Finite Group Databasebeta

← C3×#70407 #11788458

Subgroups — C3×#70407 #11788458

Order 1152.

769 conjugacy classes of subgroups.

The subgroup lattice has 521 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#949C211yesmaximal, characteristic
2C3×#5521C211yesmaximal, characteristic, complemented
3C32×#421C211yesmaximal, characteristic, complemented
4C3×#5240C211yesmaximal, characteristic, complemented
5C3×#5131C211yesmaximal, characteristic, complemented
6C3×#4559C211yesmaximal, characteristic, complemented
7C3×#4531C211yesmaximal, characteristic, complemented
8C3×#1904—31nomaximal
9#70407C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C32×#117C2211yescharacteristic
14C3×#949—22no—
15C3×#949—22no—
16C2×C3×#215C412yescomplemented
17C2×C3×#213C412yescomplemented
18C3×#926C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C3×#893—22no—
22C3×D3×C22⋊C4—22no—
23C3×C4×D12—22no—
24C32×#104—22no—
25C3×#834—22no—
26C3×#821—22no—
27C2×C3×AGL(1,ℤ/8)—31no—
28C3×#518—31no—
29C2×#949C2×C311yescharacteristic
30#5521C2×C311yescharacteristic, complemented
31C3×#421—21no—
32C3×#421D311yescharacteristic, complemented
33C3×#421C2×C311yescharacteristic, complemented
34C3×#418—31no—
35C3×#410—31no—
36#5240C2×C311yescharacteristic, complemented
37#5131C2×C311yescharacteristic, complemented
38C3×#344—31no—
39C3×H(3,ℤ/4)—31no—
40#4559C2×C311yescharacteristic, complemented
41#4531C2×C311yescharacteristic, complemented
42C23×C3×D3—21no—
43C32×#41—21no—
44C32×#41—21no—
45C32×#41—21no—
46C32×#41—21no—
47C2×C32×Q8C2×C411yescharacteristic, complemented
48C2×C32×D4—21no—
49C2×C32×D4C2×C411yescharacteristic, complemented
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12C2×C412yes—
56C2×C3×D12D412yes—
57C2×C3×D12D412yes—
58C2×C3×C4×D3—24no—
59C32×M16—21no—
60C32×M16—21no—
61C2×C32×C8—21no—
62C32×C4⋊C4—21no—
63C32×C22⋊C4—21no—
64C32×C42D412yes—
65C3×#217—21no—
66C3×#217D412yes—
67C3×#215—24no—
68C3×#213—24no—
69C3×(C2×D3)⋊C4—24no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4×Dic3—21no—
73C3×C4×Dic3—21no—
74C3×#208—21no—
75C3×#208—21no—
76C2×C3×C3⋊C8C2×C412yescomplemented
77#1904—31noSylow
78C2×C3×#41—21no—
79C2×C3×#41C2×D311yescharacteristic
80C2×C3×#41C22×C311yescharacteristic
81C22×C3×D4—31no—
82C22×D12C22×C311yescharacteristic
83C3×AGL(1,ℤ/8)—62no—
84C3×AGL(1,ℤ/8)—62no—
85C2×C3×SD16—32no—
86C2×C3×D8—32no—
87C2×C3×M16—21no—
88C2×C3×M16—31no—
89C2×C3×M16C2×D311yescharacteristic
90C2×C3×M16C22×C311yescharacteristic
91C3×C4×D4—62no—
92C3×C4×D4—62no—
93C3×#117—21no—
94C3×#117—31no—
95C3×#117—31no—
96C3×#117C2×D311yescharacteristic
97C3×#117C22×C311yescharacteristic
98C2×C3×C22⋊C4—62no—
99#949—22no—
100#949—22no—
101C2×#215C3×C412yescomplemented
102C2×#213C3×C412yescomplemented
103#926C22×C311yescharacteristic
104#926C22×C311yescharacteristic
105C2×#208C22×C311yescharacteristic
106#893—22no—
107D3×C22⋊C4—22no—
108C4×D12—22no—
109C3×#104—24no—
110C3×#104—22no—
111C3×#104—22no—
112C3×#102—62no—
113C3×#99—62no—
114#834—22no—
115#821—22no—
116C23×C32—21no—
117C23×C32C2×D411yescharacteristic
118C22×C3×D3—22no—
119C22×C3×D3—22no—
120C22×C3×D3—22no—
121C22×C3×D3—82no—
122C32×Q8—21no—
123C32×Q8—21no—
124C32×D4—21no—
125C32×D4—21no—
126C32×D4—41no—
127C32×D4—41no—
128C2×C32×C4—21no—
129C2×C32×C4—22no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C32×C4C22×C411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C3×Dic3—22no—
139C2×C3×Dic3—41no—
140C3×D12—22no—
141C3×D12—22no—
142C3×D12—22no—
143C3×D12C22⋊C414yes—
144C3×C4×D3—84no—
145C32×C8—41no—
146C3×C3⋊C8—22no—
147C2×AGL(1,ℤ/8)—31no—
148#518—31no—
149#421C3×D311yescharacteristic, complemented
150#418—31no—
151#410—31no—
152#344—31no—
