Finite Group Databasebeta

← C2×C3×#4967 #11869331

Subgroups — C2×C3×#4967 #11869331

Order 1152.

1233 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×C3×#930C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic, complemented
4C3×#4967C218yesmaximal, direct product factor
5C2×C3×#809C212yesmaximal, complemented
6C2×C3×#807C212yesmaximal, complemented
7C2×C3×#480—31nomaximal
8C2×#4967C311yesmaximal, characteristic, direct product factor
9C23×C32×C4—21no—
10C23×C32×C4C2211yescharacteristic
11C22×C3×#67—21no—
12C22×C3×D12C2211yescharacteristic
13C2×C32×C4⋊C4—22no—
14C2×C32×C4⋊C4—21no—
15C2×C32×C4⋊C4C2212yes—
16C2×C32×C4⋊C4C2214yescomplemented
17C3×#930—22no—
18C3×#930C2214yes—
19C2×C3×(C2×D3)⋊C4—21no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2212yes—
22C3×#830C2214yescomplemented
23C3×#809C2218yescomplemented
24C3×#807C2218yescomplemented
25C2×C3×#121—31no—
26C22×C3×C4⋊C4—21no—
27C22×C3×C4⋊C4D311yescharacteristic, complemented
28C22×C3×C4⋊C4C2×C311yescharacteristic, complemented
29C2×#930C2×C311yescharacteristic
30C3×#480—38no—
31C2×C3×#107—32no—
32C2×C3×#102—32no—
33C2×C3×C22⋊C8—31no—
34C2×#830C2×C311yescharacteristic, complemented
35#4967C2×C318yesdirect product factor
36C2×#809C2×C312yescomplemented
37C2×#807C2×C312yescomplemented
38C24×C32D411yescharacteristic
39C23×C3×D3—21no—
40C22×C32×C4—24no—
41C22×C32×C4—22no—
42C22×C32×C4—24no—
43C22×C32×C4—44no—
44C22×C32×C4D411yescharacteristic
45C22×C32×C4D412yes—
46C22×C32×C4C2312yes—
47C22×C32×C4C2311yescharacteristic
48C2×C3×#67—24no—
49C2×C3×#67—44no—
50C22×C3×Dic3—21no—
51C2×C3×D12—24no—
52C2×C3×D12—21no—
53C2×C3×D12C2312yes—
54C32×C4⋊C4—22no—
55C32×C4⋊C4—24no—
56C32×C4⋊C4C2314yes—
57C3×(C2×D3)⋊C4—24no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3C2312yes—
60C2×C3×C3⋊C8—24no—
61C2×C3×C3⋊C8C2314yes—
62C2×#480—31noSylow
63C22×C3×D4—31no—
64C22×C3×D4—61no—
65C23×C3×C4—22no—
66C23×C3×C4—21no—
67C23×C3×C4—21no—
68C23×C3×C4—21no—
69C23×C3×C4C2×D311yescharacteristic
70C23×C3×C4C22×C311yescharacteristic
71C22×#67—21no—
72C22×D12C22×C311yescharacteristic
73C22×C3×C8—32no—
74C3×#121—34no—
75C3×#121—62no—
76C2×C3×C4⋊C4—24no—
77C2×C3×C4⋊C4—22no—
78C2×C3×C4⋊C4—22no—
79C2×C3×C4⋊C4—21no—
80C2×C3×C4⋊C4—22no—
81C2×C3×C4⋊C4—21no—
82C2×C3×C4⋊C4—22no—
83C2×C3×C4⋊C4—24no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4C2×D312yes—
86C2×C3×C4⋊C4C2×D314yescomplemented
87C2×C3×C4⋊C4C22×C312yes—
88C2×C3×C4⋊C4C22×C314yescomplemented
89C2×C3×C22⋊C4—61no—
90#930—22no—
91#930C22×C314yes—
92C2×(C2×D3)⋊C4—21no—
93C2×C4⋊Dic3C22×C311yescharacteristic
94C22×C3⋊C8C22×C312yes—
95C3×#107—38no—
96C3×#102—38no—
97C3×C22⋊C8—34no—
98#830C22×C314yescomplemented
99#809C22×C318yescomplemented
