semidirect
151. #343C3×D3semidirect
427. C32#2051semidirect
499. C3#68986direct (N × H)
500. C3C3×#2051semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9082
C2×C3×#8232
C3×#51292
C2×C3×#8222
C3×#49662
C2×C3×#8092
C32×#3432
C3×#20513
#689863