Finite Group Databasebeta

← C3×#70323 #11787858

Subgroups — C3×#70323 #11787858

Order 1152.

983 conjugacy classes of subgroups.

The subgroup lattice has 515 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C211yesmaximal, characteristic
2C3×#5521C211yesmaximal, characteristic, complemented
3C32×#418C211yesmaximal, characteristic, complemented
4C3×#5215C211yesmaximal, characteristic, complemented
5C2×C3×#823C211yesmaximal, characteristic, complemented
6C3×#4555C211yesmaximal, characteristic, complemented
7C3×#4532C211yesmaximal, characteristic, complemented
8C3×#1887—31nomaximal
9#70323C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C22×C3×#67—22no—
12C22×C3×D12C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C32×#117C2211yescharacteristic
15C3×#940—22no—
16C3×#940C414yescomplemented
17C3×#926C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C3×#893—22no—
21C3×D3×C22⋊C4—22no—
22C3×C4×D12—22no—
23C32×#102—22no—
24C3×#832—22no—
25C3×#823—22no—
26C2×C3×#127—31no—
27C3×#518—31no—
28C2×#940C2×C311yescharacteristic
29#5521C2×C311yescharacteristic, complemented
30C3×#418—21no—
31C3×#418—31no—
32C3×#418D311yescharacteristic, complemented
33C3×#418C2×C311yescharacteristic, complemented
34C2×C3×#100—31no—
35#5215C2×C311yescharacteristic, complemented
36C2×#823C2×C311yescharacteristic, complemented
37C3×#339—31no—
38C3×#339—31no—
39#4555C2×C311yescharacteristic, complemented
40#4532C2×C311yescharacteristic, complemented
41C24×C32—21no—
42C23×C3×D3D412yes—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4C2×C412yescomplemented
49C22×C32×C4C2311yescharacteristic
50C2×C3×#67—28no—
51C2×C3×#67—48no—
52C22×C3×Dic3—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12C2×C412yes—
58C2×C3×D12D412yes—
59C2×C3×C4×D3—24no—
60C32×M16—21no—
61C32×M16—21no—
62C2×C32×C8—21no—
63C32×C4⋊C4D412yescomplemented
64C32×C22⋊C4—21no—
65C32×C42—21no—
66C3×#217—21no—
67C3×(C2×D3)⋊C4—24no—
68C3×C4⋊Dic3D412yescomplemented
69C3×C4×Dic3—21no—
70C3×C4×Dic3—21no—
71C3×C4×Dic3C2×C412yescomplemented
72C3×#208—21no—
73C3×#208—21no—
74C2×C3×C3⋊C8—21no—
75#1887—31noSylow
76C22×C3×D4—21no—
77C22×C3×D4—31no—
78C22×C3×D4—62no—
79C22×C3×D4C2×D311yescharacteristic
80C22×C3×D4C22×C311yescharacteristic
81C22×#67—22no—
82C22×D12C22×C311yescharacteristic
83C2×C3×M16—21no—
84C2×C3×M16—31no—
85C2×C3×M16C2×D311yescharacteristic
86C2×C3×M16C22×C311yescharacteristic
87C3×#127—34no—
88C3×#127—62no—
89C3×C4×D4—62no—
90C3×C4×D4—62no—
91C3×#117—21no—
92C3×#117—31no—
93C3×#117C2×D311yescharacteristic
94C3×#117C22×C311yescharacteristic
95C2×C3×C22⋊C4—62no—
96C2×C3×C42—31no—
97#940—22no—
98#940C3×C414yescomplemented
99#926C22×C311yescharacteristic
100C2×C4×Dic3C22×C311yescharacteristic
101C2×#208C22×C311yescharacteristic
102#893—22no—
103D3×C22⋊C4—22no—
104C4×D12—22no—
105C3×#102—24no—
106C3×#102—22no—
107C3×#102—22no—
108C3×#102—62no—
109C3×#100—62no—
110#832—22no—
111#823—22no—
112C23×C32—22no—
113C23×C32—41no—
114C23×C32—41no—
115C23×C32—44no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—22no—
118C22×C3×D3—22no—
119C22×C3×D3—44no—
120C22×C3×D3C22⋊C414yes—
121C32×D4—22no—
122C32×D4—22no—
123C32×D4—41no—
124C32×D4—41no—
125C2×C32×C4—22no—
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C3×#67—416no—
133C2×C3×Dic3—24no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C3×D12—22no—
137C3×D12—22no—
138C3×D12—22no—
139C3×D12—22no—
140C3×C4×D3—84no—
141C32×C8—41no—
142C3×C3⋊C8—41no—
143C2×#127—31no—
144#518—31no—
145#418—31no—
146#418C3×D311yescharacteristic, complemented
147C2×#100—31no—
148#339—31no—
149#339—31no—
150C24×C3—21no—
151C24×C3—21no—
