Finite Group Databasebeta

← C2×C3×#4847 #11868332

Subgroups — C2×C3×#4847 #11868332

Order 1152.

965 conjugacy classes of subgroups.

The subgroup lattice has 455 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D12C211yesmaximal, characteristic
2C2×C3×#870C211yesmaximal, characteristic, complemented
3C2×C32×C4⋊C8C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic
5C2×C3×#821C211yesmaximal, characteristic
6C2×C3×#818C211yesmaximal, characteristic, complemented
7C2×C3×#817C211yesmaximal, characteristic, complemented
8C3×#4847C218yesmaximal, direct product factor
9C2×C3×#478—31nomaximal
10C2×#4847C311yesmaximal, characteristic, direct product factor
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3—21no—
13C22×C32×C8C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4—21no—
21C2×C3×Dic3⋊C4—21no—
22C3×C4×D12—22no—
23C3×C4×D12C2214yes—
24C3×#870—22no—
25C3×#870C2214yescomplemented
26C32×C4⋊C8C2214yescomplemented
27C3×#821C2214yes—
28C3×#821C2214yes—
29C3×#818C2214yescomplemented
30C3×#817C2214yescomplemented
31C2×C3×#125—31no—
32C2×C3×C4×D4—31no—
33C2×C4×D12C2×C311yescharacteristic
34C2×#870C2×C311yescharacteristic, complemented
35C3×#478—38no—
36C2×C3×#107—31no—
37C2×C3×#106—31no—
38C2×C3×C4⋊C8—21no—
39C2×C3×C4⋊C8D311yescharacteristic, complemented
40C2×C3×C4⋊C8C2×C311yescharacteristic, complemented
41C2×C3×#102—31no—
42C2×C3×#102—31no—
43C2×#821C2×C311yescharacteristic
44C2×#821C2×C311yescharacteristic
45C2×#818C2×C311yescharacteristic, complemented
46C2×#817C2×C311yescharacteristic, complemented
47#4847C2×C318yesdirect product factor
48C23×C3×D3—21no—
49C22×C32×C4D411yescharacteristic
50C22×C32×C4D411yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C2×C3×D12—21no—
56C2×C3×D12—22no—
57C2×C3×D12Q814yes—
58C2×C3×D12C2312yes—
59C2×C3×C4×D3—24no—
60C2×C3×C4×D3—44no—
61C2×C32×C8—22no—
62C2×C32×C8—22no—
63C2×C32×C8C2312yes—
64C2×C32×C8C2312yes—
65C32×C42D412yes—
66C32×C42C2312yes—
67C3×(C2×D3)⋊C4—24no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2312yes—
72C3×C4⋊Dic3C2312yes—
73C3×C4⋊Dic3C2312yes—
74C3×Dic3⋊C4—24no—
75C3×Dic3⋊C4—24no—
76C2×#478—31noSylow
77C22×C3×D4—31no—
78C23×C3×C4—61no—
79C22×D12C22×C311yescharacteristic
80C22×C4×D3—21no—
81C22×C3×C8—21no—
82C22×C3×C8—21no—
83C22×C3×C8C2×D311yescharacteristic
84C22×C3×C8C2×D311yescharacteristic
85C22×C3×C8C22×C311yescharacteristic
86C22×C3×C8C22×C311yescharacteristic
87C3×#125—34no—
88C3×#125—62no—
89C3×C4×D4—34no—
90C3×C4×D4—62no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4—61no—
95C2×C3×C4⋊C4—61no—
96C2×C3×C22⋊C4—61no—
97C2×C3×C42—21no—
98C2×C3×C42C2×D311yescharacteristic
99C2×C3×C42C22×C311yescharacteristic
100C2×(C2×D3)⋊C4—21no—
101C2×C4⋊Dic3C22×C311yescharacteristic
102C2×C4⋊Dic3C22×C311yescharacteristic
103C2×C4⋊Dic3C22×C311yescharacteristic
104C2×Dic3⋊C4—21no—
105C2×Dic3⋊C4—21no—
106C4×D12—22no—