153H(3,ℤ/4)—31no—
154C24×C3—61no—
155C23×D3—21no—
156C3×#41—22no—
157C3×#41—22no—
158C3×#41—21no—
159C3×#41—21no—
160C3×#41—21no—
161C3×#41—21no—
162C3×#41—21no—
163C3×#41—21no—
164C3×#41—21no—
165C3×#41—21no—
166C3×#41—41no—
167C3×#41—41no—
168C2×C3×Q8—21no—
169C2×C3×Q8C4×D311yescharacteristic, complemented
170C2×C3×Q8C2×C3×C411yescharacteristic, complemented
171C2×C3×D4—21no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—32no—
175C2×C3×D4—32no—
176C2×C3×D4—32no—
177C2×C3×D4—41no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C2×C3×D4—61no—
181C2×C3×D4C4×D311yescharacteristic, complemented
182C2×C3×D4C2×C3×C411yescharacteristic, complemented
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—41no—
187C22×C3×C4—64no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C23×C311yescharacteristic
190C2×D12—21no—
191C2×D12—21no—
192C2×D12—21no—
193C2×D12C2×C3×C412yes—
194C2×D12C3×D412yes—
195C2×D12C3×D412yes—
196C2×C4×D3—24no—
197C3×SD16—64no—
198C3×D8—64no—
199C3×M16—22no—
200C3×M16—21no—
201C3×M16—21no—
202C3×M16—21no—
203C3×M16—21no—
204C3×M16—41no—
205C3×M16—61no—
206C3×M16—61no—
207C2×C3×C8—21no—
208C2×C3×C8—21no—
209C2×C3×C8—32no—
210C2×C3×C8—41no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—41no—
214C3×C4⋊C4—61no—
215C3×C4⋊C4—61no—
216C3×C22⋊C4—21no—
217C3×C22⋊C4—21no—
218C3×C22⋊C4—32no—
219C3×C22⋊C4—41no—
220C3×C22⋊C4—64no—
221C3×C22⋊C4—61no—
222C3×C42—22no—
223C3×C42—61no—
224C3×C42—61no—
225C3×C42#6712yes—
226C3×C42C3×D412yes—
227#217—21no—
228#217C3×D412yes—
229#215—24no—
230#213—24no—
231(C2×D3)⋊C4—24no—
232C4⋊Dic3—21no—
233C4⋊Dic3—21no—
234C4×Dic3—21no—
235C4×Dic3—21no—
236#208—21no—
237#208—21no—
238C2×C3⋊C8C2×C3×C412yescomplemented
239C22×C32—41no—
240C22×C32—41no—
241C22×C32—81no—
242C22×C32C4×D411yescharacteristic
243C22×C32#12011yescharacteristic
244C22×C32#12111yescharacteristic
245C2×C3×D3—24no—
246C2×C3×D3—44no—
247C2×C3×D3—82no—
248C2×C3×D3—82no—
249C32×C4—41no—
250C32×C4—42no—
251C32×C4C2×C22⋊C411yescharacteristic
252C32×C4C4×D411yescharacteristic
253C32×C4#12111yescharacteristic
254C32×C4#12311yescharacteristic
255C3×Dic3—42no—
256C3×Dic3—81no—
257C2×#41C2×C3×D311yescharacteristic
258C22×D4—31no—
259AGL(1,ℤ/8)—62no—
260AGL(1,ℤ/8)—62no—
261C2×SD16—32no—
262C2×D8—32no—
263C2×M16—31no—
264C2×M16C2×C3×D311yescharacteristic
265C4×D4—62no—
266C4×D4—62no—
267#117—31no—
268#117—31no—
269#117C2×C3×D311yescharacteristic
270C2×C22⋊C4—62no—
271#104—22no—
272#102—62no—
273#99—62no—
274C23×C3—21no—
275C23×C3—21no—
276C23×C3—21no—
277C23×C3—41no—
278C23×C3—62no—
279C23×C3—62no—
280C23×C3—62no—
281C23×C3—242no—
282C23×C3D3×D411yescharacteristic
283C23×C3C2×C3×D411yescharacteristic
284C22×D3—22no—
285C22×D3—22no—
286C22×D3—22no—
287C22×D3—82no—
288C3×Q8—22no—
289C3×Q8—21no—
290C3×Q8—21no—
291C3×Q8—21no—
292C3×Q8—21no—
293C3×Q8—41no—
294C3×D4—22no—
295C3×D4—21no—
296C3×D4—21no—
297C3×D4—21no—
298C3×D4—21no—
299C3×D4—34no—
300C3×D4—41no—
301C3×D4—42no—
302C3×D4—42no—
303C3×D4—41no—
304C3×D4—41no—
305C3×D4—41no—
306C3×D4—41no—
307C3×D4—62no—
308C3×D4—62no—
309C3×D4—62no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—21no—
313C2×C3×C4—22no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—41no—
321C2×C3×C4—42no—
322C2×C3×C4—42no—
323C2×C3×C4—42no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—62no—
329C2×C3×C4—121no—
330C2×C3×C4—244no—
331C2×C3×C4C2×C4×D311yescharacteristic
332C2×C3×C4#23511yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4#23711yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337C2×C3×C4C22×C3×C411yescharacteristic
338C2×C3×C4C2×C3×D411yescharacteristic
339C2×C3×C4C2×C3×D411yescharacteristic
340C2×C3×C4C2×C3×D411yescharacteristic
