Finite Group Databasebeta

← C3×C4×#951 #11860362

Subgroups — C3×C4×#951 #11860362

Order 1152.

1123 conjugacy classes of subgroups.

The subgroup lattice has 659 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×#41C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic
3C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
4C3×#5232C211yesmaximal, characteristic
5C3×#5030C212yesmaximal, complemented
6C3×C4×#216C212yesmaximal, complemented
7C3×#5018C212yesmaximal, complemented
8C3×C4×#214C212yesmaximal, complemented
9C3×#5004C211yesmaximal, characteristic, complemented
10C3×#4995C211yesmaximal, characteristic, complemented
11C3×C4×#208C211yesmaximal, characteristic, complemented
12C3×C4×#137—31nomaximal
13C4×#951C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17C32×C4×Q8C2211yescharacteristic
18C32×C4×D4—21no—
19C32×C4×D4—21no—
20C32×C4×D4C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C32×#117—21no—
23C32×#117C2211yescharacteristic
24C2×C32×C42—21no—
25C2×C32×C42C2211yescharacteristic
26C3×#951C418yesdirect product factor
27C2×C3×#216C2212yes—
28C2×C3×#214C2212yes—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4—21no—
31C2×C3×C4×Dic3—21no—
32C2×C3×#208C2211yescharacteristic
33C2×C3×#208C2211yescharacteristic
34C3×C4×Dic6—21no—
35C3×C4×Dic6—21no—
36C3×C4×Dic6C2212yes—
37C3×C4×Dic6C2212yes—
38C3×#835C2212yes—
39C3×#832C2212yes—
40C3×#810C2212yes—
41C3×#810C2212yes—
42C3×#808C2212yes—
43C3×#807C2212yes—
44C3×#803C2212yes—
45C3×C4×C3⋊C8C2212yes—
46C2×C3×#137—31no—
47C3×C4×#41—21no—
48C3×C4×#41D311yescharacteristic
49C3×C4×#41C2×C311yescharacteristic
50C2×C3×C4×Q8—31no—
51C2×#951C2×C311yescharacteristic
52C2×C4×Dic6C2×C311yescharacteristic, complemented
53C3×#441—32no—
54C3×#440—32no—
55C3×C4×Q16—32no—
56C3×C4×SD16—32no—
57C3×#428—31no—
58C3×#419—31no—
59C3×#417—31no—
60C3×C4×M16—31no—
61#5232C2×C311yescharacteristic
62#5030C2×C312yescomplemented
63C4×#216C2×C312yescomplemented
64#5018C2×C312yescomplemented
65C4×#214C2×C312yescomplemented
66#5004C2×C311yescharacteristic, complemented
67#4995C2×C311yescharacteristic, complemented
68C4×#208C2×C311yescharacteristic, complemented
69C32×#41—22no—
70C32×#41C2×C414yes—
71C2×C32×Q8C2311yescharacteristic
72C2×C32×D4—21no—
73C2×C32×D4C2311yescharacteristic
74C22×C32×C4—21no—
75C22×C32×C4—21no—
76C22×C32×C4—21no—
77C22×C32×C4D411yescharacteristic
78C22×C32×C4D411yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C22×C3×Dic3—21no—
81C22×C3×Dic3—21no—
82C2×C3×Dic6—21no—
83C2×C3×Dic6—22no—
84C2×C3×Dic6C2×C414yescomplemented
85C2×C3×Dic6C2312yes—
86C32×C4⋊C4—21no—
87C32×C4⋊C4—21no—
88C32×C4⋊C4C2311yescharacteristic
89C32×C4⋊C4C2311yescharacteristic
90C32×C22⋊C4—21no—
91C32×C22⋊C4—21no—
92C32×C22⋊C4—21no—
93C32×C42—21no—
94C32×C42—21no—
95C32×C42—21no—
96C32×C42D411yescharacteristic
97C32×C42D411yescharacteristic
98C32×C42C2311yescharacteristic
99C32×C42C2311yescharacteristic
100C3×#216C2×C418yescomplemented
101C3×#214C2×C418yescomplemented
