Finite Group Databasebeta

← C3×#70395 #11788557

Subgroups — C3×#70395 #11788557

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Dic3×#41C211yesmaximal, characteristic, complemented
2C3×#5822C211yesmaximal, characteristic
3C32×#421C211yesmaximal, characteristic, complemented
4C2×C3×#825C211yesmaximal, characteristic, complemented
5C3×#5006C211yesmaximal, characteristic, complemented
6C3×#4556C211yesmaximal, characteristic, complemented
7C3×#4532C211yesmaximal, characteristic, complemented
8C3×#1906—31nomaximal
9#70395C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C32×#117C2211yescharacteristic
14C3×#951C412yescomplemented
15C3×#950—22no—
16C3×#949C412yescomplemented
17C3×Q8×Dic3—21no—
18C3×#942—21no—
19C3×D4×Dic3—21no—
20C3×D4×Dic3—22no—
21C3×#932—21no—
22C3×#926—21no—
23C3×#926C2211yescharacteristic
24C2×C3×C4×Dic3—21no—
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C32×#104—22no—
28C3×#825—21no—
29C3×#825—21no—
30C3×#806—22no—
31C3×#575—31no—
32C3×C4×#41—31no—
33Dic3×#41C2×C311yescharacteristic, complemented
34#5822C2×C311yescharacteristic
35C3×#421—21no—
36C3×#421D311yescharacteristic, complemented
37C3×#421C2×C311yescharacteristic, complemented
38C2×C3×#104—31no—
39C3×#410—31no—
40C2×#825C2×C311yescharacteristic, complemented
41#5006C2×C311yescharacteristic, complemented
42C3×#344—31no—
43C3×#339—31no—
44#4556C2×C311yescharacteristic, complemented
45#4532C2×C311yescharacteristic, complemented
46C32×#41—21no—
47C32×#41—21no—
48C32×#41C2×C412yes—
49C32×#41D412yes—
50C2×C32×Q8D411yescharacteristic
51C2×C32×D4—21no—
52C2×C32×D4D411yescharacteristic
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C2×C3×#67—21no—
56C22×C3×Dic3—22no—
57C22×C3×Dic3—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C3×#235—21no—
62C2×C3×D12C2×C411yescharacteristic, complemented
63C2×C3×C4×D3—21no—
64C2×C3×Dic6C2×C411yescharacteristic, complemented
65C32×M16—21no—
66C32×M16—21no—
67C2×C32×C8—21no—
68C32×C4⋊C4—21no—
69C32×C22⋊C4—21no—
70C32×C42—21no—
71C3×#217—22no—
72C3×#217D412yes—
73C3×#216—22no—
74C3×#215—22no—
75C3×#214—22no—
76C3×#213—22no—
77C3×C4⋊Dic3—22no—
78C3×C4⋊Dic3—21no—
79C3×C4×Dic3—22no—
80C3×C4×Dic3—21no—
81C3×C4×Dic3—21no—
82C3×C4×Dic3D411yescharacteristic
83C3×C4×Dic3D411yescharacteristic
84C3×#208—21no—
85C3×#208C2×C412yescomplemented
86C2×C3×C3⋊C8—21no—
87#1906—31noSylow
88C2×C3×#41—21no—
89C2×C3×#41—31no—
90C2×C3×#41C2×D311yescharacteristic
91C2×C3×#41C22×C311yescharacteristic
92C2×#235C22×C311yescharacteristic
93C3×#137—32no—
94C3×#137—61no—
95C3×AGL(1,ℤ/8)—32no—
96C3×AGL(1,ℤ/8)—61no—
97C3×#135—62no—
98C2×C3×M16—21no—
99C2×C3×M16—31no—
100C2×C3×M16C2×D311yescharacteristic
101C2×C3×M16C22×C311yescharacteristic
102C3×C4×Q8—61no—
103C3×C4×D4—62no—
104C3×C4×D4—61no—
105C3×#117—21no—
106C3×#117—31no—
107C3×#117—61no—
108C3×#117C2×D311yescharacteristic
109C3×#117C22×C311yescharacteristic
110C2×C3×C42—31no—
111C2×C3×C42—61no—
112#951C3×C412yescomplemented
113#950—22no—
114#949C3×C412yescomplemented
115Q8×Dic3—21no—
