Finite Group Databasebeta

← C2×C3×#5032 #11865246

Subgroups — C2×C3×#5032 #11865246

Order 1152.

2367 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic, complemented
2C2×C32×#120C211yesmaximal, characteristic, complemented
3C2×C3×#953C212yesmaximal, complemented
4C2×C3×#834C211yesmaximal, characteristic, complemented
5C3×#5032C218yesmaximal, direct product factor
6C2×C3×#806C212yesmaximal, complemented
7C2×C3×B(4,𝔽2)—31nomaximal
8C2×#5032C311yesmaximal, characteristic, direct product factor
9C25×C32C2211yescharacteristic, complemented
10C22×C32×D4—21no—
11C22×C32×D4C2211yescharacteristic
12C22×C3×#67—21no—
13C22×C3×#67—22no—
14C22×C3×#67C2212yes—
15C3×#1004—22no—
16C3×#1004—24no—
17C3×#1004C2214yescomplemented
18C2×C3×#237—22no—
19C2×C3×D3×D4—22no—
20C2×C3×#235—21no—
21C32×#120—22no—
22C32×#120C2214yescomplemented
23C2×C32×C22⋊C4—21no—
24C2×C32×C22⋊C4C2211yescharacteristic, complemented
25C3×#953—24no—
26C3×#953C2218yescomplemented
27C2×C3×#217—22no—
28C2×C3×#217C2212yescomplemented
29C3×#834C2214yescomplemented
30C3×#806C2218yescomplemented
31C2×C3×H(5,𝔽2)—31no—
32C2×#1004C2×C311yescharacteristic, complemented
33C2×C3×#120—21no—
34C2×C3×#120—32no—
35C2×C3×#120D311yescharacteristic, complemented
36C2×C3×#120C2×C311yescharacteristic, complemented
37C2×#953C2×C312yescomplemented
38C3×B(4,𝔽2)—38no—
39C2×C3×#99—31no—
40C2×C3×#99—32no—
41C2×#834C2×C311yescharacteristic, complemented
42#5032C2×C318yesdirect product factor
43C2×#806C2×C312yescomplemented
44C24×C32—21no—
45C24×C32—22no—
46C24×C32—21no—
47C24×C32—22no—
48C24×C32—44no—
49C24×C32D411yescharacteristic, complemented
50C24×C32C2311yescharacteristic
51C24×C32C2312yescomplemented
52C23×C3×D3—21no—
53C23×C3×D3D412yescomplemented
54C2×C32×D4—22no—
55C2×C32×D4—22no—
56C2×C32×D4—24no—
57C2×C32×D4—44no—
58C2×C32×D4D412yescomplemented
59C2×C32×D4C2312yes—
60C22×C32×C4—21no—
61C22×C32×C4D411yescharacteristic, complemented
62C2×C3×#67—22no—
63C2×C3×#67—24no—
64C2×C3×#67—22no—
65C2×C3×#67—22no—
66C2×C3×#67—22no—
67C2×C3×#67—22no—
68C2×C3×#67—24no—
69C2×C3×#67—28no—
70C2×C3×#67—48no—
71C2×C3×#67D414yescomplemented
72C2×C3×#67C2314yes—
73C22×C3×Dic3—21no—
74C22×C3×Dic3—22no—
75C22×C3×Dic3D412yescomplemented
76C3×#237—28no—
77C3×#237—28no—
78C3×D3×D4—28no—
79C3×D3×D4—28no—
80C3×#235—24no—
81C3×#235—24no—
82C2×C3×D12—21no—
83C2×C3×C4×D3—22no—
84C2×C3×Dic6—21no—
85C32×C22⋊C4—21no—
86C32×C22⋊C4—24no—
87C32×C22⋊C4C2312yescomplemented
88C3×#217—22no—
89C3×#217—28no—
90C3×#217C2314yescomplemented
91C2×B(4,𝔽2)—31noSylow
92C25×C3—21no—
93C25×C3C2×D311yescharacteristic, complemented
