Finite Group Databasebeta

← C3×#83638 #11895723

Subgroups — C3×#83638 #11895723

Order 1152.

906 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#554C211yesmaximal, characteristic, complemented
2C3×#5577C211yesmaximal, characteristic, complemented
3C3×#5088C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5C3×#5067C212yesmaximal, complemented
6C3×#5066C212yesmaximal, complemented
7C3×#5024C211yesmaximal, characteristic, complemented
8C3×#5015C212yesmaximal, complemented
9C3×#5015C211yesmaximal, characteristic, complemented
10C3×#5014C212yesmaximal, complemented
11C3×C4×#213C211yesmaximal, characteristic, complemented
12C3×#3366—31nomaximal
13#83638C311yesmaximal, characteristic, direct product factor
14C2×C3×#239—21no—
15C32×C4⋊Q8C2211yescharacteristic
16C32×#125C2212yes—
17C32×C22⋊Q8—21no—
18C32×C22⋊Q8—22no—
19C32×C4×Q8C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C32×C4×D4C2212yes—
22C2×C32×C4⋊C4—21no—
23C2×C3×#213C2211yescharacteristic
24C2×C3×#213C2212yes—
25C3×#895—21no—
26C3×#895—22no—
27C3×#874C2212yes—
28C3×#874C2211yescharacteristic
29C3×C4×D12C2211yescharacteristic
30C3×C4×D12C2212yes—
31C3×#832C2211yescharacteristic
32C3×#809C2211yescharacteristic
33C3×#809C2212yes—
34C3×#809C2212yes—
35C3×#809C2212yes—
36C3×#809C2212yes—
37C3×#808C2212yes—
38C3×#807C2211yescharacteristic
39C3×C4⋊(C3⋊C8)C2212yes—
40C3×C4⋊(C3⋊C8)C2211yescharacteristic
41C3×#803C2212yes—
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#554—21no—
44C3×#554D311yescharacteristic, complemented
45C3×#554C2×C311yescharacteristic, complemented
46C3×#550—31no—
47#5577C2×C311yescharacteristic, complemented
48C3×#490—32no—
49C3×#486—31no—
50C3×#478—32no—
51C3×#476—31no—
52C3×#459—32no—
53C3×#459—31no—
54C3×#446—31no—
55C3×#442—32no—
56C3×C4×D8—31no—
57#5088C2×C311yescharacteristic, complemented
58#5084C2×C311yescharacteristic, complemented
59#5067C2×C312yescomplemented
60#5066C2×C312yescomplemented
61#5024C2×C311yescharacteristic, complemented
62#5015C2×C312yescomplemented
63#5015C2×C311yescharacteristic, complemented
64#5014C2×C312yescomplemented
65C4×#213C2×C311yescharacteristic, complemented
66C2×C32×Q8—21no—
67C2×C32×Q8D411yescharacteristic
68C2×C32×D4C2311yescharacteristic
69C22×C32×C4—21no—
70C22×C32×C4—22no—
71C3×#239—44no—
72C2×C3×D12—22no—
73C2×C3×D12—21no—
74C2×C3×D12—21no—
75C2×C3×D12—22no—
76C2×C3×D12C2311yescharacteristic
77C2×C3×D12C2312yes—
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3—21no—
80C32×C4⋊C4—22no—
81C32×C4⋊C4—21no—
82C32×C4⋊C4—22no—
83C32×C4⋊C4D411yescharacteristic
84C32×C4⋊C4D412yes—
85C32×C4⋊C4C2311yescharacteristic
86C32×C4⋊C4C2312yes—
87C32×C22⋊C4—21no—
88C32×C22⋊C4—22no—
89C32×C42C2311yescharacteristic
90C32×C42C2312yes—
91C3×#213—22no—
92C3×#213—24no—
93C3×(C2×D3)⋊C4—21no—
94C3×(C2×D3)⋊C4—22no—
95C3×C4⋊Dic3C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2312yes—
98C2×C3×C3⋊C8C2311yescharacteristic
99#3366—31noSylow
100C2×C3×#41—61no—
101C2×#239—21no—
102C2×C3×D8—31no—
103C2×C3×D8—32no—
104C3×C4⋊Q8—21no—
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×C4⋊Q8C22×C311yescharacteristic
107C3×#127—31no—
108C3×#127—32no—
109C3×#125—22no—
110C3×#125C2×D312yes—
