Finite Group Databasebeta

← C3×#15080 #10633687

Subgroups — C3×#15080 #10633687

Order 768.

1238 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×#387C212yesmaximal
2C2×C3×#387C211yesmaximal, characteristic
3C2×C3×C4×C4⋊C4C211yesmaximal, characteristic
4C3×#1444C211yesmaximal, characteristic
5C3×#1443C212yesmaximal
6C3×#1442C212yesmaximal
7C3×#1442C211yesmaximal, characteristic
8C3×#1441C211yesmaximal, characteristic
9C3×#1441C211yesmaximal, characteristic
10C3×#1434C212yesmaximal
11C3×#1434C211yesmaximal, characteristic
12#15080C311yesmaximal, 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×#387—28no—
21C3×#387—24no—
22C3×C4×C4⋊C4—24no—
23C2×C3×#95C2212yes—
24C2×C3×#95C2211yescharacteristic
25C2×C3×#95C2212yes—
26C2×C3×#95C2212yes—
27C2×C3×#95C2212yes—
28C2×C3×#95C2212yes—
29C2×C3×#95C2211yescharacteristic
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2212yes—
34C2×C3×#95C2212yes—
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2212yes—
37C2×C3×#95C2212yes—
38C2×C3×#95C2212yes—
39C2×#387C2×C311yescharacteristic
40C2×#387C2×C312yes—
41C2×C4×C4⋊C4C2×C311yescharacteristic
42#1444C2×C311yescharacteristic
43#1443C2×C312yes—
44#1442C2×C311yescharacteristic
45#1442C2×C312yes—
46#1441C2×C311yescharacteristic
47#1441C2×C311yescharacteristic
48#1434C2×C312yes—
49#1434C2×C311yescharacteristic
50C23×C3×C4C2312yes—
51C23×C3×C4C2311yescharacteristic
52C23×C3×C4C2311yescharacteristic
53C23×C3×C4C2311yescharacteristic
54C23×C3×C4C2311yescharacteristic
55C23×C3×C4C2311yescharacteristic
56C23×C3×C4C2312yes—
57C23×C3×C4C2312yes—
58C23×C3×C4C2312yes—
59C23×C3×C4C2311yescharacteristic
60C23×C3×C4C2311yescharacteristic
61C2×C3×C4⋊C4—22no—
62C2×C3×C4⋊C4—22no—
63C2×C3×C4⋊C4—24no—
64C2×C3×C4⋊C4—22no—
65C2×C3×C4⋊C4—24no—
66C2×C3×C4⋊C4—24no—
67C2×C3×C4⋊C4—24no—
68C2×C3×C4⋊C4—24no—
69C2×C3×C4⋊C4—22no—
70C2×C3×C4⋊C4—22no—
71C2×C3×C4⋊C4—22no—
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4D414yes—
74C2×C3×C42—22no—
75C2×C3×C42—22no—
76C2×C3×C42—24no—
77C2×C3×C42—24no—
78C2×C3×C42—24no—
79C2×C3×C42D414yes—
80C3×#95—24no—
81C3×#95—24no—
82C3×#95—24no—
83C3×#95—24no—
84C3×#95—22no—
85C3×#95—22no—
86C3×#95—24no—
87C3×#95—22no—
88C3×#95—22no—
89C3×#95—22no—
90C3×#95—24no—
91C3×#95—24no—
92C3×#95—24no—
93C3×#95—24no—
94C3×#95—24no—
95C3×#95—22no—
96C22×C4⋊C4C22×C311yescharacteristic
97C22×C4⋊C4C22×C311yescharacteristic
98C22×C4⋊C4C22×C311yescharacteristic
99C22×C4⋊C4C22×C312yes—
100C22×C4⋊C4C22×C311yescharacteristic
101C22×C42C22×C312yes—
102C22×C42C22×C311yescharacteristic
103#387—28no—
104#387—24no—
105C4×C4⋊C4—24no—
106C2×#95C22×C311yescharacteristic
107C2×#95C22×C312yes—
108C2×#95C22×C312yes—
109C2×#95C22×C312yes—
110C2×#95C22×C311yescharacteristic
111C2×#95C22×C311yescharacteristic
112C2×#95C22×C312yes—
113C2×#95C22×C312yes—
114C2×#95C22×C312yes—
115C2×#95C22×C312yes—
116C2×#95C22×C312yes—
117C2×#95C22×C311yescharacteristic
118C2×#95C22×C312yes—
119C2×#95C22×C312yes—
120C2×#95C22×C311yescharacteristic
121C2×#95C22×C311yescharacteristic
122C24×C3C2411yescharacteristic
123C22×C3×C4—21no—
124C22×C3×C4—21no—
125C22×C3×C4—22no—
126C22×C3×C4—22no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—22no—
130C22×C3×C4—21no—