94C25×C3C22×C311yescharacteristic, complemented
95C3×H(5,𝔽2)—34no—
96C3×H(5,𝔽2)—64no—
97C3×H(5,𝔽2)—62no—
98C2×C3×#41—62no—
99C2×C3×#41—61no—
100C22×C3×D4—22no—
101C22×C3×D4—21no—
102C22×C3×D4—21no—
103C22×C3×D4—21no—
104C22×C3×D4—32no—
105C22×C3×D4—62no—
106C22×C3×D4—61no—
107C22×C3×D4—62no—
108C22×C3×D4C2×D311yescharacteristic
109C22×C3×D4C22×C311yescharacteristic
110C22×#67—21no—
111C22×#67—22no—
112C22×#67C22×C312yes—
113#1004—22no—
114#1004—24no—
115#1004C22×C314yescomplemented
116C2×#237—22no—
117C2×D3×D4—22no—
118C2×#235—21no—
119C3×#120—24no—
120C3×#120—22no—
121C3×#120—22no—
122C3×#120—24no—
123C3×#120—38no—
124C3×#120—64no—
125C3×#120C2×D314yescomplemented
126C3×#120C22×C314yescomplemented
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—21no—
129C2×C3×C22⋊C4—21no—
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—32no—
132C2×C3×C22⋊C4—62no—
133C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
134C2×C3×C22⋊C4C22×C311yescharacteristic, complemented
135#953—24no—
136#953C22×C318yescomplemented
137C2×#217—22no—
138C2×#217C22×C312yescomplemented
139C3×#99—34no—
140C3×#99—38no—
141#834C22×C314yescomplemented
142#806C22×C318yescomplemented
143C23×C32—24no—
144C23×C32—22no—
145C23×C32—28no—
146C23×C32—21no—
147C23×C32—24no—
148C23×C32—21no—
149C23×C32—42no—
150C23×C32—44no—
151C23×C32—42no—
152C23×C32—44no—
153C23×C32—44no—
154C23×C32—48no—
155C23×C32—42no—
156C23×C32—42no—
157C23×C32—41no—
158C23×C32—41no—
159C23×C32C2×D412yes—
160C23×C32C2×D412yes—
161C23×C32C2×D411yescharacteristic
162C23×C32C2×D411yescharacteristic
163C23×C32C2×D412yescomplemented
164C23×C32C2411yescharacteristic
165C22×C3×D3—22no—
166C22×C3×D3—24no—
167C22×C3×D3—22no—
168C22×C3×D3—44no—
169C22×C3×D3—82no—
170C22×C3×D3C2×D414yescomplemented
171C32×D4—24no—
172C32×D4—24no—
173C32×D4—48no—
174C2×C32×C4—22no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—42no—
178C2×C32×C4C2×D412yescomplemented
179C3×#67—28no—
180C3×#67—24no—
181C3×#67—24no—
182C3×#67—24no—
183C3×#67—24no—
184C3×#67—416no—
185C2×C3×Dic3—24no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—24no—
189C2×C3×Dic3—44no—
190C2×C3×Dic3C2×D414yescomplemented
191C3×D12—24no—
192C3×C4×D3—28no—
193C3×Dic6—24no—
194C2×H(5,𝔽2)—31no—
195C2×#120—32no—
196C2×#120C3×D311yescharacteristic, complemented
197B(4,𝔽2)—38no—
198C2×#99—31no—
199C2×#99—32no—
200C24×C3—22no—
201C24×C3—22no—
202C24×C3—21no—
203C24×C3—22no—
204C24×C3—21no—
205C24×C3—22no—
206C24×C3—22no—
207C24×C3—21no—
208C24×C3—22no—
209C24×C3—21no—
210C24×C3—21no—
211C24×C3—21no—
212C24×C3—22no—
