Finite Group Databasebeta

← C3×#84082 #11864117

Subgroups — C3×#84082 #11864117

Order 1152.

2057 conjugacy classes of subgroups.

The subgroup lattice has 723 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×#41C211yesmaximal, characteristic, complemented
2C2×C3×#949C212yesmaximal, complemented
3C2×C3×#930C211yesmaximal, characteristic, complemented
4C3×#5238C214yesmaximal, complemented
5C3×#5232C212yesmaximal, complemented
6C3×#5227C212yesmaximal, complemented
7C3×#5217C212yesmaximal, complemented
8C3×#5207C211yesmaximal, characteristic, complemented
9C3×#3006—31nomaximal
10#84082C311yesmaximal, characteristic, direct product factor
11C2×C32×#41—28no—
12C2×C32×#41—21no—
13C2×C32×#41—21no—
14C2×C32×#41C2212yes—
15C2×C32×#41C2212yescomplemented
16C22×C32×Q8C2211yescharacteristic, complemented
17C22×C32×D4—21no—
18C22×C32×D4C2211yescharacteristic, complemented
19C23×C32×C4—21no—
20C23×C32×C4C2211yescharacteristic
21C22×C3×#67—21no—
22C22×C3×D12C2211yescharacteristic, complemented
23C3×#949—28no—
24C2×C3×#215C2214yescomplemented
25C2×C3×#213C2214yescomplemented
26C3×#930—21no—
27C3×#930—21no—
28C3×#930C2212yes—
29C3×#930C2212yescomplemented
30C2×C3×(C2×D3)⋊C4—21no—
31C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
32C2×C3×#208C2212yescomplemented
33C3×#835C2214yescomplemented
34C3×#832C2214yescomplemented
35C3×#830C2212yescomplemented
36C3×#830C2212yescomplemented
37C22×C3×#41—21no—
38C22×C3×#41D311yescharacteristic, complemented
39C22×C3×#41C2×C311yescharacteristic, complemented
40C2×C3×AGL(1,ℤ/8)—32no—
41C2×C3×#121—31no—
42C2×#949C2×C312yescomplemented
43C2×#930C2×C311yescharacteristic, complemented
44C3×#449—34no—
45C3×#448—32no—
46C3×#447—32no—
47C3×#417—32no—
48C3×#407—31no—
49#5238C2×C314yescomplemented
50#5232C2×C312yescomplemented
51#5227C2×C312yescomplemented
52#5217C2×C312yescomplemented
53#5207C2×C311yescharacteristic, complemented
54C24×C32—21no—
55C24×C32D411yescharacteristic
56C23×C3×D3—21no—
57C32×#41—28no—
58C32×#41—28no—
59C32×#41—24no—
60C32×#41—24no—
61C32×#41—24no—
62C32×#41D418yescomplemented
63C2×C32×Q8—24no—
64C2×C32×Q8—21no—
65C2×C32×Q8C2312yes—
66C2×C32×D4—28no—
67C2×C32×D4—22no—
68C2×C32×D4—22no—
69C2×C32×D4—24no—
70C2×C32×D4—21no—
71C2×C32×D4C2312yes—
72C22×C32×C4—28no—
73C22×C32×C4—21no—
74C22×C32×C4—22no—
75C22×C32×C4—22no—
76C22×C32×C4—24no—
77C22×C32×C4D411yescharacteristic
78C22×C32×C4D411yescharacteristic
79C22×C32×C4D411yescharacteristic
80C22×C32×C4C2311yescharacteristic
81C22×C32×C4C2311yescharacteristic
82C22×C32×C4C2311yescharacteristic
83C2×C3×#67—22no—
84C2×C3×#67—22no—
85C2×C3×#67—44no—
86C22×C3×Dic3—21no—
87C2×C3×D12—24no—
88C2×C3×D12—21no—
89C2×C3×D12C2312yes—
90C3×#215—28no—
91C3×#213—28no—
92C3×(C2×D3)⋊C4—22no—
93C3×(C2×D3)⋊C4—22no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2312yes—
96C3×#208—24no—
97C2×C3×C3⋊C8C2314yes—
98#3006—31noSylow
99C2×C3×#41—216no—
100C2×C3×#41—22no—
101C2×C3×#41—22no—
102C2×C3×#41—28no—
103C2×C3×#41—28no—
104C2×C3×#41—21no—
105C2×C3×#41—21no—
106C2×C3×#41—21no—
