Finite Group Databasebeta

← C3×#32904 #10651511

Subgroups — C3×#32904 #10651511

Order 768.

1608 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#41C211yesmaximal, characteristic, complemented
2C2×C3×#460C211yesmaximal, characteristic, complemented
3C2×C3×#459C211yesmaximal, characteristic, complemented
4C2×C3×#449C212yesmaximal, complemented
5C3×#2856C211yesmaximal, characteristic, complemented
6C3×#1880C212yesmaximal, complemented
7C3×#1879C212yesmaximal, complemented
8C3×#1875C212yesmaximal, complemented
9C3×#1803C211yesmaximal, characteristic, complemented
10C3×#1802C211yesmaximal, characteristic, complemented
11C3×#1797C211yesmaximal, characteristic, complemented
12#32904C311yesmaximal, characteristic, direct product factor, Sylow
13C22×C3×#41C2211yescharacteristic
14C22×C3×SD16C2212yes—
15C22×C3×D8C2212yes—
16C2×C3×#127C2211yescharacteristic
17C2×C3×#121—21no—
18C2×C3×#121—21no—
19C2×C3×#121C2212yes—
20C3×C4×#41—24no—
21C3×C4×#41—24no—
22C2×C3×C4×Q8C2211yescharacteristic
23C2×C3×C4×Q8C2211yescharacteristic
24C2×C3×C4×D4—21no—
25C2×C3×C4×D4—21no—
26C2×C3×C4×D4C2211yescharacteristic
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×#117—21no—
29C2×C3×#117C2211yescharacteristic
30C22×C3×C42—21no—
31C22×C3×C42C2211yescharacteristic
32C3×#460—24no—
33C3×#459—24no—
34C3×#449—28no—
35C2×C3×C4⋊C8C2211yescharacteristic
36C2×C3×C4⋊C8C2211yescharacteristic
37C2×C3×#103C2212yes—
38C2×C3×#102C2212yes—
39C2×C3×#102C2212yes—
40C2×C3×#102C2212yes—
41C2×C3×C22⋊C8C2212yes—
42C3×#390—21no—
43C3×#390—21no—
44C3×#390C2212yes—
45C3×#384C2211yescharacteristic
46C3×#340C2212yes—
47C3×#340C2212yes—
48C3×#336C2212yes—
49C2×C4×#41C2×C311yescharacteristic, complemented
50C2×#460C2×C311yescharacteristic, complemented
51C2×#459C2×C311yescharacteristic, complemented
52C2×#449C2×C312yescomplemented
53#2856C2×C311yescharacteristic, complemented
54#1880C2×C312yescomplemented
55#1879C2×C312yescomplemented
56#1875C2×C312yescomplemented
57#1803C2×C311yescharacteristic, complemented
58#1802C2×C311yescharacteristic, complemented
59#1797C2×C311yescharacteristic, complemented
60C2×C3×#41—22no—
61C2×C3×#41—22no—
62C2×C3×#41—22no—
63C2×C3×#41—22no—
64C2×C3×#41—22no—
65C2×C3×#41D414yescomplemented
66C22×C3×Q8C2311yescharacteristic
67C22×C3×D4—21no—
68C22×C3×D4—22no—
69C22×C3×D4—21no—
70C22×C3×D4—21no—
71C22×C3×D4C2312yes—
72C22×C3×D4C2311yescharacteristic
73C23×C3×C4—21no—
74C23×C3×C4—21no—
75C23×C3×C4—21no—
76C23×C3×C4D411yescharacteristic
77C23×C3×C4D411yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C2×C3×SD16—24no—
80C2×C3×SD16—24no—
81C2×C3×SD16—24no—
82C2×C3×D8—24no—
83C2×C3×D8—24no—
84C2×C3×D8—24no—
85C22×C3×C8C2312yes—
86C22×C3×C8C2312yes—
87C3×#127—22no—
88C3×#127—22no—
89C3×#121—24no—
90C3×#121—24no—
91C3×#121—44no—
92C3×#121—44no—
93C3×C4×Q8—22no—
94C3×C4×Q8—22no—
95C3×C4×Q8—22no—
96C3×C4×Q8D414yescomplemented
97C3×C4×D4—28no—
98C3×C4×D4—28no—
99C3×C4×D4—22no—
100C3×C4×D4—22no—
101C3×C4×D4—22no—
102C3×C4×D4D414yescomplemented
103C3×#117—28no—
