Finite Group Databasebeta

← C3×#14649 #10633256

Subgroups — C3×#14649 #10633256

Order 768.

1290 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×#393C211yesmaximal, characteristic
2C3×#1446C212yesmaximal, complemented
3C3×#1443C212yesmaximal, complemented
4C3×#1442C212yesmaximal, complemented
5C3×#1440C212yesmaximal
6C3×#1440C211yesmaximal, characteristic
7C3×#1439C212yesmaximal
8C3×#1437C211yesmaximal, characteristic
9C3×#1436C212yesmaximal, complemented
10#14649C311yesmaximal, characteristic, direct product factor, Sylow
11C23×C3×Q8C2211yescharacteristic
12C22×C3×C4⋊C4C2212yes—
13C22×C3×C22⋊C4C2212yes—
14C22×C3×C22⋊C4C2211yescharacteristic
15C22×C3×C22⋊C4C2211yescharacteristic
16C22×C3×C22⋊C4C2211yescharacteristic
17C22×C3×C22⋊C4C2212yes—
18C22×C3×C42C2211yescharacteristic
19C3×#393C418yescomplemented
20C2×C3×#95C2212yes—
21C2×C3×#95C2212yes—
22C2×C3×#95C2212yes—
23C2×C3×#95C2212yes—
24C2×C3×#95C2212yes—
25C2×C3×#95C2211yescharacteristic
26C2×C3×#95C2212yes—
27C2×C3×#95C2212yes—
28C2×C3×#95C2212yes—
29C2×C3×#95C2212yes—
30C2×C3×#95C2212yes—
31C2×C3×#95C2212yes—
32C2×C3×#95C2211yescharacteristic
33C2×#393C2×C311yescharacteristic
34#1446C2×C312yescomplemented
35#1443C2×C312yescomplemented
36#1442C2×C312yescomplemented
37#1440C2×C312yes—
38#1440C2×C311yescharacteristic
39#1439C2×C312yes—
40#1437C2×C311yescharacteristic
41#1436C2×C312yescomplemented
42C25×C3C2311yescharacteristic
43C22×C3×Q8—42no—
44C22×C3×Q8—41no—
45C22×C3×Q8—42no—
46C22×C3×Q8—41no—
47C22×C3×Q8C2×C414yes—
48C23×C3×C4C2312yes—
49C23×C3×C4C2312yes—
50C23×C3×C4C2312yes—
51C23×C3×C4C2312yes—
52C23×C3×C4C2311yescharacteristic
53C23×C3×C4C2311yescharacteristic
54C23×C3×C4C2312yes—
55C23×C3×C4C2312yes—
56C2×C3×C4⋊C4—24no—
57C2×C3×C4⋊C4—42no—
58C2×C3×C4⋊C4—42no—
59C2×C3×C22⋊C4—24no—
60C2×C3×C22⋊C4—41no—
61C2×C3×C22⋊C4—42no—
62C2×C3×C22⋊C4—41no—
63C2×C3×C22⋊C4—42no—
64C2×C3×C22⋊C4—42no—
65C2×C3×C22⋊C4—42no—
66C2×C3×C22⋊C4—41no—
67C2×C3×C22⋊C4—42no—
68C2×C3×C22⋊C4—41no—
69C2×C3×C22⋊C4—42no—
70C2×C3×C22⋊C4C2×C414yes—
71C2×C3×C22⋊C4C2×C418yes—
72C2×C3×C42—41no—
73C2×C3×C42—42no—
74C3×#95—24no—
75C3×#95—42no—
76C3×#95—42no—
77C3×#95—42no—
78C3×#95—41no—
79C3×#95—42no—
80C3×#95—42no—
81C3×#95—42no—
82C3×#95—42no—
83C3×#95—42no—
84C3×#95—42no—
85C3×#95C2×C418yes—
86C3×#95C2×C414yes—
87C23×Q8C22×C311yescharacteristic
88C22×C4⋊C4C22×C312yes—
89C22×C22⋊C4C22×C312yes—
90C22×C22⋊C4C22×C311yescharacteristic
91C22×C22⋊C4C22×C311yescharacteristic
92C22×C22⋊C4C22×C311yescharacteristic
93C22×C22⋊C4C22×C312yes—
94C22×C42C22×C311yescharacteristic
95#393C3×C418yescomplemented
96C2×#95C22×C312yes—
97C2×#95C22×C312yes—
98C2×#95C22×C312yes—
99C2×#95C22×C312yes—
100C2×#95C22×C312yes—
101C2×#95C22×C311yescharacteristic
102C2×#95C22×C312yes—
103C2×#95C22×C312yes—
104C2×#95C22×C312yes—
105C2×#95C22×C312yes—
106C2×#95C22×C312yes—
107C2×#95C22×C312yes—
108C2×#95C22×C311yescharacteristic
109C24×C3—22no—
110C24×C3—22no—
111C24×C3—22no—
112C24×C3—21no—
113C24×C3—21no—
114C24×C3—22no—
115C24×C3—22no—
116C24×C3—22no—
117C24×C3C22×C412yes—
118C24×C3C2411yescharacteristic
119C2×C3×Q8—44no—
120C2×C3×Q8—48no—
121C2×C3×Q8—48no—
122C2×C3×Q8—44no—
123C2×C3×Q8—44no—
124C22×C3×C4—22no—
125C22×C3×C4—22no—
126C22×C3×C4—22no—
127C22×C3×C4—22no—
