Finite Group Databasebeta

← C2×C3×#63825 #13174423

Subgroups — C2×C3×#63825 #13174423

Order 1728.

1714 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×C32×#235C211yesmaximal, characteristic, complemented
3C2×C32×#208C211yesmaximal, characteristic, complemented
4C2×C3×#3717C212yesmaximal, complemented
5C3×#63825C218yesmaximal, direct product factor
6C2×C3×#3714C212yesmaximal, complemented
7C2×C3×#949—31nomaximal
8C2×C3×#908—31nomaximal
9C2×#63825C311yesmaximal, characteristic, direct product factor
10C23×C3×C3⋊D3—21no—
11C22×C33×C4C2211yescharacteristic
12C2×C3×C4⋊(C3⋊D3)—22no—
13C2×C3×C4⋊(C3⋊D3)—21no—
14C2×C3×C4⋊(C3⋊D3)C2212yes—
15C2×C3×C4⋊(C3⋊D3)C2214yescomplemented
16C2×C32×#67—21no—
17C32×#235—22no—
18C32×#235C2214yescomplemented
19C2×C32×D12C2211yescharacteristic, complemented
20C2×C32×C4×D3—21no—
21C2×C32×Dic6C2211yescharacteristic, complemented
22C32×#208C2214yescomplemented
23C2×C32×C3⋊C8C2212yescomplemented
24C3×#3717C2218yescomplemented
25C3×#3714C2218yescomplemented
26C2×C32×#41—31no—
27C22×C4⋊(C3⋊D3)C2×C311yescharacteristic, complemented
28C2×C3×#235—21no—
29C2×C3×#235D311yescharacteristic, complemented
30C2×C3×#235C2×C311yescharacteristic, complemented
31C22×C3×D12—31no—
32C22×C3×D12—31no—
33C22×C3×D12—61no—
34C2×C32×M16—31no—
35C3×#949—38no—
36C2×C3×#215—32no—
37C2×C3×#213—32no—
38C2×C3×#208—21no—
39C2×C3×#208D311yescharacteristic, complemented
40C2×C3×#208C2×C311yescharacteristic, complemented
41C3×#908—38no—
42C2×C3×D24—32no—
43C2×C3×#204—32no—
44C2×#3717C2×C312yescomplemented
45#63825C2×C318yesdirect product factor
46C2×#3714C2×C312yescomplemented
47C23×C33D411yescharacteristic
48C22×C3×C3⋊D3—22no—
49C22×C3×C3⋊D3—24no—
50C22×C3×C3⋊D3—44no—
51C22×C32×D3—21no—
52C2×C33×C4D411yescharacteristic
53C2×C33×C4D412yes—
54C2×C33×C4C2311yescharacteristic
55C2×C33×C4C2312yes—
56C3×C4⋊(C3⋊D3)—22no—
57C3×C4⋊(C3⋊D3)—24no—
58C3×C4⋊(C3⋊D3)C2314yes—
59C32×#67—24no—
60C2×C32×Dic3—21no—
61C32×D12—21no—
62C32×D12C2312yescomplemented
63C32×C4×D3—24no—
64C32×Dic6—21no—
65C32×Dic6C2312yescomplemented
66C32×C3⋊C8C2314yescomplemented
67C2×C3×AGL(1,ℤ/8)—91no—
68C2×#949—31no—
69C2×#908—31no—
70C23×C3⋊D3—21no—
71C23×C3×D3—62no—
72C23×C3×D3—61no—
73C23×C3×D3—61no—
74C32×#41—34no—
75C32×#41—62no—
76C2×C32×Q8—31no—
77C2×C32×D4—31no—
78C2×C32×D4—61no—
79C22×C32×C4—21no—
80C22×C32×C4—21no—
81C22×C32×C4—21no—
82C22×C32×C4—41no—
83C22×C32×C4—61no—
84C22×C32×C4C2×D311yescharacteristic
85C22×C32×C4C2×D311yescharacteristic