111C3×#125C22×C312yes—
112C3×C22⋊Q8—22no—
113C3×C22⋊Q8—24no—
114C3×C22⋊Q8—21no—
115C3×C22⋊Q8—21no—
116C3×C22⋊Q8—22no—
117C3×C22⋊Q8—22no—
118C3×#121—61no—
119C3×#121—62no—
120C3×C4×Q8—21no—
121C3×C4×Q8C2×D311yescharacteristic
122C3×C4×Q8C22×C311yescharacteristic
123C3×C4×D4—21no—
124C3×C4×D4—22no—
125C3×C4×D4—31no—
126C3×C4×D4—32no—
127C3×C4×D4C2×D311yescharacteristic
128C3×C4×D4C2×D312yes—
129C3×C4×D4C22×C311yescharacteristic
130C3×C4×D4C22×C312yes—
131C2×C3×C4⋊C4—22no—
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4—21no—
134C2×#213C22×C311yescharacteristic
135C2×#213C22×C312yes—
136#895—21no—
137#895—22no—
138#874C22×C312yes—
139#874C22×C311yescharacteristic
140C4×D12C22×C311yescharacteristic
141C4×D12C22×C312yes—
142C3×#107—31no—
143C3×#106—32no—
144C3×C4⋊C8—31no—
145C3×C4⋊C8—32no—
146C3×#102—31no—
147C3×#102—31no—
148C3×#102—32no—
149C3×#102—32no—
150C3×#102—32no—
151C3×#102—32no—
152C3×#97—32no—
153C3×C4×C8—31no—
154#832C22×C311yescharacteristic
155#809C22×C311yescharacteristic
156#809C22×C312yes—
157#809C22×C312yes—
158#809C22×C312yes—
159#809C22×C312yes—
160#808C22×C312yes—
161#807C22×C311yescharacteristic
162C4⋊(C3⋊C8)C22×C312yes—
163C4⋊(C3⋊C8)C22×C311yescharacteristic
164#803C22×C312yes—
165C4×C3⋊C8C22×C311yescharacteristic
166C23×C32—21no—
167C22×C3×D3—22no—
168C22×C3×D3—21no—
169C32×Q8—22no—
170C32×Q8—81no—
171C32×D4—21no—
172C32×D4#4112yescomplemented
173C2×C32×C4—21no—
174C2×C32×C4—22no—
175C2×C32×C4—42no—
176C2×C32×C4—82no—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×D412yes—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2411yescharacteristic
182C2×C3×Dic3—21no—
183C3×D12—21no—
184C3×D12—22no—
185C3×D12—21no—
186C3×D12—22no—
187C3×D12—44no—
188C3×D12—42no—
189C3×D12—82no—
190C3×D12—81no—
191C3×C4×D3—44no—
192C3×C4×D3—42no—
193C3×C3⋊C8—21no—
194C3×C3⋊C8—22no—
195C3×C3⋊C8—21no—
196#554C3×D311yescharacteristic, complemented
197#550—31no—
198#490—32no—
199#486—31no—
200#478—32no—
201#476—31no—
202#459—32no—
203#459—31no—
204#446—31no—
205#442—32no—
206C4×D8—31no—
207C3×#41—124no—
208C2×C3×Q8—22no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8#6711yescharacteristic
213C2×C3×Q8C3×D411yescharacteristic
214C2×C3×D4—21no—
215C2×C3×D4—31no—
216C2×C3×D4—32no—
217C2×C3×D4—62no—
218C2×C3×D4—61no—
219C2×C3×D4—61no—
220C2×C3×D4—62no—
221C2×C3×D4C22×D311yescharacteristic
222C2×C3×D4C23×C311yescharacteristic
223C22×C3×C4—22no—
224C22×C3×C4—24no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—62no—
230C22×C3×C4—61no—
231#239—44no—
232C2×D12—22no—
233C2×D12—21no—
234C2×D12—21no—
235C2×D12—22no—
236C2×D12C23×C311yescharacteristic
237C2×D12C23×C312yes—
238C2×C4×D3—22no—
239C2×C4×D3—21no—
240C3×D8—62no—
241C3×D8—64no—
242C2×C3×C8—31no—
243C2×C3×C8—31no—
244C2×C3×C8—32no—
245C3×C4⋊C4—24no—
246C3×C4⋊C4—22no—
247C3×C4⋊C4—24no—
248C3×C4⋊C4—22no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—22no—
251C3×C4⋊C4—22no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—22no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—22no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—22no—
258C3×C4⋊C4—31no—
259C3×C4⋊C4#6711yescharacteristic
260C3×C4⋊C4#6712yes—
261C3×C4⋊C4C3×D411yescharacteristic