104C3×#117—22no—
105C3×#117—22no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4C2312yes—
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—22no—
117C2×C3×C22⋊C4—22no—
118C2×C3×C22⋊C4—22no—
119C2×C3×C42—28no—
120C2×C3×C42—21no—
121C2×C3×C42—21no—
122C2×C3×C42—21no—
123C2×C3×C42—22no—
124C2×C3×C42—22no—
125C2×C3×C42D411yescharacteristic
126C2×C3×C42D411yescharacteristic
127C2×C3×C42C2311yescharacteristic
128C2×C3×C42C2311yescharacteristic
129C3×C4⋊C8—22no—
130C3×C4⋊C8—22no—
131C3×#103—24no—
132C3×#102—24no—
133C3×#102—24no—
134C3×#102—24no—
135C3×C22⋊C8—24no—
136C22×#41C22×C311yescharacteristic
137C22×SD16C22×C312yes—
138C22×D8C22×C312yes—
139C2×#127C22×C311yescharacteristic
140C2×#121—21no—
141C2×#121—21no—
142C2×#121C22×C312yes—
143C4×#41—24no—
144C4×#41—24no—
145C2×C4×Q8C22×C311yescharacteristic
146C2×C4×Q8C22×C311yescharacteristic
147C2×C4×D4—21no—
148C2×C4×D4—21no—
149C2×C4×D4C22×C311yescharacteristic
150C2×C4×D4C22×C311yescharacteristic
151C2×#117—21no—
152C2×#117C22×C311yescharacteristic
153C22×C42—21no—
154C22×C42C22×C311yescharacteristic
155#460—24no—
156#459—24no—
157#449—28no—
158C2×C4⋊C8C22×C311yescharacteristic
159C2×C4⋊C8C22×C311yescharacteristic
160C2×#103C22×C312yes—
161C2×#102C22×C312yes—
162C2×#102C22×C312yes—
163C2×#102C22×C312yes—
164C2×C22⋊C8C22×C312yes—
165#390—21no—
166#390—21no—
167#390C22×C312yes—
168#384C22×C311yescharacteristic
169#340C22×C312yes—
170#340C22×C312yes—
171#336C22×C312yes—
172C24×C3—21no—
173C24×C3—22no—
174C24×C3C2×D411yescharacteristic
175C3×#41—28no—
176C3×#41—28no—
177C3×#41—28no—
178C3×#41—28no—
179C2×C3×Q8—21no—
180C2×C3×Q8—21no—
181C2×C3×Q8—21no—
182C2×C3×Q8C2×D412yes—
183C2×C3×Q8C2×D412yes—
184C2×C3×Q8#4112yes—
185C2×C3×D4—24no—
186C2×C3×D4—24no—
187C2×C3×D4—24no—
188C2×C3×D4—21no—
189C2×C3×D4—22no—
190C2×C3×D4—22no—
191C2×C3×D4—22no—
192C2×C3×D4—21no—
193C2×C3×D4—21no—
194C2×C3×D4—22no—
195C2×C3×D4—22no—
196C2×C3×D4—22no—
197C2×C3×D4—42no—
198C2×C3×D4—42no—
199C2×C3×D4—44no—
200C2×C3×D4—44no—
201C2×C3×D4—44no—
202C2×C3×D4—42no—
203C2×C3×D4—42no—
204C2×C3×D4—42no—
205C2×C3×D4—42no—
206C2×C3×D4C2×D412yes—
207C2×C3×D4C2×D412yes—
208C2×C3×D4#4112yes—
209C22×C3×C4—24no—
210C22×C3×C4—24no—
211C22×C3×C4—21no—
212C22×C3×C4—24no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—24no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—24no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—41no—
228C22×C3×C4—42no—
229C22×C3×C4—42no—
230C22×C3×C4—42no—
231C22×C3×C4—42no—
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D412yes—
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4#4112yes—
239C22×C3×C4C2411yescharacteristic
240C3×SD16—48no—
241C3×D8—48no—
242C2×C3×C8—22no—
243C2×C3×C8—22no—
244C2×C3×C8—22no—
245C2×C3×C8—22no—
246C2×C3×C8—22no—
247C2×C3×C8—22no—
248C3×C4⋊C4—24no—
249C3×C4⋊C4—24no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—22no—
253C3×C4⋊C4—22no—
254C3×C4⋊C4—42no—
255C3×C4⋊C4—42no—
256C3×C4⋊C4C2×D412yes—
257C3×C4⋊C4C2×D412yes—
258C3×C22⋊C4—24no—
