Finite Group Databasebeta

← C2×C3×#4971 #11869375

Subgroups — C2×C3×#4971 #11869375

Order 1152.

1129 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4⋊C4C211yesmaximal, characteristic
2C2×C3×#924C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4C3×#4971C218yesmaximal, direct product factor
5C2×C3×#810C212yesmaximal, complemented
6C2×C3×#808C212yesmaximal, complemented
7C2×C3×#483—31nomaximal
8C2×#4971C311yesmaximal, characteristic, direct product factor
9C23×C32×C4—21no—
10C23×C32×C4C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C4⋊C4—21no—
13C2×C32×C4⋊C4—22no—
14C2×C32×C4⋊C4C2212yes—
15C2×C32×C4⋊C4C2214yes—
16C2×C3×#217—21no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C3×#924—22no—
19C3×#924C2214yes—
20C2×C3×Dic3⋊C4—21no—
21C22×C3×C3⋊C8C2212yes—
22C3×#830C2214yes—
23C3×#810C2218yescomplemented
24C3×#808C2218yescomplemented
25C2×C3×C22⋊Q8—31no—
26C22×C3×C4⋊C4—21no—
27C22×C3×C4⋊C4D311yescharacteristic
28C22×C3×C4⋊C4C2×C311yescharacteristic
29C2×#924C2×C311yescharacteristic
30C3×#483—38no—
31C2×C3×#106—32no—
32C2×C3×#103—32no—
33C2×C3×C22⋊C8—31no—
34C2×#830C2×C311yescharacteristic
35#4971C2×C318yesdirect product factor
36C2×#810C2×C312yescomplemented
37C2×#808C2×C312yescomplemented
38C24×C32D411yescharacteristic
39C22×C32×C4—24no—
40C22×C32×C4—24no—
41C22×C32×C4—22no—
42C22×C32×C4—44no—
43C22×C32×C4D411yescharacteristic
44C22×C32×C4D412yes—
45C22×C32×C4C2312yes—
46C22×C32×C4C2311yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C2×C3×Dic6—24no—
50C2×C3×Dic6—21no—
51C2×C3×Dic6C2312yes—
52C32×C4⋊C4—24no—
53C32×C4⋊C4—22no—
54C32×C4⋊C4C2314yes—
55C3×#217—24no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3C2312yes—
58C3×Dic3⋊C4—24no—
59C2×C3×C3⋊C8—24no—
60C2×C3×C3⋊C8C2314yes—
61C2×#483—31noSylow
62C22×C3×Q8—31no—
63C23×C3×C4—22no—
64C23×C3×C4—21no—
65C23×C3×C4—21no—
66C23×C3×C4—21no—
67C23×C3×C4C2×D311yescharacteristic
68C23×C3×C4C22×C311yescharacteristic
69C22×Dic6C22×C311yescharacteristic
70C22×C3×C8—32no—
71C3×C22⋊Q8—34no—
72C3×C22⋊Q8—62no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—24no—
75C2×C3×C4⋊C4—22no—
76C2×C3×C4⋊C4—21no—
77C2×C3×C4⋊C4—21no—
78C2×C3×C4⋊C4—22no—
79C2×C3×C4⋊C4—22no—
80C2×C3×C4⋊C4—24no—
81C2×C3×C4⋊C4—31no—
82C2×C3×C4⋊C4—61no—
83C2×C3×C4⋊C4C2×D312yes—
84C2×C3×C4⋊C4C2×D314yes—
85C2×C3×C4⋊C4C22×C312yes—
86C2×C3×C4⋊C4C22×C314yes—
87C2×C3×C22⋊C4—61no—
88C2×#217—21no—
89C2×C4⋊Dic3C22×C311yescharacteristic
90#924—22no—
91#924C22×C314yes—
92C2×Dic3⋊C4—21no—