107C2×C3×#41—21no—
108C2×C3×#41—22no—
109C2×C3×#41—22no—
110C2×C3×#41C2×D312yes—
111C2×C3×#41C2×D312yescomplemented
112C2×C3×#41C22×C312yes—
113C2×C3×#41C22×C312yescomplemented
114C22×C3×Q8—21no—
115C22×C3×Q8C2×D311yescharacteristic, complemented
116C22×C3×Q8C22×C311yescharacteristic, complemented
117C22×C3×D4—22no—
118C22×C3×D4—21no—
119C22×C3×D4—21no—
120C22×C3×D4—21no—
121C22×C3×D4—31no—
122C22×C3×D4—61no—
123C22×C3×D4C2×D311yescharacteristic, complemented
124C22×C3×D4C22×C311yescharacteristic, complemented
125C23×C3×C4—22no—
126C23×C3×C4—21no—
127C23×C3×C4—21no—
128C23×C3×C4—21no—
129C23×C3×C4C2×D311yescharacteristic
130C23×C3×C4C22×C311yescharacteristic
131C22×#67—21no—
132C22×D12C22×C311yescharacteristic, complemented
133C3×AGL(1,ℤ/8)—68no—
134C2×C3×SD16—34no—
135C2×C3×D8—34no—
136C2×C3×M16—32no—
137C3×#121—32no—
138C3×#121—32no—
139C3×#121—61no—
140C3×#121—61no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C22⋊C4—61no—
143#949—28no—
144C2×#215C22×C314yescomplemented
145C2×#213C22×C314yescomplemented
146#930—21no—
147#930—21no—
148#930C22×C312yes—
149#930C22×C312yescomplemented
150C2×(C2×D3)⋊C4—21no—
151C2×C4⋊Dic3C22×C311yescharacteristic, complemented
152C2×#208C22×C312yescomplemented
153C3×#103—34no—
154C3×#102—34no—
155C3×C22⋊C8—32no—
156C3×C22⋊C8—32no—
157#835C22×C314yescomplemented
158#832C22×C314yescomplemented
159#830C22×C312yescomplemented
160#830C22×C312yescomplemented
161C23×C32—24no—
162C23×C32—22no—
163C23×C32—22no—
164C23×C32—22no—
165C23×C32—41no—
166C23×C32—42no—
167C23×C32—42no—
168C23×C32C2×D411yescharacteristic
169C23×C32C2×D411yescharacteristic
170C23×C32C2×D411yescharacteristic
171C22×C3×D3—22no—
172C22×C3×D3—42no—
173C22×C3×D3—42no—
174C22×C3×D3—42no—
175C32×Q8—24no—
176C32×Q8—22no—
177C32×Q8C2×D414yescomplemented
178C32×D4—28no—
179C32×D4—24no—
180C32×D4—28no—
181C32×D4—22no—
182C32×D4C2×D414yescomplemented
183C2×C32×C4—24no—
184C2×C32×C4—28no—
185C2×C32×C4—22no—
186C2×C32×C4—22no—
187C2×C32×C4—22no—
188C2×C32×C4—28no—
189C2×C32×C4—22no—
190C2×C32×C4—22no—
191C2×C32×C4—22no—
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2×D411yescharacteristic
194C2×C32×C4C2×D411yescharacteristic
195C2×C32×C4C2×D414yes—
196C2×C32×C4C2411yescharacteristic
197C3×#67—44no—
198C3×#67—44no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—42no—
201C3×D12—24no—
202C3×D12—42no—
203C3×C3⋊C8—24no—
204C22×#41C3×D311yescharacteristic, complemented
205C2×AGL(1,ℤ/8)—32no—
206C2×#121—31no—
207#449—34no—
208#448—32no—
209#447—32no—
210#417—32no—
211#407—31no—
212C24×C3—22no—
213C24×C3—21no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—61no—
217C24×C3#6711yescharacteristic
218C24×C3C3×D411yescharacteristic
219C23×D3—21no—
220C3×#41—216no—
221C3×#41—216no—
222C3×#41—28no—
223C3×#41—28no—
224C3×#41—28no—
225C3×#41—28no—
226C3×#41—28no—
227C3×#41—28no—
228C3×#41—28no—
229C3×#41—24no—
230C3×#41—24no—
231C3×#41—24no—
232C3×#41—24no—
233C3×#41—24no—
234C3×#41—24no—
235C3×#41—28no—
236C3×#41#6718yescomplemented
237C3×#41C3×D418yescomplemented
238C2×C3×Q8—28no—
