Finite Group Databasebeta

← C3×#79028 #11882313

Subgroups — C3×#79028 #11882313

Order 1152.

865 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×#5479C211yesmaximal, characteristic, complemented
2C3×#5477C211yesmaximal, characteristic, complemented
3C2×C32×C4⋊C8C211yesmaximal, characteristic, complemented
4C3×#5115C212yesmaximal, complemented
5C3×#5114C212yesmaximal, complemented
6C3×#4850C211yesmaximal, characteristic, complemented
7C3×#4848C211yesmaximal, characteristic, complemented
8C3×#4847C212yesmaximal, complemented
9C3×#4844C212yesmaximal, complemented
10C3×#4843C211yesmaximal, characteristic, complemented
11C3×#4842C211yesmaximal, characteristic, complemented
12C3×#3247—31nomaximal
13#79028C311yesmaximal, characteristic, direct product factor
14C2×C3×#235—21no—
15C22×C32×C8C2212yes—
16C2×C32×C42C2211yescharacteristic
17C3×#930—21no—
18C3×#930C2212yes—
19C3×#930C2211yescharacteristic
20C3×#929—21no—
21C3×C4×#67—21no—
22C3×#924C2211yescharacteristic
23C2×C3×D24C2212yes—
24C2×C3×#204C2212yes—
25C3×#876—21no—
26C3×#875—21no—
27C3×#875C2211yescharacteristic
28C3×#874C2211yescharacteristic
29C3×C4×D12—21no—
30C3×C4×D12C2211yescharacteristic
31C3×C4×D12C2212yes—
32C3×#872—21no—
33C3×#870C2211yescharacteristic
34C3×#869C2211yescharacteristic
35C3×C4×Dic6C2211yescharacteristic
36C32×C4⋊C8C2211yescharacteristic
37C32×C4⋊C8C2211yescharacteristic
38C32×C4⋊C8C2212yes—
39C3×#821C2212yes—
40C3×#821C2212yes—
41C3×#821C2212yes—
42C3×#818C2212yes—
43C3×#817C2212yes—
44C3×#816C2212yes—
45C3×#532—31no—
46C3×#529—31no—
47#5479C2×C311yescharacteristic, complemented
48#5477C2×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—31no—
57C2×C3×C4⋊C8—21no—
58C2×C3×C4⋊C8D311yescharacteristic, complemented
59C2×C3×C4⋊C8C2×C311yescharacteristic, complemented
60#5115C2×C312yescomplemented
61#5114C2×C312yescomplemented
62#4850C2×C311yescharacteristic, complemented
63#4848C2×C311yescharacteristic, complemented
64#4847C2×C312yescomplemented
65#4844C2×C312yescomplemented
66#4843C2×C311yescharacteristic, complemented
67#4842C2×C311yescharacteristic, complemented
68C22×C32×C4D411yescharacteristic
69C22×C32×C4D411yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C2×C3×#67—21no—
72C2×C3×#67—22no—
73C3×#235—44no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12C2312yes—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—22no—
80C2×C3×Dic6—21no—
81C2×C3×Dic6C2311yescharacteristic
82C2×C32×C8—42no—
83C2×C32×C8C2312yes—
84C2×C32×C8C2312yes—
85C32×C42D411yescharacteristic
86C32×C42D411yescharacteristic
87C32×C42C2311yescharacteristic
88C32×C42C2311yescharacteristic
89C3×#217—21no—
90C3×(C2×D3)⋊C4—21no—
91C3×(C2×D3)⋊C4—21no—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—22no—
94C3×(C2×D3)⋊C4—21no—
