Finite Group Databasebeta

← C3×#70356 #11790772

Subgroups — C3×#70356 #11790772

Order 1152.

805 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5832C211yesmaximal, characteristic
2C2×C32×#104C211yesmaximal, characteristic, complemented
3C2×C3×#837C211yesmaximal, characteristic, complemented
4C2×C3×#825C211yesmaximal, characteristic, complemented
5C3×#5118C211yesmaximal, characteristic, complemented
6C3×C42×Dic3C211yesmaximal, characteristic, complemented
7C2×C3×#805C211yesmaximal, characteristic, complemented
8C3×#1962—31nomaximal
9#70356C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C3×#947C411yescharacteristic, complemented
15C3×#944C411yescharacteristic, complemented
16C3×#940C411yescharacteristic, complemented
17C3×#939—22no—
18C3×#936C411yescharacteristic, complemented
19C3×C4×#67—22no—
20C2×C3×C4×Dic3—22no—
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C32×#104—22no—
25C3×#837—22no—
26C3×#825—22no—
27C3×Dic3⋊C8—22no—
28C3×#805—22no—
29C3×#532—31no—
30#5832C2×C311yescharacteristic
31C3×#423—31no—
32C2×C3×#104—21no—
33C2×C3×#104—31no—
34C2×C3×#104—31no—
35C2×C3×#104—31no—
36C2×C3×#104D311yescharacteristic, complemented
37C2×C3×#104C2×C311yescharacteristic, complemented
38C3×C43—31no—
39C2×#837C2×C311yescharacteristic, complemented
40C2×#825C2×C311yescharacteristic, complemented
41#5118C2×C311yescharacteristic, complemented
42C42×Dic3C2×C311yescharacteristic, complemented
43C2×#805C2×C311yescharacteristic, complemented
44C32×#41—21no—
45C32×#41—21no—
46C32×#41—21no—
47C32×#41—21no—
48C2×C32×Q8C2×C411yescharacteristic
49C2×C32×D4—21no—
50C2×C32×D4C2×C411yescharacteristic
51C22×C32×C4—21no—
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C2×C3×#67—21no—
55C2×C3×#67—22no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3D412yes—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C3×#235—21no—
62C2×C3×D12C2×C411yescharacteristic
63C2×C3×C4×D3—21no—
64C2×C3×Dic6C2×C411yescharacteristic
65C32×M16—21no—
66C32×M16—21no—
67C2×C32×C8—21no—
68C32×C42—21no—
69C32×C42D412yescomplemented
70C3×#217—22no—
71C3×(C2×D3)⋊C4—22no—
72C3×Dic3⋊C4—22no—
73C3×C4×Dic3—28no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3C2×C411yescharacteristic
76C3×C4×Dic3C2×C411yescharacteristic
77C3×C4×Dic3D412yes—
78C3×C4×Dic3D412yescomplemented
79C3×#208—21no—
80C3×#208—21no—
81C2×C3×C3⋊C8—21no—
82#1962—31noSylow
83C2×C3×#41—21no—
84C2×C3×#41—31no—
85C2×C3×#41C2×D311yescharacteristic
86C2×C3×#41C22×C311yescharacteristic
87C2×#235C22×C311yescharacteristic
88C2×C3×M16—21no—
89C2×C3×M16—31no—
90C2×C3×M16C2×D311yescharacteristic
91C2×C3×M16C22×C311yescharacteristic
92C3×C4⋊Q8—31no—
93C3×#127—31no—
94C3×#124—31no—
95C3×#124—31no—
96C3×#121—62no—
97C3×C4×D4—62no—
98C2×C3×C42—21no—
99C2×C3×C42—31no—
100C2×C3×C42—31no—
101C2×C3×C42—62no—
102C2×C3×C42C2×D311yescharacteristic
103C2×C3×C42C22×C311yescharacteristic
104#947C3×C411yescharacteristic, complemented
105#944C3×C411yescharacteristic, complemented
106#940C3×C411yescharacteristic, complemented
107#939—22no—
108#936C3×C411yescharacteristic, complemented
109C4×#67—22no—
110C2×C4×Dic3—22no—
111C2×C4×Dic3C22×C311yescharacteristic
112C2×C4×Dic3C22×C311yescharacteristic
113C2×#208C22×C311yescharacteristic
114C3×C4⋊C8—62no—
115C3×#104—24no—
116C3×#104—22no—
117C3×#104—22no—
118C3×#104—62no—
119C3×#104—62no—
120C3×#104—62no—
121#837—22no—
122#825—22no—
123Dic3⋊C8—22no—
124#805—22no—
125C23×C32—21no—
126C23×C32C2×D411yescharacteristic
127C22×C3×D3—21no—
128C32×Q8—21no—
129C32×Q8—21no—
130C32×D4—21no—
131C32×D4—21no—
132C32×D4—41no—
133C32×D4—41no—
134C2×C32×C4—24no—
135C2×C32×C4—22no—
136C2×C32×C4—21no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4C22×C411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C3×#67—41no—
146C3×#67—41no—
147C3×#67—44no—
148C2×C3×Dic3—24no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—24no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3C22⋊C412yes—
153C2×C3×Dic3C22⋊C412yes—
154C3×D12—21no—
