Finite Group Databasebeta

← C3×#81070 #11882240

Subgroups — C3×#81070 #11882240

Order 1152.

838 conjugacy classes of subgroups.

The subgroup lattice has 613 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5728C211yesmaximal, characteristic, complemented
2C3×#5548C211yesmaximal, characteristic
3C32×#476C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5C3×#5019C211yesmaximal, characteristic, complemented
6C3×#4864C212yesmaximal, complemented
7C3×#4854C212yesmaximal, complemented
8C3×#4841C211yesmaximal, characteristic, complemented
9C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
10C3×#4778C212yesmaximal, complemented
11C3×#4762C212yesmaximal, complemented
12C3×#3246—31nomaximal
13#81070C311yesmaximal, characteristic, direct product factor
14C2×C3×#235—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4×D4C2211yescharacteristic
17C3×#946—21no—
18C3×Q8×Dic3—21no—
19C3×#940C2211yescharacteristic
20C3×#938C2211yescharacteristic
21C2×C3×#214C2212yes—
22C3×C4×#67—21no—
23C2×C3×#204C2212yes—
24C2×C3×D3×C8C2212yes—
25C3×#897C2212yes—
26C3×#895C2211yescharacteristic
27C3×#892—21no—
28C3×#890—21no—
29C3×#888C2211yescharacteristic
30C3×#887C2212yes—
31C3×#885—21no—
32C3×#884—21no—
33C3×C4×D12C2211yescharacteristic
34C3×C42×D3C2211yescharacteristic
35C3×#869C2211yescharacteristic
36C32×#106C2212yes—
37C32×C4⋊C8C2211yescharacteristic
38C32×#102C2212yes—
39C3×#816C2212yes—
40C3×Dic3⋊C8C2212yes—
41C3×#810C2212yes—
42C3×#809C2212yes—
43C3×#808C2212yes—
44C3×C4⋊(C3⋊C8)C2211yescharacteristic
45C3×#533—31no—
46C3×#532—31no—
47#5728C2×C311yescharacteristic, complemented
48#5548C2×C311yescharacteristic
49C3×#476—21no—
50C3×#476—31no—
51C3×#476D311yescharacteristic, complemented
52C3×#476C2×C311yescharacteristic, complemented
53C3×#475—32no—
54C3×#465—32no—
55C3×#465—32no—
56C3×#461—31no—
57C3×#461—31no—
58C3×#460—32no—
59C2×C3×C4⋊C8—31no—
60#5084C2×C311yescharacteristic, complemented
61#5019C2×C311yescharacteristic, complemented
62#4864C2×C312yescomplemented
63#4854C2×C312yescomplemented
64#4841C2×C311yescharacteristic, complemented
65D3×C4⋊C8C2×C311yescharacteristic, complemented
66#4778C2×C312yescomplemented
67#4762C2×C312yescomplemented
68C2×C32×Q8—21no—
69C2×C32×D4C2311yescharacteristic
70C22×C32×C4—21no—
71C2×C3×#67—21no—
72C2×C3×#67—21no—
73C2×C3×#67—21no—
74C3×#235—44no—
75C2×C3×D12—21no—
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3D411yescharacteristic
79C2×C3×C4×D3D411yescharacteristic
80C2×C3×C4×D3C2311yescharacteristic
81C2×C3×Dic6—21no—
82C2×C3×Dic6C2312yes—
83C2×C32×C8C2312yes—
84C32×C4⋊C4—21no—
85C32×C4⋊C4C2312yes—
86C32×C4⋊C4C2311yescharacteristic
87C32×C22⋊C4—21no—
88C32×C42C2311yescharacteristic
89C3×#217—21no—
90C3×#214—42no—
91C3×(C2×D3)⋊C4—22no—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3—22no—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×Dic3⋊C4—21no—