86C22×C32×C4C22×C311yescharacteristic
87C2×C4⋊(C3⋊D3)—22no—
88C2×C4⋊(C3⋊D3)—21no—
89C2×C4⋊(C3⋊D3)C22×C312yes—
90C2×C4⋊(C3⋊D3)C22×C314yescomplemented
91C2×C3×#67—22no—
92C2×C3×#67—21no—
93C2×C3×#67—21no—
94C3×#235—24no—
95C3×#235—24no—
96C3×#235—22no—
97C3×#235—22no—
98C3×#235C2×D314yescomplemented
99C3×#235C22×C314yescomplemented
100C2×C3×D12—21no—
101C2×C3×D12—32no—
102C2×C3×D12—34no—
103C2×C3×D12—32no—
104C2×C3×D12—34no—
105C2×C3×D12—62no—
106C2×C3×D12—64no—
107C2×C3×D12—64no—
108C2×C3×D12—62no—
109C2×C3×D12—61no—
110C2×C3×D12—62no—
111C2×C3×D12—61no—
112C2×C3×D12—62no—
113C2×C3×D12C2×D311yescharacteristic, complemented
114C2×C3×D12C22×C311yescharacteristic, complemented
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3—21no—
118C2×C3×Dic6—21no—
119C2×C3×Dic6C2×D311yescharacteristic, complemented
120C2×C3×Dic6C22×C311yescharacteristic, complemented
121C32×M16—34no—
122C2×C32×C8—32no—
123C3×#215—38no—
124C3×#213—38no—
125C3×#208—24no—
126C3×#208C2×D314yescomplemented
127C3×#208C22×C314yescomplemented
128C2×C3×C3⋊C8—22no—
129C2×C3×C3⋊C8C2×D312yescomplemented
130C2×C3×C3⋊C8C22×C312yescomplemented
131C3×D24—38no—
132C3×#204—38no—
133#3717C22×C318yescomplemented
134#3714C22×C318yescomplemented
135C22×C33—22no—
136C22×C33C2×D412yes—
137C22×C33C2×D411yescharacteristic
138C2×C3×C3⋊D3—24no—
139C2×C3×C3⋊D3—48no—
140C2×C3×C3⋊D3—44no—
141C2×C32×D3—22no—
142C2×C32×D3—42no—
143C33×C4C2×D411yescharacteristic
144C33×C4C2×D412yes—
145C33×C4C2411yescharacteristic
146C32×Dic3—22no—
147C2×C3×#41—31no—
148C2×C3×#41—31no—
149C2×C3×#41—61no—
150C22×C3×D4—91no—
151C2×#235C3×D311yescharacteristic, complemented
152C22×D12—31no—
153C22×D12—31no—
154C22×D12—61no—
155C3×AGL(1,ℤ/8)—98no—
156C2×C3×SD16—92no—
157C2×C3×D8—92no—
158C2×C3×M16—31no—
159C2×C3×M16—31no—
160C2×C3×M16—61no—
161#949—38no—
162C2×#215—32no—
163C2×#213—32no—
164C2×#208C3×D311yescharacteristic, complemented
165#908—38no—
166C2×D24—32no—
167C2×#204—32no—
168C23×C32—21no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—41no—
172C23×C32—61no—
173C23×C32D1211yescharacteristic
174C23×C32#6711yescharacteristic
175C23×C32C3×D411yescharacteristic
176C22×C3⋊D3—22no—
177C22×C3⋊D3—24no—
178C22×C3⋊D3—44no—
179C22×C3×D3—22no—
180C22×C3×D3—21no—
181C22×C3×D3—21no—
182C22×C3×D3—68no—
183C22×C3×D3—64no—
184C22×C3×D3—64no—
185C22×C3×D3—62no—
186C22×C3×D3—64no—
187C22×C3×D3—62no—
188C22×C3×D3—128no—
189C22×C3×D3—124no—
190C22×C3×D3—124no—
191C32×Q8—32no—
192C32×Q8—61no—
193C32×D4—32no—
194C32×D4—64no—
