Finite Group Databasebeta

← C2×C3×#63981 #13175111

Subgroups — C2×C3×#63981 #13175111

Order 1728.

3898 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C3×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×C32×#67C211yesmaximal, characteristic, complemented
3C22×C3×#626C212yesmaximal, complemented
4C2×C32×#217C211yesmaximal, characteristic, complemented
5C3×#63981C218yesmaximal, direct product factor
6C2×C3×#3722C212yesmaximal, complemented
7C2×C3×#937—31nomaximal
8C2×C3×#882—31nomaximal
9C2×#63981C311yesmaximal, characteristic, direct product factor
10C24×C33C2211yescharacteristic
11C23×C3×C3⋊D3—24no—
12C23×C3×C3⋊D3—28no—
13C23×C3×C3⋊D3C2212yes—
14C23×C3×C3⋊D3C2214yescomplemented
15C23×C32×D3C2211yescharacteristic, complemented
16C2×C32×#67—24no—
17C2×C32×#67C2214yescomplemented
18C22×C32×Dic3C2212yescomplemented
19C22×C32×Dic3C2211yescharacteristic, complemented
20C2×C3×#626—28no—
21C2×C3×#626C2218yescomplemented
22C32×#217C2214yescomplemented
23C3×#3722C2218yescomplemented
24C24×C3⋊D3C2×C311yescharacteristic, complemented
25C24×C3×D3—31no—
26C24×C3×D3—31no—
27C24×C3×D3—61no—
28C22×C32×D4—31no—
29C22×C3×#67—21no—
30C22×C3×#67—32no—
31C22×C3×#67D311yescharacteristic, complemented
32C22×C3×#67C2×C311yescharacteristic, complemented
33C22×C3×D12—32no—
34C22×#626C2×C312yescomplemented
35C2×C32×C22⋊C4—31no—
36C2×C3×#217—21no—
37C2×C3×#217D311yescharacteristic, complemented
38C2×C3×#217C2×C311yescharacteristic, complemented
39C3×#937—38no—
40C2×C3×(C2×D3)⋊C4—32no—
41C2×C3×(C2×D3)⋊C4—32no—
42C3×#882—38no—
43#63981C2×C318yesdirect product factor
44C2×#3722C2×C312yescomplemented
45C23×C33—24no—
46C23×C33D414yescomplemented
47C23×C33C2312yes—
48C23×C33C2311yescharacteristic
49C22×C3×C3⋊D3—232no—
50C22×C3×C3⋊D3—24no—
51C22×C3×C3⋊D3—24no—
52C22×C3×C3⋊D3—28no—
53C22×C3×C3⋊D3—216no—
54C22×C3×C3⋊D3D418yescomplemented
55C22×C3×C3⋊D3C2314yes—
56C22×C32×D3—22no—
57C22×C32×D3—24no—
58C22×C32×D3C2312yescomplemented
59C32×#67—28no—
60C2×C32×Dic3—22no—
61C2×C32×Dic3—24no—
62C2×C32×Dic3C2314yescomplemented
63C2×C32×Dic3C2312yescomplemented
64C3×#626—216no—
65C2×C3×#120—91no—
66C2×#937—31no—
67C2×#882—31no—
68C24×C32—21no—
69C24×C32—21no—
70C24×C32—21no—
71C24×C32—31no—
72C24×C32—41no—
73C24×C32C2×D311yescharacteristic
74C24×C32C2×D311yescharacteristic
75C24×C32C22×C311yescharacteristic
76C23×C3⋊D3—24no—
77C23×C3⋊D3—28no—
78C23×C3⋊D3C22×C312yes—
79C23×C3⋊D3C22×C314yescomplemented
80C23×C3×D3—21no—
81C23×C3×D3—32no—
82C23×C3×D3—32no—
83C23×C3×D3—34no—
84C23×C3×D3—34no—
85C23×C3×D3—68no—
86C23×C3×D3—68no—
87C23×C3×D3—62no—
88C23×C3×D3—64no—
89C23×C3×D3—616no—
90C23×C3×D3—68no—