99C3×Dic3⋊C4—22no—
100C3×C4×Dic3—22no—
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C2×C3×C3⋊C8C2312yes—
105C3×#204—42no—
106C3×D3×C8—42no—
107#3246—31noSylow
108C2×C3×#41—61no—
109C2×#235—21no—
110C2×C3×SD16—32no—
111C2×C3×SD16—32no—
112C22×C3×C8—32no—
113C3×C4⋊Q8—21no—
114C3×C4⋊Q8—31no—
115C3×C4⋊Q8—31no—
116C3×C4⋊Q8C2×D311yescharacteristic
117C3×C4⋊Q8C22×C311yescharacteristic
118C3×#127—31no—
119C3×#125—61no—
120C3×#124—61no—
121C3×C22⋊Q8—32no—
122C3×C22⋊Q8—61no—
123C3×#121—31no—
124C3×#121—31no—
125C3×#121—61no—
126C3×C4×Q8—32no—
127C3×C4×Q8—61no—
128C3×C4×D4—21no—
129C3×C4×D4—31no—
130C3×C4×D4—61no—
131C3×C4×D4C2×D311yescharacteristic
132C3×C4×D4C22×C311yescharacteristic
133C3×#117—61no—
134C2×C3×C42—31no—
135#946—21no—
136Q8×Dic3—21no—
137#940C22×C311yescharacteristic
138#938C22×C311yescharacteristic
139C2×#214C22×C312yes—
140C4×#67—21no—
141C2×#204C22×C312yes—
142C2×D3×C8C22×C312yes—
143#897C22×C312yes—
144#895C22×C311yescharacteristic
145#892—21no—
146#890—21no—
147#888C22×C311yescharacteristic
148#887C22×C312yes—
149#885—21no—
150#884—21no—
151C4×D12C22×C311yescharacteristic
152C42×D3C22×C311yescharacteristic
153#869C22×C311yescharacteristic
154C3×#106—22no—
155C3×#106—32no—
156C3×#106C2×D312yes—
157C3×#106C22×C312yes—
158C3×C4⋊C8—21no—
159C3×C4⋊C8—32no—
160C3×C4⋊C8—31no—
161C3×C4⋊C8C2×D311yescharacteristic
162C3×C4⋊C8C22×C311yescharacteristic
163C3×#103—32no—
164C3×#103—32no—
165C3×#102—22no—
166C3×#102—32no—
167C3×#102C2×D312yes—
168C3×#102C22×C312yes—
169#816C22×C312yes—
170Dic3⋊C8C22×C312yes—
171#810C22×C312yes—
172#809C22×C312yes—
173#808C22×C312yes—
174C4⋊(C3⋊C8)C22×C311yescharacteristic
175C23×C32—21no—
176C22×C3×D3—21no—
177C22×C3×D3C2×D411yescharacteristic
178C32×Q8—42no—
179C32×D4—21no—
180C32×D4—21no—
181C2×C32×C4—22no—
182C2×C32×C4—21no—
183C2×C32×C4—42no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187C3×#67—42no—
188C3×#67—42no—
189C3×#67—42no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C3×D12—21no—
196C3×D12—21no—
197C3×D12—42no—
198C3×C4×D3—21no—
199C3×C4×D3—21no—
200C3×C4×D3—41no—
201C3×C4×D3—42no—
202C3×C4×D3SD1614yescomplemented
203C3×Dic6—22no—
204C3×Dic6—22no—
205C3×Dic6—42no—
206C32×C8—22no—
207C3×C3⋊C8—22no—
208#533—31no—
209#532—31no—
210#476—31no—
211#476C3×D311yescharacteristic, complemented
212#475—32no—
213#465—32no—
214#465—32no—
215#461—31no—
216#461—31no—
217#460—32no—
218C2×C4⋊C8—31no—
219C3×#41—124no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—32no—
223C2×C3×Q8—41no—
224C2×C3×Q8—61no—
225C2×C3×D4—21no—
226C2×C3×D4—31no—
227C2×C3×D4—61no—
228C2×C3×D4—61no—
229C2×C3×D4—61no—
230C2×C3×D4—61no—
231C2×C3×D4C22×D311yescharacteristic
232C2×C3×D4C23×C311yescharacteristic
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—31no—