116#942—21no—
117D4×Dic3—21no—
118D4×Dic3—22no—
119#932—21no—
120#926—21no—
121#926C22×C311yescharacteristic
122C2×C4×Dic3—21no—
123C2×C4×Dic3C22×C311yescharacteristic
124C2×#208C22×C311yescharacteristic
125C3×#104—24no—
126C3×#104—22no—
127C3×#104—22no—
128C3×#104—61no—
129C3×#104—61no—
130C3×#99—62no—
131#825—21no—
132#825—21no—
133#806—22no—
134C23×C32—21no—
135C23×C32C2×D411yescharacteristic
136C22×C3×D3—21no—
137C32×Q8—21no—
138C32×Q8C22⋊C412yes—
139C32×D4—22no—
140C32×D4—22no—
141C32×D4—21no—
142C32×D4C22⋊C412yes—
143C2×C32×C4—21no—
144C2×C32×C4—22no—
145C2×C32×C4—22no—
146C2×C32×C4—41no—
147C2×C32×C4C22×C411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4#4111yescharacteristic
152C2×C32×C4#4111yescharacteristic
153C3×#67—41no—
154C3×#67—41no—
155C2×C3×Dic3—21no—
156C2×C3×Dic3—21no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—42no—
160C2×C3×Dic3—44no—
161C3×D12—21no—
162C3×D12—21no—
163C3×C4×D3—41no—
164C3×C4×D3—41no—
165C3×Dic6—21no—
166C3×Dic6—21no—
167C32×C8—41no—
168C3×C3⋊C8—22no—
169#575—31no—
170C4×#41—31no—
171#421C3×D311yescharacteristic, complemented
172C2×#104—31no—
173#410—31no—
174#344—31no—
175#339—31no—
176C3×#41—21no—
177C3×#41—21no—
178C3×#41—21no—
179C3×#41—21no—
180C3×#41—22no—
181C3×#41—22no—
182C3×#41—41no—
183C3×#41—41no—
184C3×#41—61no—
185C3×#41—61no—
186C3×#41—61no—
187C3×#41—61no—
188C3×#41C4×D312yes—
189C3×#41#6712yes—
190C3×#41C2×C3×C412yes—
191C3×#41C3×D412yes—
192C2×C3×Q8—21no—
193C2×C3×Q8—31no—
194C2×C3×Q8D1211yescharacteristic
195C2×C3×Q8C3×D411yescharacteristic
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4—31no—
200C2×C3×D4—41no—
201C2×C3×D4—61no—
202C2×C3×D4D1211yescharacteristic
203C2×C3×D4C3×D411yescharacteristic
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—41no—
208C22×C3×C4—62no—
209C22×C3×C4—61no—
210C22×C3×C4—61no—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C23×C311yescharacteristic
213C2×#67—21no—
214C22×Dic3—22no—
215C22×Dic3—21no—
216#235—21no—
217#235—21no—
218#235—21no—
219#235—21no—
220C2×D12C2×C3×C411yescharacteristic, complemented
221C2×C4×D3—21no—
222C2×Dic6C2×C3×C411yescharacteristic, complemented
223C3×Q16—62no—
224C3×SD16—62no—
225C3×SD16—62no—
226C3×D8—62no—
227C3×M16—22no—
228C3×M16—21no—
229C3×M16—21no—
230C3×M16—21no—
231C3×M16—21no—
232C3×M16—32no—
233C3×M16—41no—
234C3×M16—61no—
235C2×C3×C8—21no—
236C2×C3×C8—21no—
237C2×C3×C8—41no—
238C2×C3×C8—61no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—41no—
242C3×C4⋊C4—62no—
243C3×C4⋊C4—61no—
244C3×C22⋊C4—21no—
245C3×C22⋊C4—21no—
246C3×C22⋊C4—32no—
247C3×C22⋊C4—41no—
248C3×C22⋊C4—62no—
249C3×C42—22no—
250C3×C42—21no—
251C3×C42—21no—
252C3×C42—31no—
253C3×C42—31no—
254C3×C42—62no—
255C3×C42—61no—
256C3×C42—61no—
257#217—22no—
258#217C3×D412yes—
259#216—22no—
260#215—22no—
261#214—22no—
262#213—22no—
263C4⋊Dic3—22no—
264C4⋊Dic3—21no—
265C4×Dic3—22no—
266C4×Dic3—21no—
267C4×Dic3—21no—
268C4×Dic3C3×D411yescharacteristic
269C4×Dic3C3×D411yescharacteristic
270#208—21no—
