Finite Group Databasebeta

← C3×#14936 #10633543

Subgroups — C3×#14936 #10633543

Order 768.

1902 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#385C212yesmaximal
2C2×C3×#381C212yesmaximal
3C2×C3×#380C211yesmaximal, characteristic
4C22×C3×#95C211yesmaximal, characteristic
5C3×#1445C212yesmaximal, complemented
6C3×#1445C214yesmaximal, complemented
7C3×#1444C212yesmaximal, complemented
8C3×C22⋊#95C211yesmaximal, characteristic
9#14936C311yesmaximal, characteristic, direct product factor, Sylow
10C24×C3×C4C2211yescharacteristic
11C24×C3×C4C2211yescharacteristic
12C24×C3×C4C2211yescharacteristic
13C22×C3×C4⋊C4C2211yescharacteristic
14C22×C3×C4⋊C4C2214yes—
15C22×C3×C4⋊C4C2211yescharacteristic
16C22×C3×C22⋊C4C2212yes—
17C22×C3×C22⋊C4C2212yes—
18C3×#385—28no—
19C3×#381—28no—
20C3×#380—24no—
21C2×C3×#95—24no—
22C2×C3×#95C2212yes—
23C2×C3×#95C2212yes—
24C2×C3×#95C2212yes—
25C2×C3×#95C2214yes—
26C2×C3×#95C2214yes—
27C2×C3×#95C2214yes—
28C2×C3×#95C2212yes—
29C2×C3×#95C2212yes—
30C2×#385C2×C312yes—
31C2×#381C2×C312yes—
32C2×#380C2×C311yescharacteristic
33C22×#95C2×C311yescharacteristic
34#1445C2×C312yescomplemented
35#1445C2×C314yescomplemented
36#1444C2×C312yescomplemented
37C22⋊#95C2×C311yescharacteristic
38C25×C3C2311yescharacteristic
39C23×C3×C4—22no—
40C23×C3×C4—22no—
41C23×C3×C4—24no—
42C23×C3×C4—24no—
43C23×C3×C4—22no—
44C23×C3×C4—24no—
45C23×C3×C4—24no—
46C23×C3×C4—24no—
47C23×C3×C4—24no—
48C23×C3×C4—42no—
49C23×C3×C4—42no—
50C23×C3×C4D414yes—
51C23×C3×C4Q814yes—
52C23×C3×C4C2312yes—
53C23×C3×C4C2312yes—
54C23×C3×C4C2311yescharacteristic
55C23×C3×C4C2314yes—
56C23×C3×C4C2312yes—
57C23×C3×C4C2312yes—
58C23×C3×C4C2311yescharacteristic
59C2×C3×C4⋊C4—22no—
60C2×C3×C4⋊C4—22no—
61C2×C3×C4⋊C4—28no—
62C2×C3×C4⋊C4—28no—
63C2×C3×C4⋊C4—24no—
64C2×C3×C4⋊C4—44no—
65C2×C3×C4⋊C4—42no—
66C2×C3×C22⋊C4—24no—
67C2×C3×C22⋊C4—24no—
68C2×C3×C22⋊C4—24no—
69C2×C3×C22⋊C4—24no—
70C2×C3×C22⋊C4—24no—
71C2×C3×C22⋊C4D418yes—
72C3×#95—24no—
73C3×#95—24no—
74C3×#95—24no—
75C3×#95—28no—
76C3×#95—28no—
77C3×#95—28no—
78C3×#95—24no—
79C3×#95—42no—
80C24×C4C22×C311yescharacteristic
81C24×C4C22×C311yescharacteristic
82C24×C4C22×C311yescharacteristic
83C22×C4⋊C4C22×C311yescharacteristic
84C22×C4⋊C4C22×C314yes—
85C22×C4⋊C4C22×C311yescharacteristic
86C22×C22⋊C4C22×C312yes—
87C22×C22⋊C4C22×C312yes—
88#385—28no—
89#381—28no—
90#380—24no—
91C2×#95—24no—
92C2×#95C22×C312yes—
93C2×#95C22×C312yes—
94C2×#95C22×C314yes—
95C2×#95C22×C312yes—
96C2×#95C22×C312yes—
97C2×#95C22×C314yes—
98C2×#95C22×C314yes—
99C2×#95C22×C312yes—
100C24×C3—22no—