236C22×C3×C4—31no—
237C22×C3×C4—31no—
238C22×C3×C4—41no—
239C22×C3×C4—61no—
240C2×#67—21no—
241C2×#67—21no—
242C2×#67—21no—
243#235—44no—
244C2×D12—21no—
245C2×D12C23×C311yescharacteristic
246C2×C4×D3—21no—
247C2×C4×D3C3×D411yescharacteristic
248C2×C4×D3C3×D411yescharacteristic
249C2×C4×D3C23×C311yescharacteristic
250C2×Dic6—21no—
251C2×Dic6C23×C312yes—
252C3×SD16—122no—
253C3×SD16—122no—
254C2×C3×C8—22no—
255C2×C3×C8—32no—
256C2×C3×C8—122no—
257C2×C3×C8C22×D312yes—
258C2×C3×C8C23×C312yes—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—22no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—31no—
264C3×C4⋊C4—41no—
265C3×C4⋊C4—61no—
266C3×C4⋊C4—62no—
267C3×C4⋊C4—62no—
268C3×C4⋊C4—61no—
269C3×C4⋊C4—61no—
270C3×C4⋊C4C22×D312yes—
271C3×C4⋊C4C22×D311yescharacteristic
272C3×C4⋊C4C23×C312yes—
273C3×C4⋊C4C23×C311yescharacteristic
274C3×C22⋊C4—21no—
275C3×C22⋊C4—21no—
276C3×C22⋊C4—41no—
277C3×C22⋊C4—61no—
278C3×C22⋊C4—62no—
279C3×C22⋊C4—61no—
280C3×C22⋊C4—61no—
281C3×C42—21no—
282C3×C42—31no—
283C3×C42—31no—
284C3×C42—31no—
285C3×C42—62no—
286C3×C42C22×D311yescharacteristic
287C3×C42C23×C311yescharacteristic
288#217—21no—
289#214—42no—
290(C2×D3)⋊C4—22no—
291(C2×D3)⋊C4—21no—
292(C2×D3)⋊C4—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3—22no—
296C4⋊Dic3C23×C311yescharacteristic
297Dic3⋊C4—21no—
298Dic3⋊C4—22no—
299C4×Dic3—22no—
300C4×Dic3C3×D411yescharacteristic
301C4×Dic3C3×D411yescharacteristic
302C4×Dic3C23×C311yescharacteristic
303C2×C3⋊C8C23×C312yes—
304#204—42no—
305D3×C8—42no—
306C22×C32—41no—
307C22×C32—41no—
308C22×C32—41no—
309C22×C32C22×D411yescharacteristic
310C2×C3×D3—21no—
311C2×C3×D3—21no—
312C2×C3×D3—41no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C2×C3×D3C2×SD1612yes—
316C32×C4—21no—
317C32×C4—41no—
318C32×C4—42no—
319C32×C4C2×SD1612yes—
320C32×C4H(5,𝔽2)11yescharacteristic
321C32×C42−1+411yescharacteristic
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—42no—
325C3×Dic3—41no—
326C3×Dic3C2×SD1612yes—
327C2×#41—61no—
328C2×SD16—32no—
329C2×SD16—32no—
330C22×C8—32no—
331C4⋊Q8—31no—
332C4⋊Q8—31no—
333C4⋊Q8C2×C3×D311yescharacteristic
334#127—31no—
335#125—61no—
336#124—61no—
337C22⋊Q8—32no—
338C22⋊Q8—61no—
339#121—31no—
340#121—31no—
341#121—61no—
342C4×Q8—32no—
343C4×Q8—61no—
344C4×D4—31no—
345C4×D4—61no—
346C4×D4C2×C3×D311yescharacteristic
347#117—61no—
348C2×C42—31no—
349#106—32no—
350#106C2×C3×D312yes—
351C4⋊C8—32no—
352C4⋊C8—31no—
353C4⋊C8C2×C3×D311yescharacteristic
354#103—32no—
355#103—32no—
356#102—32no—
357#102C2×C3×D312yes—
358C23×C3—21no—
359C23×C3—21no—
360C23×C3—31no—
361C23×C3—41no—
362C23×C3—61no—
363C22×D3—21no—
364C22×D3C2×C3×D411yescharacteristic
365C3×Q8—42no—
366C3×Q8—42no—
367C3×Q8—62no—
368C3×Q8—62no—
369C3×Q8—82no—
370C3×Q8—122no—
371C3×D4—22no—
372C3×D4—21no—
373C3×D4—21no—
374C3×D4—21no—
375C3×D4—21no—
