Finite Group Databasebeta

← C3×#14135 #10632742

Subgroups — C3×#14135 #10632742

Order 768.

2634 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#123C211yesmaximal, characteristic
2C22×C3×#117C211yesmaximal, characteristic, complemented
3C2×C3×#386C212yesmaximal
4C22×C3×#95C211yesmaximal, characteristic, complemented
5C3×#1441C212yesmaximal, complemented
6C3×#1439C212yesmaximal, complemented
7C3×#1437C212yesmaximal, complemented
8C3×#1436C212yesmaximal, complemented
9C3×C22⋊#95C212yesmaximal, complemented
10#14135C311yesmaximal, characteristic, direct product factor, Sylow
11C23×C3×D4C2211yescharacteristic
12C24×C3×C4C2212yes—
13C24×C3×C4C2211yescharacteristic
14C2×C3×#123—24no—
15C2×C3×#123—24no—
16C2×C3×#123C418yescomplemented
17C2×C3×#117—24no—
18C2×C3×#117—28no—
19C22×C3×C4⋊C4C2212yes—
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2214yes—
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2212yes—
27C22×C3×C42C2212yes—
28C3×#386—28no—
29C2×C3×#95—24no—
30C2×C3×#95C2212yes—
31C2×C3×#95C2212yes—
32C2×C3×#95C2214yes—
33C2×C3×#95C2214yes—
34C2×C3×#95C2214yes—
35C22×#123C2×C311yescharacteristic
36C22×#117C2×C311yescharacteristic, complemented
37C2×#386C2×C312yes—
38C22×#95C2×C311yescharacteristic, complemented
39#1441C2×C312yescomplemented
40#1439C2×C312yescomplemented
41#1437C2×C312yescomplemented
42#1436C2×C312yescomplemented
43C22⋊#95C2×C312yescomplemented
44C25×C3C2311yescharacteristic
45C25×C3C2311yescharacteristic
46C22×C3×D4—24no—
47C22×C3×D4—22no—
48C22×C3×D4—22no—
49C22×C3×D4—24no—
50C22×C3×D4C2×C414yes—
51C23×C3×C4—24no—
52C23×C3×C4—24no—
53C23×C3×C4—24no—
54C23×C3×C4—28no—
55C23×C3×C4—24no—
56C23×C3×C4—24no—
57C23×C3×C4—44no—
58C23×C3×C4C2×C414yes—
59C23×C3×C4D414yes—
60C23×C3×C4D414yes—
61C23×C3×C4C2311yescharacteristic
62C23×C3×C4C2311yescharacteristic
63C23×C3×C4C2311yescharacteristic
64C23×C3×C4C2314yes—
65C23×C3×C4C2314yes—
66C23×C3×C4C2311yescharacteristic
67C23×C3×C4C2311yescharacteristic
68C3×#123—232no—
69C3×#117—232no—
70C2×C3×C4⋊C4—28no—
71C2×C3×C4⋊C4—24no—
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—22no—
75C2×C3×C4⋊C4—22no—
76C2×C3×C4⋊C4C2×C414yescomplemented
77C2×C3×C4⋊C4C2×C414yescomplemented
78C2×C3×C22⋊C4—24no—
79C2×C3×C22⋊C4—24no—
80C2×C3×C22⋊C4—22no—
81C2×C3×C22⋊C4—22no—
82C2×C3×C22⋊C4—22no—
83C2×C3×C22⋊C4—22no—
84C2×C3×C22⋊C4—22no—
85C2×C3×C22⋊C4—22no—
86C2×C3×C22⋊C4—28no—
87C2×C3×C22⋊C4—28no—
88C2×C3×C22⋊C4—44no—
89C2×C3×C22⋊C4C2×C414yes—
90C2×C3×C22⋊C4C2×C414yescomplemented
91C2×C3×C22⋊C4C2×C414yescomplemented
92C2×C3×C22⋊C4D418yes—
93C2×C3×C42—28no—