271#208C2×C3×C412yescomplemented
272C2×C3⋊C8—21no—
273C22×C32—22no—
274C22×C32—41no—
275C22×C32—42no—
276C22×C32C4×D411yescharacteristic
277C22×C32#12011yescharacteristic
278C22×C32#12111yescharacteristic
279C2×C3×D3—41no—
280C2×C3×D3—81no—
281C32×C4—22no—
282C32×C4—81no—
283C32×C4C2×C22⋊C411yescharacteristic
284C32×C4C4×D411yescharacteristic
285C32×C4#12111yescharacteristic
286C32×C4#12311yescharacteristic
287C3×Dic3—22no—
288C3×Dic3—42no—
289C3×Dic3—41no—
290C3×Dic3—41no—
291C2×#41—31no—
292C2×#41C2×C3×D311yescharacteristic
293#137—32no—
294#137—61no—
295AGL(1,ℤ/8)—32no—
296AGL(1,ℤ/8)—61no—
297#135—62no—
298C2×M16—31no—
299C2×M16C2×C3×D311yescharacteristic
300C4×Q8—61no—
301C4×D4—62no—
302C4×D4—61no—
303#117—31no—
304#117—61no—
305#117C2×C3×D311yescharacteristic
306C2×C42—31no—
307C2×C42—61no—
308#104—22no—
309#104—61no—
310#104—61no—
311#99—62no—
312C23×C3—21no—
313C23×C3—21no—
314C23×C3—21no—
315C23×C3—41no—
316C23×C3—61no—
317C23×C3D3×D411yescharacteristic
318C23×C3C2×C3×D411yescharacteristic
319C22×D3—21no—
320C3×Q8—21no—
321C3×Q8—21no—
322C3×Q8—22no—
323C3×Q8—41no—
324C3×Q8—61no—
325C3×Q8—61no—
326C3×Q8(C2×D3)⋊C412yes—
327C3×Q8C3×C22⋊C412yes—
328C3×D4—22no—
329C3×D4—22no—
330C3×D4—22no—
331C3×D4—22no—
332C3×D4—21no—
333C3×D4—21no—
334C3×D4—22no—
335C3×D4—41no—
336C3×D4—42no—
337C3×D4—42no—
338C3×D4—61no—
339C3×D4—61no—
340C3×D4—121no—
341C3×D4—121no—
342C3×D4(C2×D3)⋊C412yes—
343C3×D4C3×C22⋊C412yes—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—42no—
357C2×C3×C4—42no—
358C2×C3×C4—41no—
359C2×C3×C4—42no—
360C2×C3×C4—41no—
361C2×C3×C4—41no—
362C2×C3×C4—61no—
363C2×C3×C4—61no—
364C2×C3×C4—61no—
365C2×C3×C4—62no—
366C2×C3×C4—122no—
367C2×C3×C4—124no—
368C2×C3×C4—121no—
369C2×C3×C4—121no—
370C2×C3×C4C2×C4×D311yescharacteristic
371C2×C3×C4C2×D1211yescharacteristic
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4#23711yescharacteristic
374C2×C3×C4#23711yescharacteristic
375C2×C3×C4C2×#6711yescharacteristic
376C2×C3×C4C22×C3×C411yescharacteristic
377C2×C3×C4C2×C3×D411yescharacteristic
378C2×C3×C4C2×C3×D411yescharacteristic
379C2×C3×C4C2×C3×D411yescharacteristic
380C2×C3×C4C3×#4111yescharacteristic
381C2×C3×C4C3×#4111yescharacteristic
382#67—41no—
383#67—41no—
384C2×Dic3—21no—
385C2×Dic3—21no—
386C2×Dic3—22no—
387C2×Dic3—21no—
388C2×Dic3—42no—
389C2×Dic3—44no—
390D12—21no—
391D12—21no—
392C4×D3—41no—
393C4×D3—41no—
394Dic6—21no—
395Dic6—21no—
396C3×C8—42no—
397C3×C8—41no—
398C3×C8—41no—
399C3×C8—62no—
400C3⋊C8—22no—
401C2×C32—21no—
402C2×C32—21no—
403C2×C32—21no—
404C2×C32—42no—
405C2×C32#38611yescharacteristic
406C3×D3—81no—
407#41—21no—
408#41—21no—
409#41—61no—
410#41—61no—
411#41—61no—
412#41—61no—
413#41C3×C4×D312yes—
414#41C3×#6712yes—
415C2×Q8—31no—
416C2×Q8C3×D1211yescharacteristic
417C2×D4—21no—
418C2×D4—31no—
419C2×D4—61no—
420C2×D4C3×D1211yescharacteristic
421C22×C4—21no—
422C22×C4—62no—
423C22×C4—61no—
424C22×C4—61no—
425C22×C4C22×C3×D311yescharacteristic
426Q16—62no—
427SD16—62no—
428SD16—62no—
429D8—62no—