376C3×D4—41no—
377C3×D4—61no—
378C3×D4—61no—
379C3×D4—122no—
380C3×D4—122no—
381C3×D4—122no—
382C3×D4—122no—
383C2×C3×C4—22no—
384C2×C3×C4—21no—
385C2×C3×C4—22no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—31no—
391C2×C3×C4—34no—
392C2×C3×C4—31no—
393C2×C3×C4—31no—
394C2×C3×C4—41no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4—42no—
398C2×C3×C4—61no—
399C2×C3×C4—61no—
400C2×C3×C4—62no—
401C2×C3×C4—61no—
402C2×C3×C4—82no—
403C2×C3×C4—121no—
404C2×C3×C4—122no—
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4D3×D411yescharacteristic
407C2×C3×C4C2×C3×D411yescharacteristic
408C2×C3×C4C2×C3×D411yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410C2×C3×C4C24×C311yescharacteristic
411#67—42no—
412#67—42no—
413#67—42no—
414C2×Dic3—22no—
415C2×Dic3—21no—
416C2×Dic3C2×C3×D411yescharacteristic
417C2×Dic3C2×C3×D411yescharacteristic
418C2×Dic3C2×C3×D411yescharacteristic
419D12—21no—
420D12—21no—
421D12—42no—
422C4×D3—21no—
423C4×D3—21no—
424C4×D3—41no—
425C4×D3—42no—
426C4×D3C3×SD1614yescomplemented
427Dic6—22no—
428Dic6—22no—
429Dic6—42no—
430C3×C8—22no—
431C3×C8—22no—
432C3×C8—42no—
433C3×C8—62no—
434C3⋊C8—22no—
435C2×C32—81no—
436C2×C32#53711yescharacteristic
437C2×C32C22×SD1611yescharacteristic
438C2×C32#57511yescharacteristic
439C3×D3—22no—
440C3×D3—81no—
441#41—124no—
442C2×Q8—21no—
443C2×Q8—32no—
444C2×Q8—61no—
445C2×D4—31no—
446C2×D4—61no—
447C2×D4—61no—
448C2×D4—61no—
449C2×D4—61no—
450C2×D4C22×C3×D311yescharacteristic
451C22×C4—21no—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4—31no—
455C22×C4—61no—
456SD16—122no—
457SD16—122no—
458C2×C8—32no—
459C2×C8—122no—
460C2×C8C22×C3×D312yes—
461C4⋊C4—21no—
462C4⋊C4—31no—
463C4⋊C4—61no—
464C4⋊C4—62no—
465C4⋊C4—62no—
466C4⋊C4—61no—
467C4⋊C4—61no—
468C4⋊C4C22×C3×D312yes—
469C4⋊C4C22×C3×D311yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—61no—
472C22⋊C4—62no—
473C22⋊C4—61no—
474C22⋊C4—61no—
475C42—31no—
476C42—31no—
477C42—31no—
478C42—62no—
479C42C22×C3×D311yescharacteristic
480C22×C3—21no—
481C22×C3—32no—
482C22×C3—42no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—61no—
490C22×C3—61no—
491C22×C3—81no—
492C22×C3—81no—
493C22×C3—121no—
494C22×C3—121no—
495C22×C3—121no—
496C22×C3C2×D3×D411yescharacteristic
497C22×C3C22×C3×D411yescharacteristic
498C2×D3—21no—
499C2×D3—21no—
500C2×D3—41no—
501C2×D3—41no—
502C2×D3—41no—
503C2×D3C2×C3×SD1612yes—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—22no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—32no—
510C3×C4—41no—
511C3×C4—41no—
512C3×C4—42no—
513C3×C4—41no—
514C3×C4—42no—
515C3×C4—61no—
516C3×C4—61no—
517C3×C4—81no—
518C3×C4—82no—
519C3×C4—121no—
520C3×C4—122no—
521C3×C4D3×SD1612yes—
522C3×C4C2×C3×SD1612yes—
523C3×C4#100711yescharacteristic
524C3×C4#100911yescharacteristic
525C3×C4C3×H(5,𝔽2)11yescharacteristic
