Finite Group Databasebeta

← C3×#80343 #11882298

Subgroups — C3×#80343 #11882298

Order 1152.

866 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5716C211yesmaximal, characteristic, complemented
2C3×#5557C211yesmaximal, characteristic, complemented
3C32×#459C211yesmaximal, characteristic, complemented
4C3×#5157C212yesmaximal, complemented
5C3×#5153C212yesmaximal, complemented
6C3×#5075C211yesmaximal, characteristic, complemented
7C3×#5008C211yesmaximal, characteristic, complemented
8C3×#4850C211yesmaximal, characteristic, complemented
9C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
10C3×#4778C212yesmaximal, complemented
11C3×#4766C212yesmaximal, complemented
12C3×#3247—31nomaximal
13#80343C311yesmaximal, characteristic, direct product factor
14C2×C3×#237—21no—
15C2×C32×D8C2212yes—
16C32×#127C2211yescharacteristic
17C32×C4×D4C2211yescharacteristic
18C3×#938—21no—
19C3×#938C2211yescharacteristic
20C3×#938C2212yes—
21C3×#936—21no—
22C3×#936C2211yescharacteristic
23C3×D4×Dic3—21no—
24C3×D4×Dic3C2212yes—
25C2×C3×#214C2212yes—
26C3×C4×#67—21no—
27C3×#926—21no—
28C2×C3×D3×C8C2212yes—
29C3×#897C2211yescharacteristic
30C3×#890C2211yescharacteristic
31C3×#883—21no—
32C3×#879—21no—
33C3×C42×D3C2211yescharacteristic
34C3×#869C2211yescharacteristic
35C3×C4×Dic6C2211yescharacteristic
36C32×C4⋊C8C2211yescharacteristic
37C32×#102C2212yes—
38C3×#832C2212yes—
39C3×#832C2212yes—
40C3×#818C2212yes—
41C3×#816C2212yes—
42C3×Dic3⋊C8C2212yes—
43C3×#808C2212yes—
44C3×C4⋊(C3⋊C8)C2211yescharacteristic
45C3×#532—31no—
46C3×#529—31no—
47#5716C2×C311yescharacteristic, complemented
48#5557C2×C311yescharacteristic, complemented
49C3×#478—32no—
50C3×#477—31no—
51C3×#476—31no—
52C3×#466—32no—
53C3×#465—32no—
54C3×#463—32no—
55C3×#460—31no—
56C3×#459—21no—
57C3×#459D311yescharacteristic, complemented
58C3×#459C2×C311yescharacteristic, complemented
59C2×C3×C4⋊C8—31no—
60#5157C2×C312yescomplemented
61#5153C2×C312yescomplemented
62#5075C2×C311yescharacteristic, complemented
63#5008C2×C311yescharacteristic, complemented
64#4850C2×C311yescharacteristic, complemented
65D3×C4⋊C8C2×C311yescharacteristic, complemented
66#4778C2×C312yescomplemented
67#4766C2×C312yescomplemented
68C2×C32×D4—21no—
69C2×C32×D4—21no—
70C2×C32×D4C2312yes—
71C2×C32×D4C2311yescharacteristic
72C22×C32×C4—21no—
73C2×C3×#67—21no—
74C2×C3×#67—22no—
75C22×C3×Dic3—22no—
76C3×#237—44no—
77C2×C3×C4×D3D411yescharacteristic
78C2×C3×C4×D3D411yescharacteristic
79C2×C3×C4×D3C2311yescharacteristic
80C2×C3×Dic6—21no—
81C2×C3×Dic6C2311yescharacteristic
82C32×D8—42no—
83C2×C32×C8C2312yes—
84C32×C4⋊C4C2311yescharacteristic
85C32×C22⋊C4—21no—
86C32×C42C2311yescharacteristic
87C3×#217—21no—
88C3×#217—21no—
89C3×#217—21no—
90C3×#217—22no—
91C3×#217—22no—
92C3×#214—42no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4⋊Dic3C2312yes—
99C3×Dic3⋊C4—21no—
100C3×Dic3⋊C4—21no—
101C3×C4×Dic3—21no—
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C2×C3×C3⋊C8C2312yes—
106C3×D3×C8—42no—
107#3247—31noSylow
108C2×C3×#41—61no—
109C2×#237—21no—
110C2×C3×SD16—32no—
111C2×C3×D8—22no—
112C2×C3×D8C2×D312yes—
113C2×C3×D8C22×C312yes—
114C22×C3×C8—32no—
115C3×C4⋊Q8—31no—
116C3×#127—21no—
117C3×#127C2×D311yescharacteristic
118C3×#127C22×C311yescharacteristic
119C3×#126—61no—
120C3×#125—31no—