152C24×C3—32no—
153C24×C3—41no—
154C23×D3C3×D412yes—
155C2×C3×D4—22no—
156C2×C3×D4—22no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—21no—
160C2×C3×D4—21no—
161C2×C3×D4—21no—
162C2×C3×D4—21no—
163C2×C3×D4—21no—
164C2×C3×D4—21no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—22no—
168C2×C3×D4—32no—
169C2×C3×D4—32no—
170C2×C3×D4—41no—
171C2×C3×D4—41no—
172C2×C3×D4—41no—
173C2×C3×D4—68no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—128no—
179C2×C3×D4C4×D312yescomplemented
180C2×C3×D4C2×C3×C412yescomplemented
181C22×C3×C4—21no—
182C22×C3×C4—64no—
183C22×C3×C4—61no—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C23×C311yescharacteristic
186C2×#67—28no—
187C2×#67—48no—
188C22×Dic3—21no—
189C2×D12—21no—
190C2×D12—21no—
191C2×D12—21no—
192C2×D12—21no—
193C2×D12C2×C3×C412yes—
194C2×D12C3×D412yes—
195C2×C4×D3—24no—
196C3×M16—21no—
197C3×M16—21no—
198C3×M16—21no—
199C3×M16—21no—
200C3×M16—41no—
201C3×M16—41no—
202C3×M16—61no—
203C3×M16—61no—
204C2×C3×C8—22no—
205C2×C3×C8—21no—
206C2×C3×C8—21no—
207C2×C3×C8—61no—
208C3×C4⋊C4—22no—
209C3×C4⋊C4—32no—
210C3×C4⋊C4#6712yescomplemented
211C3×C4⋊C4C3×D412yescomplemented
212C3×C22⋊C4—21no—
213C3×C22⋊C4—21no—
214C3×C22⋊C4—41no—
215C3×C22⋊C4—64no—
216C3×C22⋊C4—61no—
217C3×C42—21no—
218C3×C42—21no—
219C3×C42—32no—
220C3×C42—41no—
221C3×C42—61no—
222C3×C42—61no—
223#217—21no—
224(C2×D3)⋊C4—24no—
225C4⋊Dic3C3×D412yescomplemented
226C4×Dic3—21no—
227C4×Dic3—21no—
228C4×Dic3C2×C3×C412yescomplemented
229#208—21no—
230#208—21no—
231C2×C3⋊C8—21no—
232C22×C32—22no—
233C22×C32—42no—
234C22×C32—44no—
235C22×C32—82no—
236C22×C32—82no—
237C22×C32C2×C22⋊C411yescharacteristic
238C22×C32#12011yescharacteristic
239C22×C32#12311yescharacteristic
240C2×C3×D3—24no—
241C2×C3×D3—44no—
242C2×C3×D3—44no—
243C2×C3×D3—82no—
244C32×C4—42no—
245C32×C4C4×D411yescharacteristic
246C32×C4C4×D411yescharacteristic
247C32×C4#12111yescharacteristic
248C32×C4#12111yescharacteristic
249C3×Dic3—24no—
250C3×Dic3—42no—
251C22×D4—31no—
252C22×D4—62no—
253C22×D4C2×C3×D311yescharacteristic
254C2×M16—31no—
255C2×M16C2×C3×D311yescharacteristic
256#127—34no—
257#127—62no—
258C4×D4—62no—
259C4×D4—62no—
260#117—31no—
261#117C2×C3×D311yescharacteristic
262C2×C22⋊C4—62no—
263C2×C42—31no—
264#102—22no—
265#102—62no—
266#100—62no—
267C23×C3—22no—
268C23×C3—22no—
269C23×C3—21no—
270C23×C3—34no—
271C23×C3—42no—
272C23×C3—44no—
273C23×C3—42no—
274C23×C3—42no—
275C23×C3—44no—
276C23×C3—41no—
277C23×C3—41no—
278C23×C3—41no—
279C23×C3—41no—
280C23×C3—62no—
281C23×C3—62no—
282C23×C3—84no—
283C23×C3—124no—
284C23×C3D3×D411yescharacteristic
285C23×C3C2×C3×D411yescharacteristic
286C22×D3—22no—
287C22×D3—22no—
288C22×D3—44no—
289C22×D3C3×C22⋊C414yes—
290C3×D4—24no—
291C3×D4—22no—
292C3×D4—22no—
293C3×D4—22no—
294C3×D4—22no—
295C3×D4—42no—
296C3×D4—42no—
297C3×D4—42no—
298C3×D4—41no—
299C3×D4—41no—
300C3×D4—41no—
301C3×D4—41no—
302C3×D4—62no—
303C3×D4—62no—
304C3×D4—62no—
305C3×D4—62no—
306C3×D4—1216no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—42no—
316C2×C3×C4—64no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—244no—
320C2×C3×C4C2×C4×D311yescharacteristic
321C2×C3×C4#23511yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4#23711yescharacteristic
325C2×C3×C4C2×#6711yescharacteristic
326C2×C3×C4C22×C3×C411yescharacteristic
327C2×C3×C4C2×C3×D411yescharacteristic
328C2×C3×C4C2×C3×D411yescharacteristic
329C2×C3×C4C2×C3×D411yescharacteristic
330C2×C3×C4C3×#4111yescharacteristic
331C2×C3×C4C3×#4111yescharacteristic
332#67—416no—
333C2×Dic3—24no—
334C2×Dic3—22no—
335C2×Dic3—22no—
336D12—22no—
337D12—22no—
