Finite Group Databasebeta

← C3×#70357 #11790799

Subgroups — C3×#70357 #11790799

Order 1152.

725 conjugacy classes of subgroups.

The subgroup lattice has 562 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×#4932C211yesmaximal, characteristic, complemented
7C2×C3×#805C211yesmaximal, characteristic, complemented
8C3×#1963—31nomaximal
9#70357C311yesmaximal, 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×Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C32×#104—22no—
24C3×#837—22no—
25C3×C3⋊#95—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×#376—31no—
39C2×#837C2×C311yescharacteristic, complemented
40C2×#825C2×C311yescharacteristic, complemented
41#5118C2×C311yescharacteristic, complemented
42#4932C2×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—21no—
74C3×C4×Dic3C2×C411yescharacteristic
75C3×C4×Dic3C2×C411yescharacteristic
76C3×C4×Dic3D412yes—
77C3×C4×Dic3D412yescomplemented
78C3×#208—21no—
79C3×#208—21no—
80C2×C3×C3⋊C8—21no—
81#1963—31noSylow
82C2×C3×#41—21no—
83C2×C3×#41—31no—
84C2×C3×#41C2×D311yescharacteristic
85C2×C3×#41C22×C311yescharacteristic
86C2×#235C22×C311yescharacteristic
87C2×C3×M16—21no—
88C2×C3×M16—31no—
89C2×C3×M16C2×D311yescharacteristic
90C2×C3×M16C22×C311yescharacteristic
91C3×C4⋊Q8—31no—
92C3×#127—31no—
93C3×#124—31no—
94C3×#124—31no—
95C3×#121—62no—
96C3×C4×D4—62no—
97C2×C3×C42—21no—
98C2×C3×C42—31no—
99C2×C3×C42—31no—
100C2×C3×C42C2×D311yescharacteristic
101C2×C3×C42C22×C311yescharacteristic
102#947C3×C411yescharacteristic, complemented
103#944C3×C411yescharacteristic, complemented
104#940C3×C411yescharacteristic, complemented
105#939—22no—
106#936C3×C411yescharacteristic, complemented
107C4×#67—22no—
108C2×C4×Dic3C22×C311yescharacteristic
109C2×C4×Dic3C22×C311yescharacteristic
110C2×#208C22×C311yescharacteristic
111C3×C4⋊C8—62no—
112C3×#104—24no—
113C3×#104—22no—
114C3×#104—22no—
115C3×#104—62no—
116C3×#104—62no—
117C3×#104—62no—
118C3×#95—62no—
119#837—22no—
120C3⋊#95—22no—
121#825—22no—
122Dic3⋊C8—22no—
123#805—22no—
124C23×C32—21no—
125C23×C32C2×D411yescharacteristic
126C22×C3×D3—21no—
127C32×Q8—21no—
128C32×Q8—21no—
129C32×D4—21no—
130C32×D4—21no—
131C32×D4—41no—
132C32×D4—41no—
133C2×C32×C4—21no—
134C2×C32×C4—22no—
135C2×C32×C4—42no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4C22×C411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C3×#67—44no—
145C3×#67—41no—
146C3×#67—41no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—42no—
150C2×C3×Dic3—42no—
151C2×C3×Dic3C22⋊C412yes—
152C2×C3×Dic3C22⋊C412yes—
153C3×D12—21no—
154C3×D12—21no—
155C3×C4×D3—41no—
156C3×C4×D3—41no—
157C3×Dic6—21no—
158C3×Dic6—21no—
159C32×C8—41no—
160C3×C3⋊C8—41no—
161#532—31no—
162#423—31no—
163C2×#104—31no—
164C2×#104—31no—
165C2×#104—31no—
166C2×#104C3×D311yescharacteristic, complemented
167#376—31no—
168C3×#41—22no—
169C3×#41—22no—
170C3×#41—21no—
171C3×#41—21no—
172C3×#41—21no—
173C3×#41—21no—
174C3×#41—21no—
175C3×#41—21no—
176C3×#41—21no—
177C3×#41—21no—
178C3×#41—41no—
179C3×#41—41no—
180C3×#41—61no—
181C3×#41—61no—
182C3×#41—61no—
183C3×#41—61no—
184C2×C3×Q8—21no—
185C2×C3×Q8—31no—
186C2×C3×Q8C4×D311yescharacteristic
187C2×C3×Q8C2×C3×C411yescharacteristic
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—31no—
192C2×C3×D4—41no—
193C2×C3×D4—62no—
194C2×C3×D4—61no—
195C2×C3×D4C4×D311yescharacteristic
196C2×C3×D4C2×C3×C411yescharacteristic
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—32no—
203C22×C3×C4—41no—
204C22×C3×C4—41no—
205C22×C3×C4—61no—
206C22×C3×C4—61no—
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C23×C311yescharacteristic
209C2×#67—21no—
210C2×#67—22no—