94C2×C3×C42—24no—
95C3×#95—24no—
96C3×#95—24no—
97C3×#95—28no—
98C3×#95—28no—
99C3×#95—44no—
100C23×D4C22×C311yescharacteristic
101C24×C4C22×C312yes—
102C24×C4C22×C311yescharacteristic
103C2×#123—24no—
104C2×#123—24no—
105C2×#123C3×C418yescomplemented
106C2×#117—24no—
107C2×#117—28no—
108C22×C4⋊C4C22×C312yes—
109C22×C4⋊C4C22×C311yescharacteristic
110C22×C4⋊C4C22×C311yescharacteristic
111C22×C22⋊C4C22×C314yes—
112C22×C22⋊C4C22×C311yescharacteristic
113C22×C22⋊C4C22×C311yescharacteristic
114C22×C22⋊C4C22×C311yescharacteristic
115C22×C22⋊C4C22×C312yes—
116C22×C42C22×C312yes—
117#386—28no—
118C2×#95—24no—
119C2×#95C22×C314yes—
120C2×#95C22×C312yes—
121C2×#95C22×C314yes—
122C2×#95C22×C312yes—
123C2×#95C22×C314yes—
124C24×C3—24no—
125C24×C3—22no—
126C24×C3—22no—
127C24×C3—21no—
128C24×C3—21no—
129C24×C3—22no—
130C24×C3—24no—
131C24×C3—22no—
132C24×C3—22no—
133C24×C3—22no—
134C24×C3C22×C412yes—
135C24×C3C22×C412yes—
136C24×C3C2×D412yes—
137C24×C3C2×D412yes—
138C24×C3C2×D414yes—
139C24×C3#4114yes—
140C24×C3C2411yescharacteristic
141C2×C3×D4—28no—
142C2×C3×D4—216no—
143C2×C3×D4—44no—
144C2×C3×D4—48no—
145C2×C3×D4—44no—
146C22×C3×C4—216no—
147C22×C3×C4—28no—
148C22×C3×C4—216no—
149C22×C3×C4—28no—
150C22×C3×C4—22no—
151C22×C3×C4—22no—
152C22×C3×C4—22no—
153C22×C3×C4—22no—
154C22×C3×C4—216no—
155C22×C3×C4—24no—
156C22×C3×C4—22no—
157C22×C3×C4—24no—
158C22×C3×C4—24no—
159C22×C3×C4—24no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—24no—
167C22×C3×C4—24no—
168C22×C3×C4—24no—
169C22×C3×C4—24no—
170C22×C3×C4—24no—
171C22×C3×C4—22no—
172C22×C3×C4—22no—
173C22×C3×C4—24no—
174C22×C3×C4—24no—
175C22×C3×C4—24no—
176C22×C3×C4—22no—
177C22×C3×C4—24no—
178C22×C3×C4—416no—
179C22×C3×C4—416no—
180C22×C3×C4—48no—
181C22×C3×C4—48no—
182C22×C3×C4C22⋊C4116yescomplemented
183C22×C3×C4C22×C412yes—
184C22×C3×C4C22×C412yes—
185C22×C3×C4C22×C412yes—
186C22×C3×C4C22×C412yes—
187C22×C3×C4C22×C412yes—
188C22×C3×C4C2×D418yes—
189C22×C3×C4C2×D412yes—
190C22×C3×C4C2×D412yes—
191C22×C3×C4C2×D412yes—
192C22×C3×C4C2×D412yes—
193C22×C3×C4#4118yes—
194C3×C4⋊C4—216no—
195C3×C4⋊C4—28no—
196C3×C4⋊C4—28no—
197C3×C22⋊C4—28no—
198C3×C22⋊C4—216no—
199C3×C22⋊C4—28no—
200C3×C22⋊C4—28no—
201C3×C22⋊C4—416no—
202C3×C42—216no—
203C25C23×C311yescharacteristic
204C25C23×C311yescharacteristic
205C22×D4—22no—
206C22×D4—22no—
207C22×D4—24no—
208C22×D4—24no—
209C22×D4C2×C3×C414yes—
210C23×C4—24no—
211C23×C4—24no—
212C23×C4—24no—
213C23×C4—28no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—44no—
217C23×C4C2×C3×C414yes—
218C23×C4C3×D414yes—
219C23×C4C3×D414yes—