95C3×(C2×D3)⋊C4—22no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4⋊Dic3C2312yes—
99C3×C4⋊Dic3C2311yescharacteristic
100C3×Dic3⋊C4—21no—
101C3×Dic3⋊C4—21no—
102C3×Dic3⋊C4—21no—
103C3×Dic3⋊C4—21no—
104C3×C4×Dic3—21no—
105C3×D24—42no—
106C3×#204—42no—
107#3247—31noSylow
108C2×C3×#41—61no—
109C2×#235—21no—
110C2×C3×SD16—32no—
111C2×C3×D8—32no—
112C22×C3×C8—22no—
113C22×C3×C8C2×D312yes—
114C22×C3×C8C22×C312yes—
115C3×C4⋊Q8—31no—
116C3×#127—31no—
117C3×#126—61no—
118C3×#125—31no—
119C3×#124—31no—
120C3×#124—61no—
121C3×#123—61no—
122C3×C22⋊Q8—31no—
123C3×#121—32no—
124C3×#121—31no—
125C3×#121—61no—
126C3×C4×Q8—31no—
127C3×C4×D4—31no—
128C3×C4×D4—32no—
129C3×C4×D4—61no—
130C3×C4×D4—61no—
131C3×#117—61no—
132C2×C3×C42—21no—
133C2×C3×C42C2×D311yescharacteristic
134C2×C3×C42C22×C311yescharacteristic
135#930—21no—
136#930C22×C312yes—
137#930C22×C311yescharacteristic
138#929—21no—
139C4×#67—21no—
140#924C22×C311yescharacteristic
141C2×D24C22×C312yes—
142C2×#204C22×C312yes—
143#876—21no—
144#875—21no—
145#875C22×C311yescharacteristic
146#874C22×C311yescharacteristic
147C4×D12—21no—
148C4×D12C22×C312yes—
149C4×D12C22×C311yescharacteristic
150#872—21no—
151#870C22×C311yescharacteristic
152#869C22×C311yescharacteristic
153C4×Dic6C22×C311yescharacteristic
154C3×#107—32no—
155C3×#106—32no—
156C3×C4⋊C8—21no—
157C3×C4⋊C8—21no—
158C3×C4⋊C8—22no—
159C3×C4⋊C8C2×D311yescharacteristic
160C3×C4⋊C8C2×D311yescharacteristic
161C3×C4⋊C8C2×D312yes—
162C3×C4⋊C8C22×C311yescharacteristic
163C3×C4⋊C8C22×C311yescharacteristic
164C3×C4⋊C8C22×C312yes—
165C3×#103—32no—
166C3×#102—32no—
167C3×#102—32no—
168C3×#102—32no—
169#821C22×C312yes—
170#821C22×C312yes—
171#821C22×C312yes—
172#818C22×C312yes—
173#817C22×C312yes—
174#816C22×C312yes—
175C23×C32C2×D411yescharacteristic
176C22×C3×D3—21no—
177C22×C3×D3—22no—
178C2×C32×C4—22no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—22no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2411yescharacteristic
188C3×#67—44no—
189C3×#67—42no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—22no—
194C3×D12—22no—
195C3×D12—21no—
196C3×D12—22no—
197C3×D12—21no—
198C3×D12—42no—
199C3×D12—42no—
200C3×C4×D3—44no—
201C3×C4×D3—42no—
202C3×Dic6—21no—
203C3×Dic6—21no—
204C3×Dic6—42no—
205C32×C8—22no—
206C32×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#459—31no—
217C2×C4⋊C8C3×D311yescharacteristic, complemented
218C3×#41—124no—
219C2×C3×Q8—31no—
220C2×C3×Q8—61no—
221C2×C3×D4—31no—
222C2×C3×D4—32no—
223C2×C3×D4—61no—
224C2×C3×D4—62no—
225C2×C3×D4—61no—
226C2×C3×D4—61no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—61no—
231C22×C3×C4—62no—
232C22×C3×C4D1211yescharacteristic
233C22×C3×C4D1211yescharacteristic
234C22×C3×C4C3×D411yescharacteristic
