Finite Group Databasebeta

← C3×#10591399 #13158416

Subgroups — C3×#10591399 #13158416

Order 1728.

2474 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×D32C211yesmaximal, characteristic
2C2×C3×#3752C211yesmaximal, characteristic, complemented
3C2×C32×(C2×D3)⋊C4C212yesmaximal, complemented
4C2×C3×#3722C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊Dic3C212yesmaximal, complemented
6C3×#4955—32nomaximal
7#10591399C311yesmaximal, characteristic, direct product factor
8C23×C3×C3⋊D3C2211yescharacteristic
9C23×C32×D3C2212yes—
10C22×C3×D32—22no—
11C22×C3×D32—22no—
12C22×C3×D32—24no—
13C22×C3×D32—24no—
14C22×C3×D32C414yescomplemented
15C22×C33×C4C2211yescharacteristic, complemented
16C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
17C22×C32×Dic3C2212yescomplemented
18C3×#3752—22no—
19C32×(C2×D3)⋊C4—24no—
20C3×#3722—22no—
21C3×(C2×D3)⋊Dic3—24no—
22C24×C3×D3—32no—
23C23×D32C2×C311yescharacteristic
24C2×C32×C22⋊C4—32no—
25C2×#3752C2×C311yescharacteristic, complemented
26C2×C3×#217—32no—
27C2×C3×(C2×D3)⋊C4—22no—
28C2×C3×(C2×D3)⋊C4—32no—
29C2×C3×(C2×D3)⋊C4—32no—
30C2×C3×(C2×D3)⋊C4—32no—
31C2×C3×(C2×D3)⋊C4—61no—
32C2×C3×(C2×D3)⋊C4D312yescomplemented
33C2×C3×(C2×D3)⋊C4C2×C312yescomplemented
34C2×#3722C2×C311yescharacteristic, complemented
35C2×(C2×D3)⋊Dic3C2×C312yescomplemented
36C23×C33C2311yescharacteristic
37C22×C3×C3⋊D3—22no—
38C22×C3×C3⋊D3—22no—
39C22×C3×C3⋊D3C2×C412yes—
40C22×C3×C3⋊D3D412yes—
41C22×C3×C3⋊D3D412yes—
42C22×C32×D3—22no—
43C22×C32×D3—22no—
44C22×C32×D3—22no—
45C22×C32×D3—22no—
46C22×C32×D3C2×C414yes—
47C22×C32×D3D414yes—
48C22×C32×D3D414yes—
49C2×C3×D32—28no—
50C2×C3×D32—216no—
51C2×C3×D32—28no—
52C2×C3×D32—28no—
53C2×C3×D32—216no—
54C2×C33×C4—21no—
55C2×C33×C4—22no—
56C2×C3×C3⋊Dic3—21no—
57C2×C3×C3⋊Dic3—22no—
58C2×C32×Dic3—22no—
59C2×C32×Dic3—22no—
60C2×C32×Dic3—22no—
61C3×#379—91no—
62#4955—32no—
63C24×C32—32no—
64C23×C3⋊D3C22×C311yescharacteristic
65C23×C3×D3—22no—
66C23×C3×D3—32no—
67C23×C3×D3—38no—
68C23×C3×D3—64no—
69C23×C3×D3—64no—
70C23×C3×D3—64no—
71C23×C3×D3—64no—
72C23×C3×D3—64no—
73C23×C3×D3—64no—
74C23×C3×D3—61no—
75C23×C3×D3C2×D312yes—
76C23×C3×D3C22×C312yes—
77C22×D32—22no—
78C22×D32—22no—
79C22×D32—24no—
80C22×D32—24no—
81C22×D32C3×C414yescomplemented
82C22×C32×C4—21no—
83C22×C32×C4—22no—
84C22×C32×C4—32no—
85C22×C32×C4—41no—
86C22×C32×C4C2×D312yescomplemented
87C22×C32×C4C22×C311yescharacteristic, complemented
88C22×C3⋊Dic3C22×C311yescharacteristic, complemented
89C22×C3×Dic3—22no—
90C22×C3×Dic3—32no—
91C22×C3×Dic3—61no—
92C22×C3×Dic3C2×D312yescomplemented
93C22×C3×Dic3C22×C312yescomplemented
94C32×C22⋊C4—64no—
95#3752—22no—