101C24×C3—22no—
102C24×C3—22no—
103C24×C3—22no—
104C24×C3C2×D414yes—
105C24×C3C2×D412yes—
106C24×C3C2×Q812yes—
107C24×C3#4112yes—
108C24×C3#4114yes—
109C24×C3C2411yescharacteristic
110C22×C3×C4—22no—
111C22×C3×C4—22no—
112C22×C3×C4—28no—
113C22×C3×C4—28no—
114C22×C3×C4—216no—
115C22×C3×C4—28no—
116C22×C3×C4—22no—
117C22×C3×C4—24no—
118C22×C3×C4—22no—
119C22×C3×C4—24no—
120C22×C3×C4—24no—
121C22×C3×C4—24no—
122C22×C3×C4—24no—
123C22×C3×C4—24no—
124C22×C3×C4—22no—
125C22×C3×C4—24no—
126C22×C3×C4—22no—
127C22×C3×C4—22no—
128C22×C3×C4—22no—
129C22×C3×C4—24no—
130C22×C3×C4—22no—
131C22×C3×C4—24no—
132C22×C3×C4—24no—
133C22×C3×C4—28no—
134C22×C3×C4—22no—
135C22×C3×C4—22no—
136C22×C3×C4—22no—
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—24no—
141C22×C3×C4—24no—
142C22×C3×C4—24no—
143C22×C3×C4—24no—
144C22×C3×C4—44no—
145C22×C3×C4—416no—
146C22×C3×C4—416no—
147C22×C3×C4—44no—
148C22×C3×C4—48no—
149C22×C3×C4—44no—
150C22×C3×C4—44no—
151C22×C3×C4—44no—
152C22×C3×C4C2×D412yes—
153C22×C3×C4C2×D418yes—
154C22×C3×C4C2×D412yes—
155C22×C3×C4C2×Q814yes—
156C22×C3×C4#4114yes—
157C22×C3×C4#4114yes—
158C3×C4⋊C4—416no—
159C3×C4⋊C4—44no—
160C3×C4⋊C4—44no—
161C3×C22⋊C4—216no—
162C3×C22⋊C4—48no—
163C25C23×C311yescharacteristic
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—24no—
167C23×C4—24no—
168C23×C4—22no—
169C23×C4—24no—
170C23×C4—24no—
171C23×C4—24no—
172C23×C4—24no—
173C23×C4—42no—
174C23×C4—42no—
175C23×C4C3×D414yes—
176C23×C4C3×Q814yes—
177C23×C4C23×C312yes—
178C23×C4C23×C312yes—
179C23×C4C23×C314yes—
180C23×C4C23×C311yescharacteristic
181C23×C4C23×C312yes—
182C23×C4C23×C312yes—
183C23×C4C23×C311yescharacteristic
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—28no—
187C2×C4⋊C4—28no—
188C2×C4⋊C4—24no—
189C2×C4⋊C4—44no—
190C2×C4⋊C4—42no—
191C2×C22⋊C4—24no—
192C2×C22⋊C4—24no—
193C2×C22⋊C4—24no—
194C2×C22⋊C4—24no—
195C2×C22⋊C4—24no—
196C2×C22⋊C4C3×D418yes—
197#95—24no—
198#95—24no—
199#95—24no—
200#95—28no—
201#95—28no—
202#95—28no—
203#95—24no—
204#95—42no—
205C23×C3—22no—
206C23×C3—22no—
207C23×C3—24no—
208C23×C3—24no—
209C23×C3—22no—
210C23×C3—22no—
211C23×C3—24no—
212C23×C3—24no—
213C23×C3—28no—
214C23×C3—28no—
215C23×C3—28no—
216C23×C3—28no—
217C23×C3C22⋊Q814yes—
218C23×C3C22⋊Q818yes—
219C23×C3#12318yes—
220C23×C3#12314yes—
221C23×C3#12714yes—
222C23×C3C22×D411yescharacteristic
223C23×C3C22×D412yes—
224C23×C3C22×Q811yescharacteristic
225C23×C3C2×#4111yescharacteristic
226C23×C3C2×#4112yes—
227C23×C3C2×#4112yes—
228C23×C3C2×#4112yes—
229C23×C3H(5,𝔽2)12yes—
230C23×C32−1+412yes—