430M16—21no—
431M16—21no—
432M16—32no—
433M16—61no—
434C2×C8—21no—
435C2×C8—61no—
436C4⋊C4—21no—
437C4⋊C4—62no—
438C4⋊C4—61no—
439C22⋊C4—21no—
440C22⋊C4—32no—
441C22⋊C4—62no—
442C42—21no—
443C42—31no—
444C42—31no—
445C42—62no—
446C42—61no—
447C42—61no—
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—42no—
454C22×C3—41no—
455C22×C3—41no—
456C22×C3—42no—
457C22×C3—42no—
458C22×C3—81no—
459C22×C3—82no—
460C22×C3—121no—
461C22×C3—241no—
462C22×C3#67⋊C411yescharacteristic
463C22×C3#88211yescharacteristic
464C22×C3#93911yescharacteristic
465C22×C3C3×C4×D411yescharacteristic
466C22×C3C3×#12011yescharacteristic
467C22×C3C3×#12111yescharacteristic
468C2×D3—41no—
469C2×D3—81no—
470C3×C4—22no—
471C3×C4—22no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—42no—
477C3×C4—62no—
478C3×C4—81no—
479C3×C4—81no—
480C3×C4—82no—
481C3×C4—121no—
482C3×C4—122no—
483C3×C4—121no—
484C3×C4#67⋊C411yescharacteristic
485C3×C4#88611yescharacteristic
486C3×C4C2×(C2×D3)⋊C411yescharacteristic
487C3×C4#93911yescharacteristic
488C3×C4C2×C3×C22⋊C411yescharacteristic
489C3×C4C3×C4×D411yescharacteristic
490C3×C4C3×#12111yescharacteristic
491C3×C4C3×#12311yescharacteristic
492Dic3—22no—
493Dic3—42no—
494Dic3—41no—
495Dic3—41no—
496C32#190611yescharacteristic, complemented, Sylow
497C23—21no—
498C23—61no—
499C23C3×D3×D411yescharacteristic
500Q8—21no—
501Q8—61no—
502Q8—61no—
503Q8C3×(C2×D3)⋊C412yes—
504D4—22no—
505D4—22no—
506D4—21no—
507D4—61no—
508D4—61no—
509D4—121no—
510D4—121no—
511D4C3×(C2×D3)⋊C412yes—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—61no—
517C2×C4—61no—
518C2×C4—61no—
519C2×C4—62no—
520C2×C4—122no—
521C2×C4—124no—
522C2×C4—121no—
523C2×C4—121no—
524C2×C4C2×C3×C4×D311yescharacteristic
525C2×C4C2×C3×D1211yescharacteristic
526C2×C4C3×D3×D411yescharacteristic
527C2×C4C3×#23711yescharacteristic
528C2×C4C3×#23711yescharacteristic
529C2×C4C2×C3×#6711yescharacteristic
530C8—41no—
531C8—62no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—41no—
540C2×C3—41no—
541C2×C3—41no—
542C2×C3—42no—
543C2×C3—42no—
544C2×C3—82no—
545C2×C3—241no—
546C2×C3#495811yescharacteristic
547C2×C3C3×#38611yescharacteristic
548D3—81no—
549C22—22no—
550C22—41no—
551C22—42no—
552C22—121no—
553C22—241no—
554C22C3×#67⋊C411yescharacteristic
555C22C3×#88211yescharacteristic
556C22C3×#93911yescharacteristic
557C4—22no—
558C4—62no—
559C4—81no—
560C4—121no—
561C4—122no—
562C4—121no—
563C4C3×#67⋊C411yescharacteristic
564C4C3×#88611yescharacteristic
565C4C2×C3×(C2×D3)⋊C411yescharacteristic
566C4C3×#93911yescharacteristic
567C3—21no—
568C3#7039511yescharacteristic, direct product factor
569C3C3×#190611yescharacteristic, complemented
570C2—21no—
571C2—21no—
572C2—21no—
573C2—42no—
574C2—241no—
575C2C3×#495811yescharacteristic
subgroupG/H
centerC3×C4#939
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#421C2
socleC2×C32#386
prime radicalC3×#5822C2
cosocleC22×C3×C4C23×C3
hypercenterC3×#421D3
hypocenterC3C3×#1906
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#421