121C3×#124—31no—
122C3×#124—61no—
123C3×#123—61no—
124C3×C22⋊Q8—31no—
125C3×#121—32no—
126C3×#121—31no—
127C3×#121—61no—
128C3×C4×Q8—31no—
129C3×C4×D4—21no—
130C3×C4×D4—32no—
131C3×C4×D4—61no—
132C3×C4×D4—61no—
133C3×C4×D4C2×D311yescharacteristic
134C3×C4×D4C22×C311yescharacteristic
135C3×#117—61no—
136C2×C3×C42—31no—
137#938—21no—
138#938C22×C311yescharacteristic
139#938C22×C312yes—
140#936—21no—
141#936C22×C311yescharacteristic
142D4×Dic3—21no—
143D4×Dic3C22×C312yes—
144C2×#214C22×C312yes—
145C4×#67—21no—
146#926—21no—
147C2×D3×C8C22×C312yes—
148#897C22×C311yescharacteristic
149#890C22×C311yescharacteristic
150#883—21no—
151#879—21no—
152C42×D3C22×C311yescharacteristic
153#869C22×C311yescharacteristic
154C4×Dic6C22×C311yescharacteristic
155C3×#107—32no—
156C3×#106—32no—
157C3×C4⋊C8—21no—
158C3×C4⋊C8—32no—
159C3×C4⋊C8—31no—
160C3×C4⋊C8C2×D311yescharacteristic
161C3×C4⋊C8C22×C311yescharacteristic
162C3×#103—32no—
163C3×#102—22no—
164C3×#102—32no—
165C3×#102—32no—
166C3×#102C2×D312yes—
167C3×#102C22×C312yes—
168#832C22×C312yes—
169#832C22×C312yes—
170#818C22×C312yes—
171#816C22×C312yes—
172Dic3⋊C8C22×C312yes—
173#808C22×C312yes—
174C4⋊(C3⋊C8)C22×C311yescharacteristic
175C23×C32—21no—
176C23×C32—22no—
177C22×C3×D3C2×D411yescharacteristic
178C32×D4—21no—
179C32×D4—22no—
180C32×D4—21no—
181C32×D4—22no—
182C32×D4—42no—
183C32×D4—42no—
184C2×C32×C4—21no—
185C2×C32×C4—42no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2411yescharacteristic
189C3×#67—44no—
190C3×#67—42no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—44no—
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C2×C3×Dic3C2×D411yescharacteristic
198C3×C4×D3—22no—
199C3×C4×D3—22no—
200C3×C4×D3—21no—
201C3×C4×D3—21no—
202C3×Dic6—21no—
203C3×Dic6—21no—
204C3×Dic6—42no—
205C32×C8—22no—
206C3×C3⋊C8—22no—
207#532—31no—
208#529—31no—
209#478—32no—
210#477—31no—
211#476—31no—
212#466—32no—
213#465—32no—
214#463—32no—
215#460—31no—
216#459C3×D311yescharacteristic, complemented
217C2×C4⋊C8—31no—
218C3×#41—124no—
219C2×C3×Q8—31no—
220C2×C3×Q8—61no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—22no—
227C2×C3×D4—41no—
228C2×C3×D4—41no—
229C2×C3×D4—61no—
230C2×C3×D4—62no—
231C2×C3×D4C22×D311yescharacteristic
232C2×C3×D4C22×D312yes—
233C2×C3×D4C23×C311yescharacteristic
234C2×C3×D4C23×C312yes—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—31no—
238C22×C3×C4—31no—
239C22×C3×C4—31no—
240C22×C3×C4—41no—
241C22×C3×C4—62no—
242C2×#67—21no—
243C2×#67—22no—
244C22×Dic3—22no—
245#237—44no—
246C2×C4×D3C3×D411yescharacteristic
247C2×C4×D3C3×D411yescharacteristic
248C2×C4×D3C23×C311yescharacteristic
249C2×Dic6—21no—
250C2×Dic6C23×C311yescharacteristic
251C3×SD16—122no—
252C3×D8—42no—
253C3×D8—42no—
254C3×D8—44no—
255C2×C3×C8—22no—
256C2×C3×C8—32no—
257C2×C3×C8—122no—
258C2×C3×C8C22×D312yes—
259C2×C3×C8C23×C312yes—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—31no—
262C3×C4⋊C4—32no—
263C3×C4⋊C4—61no—
264C3×C4⋊C4—61no—
265C3×C4⋊C4—61no—
266C3×C4⋊C4—61no—
267C3×C4⋊C4—61no—
268C3×C4⋊C4C22×D311yescharacteristic
269C3×C4⋊C4C23×C311yescharacteristic
270C3×C22⋊C4—21no—
271C3×C22⋊C4—21no—
272C3×C22⋊C4—41no—
273C3×C22⋊C4—61no—
274C3×C22⋊C4—61no—
275C3×C22⋊C4—61no—
276C3×C22⋊C4—62no—
277C3×C22⋊C4—62no—
278C3×C22⋊C4—61no—
279C3×C42—21no—