91C23×C3×D3—64no—
92C23×C3×D3—64no—
93C23×C3×D3C2×D311yescharacteristic, complemented
94C23×C3×D3C22×C311yescharacteristic, complemented
95C2×C32×D4—34no—
96C2×C32×D4—64no—
97C22×C32×C4—31no—
98C22×C32×C4—32no—
99C2×C3×#67—28no—
100C2×C3×#67—24no—
101C2×C3×#67—24no—
102C2×C3×#67—24no—
103C2×C3×#67—38no—
104C2×C3×#67—68no—
105C2×C3×#67C2×D314yescomplemented
106C2×C3×#67C22×C314yescomplemented
107C22×C3×Dic3—21no—
108C22×C3×Dic3—22no—
109C22×C3×Dic3C2×D311yescharacteristic, complemented
110C22×C3×Dic3C2×D312yescomplemented
111C22×C3×Dic3C22×C312yescomplemented
112C22×C3×Dic3C22×C311yescharacteristic, complemented
113C2×C3×D12—38no—
114C2×C3×D12—68no—
115C2×#626—28no—
116C2×#626C22×C318yescomplemented
117C32×C22⋊C4—34no—
118C3×#217—24no—
119C3×#217C2×D314yescomplemented
120C3×#217C22×C314yescomplemented
121C3×(C2×D3)⋊C4—38no—
122C3×(C2×D3)⋊C4—38no—
123#3722C22×C318yescomplemented
124C22×C33—28no—
125C22×C33—24no—
126C22×C33C2×D412yes—
127C22×C33C2×D414yes—
128C22×C33C2×D414yescomplemented
129C22×C33C2411yescharacteristic
130C2×C3×C3⋊D3—232no—
131C2×C3×C3⋊D3—216no—
132C2×C3×C3⋊D3—24no—
133C2×C3×C3⋊D3—24no—
134C2×C3×C3⋊D3C2×D418yescomplemented
135C2×C32×D3—22no—
136C2×C32×D3—24no—
137C2×C32×D3—44no—
138C32×Dic3—22no—
139C32×Dic3—24no—
140C25×C3—91no—
141C24×D3—31no—
142C24×D3—31no—
143C24×D3—61no—
144C22×C3×D4—31no—
145C22×C3×D4—31no—
146C22×C3×D4—61no—
147C22×C3×D4—92no—
148C22×#67—32no—
149C22×#67C3×D311yescharacteristic, complemented
150C22×D12—32no—
151C3×#120—98no—
152C2×C3×C22⋊C4—31no—
153C2×C3×C22⋊C4—31no—
154C2×C3×C22⋊C4—61no—
155C2×C3×C22⋊C4—92no—
156C2×#217C3×D311yescharacteristic, complemented
157#937—38no—
158C2×(C2×D3)⋊C4—32no—
159C2×(C2×D3)⋊C4—32no—
160#882—38no—
161C23×C32—24no—
162C23×C32—28no—
163C23×C32—24no—
164C23×C32—24no—
165C23×C32—24no—
166C23×C32—24no—
167C23×C32—24no—
168C23×C32—22no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—21no—
172C23×C32—22no—
173C23×C32—22no—
174C23×C32—32no—
175C23×C32—44no—
176C23×C32—41no—
177C23×C32—42no—
178C23×C32—44no—
179C23×C32—44no—
180C23×C32—48no—
181C23×C32—62no—
182C23×C32—64no—
183C23×C32D1214yescomplemented
184C23×C32#6714yescomplemented
185C23×C32C3×D414yescomplemented
186C23×C32C22×D312yes—
187C23×C32C22×D312yes—
188C23×C32C22×D311yescharacteristic
189C23×C32C22×D311yescharacteristic
190C23×C32C23×C312yes—
191C23×C32C23×C311yescharacteristic
192C22×C3⋊D3—232no—
193C22×C3⋊D3—24no—
194C22×C3⋊D3—24no—
195C22×C3⋊D3—28no—
196C22×C3⋊D3—216no—
197C22×C3⋊D3C3×D418yescomplemented
198C22×C3⋊D3C23×C314yes—
199C22×C3×D3—24no—
200C22×C3×D3—24no—
201C22×C3×D3—22no—
202C22×C3×D3—24no—
203C22×C3×D3—22no—