102C3×C4⋊Dic3—21no—
103C3×C4⋊Dic3C2312yes—
104C3×Dic3⋊C4—22no—
105C3×Dic3⋊C4—22no—
106C3×C4×Dic3—22no—
107C3×C4×Dic3—22no—
108C3×#208—22no—
109C3×#208C2×C414yescomplemented
110C2×C3×C3⋊C8C2312yes—
111C2×C3×C3⋊C8C2312yes—
112C4×#137—31noSylow
113C2×C3×#41—21no—
114C2×C3×#41C2×D311yescharacteristic
115C2×C3×#41C22×C311yescharacteristic
116C22×C3×Q8—31no—
117C22×Dic6C22×C311yescharacteristic
118C3×#137—38no—
119C2×C3×Q16—32no—
120C2×C3×SD16—32no—
121C2×C3×M16—31no—
122C2×C3×M16—31no—
123C3×C4×Q8—21no—
124C3×C4×Q8—21no—
125C3×C4×Q8—32no—
126C3×C4×Q8—32no—
127C3×C4×Q8—61no—
128C3×C4×Q8—61no—
129C3×C4×Q8C2×D311yescharacteristic
130C3×C4×Q8C2×D311yescharacteristic
131C3×C4×Q8C22×C311yescharacteristic
132C3×C4×Q8C22×C311yescharacteristic
133C3×C4×D4—22no—
134C3×C4×D4—22no—
135C3×C4×D4—21no—
136C3×C4×D4—21no—
137C3×C4×D4—21no—
138C3×C4×D4—21no—
139C3×C4×D4—21no—
140C3×C4×D4—21no—
141C3×C4×D4C2×D311yescharacteristic
142C3×C4×D4C2×D311yescharacteristic
143C3×C4×D4C22×C311yescharacteristic
144C3×C4×D4C22×C311yescharacteristic
145C3×#117—22no—
146C3×#117—21no—
147C3×#117—21no—
148C3×#117—21no—
149C3×#117C2×D311yescharacteristic
150C3×#117C22×C311yescharacteristic
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—61no—
153C2×C3×C42—22no—
154C2×C3×C42—21no—
155C2×C3×C42—21no—
156C2×C3×C42—21no—
157C2×C3×C42—61no—
158C2×C3×C42C2×D311yescharacteristic
159C2×C3×C42C22×C311yescharacteristic
160#951C3×C418yesdirect product factor
161C2×#216C22×C312yes—
162C2×#214C22×C312yes—
163C2×C4⋊Dic3C22×C311yescharacteristic
164C2×Dic3⋊C4—21no—
165C2×C4×Dic3—21no—
166C2×#208C22×C311yescharacteristic
167C2×#208C22×C311yescharacteristic
168C4×Dic6—21no—
169C4×Dic6—21no—
170C4×Dic6C22×C312yes—
171C4×Dic6C22×C312yes—
172C3×#107—32no—
173C3×#106—32no—
174C3×#103—32no—
175C3×#103—32no—
176C3×#103—32no—
177C3×#102—32no—
178C3×#97—32no—
179C3×C4×C8—32no—
180#835C22×C312yes—
181#832C22×C312yes—
182#810C22×C312yes—
183#810C22×C312yes—
184#808C22×C312yes—
185#807C22×C312yes—
186#803C22×C312yes—
187C4×C3⋊C8C22×C312yes—
188C23×C32—21no—
189C23×C32C2×D411yescharacteristic
190C32×Q8—21no—
191C32×Q8C22×C412yes—
192C32×D4—24no—
193C32×D4—21no—
194C32×D4C22×C412yes—
195C2×C32×C4—21no—
196C2×C32×C4—24no—
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C32×C4—22no—
200C2×C32×C4—41no—
201C2×C32×C4—42no—
202C2×C32×C4—42no—
203C2×C32×C4C22×C412yes—
204C2×C32×C4C2×D411yescharacteristic
205C2×C32×C4C2×D411yescharacteristic
206C2×C32×C4C2×D411yescharacteristic
207C2×C32×C4C2×D411yescharacteristic
208C2×C32×C4C2×D411yescharacteristic
209C2×C32×C4#4112yes—
210C2×C32×C4C2411yescharacteristic
211C2×C3×Dic3—24no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—42no—
215C3×Dic6—24no—
216C3×Dic6—22no—
217C3×Dic6C22×C414yes—
218C3×C3⋊C8—22no—
219C3×C3⋊C8C22×C414yes—
220C2×#137—31no—
221C4×#41C3×D311yescharacteristic
222C2×C4×Q8—31no—
223#441—32no—
224#440—32no—
225C4×Q16—32no—
226C4×SD16—32no—
227#428—31no—
228#419—31no—