231C2×C3×C4—22no—
232C2×C3×C4—22no—
233C2×C3×C4—28no—
234C2×C3×C4—24no—
235C2×C3×C4—28no—
236C2×C3×C4—28no—
237C2×C3×C4—22no—
238C2×C3×C4—22no—
239C2×C3×C4—24no—
240C2×C3×C4—22no—
241C2×C3×C4—28no—
242C2×C3×C4—28no—
243C2×C3×C4—28no—
244C2×C3×C4—416no—
245C2×C3×C4—416no—
246C2×C3×C4—44no—
247C2×C3×C4—42no—
248C2×C3×C4—44no—
249C2×C3×C4—42no—
250C2×C3×C4—42no—
251C2×C3×C4—42no—
252C2×C3×C4—44no—
253C2×C3×C4—44no—
254C2×C3×C4—44no—
255C2×C3×C4—44no—
256C2×C3×C4—44no—
257C2×C3×C4—416no—
258C2×C3×C4—42no—
259C2×C3×C4—42no—
260C2×C3×C4—42no—
261C2×C3×C4—42no—
262C2×C3×C4—42no—
263C2×C3×C4—42no—
264C2×C3×C4—44no—
265C2×C3×C4—44no—
266C2×C3×C4—44no—
267C2×C3×C4—44no—
268C2×C3×C4#12314yes—
269C24—22no—
270C24—22no—
271C24—22no—
272C24—22no—
273C24C2×C3×D414yes—
274C24C2×C3×D412yes—
275C24C2×C3×Q812yes—
276C24C3×#4112yes—
277C24C3×#4114yes—
278C24C24×C311yescharacteristic
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—28no—
282C22×C4—28no—
283C22×C4—216no—
284C22×C4—28no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—22no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—22no—
294C22×C4—24no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—24no—
299C22×C4—22no—
300C22×C4—24no—
301C22×C4—24no—
302C22×C4—28no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—24no—
310C22×C4—24no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—44no—
314C22×C4—416no—
315C22×C4—416no—
316C22×C4—44no—
317C22×C4—48no—
318C22×C4—44no—
319C22×C4—44no—
320C22×C4—44no—
321C22×C4C2×C3×D412yes—
322C22×C4C2×C3×D418yes—
323C22×C4C2×C3×D412yes—
324C22×C4C2×C3×Q814yes—
325C22×C4C3×#4114yes—
326C22×C4C3×#4114yes—
327C4⋊C4—416no—
328C4⋊C4—44no—
329C4⋊C4—44no—
330C22⋊C4—216no—
331C22⋊C4—48no—
332C22×C3—24no—
333C22×C3—24no—
334C22×C3—216no—
335C22×C3—216no—
336C22×C3—24no—
337C22×C3—24no—
338C22×C3—24no—
339C22×C3—24no—
340C22×C3#39918yes—
341C22×C3C2×C22⋊Q811yescharacteristic
342C22×C3C2×C22⋊Q812yes—
343C22×C3C2×#12311yescharacteristic
344C22×C3C2×#12312yes—
345C22×C3C2×#12311yescharacteristic
346C22×C3#52511yescharacteristic
347C22×C3#52912yes—
348C22×C3C2×#12711yescharacteristic
349C22×C3#53312yes—
350C22×C3#53411yescharacteristic
351C22×C3#53611yescharacteristic
352C22×C3#53912yes—
353C22×C3#54412yes—
354C22×C3#54614yes—
355C22×C3#54714yes—
356C22×C3#55114yes—
357C22×C3#55214yes—
358C3×C4—24no—
359C3×C4—44no—
360C3×C4—48no—
361C3×C4—42no—
362C3×C4—44no—
363C3×C4—82no—
364C3×C4—82no—
365C23—22no—
366C23—22no—
367C23—24no—
368C23—24no—
369C23—22no—
370C23—22no—
371C23—24no—
372C23—24no—
373C23—28no—