195C32×D4—61no—
196C2×C32×C4—22no—
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C32×C4—22no—
200C2×C32×C4—21no—
201C2×C32×C4—22no—
202C2×C32×C4—22no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—22no—
206C2×C32×C4—21no—
207C2×C32×C4—22no—
208C2×C32×C4—41no—
209C2×C32×C4—42no—
210C2×C32×C4—41no—
211C2×C32×C4—42no—
212C2×C32×C4—61no—
213C2×C32×C4—64no—
214C2×C32×C4D1211yescharacteristic
215C2×C32×C4D1212yes—
216C2×C32×C4#6711yescharacteristic
217C2×C32×C4#6712yes—
218C2×C32×C4C3×D411yescharacteristic
219C2×C32×C4C3×D412yes—
220C2×C32×C4C22×D311yescharacteristic
221C2×C32×C4C22×D312yes—
222C2×C32×C4C22×D311yescharacteristic
223C2×C32×C4C22×D312yes—
224C2×C32×C4C23×C311yescharacteristic
225C2×C32×C4C23×C312yes—
226C4⋊(C3⋊D3)—22no—
227C4⋊(C3⋊D3)—24no—
228C4⋊(C3⋊D3)C23×C314yes—
229C3×#67—28no—
230C3×#67—24no—
231C3×#67—24no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3—21no—
234C2×C3×Dic3—21no—
235C3×D12—22no—
236C3×D12—21no—
237C3×D12—21no—
238C3×D12—22no—
239C3×D12—34no—
240C3×D12—34no—
241C3×D12—64no—
242C3×D12—64no—
243C3×D12—68no—
244C3×D12—64no—
245C3×D12—62no—
246C3×D12—62no—
247C3×D12—64no—
248C3×D12C22×D312yescomplemented
249C3×D12C23×C312yescomplemented
250C3×C4×D3—28no—
251C3×C4×D3—24no—
252C3×C4×D3—24no—
253C3×Dic6—22no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6—22no—
257C3×Dic6C22×D312yescomplemented
258C3×Dic6C23×C312yescomplemented
259C32×C8—34no—
260C3×C3⋊C8—24no—
261C3×C3⋊C8C22×D314yescomplemented
262C3×C3⋊C8C23×C314yescomplemented
263C2×AGL(1,ℤ/8)—91noSylow
264C2×C33—22no—
265C2×C33AGL(1,ℤ/8)12yescomplemented
266C2×C33C22×D411yescharacteristic
267C3×C3⋊D3—44no—
268C32×D3—42no—
269C24×C3—181no—
270C23×D3—62no—
271C23×D3—61no—
272C23×D3—61no—
273C3×#41—34no—
274C3×#41—34no—
275C3×#41—64no—
276C3×#41—64no—
277C3×#41—62no—
278C3×#41—62no—
279C2×C3×Q8—31no—
280C2×C3×Q8—31no—
281C2×C3×Q8—61no—
282C2×C3×D4—31no—
283C2×C3×D4—31no—
284C2×C3×D4—61no—
285C2×C3×D4—62no—
286C2×C3×D4—61no—
287C2×C3×D4—61no—
288C2×C3×D4—92no—
289C2×C3×D4—94no—
290C2×C3×D4—182no—
291C2×C3×D4—181no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—41no—
296C22×C3×C4—62no—
297C22×C3×C4—61no—
298C22×C3×C4—61no—
299C22×C3×C4D3211yescharacteristic
300C22×C3×C4C2×C3×D311yescharacteristic
301C22×C3×C4C2×C3×D311yescharacteristic
302C2×#67—21no—
303#235—22no—
304#235C2×C3×D314yescomplemented
305C2×D12—32no—
306C2×D12—34no—
307C2×D12—32no—
308C2×D12—34no—
309C2×D12—62no—
310C2×D12—64no—
311C2×D12—62no—
312C2×D12—64no—