155C3×D12—21no—
156C3×C4×D3—41no—
157C3×C4×D3—41no—
158C3×Dic6—21no—
159C3×Dic6—21no—
160C32×C8—41no—
161C3×C3⋊C8—41no—
162#532—31no—
163#423—31no—
164C2×#104—31no—
165C2×#104—31no—
166C2×#104—31no—
167C2×#104C3×D311yescharacteristic, complemented
168C43—31no—
169C3×#41—22no—
170C3×#41—22no—
171C3×#41—21no—
172C3×#41—21no—
173C3×#41—21no—
174C3×#41—21no—
175C3×#41—21no—
176C3×#41—21no—
177C3×#41—21no—
178C3×#41—21no—
179C3×#41—41no—
180C3×#41—41no—
181C3×#41—61no—
182C3×#41—61no—
183C3×#41—61no—
184C3×#41—61no—
185C2×C3×Q8—21no—
186C2×C3×Q8—31no—
187C2×C3×Q8C4×D311yescharacteristic
188C2×C3×Q8C2×C3×C411yescharacteristic
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—31no—
193C2×C3×D4—41no—
194C2×C3×D4—62no—
195C2×C3×D4—61no—
196C2×C3×D4C4×D311yescharacteristic
197C2×C3×D4C2×C3×C411yescharacteristic
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—32no—
204C22×C3×C4—41no—
205C22×C3×C4—41no—
206C22×C3×C4—61no—
207C22×C3×C4—61no—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C23×C311yescharacteristic
210C2×#67—21no—
211C2×#67—22no—
212C22×Dic3—21no—
213C22×Dic3C3×D412yes—
214#235—21no—
215#235—21no—
216#235—21no—
217#235—21no—
218C2×D12C2×C3×C411yescharacteristic
219C2×C4×D3—21no—
220C2×Dic6C2×C3×C411yescharacteristic
221C3×M16—22no—
222C3×M16—21no—
223C3×M16—21no—
224C3×M16—21no—
225C3×M16—21no—
226C3×M16—41no—
227C3×M16—61no—
228C3×M16—61no—
229C2×C3×C8—21no—
230C2×C3×C8—21no—
231C2×C3×C8—41no—
232C2×C3×C8—61no—
233C3×C4⋊C4—62no—
234C3×C22⋊C4—62no—
235C3×C22⋊C4—62no—
236C3×C42—21no—
237C3×C42—21no—
238C3×C42—22no—
239C3×C42—31no—
240C3×C42—31no—
241C3×C42—32no—
242C3×C42—32no—
243C3×C42—41no—
244C3×C42—68no—
245C3×C42—61no—
246C3×C42#6712yescomplemented
247C3×C42C3×D412yescomplemented
248#217—22no—
249(C2×D3)⋊C4—22no—
250Dic3⋊C4—22no—
251C4×Dic3—28no—
252C4×Dic3—21no—
253C4×Dic3C2×C3×C411yescharacteristic
254C4×Dic3C2×C3×C411yescharacteristic
255C4×Dic3C3×D412yes—
256C4×Dic3C3×D412yescomplemented
257#208—21no—
258#208—21no—
259C2×C3⋊C8—21no—
260C22×C32—22no—
261C22×C32—41no—
262C22×C32—42no—
263C22×C32C2×C22⋊C411yescharacteristic
264C22×C32#12111yescharacteristic
265C22×C32#12111yescharacteristic
266C2×C3×D3—41no—
267C2×C3×D3—42no—
268C32×C4—24no—
269C32×C4—41no—
270C32×C4C4×D411yescharacteristic
271C32×C4C4×D411yescharacteristic
272C32×C4#12411yescharacteristic
273C32×C4#12711yescharacteristic
274C3×Dic3—24no—
275C3×Dic3—22no—
276C3×Dic3—41no—
277C3×Dic3#10414yescomplemented
278C2×#41—31no—
279C2×#41C2×C3×D311yescharacteristic
280C2×M16—31no—
281C2×M16C2×C3×D311yescharacteristic
282C4⋊Q8—31no—
283#127—31no—
284#124—31no—
285#124—31no—
286#121—62no—
287C4×D4—62no—
288C2×C42—31no—
289C2×C42—31no—
290C2×C42—62no—
291C2×C42C2×C3×D311yescharacteristic
292C4⋊C8—62no—
293#104—22no—
294#104—62no—
295#104—62no—
296#104—62no—
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—41no—
301C23×C3—61no—
302C23×C3D3×D411yescharacteristic
303C23×C3C2×C3×D411yescharacteristic
304C22×D3—21no—
305C3×Q8—22no—
306C3×Q8—21no—
307C3×Q8—21no—
308C3×Q8—21no—
309C3×Q8—21no—
310C3×Q8—41no—
311C3×Q8—61no—
312C3×Q8—61no—
313C3×D4—22no—
314C3×D4—21no—
315C3×D4—21no—
316C3×D4—21no—
317C3×D4—21no—
318C3×D4—41no—
319C3×D4—42no—
320C3×D4—42no—
321C3×D4—41no—
322C3×D4—41no—
323C3×D4—41no—
324C3×D4—41no—
325C3×D4—61no—
326C3×D4—61no—
327C3×D4—124no—
328C3×D4—121no—
329C3×D4—121no—
330C2×C3×C4—24no—
331C2×C3×C4—24no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—32no—
343C2×C3×C4—32no—
344C2×C3×C4—42no—
345C2×C3×C4—41no—
346C2×C3×C4—44no—
347C2×C3×C4—42no—
348C2×C3×C4—42no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—64no—
354C2×C3×C4—64no—
355C2×C3×C4—62no—
356C2×C3×C4—61no—
357C2×C3×C4—121no—
358C2×C3×C4—121no—
359C2×C3×C4C2×C4×D311yescharacteristic
360C2×C3×C4#23511yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4#23711yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C22×C3×C411yescharacteristic
366C2×C3×C4C2×C3×D411yescharacteristic
367C2×C3×C4C2×C3×D411yescharacteristic