220C23×C4C23×C311yescharacteristic
221C23×C4C23×C311yescharacteristic
222C23×C4C23×C311yescharacteristic
223C23×C4C23×C314yes—
224C23×C4C23×C314yes—
225C23×C4C23×C311yescharacteristic
226C23×C4C23×C311yescharacteristic
227#123—232no—
228#117—232no—
229C2×C4⋊C4—28no—
230C2×C4⋊C4—24no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4C2×C3×C414yescomplemented
236C2×C4⋊C4C2×C3×C414yescomplemented
237C2×C22⋊C4—24no—
238C2×C22⋊C4—24no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—28no—
246C2×C22⋊C4—28no—
247C2×C22⋊C4—44no—
248C2×C22⋊C4C2×C3×C414yes—
249C2×C22⋊C4C2×C3×C414yescomplemented
250C2×C22⋊C4C2×C3×C414yescomplemented
251C2×C22⋊C4C3×D418yes—
252C2×C42—28no—
253C2×C42—24no—
254#95—24no—
255#95—24no—
256#95—28no—
257#95—28no—
258#95—44no—
259C23×C3—24no—
260C23×C3—24no—
261C23×C3—24no—
262C23×C3—24no—
263C23×C3—22no—
264C23×C3—22no—
265C23×C3—24no—
266C23×C3—28no—
267C23×C3—28no—
268C23×C3—28no—
269C23×C3—28no—
270C23×C3—22no—
271C23×C3—24no—
272C23×C3—24no—
273C23×C3—24no—
274C23×C3—41no—
275C23×C3—42no—
276C23×C3—41no—
277C23×C3—42no—
278C23×C3—42no—
279C23×C3—41no—
280C23×C3—41no—
281C23×C3—42no—
282C23×C3—44no—
283C23×C3—44no—
284C23×C3—44no—
285C23×C3—44no—
286C23×C3C2×C22⋊C414yes—
287C23×C3C4×D418yes—
288C23×C3#12014yes—
289C23×C3#12118yes—
290C23×C3#12314yes—
291C23×C3C23×C411yescharacteristic
292C23×C3C22×D411yescharacteristic
293C23×C3C22×D411yescharacteristic
294C23×C3C22×D412yes—
295C23×C3C2×#4112yes—
296C23×C3C2×#4114yes—
297C23×C3H(5,𝔽2)12yes—
298C23×C32−1+412yes—
299C3×D4—416no—
300C2×C3×C4—24no—
301C2×C3×C4—24no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—24no—
305C2×C3×C4—24no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—232no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—24no—
313C2×C3×C4—24no—
314C2×C3×C4—24no—
315C2×C3×C4—28no—
316C2×C3×C4—28no—
317C2×C3×C4—28no—
318C2×C3×C4—28no—
319C2×C3×C4—28no—
320C2×C3×C4—28no—
321C2×C3×C4—432no—
322C2×C3×C4—41no—
323C2×C3×C4—44no—
324C2×C3×C4—42no—
325C2×C3×C4—41no—
326C2×C3×C4—42no—
327C2×C3×C4—44no—
328C2×C3×C4—42no—
329C2×C3×C4—41no—
330C2×C3×C4—44no—
331C2×C3×C4—41no—
332C2×C3×C4—42no—
333C2×C3×C4—44no—
334C2×C3×C4—44no—
335C2×C3×C4—44no—
336C2×C3×C4—44no—
337C2×C3×C4—44no—
338C2×C3×C4C2×C22⋊C414yes—
339C2×C3×C4C2×C22⋊C414yes—
340C24—24no—
341C24—22no—
342C24—22no—
343C24—21no—
344C24—21no—
345C24—22no—
346C24—24no—
347C24—22no—
348C24—22no—
349C24—22no—
350C24C22×C3×C412yes—
351C24C22×C3×C412yes—
352C24C2×C3×D412yes—
353C24C2×C3×D412yes—
354C24C2×C3×D414yes—
355C24C3×#4114yes—
356C24C24×C311yescharacteristic
