Finite Group Databasebeta

← C3×#14908 #10633515

Subgroups — C3×#14908 #10633515

Order 768.

1230 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#400C211yesmaximal, characteristic
2C2×C3×#389C211yesmaximal, characteristic
3C2×C3×#387C211yesmaximal, characteristic
4C2×C3×#376C211yesmaximal, characteristic
5C3×#1445C211yesmaximal, characteristic
6C3×#1443C212yesmaximal
7C3×#1442C212yesmaximal
8C3×#1442C211yesmaximal, characteristic
9C3×#1441C211yesmaximal, characteristic
10C3×#1436C212yesmaximal
11C3×#1436C212yesmaximal
12#14908C311yesmaximal, characteristic, direct product factor, Sylow
13C22×C3×C4⋊C4C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C4⋊C4C2212yes—
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C42C2212yes—
19C22×C3×C42C2211yescharacteristic
20C3×#400—24no—
21C3×#389—24no—
22C3×#387—24no—
23C3×#376—24no—
24C2×C3×#95C2212yes—
25C2×C3×#95C2212yes—
26C2×C3×#95C2211yescharacteristic
27C2×C3×#95C2212yes—
28C2×C3×#95C2211yescharacteristic
29C2×C3×#95C2211yescharacteristic
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2212yes—
33C2×C3×#95C2212yes—
34C2×C3×#95C2212yes—
35C2×C3×#95C2212yes—
36C2×C3×#95C2212yes—
37C2×C3×#95C2212yes—
38C2×C3×#95C2212yes—
39C2×C3×#95C2211yescharacteristic
40C2×#400C2×C311yescharacteristic
41C2×#389C2×C311yescharacteristic
42C2×#387C2×C311yescharacteristic
43C2×#376C2×C311yescharacteristic
44#1445C2×C311yescharacteristic
45#1443C2×C312yes—
46#1442C2×C311yescharacteristic
47#1442C2×C312yes—
48#1441C2×C311yescharacteristic
49#1436C2×C312yes—
50#1436C2×C312yes—
51C23×C3×C4C2311yescharacteristic
52C23×C3×C4C2311yescharacteristic
53C23×C3×C4C2312yes—
54C23×C3×C4C2312yes—
55C23×C3×C4C2311yescharacteristic
56C23×C3×C4C2312yes—
57C23×C3×C4C2311yescharacteristic
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2312yes—
60C23×C3×C4C2311yescharacteristic
61C23×C3×C4C2311yescharacteristic
62C2×C3×C4⋊C4—22no—
63C2×C3×C4⋊C4—22no—
64C2×C3×C4⋊C4—24no—
65C2×C3×C4⋊C4—22no—
66C2×C3×C4⋊C4—22no—
67C2×C3×C4⋊C4—22no—
68C2×C3×C4⋊C4—22no—
69C2×C3×C4⋊C4—24no—
70C2×C3×C4⋊C4—22no—
71C2×C3×C4⋊C4—22no—
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—24no—
75C2×C3×C4⋊C4—24no—
76C2×C3×C42—24no—
77C2×C3×C42—22no—
78C2×C3×C42—24no—
79C2×C3×C42—24no—
80C2×C3×C42—22no—
81C2×C3×C42D414yes—
82C3×#95—24no—
83C3×#95—22no—
84C3×#95—22no—
85C3×#95—22no—
86C3×#95—22no—
87C3×#95—22no—
88C3×#95—24no—
89C3×#95—24no—
90C3×#95—24no—
91C3×#95—24no—
92C3×#95—24no—
93C3×#95—24no—
94C3×#95—24no—
95C3×#95—24no—
96C3×#95—24no—
97C3×#95D414yes—
98C22×C4⋊C4C22×C311yescharacteristic
99C22×C4⋊C4C22×C311yescharacteristic
100C22×C4⋊C4C22×C312yes—
101C22×C4⋊C4C22×C311yescharacteristic
102C22×C4⋊C4C22×C311yescharacteristic
103C22×C42C22×C312yes—
104C22×C42C22×C311yescharacteristic
105#400—24no—
106#389—24no—
107#387—24no—
108#376—24no—
109C2×#95C22×C312yes—
110C2×#95C22×C312yes—
111C2×#95C22×C311yescharacteristic
112C2×#95C22×C311yescharacteristic
113C2×#95C22×C312yes—
114C2×#95C22×C312yes—
115C2×#95C22×C312yes—
116C2×#95C22×C312yes—
117C2×#95C22×C312yes—
118C2×#95C22×C312yes—
119C2×#95C22×C311yescharacteristic
120C2×#95C22×C312yes—
121C2×#95C22×C312yes—
122C2×#95C22×C311yescharacteristic
123C2×#95C22×C311yescharacteristic
124C2×#95C22×C311yescharacteristic
125C24×C3C2411yescharacteristic
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—22no—
129C22×C3×C4—22no—
130C22×C3×C4—22no—
131C22×C3×C4—21no—
132C22×C3×C4—22no—
133C22×C3×C4—21no—