131C22×C3×C4—22no—
132C22×C3×C4—22no—
133C22×C3×C4—22no—
134C22×C3×C4—22no—
135C22×C3×C4—21no—
136C22×C3×C4—22no—
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—22no—
143C22×C3×C4—22no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—22no—
150C22×C3×C4—22no—
151C22×C3×C4—22no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—22no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—22no—
158C22×C3×C4—22no—
159C22×C3×C4—22no—
160C22×C3×C4—22no—
161C22×C3×C4—21no—
162C22×C3×C4—22no—
163C22×C3×C4—21no—
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—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4C2×D412yes—
179C22×C3×C4C2×D412yes—
180C22×C3×C4C2×D412yes—
181C22×C3×C4C2×D412yes—
182C22×C3×C4C2×D412yes—
183C22×C3×C4C2×D412yes—
184C22×C3×C4#4114yes—
185C22×C3×C4#4114yes—
186C22×C3×C4#4114yes—
187C22×C3×C4#4112yes—
188C22×C3×C4#4112yes—
189C22×C3×C4#4112yes—
190C3×C4⋊C4—28no—
191C3×C4⋊C4—28no—
192C3×C4⋊C4—216no—
193C3×C4⋊C4—28no—
194C3×C4⋊C4—44no—
195C3×C42—28no—
196C3×C42—48no—
197C23×C4C23×C311yescharacteristic
198C23×C4C23×C312yes—
199C23×C4C23×C311yescharacteristic
200C23×C4C23×C311yescharacteristic
201C23×C4C23×C311yescharacteristic
202C23×C4C23×C311yescharacteristic
203C23×C4C23×C312yes—
204C23×C4C23×C312yes—
205C23×C4C23×C312yes—
206C23×C4C23×C311yescharacteristic
207C23×C4C23×C311yescharacteristic
208C2×C4⋊C4—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—24no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—24no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4—24no—
215C2×C4⋊C4—24no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4C3×D414yes—
221C2×C42—22no—
222C2×C42—22no—
223C2×C42—24no—
224C2×C42—24no—
225C2×C42—24no—
226C2×C42C3×D414yes—
227#95—24no—
228#95—24no—
229#95—24no—
230#95—24no—
231#95—22no—
232#95—22no—
233#95—24no—
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—22no—
243C23×C3C22×D411yescharacteristic
244C23×C3C22×D411yescharacteristic
245C23×C3C2×#4111yescharacteristic
246C23×C3C2×#4111yescharacteristic
247C23×C3C2×#4111yescharacteristic
248C23×C3C2×#4112yes—
249C23×C3C2×#4112yes—
250C23×C3C2×#4112yes—
251C23×C32−1+411yescharacteristic
252C23×C32−1+411yescharacteristic
253C23×C32−1+412yes—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—22no—
257C2×C3×C4—24no—
258C2×C3×C4—24no—
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—24no—
268C2×C3×C4—24no—
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—24no—
278C2×C3×C4—24no—
279C2×C3×C4—24no—
280C2×C3×C4—24no—
281C2×C3×C4—42no—
282C2×C3×C4—42no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—42no—
288C2×C3×C4—42no—
289C2×C3×C4—41no—
290C2×C3×C4—42no—
291C2×C3×C4—41no—
292C2×C3×C4—42no—
293C2×C3×C4—42no—
294C2×C3×C4—42no—
295C2×C3×C4—42no—
296C2×C3×C4—42no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—42no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—42no—
307C2×C3×C4—42no—
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—42no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4#12114yes—
320C2×C3×C4#12314yes—
321C24C24×C311yescharacteristic
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—21no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—21no—