357C2×D4—28no—
358C2×D4—216no—
359C2×D4—44no—
360C2×D4—48no—
361C2×D4—44no—
362C22×C4—216no—
363C22×C4—28no—
364C22×C4—216no—
365C22×C4—28no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—216no—
371C22×C4—24no—
372C22×C4—22no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—24no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—22no—
393C22×C4—24no—
394C22×C4—416no—
395C22×C4—416no—
396C22×C4—48no—
397C22×C4—48no—
398C22×C4C3×C22⋊C4116yescomplemented
399C22×C4C22×C3×C412yes—
400C22×C4C22×C3×C412yes—
401C22×C4C22×C3×C412yes—
402C22×C4C22×C3×C412yes—
403C22×C4C22×C3×C412yes—
404C22×C4C2×C3×D418yes—
405C22×C4C2×C3×D412yes—
406C22×C4C2×C3×D412yes—
407C22×C4C2×C3×D412yes—
408C22×C4C2×C3×D412yes—
409C22×C4C3×#4118yes—
410C4⋊C4—216no—
411C4⋊C4—28no—
412C4⋊C4—28no—
413C22⋊C4—28no—
414C22⋊C4—216no—
415C22⋊C4—28no—
416C22⋊C4—28no—
417C22⋊C4—416no—
418C42—216no—
419C22×C3—24no—
420C22×C3—216no—
421C22×C3—28no—
422C22×C3—28no—
423C22×C3—28no—
424C22×C3—28no—
425C22×C3—24no—
426C22×C3—42no—
427C22×C3—48no—
428C22×C3—42no—
429C22×C3—42no—
430C22×C3—82no—
431C22×C3—82no—
432C22×C3—82no—
433C22×C3—82no—
434C22×C3#38618yes—
435C22×C3C22×C22⋊C411yescharacteristic
436C22×C3C2×C4×D412yes—
437C22×C3C4×#4112yes—
438C22×C3#52012yes—
439C22×C3C2×#12011yescharacteristic
440C22×C3C2×#12112yes—
441C22×C3C2×#12311yescharacteristic
442C22×C3#52512yes—
443C22×C3#53212yes—
444C22×C3#53511yescharacteristic
445C22×C3#53611yescharacteristic
446C22×C3#53712yes—
447C22×C3#54614yes—
448C22×C3#54714yes—
449C22×C3#55114yes—
450C22×C3#55214yes—
451C3×C4—24no—
452C3×C4—24no—
453C3×C4—42no—
454C3×C4—48no—
455C3×C4—48no—
456C3×C4—42no—
457C3×C4—42no—
458C23—24no—
459C23—24no—
460C23—24no—
461C23—24no—
462C23—22no—
463C23—22no—
464C23—24no—
465C23—28no—
466C23—28no—
467C23—28no—
468C23—28no—
469C23—22no—
470C23—24no—
471C23—24no—
472C23—24no—
473C23—41no—
474C23—42no—
475C23—41no—
476C23—42no—
477C23—42no—
478C23—41no—
479C23—41no—
480C23—42no—
481C23—44no—
482C23—44no—
483C23—44no—
484C23—44no—
485C23C2×C3×C22⋊C414yes—
486C23C3×C4×D418yes—
487C23C3×#12014yes—
488C23C3×#12118yes—
489C23C3×#12314yes—
490C23C23×C3×C411yescharacteristic
491C23C22×C3×D411yescharacteristic
492C23C22×C3×D411yescharacteristic
493C23C22×C3×D412yes—
494C23C2×C3×#4112yes—
495C23C2×C3×#4114yes—
496C23C3×H(5,𝔽2)12yes—
497C23C3×2−1+412yes—
498D4—416no—
499C2×C4—232no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—28no—
515C2×C4—28no—
516C2×C4—28no—
517C2×C4—28no—
518C2×C4—28no—
519C2×C4—28no—
520C2×C4—432no—
521C2×C4—41no—
