Finite Group Databasebeta

← C3×#83311 #11882292

Subgroups — C3×#83311 #11882292

Order 1152.

951 conjugacy classes of subgroups.

The subgroup lattice has 637 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#532C211yesmaximal, characteristic, complemented
2C3×#5479C211yesmaximal, characteristic, complemented
3C3×#5091C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5C3×#5075C211yesmaximal, characteristic, complemented
6C3×#5072C211yesmaximal, characteristic, complemented
7C3×#5041C212yesmaximal, complemented
8C3×#5038C212yesmaximal, complemented
9C3×#5016C212yesmaximal, complemented
10C3×#5009C212yesmaximal, complemented
11C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
12C3×#3247—31nomaximal
13#83311C311yesmaximal, characteristic, direct product factor
14C2×C32×#41—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×#127C2211yescharacteristic
17C32×#124—21no—
18C32×#121—21no—
19C32×#121C2212yes—
20C32×C4×D4—21no—
21C32×C4×D4C2212yes—
22C2×C32×C42C2211yescharacteristic
23C2×C3×#214C2212yes—
24C2×C3×#213C2212yes—
25C3×#930C2211yescharacteristic
26C3×#929—21no—
27C3×C4×#67—21no—
28C3×#924C2211yescharacteristic
29C22×C3×C3⋊C8C2212yes—
30C3×#876—21no—
31C3×#875C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×#872—21no—
34C3×#870C2211yescharacteristic
35C3×C4×Dic6C2211yescharacteristic
36C3×#832C2212yes—
37C3×#832C2212yes—
38C3×#810C2212yes—
39C3×#809C2212yes—
40C3×#808C2212yes—
41C3×#807C2212yes—
42C3×C4⋊(C3⋊C8)C2212yes—
43C3×C4⋊(C3⋊C8)C2211yescharacteristic
44C3×C4⋊(C3⋊C8)C2211yescharacteristic
45C3×#532—21no—
46C3×#532D311yescharacteristic, complemented
47C3×#532C2×C311yescharacteristic, complemented
48C3×#529—31no—
49#5479C2×C311yescharacteristic, complemented
50C3×#478—32no—
51C3×#477—31no—
52C3×#476—31no—
53C3×#466—32no—
54C3×#465—32no—
55C3×#463—32no—
56C3×#460—31no—
57C3×#459—31no—
58C2×C3×C4⋊C8—31no—
59#5091C2×C311yescharacteristic, complemented
60#5084C2×C311yescharacteristic, complemented
61#5075C2×C311yescharacteristic, complemented
62#5072C2×C311yescharacteristic, complemented
63#5041C2×C312yescomplemented
64#5038C2×C312yescomplemented
65#5016C2×C312yescomplemented
66#5009C2×C312yescomplemented
67C2×C4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
68C32×#41—44no—
69C2×C32×Q8—21no—
70C2×C32×D4—22no—
71C2×C32×D4—21no—
72C2×C32×D4—21no—
73C2×C32×D4C2312yes—
74C22×C32×C4—22no—
75C22×C32×C4D411yescharacteristic
76C22×C32×C4D411yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C2×C3×#67—21no—
79C2×C3×D12C2311yescharacteristic
80C2×C3×C4×D3—21no—
81C2×C3×Dic6C2311yescharacteristic
82C32×C4⋊C4—21no—
83C32×C4⋊C4C2312yes—
84C32×C22⋊C4—22no—
85C32×C22⋊C4—22no—
86C32×C42D411yescharacteristic
87C32×C42D411yescharacteristic
88C32×C42C2311yescharacteristic
89C32×C42C2311yescharacteristic
90C3×#217—21no—
91C3×#214—42no—
92C3×#213—42no—
93C3×(C2×D3)⋊C4—21no—
94C3×(C2×D3)⋊C4—21no—
95C3×(C2×D3)⋊C4—21no—
96C3×(C2×D3)⋊C4—21no—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4⋊Dic3C2311yescharacteristic
99C3×Dic3⋊C4—21no—
100C3×Dic3⋊C4—21no—
101C3×Dic3⋊C4—21no—
102C3×Dic3⋊C4—21no—
103C3×C4×Dic3—21no—
104C2×C3×C3⋊C8—42no—
105C2×C3×C3⋊C8C2312yes—
106C2×C3×C3⋊C8C2312yes—
107#3247—31noSylow
108C2×C3×#41—22no—
109C2×C3×#41—21no—
110C2×C3×#41—21no—
111C2×C3×SD16—32no—
112C2×C3×D8—32no—
113C22×C3×C8—32no—
114C3×C4⋊Q8—21no—
115C3×C4⋊Q8C2×D311yescharacteristic
116C3×C4⋊Q8C22×C311yescharacteristic
117C3×#127—21no—
118C3×#127C2×D311yescharacteristic