313C2×D12—61no—
314C2×D12—62no—
315C2×D12—61no—
316C2×D12—62no—
317C2×D12C2×C3×D311yescharacteristic, complemented
318C2×C4×D3—21no—
319C2×Dic6C2×C3×D311yescharacteristic, complemented
320C3×SD16—98no—
321C3×D8—98no—
322C3×M16—34no—
323C3×M16—34no—
324C3×M16—64no—
325C2×C3×C8—32no—
326C2×C3×C8—32no—
327C2×C3×C8—62no—
328#215—38no—
329#213—38no—
330#208C2×C3×D314yescomplemented
331C2×C3⋊C8C2×C3×D312yescomplemented
332D24—38no—
333#204—38no—
334C22×C32—22no—
335C22×C32—24no—
336C22×C32—22no—
337C22×C32—22no—
338C22×C32—22no—
339C22×C32—21no—
340C22×C32—21no—
341C22×C32—22no—
342C22×C32—21no—
343C22×C32—22no—
344C22×C32—41no—
345C22×C32—42no—
346C22×C32—42no—
347C22×C32—42no—
348C22×C32—44no—
349C22×C32—62no—
350C22×C32—122no—
351C22×C32C2×D1212yes—
352C22×C32C2×D1211yescharacteristic
353C22×C32C2×#6712yes—
354C22×C32C2×#6711yescharacteristic
355C22×C32C2×C3×D412yes—
356C22×C32C2×C3×D411yescharacteristic
357C2×C3⋊D3—24no—
358C2×C3⋊D3—48no—
359C2×C3⋊D3—44no—
360C2×C3×D3—24no—
361C2×C3×D3—22no—
362C2×C3×D3—22no—
363C2×C3×D3—44no—
364C2×C3×D3—42no—
365C2×C3×D3—42no—
366C2×C3×D3—68no—
367C2×C3×D3—64no—
368C2×C3×D3—64no—
369C2×C3×D3—1216no—
370C2×C3×D3—128no—
371C2×C3×D3—128no—
372C2×C3×D3—128no—
373C2×C3×D3—124no—
374C2×C3×D3—124no—
375C32×C4—21no—
376C32×C4—21no—
377C32×C4—21no—
378C32×C4—22no—
379C32×C4—21no—
380C32×C4—22no—
381C32×C4—21no—
382C32×C4—21no—
383C32×C4—22no—
384C32×C4—42no—
385C32×C4—41no—
386C32×C4—41no—
387C32×C4—62no—
388C32×C4C2×D1212yes—
389C32×C4C2×D1211yescharacteristic
390C32×C4C2×#6711yescharacteristic
391C32×C4C2×#6712yes—
392C32×C4C2×C3×D411yescharacteristic
393C32×C4C2×C3×D412yes—
394C32×C4C23×D311yescharacteristic
395C32×C4C23×D311yescharacteristic
396C32×C4C24×C311yescharacteristic
397C3×Dic3—24no—
398C3×Dic3—22no—
399C3×Dic3—22no—
400C2×#41—31no—
401C22×D4—91no—
402AGL(1,ℤ/8)—98no—
403C2×SD16—92no—
404C2×D8—92no—
405C2×M16—31no—
406C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—41no—
411C23×C3—62no—
412C23×C3—61no—
413C23×C3—61no—
414C23×C3—184no—
415C23×C3—182no—
416C23×C3—364no—
417C23×C3#62611yescharacteristic
418C23×C3C3×D1211yescharacteristic
419C23×C3C3×#6711yescharacteristic
420C22×D3—21no—
421C22×D3—64no—
422C22×D3—68no—
423C22×D3—64no—
424C22×D3—62no—
425C22×D3—64no—
426C22×D3—62no—
427C22×D3—128no—
428C22×D3—124no—
429C22×D3—124no—
430C3×Q8—32no—
431C3×Q8—32no—
432C3×Q8—62no—
433C3×Q8—62no—
434C3×Q8—61no—
435C3×Q8—61no—
436C3×D4—32no—
437C3×D4—32no—
438C3×D4—62no—
439C3×D4—62no—