235C22×C3×C4C3×D411yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C23×C311yescharacteristic
238C2×#67—21no—
239C2×#67—22no—
240#235—44no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12C23×C312yes—
244C2×D12C23×C311yescharacteristic
245C2×C4×D3—21no—
246C2×C4×D3—22no—
247C2×Dic6—21no—
248C2×Dic6C23×C311yescharacteristic
249C3×SD16—122no—
250C3×D8—122no—
251C2×C3×C8—22no—
252C2×C3×C8—22no—
253C2×C3×C8—42no—
254C2×C3×C8—42no—
255C2×C3×C8—44no—
256C2×C3×C8C22×D312yes—
257C2×C3×C8C22×D312yes—
258C2×C3×C8C23×C312yes—
259C2×C3×C8C23×C312yes—
260C3×C4⋊C4—31no—
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×C22⋊C4—61no—
269C3×C22⋊C4—61no—
270C3×C22⋊C4—61no—
271C3×C22⋊C4—62no—
272C3×C22⋊C4—61no—
273C3×C22⋊C4—62no—
274C3×C22⋊C4—61no—
275C3×C42—21no—
276C3×C42—21no—
277C3×C42—21no—
278C3×C42—21no—
279C3×C42—61no—
280C3×C42D1211yescharacteristic
281C3×C42D1211yescharacteristic
282C3×C42C3×D411yescharacteristic
283C3×C42C3×D411yescharacteristic
284C3×C42C22×D311yescharacteristic
285C3×C42C22×D311yescharacteristic
286C3×C42C23×C311yescharacteristic
287C3×C42C23×C311yescharacteristic
288#217—21no—
289(C2×D3)⋊C4—21no—
290(C2×D3)⋊C4—21no—
291(C2×D3)⋊C4—22no—
292(C2×D3)⋊C4—22no—
293(C2×D3)⋊C4—21no—
294(C2×D3)⋊C4—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3C23×C312yes—
297C4⋊Dic3C23×C311yescharacteristic
298C4⋊Dic3C23×C311yescharacteristic
299Dic3⋊C4—21no—
300Dic3⋊C4—21no—
301Dic3⋊C4—21no—
302Dic3⋊C4—21no—
303C4×Dic3—21no—
304D24—42no—
305#204—42no—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32AGL(1,ℤ/8)12yes—
309C22×C32C22×D411yescharacteristic
310C2×C3×D3—42no—
311C2×C3×D3—41no—
312C2×C3×D3—41no—
313C2×C3×D3—42no—
314C2×C3×D3—42no—
315C2×C3×D3—41no—
316C32×C4—21no—
317C32×C4—21no—
318C32×C4—21no—
319C32×C4—21no—
320C32×C4#13512yes—
321C32×C4H(5,𝔽2)11yescharacteristic
322C32×C42−1+411yescharacteristic
323C3×Dic3—41no—
324C3×Dic3—41no—
325C3×Dic3—42no—
326C3×Dic3—41no—
327C2×#41—61no—
328C2×SD16—32no—
329C2×D8—32no—
330C22×C8C2×C3×D312yes—
331C4⋊Q8—31no—
332#127—31no—
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—31no—
344C4×D4—32no—
345C4×D4—61no—
346C4×D4—61no—
347#117—61no—
348C2×C42C2×C3×D311yescharacteristic
349#107—32no—
350#106—32no—
351C4⋊C8C2×C3×D311yescharacteristic
352C4⋊C8C2×C3×D311yescharacteristic
353C4⋊C8C2×C3×D312yes—
354#103—32no—
355#102—32no—
356#102—32no—
357#102—32no—
358C23×C3—21no—
359C23×C3—61no—
360C23×C3—62no—
361C23×C3C2×D1211yescharacteristic
362C23×C3C2×C3×D411yescharacteristic
363C22×D3—21no—
364C22×D3—22no—
365C3×Q8—61no—
366C3×Q8—61no—
367C3×Q8—122no—
368C3×D4—61no—
369C3×D4—62no—
370C3×D4—61no—
371C3×D4—62no—
372C3×D4—122no—
373C3×D4—122no—
374C3×D4—124no—
375C3×D4—122no—
376C2×C3×C4—22no—
377C2×C3×C4—24no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—42no—