119C3×#127C22×C311yescharacteristic
120C3×#126—61no—
121C3×#125—31no—
122C3×#124—22no—
123C3×#124—21no—
124C3×#124—21no—
125C3×#124—31no—
126C3×#123—61no—
127C3×C22⋊Q8—31no—
128C3×#121—22no—
129C3×#121—21no—
130C3×#121—21no—
131C3×#121—22no—
132C3×#121—31no—
133C3×#121C2×D312yes—
134C3×#121C22×C312yes—
135C3×C4×Q8—31no—
136C3×C4×D4—22no—
137C3×C4×D4—21no—
138C3×C4×D4—21no—
139C3×C4×D4—22no—
140C3×C4×D4—31no—
141C3×C4×D4—61no—
142C3×C4×D4C2×D312yes—
143C3×C4×D4C22×C312yes—
144C3×#117—61no—
145C2×C3×C42—21no—
146C2×C3×C42C2×D311yescharacteristic
147C2×C3×C42C22×C311yescharacteristic
148C2×#214C22×C312yes—
149C2×#213C22×C312yes—
150#930C22×C311yescharacteristic
151#929—21no—
152C4×#67—21no—
153#924C22×C311yescharacteristic
154C22×C3⋊C8C22×C312yes—
155#876—21no—
156#875C22×C311yescharacteristic
157C4×D12C22×C311yescharacteristic
158#872—21no—
159#870C22×C311yescharacteristic
160C4×Dic6C22×C311yescharacteristic
161C3×#107—32no—
162C3×#106—32no—
163C3×C4⋊C8—31no—
164C3×C4⋊C8—31no—
165C3×C4⋊C8—32no—
166C3×#103—32no—
167C3×#102—32no—
168C3×#102—32no—
169C3×#102—32no—
170#832C22×C312yes—
171#832C22×C312yes—
172#810C22×C312yes—
173#809C22×C312yes—
174#808C22×C312yes—
175#807C22×C312yes—
176C4⋊(C3⋊C8)C22×C312yes—
177C4⋊(C3⋊C8)C22×C311yescharacteristic
178C4⋊(C3⋊C8)C22×C311yescharacteristic
179C23×C32—22no—
180C23×C32C2×D411yescharacteristic
181C22×C3×D3—21no—
182C32×Q8—42no—
183C32×D4—22no—
184C32×D4—22no—
185C32×D4—42no—
186C32×D4—44no—
187C32×D4—42no—
188C2×C32×C4—22no—
189C2×C32×C4—22no—
190C2×C32×C4—22no—
191C2×C32×C4—21no—
192C2×C32×C4—21no—
193C2×C32×C4—44no—
194C2×C32×C4C2×D411yescharacteristic
195C2×C32×C4C2×D411yescharacteristic
196C2×C32×C4C2×D411yescharacteristic
197C2×C32×C4C2×D411yescharacteristic
198C2×C32×C4C2×D411yescharacteristic
199C2×C32×C4C2411yescharacteristic
200C3×#67—42no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C3×D12—21no—
205C3×D12—21no—
206C3×C4×D3—42no—
207C3×Dic6—21no—
208C3×Dic6—21no—
209C3×C3⋊C8—22no—
210C3×C3⋊C8—22no—
211#532C3×D311yescharacteristic, complemented
212#529—31no—
213#478—32no—
214#477—31no—
215#476—31no—
216#466—32no—
217#465—32no—
218#463—32no—
219#460—31no—
220#459—31no—
221C2×C4⋊C8—31no—
222C3×#41—48no—
223C3×#41—44no—
224C3×#41—44no—
225C2×C3×Q8—22no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—31no—
229C2×C3×D4—22no—
230C2×C3×D4—24no—
231C2×C3×D4—22no—
232C2×C3×D4—22no—
233C2×C3×D4—22no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—22no—
239C2×C3×D4—31no—
240C2×C3×D4—61no—
241C2×C3×D4C22×D312yes—
242C2×C3×D4C23×C312yes—
243C22×C3×C4—24no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—61no—
250C22×C3×C4#6711yescharacteristic
251C22×C3×C4#6711yescharacteristic
252C22×C3×C4C3×D411yescharacteristic
253C22×C3×C4C3×D411yescharacteristic
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C23×C311yescharacteristic
256C2×#67—21no—
257C2×D12C23×C311yescharacteristic
258C2×C4×D3—21no—
259C2×Dic6C23×C311yescharacteristic
260C3×SD16—122no—
261C3×D8—122no—
262C2×C3×C8—32no—
263C2×C3×C8—32no—
264C2×C3×C8—122no—
265C3×C4⋊C4—22no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—22no—
269C3×C4⋊C4—31no—
270C3×C4⋊C4—31no—
271C3×C4⋊C4—61no—
272C3×C4⋊C4—61no—
273C3×C4⋊C4—61no—
274C3×C4⋊C4—61no—
275C3×C4⋊C4C22×D312yes—
276C3×C4⋊C4C23×C312yes—
277C3×C22⋊C4—24no—
278C3×C22⋊C4—24no—
279C3×C22⋊C4—22no—
280C3×C22⋊C4—22no—
281C3×C22⋊C4—22no—
282C3×C22⋊C4—22no—
283C3×C22⋊C4—61no—
284C3×C22⋊C4—61no—
285C3×C22⋊C4—61no—