204C22×C3×D3—22no—
205C22×C3×D3—38no—
206C22×C3×D3—38no—
207C22×C3×D3—34no—
208C22×C3×D3—34no—
209C22×C3×D3—44no—
210C22×C3×D3—68no—
211C22×C3×D3—64no—
212C22×C3×D3—616no—
213C22×C3×D3—616no—
214C22×C3×D3—632no—
215C22×C3×D3—664no—
216C22×C3×D3—632no—
217C22×C3×D3—632no—
218C22×C3×D3—68no—
219C22×C3×D3—616no—
220C22×C3×D3—68no—
221C22×C3×D3—64no—
222C22×C3×D3—68no—
223C22×C3×D3—64no—
224C22×C3×D3—64no—
225C22×C3×D3—64no—
226C22×C3×D3—68no—
227C22×C3×D3C22×D312yescomplemented
228C22×C3×D3C23×C312yescomplemented
229C32×D4—68no—
230C2×C32×C4—32no—
231C2×C32×C4—34no—
232C2×C32×C4—62no—
233C2×C32×C4—64no—
234C3×#67—216no—
235C3×#67—28no—
236C3×#67—28no—
237C3×#67—616no—
238C2×C3×Dic3—24no—
239C2×C3×Dic3—24no—
240C2×C3×Dic3—22no—
241C2×C3×Dic3—24no—
242C2×C3×Dic3—22no—
243C2×C3×Dic3—22no—
244C2×C3×Dic3—24no—
245C2×C3×Dic3—44no—
246C2×C3×Dic3C22×D312yescomplemented
247C2×C3×Dic3C22×D314yescomplemented
248C2×C3×Dic3C23×C312yescomplemented
249C2×C3×Dic3C23×C314yescomplemented
250C3×D12—616no—
251#626—216no—
252C2×#120—91noSylow
253C2×C33—24no—
254C2×C33#12014yescomplemented
255C2×C33C22×D411yescharacteristic
256C2×C33C22×D412yes—
257C3×C3⋊D3—28no—
258C32×D3—42no—
259C24×C3—21no—
260C24×C3—21no—
261C24×C3—21no—
262C24×C3—31no—
263C24×C3—31no—
264C24×C3—41no—
265C24×C3—61no—
266C24×C3—92no—
267C24×C3—94no—
268C24×C3—188no—
269C24×C3—184no—
270C24×C3D3211yescharacteristic
271C24×C3C2×C3×D311yescharacteristic
272C24×C3C2×C3×D311yescharacteristic
273C23×D3—32no—
274C23×D3—32no—
275C23×D3—34no—
276C23×D3—34no—
277C23×D3—62no—
278C23×D3—64no—
279C23×D3—68no—
280C23×D3—68no—
281C23×D3—616no—
282C23×D3—68no—
283C23×D3—64no—
284C23×D3—64no—
285C23×D3C2×C3×D311yescharacteristic, complemented
286C2×C3×D4—34no—
287C2×C3×D4—34no—
288C2×C3×D4—64no—
289C2×C3×D4—68no—
290C2×C3×D4—64no—
291C2×C3×D4—64no—
292C2×C3×D4—98no—
293C2×C3×D4—188no—
294C22×C3×C4—32no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—32no—
298C22×C3×C4—61no—
299C22×C3×C4—62no—
300C2×#67—24no—
301C2×#67—38no—
302C2×#67—68no—
303C2×#67C2×C3×D314yescomplemented
304C22×Dic3C2×C3×D311yescharacteristic, complemented
305C22×Dic3C2×C3×D312yescomplemented
306C2×D12—38no—
307C2×D12—68no—
308C3×C22⋊C4—34no—
309C3×C22⋊C4—34no—
310C3×C22⋊C4—64no—
311C3×C22⋊C4—98no—
312#217C2×C3×D314yescomplemented
313(C2×D3)⋊C4—38no—
314(C2×D3)⋊C4—38no—
315C22×C32—28no—
316C22×C32—24no—
317C22×C32—28no—
318C22×C32—216no—
319C22×C32—28no—
320C22×C32—28no—
321C22×C32—24no—
322C22×C32—24no—
323C22×C32—21no—
324C22×C32—21no—
325C22×C32—21no—
326C22×C32—22no—
327C22×C32—24no—
328C22×C32—24no—
329C22×C32—22no—
330C22×C32—24no—
331C22×C32—24no—
