Finite Group Databasebeta

← C3×#69647 #11791027

Subgroups — C3×#69647 #11791027

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#213C211yesmaximal, characteristic
2C32×#390C211yesmaximal, characteristic, complemented
3C2×C3×#832C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5C2×C3×#807C211yesmaximal, characteristic, complemented
6C3×#4939C211yesmaximal, characteristic, complemented
7C2×C3×C4×C3⋊C8C211yesmaximal, characteristic, complemented
8C3×#1970—31nomaximal
9#69647C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C22⋊C4—22no—
14C2×C32×C42C2211yescharacteristic
15C2×C3×#213—22no—
16C2×C3×#213—22no—
17C2×C3×#213C414yescomplemented
18C2×C3×(C2×D3)⋊C4—22no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#832—22no—
23C3×#809—22no—
24C3×#807—22no—
25C3×C4×C3⋊C8—22no—
26C22×C3×D8—31no—
27C22×#213C2×C311yescharacteristic
28C2×C3×#107—31no—
29C2×C3×#102—31no—
30C2×C3×#102—31no—
31C2×C3×C4×C8—31no—
32C3×#390—21no—
33C3×#390—31no—
34C3×#390D311yescharacteristic, complemented
35C3×#390C2×C311yescharacteristic, complemented
36C2×#832C2×C311yescharacteristic, complemented
37C2×#809C2×C311yescharacteristic, complemented
38C2×#807C2×C311yescharacteristic, complemented
39#4939C2×C311yescharacteristic, complemented
40C2×C4×C3⋊C8C2×C311yescharacteristic, complemented
41C24×C32—21no—
42C23×C3×D3—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4C2×C412yes—
49C22×C32×C4—21no—
50C22×C32×C4D412yes—
51C22×C32×C4C2311yescharacteristic
52C22×C3×Dic3—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12C2×C412yes—
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61C32×C22⋊C4—44no—
62C32×C42—21no—
63C32×C42—21no—
64C3×#213—28no—
65C3×(C2×D3)⋊C4—44no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8C2×C412yes—
71C2×C3×C3⋊C8D412yes—
72C2×C3×C3⋊C8D412yes—
73C2×C3×C3⋊C8D412yes—
74#1970—31noSylow
75C22×C3×D4—21no—
76C22×C3×D4—31no—
77C22×C3×D4C2×D311yescharacteristic
78C22×C3×D4C22×C311yescharacteristic
79C22×D12C22×C311yescharacteristic
80C2×C3×D8—34no—
81C2×C3×D8—62no—
82C2×C3×D8—62no—
83C22×C3×C8—31no—
84C22×C3×C8—31no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4—31no—
87C2×C3×C4⋊C4C2×D311yescharacteristic
88C2×C3×C4⋊C4C22×C311yescharacteristic
89C2×C3×C22⋊C4—24no—
90C2×C3×C22⋊C4—22no—
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—62no—
93C2×C3×C42—21no—
94C2×C3×C42C2×D311yescharacteristic
95C2×C3×C42C22×C311yescharacteristic
96C2×#213—22no—
97C2×#213—22no—
98C2×#213C3×C414yescomplemented
99C2×(C2×D3)⋊C4—22no—
100C2×C4⋊Dic3C22×C311yescharacteristic
101C22×C3⋊C8C22×C311yescharacteristic
102C22×C3⋊C8C22×C311yescharacteristic
103C3×#107—62no—
104C3×#102—62no—
105C3×#102—62no—
106C3×C4×C8—62no—
107#832—22no—
108#809—22no—
109#807—22no—
110C4×C3⋊C8—22no—
111C23×C32—22no—
112C23×C32—41no—
113C23×C32—41no—
114C23×C32—42no—
115C23×C32—42no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—22no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3—42no—
121C22×C3×D3—42no—
122C32×D4—22no—
123C32×D4—22no—
124C32×D4—41no—
125C32×D4—41no—