286C3×C22⋊C4—61no—
287C3×C22⋊C4—61no—
288C3×C42—21no—
289C3×C42—21no—
290C3×C42—21no—
291C3×C42—21no—
292C3×C42—61no—
293C3×C42#6711yescharacteristic
294C3×C42#6711yescharacteristic
295C3×C42C3×D411yescharacteristic
296C3×C42C3×D411yescharacteristic
297C3×C42C22×D311yescharacteristic
298C3×C42C22×D311yescharacteristic
299C3×C42C23×C311yescharacteristic
300C3×C42C23×C311yescharacteristic
301#217—21no—
302#214—42no—
303#213—42no—
304(C2×D3)⋊C4—21no—
305(C2×D3)⋊C4—21no—
306(C2×D3)⋊C4—21no—
307(C2×D3)⋊C4—21no—
308C4⋊Dic3C23×C311yescharacteristic
309C4⋊Dic3C23×C311yescharacteristic
310Dic3⋊C4—21no—
311Dic3⋊C4—21no—
312Dic3⋊C4—21no—
313Dic3⋊C4—21no—
314C4×Dic3—21no—
315C2×C3⋊C8—42no—
316C2×C3⋊C8C23×C312yes—
317C2×C3⋊C8C23×C312yes—
318C22×C32—21no—
319C22×C32—21no—
320C22×C32—42no—
321C22×C32—42no—
322C22×C32—42no—
323C22×C32AGL(1,ℤ/8)12yes—
324C22×C32C22×D411yescharacteristic
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C32×C4—21no—
329C32×C4—21no—
330C32×C4—21no—
331C32×C4—21no—
332C32×C4—42no—
333C32×C4#13512yes—
334C32×C4H(5,𝔽2)11yescharacteristic
335C32×C42−1+411yescharacteristic
336C3×Dic3—41no—
337C3×Dic3—41no—
338C3×Dic3—41no—
339C2×#41—21no—
340C2×SD16—32no—
341C2×D8—32no—
342C22×C8—32no—
343C4⋊Q8C2×C3×D311yescharacteristic
344#127C2×C3×D311yescharacteristic
345#126—61no—
346#125—31no—
347#124—21no—
348#124—31no—
349#123—61no—
350C22⋊Q8—31no—
351#121—21no—
352#121—31no—
353#121C2×C3×D312yes—
354C4×Q8—31no—
355C4×D4—21no—
356C4×D4—31no—
357C4×D4—61no—
358C4×D4C2×C3×D312yes—
359#117—61no—
360C2×C42C2×C3×D311yescharacteristic
361#107—32no—
362#106—32no—
363C4⋊C8—31no—
364C4⋊C8—31no—
365C4⋊C8—32no—
366#103—32no—
367#102—32no—
368#102—32no—
369#102—32no—
370C23×C3—24no—
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—21no—
374C23×C3—61no—
375C23×C3C2×#6711yescharacteristic
376C23×C3C2×C3×D411yescharacteristic
377C22×D3—21no—
378C3×Q8—44no—
379C3×Q8—42no—
380C3×Q8—42no—
381C3×Q8—61no—
382C3×Q8—61no—
383C3×D4—22no—
384C3×D4—22no—
385C3×D4—22no—
386C3×D4—22no—
387C3×D4—42no—
388C3×D4—42no—
389C3×D4—44no—
390C3×D4—44no—
391C3×D4—42no—
392C3×D4—42no—
393C3×D4—48no—
394C3×D4—44no—
395C3×D4—44no—
396C3×D4—42no—
397C3×D4—42no—
398C3×D4—61no—
399C3×D4—61no—
400C3×D4—122no—
401C2×C3×C4—24no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—24no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—42no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—48no—
423C2×C3×C4—44no—
424C2×C3×C4—44no—
425C2×C3×C4—61no—
426C2×C3×C4—61no—
427C2×C3×C4—61no—
428C2×C3×C4—122no—
429C2×C3×C4C2×#6711yescharacteristic
430C2×C3×C4C2×#6711yescharacteristic
431C2×C3×C4C2×#6711yescharacteristic
432C2×C3×C4C2×#6711yescharacteristic
433C2×C3×C4C2×#6711yescharacteristic
434C2×C3×C4C2×C3×D411yescharacteristic
435C2×C3×C4C2×C3×D411yescharacteristic
436C2×C3×C4C2×C3×D411yescharacteristic
437C2×C3×C4C2×C3×D411yescharacteristic
438C2×C3×C4C2×C3×D411yescharacteristic
439C2×C3×C4C23×D311yescharacteristic
440C2×C3×C4C24×C311yescharacteristic
441#67—42no—
442C2×Dic3—21no—
443C2×Dic3—21no—
444C2×Dic3—21no—
445D12—21no—
446D12—21no—
447C4×D3—42no—
448Dic6—21no—
449Dic6—21no—
450C3×C8—62no—
451C3×C8—62no—
452C3⋊C8—22no—
453C3⋊C8—22no—
454C2×C32—22no—
455C2×C32—82no—
456C2×C32#53711yescharacteristic
457C2×C32C2×#13511yescharacteristic
458C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
459C3×D3—81no—
460#41—44no—
461C2×Q8—21no—
462C2×Q8—31no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—31no—