100#807C22×C318yescomplemented
101C23×C32—22no—
102C23×C32—22no—
103C23×C32D814yes—
104C23×C32C2×D412yes—
105C23×C32C2×D411yescharacteristic
106C22×C3×D3—22no—
107C22×C3×D3—42no—
108C22×C3×D3—42no—
109C22×C3×D3—42no—
110C2×C32×C4—22no—
111C2×C32×C4—24no—
112C2×C32×C4—24no—
113C2×C32×C4—24no—
114C2×C32×C4—48no—
115C2×C32×C4—44no—
116C2×C32×C4C2×D412yes—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4#4114yes—
119C2×C32×C4C2411yescharacteristic
120C3×#67—48no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—42no—
123C3×D12—24no—
124C3×D12—42no—
125C3×C3⋊C8—24no—
126C2×#121—31no—
127C22×C4⋊C4C3×D311yescharacteristic, complemented
128#480—38no—
129C2×#107—32no—
130C2×#102—32no—
131C2×C22⋊C8—31no—
132C24×C3—21no—
133C24×C3—61no—
134C24×C3#6711yescharacteristic
135C24×C3C3×D411yescharacteristic
136C23×D3—21no—
137C2×C3×D4—32no—
138C2×C3×D4—64no—
139C2×C3×D4—64no—
140C2×C3×D4—61no—
141C2×C3×D4—124no—
142C22×C3×C4—28no—
143C22×C3×C4—24no—
144C22×C3×C4—24no—
145C22×C3×C4—24no—
146C22×C3×C4—28no—
147C22×C3×C4—24no—
148C22×C3×C4—22no—
149C22×C3×C4—22no—
150C22×C3×C4—24no—
151C22×C3×C4—21no—
152C22×C3×C4—22no—
153C22×C3×C4—22no—
154C22×C3×C4—21no—
155C22×C3×C4—48no—
156C22×C3×C4—44no—
157C22×C3×C4—44no—
158C22×C3×C4—61no—
159C22×C3×C4#6712yes—
160C22×C3×C4#6711yescharacteristic
161C22×C3×C4C3×D411yescharacteristic
162C22×C3×C4C3×D412yes—
163C22×C3×C4C22×D312yes—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C23×C312yes—
166C22×C3×C4C23×C311yescharacteristic
167C2×#67—24no—
168C2×#67—44no—
169C22×Dic3—21no—
170C2×D12—24no—
171C2×D12—21no—
172C2×D12C23×C312yes—
173C2×C3×C8—34no—
174C2×C3×C8—64no—
175C3×C4⋊C4—24no—
176C3×C4⋊C4—28no—
177C3×C4⋊C4—22no—
178C3×C4⋊C4—24no—
179C3×C4⋊C4—22no—
180C3×C4⋊C4—24no—
181C3×C4⋊C4—24no—
182C3×C4⋊C4—32no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4C22×D314yes—
185C3×C4⋊C4C23×C314yes—
186C3×C22⋊C4—64no—
187(C2×D3)⋊C4—24no—
188C4⋊Dic3—21no—
189C4⋊Dic3C23×C312yes—
190C2×C3⋊C8—24no—
191C2×C3⋊C8C23×C314yes—
192C22×C32—22no—
193C22×C32—22no—
194C22×C32—28no—
195C22×C32#12312yes—
196C22×C32C2×D814yes—
197C22×C32C2×D812yes—
198C22×C32#13712yes—
199C22×C32C22×D411yescharacteristic
200C2×C3×D3—42no—
201C2×C3×D3—42no—
202C2×C3×D3—42no—
203C2×C3×D3—84no—
204C32×C4—22no—
205C32×C4—44no—
206C32×C4#12312yes—
207C32×C4C2×#4112yes—
208C3×Dic3—42no—
209C22×D4—31no—
210C22×D4—61no—
211C23×C4—21no—
212C23×C4C2×C3×D311yescharacteristic
213C22×C8—32no—
214#121—34no—
215#121—62no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—31no—
219C2×C4⋊C4C2×C3×D312yes—
220C2×C4⋊C4C2×C3×D314yescomplemented
221C2×C22⋊C4—61no—
222#107—38no—
223#102—38no—
224C22⋊C8—34no—
225C23×C3—24no—
226C23×C3—24no—
227C23×C3—22no—
228C23×C3—22no—