341C2×C3×C4C3×#4111yescharacteristic
342C2×C3×C4C3×#4111yescharacteristic
343C2×Dic3—22no—
344C2×Dic3—41no—
345D12—22no—
346D12—22no—
347D12—22no—
348D12C3×C22⋊C414yes—
349C4×D3—84no—
350C3×C8—42no—
351C3×C8—41no—
352C3×C8—41no—
353C3×C8—62no—
354C3⋊C8—22no—
355C2×C32—21no—
356C2×C32—21no—
357C2×C32—21no—
358C2×C32—81no—
359C2×C32#38611yescharacteristic
360C3×D3—44no—
361C24—61no—
362#41—21no—
363#41—21no—
364#41—21no—
365#41—21no—
366C2×Q8C3×C4×D311yescharacteristic, complemented
367C2×D4—21no—
368C2×D4—32no—
369C2×D4—32no—
370C2×D4—32no—
371C2×D4—61no—
372C2×D4—61no—
373C2×D4—61no—
374C2×D4C3×C4×D311yescharacteristic, complemented
375C22×C4—21no—
376C22×C4—64no—
377C22×C4C22×C3×D311yescharacteristic
378SD16—64no—
379D8—64no—
380M16—21no—
381M16—21no—
382M16—61no—
383M16—61no—
384C2×C8—21no—
385C2×C8—32no—
386C4⋊C4—21no—
387C4⋊C4—61no—
388C4⋊C4—61no—
389C22⋊C4—21no—
390C22⋊C4—32no—
391C22⋊C4—64no—
392C22⋊C4—61no—
393C42—61no—
394C42—61no—
395C42C3×#6712yes—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—42no—
402C22×C3—41no—
403C22×C3—41no—
404C22×C3—64no—
405C22×C3—81no—
406C22×C3—81no—
407C22×C3—81no—
408C22×C3—82no—
409C22×C3—124no—
410C22×C3—242no—
411C22×C3—242no—
412C22×C3#67⋊C411yescharacteristic
413C22×C3#88411yescharacteristic
414C22×C3#93711yescharacteristic
415C22×C3C3×C4×D411yescharacteristic
416C22×C3C3×#12011yescharacteristic
417C22×C3C3×#12111yescharacteristic
418C2×D3—24no—
419C2×D3—44no—
420C2×D3—82no—
421C2×D3—82no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—42no—
427C3×C4—42no—
428C3×C4—42no—
429C3×C4—41no—
430C3×C4—41no—
431C3×C4—82no—
432C3×C4—122no—
433C3×C4—241no—
434C3×C4D3×C22⋊C411yescharacteristic
435C3×C4#88311yescharacteristic
436C3×C4C4×#6711yescharacteristic
437C3×C4#93811yescharacteristic
438C3×C4C2×C3×C22⋊C411yescharacteristic
439C3×C4C3×C4×D411yescharacteristic
440C3×C4C3×#12111yescharacteristic
441C3×C4C3×#12311yescharacteristic
442Dic3—42no—
443Dic3—81no—
444C32#190411yescharacteristic, complemented, Sylow
445C23—21no—
446C23—62no—
447C23—62no—
448C23—62no—
449C23—242no—
450C23C3×D3×D411yescharacteristic
451Q8—21no—
452Q8—21no—
453D4—21no—
454D4—21no—
455D4—34no—
456D4—41no—
457D4—41no—
458D4—62no—
459D4—62no—
460D4—62no—
461C2×C4—21no—
462C2×C4—22no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—62no—
466C2×C4—121no—
467C2×C4—244no—
468C2×C4C2×C3×C4×D311yescharacteristic
469C2×C4C3×#23511yescharacteristic
470C2×C4C3×D3×D411yescharacteristic
471C2×C4C3×D3×D411yescharacteristic
472C2×C4C3×#23711yescharacteristic
473C2×C4C2×C3×#6711yescharacteristic
474C8—41no—
475C8—62no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—41no—
484C2×C3—41no—
485C2×C3—41no—
486C2×C3—82no—
487C2×C3—81no—
488C2×C3—81no—
489C2×C3—124no—
490C2×C3#495611yescharacteristic
491C2×C3C3×#38611yescharacteristic
492D3—44no—
493C22—41no—
494C22—41no—
495C22—64no—
496C22—81no—
497C22—124no—
498C22—242no—
499C22—242no—
500C22C3×#67⋊C411yescharacteristic
501C22C3×#88411yescharacteristic
502C22C3×#93711yescharacteristic
503C4—42no—
504C4—41no—
505C4—122no—
506C4—241no—
507C4C3×D3×C22⋊C411yescharacteristic
508C4C3×#88311yescharacteristic
509C4C3×C4×#6711yescharacteristic
510C4C3×#93811yescharacteristic
511C3—21no—
512C3#7040711yescharacteristic, direct product factor
513C3C3×#190411yescharacteristic, complemented
514C2—21no—
515C2—21no—
516C2—21no—
517C2—81no—
518C2—124no—
519C2C3×#495611yescharacteristic
subgroupG/H
centerC2×C3#4956
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#421C2
socleC2×C32#386
prime radicalC2×C3×#949C2
cosocleC22×C3×C4C23×C3
hypercenterC3×#421D3
hypocenterC3C3×#1904
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#421