280C3×C42—31no—
281C3×C42—31no—
282C3×C42—31no—
283C3×C42—61no—
284C3×C42C22×D311yescharacteristic
285C3×C42C23×C311yescharacteristic
286#217—21no—
287#217—21no—
288#217—21no—
289#217—22no—
290#217—22no—
291#214—42no—
292(C2×D3)⋊C4—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3C23×C312yes—
297C4⋊Dic3C23×C311yescharacteristic
298Dic3⋊C4—21no—
299Dic3⋊C4—21no—
300C4×Dic3—21no—
301C4×Dic3C3×D411yescharacteristic
302C4×Dic3C3×D411yescharacteristic
303C4×Dic3C23×C311yescharacteristic
304C2×C3⋊C8C23×C312yes—
305D3×C8—42no—
306C22×C32—41no—
307C22×C32—42no—
308C22×C32—41no—
309C22×C32—42no—
310C22×C32—42no—
311C22×C32—41no—
312C22×C32C22×D411yescharacteristic
313C2×C3×D3—21no—
314C2×C3×D3—21no—
315C2×C3×D3AGL(1,ℤ/8)12yes—
316C32×C4—21no—
317C32×C4—41no—
318C32×C4#13512yes—
319C32×C4H(5,𝔽2)11yescharacteristic
320C32×C42−1+411yescharacteristic
321C3×Dic3—21no—
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—41no—
325C3×Dic3—42no—
326C3×Dic3—41no—
327C2×#41—61no—
328C2×SD16—32no—
329C2×D8C2×C3×D312yes—
330C22×C8—32no—
331C4⋊Q8—31no—
332#127C2×C3×D311yescharacteristic
333#126—61no—
334#125—31no—
335#124—31no—
336#124—61no—
337#123—61no—
338C22⋊Q8—31no—
339#121—31no—
340#121—32no—
341#121—61no—
342C4×Q8—31no—
343C4×D4—32no—
344C4×D4—61no—
345C4×D4—61no—
346C4×D4C2×C3×D311yescharacteristic
347#117—61no—
348C2×C42—31no—
349#107—32no—
350#106—32no—
351C4⋊C8—32no—
352C4⋊C8—31no—
353C4⋊C8C2×C3×D311yescharacteristic
354#103—32no—
355#102—32no—
356#102—32no—
357#102C2×C3×D312yes—
358C23×C3—21no—
359C23×C3—22no—
360C23×C3—21no—
361C23×C3—22no—
362C23×C3—31no—
363C23×C3—41no—
364C23×C3—42no—
365C22×D3C2×C3×D411yescharacteristic
366C3×Q8—61no—
367C3×Q8—61no—
368C3×Q8—122no—
369C3×D4—22no—
370C3×D4—21no—
371C3×D4—22no—
372C3×D4—21no—
373C3×D4—22no—
374C3×D4—22no—
375C3×D4—21no—
376C3×D4—21no—
377C3×D4—22no—
378C3×D4—41no—
379C3×D4—42no—
380C3×D4—42no—
381C3×D4—42no—
382C3×D4—42no—
383C3×D4—42no—
384C3×D4—42no—
385C3×D4—82no—
386C3×D4—82no—
387C3×D4—122no—
388C3×D4—124no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—31no—
395C2×C3×C4—31no—
396C2×C3×C4—31no—
397C2×C3×C4—41no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—62no—
401C2×C3×C4—62no—
402C2×C3×C4—61no—
403C2×C3×C4—61no—
404C2×C3×C4—61no—
405C2×C3×C4—61no—
406C2×C3×C4—62no—
407C2×C3×C4—82no—
408C2×C3×C4—124no—
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4D3×D411yescharacteristic
411C2×C3×C4C2×C3×D411yescharacteristic
412C2×C3×C4C2×C3×D411yescharacteristic
413C2×C3×C4C23×D311yescharacteristic
414C2×C3×C4C24×C311yescharacteristic
415#67—44no—
416#67—42no—
417C2×Dic3—21no—
418C2×Dic3—21no—
419C2×Dic3—22no—
420C2×Dic3—44no—
421C2×Dic3C2×C3×D411yescharacteristic
422C2×Dic3C2×C3×D411yescharacteristic
423C2×Dic3C2×C3×D411yescharacteristic
424C4×D3—22no—
425C4×D3—22no—
426C4×D3—21no—
427C4×D3—21no—
428Dic6—21no—
429Dic6—21no—
430Dic6—42no—
431C3×C8—22no—
432C3×C8—22no—
433C3×C8—42no—
434C3×C8—62no—
435C3⋊C8—22no—
436C2×C32—81no—
437C2×C32—82no—
438C2×C32#53711yescharacteristic
439C2×C32C2×#13511yescharacteristic
440C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
441C3×D3—22no—
442#41—124no—
443C2×Q8—31no—
444C2×Q8—61no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—61no—
448C2×D4—62no—
449C2×D4C22×C3×D311yescharacteristic