229#417—31no—
230C4×M16—31no—
231C3×#41—24no—
232C3×#41—22no—
233C3×#41—22no—
234C3×#41—24no—
235C3×#41C4×D314yes—
236C3×#41C2×C3×C414yes—
237C2×C3×Q8—21no—
238C2×C3×Q8—34no—
239C2×C3×Q8—32no—
240C2×C3×Q8—62no—
241C2×C3×Q8—61no—
242C2×C3×Q8C22×D311yescharacteristic
243C2×C3×Q8C23×C311yescharacteristic
244C2×C3×D4—22no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4C22×D311yescharacteristic
249C2×C3×D4C23×C311yescharacteristic
250C22×C3×C4—22no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—22no—
254C22×C3×C4—22no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—61no—
263C22×C3×C4—61no—
264C22×C3×C4#6711yescharacteristic
265C22×C3×C4#6711yescharacteristic
266C22×C3×C4C3×D411yescharacteristic
267C22×C3×C4C3×D411yescharacteristic
268C22×C3×C4C22×D311yescharacteristic
269C22×C3×C4C23×C311yescharacteristic
270C22×Dic3—21no—
271C22×Dic3—21no—
272C2×Dic6—21no—
273C2×Dic6—22no—
274C2×Dic6C2×C3×C414yescomplemented
275C2×Dic6C23×C312yes—
276C3×Q16—38no—
277C3×SD16—38no—
278C3×M16—34no—
279C3×M16—62no—
280C2×C3×C8—32no—
281C2×C3×C8—32no—
282C3×C4⋊C4—22no—
283C3×C4⋊C4—22no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—32no—
291C3×C4⋊C4—62no—
292C3×C4⋊C4—62no—
293C3×C4⋊C4—61no—
294C3×C4⋊C4C22×D311yescharacteristic
295C3×C4⋊C4C22×D311yescharacteristic
296C3×C4⋊C4C23×C311yescharacteristic
297C3×C4⋊C4C23×C311yescharacteristic
298C3×C22⋊C4—22no—
299C3×C22⋊C4—22no—
300C3×C22⋊C4—22no—
301C3×C22⋊C4—21no—
302C3×C22⋊C4—21no—
303C3×C22⋊C4—21no—
304C3×C22⋊C4—21no—
305C3×C22⋊C4—21no—
306C3×C22⋊C4—21no—
307C3×C42—22no—
308C3×C42—22no—
309C3×C42—22no—
310C3×C42—21no—
311C3×C42—21no—
312C3×C42—21no—
313C3×C42—21no—
314C3×C42—21no—
315C3×C42—21no—
316C3×C42—21no—
317C3×C42—21no—
318C3×C42—21no—
319C3×C42—21no—
320C3×C42—62no—
321C3×C42—62no—
322C3×C42#6711yescharacteristic
323C3×C42#6711yescharacteristic
324C3×C42C3×D411yescharacteristic
325C3×C42C3×D411yescharacteristic
326C3×C42C22×D311yescharacteristic
327C3×C42C22×D311yescharacteristic
328C3×C42C23×C311yescharacteristic
329C3×C42C23×C311yescharacteristic
330#216C2×C3×C418yescomplemented
331#214C2×C3×C418yescomplemented
332C4⋊Dic3—21no—
333C4⋊Dic3C23×C312yes—
334Dic3⋊C4—22no—
335Dic3⋊C4—22no—
336C4×Dic3—22no—
337C4×Dic3—22no—
338#208—22no—
339#208C2×C3×C414yescomplemented
340C2×C3⋊C8C23×C312yes—
341C2×C3⋊C8C23×C312yes—
342C22×C32—22no—
343C22×C32—21no—
344C22×C32—21no—
345C22×C32—41no—
346C22×C32—41no—
347C22×C32C4×D412yes—
348C22×C32C22×D411yescharacteristic
349C32×C4—22no—
350C32×C4—21no—
351C32×C4—21no—
352C32×C4—21no—
353C32×C4—41no—
354C32×C4—41no—
355C32×C4C4×D412yes—
356C32×C4#13712yescomplemented
357C32×C4C23×C411yescharacteristic
358C32×C4C2×#4111yescharacteristic
359C3×Dic3—24no—
360C3×Dic3—42no—
361C2×#41C2×C3×D311yescharacteristic
362C22×Q8—31no—
363#137—38no—
364C2×Q16—32no—
365C2×SD16—32no—
366C2×M16—31no—
367C2×M16—31no—
368C4×Q8—32no—
369C4×Q8—32no—
370C4×Q8—61no—
371C4×Q8—61no—
372C4×Q8C2×C3×D311yescharacteristic