440C3×D4—68no—
441C3×D4—64no—
442C3×D4—64no—
443C3×D4—61no—
444C3×D4—61no—
445C3×D4—94no—
446C3×D4—184no—
447C3×D4—182no—
448C2×C3×C4—21no—
449C2×C3×C4—22no—
450C2×C3×C4—21no—
451C2×C3×C4—22no—
452C2×C3×C4—21no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—22no—
456C2×C3×C4—21no—
457C2×C3×C4—22no—
458C2×C3×C4—21no—
459C2×C3×C4—22no—
460C2×C3×C4—41no—
461C2×C3×C4—42no—
462C2×C3×C4—41no—
463C2×C3×C4—42no—
464C2×C3×C4—68no—
465C2×C3×C4—62no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—64no—
469C2×C3×C4—64no—
470C2×C3×C4#62612yes—
471C2×C3×C4#62611yescharacteristic
472C2×C3×C4C3×D1211yescharacteristic
473C2×C3×C4C3×D1212yes—
474C2×C3×C4C3×#6711yescharacteristic
475C2×C3×C4C3×#6712yes—
476C2×C3×C4C2×D3212yes—
477C2×C3×C4C2×D3211yescharacteristic
478C2×C3×C4C22×C3×D311yescharacteristic
479C2×C3×C4C22×C3×D312yes—
480C2×C3×C4C22×C3×D311yescharacteristic
481C2×C3×C4C22×C3×D312yes—
482#67—24no—
483C2×Dic3—21no—
484D12—21no—
485D12—34no—
486D12—34no—
487D12—64no—
488D12—64no—
489D12—68no—
490D12—64no—
491D12—62no—
492D12—62no—
493D12—64no—
494D12C22×C3×D312yescomplemented
495C4×D3—24no—
496Dic6—21no—
497Dic6C22×C3×D312yescomplemented
498C3×C8—34no—
499C3×C8—34no—
500C3×C8—64no—
501C3⋊C8C22×C3×D314yescomplemented
502C2×C32—22no—
503C2×C32—24no—
504C2×C32—22no—
505C2×C32—22no—
506C2×C32—22no—
507C2×C32—21no—
508C2×C32—22no—
509C2×C32—22no—
510C2×C32—21no—
511C2×C32—21no—
512C2×C32—42no—
513C2×C32—41no—
514C2×C32—42no—
515C2×C32—42no—
516C2×C32—44no—
517C2×C32—122no—
518C2×C32#90812yescomplemented
519C2×C32#94912yescomplemented
520C2×C32C3×AGL(1,ℤ/8)12yescomplemented
521C2×C32C22×D1211yescharacteristic
522C2×C32C22×#6711yescharacteristic
523C2×C32C22×C3×D411yescharacteristic
524C3⋊D3—44no—
525C3×D3—44no—
526C3×D3—42no—
527C3×D3—42no—
528C3×D3—128no—
529C3×D3—124no—
530C3×D3—124no—
531C24—181no—
532#41—34no—
533#41—62no—
534C2×Q8—31no—
535C2×D4—31no—
536C2×D4—61no—
537C2×D4—92no—
538C2×D4—94no—
539C2×D4—181no—
540C2×D4—182no—
541C22×C4—61no—
542C22×C4C3×D3211yescharacteristic
543SD16—98no—
544D8—98no—
545M16—34no—
546C2×C8—32no—
547C22×C3—24no—
548C22×C3—22no—
549C22×C3—22no—
550C22×C3—22no—
551C22×C3—21no—
552C22×C3—22no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—22no—
556C22×C3—22no—
557C22×C3—42no—
558C22×C3—42no—
559C22×C3—44no—
560C22×C3—42no—
561C22×C3—41no—
562C22×C3—64no—
563C22×C3—62no—
564C22×C3—62no—
565C22×C3—124no—
566C22×C3—122no—
567C22×C3—122no—
568C22×C3—184no—
569C22×C3—368no—
570C22×C3—364no—