332C22×C32—24no—
333C22×C32—22no—
334C22×C32—24no—
335C22×C32—42no—
336C22×C32—44no—
337C22×C32—44no—
338C22×C32—41no—
339C22×C32—48no—
340C22×C32—48no—
341C22×C32—44no—
342C22×C32—44no—
343C22×C32—416no—
344C22×C32—48no—
345C22×C32—62no—
346C22×C32—64no—
347C22×C32—124no—
348C22×C32C2×D1212yes—
349C22×C32C2×D1214yescomplemented
350C22×C32D3×D414yes—
351C22×C32D3×D414yes—
352C22×C32C2×#6712yes—
353C22×C32C2×#6714yescomplemented
354C22×C32C2×C3×D412yes—
355C22×C32C2×C3×D414yes—
356C22×C32C2×C3×D414yescomplemented
357C22×C32C23×D311yescharacteristic
358C22×C32C23×D311yescharacteristic
359C22×C32C24×C311yescharacteristic
360C2×C3⋊D3—232no—
361C2×C3⋊D3—216no—
362C2×C3⋊D3—24no—
363C2×C3⋊D3—24no—
364C2×C3⋊D3C2×C3×D418yescomplemented
365C2×C3×D3—24no—
366C2×C3×D3—24no—
367C2×C3×D3—22no—
368C2×C3×D3—24no—
369C2×C3×D3—22no—
370C2×C3×D3—38no—
371C2×C3×D3—38no—
372C2×C3×D3—44no—
373C2×C3×D3—48no—
374C2×C3×D3—44no—
375C2×C3×D3—44no—
376C2×C3×D3—68no—
377C2×C3×D3—664no—
378C2×C3×D3—632no—
379C2×C3×D3—632no—
380C2×C3×D3—68no—
381C2×C3×D3—68no—
382C2×C3×D3—632no—
383C2×C3×D3—616no—
384C2×C3×D3—616no—
385C2×C3×D3—64no—
386C2×C3×D3—64no—
387C2×C3×D3—64no—
388C2×C3×D3—64no—
389C32×C4—62no—
390C32×C4—64no—
391C3×Dic3—24no—
392C3×Dic3—24no—
393C3×Dic3—22no—
394C3×Dic3—24no—
395C3×Dic3—22no—
396C3×Dic3—44no—
397C25—91no—
398C22×D4—31no—
399C22×D4—92no—
400#120—98no—
401C2×C22⋊C4—31no—
402C2×C22⋊C4—92no—
403C33C2×#12011yescharacteristic, complemented, Sylow
404C23×C3—28no—
405C23×C3—24no—
406C23×C3—24no—
407C23×C3—24no—
408C23×C3—24no—
409C23×C3—24no—
410C23×C3—24no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—22no—
414C23×C3—21no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—32no—
418C23×C3—32no—
419C23×C3—44no—
420C23×C3—44no—
421C23×C3—48no—
422C23×C3—44no—
423C23×C3—42no—
424C23×C3—41no—
425C23×C3—62no—
426C23×C3—64no—
427C23×C3—62no—
428C23×C3—64no—
429C23×C3—62no—
430C23×C3—64no—
431C23×C3—94no—
432C23×C3—98no—
433C23×C3—124no—
434C23×C3—1816no—
435C23×C3—1832no—
436C23×C3—184no—
437C23×C3—188no—
438C23×C3—184no—
439C23×C3#62614yescomplemented
440C23×C3C3×D1214yescomplemented
441C23×C3C3×#6714yescomplemented
442C23×C3C2×D3212yes—
443C23×C3C2×D3211yescharacteristic
444C23×C3C22×C3×D312yes—
445C23×C3C22×C3×D312yes—
446C23×C3C22×C3×D311yescharacteristic
447C23×C3C22×C3×D311yescharacteristic
448C22×D3—24no—
449C22×D3—22no—
450C22×D3—34no—
451C22×D3—34no—
452C22×D3—38no—
453C22×D3—38no—
454C22×D3—68no—
455C22×D3—64no—
456C22×D3—616no—
457C22×D3—616no—
458C22×D3—632no—
459C22×D3—664no—
460C22×D3—632no—
461C22×D3—632no—
462C22×D3—68no—
463C22×D3—616no—
464C22×D3—68no—
