Finite Group Databasebeta

← C3×#15085 #10633692

Subgroups — C3×#15085 #10633692

Order 768.

1222 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#400C211yesmaximal, characteristic
2C2×C3×#398C211yesmaximal, characteristic
3C2×C3×#382C211yesmaximal, characteristic
4C2×C3×C4×C4⋊C4C211yesmaximal, characteristic
5C3×#1445C211yesmaximal, characteristic
6C3×#1445C211yesmaximal, characteristic
7C3×#1443C212yesmaximal
8C3×#1441C212yesmaximal
9C3×#1436C212yesmaximal
10C3×#1434C212yesmaximal
11C3×#1434C211yesmaximal, characteristic
12#15085C311yesmaximal, characteristic, direct product factor, Sylow
13C22×C3×C4⋊C4C2211yescharacteristic
14C22×C3×C4⋊C4C2212yes—
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C4⋊C4C2211yescharacteristic
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C42C2211yescharacteristic
19C22×C3×C42C2211yescharacteristic
20C22×C3×C42C2211yescharacteristic
21C3×#400—24no—
22C3×#398—24no—
23C3×#382—24no—
24C3×C4×C4⋊C4—24no—
25C2×C3×#95C2212yes—
26C2×C3×#95C2211yescharacteristic
27C2×C3×#95C2212yes—
28C2×C3×#95C2211yescharacteristic
29C2×C3×#95C2212yes—
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×#95C2212yes—
40C2×#400C2×C311yescharacteristic
41C2×#398C2×C311yescharacteristic
42C2×#382C2×C311yescharacteristic
43C2×C4×C4⋊C4C2×C311yescharacteristic
44#1445C2×C311yescharacteristic
45#1445C2×C311yescharacteristic
46#1443C2×C312yes—
47#1441C2×C312yes—
48#1436C2×C312yes—
49#1434C2×C312yes—
50#1434C2×C311yescharacteristic
51C23×C3×C4C2312yes—
52C23×C3×C4C2312yes—
53C23×C3×C4C2312yes—
54C23×C3×C4C2311yescharacteristic
55C23×C3×C4C2311yescharacteristic
56C23×C3×C4C2311yescharacteristic
57C23×C3×C4C2312yes—
58C23×C3×C4C2311yescharacteristic
59C23×C3×C4C2311yescharacteristic
60C23×C3×C4C2311yescharacteristic
61C23×C3×C4C2311yescharacteristic
62C2×C3×C4⋊C4—22no—
63C2×C3×C4⋊C4—22no—
64C2×C3×C4⋊C4—22no—
65C2×C3×C4⋊C4—22no—
66C2×C3×C4⋊C4—22no—
67C2×C3×C4⋊C4—22no—
68C2×C3×C4⋊C4—22no—
69C2×C3×C4⋊C4—22no—
70C2×C3×C4⋊C4—24no—
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×C4⋊C4D414yes—
77C2×C3×C42—22no—
78C2×C3×C42—22no—
79C2×C3×C42—22no—
80C2×C3×C42—24no—
81C2×C3×C42—22no—
82C2×C3×C42—24no—
83C2×C3×C42D414yes—
84C3×#95—22no—
85C3×#95—22no—
86C3×#95—24no—
87C3×#95—24no—
88C3×#95—22no—
89C3×#95—24no—
90C3×#95—22no—
91C3×#95—24no—
92C3×#95—24no—
93C3×#95—24no—
94C3×#95—24no—
95C3×#95—24no—
96C3×#95—24no—
97C3×#95—24no—
98C3×#95—24no—
99C22×C4⋊C4C22×C312yes—
100C22×C4⋊C4C22×C311yescharacteristic
101C22×C4⋊C4C22×C311yescharacteristic
102C22×C4⋊C4C22×C311yescharacteristic
103C22×C4⋊C4C22×C311yescharacteristic
104C22×C42C22×C311yescharacteristic
105C22×C42C22×C311yescharacteristic
106C22×C42C22×C311yescharacteristic
107#400—24no—
108#398—24no—
109#382—24no—
110C4×C4⋊C4—24no—
111C2×#95C22×C312yes—
112C2×#95C22×C311yescharacteristic
113C2×#95C22×C312yes—
114C2×#95C22×C311yescharacteristic
115C2×#95C22×C312yes—
116C2×#95C22×C312yes—
117C2×#95C22×C312yes—
118C2×#95C22×C312yes—
119C2×#95C22×C312yes—
120C2×#95C22×C312yes—
121C2×#95C22×C312yes—
122C2×#95C22×C312yes—
123C2×#95C22×C312yes—
124C2×#95C22×C311yescharacteristic
125C2×#95C22×C311yescharacteristic
126C24×C3C2411yescharacteristic
127C22×C3×C4—21no—
128C22×C3×C4—22no—
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—21no—
134C22×C3×C4—22no—
135C22×C3×C4—22no—