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—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
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×#4114yes—
385C22×C4C3×#4114yes—
386C22×C4C3×#4112yes—
387C22×C4C3×#4112yes—
388C22×C4C3×#4112yes—
389C4⋊C4—28no—
390C4⋊C4—28no—
391C4⋊C4—216no—
392C4⋊C4—28no—
393C4⋊C4—44no—
394C42—28no—
395C42—48no—
396C22×C3C2×#12111yescharacteristic
397C22×C3C2×#12311yescharacteristic
398C22×C3#52511yescharacteristic
399C22×C3#52511yescharacteristic
400C22×C3#52512yes—
401C22×C3#52912yes—
402C22×C3#52912yes—
403C22×C3#52912yes—
404C22×C3#53211yescharacteristic
405C22×C3#53611yescharacteristic
406C22×C3#53611yescharacteristic
407C22×C3#54112yes—
408C22×C3#54112yes—
409C22×C3#54711yescharacteristic
410C22×C3#54711yescharacteristic
411C22×C3#54812yes—
412C22×C3#55212yes—
413C22×C3#55212yes—
414C22×C3#55211yescharacteristic
415C22×C3#55211yescharacteristic
416C22×C3#55212yes—
417C22×C3#55612yes—
418C22×C3#55612yes—
419C3×C4—24no—
420C3×C4—24no—
421C3×C4—42no—
422C3×C4—44no—
423C3×C4—44no—
424C3×C4—42no—
425C3×C4—42no—
426C3×C4—44no—
427C3×C4—81no—
428C3×C4—81no—
429C3×C4—82no—
430C23C22×C3×D411yescharacteristic
431C23C22×C3×D411yescharacteristic
432C23C2×C3×#4111yescharacteristic
433C23C2×C3×#4111yescharacteristic
434C23C2×C3×#4111yescharacteristic
435C23C2×C3×#4112yes—
436C23C2×C3×#4112yes—
437C23C2×C3×#4112yes—
438C23C3×2−1+411yescharacteristic
439C23C3×2−1+411yescharacteristic
440C23C3×2−1+412yes—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4C3×#12114yes—
507C2×C4C3×#12314yes—
508C2×C3#239211yescharacteristic
509C2×C3#246912yes—
510C2×C3#247512yes—
511C2×C3#248611yescharacteristic
512C2×C3#249911yescharacteristic
513C2×C3#252412yes—
514C2×C3#252812yes—
515C2×C3#253611yescharacteristic
516C2×C3#260411yescharacteristic
517C2×C3#263411yescharacteristic
518C2×C3#285311yescharacteristic
519C22C2×C3×#12111yescharacteristic
520C22C2×C3×#12311yescharacteristic
521C22C3×#52511yescharacteristic
522C22C3×#52512yes—
523C22C3×#52511yescharacteristic
524C22C3×#52912yes—
525C22C3×#52912yes—
526C22C3×#52912yes—
527C22C3×#53211yescharacteristic
528C22C3×#53611yescharacteristic
529C22C3×#53611yescharacteristic
530C22C3×#54112yes—
531C22C3×#54112yes—
532C22C3×#54711yescharacteristic
533C22C3×#54711yescharacteristic
534C22C3×#54812yes—
535C22C3×#55212yes—
536C22C3×#55212yes—
537C22C3×#55211yescharacteristic
538C22C3×#55211yescharacteristic
539C22C3×#55212yes—
540C22C3×#55612yes—
541C22C3×#55612yes—
542C4—24no—
543C4—24no—
544C4—42no—
545C4—44no—
546C4—44no—
547C4—42no—
548C4—42no—
549C4—44no—
550C4—82no—
551C4—81no—
552C4—81no—
553C3#1508011yescharacteristic, direct product factor, Sylow
554C2C3×#239211yescharacteristic
555C2C3×#246912yes—
556C2C3×#247512yes—
557C2C3×#248611yescharacteristic
558C2C3×#249911yescharacteristic
559C2C3×#252412yes—
560C2C3×#252812yes—
561C2C3×#253611yescharacteristic
562C2C3×#260411yescharacteristic
563C2C3×#263411yescharacteristic
564C2C3×#285311yescharacteristic
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. #15080C3direct (N × H)
553. C3#15080direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3872
C2×C3×C4×C4⋊C42
C3×#14442
C3×#14432
C3×#14422
C3×#14412
C3×#14342
#150803