571C22×C3C2×#62612yes—
572C22×C3C2×#62611yescharacteristic
573C22×C3C2×C3×D1212yes—
574C22×C3C2×C3×D1211yescharacteristic
575C22×C3C2×C3×#6712yes—
576C22×C3C2×C3×#6711yescharacteristic
577C2×D3—22no—
578C2×D3—42no—
579C2×D3—68no—
580C2×D3—64no—
581C2×D3—64no—
582C2×D3—1216no—
583C2×D3—128no—
584C2×D3—128no—
585C2×D3—128no—
586C2×D3—124no—
587C2×D3—124no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—22no—
592C3×C4—21no—
593C3×C4—22no—
594C3×C4—21no—
595C3×C4—22no—
596C3×C4—21no—
597C3×C4—41no—
598C3×C4—42no—
599C3×C4—41no—
600C3×C4—64no—
601C3×C4—62no—
602C3×C4—62no—
603C3×C4C2×#62612yes—
604C3×C4C2×#62611yescharacteristic
605C3×C4C2×C3×D1212yes—
606C3×C4C2×C3×D1211yescharacteristic
607C3×C4C2×C3×#6711yescharacteristic
608C3×C4C2×C3×#6712yes—
609C3×C4C22×D3211yescharacteristic
610C3×C4C23×C3×D311yescharacteristic
611C3×C4C23×C3×D311yescharacteristic
612Dic3—22no—
613C32—21no—
614C32—21no—
615C32—21no—
616C32—41no—
617C32C2×#90811yescharacteristic, complemented
618C32C2×#94911yescharacteristic, complemented
619C32C2×C3×AGL(1,ℤ/8)11yescharacteristic, complemented
620C23—61no—
621C23—184no—
622C23—182no—
623C23—364no—
624C23C3×#62611yescharacteristic
625Q8—32no—
626Q8—61no—
627D4—32no—
628D4—64no—
629D4—61no—
630D4—94no—
631D4—184no—
632D4—182no—
633C2×C4—61no—
634C2×C4—64no—
635C2×C4C3×#62611yescharacteristic
636C2×C4C3×#62612yes—
637C2×C4C2×C3×D3211yescharacteristic
638C2×C4C2×C3×D3212yes—
639C8—34no—
640C2×C3—24no—
641C2×C3—22no—
642C2×C3—22no—
643C2×C3—22no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—22no—
648C2×C3—22no—
649C2×C3—22no—
650C2×C3—42no—
651C2×C3—42no—
652C2×C3—44no—
653C2×C3—41no—
654C2×C3—42no—
655C2×C3—124no—
656C2×C3—122no—
657C2×C3—122no—
658C2×C3—364no—
659C2×C3#6382512yesdirect product factor
660C2×C3C3×#90812yescomplemented
661C2×C3C3×#94912yescomplemented
662C2×C3C22×#62611yescharacteristic
663C2×C3C22×C3×D1211yescharacteristic
664C2×C3C22×C3×#6711yescharacteristic
665D3—42no—
666D3—128no—
667D3—124no—
668D3—124no—
669C22—22no—
670C22—62no—
671C22—122no—
672C22—184no—
673C22—368no—
674C22—364no—
675C22C2×C3×#62612yes—
676C22C2×C3×#62611yescharacteristic
677C4—62no—
678C4C2×C3×#62612yes—
679C4C2×C3×#62611yescharacteristic
680C4C22×C3×D3211yescharacteristic
681C3—21no—
682C3—21no—
683C3—21no—
684C3—41no—
685C3C2×#6382511yescharacteristic, direct product factor
686C3C2×C3×#90811yescharacteristic, complemented
687C3C2×C3×#94911yescharacteristic, complemented
688C2—22no—
689C2—122no—