96C3×#217—64no—
97C3×(C2×D3)⋊C4—28no—
98C3×(C2×D3)⋊C4—24no—
99C3×(C2×D3)⋊C4—24no—
100C3×(C2×D3)⋊C4—64no—
101C3×(C2×D3)⋊C4—64no—
102C3×(C2×D3)⋊C4—64no—
103C3×(C2×D3)⋊C4—64no—
104#3722—22no—
105(C2×D3)⋊Dic3—24no—
106C22×C33C22×C411yescharacteristic
107C22×C33C2×D412yes—
108C22×C33C2×D411yescharacteristic
109C22×C33C2×D411yescharacteristic
110C22×C33C2×D412yes—
111C2×C3×C3⋊D3—24no—
112C2×C3×C3⋊D3—22no—
113C2×C3×C3⋊D3—24no—
114C2×C3×C3⋊D3—22no—
115C2×C3×C3⋊D3C22⋊C414yescomplemented
116C2×C32×D3—24no—
117C2×C32×D3—24no—
118C2×C32×D3—24no—
119C2×C32×D3—24no—
120C2×C32×D3—24no—
121C2×C32×D3—24no—
122C2×C32×D3C22⋊C418yescomplemented
123C3×D32—232no—
124C33×C4—41no—
125C3×C3⋊Dic3—41no—
126C32×Dic3—42no—
127C25×C3—91no—
128C24×D3—32no—
129C2×C3×C22⋊C4—32no—
130C2×C3×C22⋊C4—32no—
131C2×C3×C22⋊C4—62no—
132C2×C3×C22⋊C4—91no—
133C2×C3×C22⋊C4—92no—
134C2×C3×C22⋊C4—91no—
135C2×#217—32no—
136C2×(C2×D3)⋊C4—32no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4—61no—
140C2×(C2×D3)⋊C4C3×D312yescomplemented
141C23×C32—21no—
142C23×C32—22no—
143C23×C32—34no—
144C23×C32—34no—
145C23×C32—34no—
146C23×C32—41no—
147C23×C32—62no—
148C23×C32—62no—
149C23×C32—62no—
150C23×C32—62no—
151C23×C32C22×D312yes—
152C23×C32C23×C311yescharacteristic
153C22×C3⋊D3—22no—
154C22×C3⋊D3—22no—
155C22×C3⋊D3C2×C3×C412yes—
156C22×C3⋊D3C3×D412yes—
157C22×C3⋊D3C3×D412yes—
158C22×C3×D3—22no—
159C22×C3×D3—22no—
160C22×C3×D3—22no—
161C22×C3×D3—22no—
162C22×C3×D3—22no—
163C22×C3×D3—22no—
164C22×C3×D3—22no—
165C22×C3×D3—22no—
166C22×C3×D3—24no—
167C22×C3×D3—24no—
168C22×C3×D3—24no—
169C22×C3×D3—34no—
170C22×C3×D3—34no—
171C22×C3×D3—34no—
172C22×C3×D3—42no—
173C22×C3×D3—42no—
174C22×C3×D3—42no—
175C22×C3×D3—42no—
176C22×C3×D3—62no—
177C22×C3×D3—62no—
178C22×C3×D3—62no—
179C22×C3×D3—616no—
180C22×C3×D3—616no—
181C22×C3×D3—616no—
182C22×C3×D3—616no—
183C22×C3×D3—616no—
184C22×C3×D3—616no—
185C22×C3×D3—62no—
186C22×C3×D3—62no—
187C22×C3×D3—62no—
188C22×C3×D3—62no—
189C22×C3×D3—616no—
190C22×C3×D3—122no—
191C22×C3×D3—122no—
192C22×C3×D3C4×D314yes—
193C22×C3×D3D1214yes—
194C22×C3×D3#6714yes—
195C22×C3×D3C2×C3×C414yes—
196C22×C3×D3C3×D414yes—
197C22×C3×D3C3×D414yes—
198C2×D32—28no—
199C2×D32—216no—
200C2×D32—28no—
201C2×D32—28no—
202C2×D32—216no—
203C2×C32×C4—22no—
204C2×C32×C4—21no—
205C2×C32×C4—24no—
206C2×C32×C4—22no—
207C2×C32×C4—22no—
208C2×C32×C4—22no—
209C2×C32×C4—22no—
210C2×C32×C4—42no—
211C2×C32×C4—42no—
212C2×C32×C4—42no—
213C2×C32×C4—42no—
214C2×C32×C4—44no—
215C2×C32×C4—62no—
216C2×C32×C4—62no—
217C2×C32×C4—62no—
218C2×C3⋊Dic3—21no—
219C2×C3⋊Dic3—22no—
220C2×C3×Dic3—24no—
221C2×C3×Dic3—22no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—42no—