522C2×C4—44no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—42no—
528C2×C4—44no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—44no—
532C2×C4—42no—
533C2×C4—44no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4C2×C3×C22⋊C414yes—
538C2×C4C2×C3×C22⋊C414yes—
539C2×C3—28no—
540C2×C3—82no—
541C2×C3C2×#38611yescharacteristic
542C2×C3#229711yescharacteristic
543C2×C3#231111yescharacteristic
544C2×C3#235914yes—
545C2×C3#241112yes—
546C2×C3#241312yes—
547C2×C3#243012yes—
548C2×C3#249812yes—
549C22—28no—
550C22—28no—
551C22—28no—
552C22—28no—
553C22—24no—
554C22—24no—
555C22—216no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—48no—
560C22—82no—
561C22—82no—
562C22—82no—
563C22—82no—
564C22C3×#38618yes—
565C22C22×C3×C22⋊C411yescharacteristic
566C22C2×C3×C4×D412yes—
567C22C3×C4×#4112yes—
568C22C3×#52012yes—
569C22C2×C3×#12011yescharacteristic
570C22C2×C3×#12112yes—
571C22C2×C3×#12311yescharacteristic
572C22C3×#52512yes—
573C22C3×#53212yes—
574C22C3×#53511yescharacteristic
575C22C3×#53611yescharacteristic
576C22C3×#53712yes—
577C22C3×#54614yes—
578C22C3×#54714yes—
579C22C3×#55114yes—
580C22C3×#55214yes—
581C4—24no—
582C4—24no—
583C4—48no—
584C4—48no—
585C4—42no—
586C4—42no—
587C4—42no—
588C3#1413511yescharacteristic, direct product factor, Sylow
589C2—28no—
590C2—82no—
591C2C2×C3×#38611yescharacteristic
592C2C3×#229711yescharacteristic
593C2C3×#231111yescharacteristic
594C2C3×#235914yes—
595C2C3×#241112yes—
596C2C3×#241312yes—
597C2C3×#243012yes—
598C2C3×#249812yes—
subgroupG/H
center, socleC24×C3C24
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
prime radicalC23×C3×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C3×#117C2semidirect
4. C22×C3×#95C2semidirect
5. C3×#1441C2semidirect
6. C3×#1439C2semidirect
7. C3×#1437C2semidirect
8. C3×#1436C2semidirect
9. C3×C22⋊#95C2semidirect
10. #14135C3direct (N × H)
16. C2×C3×#123C4semidirect
36. C22×#117C2×C3semidirect
38. C22×#95C2×C3semidirect
39. #1441C2×C3semidirect
40. #1439C2×C3semidirect
41. #1437C2×C3semidirect
42. #1436C2×C3semidirect
43. C22⋊#95C2×C3semidirect
76. C2×C3×C4⋊C4C2×C4semidirect
77. C2×C3×C4⋊C4C2×C4semidirect
90. C2×C3×C22⋊C4C2×C4semidirect
91. C2×C3×C22⋊C4C2×C4semidirect
105. C2×#123C3×C4semidirect
182. C22×C3×C4C22⋊C4semidirect
235. C2×C4⋊C4C2×C3×C4semidirect
236. C2×C4⋊C4C2×C3×C4semidirect
249. C2×C22⋊C4C2×C3×C4semidirect
250. C2×C22⋊C4C2×C3×C4semidirect
398. C22×C4C3×C22⋊C4semidirect
588. C3#14135direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1232
C22×C3×#1172
C2×C3×#3862
C22×C3×#952
C3×#14412
C3×#14392
C3×#14372
C3×#14362
C3×C22⋊#952
#141353