239C2×C3×Q8—22no—
240C2×C3×Q8—24no—
241C2×C3×Q8—24no—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—22no—
245C2×C3×Q8C22×D312yes—
246C2×C3×Q8C23×C312yes—
247C2×C3×D4—216no—
248C2×C3×D4—28no—
249C2×C3×D4—28no—
250C2×C3×D4—24no—
251C2×C3×D4—24no—
252C2×C3×D4—28no—
253C2×C3×D4—22no—
254C2×C3×D4—22no—
255C2×C3×D4—22no—
256C2×C3×D4—22no—
257C2×C3×D4—22no—
258C2×C3×D4—24no—
259C2×C3×D4—24no—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—22no—
263C2×C3×D4—32no—
264C2×C3×D4—62no—
265C2×C3×D4—62no—
266C2×C3×D4—64no—
267C2×C3×D4—61no—
268C2×C3×D4—124no—
269C2×C3×D4C22×D312yes—
270C2×C3×D4C23×C312yes—
271C22×C3×C4—22no—
272C22×C3×C4—216no—
273C22×C3×C4—28no—
274C22×C3×C4—28no—
275C22×C3×C4—24no—
276C22×C3×C4—24no—
277C22×C3×C4—28no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4—24no—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—24no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—61no—
293C22×C3×C4#6711yescharacteristic
294C22×C3×C4#6711yescharacteristic
295C22×C3×C4#6711yescharacteristic
296C22×C3×C4C3×D411yescharacteristic
297C22×C3×C4C3×D411yescharacteristic
298C22×C3×C4C3×D411yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C23×C311yescharacteristic
303C22×C3×C4C23×C311yescharacteristic
304C22×C3×C4C23×C311yescharacteristic
305C2×#67—22no—
306C2×#67—22no—
307C2×#67—44no—
308C22×Dic3—21no—
309C2×D12—24no—
310C2×D12—21no—
311C2×D12C23×C312yes—
312C3×SD16—68no—
313C3×D8—68no—
314C3×M16—64no—
315C2×C3×C8—34no—
316C3×C4⋊C4—32no—
317C3×C4⋊C4—61no—
318C3×C22⋊C4—62no—
319C3×C22⋊C4—62no—
320#215—28no—
321#213—28no—
322(C2×D3)⋊C4—22no—
323(C2×D3)⋊C4—22no—
324C4⋊Dic3—21no—
325C4⋊Dic3C23×C312yes—
326#208—24no—
327C2×C3⋊C8C23×C314yes—
328C22×C32—21no—
329C22×C32—21no—
330C22×C32—21no—
331C22×C32—24no—
332C22×C32—21no—
333C22×C32—21no—
334C22×C32—21no—
335C22×C32—21no—
336C22×C32—44no—
337C22×C32—48no—
338C22×C32—42no—
339C22×C32—42no—
340C22×C32#12012yes—
341C22×C32AGL(1,ℤ/8)12yescomplemented
342C22×C32C22×D411yescharacteristic
343C2×C3×D3—42no—
344C2×C3×D3—42no—
345C2×C3×D3—42no—
346C2×C3×D3—84no—
347C32×C4—21no—
348C32×C4—24no—
349C32×C4—21no—
350C32×C4#12012yes—
351C32×C4C22×D412yes—
352C3×Dic3—42no—
353C2×#41—28no—
354C2×#41—21no—
355C2×#41—21no—
356C2×#41C2×C3×D312yes—
357C2×#41C2×C3×D312yescomplemented
358C22×Q8C2×C3×D311yescharacteristic, complemented
359C22×D4—21no—
360C22×D4—31no—
361C22×D4—61no—
362C22×D4C2×C3×D311yescharacteristic, complemented
363C23×C4—21no—
364C23×C4C2×C3×D311yescharacteristic
365AGL(1,ℤ/8)—68no—
366C2×SD16—34no—
367C2×D8—34no—
368C2×M16—32no—
369#121—32no—
370#121—32no—
371#121—61no—
372#121—61no—
373C2×C4⋊C4—31no—
374C2×C22⋊C4—61no—
375#103—34no—
376#102—34no—
377C22⋊C8—32no—
378C22⋊C8—32no—
379C23×C3—28no—
380C23×C3—24no—
381C23×C3—24no—
382C23×C3—24no—
383C23×C3—24no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—42no—
394C23×C3—41no—
395C23×C3—41no—
396C23×C3—42no—
397C23×C3—44no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3—44no—
401C23×C3—42no—
402C23×C3—42no—
403C23×C3—62no—
404C23×C3—122no—