374C23—28no—
375C23—28no—
376C23—28no—
377C23C3×C22⋊Q814yes—
378C23C3×C22⋊Q818yes—
379C23C3×#12318yes—
380C23C3×#12314yes—
381C23C3×#12714yes—
382C23C22×C3×D411yescharacteristic
383C23C22×C3×D412yes—
384C23C22×C3×Q811yescharacteristic
385C23C2×C3×#4111yescharacteristic
386C23C2×C3×#4112yes—
387C23C2×C3×#4112yes—
388C23C2×C3×#4112yes—
389C23C3×H(5,𝔽2)12yes—
390C23C3×2−1+412yes—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—28no—
394C2×C4—24no—
395C2×C4—28no—
396C2×C4—28no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—24no—
400C2×C4—22no—
401C2×C4—28no—
402C2×C4—28no—
403C2×C4—28no—
404C2×C4—416no—
405C2×C4—416no—
406C2×C4—416no—
407C2×C4—44no—
408C2×C4—42no—
409C2×C4—44no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—44no—
425C2×C4—44no—
426C2×C4—44no—
427C2×C4—44no—
428C2×C4C3×#12314yes—
429C2×C3—28no—
430C2×C3C2×#39911yescharacteristic
431C2×C3#241914yes—
432C2×C3#243814yes—
433C2×C3#248311yescharacteristic
434C2×C3#248411yescharacteristic
435C2×C3#250111yescharacteristic
436C2×C3#253911yescharacteristic
437C2×C3#262711yescharacteristic
438C2×C3#285511yescharacteristic
439C22—24no—
440C22—216no—
441C22—216no—
442C22—24no—
443C22—24no—
444C22—24no—
445C22—24no—
446C22—24no—
447C22C3×#39918yes—
448C22C2×C3×C22⋊Q811yescharacteristic
449C22C2×C3×C22⋊Q812yes—
450C22C2×C3×#12312yes—
451C22C2×C3×#12311yescharacteristic
452C22C2×C3×#12311yescharacteristic
453C22C3×#52511yescharacteristic
454C22C3×#52912yes—
455C22C2×C3×#12711yescharacteristic
456C22C3×#53312yes—
457C22C3×#53411yescharacteristic
458C22C3×#53611yescharacteristic
459C22C3×#53912yes—
460C22C3×#54412yes—
461C22C3×#54614yes—
462C22C3×#54714yes—
463C22C3×#55114yes—
464C22C3×#55214yes—
465C4—24no—
466C4—44no—
467C4—48no—
468C4—42no—
469C4—44no—
470C4—82no—
471C4—82no—
472C3#1493611yescharacteristic, direct product factor, Sylow
473C2—28no—
474C2C2×C3×#39911yescharacteristic
475C2C3×#241914yes—
476C2C3×#243814yes—
477C2C3×#248311yescharacteristic
478C2C3×#248411yescharacteristic
479C2C3×#250111yescharacteristic
480C2C3×#253911yescharacteristic
481C2C3×#262711yescharacteristic
482C2C3×#285511yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC25×C3C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
5. C3×#1445C2semidirect
6. C3×#1445C2semidirect
7. C3×#1444C2semidirect
9. #14936C3direct (N × H)
34. #1445C2×C3semidirect
35. #1445C2×C3semidirect
36. #1444C2×C3semidirect
472. C3#14936direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3852
C2×C3×#3812
C2×C3×#3802
C22×C3×#952
C3×#14452
C3×#14442
C3×C22⋊#952
#149363