259C3×C22⋊C4—24no—
260C3×C22⋊C4—24no—
261C3×C22⋊C4—44no—
262C3×C22⋊C4—44no—
263C3×C22⋊C4—44no—
264C3×C42—24no—
265C3×C42—24no—
266C3×C42—22no—
267C3×C42—24no—
268C3×C42—22no—
269C3×C42—21no—
270C3×C42—21no—
271C3×C42C2×D412yes—
272C3×C42C2×D412yes—
273C2×#41—22no—
274C2×#41—22no—
275C2×#41—22no—
276C2×#41—22no—
277C2×#41—22no—
278C2×#41C3×D414yescomplemented
279C22×Q8C23×C311yescharacteristic
280C22×D4—21no—
281C22×D4—22no—
282C22×D4—21no—
283C22×D4—21no—
284C22×D4C23×C312yes—
285C22×D4C23×C311yescharacteristic
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4C3×D411yescharacteristic
290C23×C4C3×D411yescharacteristic
291C23×C4C23×C311yescharacteristic
292C2×SD16—24no—
293C2×SD16—24no—
294C2×SD16—24no—
295C2×D8—24no—
296C2×D8—24no—
297C2×D8—24no—
298C22×C8C23×C312yes—
299C22×C8C23×C312yes—
300#127—22no—
301#127—22no—
302#121—24no—
303#121—24no—
304#121—44no—
305#121—44no—
306C4×Q8—22no—
307C4×Q8—22no—
308C4×Q8—22no—
309C4×Q8C3×D414yescomplemented
310C4×D4—28no—
311C4×D4—28no—
312C4×D4—22no—
313C4×D4—22no—
314C4×D4—22no—
315C4×D4C3×D414yescomplemented
316#117—28no—
317#117—22no—
318#117—22no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4C23×C312yes—
324C2×C4⋊C4C23×C311yescharacteristic
325C2×C4⋊C4C23×C311yescharacteristic
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C42—28no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—22no—
337C2×C42—22no—
338C2×C42C3×D411yescharacteristic
339C2×C42C3×D411yescharacteristic
340C2×C42C23×C311yescharacteristic
341C2×C42C23×C311yescharacteristic
342C4⋊C8—22no—
343C4⋊C8—22no—
344#103—24no—
345#102—24no—
346#102—24no—
347#102—24no—
348C22⋊C8—24no—
349C23×C3—21no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—21no—
353C23×C3—22no—
354C23×C3—21no—
355C23×C3—21no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—41no—
359C23×C3—41no—
360C23×C3—41no—
361C23×C3—41no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3#12112yes—
370C23×C3C22×D411yescharacteristic
371C3×Q8—22no—
372C3×Q8—22no—
373C3×Q8—22no—
374C3×Q8#12114yescomplemented
375C3×D4—216no—
376C3×D4—22no—
377C3×D4—22no—
378C3×D4—22no—
379C3×D4—42no—
380C3×D4—42no—
381C3×D4—42no—
382C3×D4—42no—
383C3×D4—84no—
384C3×D4—88no—
385C3×D4—84no—
386C3×D4#12114yescomplemented
387C2×C3×C4—216no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—21no—
393C2×C3×C4—22no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—21no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—44no—
407C2×C3×C4—48no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—44no—
413C2×C3×C4—48no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—42no—
417C2×C3×C4#12012yes—
418C2×C3×C4#12012yes—
419C2×C3×C4#12112yes—
420C2×C3×C4#13512yes—
421C2×C3×C4AGL(1,ℤ/8)12yes—
422C2×C3×C4AGL(1,ℤ/8)12yes—
423C2×C3×C4C22×D411yescharacteristic
424C2×C3×C4C22×D411yescharacteristic
425C2×C3×C4C22×D411yescharacteristic
426C2×C3×C4C2×#4111yescharacteristic
427C2×C3×C4C2×#4111yescharacteristic
428C2×C3×C4C2×#4111yescharacteristic
429C3×C8—42no—
430C3×C8—42no—