690C2—364no—
691C2C3×#6382512yesdirect product factor
692C2C22×C3×#62611yescharacteristic
subgroupG/H
centerC22×C3C2×#626
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C2×D4
hypercenterC22×C3×C4D32
hypocenterC32C2×C3×AGL(1,ℤ/8)
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4⋊(C3⋊D3)C2semidirect
2. C2×C32×#235C2semidirect
3. C2×C32×#208C2semidirect
4. C2×C3×#3717C2semidirect
5. C3×#63825C2direct (N × H)
6. C2×C3×#3714C2semidirect
9. C2×#63825C3direct (N × H)
15. C2×C3×C4⋊(C3⋊D3)C22semidirect
18. C32×#235C22semidirect
19. C2×C32×D12C22semidirect
21. C2×C32×Dic6C22semidirect
22. C32×#208C22semidirect
23. C2×C32×C3⋊C8C22semidirect
24. C3×#3717C22semidirect
25. C3×#3714C22semidirect
27. C22×C4⋊(C3⋊D3)C2×C3semidirect
29. C2×C3×#235D3semidirect
30. C2×C3×#235C2×C3semidirect
39. C2×C3×#208D3semidirect
40. C2×C3×#208C2×C3semidirect
44. C2×#3717C2×C3semidirect
45. #63825C2×C3direct (N × H)
46. C2×#3714C2×C3semidirect
62. C32×D12C23semidirect
65. C32×Dic6C23semidirect
66. C32×C3⋊C8C23semidirect
90. C2×C4⋊(C3⋊D3)C22×C3semidirect
98. C3×#235C2×D3semidirect
99. C3×#235C22×C3semidirect
113. C2×C3×D12C2×D3semidirect
114. C2×C3×D12C22×C3semidirect
119. C2×C3×Dic6C2×D3semidirect
120. C2×C3×Dic6C22×C3semidirect
126. C3×#208C2×D3semidirect
127. C3×#208C22×C3semidirect
129. C2×C3×C3⋊C8C2×D3semidirect
130. C2×C3×C3⋊C8C22×C3semidirect
133. #3717C22×C3semidirect
134. #3714C22×C3semidirect
151. C2×#235C3×D3semidirect
164. C2×#208C3×D3semidirect
248. C3×D12C22×D3semidirect
249. C3×D12C23×C3semidirect
257. C3×Dic6C22×D3semidirect
258. C3×Dic6C23×C3semidirect
261. C3×C3⋊C8C22×D3semidirect
262. C3×C3⋊C8C23×C3semidirect
265. C2×C33AGL(1,ℤ/8)semidirect
304. #235C2×C3×D3semidirect
317. C2×D12C2×C3×D3semidirect
319. C2×Dic6C2×C3×D3semidirect
330. #208C2×C3×D3semidirect
331. C2×C3⋊C8C2×C3×D3semidirect
406. C33C2×AGL(1,ℤ/8)semidirect
494. D12C22×C3×D3semidirect
497. Dic6C22×C3×D3semidirect
501. C3⋊C8C22×C3×D3semidirect
518. C2×C32#908semidirect
519. C2×C32#949semidirect
520. C2×C32C3×AGL(1,ℤ/8)semidirect
617. C32C2×#908semidirect
618. C32C2×#949semidirect
619. C32C2×C3×AGL(1,ℤ/8)semidirect
659. C2×C3#63825direct (N × H)
660. C2×C3C3×#908semidirect
661. C2×C3C3×#949semidirect
685. C3C2×#63825direct (N × H)
686. C3C2×C3×#908semidirect
687. C3C2×C3×#949semidirect
691. C2C3×#63825direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊(C3⋊D3)2
C2×C32×#2352
C2×C32×#2082
C2×C3×#37172
C3×#638252
C2×C3×#37142
C2×C3×#9493
C2×C3×#9083
C2×#638253