229C23×C3—22no—
230C23×C3—22no—
231C23×C3—24no—
232C23×C3—22no—
233C23×C3—21no—
234C23×C3—62no—
235C23×C3—122no—
236C23×C3—122no—
237C23×C3—122no—
238C23×C3#21314yes—
239C23×C3C3×D814yes—
240C23×C3C2×#6712yes—
241C23×C3C2×#6711yescharacteristic
242C23×C3C2×C3×D412yes—
243C23×C3C2×C3×D411yescharacteristic
244C22×D3—22no—
245C22×D3—42no—
246C22×D3—42no—
247C22×D3—42no—
248C3×D4—64no—
249C3×D4—128no—
250C3×D4—122no—
251C2×C3×C4—24no—
252C2×C3×C4—28no—
253C2×C3×C4—28no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—24no—
257C2×C3×C4—24no—
258C2×C3×C4—24no—
259C2×C3×C4—24no—
260C2×C3×C4—28no—
261C2×C3×C4—24no—
262C2×C3×C4—24no—
263C2×C3×C4—21no—
264C2×C3×C4—24no—
265C2×C3×C4—22no—
266C2×C3×C4—21no—
267C2×C3×C4—416no—
268C2×C3×C4—48no—
269C2×C3×C4—48no—
270C2×C3×C4—44no—
271C2×C3×C4—48no—
272C2×C3×C4—44no—
273C2×C3×C4—62no—
274C2×C3×C4—122no—
275C2×C3×C4#23514yes—
276C2×C3×C4C2×#6712yes—
277C2×C3×C4C2×#6711yescharacteristic
278C2×C3×C4C2×C3×D412yes—
279C2×C3×C4C2×C3×D411yescharacteristic
280C2×C3×C4C3×#4114yes—
281C2×C3×C4C23×D311yescharacteristic
282C2×C3×C4C24×C311yescharacteristic
283#67—48no—
284C2×Dic3—22no—
285C2×Dic3—42no—
286D12—24no—
287D12—42no—
288C3×C8—64no—
289C3⋊C8—24no—
290C2×C32—24no—
291C2×C32#48014yescomplemented
292C2×C32C2×#12311yescharacteristic
293C2×C32C22×D811yescharacteristic
294C2×C32C2×#13711yescharacteristic
295C3×D3—82no—
296C24—61no—
297C24C3×#6711yescharacteristic
298C2×D4—32no—
299C2×D4—64no—
300C2×D4—64no—
301C2×D4—61no—
302C2×D4—124no—
303C22×C4—24no—
304C22×C4—22no—
305C22×C4—24no—
306C22×C4—44no—
307C22×C4—61no—
308C22×C4C3×#6711yescharacteristic
309C22×C4C3×#6712yes—
310C22×C4C22×C3×D312yes—
311C22×C4C22×C3×D311yescharacteristic
312C2×C8—34no—
313C2×C8—64no—
314C4⋊C4—22no—
315C4⋊C4—24no—
316C4⋊C4—32no—
317C4⋊C4—61no—
318C4⋊C4C22×C3×D314yes—
319C22⋊C4—64no—
320C22×C3—24no—
321C22×C3—216no—
322C22×C3—24no—
323C22×C3—22no—
324C22×C3—28no—
325C22×C3—22no—
326C22×C3—22no—
327C22×C3—22no—
328C22×C3—28no—
329C22×C3—22no—
330C22×C3—24no—
331C22×C3—22no—
332C22×C3—22no—
333C22×C3—21no—
334C22×C3—122no—
335C22×C3—122no—
336C22×C3—122no—
337C22×C3—244no—
338C22×C3#92912yes—
339C22×C3C2×#21314yes—
340C22×C3C2×#21312yes—
341C22×C3#94212yes—
342C22×C3C3×#12312yes—
343C22×C3C2×C3×D814yes—
344C22×C3C2×C3×D812yes—
345C22×C3C3×#13712yes—
346C22×C3C22×#6711yescharacteristic
347C22×C3C22×C3×D411yescharacteristic
348C2×D3—42no—
349C2×D3—42no—
350C2×D3—42no—
351C2×D3—84no—
352C3×C4—24no—
353C3×C4—22no—
354C3×C4—22no—
355C3×C4—22no—
356C3×C4—22no—
357C3×C4—48no—
358C3×C4—44no—
359C3×C4—44no—
360C3×C4—122no—
361C3×C4#92912yes—
362C3×C4C3×#12312yes—
363C3×C4C2×#23512yes—
364C3×C4C2×C3×#4112yes—
365Dic3—42no—