262C3×C4⋊C4C3×D412yes—
263C3×C4⋊C4C22×D312yes—
264C3×C4⋊C4C22×D311yescharacteristic
265C3×C4⋊C4C23×C311yescharacteristic
266C3×C4⋊C4C23×C312yes—
267C3×C22⋊C4—22no—
268C3×C22⋊C4—24no—
269C3×C22⋊C4—21no—
270C3×C22⋊C4—22no—
271C3×C22⋊C4—21no—
272C3×C22⋊C4—22no—
273C3×C22⋊C4—61no—
274C3×C22⋊C4—62no—
275C3×C42—22no—
276C3×C42—21no—
277C3×C42C22×D311yescharacteristic
278C3×C42C22×D312yes—
279C3×C42C23×C311yescharacteristic
280C3×C42C23×C312yes—
281#213—22no—
282#213—24no—
283(C2×D3)⋊C4—21no—
284(C2×D3)⋊C4—22no—
285C4⋊Dic3C23×C311yescharacteristic
286C2×C3⋊C8C23×C311yescharacteristic
287C2×C3⋊C8C23×C311yescharacteristic
288C2×C3⋊C8C23×C312yes—
289C22×C32—22no—
290C22×C32—41no—
291C22×C32—41no—
292C22×C32C22×D411yescharacteristic
293C2×C3×D3—42no—
294C2×C3×D3—41no—
295C2×C3×D3—42no—
296C2×C3×D3—41no—
297C2×C3×D3—41no—
298C2×C3×D3—42no—
299C32×C4—22no—
300C32×C4—22no—
301C32×C4—21no—
302C32×C4—41no—
303C32×C4—42no—
304C32×C4AGL(1,ℤ/8)12yes—
305C32×C4C2×#4111yescharacteristic
306C32×C42−1+411yescharacteristic
307C3×Dic3—41no—
308C2×#41—61no—
309C2×D8—31no—
310C2×D8—32no—
311C4⋊Q8C2×C3×D311yescharacteristic
312#127—31no—
313#127—32no—
314#125C2×C3×D312yes—
315C22⋊Q8—21no—
316C22⋊Q8—22no—
317#121—61no—
318#121—62no—
319C4×Q8C2×C3×D311yescharacteristic
320C4×D4—31no—
321C4×D4—32no—
322C4×D4C2×C3×D311yescharacteristic
323C4×D4C2×C3×D312yes—
324C2×C4⋊C4—21no—
325#107—31no—
326#106—32no—
327C4⋊C8—31no—
328C4⋊C8—32no—
329#102—31no—
330#102—31no—
331#102—32no—
332#102—32no—
333#102—32no—
334#102—32no—
335#97—32no—
336C4×C8—31no—
337C23×C3—22no—
338C23×C3—21no—
339C23×C3—21no—
340C23×C3—62no—
341C23×C3—61no—
342C22×D3—22no—
343C22×D3—21no—
344C3×Q8—22no—
345C3×Q8—22no—
346C3×Q8—42no—
347C3×Q8—81no—
348C3×Q8—81no—
349C3×Q8—82no—
350C3×D4—22no—
351C3×D4—21no—
352C3×D4—21no—
353C3×D4—22no—
354C3×D4—61no—
355C3×D4—62no—
356C3×D4—61no—
357C3×D4—62no—
358C3×D4—124no—
359C3×D4—122no—
360C3×D4—242no—
361C3×D4—241no—
362C3×D4#23912yescomplemented
363C3×D4C3×#4112yescomplemented
364C2×C3×C4—22no—
365C2×C3×C4—24no—
366C2×C3×C4—21no—
367C2×C3×C4—22no—
368C2×C3×C4—21no—
369C2×C3×C4—22no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—22no—
373C2×C3×C4—21no—
374C2×C3×C4—22no—
375C2×C3×C4—44no—
376C2×C3×C4—42no—
377C2×C3×C4—42no—
378C2×C3×C4—61no—
379C2×C3×C4—82no—
380C2×C3×C4—82no—
381C2×C3×C4—84no—
382C2×C3×C4—124no—
383C2×C3×C4—122no—
384C2×C3×C4C2×#6711yescharacteristic
385C2×C3×C4C2×#6712yes—
386C2×C3×C4C2×#6712yes—
387C2×C3×C4C2×#6711yescharacteristic
388C2×C3×C4C2×C3×D411yescharacteristic
389C2×C3×C4C2×C3×D412yes—
390C2×C3×C4C2×C3×D412yes—
391C2×C3×C4C2×C3×D411yescharacteristic
392C2×C3×C4C23×D311yescharacteristic
393C2×C3×C4C24×C311yescharacteristic
394C2×Dic3—21no—
395D12—21no—
396D12—22no—
397D12—21no—
398D12—22no—
399D12—44no—
400D12—42no—
401D12—82no—
402D12—81no—
403C4×D3—44no—
404C4×D3—42no—
405C3×C8—61no—
406C3×C8—62no—
407C3×C8—61no—
408C3⋊C8—21no—
409C3⋊C8—22no—
410C3⋊C8—21no—
411C2×C32—42no—
412C2×C32#54811yescharacteristic
413C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
414C2×C32#57611yescharacteristic
415C3×D3—82no—
416C3×D3—81no—
417#41—124no—
418C2×Q8—21no—
419C2×Q8C3×#6711yescharacteristic
420C2×D4—31no—