338D12—22no—
339D12—22no—
340C4×D3—84no—
341C3×C8—42no—
342C3×C8—41no—
343C3×C8—41no—
344C3×C8—121no—
345C3⋊C8—41no—
346C2×C32—21no—
347C2×C32—21no—
348C2×C32—82no—
349C2×C32#38611yescharacteristic
350C2×C32#45312yes—
351C3×D3—44no—
352C24—21no—
353C24—32no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—32no—
360C2×D4—32no—
361C2×D4—68no—
362C2×D4—61no—
363C2×D4—61no—
364C2×D4—61no—
365C2×D4—61no—
366C2×D4—128no—
367C2×D4C3×C4×D312yescomplemented
368C22×C4—64no—
369C22×C4—61no—
370C22×C4C22×C3×D311yescharacteristic
371M16—21no—
372M16—21no—
373M16—61no—
374M16—61no—
375C2×C8—21no—
376C2×C8—61no—
377C4⋊C4—32no—
378C4⋊C4C3×#6712yescomplemented
379C22⋊C4—21no—
380C22⋊C4—64no—
381C22⋊C4—61no—
382C42—21no—
383C42—32no—
384C42—61no—
385C42—61no—
386C22×C3—22no—
387C22×C3—22no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—42no—
392C22×C3—44no—
393C22×C3—44no—
394C22×C3—44no—
395C22×C3—42no—
396C22×C3—42no—
397C22×C3—64no—
398C22×C3—84no—
399C22×C3—82no—
400C22×C3—82no—
401C22×C3—84no—
402C22×C3—84no—
403C22×C3—82no—
404C22×C3—82no—
405C22×C3—124no—
406C22×C3—124no—
407C22×C3—242no—
408C22×C3D3×C22⋊C411yescharacteristic
409C22×C3#88311yescharacteristic
410C22×C3#93711yescharacteristic
411C22×C3C2×C3×C22⋊C411yescharacteristic
412C22×C3C3×#12011yescharacteristic
413C22×C3C3×#12311yescharacteristic
414C2×D3—24no—
415C2×D3—44no—
416C2×D3—44no—
417C2×D3—82no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—42no—
423C3×C4—42no—
424C3×C4—64no—
425C3×C4—82no—
426C3×C4—122no—
427C3×C4#67⋊C411yescharacteristic
428C3×C4#88411yescharacteristic
429C3×C4C4×#6711yescharacteristic
430C3×C4#93811yescharacteristic
431C3×C4C3×C4×D411yescharacteristic
432C3×C4C3×C4×D411yescharacteristic
433C3×C4C3×#12111yescharacteristic
434C3×C4C3×#12111yescharacteristic
435Dic3—24no—
436Dic3—42no—
437C32#188711yescharacteristic, complemented, Sylow
438C23—22no—
439C23—34no—
440C23—44no—
441C23—41no—
442C23—41no—
443C23—62no—
444C23—62no—
445C23—124no—
446C23C3×D3×D411yescharacteristic
447D4—22no—
448D4—22no—
449D4—41no—
450D4—41no—
451D4—62no—
452D4—62no—
453D4—62no—
454D4—62no—
455D4—1216no—
456C2×C4—22no—
457C2×C4—64no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—244no—
461C2×C4C2×C3×C4×D311yescharacteristic
462C2×C4C3×#23511yescharacteristic
463C2×C4C3×D3×D411yescharacteristic
464C2×C4C3×D3×D411yescharacteristic
465C2×C4C3×#23711yescharacteristic
466C2×C4C2×C3×#6711yescharacteristic
467C8—41no—
468C8—121no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—22no—
474C2×C3—21no—
475C2×C3—41no—
476C2×C3—41no—
477C2×C3—84no—
478C2×C3—82no—
479C2×C3—82no—
480C2×C3—124no—
481C2×C3#495611yescharacteristic
482C2×C3#519812yes—
483C2×C3C3×#38611yescharacteristic
484C2×C3C3×#45312yes—
485D3—44no—
486C22—22no—
487C22—44no—
488C22—42no—
489C22—64no—
490C22—82no—
491C22—82no—
492C22—124no—
493C22—124no—
494C22—242no—
495C22C3×D3×C22⋊C411yescharacteristic
496C22C3×#88311yescharacteristic
497C22C3×#93711yescharacteristic
498C4—42no—
499C4—64no—
500C4—122no—
501C4C3×#67⋊C411yescharacteristic
502C4C3×#88411yescharacteristic
503C4C3×C4×#6711yescharacteristic
504C4C3×#93811yescharacteristic
505C3—21no—
506C3#7032311yescharacteristic, direct product factor
507C3C3×#188711yescharacteristic, complemented
508C2—21no—
509C2—21no—
510C2—82no—
511C2—124no—
512C2C3×#495611yescharacteristic
513C2C3×#519812yes—
subgroupG/H
centerC22×C3#937
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#418C2
socleC22×C32#120
prime radicalC2×C3×#940C2
cosocleC22×C3×C4C23×C3
hypercenterC3×#418D3
hypocenterC3C3×#1887
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#418