128C22×C3×C4—22no—
129C22×C3×C4—21no—
130C22×C3×C4—22no—
131C22×C3×C4—22no—
132C22×C3×C4—22no—
133C22×C3×C4—22no—
134C22×C3×C4—22no—
135C22×C3×C4—22no—
136C22×C3×C4—22no—
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—21no—
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—21no—
147C22×C3×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—22no—
150C22×C3×C4—22no—
151C22×C3×C4—22no—
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×C4C22×C414yes—
172C22×C3×C4C22×C412yes—
173C22×C3×C4C22×C412yes—
174C22×C3×C4C22×C414yes—
175C22×C3×C4#4114yes—
176C3×C4⋊C4—48no—
177C3×C22⋊C4—48no—
178C3×C22⋊C4—44no—
179C3×C22⋊C4—48no—
180C3×C22⋊C4—44no—
181C3×C22⋊C4—44no—
182C3×C42—44no—
183C25C23×C311yescharacteristic
184C22×Q8—41no—
185C22×Q8—42no—
186C22×Q8—41no—
187C22×Q8—42no—
188C22×Q8C2×C3×C414yes—
189C23×C4C23×C312yes—
190C23×C4C23×C312yes—
191C23×C4C23×C312yes—
192C23×C4C23×C312yes—
193C23×C4C23×C311yescharacteristic
194C23×C4C23×C312yes—
195C23×C4C23×C311yescharacteristic
196C23×C4C23×C312yes—
197C2×C4⋊C4—24no—
198C2×C4⋊C4—42no—
199C2×C4⋊C4—42no—
200C2×C22⋊C4—24no—
201C2×C22⋊C4—41no—
202C2×C22⋊C4—42no—
203C2×C22⋊C4—41no—
204C2×C22⋊C4—42no—
205C2×C22⋊C4—42no—
206C2×C22⋊C4—42no—
207C2×C22⋊C4—41no—
208C2×C22⋊C4—41no—
209C2×C22⋊C4—42no—
210C2×C22⋊C4—42no—
211C2×C22⋊C4C2×C3×C414yes—
212C2×C22⋊C4C2×C3×C418yes—
213C2×C42—41no—
214C2×C42—42no—
215#95—24no—
216#95—42no—
217#95—42no—
218#95—42no—
219#95—41no—
220#95—42no—
221#95—42no—
222#95—42no—
223#95—42no—
224#95—42no—
225#95—42no—
226#95C2×C3×C418yes—
227#95C2×C3×C414yes—
228C23×C3—22no—
229C23×C3—22no—
230C23×C3—24no—
231C23×C3—22no—
232C23×C3—24no—
233C23×C3—42no—
234C23×C3—42no—
235C23×C3—42no—
236C23×C3—42no—
237C23×C3—42no—
238C23×C3—42no—
239C23×C3—42no—
240C23×C3—41no—
241C23×C3—41no—
242C23×C3—41no—
243C23×C3—42no—
244C23×C3—42no—
245C23×C3—42no—
246C23×C3—42no—
247C23×C3—42no—
248C23×C3—41no—
249C23×C3C23×C411yescharacteristic
250C23×C3C2×#4112yes—
251C23×C3H(5,𝔽2)12yes—
252C23×C3H(5,𝔽2)12yes—
253C23×C3H(5,𝔽2)11yescharacteristic
254C23×C3H(5,𝔽2)11yescharacteristic
255C23×C3H(5,𝔽2)12yes—
256C23×C32−1+412yes—
257C23×C32−1+412yes—
258C3×Q8—416no—
259C2×C3×C4—24no—
260C2×C3×C4—24no—
261C2×C3×C4—22no—
262C2×C3×C4—22no—
263C2×C3×C4—24no—
264C2×C3×C4—24no—
265C2×C3×C4—24no—
266C2×C3×C4—24no—
267C2×C3×C4—24no—
268C2×C3×C4—24no—
269C2×C3×C4—24no—
270C2×C3×C4—24no—
271C2×C3×C4—24no—
272C2×C3×C4—42no—
273C2×C3×C4—42no—
274C2×C3×C4—42no—
275C2×C3×C4—42no—
276C2×C3×C4—42no—
277C2×C3×C4—42no—
278C2×C3×C4—42no—
279C2×C3×C4—42no—
280C2×C3×C4—41no—
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—42no—
292C2×C3×C4—42no—
293C2×C3×C4—42no—
294C2×C3×C4—42no—
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—
311C24—22no—
312C24—21no—
313C24—22no—
314C24—21no—
315C24—22no—
316C24—22no—
317C24—22no—
318C24—22no—
319C24C22×C3×C412yes—
320C24C24×C311yescharacteristic
321C2×Q8—48no—
322C2×Q8—44no—
323C2×Q8—48no—
324C2×Q8—44no—
325C2×Q8—44no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—22no—
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×C4C22×C3×C414yes—
374C22×C4C22×C3×C412yes—
375C22×C4C22×C3×C414yes—
376C22×C4C22×C3×C412yes—
377C22×C4C3×#4114yes—
378C4⋊C4—48no—
379C22⋊C4—48no—
380C22⋊C4—44no—
381C22⋊C4—48no—