373C4×Q8C2×C3×D311yescharacteristic
374C4×D4—21no—
375C4×D4—21no—
376C4×D4C2×C3×D311yescharacteristic
377C4×D4C2×C3×D311yescharacteristic
378#117—21no—
379#117C2×C3×D311yescharacteristic
380C2×C4⋊C4—31no—
381C2×C4⋊C4—61no—
382C2×C42—21no—
383C2×C42—61no—
384C2×C42C2×C3×D311yescharacteristic
385#107—32no—
386#106—32no—
387#103—32no—
388#103—32no—
389#103—32no—
390#102—32no—
391#97—32no—
392C4×C8—32no—
393C23×C3—22no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3C2×#6711yescharacteristic
398C23×C3C2×C3×D411yescharacteristic
399C3×Q8—22no—
400C3×Q8—21no—
401C3×Q8—21no—
402C3×Q8—22no—
403C3×Q8—34no—
404C3×Q8—64no—
405C3×Q8—62no—
406C3×Q8C2×C4×D312yes—
407C3×Q8C22×C3×C412yes—
408C3×D4—28no—
409C3×D4—22no—
410C3×D4—24no—
411C3×D4—24no—
412C3×D4—21no—
413C3×D4—21no—
414C3×D4—22no—
415C3×D4C2×C4×D312yes—
416C3×D4C22×C3×C412yes—
417C2×C3×C4—22no—
418C2×C3×C4—28no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—24no—
422C2×C3×C4—22no—
423C2×C3×C4—24no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—42no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—42no—
443C2×C3×C4—44no—
444C2×C3×C4—42no—
445C2×C3×C4—42no—
446C2×C3×C4—44no—
447C2×C3×C4—42no—
448C2×C3×C4—42no—
449C2×C3×C4—64no—
450C2×C3×C4—62no—
451C2×C3×C4—62no—
452C2×C3×C4—122no—
453C2×C3×C4C2×C4×D312yes—
454C2×C3×C4#23512yes—
455C2×C3×C4C2×#6711yescharacteristic
456C2×C3×C4C2×#6711yescharacteristic
457C2×C3×C4C2×#6711yescharacteristic
458C2×C3×C4C2×#6711yescharacteristic
459C2×C3×C4C2×#6711yescharacteristic
460C2×C3×C4C22×C3×C412yes—
461C2×C3×C4C2×C3×D411yescharacteristic
462C2×C3×C4C2×C3×D411yescharacteristic
463C2×C3×C4C2×C3×D411yescharacteristic
464C2×C3×C4C2×C3×D411yescharacteristic
465C2×C3×C4C2×C3×D411yescharacteristic
466C2×C3×C4C3×#4112yes—
467C2×C3×C4C23×D311yescharacteristic
468C2×C3×C4C24×C311yescharacteristic
469C2×Dic3—24no—
470C2×Dic3—22no—
471C2×Dic3—22no—
472C2×Dic3—42no—
473Dic6—24no—
474Dic6—22no—
475Dic6C22×C3×C414yes—
476C3×C8—34no—
477C3×C8—62no—
478C3⋊C8—22no—
479C3⋊C8C22×C3×C414yes—
480C2×C32—22no—
481C2×C32—42no—
482C2×C32C2×C4×D411yescharacteristic
483C2×C32C2×#13711yescharacteristic
484C2×C32#57511yescharacteristic
485#41—22no—
486#41C3×C4×D314yes—
487C2×Q8—32no—
488C2×Q8—34no—
489C2×Q8—62no—
490C2×Q8—61no—
491C2×Q8C22×C3×D311yescharacteristic
492C2×D4—21no—
493C2×D4C22×C3×D311yescharacteristic
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—61no—
498C22×C4—61no—
499C22×C4C3×#6711yescharacteristic
500C22×C4C3×#6711yescharacteristic
501C22×C4C22×C3×D311yescharacteristic
502Q16—38no—
503SD16—38no—
504M16—34no—
505M16—62no—
506C2×C8—32no—
507C2×C8—32no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—32no—
511C4⋊C4—61no—
512C4⋊C4—62no—
513C4⋊C4—62no—
514C4⋊C4C22×C3×D311yescharacteristic
515C4⋊C4C22×C3×D311yescharacteristic
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—62no—
523C42—62no—
524C42C3×#6711yescharacteristic
525C42C3×#6711yescharacteristic
526C42C22×C3×D311yescharacteristic