467C2×D4—61no—
468C2×D4C22×C3×D312yes—
469C22×C4—22no—
470C22×C4—61no—
471C22×C4C3×#6711yescharacteristic
472C22×C4C3×#6711yescharacteristic
473C22×C4C22×C3×D311yescharacteristic
474SD16—122no—
475D8—122no—
476C2×C8—32no—
477C2×C8—32no—
478C2×C8—122no—
479C4⋊C4—21no—
480C4⋊C4—31no—
481C4⋊C4—31no—
482C4⋊C4—61no—
483C4⋊C4—61no—
484C4⋊C4—61no—
485C4⋊C4—61no—
486C4⋊C4C22×C3×D312yes—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—61no—
490C22⋊C4—61no—
491C22⋊C4—61no—
492C22⋊C4—61no—
493C22⋊C4—61no—
494C42—61no—
495C42C3×#6711yescharacteristic
496C42C3×#6711yescharacteristic
497C42C22×C3×D311yescharacteristic
498C42C22×C3×D311yescharacteristic
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—22no—
504C22×C3—21no—
505C22×C3—41no—
506C22×C3—41no—
507C22×C3—44no—
508C22×C3—44no—
509C22×C3—44no—
510C22×C3—42no—
511C22×C3—42no—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3—42no—
515C22×C3—42no—
516C22×C3—121no—
517C22×C3—121no—
518C22×C3—121no—
519C22×C3#93212yes—
520C22×C3C3×AGL(1,ℤ/8)12yes—
521C22×C3C22×#6711yescharacteristic
522C22×C3C22×C3×D411yescharacteristic
523C2×D3—41no—
524C2×D3—41no—
525C2×D3—41no—
526C3×C4—22no—
527C3×C4—22no—
528C3×C4—21no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—21no—
535C3×C4—21no—
536C3×C4—22no—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—41no—
540C3×C4—41no—
541C3×C4—44no—
542C3×C4—42no—
543C3×C4—42no—
544C3×C4—121no—
545C3×C4—121no—
546C3×C4—121no—
547C3×C4#95012yes—
548C3×C4C3×#13512yes—
549C3×C4#100911yescharacteristic
550C3×C4#101011yescharacteristic
551C3×C4C3×H(5,𝔽2)11yescharacteristic
552C3×C4C3×2−1+411yescharacteristic
553Dic3—41no—
554Dic3—41no—
555Dic3—41no—
556C32#324711yescharacteristic, complemented, Sylow
557C23—22no—
558C23—61no—
559C23C2×C3×#6711yescharacteristic
560Q8—42no—
561Q8—61no—
562Q8—61no—
563D4—22no—
564D4—22no—
565D4—42no—
566D4—44no—
567D4—42no—
568D4—61no—
569D4—61no—
570D4—122no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—44no—
577C2×C4—61no—
578C2×C4—61no—
579C2×C4—61no—
580C2×C4—122no—
581C2×C4C2×C3×#6711yescharacteristic
582C2×C4C2×C3×#6711yescharacteristic
583C2×C4C2×C3×#6711yescharacteristic
584C2×C4C2×C3×#6711yescharacteristic
585C2×C4C2×C3×#6711yescharacteristic
586C2×C4C23×C3×D311yescharacteristic
587C8—62no—
588C8—62no—
589C2×C3—22no—
590C2×C3—22no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—42no—
595C2×C3—84no—
596C2×C3—82no—
597C2×C3—82no—
598C2×C3—241no—
599C2×C3C2×#93211yescharacteristic
600C2×C3C2×#95011yescharacteristic
601C2×C3#583311yescharacteristic
602C2×C3C3×#53711yescharacteristic
603C2×C3C2×C3×#13511yescharacteristic
604C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
605D3—81no—
606C22—21no—
607C22—21no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—121no—
612C22—121no—
613C22—121no—
614C22C3×#93212yes—
615C22C22×C3×#6711yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—42no—
621C4—121no—
622C4—121no—
623C4—121no—
624C4C3×#95012yes—
625C4C3×#100911yescharacteristic
626C4C3×#101011yescharacteristic
627C3—21no—
628C3#8331111yescharacteristic, direct product factor
629C3C3×#324711yescharacteristic, complemented
630C2—22no—
631C2—82no—
632C2—241no—
633C2C2×C3×#93211yescharacteristic
634C2C2×C3×#95011yescharacteristic
635C2C3×#583311yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#532C2
socleC22×C32C22×D4
hypercenterC3×#532D3
hypocenterC3C3×#3247
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#532