213C24×C3—32no—
214C24×C3—42no—
215C24×C3—42no—
216C24×C3—44no—
217C24×C3—44no—
218C24×C3—48no—
219C24×C3—61no—
220C24×C3#6711yescharacteristic, complemented
221C24×C3C3×D411yescharacteristic, complemented
222C24×C3C22×D311yescharacteristic
223C24×C3C22×D312yescomplemented
224C24×C3C23×C311yescharacteristic
225C24×C3C23×C312yescomplemented
226C23×D3—21no—
227C23×D3C3×D412yescomplemented
228C3×#41—64no—
229C3×#41—68no—
230C3×#41—68no—
231C3×#41—64no—
232C2×C3×Q8—61no—
233C2×C3×D4—22no—
234C2×C3×D4—22no—
235C2×C3×D4—22no—
236C2×C3×D4—22no—
237C2×C3×D4—28no—
238C2×C3×D4—24no—
239C2×C3×D4—24no—
240C2×C3×D4—22no—
241C2×C3×D4—22no—
242C2×C3×D4—34no—
243C2×C3×D4—34no—
244C2×C3×D4—42no—
245C2×C3×D4—42no—
246C2×C3×D4—44no—
247C2×C3×D4—44no—
248C2×C3×D4—48no—
249C2×C3×D4—61no—
250C2×C3×D4—68no—
251C2×C3×D4—68no—
252C2×C3×D4—62no—
253C2×C3×D4—64no—
254C2×C3×D4—62no—
255C2×C3×D4—62no—
256C2×C3×D4—62no—
257C2×C3×D4—62no—
258C2×C3×D4—64no—
259C2×C3×D4—68no—
260C2×C3×D4—128no—
261C2×C3×D4#6712yescomplemented
262C2×C3×D4C3×D412yescomplemented
263C2×C3×D4C22×D312yes—
264C2×C3×D4C23×C312yes—
265C22×C3×C4—22no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—32no—
270C22×C3×C4—62no—
271C22×C3×C4—61no—
272C22×C3×C4—62no—
273C22×C3×C4#6711yescharacteristic, complemented
274C22×C3×C4C3×D411yescharacteristic, complemented
275C2×#67—22no—
276C2×#67—24no—
277C2×#67—22no—
278C2×#67—22no—
279C2×#67—22no—
280C2×#67—22no—
281C2×#67—24no—
282C2×#67—28no—
283C2×#67—48no—
284C2×#67C3×D414yescomplemented
285C2×#67C23×C314yes—
286C22×Dic3—21no—
287C22×Dic3—22no—
288C22×Dic3C3×D412yescomplemented
289#237—28no—
290#237—28no—
291D3×D4—28no—
292D3×D4—28no—
293#235—24no—
294#235—24no—
295C2×D12—21no—
296C2×C4×D3—22no—
297C2×Dic6—21no—
298C3×C22⋊C4—22no—
299C3×C22⋊C4—28no—
300C3×C22⋊C4—21no—
301C3×C22⋊C4—21no—
302C3×C22⋊C4—24no—
303C3×C22⋊C4—24no—
304C3×C22⋊C4—22no—
305C3×C22⋊C4—34no—
306C3×C22⋊C4—68no—
307C3×C22⋊C4—62no—
308C3×C22⋊C4C22×D312yescomplemented
309C3×C22⋊C4C23×C312yescomplemented
310#217—22no—
311#217—28no—
312#217C23×C314yescomplemented
313C22×C32—22no—
314C22×C32—24no—
315C22×C32—24no—
316C22×C32—28no—
317C22×C32—22no—
318C22×C32—42no—
319C22×C32—41no—
320C22×C32—41no—
321C22×C32—42no—
322C22×C32—42no—
323C22×C32—44no—
324C22×C32—44no—
325C22×C32—48no—
326C22×C32—42no—
327C22×C32—44no—
328C22×C32—42no—
329C22×C32—81no—
330C22×C32#12012yes—
331C22×C32#12011yescharacteristic
332C22×C32#12011yescharacteristic
333C22×C32C22×D412yes—
334C22×C32C22×D411yescharacteristic
335C2×C3×D3—24no—
336C2×C3×D3—44no—
337C2×C3×D3—44no—
338C2×C3×D3—82no—