421C2×D4—32no—
422C2×D4—62no—
423C2×D4—61no—
424C2×D4—61no—
425C2×D4—62no—
426C2×D4C22×C3×D311yescharacteristic
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—62no—
430C22×C4—61no—
431D8—62no—
432D8—64no—
433C2×C8—31no—
434C2×C8—31no—
435C2×C8—32no—
436C4⋊C4—22no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—31no—
440C4⋊C4C3×#6711yescharacteristic
441C4⋊C4C3×#6712yes—
442C4⋊C4C22×C3×D312yes—
443C4⋊C4C22×C3×D311yescharacteristic
444C22⋊C4—21no—
445C22⋊C4—22no—
446C22⋊C4—61no—
447C22⋊C4—62no—
448C42C22×C3×D311yescharacteristic
449C42C22×C3×D312yes—
450C22×C3—24no—
451C22×C3—22no—
452C22×C3—22no—
453C22×C3—21no—
454C22×C3—42no—
455C22×C3—42no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—122no—
461C22×C3—121no—
462C22×C3—122no—
463C22×C3—121no—
464C22×C3—121no—
465C22×C3—122no—
466C22×C3C22×#6711yescharacteristic
467C22×C3C22×C3×D411yescharacteristic
468C2×D3—42no—
469C2×D3—41no—
470C2×D3—41no—
471C2×D3—42no—
472C2×D3—42no—
473C2×D3—41no—
474C3×C4—22no—
475C3×C4—22no—
476C3×C4—21no—
477C3×C4—22no—
478C3×C4—22no—
479C3×C4—21no—
480C3×C4—22no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—42no—
484C3×C4—42no—
485C3×C4—41no—
486C3×C4—42no—
487C3×C4—44no—
488C3×C4—41no—
489C3×C4—42no—
490C3×C4—41no—
491C3×C4—42no—
492C3×C4—121no—
493C3×C4#94912yes—
494C3×C4C3×AGL(1,ℤ/8)12yes—
495C3×C4C2×#23911yescharacteristic
496C3×C4#100711yescharacteristic
497C3×C4C2×C3×#4111yescharacteristic
498C3×C4C3×2−1+411yescharacteristic
499Dic3—41no—
500C32#336611yescharacteristic, complemented, Sylow
501C23—21no—
502C23—62no—
503C23—61no—
504Q8—22no—
505Q8—81no—
506D4—21no—
507D4—61no—
508D4—62no—
509D4—61no—
510D4—62no—
511D4—124no—
512D4—122no—
513D4—242no—
514D4—241no—
515D4C3×#23912yescomplemented
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—42no—
519C2×C4—61no—
520C2×C4—82no—
521C2×C4—124no—
522C2×C4—122no—
523C2×C4C2×C3×#6711yescharacteristic
524C2×C4C2×C3×#6712yes—
525C2×C4C2×C3×#6712yes—
526C2×C4C2×C3×#6711yescharacteristic
527C2×C4C23×C3×D311yescharacteristic
528C8—61no—
529C8—62no—
530C8—61no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—44no—
535C2×C3—42no—
536C2×C3—42no—
537C2×C3—242no—
538C2×C3—241no—
539C2×C3#581711yescharacteristic
540C2×C3C2×#94911yescharacteristic
541C2×C3#583511yescharacteristic
542C2×C3C3×#54811yescharacteristic
543C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
544C2×C3C3×#57611yescharacteristic
545D3—82no—
546D3—81no—
547C22—22no—
548C22—41no—
549C22—41no—
550C22—122no—
551C22—121no—
552C22—122no—
553C22—121no—
554C22—121no—
555C22—122no—
556C22C22×C3×#6711yescharacteristic
557C4—22no—
558C4—22no—
559C4—21no—
560C4—41no—
561C4—42no—
562C4—121no—
563C4C3×#94912yes—
564C4C2×C3×#23911yescharacteristic
565C4C3×#100711yescharacteristic
566C3—21no—
567C3#8363811yescharacteristic, direct product factor
568C3C3×#336611yescharacteristic, complemented
569C2—42no—
570C2—242no—
571C2—241no—
572C2C3×#581711yescharacteristic
573C2C2×C3×#94911yescharacteristic
574C2C3×#583511yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#554C2
socleC22×C32C22×D4
hypercenterC3×#554D3
hypocenterC3C3×#3366
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ C3×#554

