Finite Group Databasebeta

← C3×#14748 #10633355

Subgroups — C3×#14748 #10633355

Order 768.

2254 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#396C211yesmaximal, characteristic, complemented
2C2×C3×#386C213yesmaximal
3C2×C3×#385C213yesmaximal, complemented
4C22×C3×#95C211yesmaximal, characteristic, complemented
5C3×#1443C211yesmaximal, characteristic, complemented
6C3×#1441C213yesmaximal, complemented
7C3×#1439C213yesmaximal, complemented
8#14748C311yesmaximal, characteristic, direct product factor, Sylow
9C23×C3×D4C2211yescharacteristic
10C24×C3×C4C2213yes—
11C22×C3×C4⋊C4C2213yes—
12C22×C3×C4⋊C4C2213yes—
13C22×C3×C22⋊C4C2213yes—
14C22×C3×C22⋊C4C2213yes—
15C22×C3×C22⋊C4C2213yes—
16C3×#396—24no—
17C3×#386—212no—
18C3×#385—212no—
19C2×C3×#95—24no—
20C2×C3×#95C2213yes—
21C2×C3×#95C2213yes—
22C2×C3×#95C2213yes—
23C2×C3×#95C2213yes—
24C2×C3×#95C2213yes—
25C2×C3×#95C2211yescharacteristic
26C2×#396C2×C311yescharacteristic, complemented
27C2×#386C2×C313yes—
28C2×#385C2×C313yescomplemented
29C22×#95C2×C311yescharacteristic, complemented
30#1443C2×C311yescharacteristic, complemented
31#1441C2×C313yescomplemented
32#1439C2×C313yescomplemented
33C25×C3C2311yescharacteristic
34C25×C3C2311yescharacteristic
35C22×C3×D4—26no—
36C22×C3×D4—26no—
37C22×C3×D4Q814yes—
38C23×C3×C4—26no—
39C23×C3×C4—26no—
40C23×C3×C4—26no—
41C23×C3×C4—26no—
42C23×C3×C4—26no—
43C23×C3×C4—43no—
44C23×C3×C4—43no—
45C23×C3×C4C2313yes—
46C23×C3×C4C2313yes—
47C23×C3×C4C2313yes—
48C23×C3×C4C2311yescharacteristic
49C23×C3×C4C2313yes—
50C2×C3×C4⋊C4—26no—
51C2×C3×C4⋊C4—26no—
52C2×C3×C4⋊C4—26no—
53C2×C3×C4⋊C4—26no—
54C2×C3×C4⋊C4—43no—
55C2×C3×C4⋊C4—43no—
56C2×C3×C22⋊C4—26no—
57C2×C3×C22⋊C4—26no—
58C2×C3×C22⋊C4—26no—
59C2×C3×C22⋊C4—26no—
60C2×C3×C22⋊C4—26no—
61C2×C3×C22⋊C4—26no—
62C2×C3×C22⋊C4—43no—
63C2×C3×C22⋊C4—43no—
64C2×C3×C22⋊C4D4112yes—
65C3×#95—26no—
66C3×#95—26no—
67C3×#95—26no—
68C3×#95—26no—
69C3×#95—26no—
70C3×#95D414yescomplemented
71C23×D4C22×C311yescharacteristic
72C24×C4C22×C313yes—
73C22×C4⋊C4C22×C313yes—
74C22×C4⋊C4C22×C313yes—
75C22×C22⋊C4C22×C313yes—
76C22×C22⋊C4C22×C313yes—
77C22×C22⋊C4C22×C313yes—
78#396—24no—
79#386—212no—
80#385—212no—
81C2×#95—24no—
82C2×#95C22×C313yes—
83C2×#95C22×C313yes—
84C2×#95C22×C313yes—
85C2×#95C22×C313yes—
86C2×#95C22×C313yes—
87C2×#95C22×C311yescharacteristic
88C24×C3—21no—
89C24×C3—23no—
90C24×C3—23no—
91C24×C3—21no—
92C24×C3—21no—
93C24×C3—23no—
94C24×C3—23no—
95C24×C3—23no—
96C24×C3—23no—
97C24×C3—21no—