339C2×C3×D3—84no—
340C32×C4—22no—
341C32×C4—42no—
342C3×Dic3—24no—
343C3×Dic3—44no—
344C25C2×C3×D311yescharacteristic, complemented
345H(5,𝔽2)—34no—
346H(5,𝔽2)—64no—
347H(5,𝔽2)—62no—
348C2×#41—62no—
349C2×#41—61no—
350C22×D4—21no—
351C22×D4—32no—
352C22×D4—62no—
353C22×D4—61no—
354C22×D4—62no—
355C22×D4C2×C3×D311yescharacteristic
356#120—22no—
357#120—38no—
358#120—64no—
359#120C2×C3×D314yescomplemented
360C2×C22⋊C4—21no—
361C2×C22⋊C4—32no—
362C2×C22⋊C4—62no—
363C2×C22⋊C4C2×C3×D311yescharacteristic, complemented
364#99—34no—
365#99—38no—
366C23×C3—24no—
367C23×C3—28no—
368C23×C3—28no—
369C23×C3—24no—
370C23×C3—24no—
371C23×C3—28no—
372C23×C3—21no—
373C23×C3—21no—
374C23×C3—24no—
375C23×C3—22no—
376C23×C3—24no—
377C23×C3—22no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—22no—
386C23×C3—34no—
387C23×C3—44no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3—48no—
391C23×C3—42no—
392C23×C3—44no—
393C23×C3—42no—
394C23×C3—44no—
395C23×C3—44no—
396C23×C3—48no—
397C23×C3—44no—
398C23×C3—42no—
399C23×C3—44no—
400C23×C3—44no—
401C23×C3—42no—
402C23×C3—48no—
403C23×C3—44no—
404C23×C3—44no—
405C23×C3—48no—
406C23×C3—48no—
407C23×C3—42no—
408C23×C3—42no—
409C23×C3—44no—
410C23×C3—42no—
411C23×C3—42no—
412C23×C3—44no—
413C23×C3—48no—
414C23×C3—416no—
415C23×C3—41no—
416C23×C3—42no—
417C23×C3—41no—
418C23×C3—42no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—64no—
422C23×C3—62no—
423C23×C3—62no—
424C23×C3—124no—
425C23×C3—242no—
426C23×C3D3×D412yes—
427C23×C3D3×D412yes—
428C23×C3C2×#6711yescharacteristic
429C23×C3C2×#6711yescharacteristic
430C23×C3C2×#6712yescomplemented
431C23×C3C2×C3×D412yes—
432C23×C3C2×C3×D412yes—
433C23×C3C2×C3×D411yescharacteristic
434C23×C3C2×C3×D411yescharacteristic
435C23×C3C2×C3×D412yescomplemented
436C23×C3C23×D311yescharacteristic
437C23×C3C24×C311yescharacteristic
438C22×D3—22no—
439C22×D3—24no—
440C22×D3—22no—
441C22×D3—44no—
442C22×D3—82no—
443C22×D3C2×C3×D414yescomplemented
444C3×Q8—64no—
445C3×D4—24no—
446C3×D4—24no—
447C3×D4—24no—
448C3×D4—24no—
449C3×D4—44no—
450C3×D4—44no—
451C3×D4—48no—
452C3×D4—48no—
453C3×D4—416no—
454C3×D4—64no—
455C3×D4—68no—
456C3×D4—64no—
457C3×D4—64no—
458C3×D4—64no—
459C3×D4—64no—
460C3×D4—1216no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—24no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—34no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—44no—
473C2×C3×C4—42no—
474C2×C3×C4—42no—
475C2×C3×C4—68no—
476C2×C3×C4—64no—
477C2×C3×C4—62no—
478C2×C3×C4—62no—
479C2×C3×C4—64no—
480C2×C3×C4—124no—
481C2×C3×C4C2×#6712yescomplemented
