Finite Group Databasebeta

← C3×#79300 #11870856

Subgroups — C3×#79300 #11870856

Order 1152.

967 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5479C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic, complemented
3C32×#431C211yesmaximal, characteristic, complemented
4C3×#4847C212yesmaximal, complemented
5C3×#4844C212yesmaximal, complemented
6C3×#4735C211yesmaximal, characteristic, complemented
7C3×#4732C211yesmaximal, characteristic
8C3×#4731C211yesmaximal, characteristic, complemented
9C3×#4722C211yesmaximal, characteristic, complemented
10C3×C4×D24C212yesmaximal, complemented
11C3×C4×#204C212yesmaximal, complemented
12C3×#3105—31nomaximal
13#79300C311yesmaximal, characteristic, direct product factor
14C22×C3×D12C2211yescharacteristic
15C22×C3×C4×D3—21no—
16C2×C32×C42C2211yescharacteristic
17C3×#930C2211yescharacteristic
18C3×#929—21no—
19C3×C4×#67—21no—
20C2×C3×(C2×D3)⋊C4—21no—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C3×#924C2211yescharacteristic
23C2×C3×D24C2212yes—
24C2×C3×#204C2212yes—
25C3×#876—21no—
26C3×#875C2211yescharacteristic, complemented
27C3×C4×D12—21no—
28C3×C4×D12—21no—
29C3×C4×D12C2212yes—
30C3×C4×D12C2212yes—
31C3×C4×D12C2211yescharacteristic, complemented
32C3×#872—21no—
33C3×#870C2211yescharacteristic, complemented
34C3×C4×Dic6C2211yescharacteristic, complemented
35C32×C4⋊C8C2212yescomplemented
36C32×C22⋊C8C2211yescharacteristic
37C32×C22⋊C8C2211yescharacteristic
38C32×C4×C8C2212yescomplemented
39C3×#821C2212yes—
40C3×#821C2212yes—
41C3×#821C2212yescomplemented
42C3×#818C2212yescomplemented
43C3×#817C2212yescomplemented
44C3×#816C2212yescomplemented
45C3×#529—31no—
46C2×C3×C4×D4—31no—
47#5479C2×C311yescharacteristic, complemented
48C2×C4×D12C2×C311yescharacteristic, complemented
49C3×#484—31no—
50C3×#481—31no—
51C3×#478—32no—
52C3×#463—32no—
53C3×#450—31no—
54C3×#447—31no—
55C3×C4×SD16—32no—
56C3×C4×D8—32no—
57C3×#431—21no—
58C3×#431D311yescharacteristic, complemented
59C3×#431C2×C311yescharacteristic, complemented
60#4847C2×C312yescomplemented
61#4844C2×C312yescomplemented
62#4735C2×C311yescharacteristic, complemented
63#4732C2×C311yescharacteristic
64#4731C2×C311yescharacteristic, complemented
65#4722C2×C311yescharacteristic, complemented
66C4×D24C2×C312yescomplemented
67C4×#204C2×C312yescomplemented
68C23×C3×D3—21no—
69C22×C32×C4D411yescharacteristic
70C22×C32×C4D411yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C2×C3×#67—21no—
73C22×C3×Dic3—21no—
74C2×C3×D12—21no—
75C2×C3×D12—24no—
76C2×C3×D12C2311yescharacteristic
77C2×C3×D12C2312yes—
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3—44no—
82C2×C3×Dic6C2311yescharacteristic
83C2×C32×C8C2312yes—
84C2×C32×C8C2312yes—
85C32×C42D411yescharacteristic
86C32×C42D411yescharacteristic
87C32×C42C2311yescharacteristic
88C32×C42C2311yescharacteristic
89C3×#217—21no—
90C3×(C2×D3)⋊C4—22no—
91C3×(C2×D3)⋊C4—22no—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—21no—
94C3×(C2×D3)⋊C4—21no—
95C3×(C2×D3)⋊C4—21no—
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—24no—
106C3×#204—24no—
107#3105—31noSylow
108C22×C3×D4—31no—
109C23×C3×C4—61no—
110C22×D12C22×C311yescharacteristic
111C22×C4×D3—21no—
112C2×C3×SD16—32no—
113C2×C3×D8—32no—
114C3×#126—61no—
115C3×#125—31no—
116C3×#124—31no—
117C3×#123—61no—
118C3×C22⋊Q8—31no—