93C22×C3⋊C8C22×C312yes—
94C3×#106—38no—
95C3×#103—38no—
96C3×C22⋊C8—34no—
97#830C22×C314yes—
98#810C22×C318yescomplemented
99#808C22×C318yescomplemented
100C23×C32—22no—
101C23×C32—22no—
102C23×C32SD1614yes—
103C23×C32C2×D412yes—
104C23×C32C2×D411yescharacteristic
105C2×C32×C4—22no—
106C2×C32×C4—24no—
107C2×C32×C4—24no—
108C2×C32×C4—24no—
109C2×C32×C4—48no—
110C2×C32×C4—44no—
111C2×C32×C4C2×D412yes—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4#4114yes—
114C2×C32×C4C2411yescharacteristic
115C2×C3×Dic3—22no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—42no—
118C2×C3×Dic3—42no—
119C3×Dic6—24no—
120C3×Dic6—42no—
121C3×C3⋊C8—24no—
122C2×C22⋊Q8—31no—
123C22×C4⋊C4C3×D311yescharacteristic
124#483—38no—
125C2×#106—32no—
126C2×#103—32no—
127C2×C22⋊C8—31no—
128C24×C3—21no—
129C24×C3#6711yescharacteristic
130C24×C3C3×D411yescharacteristic
131C2×C3×Q8—32no—
132C2×C3×Q8—61no—
133C2×C3×Q8—64no—
134C22×C3×C4—28no—
135C22×C3×C4—24no—
136C22×C3×C4—24no—
137C22×C3×C4—28no—
138C22×C3×C4—24no—
139C22×C3×C4—24no—
140C22×C3×C4—22no—
141C22×C3×C4—24no—
142C22×C3×C4—22no—
143C22×C3×C4—21no—
144C22×C3×C4—22no—
145C22×C3×C4—22no—
146C22×C3×C4—21no—
147C22×C3×C4—48no—
148C22×C3×C4—44no—
149C22×C3×C4—44no—
150C22×C3×C4—61no—
151C22×C3×C4—61no—
152C22×C3×C4#6712yes—
153C22×C3×C4#6711yescharacteristic
154C22×C3×C4C3×D411yescharacteristic
155C22×C3×C4C3×D412yes—
156C22×C3×C4C22×D312yes—
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C23×C312yes—
159C22×C3×C4C23×C311yescharacteristic
160C22×Dic3—21no—
161C22×Dic3—21no—
162C2×Dic6—24no—
163C2×Dic6—21no—
164C2×Dic6C23×C312yes—
165C2×C3×C8—34no—
166C2×C3×C8—64no—
167C3×C4⋊C4—28no—
168C3×C4⋊C4—24no—
169C3×C4⋊C4—24no—
170C3×C4⋊C4—22no—
171C3×C4⋊C4—24no—
172C3×C4⋊C4—22no—
173C3×C4⋊C4—24no—
174C3×C4⋊C4—32no—
175C3×C4⋊C4—64no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4C22×D314yes—
178C3×C4⋊C4C23×C314yes—
179C3×C22⋊C4—64no—
180#217—24no—
181C4⋊Dic3—21no—
182C4⋊Dic3C23×C312yes—
183Dic3⋊C4—24no—
184C2×C3⋊C8—24no—
185C2×C3⋊C8C23×C314yes—
186C22×C32—22no—
187C22×C32—22no—
188C22×C32—28no—
189C22×C32#12312yes—
190C22×C32C2×SD1614yes—
191C22×C32C2×SD1612yes—
192C22×C32#13712yes—
193C22×C32C22×D411yescharacteristic
194C32×C4—22no—
195C32×C4—44no—
196C32×C4#12312yes—
197C32×C4C2×#4112yes—
198C3×Dic3—42no—
199C3×Dic3—42no—
200C22×Q8—31no—
201C23×C4—21no—
202C23×C4C2×C3×D311yescharacteristic
203C22×C8—32no—
204C22⋊Q8—34no—
205C22⋊Q8—62no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—31no—