405C23×C3—122no—
406C23×C3—122no—
407C23×C3C2×#6711yescharacteristic
408C23×C3C2×#6711yescharacteristic
409C23×C3C2×#6711yescharacteristic
410C23×C3C2×C3×D411yescharacteristic
411C23×C3C2×C3×D411yescharacteristic
412C23×C3C2×C3×D411yescharacteristic
413C22×D3—22no—
414C22×D3—42no—
415C22×D3—42no—
416C22×D3—42no—
417C3×Q8—28no—
418C3×Q8—24no—
419C3×Q8—24no—
420C3×Q8—24no—
421C3×Q8—22no—
422C3×Q8—22no—
423C3×Q8—24no—
424C3×Q8C2×#6714yescomplemented
425C3×Q8C2×C3×D414yescomplemented
426C3×D4—216no—
427C3×D4—28no—
428C3×D4—28no—
429C3×D4—24no—
430C3×D4—28no—
431C3×D4—24no—
432C3×D4—216no—
433C3×D4—24no—
434C3×D4—28no—
435C3×D4—28no—
436C3×D4—22no—
437C3×D4—22no—
438C3×D4—24no—
439C3×D4—64no—
440C3×D4—124no—
441C3×D4—124no—
442C3×D4—122no—
443C3×D4C2×#6714yescomplemented
444C3×D4C2×C3×D414yescomplemented
445C2×C3×C4—24no—
446C2×C3×C4—28no—
447C2×C3×C4—24no—
448C2×C3×C4—24no—
449C2×C3×C4—24no—
450C2×C3×C4—24no—
451C2×C3×C4—216no—
452C2×C3×C4—28no—
453C2×C3×C4—28no—
454C2×C3×C4—24no—
455C2×C3×C4—216no—
456C2×C3×C4—24no—
457C2×C3×C4—24no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—28no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—28no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—24no—
477C2×C3×C4—62no—
478C2×C3×C4—122no—
479C2×C3×C4C2×#6711yescharacteristic
480C2×C3×C4C2×#6711yescharacteristic
481C2×C3×C4C2×#6711yescharacteristic
482C2×C3×C4C2×#6714yes—
483C2×C3×C4C2×C3×D411yescharacteristic
484C2×C3×C4C2×C3×D411yescharacteristic
485C2×C3×C4C2×C3×D411yescharacteristic
486C2×C3×C4C2×C3×D414yes—
487C2×C3×C4C23×D311yescharacteristic
488C2×C3×C4C24×C311yescharacteristic
489#67—44no—
490#67—44no—
491C2×Dic3—22no—
492C2×Dic3—42no—
493D12—24no—
494D12—42no—
495C3×C8—64no—
496C3⋊C8—24no—
497C2×C32—22no—
498C2×C32—22no—
499C2×C32—41no—
500C2×C32—44no—
501C2×C32C2×#12011yescharacteristic
502C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
503C2×C32#57511yescharacteristic
504C3×D3—82no—
505C24—21no—
506C24—61no—
507C24C3×#6711yescharacteristic
508#41—28no—
509#41—28no—
510#41—24no—
511#41—24no—
512#41—24no—
513#41C3×#6718yescomplemented
514C2×Q8—24no—
515C2×Q8—21no—
516C2×Q8C22×C3×D312yes—
517C2×D4—28no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—24no—
521C2×D4—21no—
522C2×D4—32no—
523C2×D4—62no—
524C2×D4—62no—
525C2×D4—64no—
526C2×D4—61no—
527C2×D4—124no—
528C2×D4C22×C3×D312yes—
529C22×C4—28no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—61no—
535C22×C4C3×#6711yescharacteristic
536C22×C4C3×#6711yescharacteristic
537C22×C4C3×#6711yescharacteristic
538C22×C4C22×C3×D311yescharacteristic
539C22×C4C22×C3×D311yescharacteristic
540C22×C4C22×C3×D311yescharacteristic
541SD16—68no—
542D8—68no—
543M16—64no—
544C2×C8—34no—
545C4⋊C4—32no—
546C4⋊C4—61no—
547C22⋊C4—62no—
548C22⋊C4—62no—
549C22×C3—22no—
550C22×C3—22no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—22no—
560C22×C3—28no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—24no—
567C22×C3—21no—
568C22×C3—24no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—21no—
572C22×C3—41no—