119C3×#121—31no—
120C3×C4×Q8—31no—
121C3×C4×D4—31no—
122C3×C4×D4—32no—
123C3×C4×D4—32no—
124C3×C4×D4—61no—
125C3×C4×D4—61no—
126C3×C4×D4—61no—
127C3×#117—61no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C22⋊C4—61no—
130C2×C3×C42—21no—
131C2×C3×C42C2×D311yescharacteristic
132C2×C3×C42C22×C311yescharacteristic
133#930C22×C311yescharacteristic
134#929—21no—
135C4×#67—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×C4⋊Dic3C22×C311yescharacteristic
138#924C22×C311yescharacteristic
139C2×D24C22×C312yes—
140C2×#204C22×C312yes—
141#876—21no—
142#875C22×C311yescharacteristic, complemented
143C4×D12—21no—
144C4×D12—21no—
145C4×D12C22×C312yes—
146C4×D12C22×C312yes—
147C4×D12C22×C311yescharacteristic, complemented
148#872—21no—
149#870C22×C311yescharacteristic, complemented
150C4×Dic6C22×C311yescharacteristic, complemented
151C3×#107—32no—
152C3×#106—32no—
153C3×C4⋊C8—22no—
154C3×C4⋊C8C2×D312yescomplemented
155C3×C4⋊C8C22×C312yescomplemented
156C3×#103—32no—
157C3×#102—32no—
158C3×#102—32no—
159C3×#102—32no—
160C3×C22⋊C8—21no—
161C3×C22⋊C8—21no—
162C3×C22⋊C8C2×D311yescharacteristic
163C3×C22⋊C8C2×D311yescharacteristic
164C3×C22⋊C8C22×C311yescharacteristic
165C3×C22⋊C8C22×C311yescharacteristic
166C3×C4×C8—22no—
167C3×C4×C8C2×D312yescomplemented
168C3×C4×C8C22×C312yescomplemented
169#821C22×C312yes—
170#821C22×C312yes—
171#821C22×C312yescomplemented
172#818C22×C312yescomplemented
173#817C22×C312yescomplemented
174#816C22×C312yescomplemented
175C23×C32C2×D411yescharacteristic
176C22×C3×D3—24no—
177C22×C3×D3—22no—
178C22×C3×D3—21no—
179C22×C3×D3—42no—
180C22×C3×D3—42no—
181C2×C32×C4—22no—
182C2×C32×C4—22no—
183C2×C32×C4—22no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2411yescharacteristic
190C3×#67—42no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—42no—
196C3×D12—24no—
197C3×D12—22no—
198C3×D12—22no—
199C3×D12#4114yes—
200C3×C4×D3—44no—
201C3×C4×D3—42no—
202C3×C4×D3—44no—
203C3×Dic6—22no—
204C32×C8—22no—
205C32×C8—22no—
206#529—31no—
207C2×C4×D4—31no—
208#484—31no—
209#481—31no—
210#478—32no—
211#463—32no—
212#450—31no—
213#447—31no—
214C4×SD16—32no—
215C4×D8—32no—
216#431C3×D311yescharacteristic, complemented
217C24×C3—61no—
218C23×D3—21no—
219C2×C3×Q8—31no—
220C2×C3×D4—32no—
221C2×C3×D4—31no—
222C2×C3×D4—64no—
223C2×C3×D4—61no—
224C2×C3×D4—61no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—61no—
229C22×C3×C4—62no—
230C22×C3×C4—61no—
231C22×C3×C4—62no—
232C22×C3×C4—124no—
233C22×C3×C4D1211yescharacteristic
234C22×C3×C4D1211yescharacteristic
235C22×C3×C4C3×D411yescharacteristic
236C22×C3×C4C3×D411yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C23×C311yescharacteristic
239C2×#67—21no—
240C22×Dic3—21no—
241C2×D12—21no—
242C2×D12—24no—
243C2×D12C23×C311yescharacteristic
244C2×D12C23×C312yes—
245C2×C4×D3—21no—
246C2×C4×D3—22no—
247C2×C4×D3—22no—
248C2×C4×D3—44no—
249C2×Dic6C23×C311yescharacteristic
250C3×SD16—64no—
251C3×D8—64no—
252C2×C3×C8—22no—
253C2×C3×C8—22no—
254C2×C3×C8C22×D312yes—
255C2×C3×C8C22×D312yes—
256C2×C3×C8C23×C312yes—
257C2×C3×C8C23×C312yes—
258C3×C4⋊C4—31no—
259C3×C4⋊C4—31no—
260C3×C4⋊C4—32no—
261C3×C4⋊C4—61no—
262C3×C4⋊C4—61no—
263C3×C4⋊C4—61no—
264C3×C4⋊C4—61no—
265C3×C4⋊C4—61no—
266C3×C22⋊C4—61no—
267C3×C22⋊C4—62no—
268C3×C22⋊C4—62no—
269C3×C22⋊C4—61no—
270C3×C22⋊C4—61no—