209C2×C4⋊C4—61no—
210C2×C4⋊C4C2×C3×D312yes—
211C2×C4⋊C4C2×C3×D314yes—
212C2×C22⋊C4—61no—
213#106—38no—
214#103—38no—
215C22⋊C8—34no—
216C23×C3—24no—
217C23×C3—24no—
218C23×C3—22no—
219C23×C3—22no—
220C23×C3—22no—
221C23×C3—22no—
222C23×C3—24no—
223C23×C3—22no—
224C23×C3—21no—
225C23×C3#21414yes—
226C23×C3C3×SD1614yes—
227C23×C3C2×#6712yes—
228C23×C3C2×#6711yescharacteristic
229C23×C3C2×C3×D412yes—
230C23×C3C2×C3×D411yescharacteristic
231C3×Q8—64no—
232C3×Q8—122no—
233C2×C3×C4—24no—
234C2×C3×C4—28no—
235C2×C3×C4—28no—
236C2×C3×C4—22no—
237C2×C3×C4—22no—
238C2×C3×C4—24no—
239C2×C3×C4—24no—
240C2×C3×C4—24no—
241C2×C3×C4—24no—
242C2×C3×C4—28no—
243C2×C3×C4—24no—
244C2×C3×C4—24no—
245C2×C3×C4—21no—
246C2×C3×C4—24no—
247C2×C3×C4—22no—
248C2×C3×C4—21no—
249C2×C3×C4—416no—
250C2×C3×C4—48no—
251C2×C3×C4—48no—
252C2×C3×C4—44no—
253C2×C3×C4—48no—
254C2×C3×C4—44no—
255C2×C3×C4—62no—
256C2×C3×C4—62no—
257C2×C3×C4—122no—
258C2×C3×C4—122no—
259C2×C3×C4#23514yes—
260C2×C3×C4C2×#6712yes—
261C2×C3×C4C2×#6711yescharacteristic
262C2×C3×C4C2×C3×D412yes—
263C2×C3×C4C2×C3×D411yescharacteristic
264C2×C3×C4C3×#4114yes—
265C2×C3×C4C23×D311yescharacteristic
266C2×C3×C4C24×C311yescharacteristic
267C2×Dic3—22no—
268C2×Dic3—22no—
269C2×Dic3—42no—
270C2×Dic3—42no—
271Dic6—24no—
272Dic6—42no—
273C3×C8—64no—
274C3⋊C8—24no—
275C2×C32—24no—
276C2×C32#48314yescomplemented
277C2×C32C2×#12311yescharacteristic
278C2×C32C22×SD1611yescharacteristic
279C2×C32C2×#13711yescharacteristic
280C24C3×#6711yescharacteristic
281C2×Q8—32no—
282C2×Q8—61no—
283C2×Q8—64no—
284C22×C4—24no—
285C22×C4—24no—
286C22×C4—22no—
287C22×C4—44no—
288C22×C4—61no—
289C22×C4—61no—
290C22×C4C3×#6711yescharacteristic
291C22×C4C3×#6712yes—
292C22×C4C22×C3×D312yes—
293C22×C4C22×C3×D311yescharacteristic
294C2×C8—34no—
295C2×C8—64no—
296C4⋊C4—24no—
297C4⋊C4—22no—
298C4⋊C4—32no—
299C4⋊C4—61no—
300C4⋊C4—64no—
301C4⋊C4C22×C3×D314yes—
302C22⋊C4—64no—
303C22×C3—24no—
304C22×C3—24no—
305C22×C3—216no—
306C22×C3—22no—
307C22×C3—28no—
308C22×C3—22no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—28no—
312C22×C3—22no—
313C22×C3—24no—
314C22×C3—22no—
315C22×C3—22no—
316C22×C3—21no—
317C22×C3#92912yes—
318C22×C3C2×#21414yes—
319C22×C3C2×#21412yes—
320C22×C3#94212yes—
321C22×C3C3×#12312yes—
322C22×C3C2×C3×SD1614yes—
323C22×C3C2×C3×SD1612yes—
324C22×C3C3×#13712yes—
325C22×C3C22×#6711yescharacteristic
326C22×C3C22×C3×D411yescharacteristic
327C3×C4—24no—
328C3×C4—22no—
329C3×C4—22no—
330C3×C4—22no—
331C3×C4—22no—