482C2×C3×C4C2×C3×D412yescomplemented
483#67—28no—
484#67—24no—
485#67—24no—
486#67—24no—
487#67—24no—
488#67—416no—
489C2×Dic3—24no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—24no—
493C2×Dic3—44no—
494C2×Dic3C2×C3×D414yescomplemented
495D12—24no—
496C4×D3—28no—
497Dic6—24no—
498C2×C32—21no—
499C2×C32—21no—
500C2×C32—22no—
501C2×C32—22no—
502C2×C32—44no—
503C2×C32—42no—
504C2×C32B(4,𝔽2)12yescomplemented
505C2×C32C2×#12011yescharacteristic
506C3×D3—44no—
507C24—22no—
508C24—21no—
509C24—22no—
510C24—21no—
511C24—32no—
512C24—44no—
513C24—61no—
514C24C3×#6711yescharacteristic, complemented
515C24C22×C3×D311yescharacteristic
516C24C22×C3×D312yescomplemented
517#41—64no—
518#41—68no—
519#41—68no—
520#41—64no—
521C2×Q8—61no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—24no—
525C2×D4—34no—
526C2×D4—34no—
527C2×D4—44no—
528C2×D4—61no—
529C2×D4—68no—
530C2×D4—68no—
531C2×D4—62no—
532C2×D4—64no—
533C2×D4—62no—
534C2×D4—62no—
535C2×D4—62no—
536C2×D4—62no—
537C2×D4—64no—
538C2×D4—68no—
539C2×D4—128no—
540C2×D4C3×#6712yescomplemented
541C2×D4C22×C3×D312yes—
542C22×C4—21no—
543C22×C4—32no—
544C22×C4—62no—
545C22×C4—61no—
546C22×C4—62no—
547C22×C4C3×#6711yescharacteristic, complemented
548C22⋊C4—21no—
549C22⋊C4—24no—
550C22⋊C4—34no—
551C22⋊C4—68no—
552C22⋊C4—62no—
553C22⋊C4C22×C3×D312yescomplemented
554C22×C3—24no—
555C22×C3—22no—
556C22×C3—24no—
557C22×C3—24no—
558C22×C3—22no—
559C22×C3—28no—
560C22×C3—28no—
561C22×C3—24no—
562C22×C3—24no—
563C22×C3—28no—
564C22×C3—22no—
565C22×C3—22no—
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—21no—
571C22×C3—44no—
572C22×C3—42no—
573C22×C3—48no—
574C22×C3—42no—
575C22×C3—41no—
576C22×C3—42no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—42no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—44no—
584C22×C3—42no—
585C22×C3—44no—
586C22×C3—48no—
587C22×C3—44no—
588C22×C3—42no—
589C22×C3—48no—
590C22×C3—44no—
591C22×C3—42no—
592C22×C3—44no—
593C22×C3—44no—
594C22×C3—48no—
595C22×C3—44no—
596C22×C3—48no—
597C22×C3—44no—
598C22×C3—48no—
599C22×C3—416no—
600C22×C3—42no—
601C22×C3—44no—
602C22×C3—42no—
603C22×C3—42no—
604C22×C3—44no—
605C22×C3—42no—
606C22×C3—64no—
607C22×C3—82no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—82no—
611C22×C3—124no—
612C22×C3—124no—
613C22×C3—242no—
614C22×C3—244no—
615C22×C3#93711yescharacteristic
616C22×C3#93712yes—
617C22×C3#93711yescharacteristic
618C22×C3C3×#12012yes—
619C22×C3C3×#12011yescharacteristic
620C22×C3C3×#12011yescharacteristic
621C22×C3C2×D3×D412yes—
622C22×C3C22×#6711yescharacteristic