368C2×C3×C4C2×C3×D411yescharacteristic
369C2×C3×C4C3×#4111yescharacteristic
370C2×C3×C4C3×#4111yescharacteristic
371#67—41no—
372#67—41no—
373#67—44no—
374C2×Dic3—24no—
375C2×Dic3—22no—
376C2×Dic3—24no—
377C2×Dic3—21no—
378C2×Dic3C3×C22⋊C412yes—
379C2×Dic3C3×C22⋊C412yes—
380D12—21no—
381D12—21no—
382C4×D3—41no—
383C4×D3—41no—
384Dic6—21no—
385Dic6—21no—
386C3×C8—42no—
387C3×C8—41no—
388C3×C8—41no—
389C3×C8—121no—
390C3⋊C8—41no—
391C2×C32—21no—
392C2×C32—21no—
393C2×C32—81no—
394C2×C32#39011yescharacteristic
395C2×C32C2×#10412yes—
396C3×D3—81no—
397#41—21no—
398#41—21no—
399#41—21no—
400#41—21no—
401#41—61no—
402#41—61no—
403#41—61no—
404#41—61no—
405C2×Q8—31no—
406C2×Q8C3×C4×D311yescharacteristic
407C2×D4—21no—
408C2×D4—31no—
409C2×D4—62no—
410C2×D4—61no—
411C2×D4C3×C4×D311yescharacteristic
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—32no—
415C22×C4—61no—
416C22×C4—61no—
417C22×C4C22×C3×D311yescharacteristic
418M16—21no—
419M16—21no—
420M16—61no—
421M16—61no—
422C2×C8—21no—
423C2×C8—61no—
424C4⋊C4—62no—
425C22⋊C4—62no—
426C22⋊C4—62no—
427C42—21no—
428C42—31no—
429C42—31no—
430C42—32no—
431C42—32no—
432C42—68no—
433C42—61no—
434C42C3×#6712yescomplemented
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—42no—
445C22×C3—42no—
446C22×C3—82no—
447C22×C3—121no—
448C22×C3—122no—
449C22×C3D3×C22⋊C411yescharacteristic
450C22×C3#88411yescharacteristic
451C22×C3#93911yescharacteristic
452C22×C3C2×C3×C22⋊C411yescharacteristic
453C22×C3C3×#12111yescharacteristic
454C22×C3C3×#12111yescharacteristic
455C2×D3—41no—
456C2×D3—42no—
457C3×C4—24no—
458C3×C4—24no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—34no—
464C3×C4—44no—
465C3×C4—42no—
466C3×C4—41no—
467C3×C4—41no—
468C3×C4—64no—
469C3×C4—62no—
470C3×C4—121no—
471C3×C4#67⋊C411yescharacteristic
472C3×C4#88511yescharacteristic
473C3×C4C4×#6711yescharacteristic
474C3×C4#94011yescharacteristic
475C3×C4C3×C4×D411yescharacteristic
476C3×C4C3×C4×D411yescharacteristic
477C3×C4C3×#12411yescharacteristic
478C3×C4C3×#12711yescharacteristic
479Dic3—24no—
480Dic3—22no—
481Dic3—41no—
482Dic3C3×#10414yescomplemented
483C32#196211yescharacteristic, complemented, Sylow
484C23—21no—
485C23—61no—
486C23C3×D3×D411yescharacteristic
487Q8—21no—
488Q8—21no—
489Q8—61no—
490Q8—61no—
491D4—21no—
492D4—21no—
493D4—41no—
494D4—41no—
495D4—61no—
496D4—61no—
497D4—124no—
498D4—121no—
499D4—121no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—32no—
504C2×C4—32no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—64no—
508C2×C4—64no—
509C2×C4—62no—
510C2×C4—61no—
511C2×C4—121no—
512C2×C4—121no—
513C2×C4C2×C3×C4×D311yescharacteristic
514C2×C4C3×#23511yescharacteristic
515C2×C4C3×D3×D411yescharacteristic
516C2×C4C3×D3×D411yescharacteristic
517C2×C4C3×#23711yescharacteristic
518C2×C4C2×C3×#6711yescharacteristic
519C8—41no—
520C8—121no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—22no—
527C2×C3—41no—
528C2×C3—41no—
529C2×C3—82no—
530C2×C3—81no—
531C2×C3—81no—
532C2×C3—241no—
533C2×C3D3×#10412yes—
534C2×C3#495711yescharacteristic
535C2×C3C3×#39011yescharacteristic
536C2×C3C2×C3×#10412yes—
537D3—81no—
538C22—22no—
539C22—41no—
540C22—42no—
541C22—121no—
542C22—122no—
543C22C3×D3×C22⋊C411yescharacteristic
544C22C3×#88411yescharacteristic
545C22C3×#93911yescharacteristic
546C4—24no—
547C4—34no—
548C4—41no—
549C4—64no—
550C4—62no—
551C4—121no—
552C4C3×#67⋊C411yescharacteristic
553C4C3×#88511yescharacteristic
554C4C3×C4×#6711yescharacteristic
555C4C3×#94011yescharacteristic
556C3—21no—
557C3#7035611yescharacteristic, direct product factor
558C3C3×#196211yescharacteristic, complemented
559C2—21no—
560C2—21no—
561C2—81no—
562C2—241no—
563C2C3×D3×#10412yes—
564C2C3×#495711yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#104C2
socleC22×C32C2×C22⋊C4
prime radicalC3×#5832C2
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#104D3
hypocenterC3C3×#1962
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ C2×C3×#104