573C22×C3—41no—
574C22×C3—41no—
575C22×C3—41no—
576C22×C3—44no—
577C22×C3—44no—
578C22×C3—48no—
579C22×C3—416no—
580C22×C3—48no—
581C22×C3—48no—
582C22×C3—44no—
583C22×C3—44no—
584C22×C3—42no—
585C22×C3—42no—
586C22×C3—42no—
587C22×C3—42no—
588C22×C3—122no—
589C22×C3—122no—
590C22×C3—122no—
591C22×C3—244no—
592C22×C3#94912yescomplemented
593C22×C3#95312yes—
594C22×C3C3×#12012yes—
595C22×C3C3×AGL(1,ℤ/8)12yescomplemented
596C22×C3C22×#6711yescharacteristic
597C22×C3C22×C3×D411yescharacteristic
598C2×D3—42no—
599C2×D3—42no—
600C2×D3—42no—
601C2×D3—84no—
602C3×C4—22no—
603C3×C4—28no—
604C3×C4—22no—
605C3×C4—21no—
606C3×C4—24no—
607C3×C4—21no—
608C3×C4—21no—
609C3×C4—24no—
610C3×C4—21no—
611C3×C4—22no—
612C3×C4—22no—
613C3×C4—122no—
614C3×C4#95312yes—
615C3×C4C3×#12012yes—
616C3×C4C22×#6712yes—
617C3×C4C22×C3×D412yes—
618Dic3—42no—
619C32#300611yescharacteristic, complemented, Sylow
620C23—24no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—41no—
625C23—42no—
626C23—42no—
627C23—62no—
628C23—122no—
629C23—122no—
630C23—122no—
631C23C2×C3×#6711yescharacteristic
632C23C2×C3×#6711yescharacteristic
633C23C2×C3×#6711yescharacteristic
634Q8—24no—
635Q8—22no—
636Q8C2×C3×#6714yescomplemented
637D4—28no—
638D4—24no—
639D4—28no—
640D4—22no—
641D4—64no—
642D4—124no—
643D4—124no—
644D4—122no—
645D4C2×C3×#6714yescomplemented
646C2×C4—24no—
647C2×C4—28no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—28no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—62no—
656C2×C4—122no—
657C2×C4C2×C3×#6711yescharacteristic
658C2×C4C2×C3×#6711yescharacteristic
659C2×C4C2×C3×#6711yescharacteristic
660C2×C4C2×C3×#6714yes—
661C2×C4C23×C3×D311yescharacteristic
662C8—64no—
663C2×C3—24no—
664C2×C3—22no—
665C2×C3—22no—
666C2×C3—22no—
667C2×C3—22no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—42no—
672C2×C3—42no—
673C2×C3—48no—
674C2×C3—41no—
675C2×C3—44no—
676C2×C3—41no—
677C2×C3—44no—
678C2×C3—242no—
679C2×C3C2×#94911yescharacteristic
680C2×C3#582211yescharacteristic
681C2×C3C2×#95311yescharacteristic
682C2×C3C2×C3×#12011yescharacteristic
683C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
684C2×C3C3×#57511yescharacteristic
685D3—82no—
686C22—21no—
687C22—21no—
688C22—21no—
689C22—21no—
690C22—21no—
691C22—21no—
692C22—21no—
693C22—24no—
694C22—44no—
695C22—48no—
696C22—42no—
697C22—42no—
698C22—122no—
699C22—122no—
700C22—122no—
701C22—244no—
702C22C3×#94912yescomplemented
703C22C3×#95312yes—
704C22C22×C3×#6711yescharacteristic
705C4—21no—
706C4—24no—
707C4—21no—
708C4—122no—
709C4C3×#95312yes—
710C4C22×C3×#6712yes—
711C3—21no—
712C3#8408211yescharacteristic, direct product factor
713C3C3×#300611yescharacteristic, complemented
714C2—22no—
715C2—22no—
716C2—41no—
717C2—44no—
718C2—242no—
719C2C2×C3×#94911yescharacteristic
720C2C3×#582211yescharacteristic
721C2C2×C3×#95311yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC22×C32×#41C2
socleC22×C32C22×D4
hypercenterC22×C3×#41D3
hypocenterC3C3×#3006
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C22×C3×#41