Complements

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

NH ≅ G/Ntype
1. C3×Dic3×#41C2semidirect
3. C32×#421C2semidirect
4. C2×C3×#825C2semidirect
5. C3×#5006C2semidirect
6. C3×#4556C2semidirect
7. C3×#4532C2semidirect
9. #70395C3direct (N × H)
14. C3×#951C4semidirect
16. C3×#949C4semidirect
33. Dic3×#41C2×C3semidirect
36. C3×#421D3semidirect
37. C3×#421C2×C3semidirect
40. C2×#825C2×C3semidirect
41. #5006C2×C3semidirect
44. #4556C2×C3semidirect
45. #4532C2×C3semidirect
62. C2×C3×D12C2×C4semidirect
64. C2×C3×Dic6C2×C4semidirect
85. C3×#208C2×C4semidirect
112. #951C3×C4semidirect
114. #949C3×C4semidirect
171. #421C3×D3semidirect
220. C2×D12C2×C3×C4semidirect
222. C2×Dic6C2×C3×C4semidirect
271. #208C2×C3×C4semidirect
496. C32#1906semidirect
568. C3#70395direct (N × H)
569. C3C3×#1906semidirect

Maximal subgroups

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

subgroupindex
C3×Dic3×#412
C3×#58222
C32×#4212
C2×C3×#8252
C3×#50062
C3×#45562
C3×#45322
C3×#19063
#703953