228C2×C3×Dic3—42no—
229C2×C3×Dic3—62no—
230C2×C3×Dic3—62no—
231C2×C3×Dic3—62no—
232C2×C3×Dic3—62no—
233C2×C3×Dic3—122no—
234#379—91noSylow
235C2×C33C2×C22⋊C411yescharacteristic
236C2×C33C2×C22⋊C412yes—
237C2×C33#12011yescharacteristic
238C2×C33#12012yes—
239C2×C33#12011yescharacteristic
240C3×C3⋊D3—24no—
241C32×D3—28no—
242C24×C3—32no—
243C24×C3—32no—
244C24×C3—62no—
245C24×C3—94no—
246C24×C3—91no—
247C24×C3—184no—
248C24×C3—184no—
249C24×C3—182no—
250C24×C3—182no—
251C23×D3—32no—
252C23×D3—38no—
253C23×D3—61no—
254C23×D3—64no—
255C23×D3—64no—
256C23×D3—64no—
257C23×D3—64no—
258C23×D3—64no—
259C23×D3—64no—
260C23×D3C2×C3×D312yes—
261C22×C3×C4—21no—
262C22×C3×C4—22no—
263C22×C3×C4—32no—
264C22×C3×C4—32no—
265C22×C3×C4—41no—
266C22×C3×C4—62no—
267C22×C3×C4—91no—
268C22×C3×C4D3211yescharacteristic, complemented
269C22×C3×C4C2×C3×D312yescomplemented
270C22×Dic3—32no—
271C22×Dic3—61no—
272C22×Dic3C2×C3×D312yescomplemented
273C3×C22⋊C4—64no—
274C3×C22⋊C4—64no—
275C3×C22⋊C4—68no—
276C3×C22⋊C4—182no—
277C3×C22⋊C4—182no—
278C3×C22⋊C4—184no—
279#217—64no—
280(C2×D3)⋊C4—24no—
281(C2×D3)⋊C4—64no—
282(C2×D3)⋊C4—64no—
283(C2×D3)⋊C4—64no—
284(C2×D3)⋊C4—64no—
285C22×C32—21no—
286C22×C32—22no—
287C22×C32—21no—
288C22×C32—22no—
289C22×C32—21no—
290C22×C32—22no—
291C22×C32—22no—
292C22×C32—22no—
293C22×C32—22no—
294C22×C32—22no—
295C22×C32—22no—
296C22×C32—22no—
297C22×C32—38no—
298C22×C32—41no—
299C22×C32—42no—
300C22×C32—41no—
301C22×C32—42no—
302C22×C32—41no—
303C22×C32—64no—
304C22×C32—64no—
305C22×C32—64no—
306C22×C32—64no—
307C22×C32—64no—
308C22×C32—64no—
309C22×C32C2×C4×D312yes—
310C22×C32C2×D1212yes—
311C22×C32D3×D412yes—
312C22×C32D3×D412yes—
313C22×C32D3×D412yes—
314C22×C32D3×D412yes—
315C22×C32C2×#6712yes—
316C22×C32C22×C3×C411yescharacteristic
317C22×C32C2×C3×D412yes—
318C22×C32C2×C3×D411yescharacteristic
319C22×C32C2×C3×D411yescharacteristic
320C22×C32C2×C3×D412yes—
321C2×C3⋊D3—24no—
322C2×C3⋊D3—22no—
323C2×C3⋊D3—24no—
324C2×C3⋊D3—22no—
325C2×C3⋊D3C3×C22⋊C414yescomplemented
326C2×C3×D3—24no—
327C2×C3×D3—24no—
328C2×C3×D3—24no—
329C2×C3×D3—24no—
330C2×C3×D3—24no—
331C2×C3×D3—24no—
332C2×C3×D3—24no—
333C2×C3×D3—24no—
334C2×C3×D3—24no—
335C2×C3×D3—24no—
336C2×C3×D3—24no—
337C2×C3×D3—24no—
338C2×C3×D3—28no—
339C2×C3×D3—38no—
340C2×C3×D3—44no—
341C2×C3×D3—44no—
342C2×C3×D3—44no—
343C2×C3×D3—44no—
344C2×C3×D3—44no—
345C2×C3×D3—44no—
346C2×C3×D3—64no—
347C2×C3×D3—664no—
348C2×C3×D3—64no—
349C2×C3×D3—64no—
350C2×C3×D3—64no—
351C2×C3×D3—64no—
352C2×C3×D3—64no—
353C2×C3×D3—64no—
354C2×C3×D3—124no—
355C2×C3×D3—124no—
356C2×C3×D3—122no—
357C2×C3×D3—122no—