623C22×C3C22×C3×D412yes—
624C22×C3C22×C3×D411yescharacteristic
625C2×D3—24no—
626C2×D3—44no—
627C2×D3—44no—
628C2×D3—82no—
629C2×D3—84no—
630C3×C4—22no—
631C3×C4—22no—
632C3×C4—42no—
633C3×C4—44no—
634C3×C4—42no—
635C3×C4—42no—
636C3×C4—64no—
637C3×C4—124no—
638Dic3—24no—
639Dic3—44no—
640C32C2×B(4,𝔽2)11yescharacteristic, complemented, Sylow
641C23—24no—
642C23—28no—
643C23—21no—
644C23—24no—
645C23—22no—
646C23—21no—
647C23—34no—
648C23—42no—
649C23—44no—
650C23—42no—
651C23—44no—
652C23—44no—
653C23—48no—
654C23—42no—
655C23—41no—
656C23—42no—
657C23—41no—
658C23—64no—
659C23—62no—
660C23—62no—
661C23—124no—
662C23—242no—
663C23C3×D3×D412yes—
664C23C3×D3×D412yes—
665C23C2×C3×#6711yescharacteristic
666C23C2×C3×#6711yescharacteristic
667C23C2×C3×#6712yescomplemented
668C23C23×C3×D311yescharacteristic
669Q8—64no—
670D4—24no—
671D4—24no—
672D4—48no—
673D4—64no—
674D4—68no—
675D4—64no—
676D4—64no—
677D4—64no—
678D4—64no—
679D4—1216no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—34no—
684C2×C4—42no—
685C2×C4—68no—
686C2×C4—64no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—64no—
690C2×C4—124no—
691C2×C4C2×C3×#6712yescomplemented
692C2×C3—22no—
693C2×C3—22no—
694C2×C3—22no—
695C2×C3—21no—
696C2×C3—22no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—22no—
700C2×C3—21no—
701C2×C3—22no—
702C2×C3—21no—
703C2×C3—22no—
704C2×C3—42no—
705C2×C3—42no—
706C2×C3—48no—
707C2×C3—42no—
708C2×C3—44no—
709C2×C3—44no—
710C2×C3—42no—
711C2×C3—82no—
712C2×C3—124no—
713C2×C3#503212yesdirect product factor
714C2×C3C3×B(4,𝔽2)12yescomplemented
715C2×C3C2×#93711yescharacteristic
716C2×C3C2×C3×#12011yescharacteristic
717D3—44no—
718C22—22no—
719C22—24no—
720C22—24no—
721C22—28no—
722C22—22no—
723C22—41no—
724C22—42no—
725C22—41no—
726C22—42no—
727C22—42no—
728C22—44no—
729C22—44no—
730C22—48no—
731C22—42no—
732C22—44no—
733C22—42no—
734C22—64no—
735C22—81no—
736C22—124no—
737C22—124no—
738C22—242no—
739C22—244no—
740C22C3×#93711yescharacteristic
741C22C3×#93712yes—
742C22C3×#93711yescharacteristic
743C22C2×C3×D3×D412yes—
744C22C22×C3×#6711yescharacteristic
745C4—22no—
746C4—42no—
747C4—64no—
748C4—124no—
749C3—21no—
750C3C2×#503211yescharacteristic, direct product factor
751C3C2×C3×B(4,𝔽2)11yescharacteristic, complemented
752C2—21no—
753C2—22no—
754C2—21no—
755C2—22no—
756C2—44no—
757C2—42no—
758C2—124no—
759C2C3×#503212yesdirect product factor
760C2C2×C3×#93711yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×#120C2
socleC22×C32#120
hypercenterC2×C3×#120D3
hypocenterC3C2×C3×B(4,𝔽2)
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C2×C3×#120