271C3×C22⋊C4—61no—
272C3×C22⋊C4—61no—
273C3×C42—21no—
274C3×C42—21no—
275C3×C42—21no—
276C3×C42—21no—
277C3×C42—61no—
278C3×C42D1211yescharacteristic
279C3×C42D1211yescharacteristic
280C3×C42C3×D411yescharacteristic
281C3×C42C3×D411yescharacteristic
282C3×C42C22×D311yescharacteristic
283C3×C42C22×D311yescharacteristic
284C3×C42C23×C311yescharacteristic
285C3×C42C23×C311yescharacteristic
286#217—21no—
287(C2×D3)⋊C4—21no—
288(C2×D3)⋊C4—21no—
289(C2×D3)⋊C4—22no—
290(C2×D3)⋊C4—22no—
291(C2×D3)⋊C4—21no—
292(C2×D3)⋊C4—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3C23×C312yes—
295C4⋊Dic3C23×C311yescharacteristic
296C4⋊Dic3C23×C311yescharacteristic
297Dic3⋊C4—21no—
298Dic3⋊C4—21no—
299Dic3⋊C4—21no—
300Dic3⋊C4—21no—
301C4×Dic3—21no—
302D24—24no—
303#204—24no—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32#13512yes—
307C22×C32C22×D411yescharacteristic
308C2×C3×D3—24no—
309C2×C3×D3—48no—
310C2×C3×D3—42no—
311C2×C3×D3—42no—
312C2×C3×D3—41no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C32×C4—21no—
316C32×C4—21no—
317C32×C4—21no—
318C32×C4—21no—
319C32×C4AGL(1,ℤ/8)12yes—
320C32×C4C2×#4112yes—
321C3×Dic3—41no—
322C3×Dic3—41no—
323C3×Dic3—42no—
324C3×Dic3—41no—
325C22×D4—31no—
326C23×C4—61no—
327C2×SD16—32no—
328C2×D8—32no—
329#126—61no—
330#125—31no—
331#124—31no—
332#123—61no—
333C22⋊Q8—31no—
334#121—31no—
335C4×Q8—31no—
336C4×D4—32no—
337C4×D4—32no—
338C4×D4—31no—
339C4×D4—61no—
340C4×D4—61no—
341C4×D4—61no—
342#117—61no—
343C2×C4⋊C4—31no—
344C2×C22⋊C4—61no—
345C2×C42C2×C3×D311yescharacteristic
346#107—32no—
347#106—32no—
348C4⋊C8C2×C3×D312yescomplemented
349#103—32no—
350#102—32no—
351#102—32no—
352#102—32no—
353C22⋊C8C2×C3×D311yescharacteristic
354C22⋊C8C2×C3×D311yescharacteristic
355C4×C8C2×C3×D312yescomplemented
356C23×C3—21no—
357C23×C3—64no—
358C23×C3—62no—
359C23×C3—61no—
360C23×C3—122no—
361C23×C3—122no—
362C23×C3C2×D1211yescharacteristic
363C23×C3C2×C3×D411yescharacteristic
364C22×D3—24no—
365C22×D3—22no—
366C22×D3—21no—
367C22×D3—42no—
368C22×D3—42no—
369C3×Q8—62no—
370C3×D4—34no—
371C3×D4—64no—
372C3×D4—62no—
373C3×D4—62no—
374C3×D4—122no—
375C2×C3×C4—24no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—61no—
391C2×C3×C4—61no—
392C2×C3×C4—61no—
393C2×C3×C4—62no—
394C2×C3×C4—124no—
395C2×C3×C4—122no—
396C2×C3×C4—122no—
397C2×C3×C4—124no—
398C2×C3×C4C2×D1211yescharacteristic
399C2×C3×C4C2×D1211yescharacteristic
400C2×C3×C4C2×D1211yescharacteristic
401C2×C3×C4C2×D1211yescharacteristic
402C2×C3×C4C2×D1211yescharacteristic
403C2×C3×C4C2×C3×D411yescharacteristic
404C2×C3×C4C2×C3×D411yescharacteristic
405C2×C3×C4C2×C3×D411yescharacteristic
406C2×C3×C4C2×C3×D411yescharacteristic
407C2×C3×C4C2×C3×D411yescharacteristic
408C2×C3×C4C23×D311yescharacteristic
409C2×C3×C4C24×C311yescharacteristic
410#67—42no—
411C2×Dic3—21no—
412C2×Dic3—21no—
413C2×Dic3—21no—
414C2×Dic3—22no—
415C2×Dic3—42no—
416D12—24no—
417D12—22no—
418D12—22no—
419D12C3×#4114yes—
420C4×D3—44no—
421C4×D3—42no—
422C4×D3—44no—
423Dic6—22no—
424C3×C8—22no—
425C3×C8—22no—
426C3×C8—22no—
427C3×C8—22no—
428C3×C8—42no—
429C3×C8—42no—
430C2×C32—22no—
431C2×C32#52511yescharacteristic
432C2×C32C2×#13511yescharacteristic
433C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
434C3×D3—44no—
435C3×D3—81no—
436C24—61no—
437C2×Q8—31no—
438C2×D4—32no—