211C22×Dic3—21no—
212C22×Dic3C3×D412yes—
213#235—21no—
214#235—21no—
215#235—21no—
216#235—21no—
217C2×D12C2×C3×C411yescharacteristic
218C2×C4×D3—21no—
219C2×Dic6C2×C3×C411yescharacteristic
220C3×M16—22no—
221C3×M16—21no—
222C3×M16—21no—
223C3×M16—21no—
224C3×M16—21no—
225C3×M16—41no—
226C3×M16—61no—
227C3×M16—61no—
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8—41no—
231C2×C3×C8—61no—
232C3×C4⋊C4—62no—
233C3×C22⋊C4—62no—
234C3×C22⋊C4—62no—
235C3×C42—21no—
236C3×C42—21no—
237C3×C42—22no—
238C3×C42—31no—
239C3×C42—31no—
240C3×C42—32no—
241C3×C42—32no—
242C3×C42—41no—
243C3×C42—61no—
244C3×C42#6712yescomplemented
245C3×C42C3×D412yescomplemented
246#217—22no—
247(C2×D3)⋊C4—22no—
248Dic3⋊C4—22no—
249C4×Dic3—21no—
250C4×Dic3C2×C3×C411yescharacteristic
251C4×Dic3C2×C3×C411yescharacteristic
252C4×Dic3C3×D412yes—
253C4×Dic3C3×D412yescomplemented
254#208—21no—
255#208—21no—
256C2×C3⋊C8—21no—
257C22×C32—22no—
258C22×C32—41no—
259C22×C32—42no—
260C22×C32C2×C22⋊C411yescharacteristic
261C22×C32#12111yescharacteristic
262C22×C32#12111yescharacteristic
263C2×C3×D3—41no—
264C2×C3×D3—42no—
265C32×C4—42no—
266C32×C4—41no—
267C32×C4C4×D411yescharacteristic
268C32×C4C4×D411yescharacteristic
269C32×C4#12411yescharacteristic
270C32×C4#12711yescharacteristic
271C3×Dic3—22no—
272C3×Dic3—22no—
273C3×Dic3—42no—
274C3×Dic3—41no—
275C2×#41—31no—
276C2×#41C2×C3×D311yescharacteristic
277C2×M16—31no—
278C2×M16C2×C3×D311yescharacteristic
279C4⋊Q8—31no—
280#127—31no—
281#124—31no—
282#124—31no—
283#121—62no—
284C4×D4—62no—
285C2×C42—31no—
286C2×C42—31no—
287C2×C42C2×C3×D311yescharacteristic
288C4⋊C8—62no—
289#104—22no—
290#104—62no—
291#104—62no—
292#104—62no—
293#95—62no—
294C23×C3—21no—
295C23×C3—21no—
296C23×C3—21no—
297C23×C3—41no—
298C23×C3—61no—
299C23×C3D3×D411yescharacteristic
300C23×C3C2×C3×D411yescharacteristic
301C22×D3—21no—
302C3×Q8—22no—
303C3×Q8—21no—
304C3×Q8—21no—
305C3×Q8—21no—
306C3×Q8—21no—
307C3×Q8—41no—
308C3×Q8—61no—
309C3×Q8—61no—
310C3×D4—22no—
311C3×D4—21no—
312C3×D4—21no—
313C3×D4—21no—
314C3×D4—21no—
315C3×D4—41no—
316C3×D4—42no—
317C3×D4—42no—
318C3×D4—41no—
319C3×D4—41no—
320C3×D4—41no—
321C3×D4—41no—
322C3×D4—61no—
323C3×D4—61no—
324C3×D4—124no—
325C3×D4—121no—
326C3×D4—121no—
327C2×C3×C4—21no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—22no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—32no—
338C2×C3×C4—32no—
339C2×C3×C4—42no—
340C2×C3×C4—41no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—44no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—61no—
351C2×C3×C4—62no—
352C2×C3×C4—122no—
353C2×C3×C4—122no—
354C2×C3×C4—121no—
355C2×C3×C4—121no—
356C2×C3×C4C2×C4×D311yescharacteristic
357C2×C3×C4#23511yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4#23711yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C22×C3×C411yescharacteristic
363C2×C3×C4C2×C3×D411yescharacteristic
364C2×C3×C4C2×C3×D411yescharacteristic
365C2×C3×C4C2×C3×D411yescharacteristic
366C2×C3×C4C3×#4111yescharacteristic
367C2×C3×C4C3×#4111yescharacteristic
368#67—44no—
369#67—41no—
370#67—41no—
371C2×Dic3—21no—
372C2×Dic3—22no—
373C2×Dic3—42no—
374C2×Dic3—42no—
375C2×Dic3C3×C22⋊C412yes—
376C2×Dic3C3×C22⋊C412yes—
377D12—21no—
378D12—21no—
379C4×D3—41no—
380C4×D3—41no—
381Dic6—21no—
382Dic6—21no—
383C3×C8—42no—
384C3×C8—41no—
385C3×C8—41no—
386C3×C8—121no—
387C3⋊C8—41no—
388C2×C32—21no—
389C2×C32—21no—
390C2×C32—81no—
391C2×C32#39011yescharacteristic
392C2×C32#42112yes—
393C3×D3—81no—
394#41—21no—
395#41—21no—
396#41—21no—
397#41—21no—
398#41—61no—
399#41—61no—
400#41—61no—
401#41—61no—
402C2×Q8—31no—
403C2×Q8C3×C4×D311yescharacteristic
404C2×D4—21no—