450C2×D4C22×C3×D312yes—
451C22×C4—21no—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4—31no—
455C22×C4—62no—
456SD16—122no—
457D8—42no—
458C2×C8—32no—
459C2×C8—122no—
460C2×C8C22×C3×D312yes—
461C4⋊C4—31no—
462C4⋊C4—32no—
463C4⋊C4—61no—
464C4⋊C4—61no—
465C4⋊C4—61no—
466C4⋊C4—61no—
467C4⋊C4—61no—
468C4⋊C4C22×C3×D311yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—61no—
471C22⋊C4—61no—
472C22⋊C4—61no—
473C22⋊C4—62no—
474C22⋊C4—62no—
475C22⋊C4—61no—
476C42—31no—
477C42—31no—
478C42—31no—
479C42—61no—
480C42C22×C3×D311yescharacteristic
481C22×C3—21no—
482C22×C3—32no—
483C22×C3—42no—
484C22×C3—41no—
485C22×C3—42no—
486C22×C3—42no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—42no—
490C22×C3—42no—
491C22×C3—41no—
492C22×C3—41no—
493C22×C3—42no—
494C22×C3—41no—
495C22×C3—42no—
496C22×C3—61no—
497C22×C3—61no—
498C22×C3—81no—
499C22×C3—81no—
500C22×C3—82no—
501C22×C3—82no—
502C22×C3—82no—
503C22×C3C2×D3×D411yescharacteristic
504C22×C3C22×C3×D411yescharacteristic
505C2×D3—21no—
506C2×D3—21no—
507C2×D3C3×AGL(1,ℤ/8)12yes—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—22no—
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—41no—
514C3×C4—41no—
515C3×C4—41no—
516C3×C4—61no—
517C3×C4—61no—
518C3×C4—61no—
519C3×C4—81no—
520C3×C4—122no—
521C3×C4—121no—
522C3×C4—121no—
523C3×C4#91212yes—
524C3×C4C3×#13512yes—
525C3×C4#100411yescharacteristic
526C3×C4#101011yescharacteristic
527C3×C4C3×H(5,𝔽2)11yescharacteristic
528C3×C4C3×2−1+411yescharacteristic
529Dic3—21no—
530Dic3—21no—
531Dic3—21no—
532Dic3—42no—
533Dic3—41no—
534Dic3—41no—
535C32#324711yescharacteristic, complemented, Sylow
536C23—21no—
537C23—22no—
538C23—31no—
539Q8—61no—
540Q8—61no—
541Q8—122no—
542D4—21no—
543D4—22no—
544D4—21no—
545D4—22no—
546D4—42no—
547D4—42no—
548D4—124no—
549D4—122no—
550C2×C4—21no—
551C2×C4—31no—
552C2×C4—31no—
553C2×C4—31no—
554C2×C4—42no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—61no—
560C2×C4—61no—
561C2×C4—62no—
562C2×C4—124no—
563C2×C4C3×D3×D411yescharacteristic
564C2×C4C3×D3×D411yescharacteristic
565C2×C4C23×C3×D311yescharacteristic
566C8—22no—
567C8—62no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—62no—
572C2×C3—82no—
573C2×C3—81no—
574C2×C3—82no—
575C2×C3—81no—
576C2×C3—82no—
577C2×C3—162no—
578C2×C3#560811yescharacteristic
579C2×C3C2×#91211yescharacteristic
580C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
581C2×C3C3×#53711yescharacteristic
582C2×C3C2×C3×#13511yescharacteristic
583C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
584D3—22no—
585C22—32no—
586C22—41no—
587C22—42no—
588C22—42no—
589C22—41no—
590C22—41no—
591C22—42no—
592C22—61no—
593C22—61no—
594C22C2×C3×D3×D411yescharacteristic
595C4—21no—
596C4—41no—
597C4—61no—
598C4—61no—
599C4—61no—
600C4—122no—
601C4—121no—
602C4—121no—
603C4C3×#91212yes—
604C4C3×#100411yescharacteristic
605C4C3×#101011yescharacteristic
606C3—21no—
607C3#8034311yescharacteristic, direct product factor
608C3C3×#324711yescharacteristic, complemented
609C2—62no—
610C2—81no—
611C2—82no—
612C2C3×#560811yescharacteristic
613C2C2×C3×#91211yescharacteristic
614C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#459C2
socleC22×C32C22×D4
hypercenterC3×#459D3
hypocenterC3C3×#3247
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#459