465C22×D3—64no—
466C22×D3—68no—
467C22×D3—64no—
468C22×D3—64no—
469C22×D3—64no—
470C22×D3—68no—
471C22×D3C22×C3×D312yescomplemented
472C3×D4—616no—
473C3×D4—68no—
474C3×D4—68no—
475C3×D4—1816no—
476C2×C3×C4—34no—
477C2×C3×C4—32no—
478C2×C3×C4—32no—
479C2×C3×C4—34no—
480C2×C3×C4—62no—
481C2×C3×C4—64no—
482C2×C3×C4—64no—
483C2×C3×C4—62no—
484C2×C3×C4—64no—
485C2×C3×C4—62no—
486C2×C3×C4—64no—
487C2×C3×C4—124no—
488#67—28no—
489#67—616no—
490C2×Dic3—24no—
491C2×Dic3—22no—
492C2×Dic3C22×C3×D312yescomplemented
493C2×Dic3C22×C3×D314yescomplemented
494D12—616no—
495C2×C32—24no—
496C2×C32—28no—
497C2×C32—24no—
498C2×C32—24no—
499C2×C32—24no—
500C2×C32—24no—
501C2×C32—21no—
502C2×C32—22no—
503C2×C32—21no—
504C2×C32—22no—
505C2×C32—22no—
506C2×C32—21no—
507C2×C32—24no—
508C2×C32—44no—
509C2×C32—41no—
510C2×C32—42no—
511C2×C32—44no—
512C2×C32—44no—
513C2×C32—48no—
514C2×C32—122no—
515C2×C32#88214yescomplemented
516C2×C32#93714yescomplemented
517C2×C32C3×#12014yescomplemented
518C2×C32C22×D1211yescharacteristic
519C2×C32C2×D3×D412yes—
520C2×C32C2×D3×D412yes—
521C2×C32C22×#6711yescharacteristic
522C2×C32C22×C3×D411yescharacteristic
523C2×C32C22×C3×D412yes—
524C3⋊D3—28no—
525C3×D3—44no—
526C3×D3—42no—
527C3×D3—42no—
528C3×D3—616no—
529C3×D3—68no—
530C3×D3—68no—
531C24—31no—
532C24—92no—
533C24—94no—
534C24—188no—
535C24—184no—
536C24C3×D3211yescharacteristic
537C2×D4—34no—
538C2×D4—64no—
539C2×D4—98no—
540C2×D4—188no—
541C22×C4—32no—
542C22×C4—31no—
543C22⋊C4—34no—
544C22⋊C4—98no—
545C22×C3—28no—
546C22×C3—216no—
547C22×C3—28no—
548C22×C3—28no—
549C22×C3—24no—
550C22×C3—24no—
551C22×C3—24no—
552C22×C3—28no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—22no—
557C22×C3—22no—
558C22×C3—22no—
559C22×C3—24no—
560C22×C3—24no—
561C22×C3—24no—
562C22×C3—24no—
563C22×C3—24no—
564C22×C3—24no—
565C22×C3—44no—
566C22×C3—44no—
567C22×C3—48no—
568C22×C3—48no—
569C22×C3—48no—
570C22×C3—416no—
571C22×C3—41no—
572C22×C3—42no—
573C22×C3—44no—
574C22×C3—44no—
575C22×C3—64no—
576C22×C3—62no—
577C22×C3—64no—
578C22×C3—62no—
579C22×C3—64no—
580C22×C3—98no—
581C22×C3—124no—
582C22×C3—128no—
583C22×C3—124no—
584C22×C3—124no—
585C22×C3—1832no—
586C22×C3—184no—
587C22×C3—184no—
588C22×C3—1816no—
589C22×C3C2×#62612yes—
590C22×C3C2×#62614yescomplemented
591C22×C3#381114yes—
592C22×C3C2×C3×D1212yes—
593C22×C3C2×C3×D1214yescomplemented
594C22×C3C3×D3×D414yes—
595C22×C3C3×D3×D414yes—
596C22×C3C2×C3×#6712yes—
597C22×C3C2×C3×#6714yescomplemented
598C22×C3C22×D3211yescharacteristic
599C22×C3C23×C3×D311yescharacteristic
600C22×C3C23×C3×D311yescharacteristic
601C2×D3—24no—
602C2×D3—22no—
603C2×D3—38no—