439C2×D4—31no—
440C2×D4—64no—
441C2×D4—61no—
442C2×D4—61no—
443C22×C4—61no—
444C22×C4—61no—
445C22×C4—62no—
446C22×C4—62no—
447C22×C4—124no—
448C22×C4C3×D1211yescharacteristic
449C22×C4C3×D1211yescharacteristic
450C22×C4C22×C3×D311yescharacteristic
451SD16—64no—
452D8—64no—
453C2×C8C22×C3×D312yes—
454C2×C8C22×C3×D312yes—
455C4⋊C4—31no—
456C4⋊C4—31no—
457C4⋊C4—32no—
458C4⋊C4—61no—
459C4⋊C4—61no—
460C4⋊C4—61no—
461C4⋊C4—61no—
462C4⋊C4—61no—
463C22⋊C4—61no—
464C22⋊C4—62no—
465C22⋊C4—62no—
466C22⋊C4—61no—
467C22⋊C4—61no—
468C22⋊C4—61no—
469C22⋊C4—61no—
470C42—61no—
471C42C3×D1211yescharacteristic
472C42C3×D1211yescharacteristic
473C42C22×C3×D311yescharacteristic
474C42C22×C3×D311yescharacteristic
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—22no—
480C22×C3—21no—
481C22×C3—41no—
482C22×C3—41no—
483C22×C3—64no—
484C22×C3—128no—
485C22×C3—122no—
486C22×C3—122no—
487C22×C3—121no—
488C22×C3—121no—
489C22×C3—121no—
490C22×C3#90412yes—
491C22×C3C3×#13512yes—
492C22×C3C22×D1211yescharacteristic
493C22×C3C22×C3×D411yescharacteristic
494C2×D3—24no—
495C2×D3—48no—
496C2×D3—42no—
497C2×D3—42no—
498C2×D3—41no—
499C2×D3—41no—
500C2×D3—41no—
501C3×C4—22no—
502C3×C4—22no—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—22no—
512C3×C4—22no—
513C3×C4—41no—
514C3×C4—41no—
515C3×C4—121no—
516C3×C4—122no—
517C3×C4—121no—
518C3×C4—121no—
519C3×C4#90812yes—
520C3×C4C3×AGL(1,ℤ/8)12yes—
521C3×C4D3×#4112yes—
522C3×C4C2×C3×#4112yes—
523Dic3—41no—
524Dic3—42no—
525Dic3—41no—
526Dic3—41no—
527C32#310511yescharacteristic, complemented, Sylow
528C23—64no—
529C23—62no—
530C23—61no—
531C23—122no—
532C23—122no—
533C23C2×C3×D1211yescharacteristic
534Q8—62no—
535D4—34no—
536D4—64no—
537D4—62no—
538D4—62no—
539D4—122no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—61no—
544C2×C4—61no—
545C2×C4—61no—
546C2×C4—62no—
547C2×C4—124no—
548C2×C4—122no—
549C2×C4—124no—
550C2×C4—122no—
551C2×C4C2×C3×D1211yescharacteristic
552C2×C4C2×C3×D1211yescharacteristic
553C2×C4C2×C3×D1211yescharacteristic
554C2×C4C2×C3×D1211yescharacteristic
555C2×C4C2×C3×D1211yescharacteristic
556C2×C4C23×C3×D311yescharacteristic
557C8—22no—
558C8—22no—
559C2×C3—22no—
560C2×C3—22no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—42no—
565C2×C3—124no—
566C2×C3—241no—
567C2×C3#552411yescharacteristic
568C2×C3C2×#90411yescharacteristic
569C2×C3C2×#90811yescharacteristic
570C2×C3C3×#52511yescharacteristic
571C2×C3C2×C3×#13511yescharacteristic
572C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
573D3—44no—
574D3—81no—
575C22—21no—
576C22—21no—
577C22—64no—
578C22—128no—
579C22—122no—
580C22—122no—
581C22—121no—
582C22—121no—
583C22—121no—
584C22C3×#90412yes—
585C22C22×C3×D1211yescharacteristic
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—122no—
591C4—121no—
592C4—121no—
593C4—121no—
594C4C3×#90812yes—
595C4C3×D3×#4112yes—
596C3—21no—
597C3#7930011yescharacteristic, direct product factor
598C3C3×#310511yescharacteristic, complemented
599C2—22no—
600C2—124no—
601C2—241no—
602C2C3×#552411yescharacteristic
603C2C2×C3×#90411yescharacteristic
604C2C2×C3×#90811yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#431C2
socleC22×C32C22×D4
prime radicalC3×#4732C2
hypercenterC3×#431D3
hypocenterC3C3×#3105
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×#431