394C2×C3×C4—61no—
395C2×C3×C4—61no—
396C2×C3×C4—61no—
397C2×C3×C4—62no—
398C2×C3×C4—124no—
399C2×C3×C4—122no—
400C2×C3×C4C2×D1211yescharacteristic
401C2×C3×C4C2×D1211yescharacteristic
402C2×C3×C4C2×D1211yescharacteristic
403C2×C3×C4C2×D1211yescharacteristic
404C2×C3×C4C2×D1211yescharacteristic
405C2×C3×C4C2×C3×D411yescharacteristic
406C2×C3×C4C2×C3×D411yescharacteristic
407C2×C3×C4C2×C3×D411yescharacteristic
408C2×C3×C4C2×C3×D411yescharacteristic
409C2×C3×C4C2×C3×D411yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411C2×C3×C4C24×C311yescharacteristic
412#67—44no—
413#67—42no—
414C2×Dic3—21no—
415C2×Dic3—21no—
416C2×Dic3—21no—
417C2×Dic3—22no—
418D12—22no—
419D12—21no—
420D12—22no—
421D12—21no—
422D12—42no—
423D12—42no—
424C4×D3—44no—
425C4×D3—42no—
426Dic6—21no—
427Dic6—21no—
428Dic6—42no—
429C3×C8—22no—
430C3×C8—22no—
431C3×C8—22no—
432C3×C8—22no—
433C3×C8—42no—
434C3×C8—42no—
435C2×C32—22no—
436C2×C32#53711yescharacteristic
437C2×C32C2×#13511yescharacteristic
438C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
439C3×D3—81no—
440C3×D3—82no—
441#41—124no—
442C2×Q8—31no—
443C2×Q8—61no—
444C2×D4—31no—
445C2×D4—32no—
446C2×D4—61no—
447C2×D4—62no—
448C2×D4—61no—
449C2×D4—61no—
450C22×C4—61no—
451C22×C4—62no—
452C22×C4C3×D1211yescharacteristic
453C22×C4C3×D1211yescharacteristic
454C22×C4C22×C3×D311yescharacteristic
455SD16—122no—
456D8—122no—
457C2×C8—42no—
458C2×C8C22×C3×D312yes—
459C2×C8C22×C3×D312yes—
460C4⋊C4—31no—
461C4⋊C4—31no—
462C4⋊C4—32no—
463C4⋊C4—61no—
464C4⋊C4—61no—
465C4⋊C4—61no—
466C4⋊C4—61no—
467C4⋊C4—61no—
468C22⋊C4—61no—
469C22⋊C4—61no—
470C22⋊C4—61no—
471C22⋊C4—62no—
472C22⋊C4—61no—
473C22⋊C4—62no—
474C22⋊C4—61no—
475C42—61no—
476C42C3×D1211yescharacteristic
477C42C3×D1211yescharacteristic
478C42C22×C3×D311yescharacteristic
479C42C22×C3×D311yescharacteristic
480C22×C3—22no—
481C22×C3—22no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—22no—
487C22×C3—21no—
488C22×C3—121no—
489C22×C3—122no—
490C22×C3—122no—
491C22×C3—121no—
492C22×C3—121no—
493C22×C3—122no—
494C22×C3#90812yes—
495C22×C3C3×AGL(1,ℤ/8)12yes—
496C22×C3C22×D1211yescharacteristic
497C22×C3C22×C3×D411yescharacteristic
498C2×D3—41no—
499C2×D3—42no—
500C2×D3—42no—
501C2×D3—41no—
502C2×D3—42no—
503C2×D3—41no—
504C3×C4—22no—
505C3×C4—22no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—22no—
515C3×C4—21no—
516C3×C4—21no—
517C3×C4—41no—
518C3×C4—41no—
519C3×C4—121no—
520C3×C4—122no—
521C3×C4—121no—
522C3×C4—121no—
523C3×C4#90412yes—
524C3×C4C3×#13512yes—
525C3×C4#100411yescharacteristic
526C3×C4#100711yescharacteristic
527C3×C4C3×H(5,𝔽2)11yescharacteristic
528C3×C4C3×2−1+411yescharacteristic
529Dic3—41no—
530Dic3—42no—
531Dic3—41no—
532Dic3—41no—
533C32#324711yescharacteristic, complemented, Sylow