107C4×D12C22×C314yes—
108#870—22no—
109#870C22×C314yescomplemented
110C3×#107—34no—
111C3×#106—34no—
112C3×C4⋊C8—24no—
113C3×C4⋊C8C2×D314yescomplemented
114C3×C4⋊C8C22×C314yescomplemented
115C3×#102—34no—
116C3×#102—34no—
117#821C22×C314yes—
118#821C22×C314yes—
119#818C22×C314yescomplemented
120#817C22×C314yescomplemented
121C23×C32C2×D411yescharacteristic
122C22×C3×D3—24no—
123C22×C3×D3—22no—
124C22×C3×D3—42no—
125C22×C3×D3—42no—
126C2×C32×C4—22no—
127C2×C32×C4—22no—
128C2×C32×C4C2×D412yes—
129C2×C32×C4C2×D412yes—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×Q812yes—
132C2×C32×C4#4112yes—
133C2×C32×C4C2411yescharacteristic
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—42no—
138C2×C3×Dic3—42no—
139C2×C3×Dic3—42no—
140C3×D12—24no—
141C3×D12—22no—
142C3×D12C2×Q814yes—
143C3×C4×D3—48no—
144C32×C8—22no—
145C32×C8—22no—
146C2×#125—31no—
147C2×C4×D4—31no—
148#478—38no—
149C2×#107—31no—
150C2×#106—31no—
151C2×C4⋊C8C3×D311yescharacteristic, complemented
152C2×#102—31no—
153C2×#102—31no—
154C24×C3—61no—
155C23×D3—21no—
156C2×C3×D4—34no—
157C2×C3×D4—32no—
158C2×C3×D4—61no—
159C2×C3×D4—62no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166C22×C3×C4—64no—
167C22×C3×C4—124no—
168C22×C3×C4D1211yescharacteristic
169C22×C3×C4D1211yescharacteristic
170C22×C3×C4C3×D411yescharacteristic
171C22×C3×C4C3×D411yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C23×C311yescharacteristic
174C22×Dic3—21no—
175C22×Dic3—21no—
176C22×Dic3—21no—
177C2×D12—21no—
178C2×D12—22no—
179C2×D12C3×Q814yes—
180C2×D12C23×C312yes—
181C2×C4×D3—24no—
182C2×C4×D3—44no—
183C2×C3×C8—22no—
184C2×C3×C8—22no—
185C2×C3×C8—22no—
186C2×C3×C8—22no—
187C2×C3×C8—22no—
188C2×C3×C8—22no—
189C2×C3×C8—42no—
190C2×C3×C8—42no—
191C2×C3×C8C22×D312yes—
192C2×C3×C8C22×D312yes—
193C2×C3×C8C23×C312yes—
194C2×C3×C8C23×C312yes—
195C3×C4⋊C4—32no—
196C3×C4⋊C4—32no—
197C3×C4⋊C4—32no—
198C3×C4⋊C4—64no—
199C3×C4⋊C4—64no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4—61no—
202C3×C4⋊C4—61no—
203C3×C22⋊C4—64no—
204C3×C42—22no—
205C3×C42—22no—
206C3×C42D1212yes—
207C3×C42C3×D412yes—
208C3×C42C22×D312yes—
209C3×C42C23×C312yes—
210(C2×D3)⋊C4—24no—
211C4⋊Dic3—21no—
212C4⋊Dic3—21no—
213C4⋊Dic3—21no—
214C4⋊Dic3C23×C312yes—
215C4⋊Dic3C23×C312yes—
216C4⋊Dic3C23×C312yes—
217Dic3⋊C4—24no—
218Dic3⋊C4—24no—
219C22×C32C22⋊Q812yes—
220C22×C32#13512yes—
221C22×C32AGL(1,ℤ/8)12yes—
222C22×C32C22×D411yescharacteristic
223C2×C3×D3—24no—
224C2×C3×D3—42no—
225C2×C3×D3—42no—
226C2×C3×D3—48no—
227C32×C4—22no—
228C32×C4—22no—
229C32×C4C22⋊Q812yes—
230C32×C4C22×Q811yescharacteristic
231C32×C4C2×#4111yescharacteristic
232C3×Dic3—42no—
233C3×Dic3—42no—
234C3×Dic3—42no—
235C22×D4—31no—
236C23×C4—61no—
237C22×C8C2×C3×D311yescharacteristic
238C22×C8C2×C3×D311yescharacteristic
239#125—34no—
240#125—62no—
241C4×D4—34no—
242C4×D4—62no—
243C2×C4⋊C4—31no—