98C24×C3C2×D416yes—
99C24×C3C2×Q812yes—
100C24×C3C2×Q812yes—
101C24×C3#4116yes—
102C24×C3C2411yescharacteristic
103C2×C3×D4—224no—
104C2×C3×D4—412no—
105C2×C3×D4—44no—
106C22×C3×C4—224no—
107C22×C3×C4—23no—
108C22×C3×C4—23no—
109C22×C3×C4—23no—
110C22×C3×C4—23no—
111C22×C3×C4—23no—
112C22×C3×C4—23no—
113C22×C3×C4—23no—
114C22×C3×C4—23no—
115C22×C3×C4—23no—
116C22×C3×C4—23no—
117C22×C3×C4—23no—
118C22×C3×C4—23no—
119C22×C3×C4—23no—
120C22×C3×C4—23no—
121C22×C3×C4—23no—
122C22×C3×C4—23no—
123C22×C3×C4—23no—
124C22×C3×C4—23no—
125C22×C3×C4—23no—
126C22×C3×C4—23no—
127C22×C3×C4—23no—
128C22×C3×C4—23no—
129C22×C3×C4—23no—
130C22×C3×C4—23no—
131C22×C3×C4—23no—
132C22×C3×C4—23no—
133C22×C3×C4—412no—
134C22×C3×C4—412no—
135C22×C3×C4—412no—
136C22×C3×C4—412no—
137C22×C3×C4—412no—
138C22×C3×C4—412no—
139C22×C3×C4C2×D416yes—
140C22×C3×C4C2×D416yes—
141C22×C3×C4C2×D416yes—
142C22×C3×C4C2×Q812yes—
143C22×C3×C4#4116yes—
144C3×C4⋊C4—412no—
145C3×C4⋊C4—412no—
146C3×C22⋊C4—224no—
147C3×C22⋊C4—412no—
148C3×C22⋊C4—412no—
149C25C23×C311yescharacteristic
150C25C23×C311yescharacteristic
151C22×D4—26no—
152C22×D4—26no—
153C22×D4C3×Q814yes—
154C23×C4—26no—
155C23×C4—26no—
156C23×C4—26no—
157C23×C4—26no—
158C23×C4—26no—
159C23×C4—43no—
160C23×C4—43no—
161C23×C4C23×C313yes—
162C23×C4C23×C313yes—
163C23×C4C23×C313yes—
164C23×C4C23×C311yescharacteristic
165C23×C4C23×C313yes—
166C2×C4⋊C4—26no—
167C2×C4⋊C4—26no—
168C2×C4⋊C4—26no—
169C2×C4⋊C4—26no—
170C2×C4⋊C4—43no—
171C2×C4⋊C4—43no—
172C2×C22⋊C4—26no—
173C2×C22⋊C4—26no—
174C2×C22⋊C4—26no—
175C2×C22⋊C4—26no—
176C2×C22⋊C4—26no—
177C2×C22⋊C4—26no—
178C2×C22⋊C4—43no—
179C2×C22⋊C4—43no—
180C2×C22⋊C4C3×D4112yes—
181#95—26no—
182#95—26no—
183#95—26no—
184#95—26no—
185#95—26no—
186#95C3×D414yescomplemented
187C23×C3—26no—
188C23×C3—26no—
189C23×C3—26no—
190C23×C3—26no—
191C23×C3—26no—
192C23×C3—26no—
193C23×C3—26no—
194C23×C3—26no—
195C23×C3—22no—
196C23×C3—26no—
197C23×C3—26no—
198C23×C3—22no—
199C23×C3—26no—
200C23×C3—43no—
201C23×C3—43no—
202C23×C3—41no—
203C23×C3—43no—
204C23×C3—43no—
205C23×C3—43no—
206C23×C3—43no—
207C23×C3—43no—
208C23×C3—43no—
209C23×C3—43no—
210C23×C3#121112yes—
211C23×C3C22⋊Q8112yes—
212C23×C3#12614yes—
213C23×C3C22×D413yes—
214C23×C3C22×D411yescharacteristic
215C23×C3C22×Q811yescharacteristic
216C23×C3C2×#4113yes—
217C23×C3C2×#4113yes—
218C23×C3H(5,𝔽2)13yes—
219C23×C32−1+411yescharacteristic
220C3×D4—416no—
221C2×C3×C4—26no—
222C2×C3×C4—26no—
223C2×C3×C4—26no—
224C2×C3×C4—26no—
225C2×C3×C4—26no—