332C3×C4—48no—
333C3×C4—44no—
334C3×C4—44no—
335C3×C4—122no—
336C3×C4—122no—
337C3×C4#92912yes—
338C3×C4C3×#12312yes—
339C3×C4C2×#23512yes—
340C3×C4C2×C3×#4112yes—
341Dic3—42no—
342Dic3—42no—
343C32C2×#48311yescharacteristic, complemented, Sylow
344C23—22no—
345C23—22no—
346C23C3×#21414yes—
347C23C2×C3×#6712yes—
348C23C2×C3×#6711yescharacteristic
349Q8—64no—
350Q8—122no—
351C2×C4—22no—
352C2×C4—24no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—48no—
356C2×C4—44no—
357C2×C4—62no—
358C2×C4—62no—
359C2×C4—122no—
360C2×C4—122no—
361C2×C4C3×#23514yes—
362C2×C4C2×C3×#6712yes—
363C2×C4C2×C3×#6711yescharacteristic
364C2×C4C23×C3×D311yescharacteristic
365C8—64no—
366C2×C3—28no—
367C2×C3—24no—
368C2×C3—24no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—24no—
373C2×C3#497114yesdirect product factor
374C2×C3C3×#48314yescomplemented
375C2×C3C2×#92911yescharacteristic
376C2×C3C22×#21411yescharacteristic
377C2×C3C2×#94211yescharacteristic
378C2×C3C2×C3×#12311yescharacteristic
379C2×C3C22×C3×SD1611yescharacteristic
380C2×C3C2×C3×#13711yescharacteristic
381C22—22no—
382C22—22no—
383C22—28no—
384C22C3×#92912yes—
385C22C2×C3×#21414yes—
386C22C2×C3×#21412yes—
387C22C3×#94212yes—
388C22C22×C3×#6711yescharacteristic
389C4—22no—
390C4—44no—
391C4—122no—
392C4—122no—
393C4C3×#92912yes—
394C4C2×C3×#23512yes—
395C3—21no—
396C3C2×#497111yescharacteristic, direct product factor
397C3C2×C3×#48311yescharacteristic, complemented
398C2—24no—
399C2C3×#497114yesdirect product factor
400C2C2×C3×#92911yescharacteristic
401C2C22×C3×#21411yescharacteristic
402C2C2×C3×#94211yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC22×C32×C4⋊C4C2
socleC23×C32C2×D4
prime radicalC24×C32D4
hypercenterC22×C3×C4⋊C4D3
hypocenterC3C2×C3×#483
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C22×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C3×#4971C2direct (N × H)
5. C2×C3×#810C2semidirect
6. C2×C3×#808C2semidirect
8. C2×#4971C3direct (N × H)
23. C3×#810C22semidirect
24. C3×#808C22semidirect
35. #4971C2×C3direct (N × H)
36. C2×#810C2×C3semidirect
37. C2×#808C2×C3semidirect
98. #810C22×C3semidirect
99. #808C22×C3semidirect
276. C2×C32#483semidirect
343. C32C2×#483semidirect
373. C2×C3#4971direct (N × H)
374. C2×C3C3×#483semidirect
396. C3C2×#4971direct (N × H)
397. C3C2×C3×#483semidirect
399. C2C3×#4971direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C4⋊C42
C2×C3×#9242
C2×C3×#8302
C3×#49712
C2×C3×#8102
C2×C3×#8082
C2×C3×#4833
C2×#49713