126C2×C32×C4—22no—
127C2×C32×C4—22no—
128C2×C32×C4—41no—
129C2×C32×C4—42no—
130C2×C32×C4D814yescomplemented
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C3×Dic3—41no—
138C2×C3×Dic3—42no—
139C3×D12—22no—
140C3×D12—22no—
141C3×D12—41no—
142C3×D12—41no—
143C3×C3⋊C8—22no—
144C3×C3⋊C8C22⋊C414yescomplemented
145C22×D8—31no—
146C2×#107—31no—
147C2×#102—31no—
148C2×#102—31no—
149C2×C4×C8—31no—
150#390—31no—
151#390C3×D311yescharacteristic, complemented
152C24×C3—22no—
153C24×C3—21no—
154C24×C3—21no—
155C24×C3—61no—
156C23×D3—21no—
157C2×C3×D4—22no—
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—21no—
168C2×C3×D4—22no—
169C2×C3×D4—32no—
170C2×C3×D4—41no—
171C2×C3×D4—41no—
172C2×C3×D4—41no—
173C2×C3×D4—41no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4C4×D312yes—
180C2×C3×D4C2×C3×C412yes—
181C22×C3×C4—22no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C22×C3×C4—61no—
187C22×C3×C4#6712yes—
188C22×C3×C4C3×D412yes—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C23×C311yescharacteristic
191C22×Dic3—21no—
192C2×D12—21no—
193C2×D12—21no—
194C2×D12—21no—
195C2×D12—21no—
196C2×D12—21no—
197C2×D12C2×C3×C412yes—
198C3×D8—68no—
199C2×C3×C8—32no—
200C2×C3×C8—32no—
201C2×C3×C8—32no—
202C2×C3×C8—32no—
203C2×C3×C8—61no—
204C2×C3×C8—61no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—41no—
210C3×C4⋊C4—41no—
211C3×C4⋊C4—61no—
212C3×C4⋊C4—61no—
213C3×C22⋊C4—48no—
214C3×C22⋊C4—44no—
215C3×C22⋊C4—44no—
216C3×C22⋊C4—124no—
217C3×C42—21no—
218C3×C42—21no—
219C3×C42—21no—
220C3×C42—21no—
221C3×C42—41no—
222C3×C42—41no—
223#213—28no—
224(C2×D3)⋊C4—44no—
225C4⋊Dic3—21no—
226C4⋊Dic3—21no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—21no—
229C2×C3⋊C8C2×C3×C412yes—
230C2×C3⋊C8C3×D412yes—
231C2×C3⋊C8C3×D412yes—
232C2×C3⋊C8C3×D412yes—
233C22×C32—42no—
234C22×C32—44no—
235C22×C32—82no—
236C22×C32—81no—
237C22×C32—81no—
238C22×C32C4×D411yescharacteristic
239C22×C32#12111yescharacteristic
240C22×C32#12711yescharacteristic
241C22×C32C2×D812yes—
242C22×C32#13512yes—
243C2×C3×D3—42no—
244C2×C3×D3—44no—
245C2×C3×D3—82no—
246C2×C3×D3—81no—
247C2×C3×D3—81no—
248C32×C4—24no—
249C32×C4—81no—
250C32×C4C2×C22⋊C411yescharacteristic
251C32×C4C4×D411yescharacteristic
252C32×C4#12111yescharacteristic
253C32×C4#12411yescharacteristic
254C3×Dic3—81no—
255C22×D4—31no—
256C22×D4C2×C3×D311yescharacteristic
257C2×D8—34no—
258C2×D8—62no—
259C2×D8—62no—
260C22×C8—31no—
261C22×C8—31no—
262C2×C4⋊C4—31no—
263C2×C4⋊C4C2×C3×D311yescharacteristic
264C2×C22⋊C4—22no—
265C2×C22⋊C4—62no—
266C2×C42C2×C3×D311yescharacteristic
267#107—62no—
268#102—62no—
269#102—62no—
270C4×C8—62no—
271C23×C3—24no—
272C23×C3—22no—
273C23×C3—22no—
274C23×C3—21no—
275C23×C3—44no—
276C23×C3—42no—
277C23×C3—42no—
278C23×C3—44no—
279C23×C3—42no—
280C23×C3—41no—
281C23×C3—41no—
282C23×C3—42no—
283C23×C3—41no—
284C23×C3—41no—
285C23×C3—42no—
286C23×C3—42no—
287C23×C3—62no—
288C23×C3—122no—
289C23×C3—121no—
290C23×C3—121no—
291C23×C3—122no—
292C23×C3C2×#6711yescharacteristic
293C23×C3C2×C3×D411yescharacteristic