431C24—21no—
432C24—22no—
433C24C2×C3×D411yescharacteristic
434#41—28no—
435#41—28no—
436#41—28no—
437#41—28no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8C2×C3×D412yes—
442C2×Q8C2×C3×D412yes—
443C2×Q8C3×#4112yes—
444C2×D4—24no—
445C2×D4—24no—
446C2×D4—24no—
447C2×D4—21no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—42no—
457C2×D4—42no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4C2×C3×D412yes—
466C2×D4C2×C3×D412yes—
467C2×D4C3×#4112yes—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—21no—
471C22×C4—24no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—24no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—41no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4C2×C3×D411yescharacteristic
492C22×C4C2×C3×D411yescharacteristic
493C22×C4C2×C3×D411yescharacteristic
494C22×C4C2×C3×D412yes—
495C22×C4C2×C3×D411yescharacteristic
496C22×C4C2×C3×D411yescharacteristic
497C22×C4C3×#4112yes—
498C22×C4C24×C311yescharacteristic
499SD16—48no—
500D8—48no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C4⋊C4—24no—
508C4⋊C4—24no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—42no—
514C4⋊C4—42no—
515C4⋊C4C2×C3×D412yes—
516C4⋊C4C2×C3×D412yes—
517C22⋊C4—24no—
518C22⋊C4—24no—
519C22⋊C4—24no—
520C22⋊C4—44no—
521C22⋊C4—44no—
522C22⋊C4—44no—
523C42—24no—
524C42—24no—
525C42—22no—
526C42—24no—
527C42—22no—
528C42—21no—
529C42—21no—
530C42C2×C3×D412yes—
531C42C2×C3×D412yes—
532C22×C3—22no—
533C22×C3—24no—
534C22×C3—22no—
535C22×C3—22no—
536C22×C3—41no—
537C22×C3—42no—
538C22×C3—41no—
539C22×C3—42no—
540C22×C3—41no—
541C22×C3—42no—
542C22×C3—41no—
543C22×C3—42no—
544C22×C3—42no—
545C22×C3—42no—
546C22×C3—82no—
547C22×C3—82no—
548C22×C3—82no—
549C22×C3—82no—
550C22×C3—82no—
551C22×C3—82no—
552C22×C3—82no—
553C22×C3C2×#12011yescharacteristic
554C22×C3C2×#12111yescharacteristic
555C22×C3#52511yescharacteristic
556C22×C3C2×#13511yescharacteristic
557C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
558C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
559C22×C3#57511yescharacteristic
560C3×C4—22no—
561C3×C4—24no—
562C3×C4—22no—
563C3×C4—22no—
564C3×C4—41no—
565C3×C4—42no—
566C3×C4—42no—
567C3×C4—82no—
568C3×C4#44914yescomplemented
569C3×C4C2×#12111yescharacteristic
570C3×C4C2×#12111yescharacteristic
571C3×C4#52511yescharacteristic
572C3×C4#52511yescharacteristic
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—22no—
579C23—22no—
580C23—21no—
581C23—22no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23C3×#12112yes—
594C23C22×C3×D411yescharacteristic
595Q8—22no—
596Q8—22no—
597Q8—22no—
598Q8C3×#12114yescomplemented
599D4—216no—
600D4—22no—
601D4—22no—
602D4—22no—
603D4—42no—
604D4—42no—
605D4—42no—
606D4—42no—
607D4—84no—
608D4—88no—
609D4—84no—
610D4C3×#12114yescomplemented
611C2×C4—216no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—44no—
631C2×C4—48no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—44no—
637C2×C4—48no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4C3×#12012yes—