604C2×D3—38no—
605C2×D3—44no—
606C2×D3—68no—
607C2×D3—664no—
608C2×D3—632no—
609C2×D3—632no—
610C2×D3—68no—
611C2×D3—68no—
612C2×D3—632no—
613C2×D3—616no—
614C2×D3—616no—
615C2×D3—64no—
616C2×D3—64no—
617C2×D3—64no—
618C2×D3—64no—
619C3×C4—64no—
620C3×C4—62no—
621C3×C4—64no—
622C3×C4—62no—
623C3×C4—64no—
624C3×C4—124no—
625Dic3—24no—
626Dic3—22no—
627C32—21no—
628C32—21no—
629C32—21no—
630C32—41no—
631C32C2×#88211yescharacteristic, complemented
632C32C2×#93711yescharacteristic, complemented
633C32C2×C3×#12011yescharacteristic, complemented
634C23—24no—
635C23—32no—
636C23—62no—
637C23—64no—
638C23—94no—
639C23—98no—
640C23—1816no—
641C23—1832no—
642C23—184no—
643C23—188no—
644C23—184no—
645C23C3×#62614yescomplemented
646C23C2×C3×D3212yes—
647C23C2×C3×D3211yescharacteristic
648D4—68no—
649D4—1816no—
650C2×C4—34no—
651C2×C4—32no—
652C2×C4—62no—
653C2×C4—64no—
654C2×C3—28no—
655C2×C3—24no—
656C2×C3—24no—
657C2×C3—24no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—21no—
661C2×C3—22no—
662C2×C3—22no—
663C2×C3—22no—
664C2×C3—24no—
665C2×C3—24no—
666C2×C3—24no—
667C2×C3—44no—
668C2×C3—44no—
669C2×C3—48no—
670C2×C3—41no—
671C2×C3—42no—
672C2×C3—44no—
673C2×C3—124no—
674C2×C3—122no—
675C2×C3—122no—
676C2×C3—188no—
677C2×C3#6398114yesdirect product factor
678C2×C3C3×#88214yescomplemented
679C2×C3C3×#93714yescomplemented
680C2×C3C22×#62611yescharacteristic
681C2×C3C2×#381112yes—
682C2×C3C22×C3×D1211yescharacteristic
683C2×C3C2×C3×D3×D412yes—
684C2×C3C2×C3×D3×D412yes—
685C2×C3C22×C3×#6711yescharacteristic
686D3—42no—
687D3—616no—
688D3—68no—
689D3—68no—
690C22—24no—
691C22—28no—
692C22—62no—
693C22—64no—
694C22—98no—
695C22—124no—
696C22—1832no—
697C22—184no—
698C22—184no—
699C22—1816no—
700C22C2×C3×#62612yes—
701C22C2×C3×#62614yescomplemented
702C22C3×#381114yes—
703C22C22×C3×D3211yescharacteristic
704C4—62no—
705C4—64no—
706C3—21no—
707C3—21no—
708C3—21no—
709C3—41no—
710C3C2×#6398111yescharacteristic, direct product factor
711C3C2×C3×#88211yescharacteristic, complemented
712C3C2×C3×#93711yescharacteristic, complemented
713C2—24no—
714C2—122no—
715C2—188no—
716C2C3×#6398114yesdirect product factor
717C2C22×C3×#62611yescharacteristic
718C2C2×C3×#381112yes—
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC24×C33C22
socleC23×C33C23
hypercenterC24×C3D32
hypocenterC32C2×C3×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C24×C3

Complements

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

NH ≅ G/Ntype
1. C24×C3×C3⋊D3C2semidirect
2. C22×C32×#67C2semidirect
3. C22×C3×#626C2semidirect
4. C2×C32×#217C2semidirect
5. C3×#63981C2direct (N × H)
6. C2×C3×#3722C2semidirect