Complements

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

NH ≅ G/Ntype
1. C22×C32×#41C2semidirect
2. C2×C3×#949C2semidirect
3. C2×C3×#930C2semidirect
4. C3×#5238C2semidirect
5. C3×#5232C2semidirect
6. C3×#5227C2semidirect
7. C3×#5217C2semidirect
8. C3×#5207C2semidirect
10. #84082C3direct (N × H)
15. C2×C32×#41C22semidirect
16. C22×C32×Q8C22semidirect
18. C22×C32×D4C22semidirect
22. C22×C3×D12C22semidirect
24. C2×C3×#215C22semidirect
25. C2×C3×#213C22semidirect
29. C3×#930C22semidirect
31. C2×C3×C4⋊Dic3C22semidirect
32. C2×C3×#208C22semidirect
33. C3×#835C22semidirect
34. C3×#832C22semidirect
35. C3×#830C22semidirect
36. C3×#830C22semidirect
38. C22×C3×#41D3semidirect
39. C22×C3×#41C2×C3semidirect
42. C2×#949C2×C3semidirect
43. C2×#930C2×C3semidirect
49. #5238C2×C3semidirect
50. #5232C2×C3semidirect
51. #5227C2×C3semidirect
52. #5217C2×C3semidirect
53. #5207C2×C3semidirect
62. C32×#41D4semidirect
111. C2×C3×#41C2×D3semidirect
113. C2×C3×#41C22×C3semidirect
115. C22×C3×Q8C2×D3semidirect
116. C22×C3×Q8C22×C3semidirect
123. C22×C3×D4C2×D3semidirect
124. C22×C3×D4C22×C3semidirect
132. C22×D12C22×C3semidirect
144. C2×#215C22×C3semidirect
145. C2×#213C22×C3semidirect
149. #930C22×C3semidirect
151. C2×C4⋊Dic3C22×C3semidirect
152. C2×#208C22×C3semidirect
157. #835C22×C3semidirect
158. #832C22×C3semidirect
159. #830C22×C3semidirect
160. #830C22×C3semidirect
177. C32×Q8C2×D4semidirect
182. C32×D4C2×D4semidirect
204. C22×#41C3×D3semidirect
236. C3×#41#67semidirect
237. C3×#41C3×D4semidirect
341. C22×C32AGL(1,ℤ/8)semidirect
357. C2×#41C2×C3×D3semidirect
358. C22×Q8C2×C3×D3semidirect
362. C22×D4C2×C3×D3semidirect
424. C3×Q8C2×#67semidirect
425. C3×Q8C2×C3×D4semidirect
443. C3×D4C2×#67semidirect
444. C3×D4C2×C3×D4semidirect
513. #41C3×#67semidirect
592. C22×C3#949semidirect
595. C22×C3C3×AGL(1,ℤ/8)semidirect
619. C32#3006semidirect
636. Q8C2×C3×#67semidirect
645. D4C2×C3×#67semidirect
702. C22C3×#949semidirect
712. C3#84082direct (N × H)
713. C3C3×#3006semidirect

Maximal subgroups

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

subgroupindex
C22×C32×#412
C2×C3×#9492
C2×C3×#9302
C3×#52382
C3×#52322
C3×#52272
C3×#52172
C3×#52072
C3×#30063
#840823