244C2×C4⋊C4—31no—
245C2×C4⋊C4—31no—
246C2×C4⋊C4—61no—
247C2×C4⋊C4—61no—
248C2×C22⋊C4—61no—
249C2×C42C2×C3×D311yescharacteristic
250#107—34no—
251#106—34no—
252C4⋊C8C2×C3×D314yescomplemented
253#102—34no—
254#102—34no—
255C23×C3—21no—
256C23×C3—64no—
257C23×C3—62no—
258C23×C3—122no—
259C23×C3—122no—
260C23×C3C2×D1211yescharacteristic
261C23×C3C2×C3×D411yescharacteristic
262C22×D3—24no—
263C22×D3—22no—
264C22×D3—42no—
265C22×D3—42no—
266C3×D4—34no—
267C3×D4—64no—
268C3×D4—62no—
269C2×C3×C4—24no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—21no—
275C2×C3×C4—22no—
276C2×C3×C4—21no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—42no—
281C2×C3×C4—62no—
282C2×C3×C4—62no—
283C2×C3×C4—62no—
284C2×C3×C4—128no—
285C2×C3×C4—122no—
286C2×C3×C4—122no—
287C2×C3×C4—122no—
288C2×C3×C4C2×D1212yes—
289C2×C3×C4C2×D1212yes—
290C2×C3×C4C2×D1211yescharacteristic
291C2×C3×C4#23712yes—
292C2×C3×C4D3×Q812yes—
293C2×C3×C4C2×C3×D412yes—
294C2×C3×C4C2×C3×D412yes—
295C2×C3×C4C2×C3×D411yescharacteristic
296C2×C3×C4C2×C3×Q812yes—
297C2×C3×C4C3×#4112yes—
298C2×C3×C4C23×D311yescharacteristic
299C2×C3×C4C24×C311yescharacteristic
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—42no—
304C2×Dic3—42no—
305C2×Dic3—42no—
306D12—24no—
307D12—22no—
308D12C2×C3×Q814yes—
309C4×D3—48no—
310C3×C8—22no—
311C3×C8—22no—
312C3×C8—22no—
313C3×C8—22no—
314C3×C8—42no—
315C3×C8—42no—
316C2×C32#47814yescomplemented
317C2×C32C2×C22⋊Q811yescharacteristic
318C2×C32C2×#13511yescharacteristic
319C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
320C3×D3—44no—
321C24—61no—
322C2×D4—32no—
323C2×D4—34no—
324C2×D4—61no—
325C2×D4—62no—
326C22×C4—61no—
327C22×C4—61no—
328C22×C4—61no—
329C22×C4—64no—
330C22×C4—124no—
331C22×C4C3×D1211yescharacteristic
332C22×C4C3×D1211yescharacteristic
333C22×C4C22×C3×D311yescharacteristic
334C2×C8—22no—
335C2×C8—22no—
336C2×C8C22×C3×D312yes—
337C2×C8C22×C3×D312yes—
338C4⋊C4—32no—
339C4⋊C4—32no—
340C4⋊C4—32no—
341C4⋊C4—61no—
342C4⋊C4—61no—
343C4⋊C4—61no—
344C4⋊C4—64no—
345C4⋊C4—64no—
346C22⋊C4—64no—
347C42C3×D1212yes—
348C42C22×C3×D312yes—
349C22×C3—22no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3—21no—
353C22×C3—64no—
354C22×C3—122no—
355C22×C3—122no—
356C22×C3—128no—
357C22×C3#89712yes—
358C22×C3#90412yes—
359C22×C3#90812yes—
360C22×C3C3×C22⋊Q812yes—
361C22×C3C3×#13512yes—
362C22×C3C3×AGL(1,ℤ/8)12yes—
363C22×C3C22×D1211yescharacteristic
364C22×C3C22×C3×D411yescharacteristic
365C2×D3—24no—
366C2×D3—42no—
367C2×D3—42no—
368C2×D3—48no—
369C3×C4—24no—
370C3×C4—22no—
371C3×C4—22no—
372C3×C4—22no—
373C3×C4—22no—
374C3×C4—22no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—42no—
378C3×C4—122no—
379C3×C4—122no—
380C3×C4—122no—
381C3×C4#89712yes—
382C3×C4C3×C22⋊Q812yes—
383C3×C4C2×#23711yescharacteristic
384C3×C4C2×D3×Q811yescharacteristic
385C3×C4C22×C3×Q811yescharacteristic