Complements

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

NH ≅ G/Ntype
1. C32×#554C2semidirect
2. C3×#5577C2semidirect
3. C3×#5088C2semidirect
4. C3×#5084C2semidirect
5. C3×#5067C2semidirect
6. C3×#5066C2semidirect
7. C3×#5024C2semidirect
8. C3×#5015C2semidirect
9. C3×#5015C2semidirect
10. C3×#5014C2semidirect
11. C3×C4×#213C2semidirect
13. #83638C3direct (N × H)
44. C3×#554D3semidirect
45. C3×#554C2×C3semidirect
47. #5577C2×C3semidirect
57. #5088C2×C3semidirect
58. #5084C2×C3semidirect
59. #5067C2×C3semidirect
60. #5066C2×C3semidirect
61. #5024C2×C3semidirect
62. #5015C2×C3semidirect
63. #5015C2×C3semidirect
64. #5014C2×C3semidirect
65. C4×#213C2×C3semidirect
172. C32×D4#41semidirect
196. #554C3×D3semidirect
362. C3×D4#239semidirect
363. C3×D4C3×#41semidirect
500. C32#3366semidirect
515. D4C3×#239semidirect
567. C3#83638direct (N × H)
568. C3C3×#3366semidirect

Maximal subgroups

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

subgroupindex
C32×#5542
C3×#55772
C3×#50882
C3×#50842
C3×#50672
C3×#50662
C3×#50242
C3×#50152
C3×#50142
C3×C4×#2132
C3×#33663
#836383