526C3×C4C3×2−1+411yescharacteristic
527Dic3—21no—
528Dic3—21no—
529Dic3—41no—
530Dic3—42no—
531Dic3C2×C3×SD1612yes—
532C32#324611yescharacteristic, complemented, Sylow
533C23—21no—
534C23—31no—
535C23—61no—
536Q8—42no—
537Q8—62no—
538Q8—62no—
539Q8—122no—
540D4—21no—
541D4—21no—
542D4—61no—
543D4—61no—
544D4—122no—
545D4—122no—
546D4—122no—
547D4—122no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—31no—
551C2×C4—34no—
552C2×C4—31no—
553C2×C4—31no—
554C2×C4—42no—
555C2×C4—61no—
556C2×C4—61no—
557C2×C4—62no—
558C2×C4—61no—
559C2×C4—121no—
560C2×C4—122no—
561C2×C4C3×D3×D411yescharacteristic
562C2×C4C3×D3×D411yescharacteristic
563C2×C4C23×C3×D311yescharacteristic
564C8—22no—
565C8—62no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—62no—
570C2×C3—82no—
571C2×C3—81no—
572C2×C3—81no—
573C2×C3—241no—
574C2×C3#562911yescharacteristic
575C2×C3C2×D3×SD1611yescharacteristic
576C2×C3#577311yescharacteristic
577C2×C3C3×#53711yescharacteristic
578C2×C3C22×C3×SD1611yescharacteristic
579C2×C3C3×#57511yescharacteristic
580D3—22no—
581D3—81no—
582C22—32no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—61no—
587C22—61no—
588C22—121no—
589C22—121no—
590C22—121no—
591C22C2×C3×D3×D411yescharacteristic
592C4—21no—
593C4—32no—
594C4—41no—
595C4—42no—
596C4—61no—
597C4—61no—
598C4—121no—
599C4—122no—
600C4C3×D3×SD1612yes—
601C4C3×#100711yescharacteristic
602C4C3×#100911yescharacteristic
603C3—21no—
604C3#8107011yescharacteristic, direct product factor
605C3C3×#324611yescharacteristic, complemented
606C2—62no—
607C2—81no—
608C2—241no—
609C2C3×#562911yescharacteristic
610C2C2×C3×D3×SD1611yescharacteristic
611C2C3×#577311yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#476C2
socleC22×C32C22×D4
prime radicalC3×#5548C2
hypercenterC3×#476D3
hypocenterC3C3×#3246
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#476

Complements

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

NH ≅ G/Ntype
1. C3×#5728C2semidirect
3. C32×#476C2semidirect
4. C3×#5084C2semidirect
5. C3×#5019C2semidirect
6. C3×#4864C2semidirect
7. C3×#4854C2semidirect
8. C3×#4841C2semidirect
9. C3×D3×C4⋊C8C2semidirect
10. C3×#4778C2semidirect
11. C3×#4762C2semidirect
13. #81070C3direct (N × H)
47. #5728C2×C3semidirect
51. C3×#476D3semidirect
52. C3×#476C2×C3semidirect
60. #5084C2×C3semidirect
61. #5019C2×C3semidirect
62. #4864C2×C3semidirect
63. #4854C2×C3semidirect
64. #4841C2×C3semidirect
65. D3×C4⋊C8C2×C3semidirect
66. #4778C2×C3semidirect
67. #4762C2×C3semidirect
202. C3×C4×D3SD16semidirect
211. #476C3×D3semidirect
426. C4×D3C3×SD16semidirect
532. C32#3246semidirect
604. C3#81070direct (N × H)
605. C3C3×#3246semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
C3×#55482
C32×#4762
C3×#50842
C3×#50192
C3×#48642
C3×#48542
C3×#48412
C3×D3×C4⋊C82
C3×#47782
C3×#47622
C3×#32463
#810703