Complements

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

NH ≅ G/Ntype
2. C3×#5521C2semidirect
3. C32×#421C2semidirect
4. C3×#5240C2semidirect
5. C3×#5131C2semidirect
6. C3×#4559C2semidirect
7. C3×#4531C2semidirect
9. #70407C3direct (N × H)
16. C2×C3×#215C4semidirect
17. C2×C3×#213C4semidirect
30. #5521C2×C3semidirect
32. C3×#421D3semidirect
33. C3×#421C2×C3semidirect
36. #5240C2×C3semidirect
37. #5131C2×C3semidirect
40. #4559C2×C3semidirect
41. #4531C2×C3semidirect
47. C2×C32×Q8C2×C4semidirect
49. C2×C32×D4C2×C4semidirect
76. C2×C3×C3⋊C8C2×C4semidirect
101. C2×#215C3×C4semidirect
102. C2×#213C3×C4semidirect
149. #421C3×D3semidirect
169. C2×C3×Q8C4×D3semidirect
170. C2×C3×Q8C2×C3×C4semidirect
181. C2×C3×D4C4×D3semidirect
182. C2×C3×D4C2×C3×C4semidirect
238. C2×C3⋊C8C2×C3×C4semidirect
366. C2×Q8C3×C4×D3semidirect
374. C2×D4C3×C4×D3semidirect
444. C32#1904semidirect
512. C3#70407direct (N × H)
513. C3C3×#1904semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9492
C3×#55212
C32×#4212
C3×#52402
C3×#51312
C3×#45592
C3×#45312
C3×#19043
#704073