226C2×C3×C4—26no—
227C2×C3×C4—26no—
228C2×C3×C4—26no—
229C2×C3×C4—26no—
230C2×C3×C4—26no—
231C2×C3×C4—26no—
232C2×C3×C4—26no—
233C2×C3×C4—26no—
234C2×C3×C4—448no—
235C2×C3×C4—43no—
236C2×C3×C4—43no—
237C2×C3×C4—43no—
238C2×C3×C4—43no—
239C2×C3×C4—41no—
240C2×C3×C4—43no—
241C2×C3×C4—43no—
242C2×C3×C4—43no—
243C2×C3×C4—43no—
244C2×C3×C4—43no—
245C2×C3×C4—43no—
246C2×C3×C4—43no—
247C2×C3×C4—43no—
248C2×C3×C4—43no—
249C2×C3×C4—43no—
250C2×C3×C4—43no—
251C2×C3×C4—43no—
252C2×C3×C4—43no—
253C24—21no—
254C24—23no—
255C24—23no—
256C24—21no—
257C24—21no—
258C24—23no—
259C24—23no—
260C24—23no—
261C24—23no—
262C24—21no—
263C24C2×C3×D416yes—
264C24C2×C3×Q812yes—
265C24C2×C3×Q812yes—
266C24C3×#4116yes—
267C24C24×C311yescharacteristic
268C2×D4—224no—
269C2×D4—412no—
270C2×D4—44no—
271C22×C4—224no—
272C22×C4—23no—
273C22×C4—23no—
274C22×C4—23no—
275C22×C4—23no—
276C22×C4—23no—
277C22×C4—23no—
278C22×C4—23no—
279C22×C4—23no—
280C22×C4—23no—
281C22×C4—23no—
282C22×C4—23no—
283C22×C4—23no—
284C22×C4—23no—
285C22×C4—23no—
286C22×C4—23no—
287C22×C4—23no—
288C22×C4—23no—
289C22×C4—23no—
290C22×C4—23no—
291C22×C4—23no—
292C22×C4—23no—
293C22×C4—23no—
294C22×C4—23no—
295C22×C4—23no—
296C22×C4—23no—
297C22×C4—23no—
298C22×C4—412no—
299C22×C4—412no—
300C22×C4—412no—
301C22×C4—412no—
302C22×C4—412no—
303C22×C4—412no—
304C22×C4C2×C3×D416yes—
305C22×C4C2×C3×D416yes—
306C22×C4C2×C3×D416yes—
307C22×C4C2×C3×Q812yes—
308C22×C4C3×#4116yes—
309C4⋊C4—412no—
310C4⋊C4—412no—
311C22⋊C4—224no—
312C22⋊C4—412no—
313C22⋊C4—412no—
314C22×C3—24no—
315C22×C3—24no—
316C22×C3—212no—
317C22×C3—212no—
318C22×C3—212no—
319C22×C3—212no—
320C22×C3—42no—
321C22×C3—46no—
322C22×C3—46no—
323C22×C3—81no—
324C22×C3—81no—
325C22×C3—83no—
326C22×C3—83no—
327C22×C3#39618yescomplemented
328C22×C3C2×#12113yes—
329C22×C3C2×C22⋊Q813yes—
330C22×C3#52513yes—
331C22×C3C2×#12611yescharacteristic
332C22×C3#52913yes—
333C22×C3#53813yes—
334C22×C3#53913yes—
335C22×C3D4213yes—
336C22×C3#54613yes—
337C22×C3#54613yes—
338C22×C3#54713yes—
339C22×C3D4×Q811yescharacteristic
340C22×C3#55413yes—
341C3×C4—42no—
342C3×C4—46no—
343C3×C4—46no—
344C3×C4—46no—
345C3×C4—46no—
346C23—26no—
347C23—26no—
348C23—26no—
349C23—26no—
350C23—26no—
351C23—26no—
352C23—26no—
353C23—26no—
354C23—22no—
355C23—26no—
356C23—26no—
357C23—22no—
358C23—26no—
359C23—43no—
360C23—43no—
361C23—41no—
362C23—43no—
363C23—43no—
364C23—43no—
365C23—43no—
366C23—43no—
367C23—43no—
368C23—43no—
369C23C3×#121112yes—
370C23C3×C22⋊Q8112yes—