294C22×D3—22no—
295C22×D3—41no—
296C22×D3—41no—
297C22×D3—42no—
298C22×D3—42no—
299C3×D4—22no—
300C3×D4—22no—
301C3×D4—22no—
302C3×D4—22no—
303C3×D4—42no—
304C3×D4—42no—
305C3×D4—42no—
306C3×D4—42no—
307C3×D4—41no—
308C3×D4—41no—
309C3×D4—41no—
310C3×D4—41no—
311C3×D4—62no—
312C3×D4—62no—
313C3×D4—121no—
314C3×D4—121no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—24no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—42no—
327C2×C3×C4—42no—
328C2×C3×C4—44no—
329C2×C3×C4—42no—
330C2×C3×C4—42no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—42no—
334C2×C3×C4—122no—
335C2×C3×C4—121no—
336C2×C3×C4#21314yescomplemented
337C2×C3×C4C3×D814yescomplemented
338C2×C3×C4C2×C4×D311yescharacteristic
339C2×C3×C4#23511yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4#23711yescharacteristic
344C2×C3×C4C22×C3×C411yescharacteristic
345C2×C3×C4C2×C3×D411yescharacteristic
346C2×C3×C4C2×C3×D411yescharacteristic
347C2×C3×C4C2×C3×D411yescharacteristic
348C2×C3×C4C3×#4111yescharacteristic
349C2×C3×C4C3×#4111yescharacteristic
350C2×Dic3—41no—
351C2×Dic3—42no—
352D12—22no—
353D12—22no—
354D12—41no—
355D12—41no—
356C3×C8—34no—
357C3×C8—62no—
358C3⋊C8—22no—
359C3⋊C8C3×C22⋊C414yescomplemented
360C2×C32—82no—
361C2×C32#39011yescharacteristic
362C2×C32C4×D812yes—
363C2×C32#46612yes—
364C2×C32#49311yescharacteristic
365C2×C32#49511yescharacteristic
366C3×D3—82no—
367C24—21no—
368C24—61no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—32no—
375C2×D4—61no—
376C2×D4—61no—
377C2×D4—61no—
378C2×D4—61no—
379C2×D4—61no—
380C2×D4C3×C4×D312yes—
381C22×C4—21no—
382C22×C4—61no—
383C22×C4C3×#6712yes—
384C22×C4C22×C3×D311yescharacteristic
385D8—68no—
386C2×C8—32no—
387C2×C8—32no—
388C2×C8—32no—
389C2×C8—32no—
390C2×C8—61no—
391C2×C8—61no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—61no—
395C4⋊C4—61no—
396C22⋊C4—44no—
397C22⋊C4—124no—
398C42—21no—
399C42—21no—
400C22×C3—21no—
401C22×C3—22no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—22no—
405C22×C3—44no—
406C22×C3—48no—
407C22×C3—42no—
408C22×C3—42no—
409C22×C3—44no—
410C22×C3—44no—
411C22×C3—84no—
412C22×C3—82no—
413C22×C3—82no—
414C22×C3—82no—
415C22×C3—81no—
416C22×C3—81no—
417C22×C3—82no—
418C22×C3—81no—
419C22×C3—81no—
420C22×C3—122no—
421C22×C3—124no—
422C22×C3—242no—
423C22×C3—241no—
424C22×C3—241no—
425C22×C3C4×#6711yescharacteristic
426C22×C3C2×#21312yes—
427C22×C3#93911yescharacteristic
428C22×C3#94011yescharacteristic
429C22×C3#95012yes—
430C22×C3C3×C4×D411yescharacteristic
431C22×C3C3×#12111yescharacteristic
432C22×C3C3×#12711yescharacteristic
433C22×C3C2×C3×D812yes—
434C22×C3C3×#13512yes—
435C2×D3—42no—
436C2×D3—44no—
437C2×D3—82no—
438C2×D3—81no—
439C2×D3—81no—
440C3×C4—24no—
441C3×C4—24no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—44no—
447C3×C4—82no—
448C3×C4—81no—
449C3×C4—81no—
450C3×C4—241no—
451C3×C4D3×C22⋊C411yescharacteristic
452C3×C4#67⋊C411yescharacteristic
453C3×C4#88411yescharacteristic
454C3×C4#88511yescharacteristic
455C3×C4C2×C3×C22⋊C411yescharacteristic