Complements

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

NH ≅ G/Ntype
1. C3×#5479C2semidirect
2. C2×C3×C4×D12C2semidirect
3. C32×#431C2semidirect
4. C3×#4847C2semidirect
5. C3×#4844C2semidirect
6. C3×#4735C2semidirect
8. C3×#4731C2semidirect
9. C3×#4722C2semidirect
10. C3×C4×D24C2semidirect
11. C3×C4×#204C2semidirect
13. #79300C3direct (N × H)
26. C3×#875C22semidirect
31. C3×C4×D12C22semidirect
33. C3×#870C22semidirect
34. C3×C4×Dic6C22semidirect
35. C32×C4⋊C8C22semidirect
38. C32×C4×C8C22semidirect
41. C3×#821C22semidirect
42. C3×#818C22semidirect
43. C3×#817C22semidirect
44. C3×#816C22semidirect
47. #5479C2×C3semidirect
48. C2×C4×D12C2×C3semidirect
58. C3×#431D3semidirect
59. C3×#431C2×C3semidirect
60. #4847C2×C3semidirect
61. #4844C2×C3semidirect
62. #4735C2×C3semidirect
64. #4731C2×C3semidirect
65. #4722C2×C3semidirect
66. C4×D24C2×C3semidirect
67. C4×#204C2×C3semidirect
142. #875C22×C3semidirect
147. C4×D12C22×C3semidirect
149. #870C22×C3semidirect
150. C4×Dic6C22×C3semidirect
154. C3×C4⋊C8C2×D3semidirect
155. C3×C4⋊C8C22×C3semidirect
167. C3×C4×C8C2×D3semidirect
168. C3×C4×C8C22×C3semidirect
171. #821C22×C3semidirect
172. #818C22×C3semidirect
173. #817C22×C3semidirect
174. #816C22×C3semidirect
216. #431C3×D3semidirect
348. C4⋊C8C2×C3×D3semidirect
355. C4×C8C2×C3×D3semidirect
527. C32#3105semidirect
597. C3#79300direct (N × H)
598. C3C3×#3105semidirect

Maximal subgroups

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

subgroupindex
C3×#54792
C2×C3×C4×D122
C32×#4312
C3×#48472
C3×#48442
C3×#47352
C3×#47322
C3×#47312
C3×#47222
C3×C4×D242
C3×C4×#2042
C3×#31053
#793003