358C2×C3×D3(C2×D3)⋊C418yescomplemented
359C2×C3×D3C3×C22⋊C418yescomplemented
360D32—232no—
361C32×C4—44no—
362C32×C4—42no—
363C32×C4—44no—
364C32×C4—42no—
365C32×C4—41no—
366C32×C4—122no—
367C3⋊Dic3—41no—
368C3×Dic3—44no—
369C3×Dic3—42no—
370C3×Dic3—42no—
371C3×Dic3—122no—
372C3×Dic3—122no—
373C25—91no—
374C2×C22⋊C4—32no—
375C2×C22⋊C4—91no—
376C2×C22⋊C4—92no—
377C2×C22⋊C4—91no—
378C33#37911yescharacteristic, complemented, Sylow
379C23×C3—22no—
380C23×C3—21no—
381C23×C3—34no—
382C23×C3—34no—
383C23×C3—34no—
384C23×C3—34no—
385C23×C3—34no—
386C23×C3—34no—
387C23×C3—41no—
388C23×C3—64no—
389C23×C3—64no—
390C23×C3—64no—
391C23×C3—62no—
392C23×C3—62no—
393C23×C3—62no—
394C23×C3—62no—
395C23×C3—62no—
396C23×C3—62no—
397C23×C3—62no—
398C23×C3—62no—
399C23×C3—92no—
400C23×C3—92no—
401C23×C3—92no—
402C23×C3—122no—
403C23×C3—122no—
404C23×C3—122no—
405C23×C3—122no—
406C23×C3—1816no—
407C23×C3—188no—
408C23×C3—1816no—
409C23×C3—188no—
410C23×C3—188no—
411C23×C3—182no—
412C23×C3—182no—
413C23×C3C2×D3211yescharacteristic
414C23×C3C22×C3×D312yes—
415C22×D3—22no—
416C22×D3—22no—
417C22×D3—22no—
418C22×D3—22no—
419C22×D3—34no—
420C22×D3—34no—
421C22×D3—34no—
422C22×D3—62no—
423C22×D3—62no—
424C22×D3—62no—
425C22×D3—616no—
426C22×D3—616no—
427C22×D3—616no—
428C22×D3—616no—
429C22×D3—616no—
430C22×D3—616no—
431C22×D3—62no—
432C22×D3—62no—
433C22×D3—62no—
434C22×D3—62no—
435C22×D3—616no—
436C22×D3—122no—
437C22×D3—122no—
438C22×D3C3×C4×D314yes—
439C22×D3C3×D1214yes—
440C22×D3C3×#6714yes—
441C2×C3×C4—22no—
442C2×C3×C4—24no—
443C2×C3×C4—22no—
444C2×C3×C4—21no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—42no—
449C2×C3×C4—42no—
450C2×C3×C4—42no—
451C2×C3×C4—44no—
452C2×C3×C4—42no—
453C2×C3×C4—64no—
454C2×C3×C4—62no—
455C2×C3×C4—62no—
456C2×C3×C4—62no—
457C2×C3×C4—62no—
458C2×C3×C4—62no—
459C2×C3×C4—62no—
460C2×C3×C4—122no—
461C2×C3×C4—122no—
462C2×C3×C4—182no—
463C2×C3×C4—181no—
464C2×Dic3—22no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—62no—
468C2×Dic3—62no—
469C2×Dic3—62no—
470C2×Dic3—62no—
471C2×Dic3—122no—
472C2×C32—22no—
473C2×C32—22no—
474C2×C32—22no—
475C2×C32—22no—
476C2×C32—22no—
477C2×C32—22no—
478C2×C32—22no—
479C2×C32—22no—
480C2×C32—21no—
481C2×C32—22no—
482C2×C32—21no—
483C2×C32—21no—
484C2×C32—42no—
485C2×C32—41no—
486C2×C32—41no—
487C2×C32—42no—
488C2×C32—41no—
489C2×C32—68no—
490C2×C32D3×C22⋊C412yes—
491C2×C32D3×C22⋊C412yes—
492C2×C32#88212yes—
493C2×C32#88212yes—
494C2×C32C2×(C2×D3)⋊C412yes—
495C2×C32#93712yes—
496C2×C32#93712yes—
497C2×C32C2×C3×C22⋊C411yescharacteristic
498C2×C32C2×C3×C22⋊C412yes—
499C2×C32C3×#12011yescharacteristic
500C2×C32C3×#12012yes—