371C23C3×#12614yes—
372C23C22×C3×D413yes—
373C23C22×C3×D411yescharacteristic
374C23C22×C3×Q811yescharacteristic
375C23C2×C3×#4113yes—
376C23C2×C3×#4113yes—
377C23C3×H(5,𝔽2)13yes—
378C23C3×2−1+411yescharacteristic
379D4—416no—
380C2×C4—26no—
381C2×C4—26no—
382C2×C4—26no—
383C2×C4—26no—
384C2×C4—26no—
385C2×C4—26no—
386C2×C4—26no—
387C2×C4—26no—
388C2×C4—26no—
389C2×C4—26no—
390C2×C4—26no—
391C2×C4—26no—
392C2×C4—26no—
393C2×C4—448no—
394C2×C4—43no—
395C2×C4—43no—
396C2×C4—43no—
397C2×C4—43no—
398C2×C4—41no—
399C2×C4—43no—
400C2×C4—43no—
401C2×C4—43no—
402C2×C4—43no—
403C2×C4—43no—
404C2×C4—43no—
405C2×C4—43no—
406C2×C4—43no—
407C2×C4—43no—
408C2×C4—43no—
409C2×C4—43no—
410C2×C4—43no—
411C2×C4—43no—
412C2×C3—28no—
413C2×C3—82no—
414C2×C3C2×#39611yescharacteristic
415C2×C3#242413yes—
416C2×C3#242513yes—
417C2×C3#244913yes—
418C2×C3#245013yes—
419C2×C3#264311yescharacteristic
420C2×C3#285211yescharacteristic
421C22—24no—
422C22—212no—
423C22—212no—
424C22—212no—
425C22—212no—
426C22—24no—
427C22—42no—
428C22—46no—
429C22—46no—
430C22—81no—
431C22—83no—
432C22—83no—
433C22—81no—
434C22C3×#39618yescomplemented
435C22C2×C3×#12113yes—
436C22C2×C3×C22⋊Q813yes—
437C22C3×#52513yes—
438C22C2×C3×#12611yescharacteristic
439C22C3×#52913yes—
440C22C3×#53813yes—
441C22C3×#53913yes—
442C22C3×D4213yes—
443C22C3×#54613yes—
444C22C3×#54613yes—
445C22C3×#54713yes—
446C22C3×D4×Q811yescharacteristic
447C22C3×#55413yes—
448C4—42no—
449C4—46no—
450C4—46no—
451C4—46no—
452C4—46no—
453C3#1474811yescharacteristic, direct product factor, Sylow
454C2—28no—
455C2—82no—
456C2C2×C3×#39611yescharacteristic
457C2C3×#242413yes—
458C2C3×#242513yes—
459C2C3×#244913yes—
460C2C3×#245013yes—
461C2C3×#264311yescharacteristic
462C2C3×#285211yescharacteristic
subgroupG/H
center, socleC24×C3C24
commutator, Frattini, cosocleC24C24×C3
prime radicalC23×C3×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#396C2semidirect
3. C2×C3×#385C2semidirect
4. C22×C3×#95C2semidirect
5. C3×#1443C2semidirect
6. C3×#1441C2semidirect
7. C3×#1439C2semidirect
8. #14748C3direct (N × H)
26. C2×#396C2×C3semidirect
28. C2×#385C2×C3semidirect
29. C22×#95C2×C3semidirect
30. #1443C2×C3semidirect
31. #1441C2×C3semidirect
32. #1439C2×C3semidirect
70. C3×#95D4semidirect
186. #95C3×D4semidirect
327. C22×C3#396semidirect
434. C22C3×#396semidirect
453. C3#14748direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3962
C2×C3×#3862
C2×C3×#3852
C22×C3×#952
C3×#14432
C3×#14412
C3×#14392
#147483