134C22×C3×C4—21no—
135C22×C3×C4—21no—
136C22×C3×C4—22no—
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—22no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—22no—
144C22×C3×C4—21no—
145C22×C3×C4—22no—
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—22no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—22no—
154C22×C3×C4—22no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—22no—
159C22×C3×C4—22no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—22no—
163C22×C3×C4—22no—
164C22×C3×C4—22no—
165C22×C3×C4—21no—
166C22×C3×C4—22no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—22no—
170C22×C3×C4—22no—
171C22×C3×C4—22no—
172C22×C3×C4—22no—
173C22×C3×C4—22no—
174C22×C3×C4—22no—
175C22×C3×C4—22no—
176C22×C3×C4—21no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4C2×D414yes—
183C22×C3×C4C2×D412yes—
184C22×C3×C4C2×D412yes—
185C22×C3×C4C2×D412yes—
186C22×C3×C4C2×D412yes—
187C22×C3×C4#4114yes—
188C22×C3×C4#4114yes—
189C22×C3×C4#4112yes—
190C22×C3×C4#4112yes—
191C22×C3×C4#4112yes—
192C22×C3×C4#4114yes—
193C3×C4⋊C4—28no—
194C3×C4⋊C4—28no—
195C3×C4⋊C4—44no—
196C3×C4⋊C4—44no—
197C3×C4⋊C4—48no—
198C3×C42—216no—
199C3×C42—28no—
200C23×C4C23×C312yes—
201C23×C4C23×C311yescharacteristic
202C23×C4C23×C311yescharacteristic
203C23×C4C23×C311yescharacteristic
204C23×C4C23×C312yes—
205C23×C4C23×C311yescharacteristic
206C23×C4C23×C312yes—
207C23×C4C23×C311yescharacteristic
208C23×C4C23×C312yes—
209C23×C4C23×C311yescharacteristic
210C23×C4C23×C311yescharacteristic
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—24no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—24no—
224C2×C4⋊C4—24no—
225C2×C42—24no—
226C2×C42—22no—
227C2×C42—24no—
228C2×C42—24no—
229C2×C42—22no—
230C2×C42C3×D414yes—
231#95—24no—
232#95—22no—
233#95—22no—
234#95—22no—
235#95—22no—
236#95—22no—
237#95—24no—
238#95—24no—
239#95—24no—
240#95—24no—
241#95—24no—
242#95—24no—
243#95—24no—
244#95—24no—
245#95—24no—
246#95C3×D414yes—
247C23×C3C22×D411yescharacteristic
248C23×C3C22×D411yescharacteristic
249C23×C3C2×#4111yescharacteristic
250C23×C3C2×#4112yes—
251C23×C3C2×#4112yes—
252C23×C3C2×#4111yescharacteristic
253C23×C3C2×#4111yescharacteristic
254C23×C3C2×#4112yes—
255C23×C32−1+412yes—
256C23×C32−1+411yescharacteristic
257C23×C32−1+411yescharacteristic
258C2×C3×C4—22no—
259C2×C3×C4—24no—
260C2×C3×C4—22no—
261C2×C3×C4—24no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—24no—
265C2×C3×C4—24no—
266C2×C3×C4—22no—
267C2×C3×C4—24no—
268C2×C3×C4—24no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—24no—
272C2×C3×C4—22no—
273C2×C3×C4—24no—
274C2×C3×C4—24no—
275C2×C3×C4—22no—
276C2×C3×C4—24no—
277C2×C3×C4—24no—
278C2×C3×C4—22no—
279C2×C3×C4—24no—
280C2×C3×C4—22no—
281C2×C3×C4—24no—
282C2×C3×C4—24no—
283C2×C3×C4—41no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—42no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—42no—
294C2×C3×C4—42no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—42no—
298C2×C3×C4—41no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—41no—
302C2×C3×C4—42no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—42no—
306C2×C3×C4—42no—
307C2×C3×C4—41no—
308C2×C3×C4—42no—
309C2×C3×C4—42no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—42no—
313C2×C3×C4—42no—
314C2×C3×C4—42no—
315C2×C3×C4—42no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—42no—
320C2×C3×C4—42no—
321C2×C3×C4—42no—
322C2×C3×C4—42no—
323C2×C3×C4#12114yes—