136C22×C3×C4—21no—
137C22×C3×C4—22no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—22no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—22no—
144C22×C3×C4—22no—
145C22×C3×C4—21no—
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—22no—
153C22×C3×C4—22no—
154C22×C3×C4—22no—
155C22×C3×C4—22no—
156C22×C3×C4—22no—
157C22×C3×C4—22no—
158C22×C3×C4—22no—
159C22×C3×C4—22no—
160C22×C3×C4—22no—
161C22×C3×C4—22no—
162C22×C3×C4—22no—
163C22×C3×C4—22no—
164C22×C3×C4—22no—
165C22×C3×C4—22no—
166C22×C3×C4—22no—
167C22×C3×C4—22no—
168C22×C3×C4—22no—
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—22no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4C2×D412yes—
180C22×C3×C4C2×D412yes—
181C22×C3×C4C2×D412yes—
182C22×C3×C4C2×D412yes—
183C22×C3×C4C2×D412yes—
184C22×C3×C4C2×D412yes—
185C22×C3×C4#4114yes—
186C22×C3×C4#4112yes—
187C22×C3×C4#4112yes—
188C22×C3×C4#4112yes—
189C22×C3×C4#4114yes—
190C22×C3×C4#4112yes—
191C22×C3×C4#4112yes—
192C3×C4⋊C4—28no—
193C3×C4⋊C4—28no—
194C3×C4⋊C4—44no—
195C3×C4⋊C4—44no—
196C3×C4⋊C4—48no—
197C3×C42—28no—
198C3×C42—28no—
199C3×C42—44no—
200C23×C4C23×C312yes—
201C23×C4C23×C312yes—
202C23×C4C23×C312yes—
203C23×C4C23×C311yescharacteristic
204C23×C4C23×C311yescharacteristic
205C23×C4C23×C312yes—
206C23×C4C23×C311yescharacteristic
207C23×C4C23×C311yescharacteristic
208C23×C4C23×C311yescharacteristic
209C23×C4C23×C311yescharacteristic
210C23×C4C23×C311yescharacteristic
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—24no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—24no—
224C2×C4⋊C4—24no—
225C2×C4⋊C4C3×D414yes—
226C2×C42—22no—
227C2×C42—22no—
228C2×C42—22no—
229C2×C42—24no—
230C2×C42—22no—
231C2×C42—24no—
232C2×C42C3×D414yes—
233#95—22no—
234#95—22no—
235#95—24no—
236#95—24no—
237#95—22no—
238#95—24no—
239#95—22no—
240#95—24no—
241#95—24no—
242#95—24no—
243#95—24no—
244#95—24no—
245#95—24no—
246#95—24no—
247#95—24no—
248C23×C3C22×D411yescharacteristic
249C23×C3C22×D411yescharacteristic
250C23×C3C2×#4111yescharacteristic
251C23×C3C2×#4112yes—
252C23×C3C2×#4111yescharacteristic
253C23×C3C2×#4111yescharacteristic
254C23×C3C2×#4111yescharacteristic
255C23×C3C2×#4111yescharacteristic
256C23×C3C2×#4112yes—
257C23×C32−1+412yes—
258C23×C32−1+412yes—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—24no—
270C2×C3×C4—24no—
271C2×C3×C4—24no—
272C2×C3×C4—24no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—24no—
279C2×C3×C4—24no—
280C2×C3×C4—22no—
281C2×C3×C4—24no—
282C2×C3×C4—24no—
283C2×C3×C4—24no—
284C2×C3×C4—24no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—42no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—42no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—42no—
296C2×C3×C4—42no—
297C2×C3×C4—42no—
298C2×C3×C4—42no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—42no—
302C2×C3×C4—42no—
303C2×C3×C4—42no—
304C2×C3×C4—42no—
305C2×C3×C4—42no—
306C2×C3×C4—42no—
307C2×C3×C4—42no—
308C2×C3×C4—42no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—42no—
312C2×C3×C4—42no—
313C2×C3×C4—42no—
314C2×C3×C4—42no—
315C2×C3×C4—42no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—42no—
320C2×C3×C4—42no—
321C2×C3×C4#12114yes—
322C2×C3×C4#12314yes—
323C2×C3×C4#12414yes—
324C24C24×C311yescharacteristic
325C22×C4—21no—
326C22×C4—22no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4C2×C3×D412yes—