501C2×C32C3×#12011yescharacteristic
502C3⋊D3—24no—
503C3×D3—28no—
504C3×D3—28no—
505C3×D3—48no—
506C3×D3—68no—
507C3×D3—124no—
508C24—32no—
509C24—94no—
510C24—91no—
511C24—184no—
512C24—184no—
513C24—182no—
514C24—182no—
515C22×C4—32no—
516C22×C4—91no—
517C22×C4C3×D3211yescharacteristic, complemented
518C22⋊C4—64no—
519C22⋊C4—182no—
520C22⋊C4—182no—
521C22⋊C4—184no—
522C22×C3—21no—
523C22×C3—22no—
524C22×C3—22no—
525C22×C3—22no—
526C22×C3—22no—
527C22×C3—22no—
528C22×C3—21no—
529C22×C3—22no—
530C22×C3—22no—
531C22×C3—22no—
532C22×C3—21no—
533C22×C3—22no—
534C22×C3—38no—
535C22×C3—38no—
536C22×C3—41no—
537C22×C3—42no—
538C22×C3—41no—
539C22×C3—42no—
540C22×C3—41no—
541C22×C3—68no—
542C22×C3—64no—
543C22×C3—64no—
544C22×C3—64no—
545C22×C3—64no—
546C22×C3—64no—
547C22×C3—64no—
548C22×C3—64no—
549C22×C3—64no—
550C22×C3—64no—
551C22×C3—64no—
552C22×C3—64no—
553C22×C3—64no—
554C22×C3—94no—
555C22×C3—124no—
556C22×C3—124no—
557C22×C3—124no—
558C22×C3—124no—
559C22×C3—124no—
560C22×C3—124no—
561C22×C3—1832no—
562C22×C3—184no—
563C22×C3—184no—
564C22×C3—182no—
565C22×C3—182no—
566C22×C3C4×D3211yescharacteristic
567C22×C3D3×D1212yes—
568C22×C3#380211yescharacteristic
569C22×C3D3×#6712yes—
570C22×C3#381111yescharacteristic
571C22×C3C2×C3×C4×D312yes—
572C22×C3C2×C3×D1212yes—
573C22×C3C3×D3×D412yes—
574C22×C3C3×D3×D412yes—
575C22×C3C3×D3×D412yes—
576C22×C3C3×D3×D412yes—
577C22×C3C2×C3×#6712yes—
578C2×D3—24no—
579C2×D3—24no—
580C2×D3—24no—
581C2×D3—24no—
582C2×D3—24no—
583C2×D3—24no—
584C2×D3—38no—
585C2×D3—64no—
586C2×D3—664no—
587C2×D3—64no—
588C2×D3—64no—
589C2×D3—64no—
590C2×D3—64no—
591C2×D3—64no—
592C2×D3—64no—
593C2×D3—122no—
594C2×D3—124no—
595C2×D3—124no—
596C2×D3—122no—
597C2×D3C3×(C2×D3)⋊C418yescomplemented
598C3×C4—42no—
599C3×C4—44no—
600C3×C4—44no—
601C3×C4—42no—
602C3×C4—41no—
603C3×C4—124no—
604C3×C4—122no—
605C3×C4—122no—
606C3×C4—361no—
607Dic3—42no—
608Dic3—122no—
609Dic3—122no—
610C32—22no—
611C32—21no—
612C32—41no—
613C32#495512yescomplemented
614C32C3×#37911yescharacteristic, complemented
615C23—34no—
616C23—34no—
617C23—34no—
618C23—62no—
619C23—62no—
620C23—62no—
621C23—62no—
622C23—92no—
623C23—92no—
624C23—92no—
625C23—1816no—
626C23—188no—
627C23—188no—
628C23—1816no—
629C23—188no—
630C23—182no—
631C23—182no—
632C23C2×C3×D3211yescharacteristic
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—62no—
636C2×C4—62no—
637C2×C4—62no—
638C2×C4—182no—
639C2×C4—181no—
640C2×C3—21no—
641C2×C3—22no—
642C2×C3—22no—
643C2×C3—22no—
644C2×C3—22no—
645C2×C3—21no—
646C2×C3—22no—
647C2×C3—22no—
648C2×C3—22no—
649C2×C3—22no—
650C2×C3—21no—
651C2×C3—22no—
652C2×C3—41no—
653C2×C3—42no—