366C32C2×#48011yescharacteristic, complemented, Sylow
367C23—22no—
368C23—22no—
369C23—62no—
370C23—122no—
371C23—122no—
372C23—122no—
373C23C3×#21314yes—
374C23C2×C3×#6712yes—
375C23C2×C3×#6711yescharacteristic
376D4—64no—
377D4—128no—
378D4—122no—
379C2×C4—22no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—24no—
383C2×C4—48no—
384C2×C4—44no—
385C2×C4—62no—
386C2×C4—122no—
387C2×C4C3×#23514yes—
388C2×C4C2×C3×#6712yes—
389C2×C4C2×C3×#6711yescharacteristic
390C2×C4C23×C3×D311yescharacteristic
391C8—64no—
392C2×C3—28no—
393C2×C3—24no—
394C2×C3—24no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—24no—
398C2×C3—21no—
399C2×C3—242no—
400C2×C3#496714yesdirect product factor
401C2×C3C3×#48014yescomplemented
402C2×C3C2×#92911yescharacteristic
403C2×C3C22×#21311yescharacteristic
404C2×C3C2×#94211yescharacteristic
405C2×C3C2×C3×#12311yescharacteristic
406C2×C3C22×C3×D811yescharacteristic
407C2×C3C2×C3×#13711yescharacteristic
408D3—82no—
409C22—22no—
410C22—28no—
411C22—22no—
412C22—122no—
413C22—122no—
414C22—122no—
415C22—244no—
416C22C3×#92912yes—
417C22C2×C3×#21314yes—
418C22C2×C3×#21312yes—
419C22C3×#94212yes—
420C22C22×C3×#6711yescharacteristic
421C4—22no—
422C4—44no—
423C4—122no—
424C4C3×#92912yes—
425C4C2×C3×#23512yes—
426C3—21no—
427C3C2×#496711yescharacteristic, direct product factor
428C3C2×C3×#48011yescharacteristic, complemented
429C2—24no—
430C2—242no—
431C2C3×#496714yesdirect product factor
432C2C2×C3×#92911yescharacteristic
433C2C22×C3×#21311yescharacteristic
434C2C2×C3×#94211yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC22×C32×C4⋊C4C2
socleC23×C32C2×D4
prime radicalC2×C3×#930C2
hypercenterC22×C3×C4⋊C4D3
hypocenterC3C2×C3×#480
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
1. C22×C32×C4⋊C4C2semidirect
3. C2×C3×#830C2semidirect
4. C3×#4967C2direct (N × H)
5. C2×C3×#809C2semidirect
6. C2×C3×#807C2semidirect
8. C2×#4967C3direct (N × H)
16. C2×C32×C4⋊C4C22semidirect
22. C3×#830C22semidirect
23. C3×#809C22semidirect
24. C3×#807C22semidirect
27. C22×C3×C4⋊C4D3semidirect
28. C22×C3×C4⋊C4C2×C3semidirect
34. C2×#830C2×C3semidirect
35. #4967C2×C3direct (N × H)
36. C2×#809C2×C3semidirect
37. C2×#807C2×C3semidirect
86. C2×C3×C4⋊C4C2×D3semidirect
88. C2×C3×C4⋊C4C22×C3semidirect
98. #830C22×C3semidirect
99. #809C22×C3semidirect
100. #807C22×C3semidirect
127. C22×C4⋊C4C3×D3semidirect
220. C2×C4⋊C4C2×C3×D3semidirect
291. C2×C32#480semidirect
366. C32C2×#480semidirect
400. C2×C3#4967direct (N × H)
401. C2×C3C3×#480semidirect
427. C3C2×#4967direct (N × H)
428. C3C2×C3×#480semidirect
431. C2C3×#4967direct (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×#9302
C2×C3×#8302
C3×#49672
C2×C3×#8092
C2×C3×#8072
C2×C3×#4803
C2×#49673