527C42C22×C3×D311yescharacteristic
528C22×C3—21no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—24no—
533C22×C3—22no—
534C22×C3—22no—
535C22×C3—22no—
536C22×C3—21no—
537C22×C3—41no—
538C22×C3—41no—
539C22×C3—42no—
540C22×C3—42no—
541C22×C3—41no—
542C22×C3—41no—
543C22×C3—41no—
544C22×C3—41no—
545C22×C3C4×#6712yes—
546C22×C3C3×C4×D412yes—
547C22×C3C22×#6711yescharacteristic
548C22×C3C22×C3×D411yescharacteristic
549C3×C4—24no—
550C3×C4—22no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—21no—
554C3×C4—22no—
555C3×C4—21no—
556C3×C4—21no—
557C3×C4—21no—
558C3×C4—22no—
559C3×C4—22no—
560C3×C4—22no—
561C3×C4—21no—
562C3×C4—21no—
563C3×C4—41no—
564C3×C4—41no—
565C3×C4—42no—
566C3×C4—42no—
567C3×C4—41no—
568C3×C4—41no—
569C3×C4—41no—
570C3×C4—41no—
571C3×C4—64no—
572C3×C4—122no—
573C3×C4C4×#6712yes—
574C3×C4#95112yesdirect product factor
575C3×C4C3×C4×D412yes—
576C3×C4C3×#13712yescomplemented
577C3×C4C22×C4×D311yescharacteristic
578C3×C4C2×#23511yescharacteristic
579C3×C4C23×C3×C411yescharacteristic
580C3×C4C2×C3×#4111yescharacteristic
581Dic3—24no—
582Dic3—42no—
583C32C4×#13711yescharacteristic, complemented, Sylow
584C23—21no—
585C23C2×C3×#6711yescharacteristic
586Q8—21no—
587Q8—34no—
588Q8—64no—
589Q8—62no—
590Q8C2×C3×C4×D312yes—
591D4—24no—
592D4—21no—
593D4C2×C3×C4×D312yes—
594C2×C4—21no—
595C2×C4—24no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—64no—
603C2×C4—62no—
604C2×C4—62no—
605C2×C4—122no—
606C2×C4C2×C3×C4×D312yes—
607C2×C4C3×#23512yes—
608C2×C4C2×C3×#6711yescharacteristic
609C2×C4C2×C3×#6711yescharacteristic
610C2×C4C2×C3×#6711yescharacteristic
611C2×C4C2×C3×#6711yescharacteristic
612C2×C4C2×C3×#6711yescharacteristic
613C2×C4C23×C3×D311yescharacteristic
614C8—34no—
615C8—62no—
616C2×C3—22no—
617C2×C3—22no—
618C2×C3—21no—
619C2×C3—21no—
620C2×C3—21no—
621C2×C3—42no—
622C2×C3—44no—
623C2×C3—42no—
624C2×C3—42no—
625C2×C3C2×C4×#6711yescharacteristic
626C2×C3#582211yescharacteristic
627C2×C3C2×#95111yescharacteristic
628C2×C3C2×C3×C4×D411yescharacteristic
629C2×C3C2×C3×#13711yescharacteristic
630C2×C3C3×#57511yescharacteristic
631C22—21no—
632C22—21no—
633C22—22no—
634C22—41no—
635C22—41no—
636C22C3×C4×#6712yes—
637C22C22×C3×#6711yescharacteristic
638C4—22no—
639C4—21no—
640C4—21no—
641C4—21no—
642C4—41no—
643C4—41no—
644C4—64no—
645C4—122no—
646C4C3×C4×#6712yes—
647C4C3×#95112yesdirect product factor
648C4C22×C3×C4×D311yescharacteristic
649C4C2×C3×#23511yescharacteristic
650C3—21no—
651C3C4×#95111yescharacteristic, direct product factor
652C3C3×C4×#13711yescharacteristic, complemented
653C2—22no—
654C2—42no—
655C2C2×C3×C4×#6711yescharacteristic
656C2C3×#582211yescharacteristic
657C2C2×C3×#95111yescharacteristic
subgroupG/H
centerC2×C3×C4C2×#67
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×C4×#41C2
socleC22×C32C22×D4
prime radicalC2×C32×#41C22
cosocleC2×C3×C4C24×C3
hypercenterC3×C4×#41D3
hypocenterC3C3×C4×#137
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×C4×#41