534C23—61no—
535C23—62no—
536C23C2×C3×D1211yescharacteristic
537Q8—61no—
538Q8—61no—
539Q8—122no—
540D4—61no—
541D4—62no—
542D4—61no—
543D4—62no—
544D4—122no—
545D4—124no—
546D4—122no—
547D4—122no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—61no—
553C2×C4—61no—
554C2×C4—61no—
555C2×C4—62no—
556C2×C4—124no—
557C2×C4—122no—
558C2×C4C2×C3×D1211yescharacteristic
559C2×C4C2×C3×D1211yescharacteristic
560C2×C4C2×C3×D1211yescharacteristic
561C2×C4C2×C3×D1211yescharacteristic
562C2×C4C2×C3×D1211yescharacteristic
563C2×C4C23×C3×D311yescharacteristic
564C8—22no—
565C8—22no—
566C2×C3—24no—
567C2×C3—22no—
568C2×C3—22no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—241no—
573C2×C3—242no—
574C2×C3#551011yescharacteristic
575C2×C3C2×#90411yescharacteristic
576C2×C3C2×#90811yescharacteristic
577C2×C3C3×#53711yescharacteristic
578C2×C3C2×C3×#13511yescharacteristic
579C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
580D3—81no—
581D3—82no—
582C22—21no—
583C22—21no—
584C22—122no—
585C22—121no—
586C22—121no—
587C22—122no—
588C22—121no—
589C22—122no—
590C22C3×#90812yes—
591C22C22×C3×D1211yescharacteristic
592C4—21no—
593C4—21no—
594C4—21no—
595C4—21no—
596C4—122no—
597C4—121no—
598C4—121no—
599C4—121no—
600C4C3×#90412yes—
601C4C3×#100411yescharacteristic
602C4C3×#100711yescharacteristic
603C3—21no—
604C3#7902811yescharacteristic, direct product factor
605C3C3×#324711yescharacteristic, complemented
606C2—22no—
607C2—242no—
608C2—241no—
609C2C3×#551011yescharacteristic
610C2C2×C3×#90411yescharacteristic
611C2C2×C3×#90811yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C4⋊C8C2
socleC22×C32C22×D4
hypercenterC2×C3×C4⋊C8D3
hypocenterC3C3×#3247
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C2×C3×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C3×#5479C2semidirect
2. C3×#5477C2semidirect
3. C2×C32×C4⋊C8C2semidirect
4. C3×#5115C2semidirect
5. C3×#5114C2semidirect
6. C3×#4850C2semidirect
7. C3×#4848C2semidirect
8. C3×#4847C2semidirect
9. C3×#4844C2semidirect
10. C3×#4843C2semidirect
11. C3×#4842C2semidirect
13. #79028C3direct (N × H)
47. #5479C2×C3semidirect
48. #5477C2×C3semidirect
58. C2×C3×C4⋊C8D3semidirect
59. C2×C3×C4⋊C8C2×C3semidirect
60. #5115C2×C3semidirect
61. #5114C2×C3semidirect
62. #4850C2×C3semidirect
63. #4848C2×C3semidirect
64. #4847C2×C3semidirect
65. #4844C2×C3semidirect
66. #4843C2×C3semidirect
67. #4842C2×C3semidirect
217. C2×C4⋊C8C3×D3semidirect
533. C32#3247semidirect
604. C3#79028direct (N × H)
605. C3C3×#3247semidirect

Maximal subgroups

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

subgroupindex
C3×#54792
C3×#54772
C2×C32×C4⋊C82
C3×#51152
C3×#51142
C3×#48502
C3×#48482
C3×#48472
C3×#48442
C3×#48432
C3×#48422
C3×#32473
#790283