642C2×C4C3×#12012yes—
643C2×C4C3×#12112yes—
644C2×C4C3×#13512yes—
645C2×C4C3×AGL(1,ℤ/8)12yes—
646C2×C4C3×AGL(1,ℤ/8)12yes—
647C2×C4C22×C3×D411yescharacteristic
648C2×C4C22×C3×D411yescharacteristic
649C2×C4C22×C3×D411yescharacteristic
650C2×C4C2×C3×#4111yescharacteristic
651C2×C4C2×C3×#4111yescharacteristic
652C2×C4C2×C3×#4111yescharacteristic
653C8—42no—
654C8—42no—
655C2×C3—42no—
656C2×C3—44no—
657C2×C3—162no—
658C2×C3#284711yescharacteristic
659C2×C3C2×#44911yescharacteristic
660C2×C3#300611yescharacteristic
661C2×C3#303511yescharacteristic
662C2×C3#303811yescharacteristic
663C2×C3#310611yescharacteristic
664C2×C3#311511yescharacteristic
665C22—22no—
666C22—22no—
667C22—22no—
668C22—24no—
669C22—41no—
670C22—42no—
671C22—41no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—41no—
676C22—42no—
677C22—41no—
678C22—42no—
679C22—82no—
680C22—82no—
681C22—82no—
682C22—82no—
683C22—82no—
684C22—82no—
685C22—82no—
686C22C2×C3×#12011yescharacteristic
687C22C2×C3×#12111yescharacteristic
688C22C3×#52511yescharacteristic
689C22C2×C3×#13511yescharacteristic
690C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
691C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
692C22C3×#57511yescharacteristic
693C4—22no—
694C4—22no—
695C4—22no—
696C4—24no—
697C4—41no—
698C4—42no—
699C4—42no—
700C4—82no—
701C4C3×#44914yescomplemented
702C4C2×C3×#12111yescharacteristic
703C4C2×C3×#12111yescharacteristic
704C4C3×#52511yescharacteristic
705C4C3×#52511yescharacteristic
706C3#3290411yescharacteristic, direct product factor, Sylow
707C2—42no—
708C2—44no—
709C2—162no—
710C2C3×#284711yescharacteristic
711C2C2×C3×#44911yescharacteristic
712C2C3×#300611yescharacteristic
713C2C3×#303511yescharacteristic
714C2C3×#303811yescharacteristic
715C2C3×#310611yescharacteristic
716C2C3×#311511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C22×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×#41C2semidirect
2. C2×C3×#460C2semidirect
3. C2×C3×#459C2semidirect
4. C2×C3×#449C2semidirect
5. C3×#2856C2semidirect
6. C3×#1880C2semidirect
7. C3×#1879C2semidirect
8. C3×#1875C2semidirect
9. C3×#1803C2semidirect
10. C3×#1802C2semidirect
11. C3×#1797C2semidirect
12. #32904C3direct (N × H)
49. C2×C4×#41C2×C3semidirect
50. C2×#460C2×C3semidirect
51. C2×#459C2×C3semidirect
52. C2×#449C2×C3semidirect
53. #2856C2×C3semidirect
54. #1880C2×C3semidirect
55. #1879C2×C3semidirect
56. #1875C2×C3semidirect
57. #1803C2×C3semidirect
58. #1802C2×C3semidirect
59. #1797C2×C3semidirect
65. C2×C3×#41D4semidirect
96. C3×C4×Q8D4semidirect
102. C3×C4×D4D4semidirect
278. C2×#41C3×D4semidirect
309. C4×Q8C3×D4semidirect
315. C4×D4C3×D4semidirect
374. C3×Q8#121semidirect
386. C3×D4#121semidirect
568. C3×C4#449semidirect
598. Q8C3×#121semidirect
610. D4C3×#121semidirect
701. C4C3×#449semidirect
706. C3#32904direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×#412
C2×C3×#4602
C2×C3×#4592
C2×C3×#4492
C3×#28562
C3×#18802
C3×#18792
C3×#18752
C3×#18032
C3×#18022
C3×#17972
#329043