Complements

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

NH ≅ G/Ntype
1. C32×#532C2semidirect
2. C3×#5479C2semidirect
3. C3×#5091C2semidirect
4. C3×#5084C2semidirect
5. C3×#5075C2semidirect
6. C3×#5072C2semidirect
7. C3×#5041C2semidirect
8. C3×#5038C2semidirect
9. C3×#5016C2semidirect
10. C3×#5009C2semidirect
11. C2×C3×C4⋊(C3⋊C8)C2semidirect
13. #83311C3direct (N × H)
46. C3×#532D3semidirect
47. C3×#532C2×C3semidirect
49. #5479C2×C3semidirect
59. #5091C2×C3semidirect
60. #5084C2×C3semidirect
61. #5075C2×C3semidirect
62. #5072C2×C3semidirect
63. #5041C2×C3semidirect
64. #5038C2×C3semidirect
65. #5016C2×C3semidirect
66. #5009C2×C3semidirect
67. C2×C4⋊(C3⋊C8)C2×C3semidirect
211. #532C3×D3semidirect
556. C32#3247semidirect
628. C3#83311direct (N × H)
629. C3C3×#3247semidirect

Maximal subgroups

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

subgroupindex
C32×#5322
C3×#54792
C3×#50912
C3×#50842
C3×#50752
C3×#50722
C3×#50412
C3×#50382
C3×#50162
C3×#50092
C2×C3×C4⋊(C3⋊C8)2
C3×#32473
#833113