378C22×C4C2×C3×D412yes—
379C22×C4C2×C3×D412yes—
380C22×C4C2×C3×D412yes—
381C22×C4C2×C3×D412yes—
382C22×C4C2×C3×D412yes—
383C22×C4C3×#4114yes—
384C22×C4C3×#4112yes—
385C22×C4C3×#4112yes—
386C22×C4C3×#4112yes—
387C22×C4C3×#4114yes—
388C22×C4C3×#4112yes—
389C22×C4C3×#4112yes—
390C4⋊C4—28no—
391C4⋊C4—28no—
392C4⋊C4—44no—
393C4⋊C4—44no—
394C4⋊C4—48no—
395C42—28no—
396C42—28no—
397C42—44no—
398C22×C3C2×#12111yescharacteristic
399C22×C3C2×#12311yescharacteristic
400C22×C3#52511yescharacteristic
401C22×C3#52511yescharacteristic
402C22×C3C2×#12411yescharacteristic
403C22×C3#52911yescharacteristic
404C22×C3#52911yescharacteristic
405C22×C3#52912yes—
406C22×C3#52912yes—
407C22×C3#53211yescharacteristic
408C22×C3#53211yescharacteristic
409C22×C3#53611yescharacteristic
410C22×C3#53611yescharacteristic
411C22×C3#54112yes—
412C22×C3#54112yes—
413C22×C3#54712yes—
414C22×C3#54812yes—
415C22×C3#55212yes—
416C22×C3#55212yes—
417C22×C3#55212yes—
418C22×C3#55212yes—
419C22×C3#55212yes—
420C22×C3#55612yes—
421C3×C4—24no—
422C3×C4—24no—
423C3×C4—24no—
424C3×C4—42no—
425C3×C4—42no—
426C3×C4—42no—
427C3×C4—42no—
428C3×C4—44no—
429C3×C4—82no—
430C3×C4—82no—
431C3×C4—82no—
432C23C22×C3×D411yescharacteristic
433C23C22×C3×D411yescharacteristic
434C23C2×C3×#4111yescharacteristic
435C23C2×C3×#4112yes—
436C23C2×C3×#4111yescharacteristic
437C23C2×C3×#4111yescharacteristic
438C23C2×C3×#4111yescharacteristic
439C23C2×C3×#4111yescharacteristic
440C23C2×C3×#4112yes—
441C23C3×2−1+412yes—
442C23C3×2−1+412yes—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4C3×#12114yes—
506C2×C4C3×#12314yes—
507C2×C4C3×#12414yes—
508C2×C3#239511yescharacteristic
509C2×C3#248411yescharacteristic
510C2×C3#248611yescharacteristic
511C2×C3#248912yes—
512C2×C3#251912yes—
513C2×C3#252412yes—
514C2×C3#252812yes—
515C2×C3#254511yescharacteristic
516C2×C3#261111yescharacteristic
517C2×C3#263411yescharacteristic
518C2×C3#285011yescharacteristic
519C22C2×C3×#12111yescharacteristic
520C22C2×C3×#12311yescharacteristic
521C22C3×#52511yescharacteristic
522C22C3×#52511yescharacteristic
523C22C2×C3×#12411yescharacteristic
524C22C3×#52912yes—
525C22C3×#52912yes—
526C22C3×#52911yescharacteristic
527C22C3×#52911yescharacteristic
528C22C3×#53211yescharacteristic
529C22C3×#53211yescharacteristic
530C22C3×#53611yescharacteristic
531C22C3×#53611yescharacteristic
532C22C3×#54112yes—
533C22C3×#54112yes—
534C22C3×#54712yes—
535C22C3×#54812yes—
536C22C3×#55212yes—
537C22C3×#55212yes—
538C22C3×#55212yes—
539C22C3×#55212yes—
540C22C3×#55212yes—
541C22C3×#55612yes—
542C4—24no—
543C4—24no—
544C4—24no—
545C4—42no—
546C4—42no—
547C4—42no—
548C4—44no—
549C4—42no—
550C4—82no—
551C4—82no—
552C4—82no—
553C3#1508511yescharacteristic, direct product factor, Sylow
554C2C3×#239511yescharacteristic
555C2C3×#248411yescharacteristic
556C2C3×#248611yescharacteristic
557C2C3×#248912yes—
558C2C3×#251912yes—
559C2C3×#252412yes—
560C2C3×#252812yes—
561C2C3×#254511yescharacteristic
562C2C3×#261111yescharacteristic
563C2C3×#263411yescharacteristic
564C2C3×#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. #15085C3direct (N × H)
553. C3#15085direct (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×#3982
C2×C3×#3822
C2×C3×C4×C4⋊C42
C3×#14452
C3×#14432
C3×#14412
C3×#14362
C3×#14342
#150853