Complements

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

NH ≅ G/Ntype
3. C2×C3×C4×Dic6C2semidirect
5. C3×#5030C2semidirect
6. C3×C4×#216C2semidirect
7. C3×#5018C2semidirect
8. C3×C4×#214C2semidirect
9. C3×#5004C2semidirect
10. C3×#4995C2semidirect
11. C3×C4×#208C2semidirect
13. C4×#951C3direct (N × H)
26. C3×#951C4direct (N × H)
52. C2×C4×Dic6C2×C3semidirect
62. #5030C2×C3semidirect
63. C4×#216C2×C3semidirect
64. #5018C2×C3semidirect
65. C4×#214C2×C3semidirect
66. #5004C2×C3semidirect
67. #4995C2×C3semidirect
68. C4×#208C2×C3semidirect
84. C2×C3×Dic6C2×C4semidirect
100. C3×#216C2×C4semidirect
101. C3×#214C2×C4semidirect
109. C3×#208C2×C4semidirect
160. #951C3×C4direct (N × H)
274. C2×Dic6C2×C3×C4semidirect
330. #216C2×C3×C4semidirect
331. #214C2×C3×C4semidirect
339. #208C2×C3×C4semidirect
356. C32×C4#137semidirect
574. C3×C4#951direct (N × H)
576. C3×C4C3×#137semidirect
583. C32C4×#137semidirect
647. C4C3×#951direct (N × H)
651. C3C4×#951direct (N × H)
652. C3C3×C4×#137semidirect

Maximal subgroups

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

subgroupindex
C32×C4×#412
C2×C3×#9512
C2×C3×C4×Dic62
C3×#52322
C3×#50302
C3×C4×#2162
C3×#50182
C3×C4×#2142
C3×#50042
C3×#49952
C3×C4×#2082
C3×C4×#1373
C4×#9513