405C2×D4—31no—
406C2×D4—62no—
407C2×D4—61no—
408C2×D4C3×C4×D311yescharacteristic
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—32no—
412C22×C4—61no—
413C22×C4—61no—
414C22×C4C22×C3×D311yescharacteristic
415M16—21no—
416M16—21no—
417M16—61no—
418M16—61no—
419C2×C8—21no—
420C2×C8—61no—
421C4⋊C4—62no—
422C22⋊C4—62no—
423C22⋊C4—62no—
424C42—21no—
425C42—31no—
426C42—31no—
427C42—32no—
428C42—32no—
429C42—61no—
430C42C3×#6712yescomplemented
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—82no—
443C22×C3—121no—
444C22×C3—122no—
445C22×C3D3×C22⋊C411yescharacteristic
446C22×C3#88411yescharacteristic
447C22×C3#93911yescharacteristic
448C22×C3C2×C3×C22⋊C411yescharacteristic
449C22×C3C3×#12111yescharacteristic
450C22×C3C3×#12111yescharacteristic
451C2×D3—41no—
452C2×D3—42no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—42no—
458C3×C4—42no—
459C3×C4—42no—
460C3×C4—44no—
461C3×C4—41no—
462C3×C4—41no—
463C3×C4—62no—
464C3×C4—62no—
465C3×C4—122no—
466C3×C4—121no—
467C3×C4#67⋊C411yescharacteristic
468C3×C4#88511yescharacteristic
469C3×C4C4×#6711yescharacteristic
470C3×C4#94011yescharacteristic
471C3×C4C3×C4×D411yescharacteristic
472C3×C4C3×C4×D411yescharacteristic
473C3×C4C3×#12411yescharacteristic
474C3×C4C3×#12711yescharacteristic
475Dic3—22no—
476Dic3—22no—
477Dic3—42no—
478Dic3—41no—
479C32#196311yescharacteristic, complemented, Sylow
480C23—21no—
481C23—61no—
482C23C3×D3×D411yescharacteristic
483Q8—21no—
484Q8—21no—
485Q8—61no—
486Q8—61no—
487D4—21no—
488D4—21no—
489D4—41no—
490D4—41no—
491D4—61no—
492D4—61no—
493D4—124no—
494D4—121no—
495D4—121no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—32no—
499C2×C4—32no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—61no—
504C2×C4—62no—
505C2×C4—122no—
506C2×C4—122no—
507C2×C4—121no—
508C2×C4—121no—
509C2×C4C2×C3×C4×D311yescharacteristic
510C2×C4C3×#23511yescharacteristic
511C2×C4C3×D3×D411yescharacteristic
512C2×C4C3×D3×D411yescharacteristic
513C2×C4C3×#23711yescharacteristic
514C2×C4C2×C3×#6711yescharacteristic
515C8—41no—
516C8—121no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—22no—
523C2×C3—41no—
524C2×C3—41no—
525C2×C3—82no—
526C2×C3—81no—
527C2×C3—81no—
528C2×C3—241no—
529C2×C3#482112yes—
530C2×C3#495711yescharacteristic
531C2×C3C3×#39011yescharacteristic
532C2×C3C3×#42112yes—
533D3—81no—
534C22—22no—
535C22—41no—
536C22—42no—
537C22—121no—
538C22—122no—
539C22C3×D3×C22⋊C411yescharacteristic
540C22C3×#88411yescharacteristic
541C22C3×#93911yescharacteristic
542C4—42no—
543C4—41no—
544C4—62no—
545C4—62no—
546C4—122no—
547C4—121no—
548C4C3×#67⋊C411yescharacteristic
549C4C3×#88511yescharacteristic
550C4C3×C4×#6711yescharacteristic
551C4C3×#94011yescharacteristic
552C3—21no—
553C3#7035711yescharacteristic, direct product factor
554C3C3×#196311yescharacteristic, complemented
555C2—21no—
556C2—21no—
557C2—81no—
558C2—241no—
559C2C3×#482112yes—
560C2C3×#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×#1963
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×#4932C2semidirect
7. C2×C3×#805C2semidirect
9. #70357C3direct (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. #4932C2×C3semidirect
43. C2×#805C2×C3semidirect
69. C32×C42D4semidirect
77. C3×C4×Dic3D4semidirect
102. #947C3×C4semidirect
103. #944C3×C4semidirect
104. #940C3×C4semidirect
106. #936C3×C4semidirect
166. C2×#104C3×D3semidirect
244. C3×C42#67semidirect
245. C3×C42C3×D4semidirect
253. C4×Dic3C3×D4semidirect
430. C42C3×#67semidirect
479. C32#1963semidirect
553. C3#70357direct (N × H)
554. C3C3×#1963semidirect

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×#49322
C2×C3×#8052
C3×#19633
#703573