386C3×C4C2×C3×#4111yescharacteristic
387Dic3—42no—
388Dic3—42no—
389Dic3—42no—
390C32C2×#47811yescharacteristic, complemented, Sylow
391C23—64no—
392C23—62no—
393C23—122no—
394C23—122no—
395C23C2×C3×D1211yescharacteristic
396D4—34no—
397D4—64no—
398D4—62no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—62no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—128no—
405C2×C4—122no—
406C2×C4—122no—
407C2×C4—122no—
408C2×C4C2×C3×D1212yes—
409C2×C4C2×C3×D1212yes—
410C2×C4C2×C3×D1211yescharacteristic
411C2×C4C3×#23712yes—
412C2×C4C3×D3×Q812yes—
413C2×C4C23×C3×D311yescharacteristic
414C8—22no—
415C8—22no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—24no—
419C2×C3—21no—
420C2×C3—124no—
421C2×C3#484714yesdirect product factor
422C2×C3C3×#47814yescomplemented
423C2×C3C2×#89711yescharacteristic
424C2×C3C2×#90411yescharacteristic
425C2×C3C2×#90811yescharacteristic
426C2×C3C2×C3×C22⋊Q811yescharacteristic
427C2×C3C2×C3×#13511yescharacteristic
428C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
429D3—44no—
430C22—64no—
431C22—122no—
432C22—128no—
433C22—122no—
434C22C3×#89712yes—
435C22C3×#90412yes—
436C22C3×#90812yes—
437C22C22×C3×D1211yescharacteristic
438C4—22no—
439C4—22no—
440C4—122no—
441C4—122no—
442C4—122no—
443C4C3×#89712yes—
444C4C2×C3×#23711yescharacteristic
445C4C2×C3×D3×Q811yescharacteristic
446C3—21no—
447C3C2×#484711yescharacteristic, direct product factor
448C3C2×C3×#47811yescharacteristic, complemented
449C2—124no—
450C2C3×#484714yesdirect product factor
451C2C2×C3×#89711yescharacteristic
452C2C2×C3×#90411yescharacteristic
453C2C2×C3×#90811yescharacteristic
subgroupG/H
centerC23×C3C2×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C4⋊C8C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C3×C4⋊C8D3
hypocenterC3C2×C3×#478
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C2×C3×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#870C2semidirect
3. C2×C32×C4⋊C8C2semidirect
6. C2×C3×#818C2semidirect
7. C2×C3×#817C2semidirect
8. C3×#4847C2direct (N × H)
10. C2×#4847C3direct (N × H)
25. C3×#870C22semidirect
26. C32×C4⋊C8C22semidirect
29. C3×#818C22semidirect
30. C3×#817C22semidirect
34. C2×#870C2×C3semidirect
39. C2×C3×C4⋊C8D3semidirect
40. C2×C3×C4⋊C8C2×C3semidirect
45. C2×#818C2×C3semidirect
46. C2×#817C2×C3semidirect
47. #4847C2×C3direct (N × H)
109. #870C22×C3semidirect
113. C3×C4⋊C8C2×D3semidirect
114. C3×C4⋊C8C22×C3semidirect
119. #818C22×C3semidirect
120. #817C22×C3semidirect
151. C2×C4⋊C8C3×D3semidirect
252. C4⋊C8C2×C3×D3semidirect
316. C2×C32#478semidirect
390. C32C2×#478semidirect
421. C2×C3#4847direct (N × H)
422. C2×C3C3×#478semidirect
447. C3C2×#4847direct (N × H)
448. C3C2×C3×#478semidirect
450. C2C3×#4847direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×D122
C2×C3×#8702
C2×C32×C4⋊C82
C2×C3×#8212
C2×C3×#8182
C2×C3×#8172
C3×#48472
C2×C3×#4783
C2×#48473