Complements

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

NH ≅ G/Ntype
1. C3×#5716C2semidirect
2. C3×#5557C2semidirect
3. C32×#459C2semidirect
4. C3×#5157C2semidirect
5. C3×#5153C2semidirect
6. C3×#5075C2semidirect
7. C3×#5008C2semidirect
8. C3×#4850C2semidirect
9. C3×D3×C4⋊C8C2semidirect
10. C3×#4778C2semidirect
11. C3×#4766C2semidirect
13. #80343C3direct (N × H)
47. #5716C2×C3semidirect
48. #5557C2×C3semidirect
57. C3×#459D3semidirect
58. C3×#459C2×C3semidirect
60. #5157C2×C3semidirect
61. #5153C2×C3semidirect
62. #5075C2×C3semidirect
63. #5008C2×C3semidirect
64. #4850C2×C3semidirect
65. D3×C4⋊C8C2×C3semidirect
66. #4778C2×C3semidirect
67. #4766C2×C3semidirect
216. #459C3×D3semidirect
535. C32#3247semidirect
607. C3#80343direct (N × H)
608. C3C3×#3247semidirect

Maximal subgroups

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

subgroupindex
C3×#57162
C3×#55572
C32×#4592
C3×#51572
C3×#51532
C3×#50752
C3×#50082
C3×#48502
C3×D3×C4⋊C82
C3×#47782
C3×#47662
C3×#32473
#803433