382C22⋊C4—44no—
383C22⋊C4—44no—
384C42—44no—
385C22×C3—42no—
386C22×C3—44no—
387C22×C3—42no—
388C22×C3—44no—
389C22×C3—42no—
390C22×C3—82no—
391C22×C3—82no—
392C22×C3—82no—
393C22×C3—82no—
394C22×C3C4×#4111yescharacteristic
395C22×C3#51811yescharacteristic
396C22×C3#51812yes—
397C22×C3#51911yescharacteristic
398C22×C3#52012yes—
399C22×C3#53812yes—
400C22×C3#53812yes—
401C22×C3#53912yes—
402C22×C3#54212yes—
403C22×C3#54212yes—
404C22×C3#54212yes—
405C22×C3#56012yes—
406C22×C3#56011yescharacteristic
407C22×C3H(3,𝔽4)11yescharacteristic
408C22×C3H(3,𝔽4)11yescharacteristic
409C22×C3#56212yes—
410C22×C3#56212yes—
411C22×C3#56212yes—
412C22×C3#56312yes—
413C22×C3#56312yes—
414C22×C3#56311yescharacteristic
415C3×C4—44no—
416C3×C4—44no—
417C3×C4—42no—
418C3×C4—44no—
419C3×C4—42no—
420C3×C4—82no—
421C3×C4—82no—
422C3×C4—82no—
423C23—22no—
424C23—24no—
425C23—22no—
426C23—22no—
427C23—24no—
428C23—42no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—41no—
438C23—42no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23C23×C3×C411yescharacteristic
445C23C2×C3×#4112yes—
446C23C3×H(5,𝔽2)11yescharacteristic
447C23C3×H(5,𝔽2)12yes—
448C23C3×H(5,𝔽2)11yescharacteristic
449C23C3×H(5,𝔽2)12yes—
450C23C3×H(5,𝔽2)12yes—
451C23C3×2−1+412yes—
452C23C3×2−1+412yes—
453Q8—416no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
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×C4—42no—
506C2×C3—82no—
507C2×C3#233211yescharacteristic
508C2×C3#233712yes—
509C2×C3#237511yescharacteristic
510C2×C3#237812yes—
511C2×C3#237911yescharacteristic
512C2×C3#282412yes—
513C2×C3#283012yes—
514C2×C3#283212yes—
515C2×C3#283812yes—
516C22—42no—
517C22—44no—
518C22—42no—
519C22—42no—
520C22—44no—
521C22—82no—
522C22—82no—
523C22—82no—
524C22—82no—
525C22C3×C4×#4111yescharacteristic
526C22C3×#51812yes—
527C22C3×#51811yescharacteristic
528C22C3×#51911yescharacteristic
529C22C3×#52012yes—
530C22C3×#53812yes—
531C22C3×#53812yes—
532C22C3×#53912yes—
533C22C3×#54212yes—
534C22C3×#54212yes—
535C22C3×#54212yes—
536C22C3×#56012yes—
537C22C3×#56011yescharacteristic
538C22C3×H(3,𝔽4)11yescharacteristic
539C22C3×H(3,𝔽4)11yescharacteristic
540C22C3×#56212yes—
541C22C3×#56212yes—
542C22C3×#56212yes—
543C22C3×#56312yes—
544C22C3×#56312yes—
545C22C3×#56311yescharacteristic
546C4—44no—
547C4—42no—
548C4—42no—
549C4—44no—
550C4—44no—
551C4—82no—
552C4—82no—
553C4—82no—
554C3#1464911yescharacteristic, direct product factor, Sylow
555C2—82no—
556C2C3×#233211yescharacteristic
557C2C3×#233712yes—
558C2C3×#237511yescharacteristic
559C2C3×#237812yes—
560C2C3×#237911yescharacteristic
561C2C3×#282412yes—
562C2C3×#283012yes—
563C2C3×#283212yes—
564C2C3×#283812yes—
subgroupG/H
center, socleC24×C3C24
commutatorC23C23×C3×C4
Frattini, cosocleC24C24×C3
prime radicalC25×C3C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#1446C2semidirect
3. C3×#1443C2semidirect
4. C3×#1442C2semidirect
9. C3×#1436C2semidirect
10. #14649C3direct (N × H)
19. C3×#393C4semidirect
34. #1446C2×C3semidirect
35. #1443C2×C3semidirect
36. #1442C2×C3semidirect
41. #1436C2×C3semidirect
95. #393C3×C4semidirect
554. C3#14649direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3932
C3×#14462
C3×#14432
C3×#14422
C3×#14402
C3×#14392
C3×#14372
C3×#14362
#146493