Complements

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

NH ≅ G/Ntype
2. C2×C32×#104C2semidirect
3. C2×C3×#837C2semidirect
4. C2×C3×#825C2semidirect
5. C3×#5118C2semidirect
6. C3×C42×Dic3C2semidirect
7. C2×C3×#805C2semidirect
9. #70356C3direct (N × H)
14. C3×#947C4semidirect
15. C3×#944C4semidirect
16. C3×#940C4semidirect
18. C3×#936C4semidirect
36. C2×C3×#104D3semidirect
37. C2×C3×#104C2×C3semidirect
39. C2×#837C2×C3semidirect
40. C2×#825C2×C3semidirect
41. #5118C2×C3semidirect
42. C42×Dic3C2×C3semidirect
43. C2×#805C2×C3semidirect
69. C32×C42D4semidirect
78. C3×C4×Dic3D4semidirect
104. #947C3×C4semidirect
105. #944C3×C4semidirect
106. #940C3×C4semidirect
108. #936C3×C4semidirect
167. C2×#104C3×D3semidirect
246. C3×C42#67semidirect
247. C3×C42C3×D4semidirect
256. C4×Dic3C3×D4semidirect
277. C3×Dic3#104semidirect
434. C42C3×#67semidirect
482. Dic3C3×#104semidirect
483. C32#1962semidirect
557. C3#70356direct (N × H)
558. C3C3×#1962semidirect

Maximal subgroups

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

subgroupindex
C3×#58322
C2×C32×#1042
C2×C3×#8372
C2×C3×#8252
C3×#51182
C3×C42×Dic32
C2×C3×#8052
C3×#19623
#703563