9. C2×#63981C3direct (N × H)
14. C23×C3×C3⋊D3C22semidirect
15. C23×C32×D3C22semidirect
17. C2×C32×#67C22semidirect
18. C22×C32×Dic3C22semidirect
19. C22×C32×Dic3C22semidirect
21. C2×C3×#626C22semidirect
22. C32×#217C22semidirect
23. C3×#3722C22semidirect
24. C24×C3⋊D3C2×C3semidirect
31. C22×C3×#67D3semidirect
32. C22×C3×#67C2×C3semidirect
34. C22×#626C2×C3semidirect
37. C2×C3×#217D3semidirect
38. C2×C3×#217C2×C3semidirect
43. #63981C2×C3direct (N × H)
44. C2×#3722C2×C3semidirect
46. C23×C33D4semidirect
54. C22×C3×C3⋊D3D4semidirect
58. C22×C32×D3C23semidirect
62. C2×C32×Dic3C23semidirect
63. C2×C32×Dic3C23semidirect
79. C23×C3⋊D3C22×C3semidirect
93. C23×C3×D3C2×D3semidirect
94. C23×C3×D3C22×C3semidirect
105. C2×C3×#67C2×D3semidirect
106. C2×C3×#67C22×C3semidirect
109. C22×C3×Dic3C2×D3semidirect
110. C22×C3×Dic3C2×D3semidirect
111. C22×C3×Dic3C22×C3semidirect
112. C22×C3×Dic3C22×C3semidirect
116. C2×#626C22×C3semidirect
119. C3×#217C2×D3semidirect
120. C3×#217C22×C3semidirect
123. #3722C22×C3semidirect
128. C22×C33C2×D4semidirect
134. C2×C3×C3⋊D3C2×D4semidirect
149. C22×#67C3×D3semidirect
156. C2×#217C3×D3semidirect
183. C23×C32D12semidirect
184. C23×C32#67semidirect
185. C23×C32C3×D4semidirect
197. C22×C3⋊D3C3×D4semidirect
227. C22×C3×D3C22×D3semidirect
228. C22×C3×D3C23×C3semidirect
246. C2×C3×Dic3C22×D3semidirect
247. C2×C3×Dic3C22×D3semidirect
248. C2×C3×Dic3C23×C3semidirect
249. C2×C3×Dic3C23×C3semidirect
254. C2×C33#120semidirect
285. C23×D3C2×C3×D3semidirect
303. C2×#67C2×C3×D3semidirect
304. C22×Dic3C2×C3×D3semidirect
305. C22×Dic3C2×C3×D3semidirect
312. #217C2×C3×D3semidirect
349. C22×C32C2×D12semidirect
353. C22×C32C2×#67semidirect
356. C22×C32C2×C3×D4semidirect
364. C2×C3⋊D3C2×C3×D4semidirect
403. C33C2×#120semidirect
439. C23×C3#626semidirect
440. C23×C3C3×D12semidirect
441. C23×C3C3×#67semidirect
471. C22×D3C22×C3×D3semidirect
492. C2×Dic3C22×C3×D3semidirect
493. C2×Dic3C22×C3×D3semidirect
515. C2×C32#882semidirect
516. C2×C32#937semidirect
517. C2×C32C3×#120semidirect
590. C22×C3C2×#626semidirect
593. C22×C3C2×C3×D12semidirect
597. C22×C3C2×C3×#67semidirect
631. C32C2×#882semidirect
632. C32C2×#937semidirect
633. C32C2×C3×#120semidirect
645. C23C3×#626semidirect
677. C2×C3#63981direct (N × H)
678. C2×C3C3×#882semidirect
679. C2×C3C3×#937semidirect
701. C22C2×C3×#626semidirect
710. C3C2×#63981direct (N × H)
711. C3C2×C3×#882semidirect
712. C3C2×C3×#937semidirect
716. C2C3×#63981direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C3×C3⋊D32
C22×C32×#672
C22×C3×#6262
C2×C32×#2172
C3×#639812
C2×C3×#37222
C2×C3×#9373
C2×C3×#8823
C2×#639813