324C2×C3×C4#12414yes—
325C24C24×C311yescharacteristic
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4C2×C3×D414yes—
383C22×C4C2×C3×D412yes—
384C22×C4C2×C3×D412yes—
385C22×C4C2×C3×D412yes—
386C22×C4C2×C3×D412yes—
387C22×C4C3×#4114yes—
388C22×C4C3×#4114yes—
389C22×C4C3×#4112yes—
390C22×C4C3×#4112yes—
391C22×C4C3×#4112yes—
392C22×C4C3×#4114yes—
393C4⋊C4—28no—
394C4⋊C4—28no—
395C4⋊C4—44no—
396C4⋊C4—44no—
397C4⋊C4—48no—
398C42—216no—
399C42—28no—
400C22×C3C2×#12111yescharacteristic
401C22×C3#52512yes—
402C22×C3#52511yescharacteristic
403C22×C3#52511yescharacteristic
404C22×C3C2×#12411yescharacteristic
405C22×C3#52912yes—
406C22×C3#52912yes—
407C22×C3#52912yes—
408C22×C3#53211yescharacteristic
409C22×C3#53611yescharacteristic
410C22×C3#53611yescharacteristic
411C22×C3#54112yes—
412C22×C3#54112yes—
413C22×C3#54712yes—
414C22×C3#54711yescharacteristic
415C22×C3#54811yescharacteristic
416C22×C3#55212yes—
417C22×C3#55212yes—
418C22×C3#55212yes—
419C22×C3#55212yes—
420C22×C3#55211yescharacteristic
421C22×C3#55612yes—
422C22×C3#55611yescharacteristic
423C3×C4—24no—
424C3×C4—24no—
425C3×C4—42no—
426C3×C4—44no—
427C3×C4—42no—
428C3×C4—42no—
429C3×C4—44no—
430C3×C4—44no—
431C3×C4—82no—
432C3×C4—81no—
433C3×C4—81no—
434C23C22×C3×D411yescharacteristic
435C23C22×C3×D411yescharacteristic
436C23C2×C3×#4111yescharacteristic
437C23C2×C3×#4112yes—
438C23C2×C3×#4112yes—
439C23C2×C3×#4111yescharacteristic
440C23C2×C3×#4111yescharacteristic
441C23C2×C3×#4112yes—
442C23C3×2−1+412yes—
443C23C3×2−1+411yescharacteristic
444C23C3×2−1+411yescharacteristic
445C2×C4—22no—
446C2×C4—24no—
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4C3×#12114yes—
511C2×C4C3×#12414yes—
512C2×C3#239811yescharacteristic
513C2×C3#241311yescharacteristic
514C2×C3#241511yescharacteristic
515C2×C3#247512yes—
516C2×C3#247812yes—
517C2×C3#252812yes—
518C2×C3#253312yes—
519C2×C3#260411yescharacteristic
520C2×C3#261111yescharacteristic
521C2×C3#264211yescharacteristic
522C2×C3#285011yescharacteristic
523C22C2×C3×#12111yescharacteristic
524C22C3×#52511yescharacteristic
525C22C3×#52511yescharacteristic
526C22C3×#52512yes—
527C22C2×C3×#12411yescharacteristic
528C22C3×#52912yes—
529C22C3×#52912yes—
530C22C3×#52912yes—
531C22C3×#53211yescharacteristic
532C22C3×#53611yescharacteristic
533C22C3×#53611yescharacteristic
534C22C3×#54112yes—
535C22C3×#54112yes—
536C22C3×#54712yes—
537C22C3×#54711yescharacteristic
538C22C3×#54811yescharacteristic
539C22C3×#55212yes—
540C22C3×#55211yescharacteristic
541C22C3×#55212yes—
542C22C3×#55212yes—
543C22C3×#55212yes—
544C22C3×#55611yescharacteristic
545C22C3×#55612yes—
546C4—24no—
547C4—24no—
548C4—44no—
549C4—42no—
550C4—42no—
551C4—44no—
552C4—44no—
553C4—42no—
554C4—81no—
555C4—82no—
556C4—81no—
557C3#1490811yescharacteristic, direct product factor, Sylow
558C2C3×#239811yescharacteristic
559C2C3×#241311yescharacteristic
560C2C3×#241511yescharacteristic
561C2C3×#247512yes—
562C2C3×#247812yes—
563C2C3×#252812yes—
564C2C3×#253312yes—
565C2C3×#260411yescharacteristic
566C2C3×#261111yescharacteristic
567C2C3×#264211yescharacteristic
568C2C3×#285011yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C3C24
commutator, Frattini, cosocleC24C24×C3
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
12. #14908C3direct (N × H)
557. C3#14908direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4002
C2×C3×#3892
C2×C3×#3872
C2×C3×#3762
C3×#14452
C3×#14432
C3×#14422
C3×#14412
C3×#14362
#149083