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1004C2semidirect
2. C2×C32×#120C2semidirect
3. C2×C3×#953C2semidirect
4. C2×C3×#834C2semidirect
5. C3×#5032C2direct (N × H)
6. C2×C3×#806C2semidirect
8. C2×#5032C3direct (N × H)
9. C25×C32C22semidirect
17. C3×#1004C22semidirect
22. C32×#120C22semidirect
24. C2×C32×C22⋊C4C22semidirect
26. C3×#953C22semidirect
28. C2×C3×#217C22semidirect
29. C3×#834C22semidirect
30. C3×#806C22semidirect
32. C2×#1004C2×C3semidirect
35. C2×C3×#120D3semidirect
36. C2×C3×#120C2×C3semidirect
37. C2×#953C2×C3semidirect
41. C2×#834C2×C3semidirect
42. #5032C2×C3direct (N × H)
43. C2×#806C2×C3semidirect
49. C24×C32D4semidirect
51. C24×C32C23semidirect
53. C23×C3×D3D4semidirect
58. C2×C32×D4D4semidirect
61. C22×C32×C4D4semidirect
71. C2×C3×#67D4semidirect
75. C22×C3×Dic3D4semidirect
87. C32×C22⋊C4C23semidirect
90. C3×#217C23semidirect
93. C25×C3C2×D3semidirect
94. C25×C3C22×C3semidirect
115. #1004C22×C3semidirect
125. C3×#120C2×D3semidirect
126. C3×#120C22×C3semidirect
133. C2×C3×C22⋊C4C2×D3semidirect
134. C2×C3×C22⋊C4C22×C3semidirect
136. #953C22×C3semidirect
138. C2×#217C22×C3semidirect
141. #834C22×C3semidirect
142. #806C22×C3semidirect
163. C23×C32C2×D4semidirect
170. C22×C3×D3C2×D4semidirect
178. C2×C32×C4C2×D4semidirect
190. C2×C3×Dic3C2×D4semidirect
196. C2×#120C3×D3semidirect
220. C24×C3#67semidirect
221. C24×C3C3×D4semidirect
223. C24×C3C22×D3semidirect
225. C24×C3C23×C3semidirect
227. C23×D3C3×D4semidirect
261. C2×C3×D4#67semidirect
262. C2×C3×D4C3×D4semidirect
273. C22×C3×C4#67semidirect
274. C22×C3×C4C3×D4semidirect
284. C2×#67C3×D4semidirect
288. C22×Dic3C3×D4semidirect
308. C3×C22⋊C4C22×D3semidirect
309. C3×C22⋊C4C23×C3semidirect
312. #217C23×C3semidirect
344. C25C2×C3×D3semidirect
359. #120C2×C3×D3semidirect
363. C2×C22⋊C4C2×C3×D3semidirect
430. C23×C3C2×#67semidirect
435. C23×C3C2×C3×D4semidirect
443. C22×D3C2×C3×D4semidirect
481. C2×C3×C4C2×#67semidirect
482. C2×C3×C4C2×C3×D4semidirect
494. C2×Dic3C2×C3×D4semidirect
504. C2×C32B(4,𝔽2)semidirect
514. C24C3×#67semidirect
516. C24C22×C3×D3semidirect
540. C2×D4C3×#67semidirect
547. C22×C4C3×#67semidirect
553. C22⋊C4C22×C3×D3semidirect
640. C32C2×B(4,𝔽2)semidirect
667. C23C2×C3×#67semidirect
691. C2×C4C2×C3×#67semidirect
713. C2×C3#5032direct (N × H)
714. C2×C3C3×B(4,𝔽2)semidirect
750. C3C2×#5032direct (N × H)
751. C3C2×C3×B(4,𝔽2)semidirect
759. C2C3×#5032direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C2×C32×#1202
C2×C3×#9532
C2×C3×#8342
C3×#50322
C2×C3×#8062
C2×C3×B(4,𝔽2)3
C2×#50323