Complements

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

NH ≅ G/Ntype
2. C3×#5521C2semidirect
3. C32×#418C2semidirect
4. C3×#5215C2semidirect
5. C2×C3×#823C2semidirect
6. C3×#4555C2semidirect
7. C3×#4532C2semidirect
9. #70323C3direct (N × H)
16. C3×#940C4semidirect
29. #5521C2×C3semidirect
32. C3×#418D3semidirect
33. C3×#418C2×C3semidirect
35. #5215C2×C3semidirect
36. C2×#823C2×C3semidirect
39. #4555C2×C3semidirect
40. #4532C2×C3semidirect
48. C2×C32×D4C2×C4semidirect
63. C32×C4⋊C4D4semidirect
68. C3×C4⋊Dic3D4semidirect
71. C3×C4×Dic3C2×C4semidirect
98. #940C3×C4semidirect
146. #418C3×D3semidirect
179. C2×C3×D4C4×D3semidirect
180. C2×C3×D4C2×C3×C4semidirect
210. C3×C4⋊C4#67semidirect
211. C3×C4⋊C4C3×D4semidirect
225. C4⋊Dic3C3×D4semidirect
228. C4×Dic3C2×C3×C4semidirect
367. C2×D4C3×C4×D3semidirect
378. C4⋊C4C3×#67semidirect
437. C32#1887semidirect
506. C3#70323direct (N × H)
507. C3C3×#1887semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9402
C3×#55212
C32×#4182
C3×#52152
C2×C3×#8232
C3×#45552
C3×#45322
C3×#18873
#703233