654C2×C3—41no—
655C2×C3—42no—
656C2×C3—41no—
657C2×C3—68no—
658C2×C3—68no—
659C2×C3—128no—
660C2×C3—184no—
661C2×C3D3×(C2×D3)⋊C412yes—
662C2×C3#6392111yescharacteristic
663C2×C3#6392212yes—
664C2×C3#6392311yescharacteristic
665C2×C3#6398311yescharacteristic
666C2×C3C3×D3×C22⋊C412yes—
667C2×C3C3×D3×C22⋊C412yes—
668C2×C3C3×#88212yes—
669C2×C3C3×#88212yes—
670C2×C3C2×C3×(C2×D3)⋊C412yes—
671C2×C3C3×#93712yes—
672C2×C3C3×#93712yes—
673D3—28no—
674D3—68no—
675D3—124no—
676C22—38no—
677C22—64no—
678C22—64no—
679C22—64no—
680C22—64no—
681C22—64no—
682C22—64no—
683C22—94no—
684C22—1832no—
685C22—182no—
686C22—184no—
687C22—184no—
688C22—182no—
689C22C3×C4×D3211yescharacteristic
690C22C3×D3×D1212yes—
691C22C3×#380211yescharacteristic
692C22C3×D3×#6712yes—
693C22C3×#381111yescharacteristic
694C4—41no—
695C4—122no—
696C4—361no—
697C3—21no—
698C3—22no—
699C3—41no—
700C3#1059139911yescharacteristic, direct product factor
701C3C3×#495512yescomplemented
702C2—68no—
703C2—184no—
704C2C3×D3×(C2×D3)⋊C412yes—
705C2C3×#6392111yescharacteristic
706C2C3×#6392212yes—
707C2C3×#6392311yescharacteristic
708C2C3×#6398311yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC22×C32C22×C3×C4
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C3×D32C2
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#379
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#3752C2semidirect
3. C2×C32×(C2×D3)⋊C4C2semidirect
4. C2×C3×#3722C2semidirect
5. C2×C3×(C2×D3)⋊Dic3C2semidirect
7. #10591399C3direct (N × H)
14. C22×C3×D32C4semidirect
15. C22×C33×C4C22semidirect
16. C22×C3×C3⋊Dic3C22semidirect
17. C22×C32×Dic3C22semidirect
25. C2×#3752C2×C3semidirect
32. C2×C3×(C2×D3)⋊C4D3semidirect
33. C2×C3×(C2×D3)⋊C4C2×C3semidirect
34. C2×#3722C2×C3semidirect
35. C2×(C2×D3)⋊Dic3C2×C3semidirect
81. C22×D32C3×C4semidirect
86. C22×C32×C4C2×D3semidirect
87. C22×C32×C4C22×C3semidirect
88. C22×C3⋊Dic3C22×C3semidirect
92. C22×C3×Dic3C2×D3semidirect
93. C22×C3×Dic3C22×C3semidirect
115. C2×C3×C3⋊D3C22⋊C4semidirect
122. C2×C32×D3C22⋊C4semidirect
140. C2×(C2×D3)⋊C4C3×D3semidirect
268. C22×C3×C4D32semidirect
269. C22×C3×C4C2×C3×D3semidirect
272. C22×Dic3C2×C3×D3semidirect
325. C2×C3⋊D3C3×C22⋊C4semidirect
358. C2×C3×D3(C2×D3)⋊C4semidirect
359. C2×C3×D3C3×C22⋊C4semidirect
378. C33#379semidirect
517. C22×C4C3×D32semidirect
597. C2×D3C3×(C2×D3)⋊C4semidirect
613. C32#4955semidirect
614. C32C3×#379semidirect
700. C3#10591399direct (N × H)
701. C3C3×#4955semidirect

Maximal subgroups

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

subgroupindex
C23×C3×D322
C2×C3×#37522
C2×C32×(C2×D3)⋊C42
C2×C3×#37222
C2×C3×(C2×D3)⋊Dic32
C3×#49553
#105913993