456C3×C4C3×C4×D411yescharacteristic
457C3×C4C3×#12111yescharacteristic
458C3×C4C3×#12411yescharacteristic
459Dic3—81no—
460C32#197011yescharacteristic, complemented, Sylow
461C23—22no—
462C23—42no—
463C23—41no—
464C23—41no—
465C23—42no—
466C23—62no—
467C23—122no—
468C23—121no—
469C23—121no—
470C23—122no—
471C23C2×C3×#6711yescharacteristic
472D4—22no—
473D4—22no—
474D4—41no—
475D4—41no—
476D4—62no—
477D4—62no—
478D4—121no—
479D4—121no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—122no—
485C2×C4—121no—
486C2×C4C3×#21314yescomplemented
487C2×C4C2×C3×C4×D311yescharacteristic
488C2×C4C3×#23511yescharacteristic
489C2×C4C3×D3×D411yescharacteristic
490C2×C4C3×D3×D411yescharacteristic
491C2×C4C3×D3×D411yescharacteristic
492C2×C4C3×#23711yescharacteristic
493C8—34no—
494C8—62no—
495C2×C3—21no—
496C2×C3—22no—
497C2×C3—22no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—84no—
501C2×C3—82no—
502C2×C3—82no—
503C2×C3—242no—
504C2×C3#495711yescharacteristic
505C2×C3C4×#21312yes—
506C2×C3#503812yes—
507C2×C3#505911yescharacteristic
508C2×C3#507311yescharacteristic
509C2×C3C3×#39011yescharacteristic
510C2×C3C3×C4×D812yes—
511C2×C3C3×#46612yes—
512C2×C3C3×#49311yescharacteristic
513C2×C3C3×#49511yescharacteristic
514D3—82no—
515C22—42no—
516C22—44no—
517C22—82no—
518C22—81no—
519C22—81no—
520C22—122no—
521C22—124no—
522C22—242no—
523C22—241no—
524C22—241no—
525C22C3×C4×#6711yescharacteristic
526C22C2×C3×#21312yes—
527C22C3×#93911yescharacteristic
528C22C3×#94011yescharacteristic
529C22C3×#95012yes—
530C4—24no—
531C4—81no—
532C4—241no—
533C4C3×D3×C22⋊C411yescharacteristic
534C4C3×#67⋊C411yescharacteristic
535C4C3×#88411yescharacteristic
536C4C3×#88511yescharacteristic
537C3—21no—
538C3#6964711yescharacteristic, direct product factor
539C3C3×#197011yescharacteristic, complemented
540C2—82no—
541C2—242no—
542C2C3×#495711yescharacteristic
543C2C3×C4×#21312yes—
544C2C3×#503812yes—
545C2C3×#505911yescharacteristic
546C2C3×#507311yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#390C2
socleC23×C32C2×D4
prime radicalC22×C3×#213C2
cosocleC22×C3×C4C23×C3
hypercenterC3×#390D3
hypocenterC3C3×#1970
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
2. C32×#390C2semidirect
3. C2×C3×#832C2semidirect
4. C2×C3×#809C2semidirect
5. C2×C3×#807C2semidirect
6. C3×#4939C2semidirect
7. C2×C3×C4×C3⋊C8C2semidirect
9. #69647C3direct (N × H)
17. C2×C3×#213C4semidirect
34. C3×#390D3semidirect
35. C3×#390C2×C3semidirect
36. C2×#832C2×C3semidirect
37. C2×#809C2×C3semidirect
38. C2×#807C2×C3semidirect
39. #4939C2×C3semidirect
40. C2×C4×C3⋊C8C2×C3semidirect
98. C2×#213C3×C4semidirect
130. C2×C32×C4D8semidirect
144. C3×C3⋊C8C22⋊C4semidirect
151. #390C3×D3semidirect
336. C2×C3×C4#213semidirect
337. C2×C3×C4C3×D8semidirect
359. C3⋊C8C3×C22⋊C4semidirect
460. C32#1970semidirect
486. C2×C4C3×#213semidirect
538. C3#69647direct (N × H)
539. C3C3×#1970semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2132
C32×#3902
C2×C3×#8322
C2×C3×#8092
C2×C3×#8072
C3×#49392
C2×C3×C4×C3⋊C82
C3×#19703
#696473