Finite Group Databasebeta

← C2×C3×#4736 #11869334

Subgroups — C2×C3×#4736 #11869334

Order 1152.

1125 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#930C211yesmaximal, characteristic
2C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C32×C22⋊C8C211yesmaximal, characteristic, complemented
4C2×C3×#821C212yesmaximal, complemented
5C2×C3×#818C212yesmaximal, complemented
6C3×#4736C218yesmaximal, direct product factor
7C2×C3×#480—31nomaximal
8C2×#4736C311yesmaximal, characteristic, direct product factor
9C23×C32×C4C2211yescharacteristic
10C22×C3×#67—21no—
11C23×C3×Dic3—21no—
12C22×C3×D12C2211yescharacteristic
13C22×C32×C8C2212yes—
14C3×#930—22no—
15C3×#930C2214yes—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3—22no—
18C2×C3×C4⋊Dic3—21no—
19C2×C3×C4⋊Dic3C2212yes—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2214yescomplemented
22C32×C22⋊C8C2214yescomplemented
23C3×#821C2218yescomplemented
24C3×#818C2218yescomplemented
25C2×C3×#121—31no—
26C22×C3×C4⋊C4—31no—
27C2×#930C2×C311yescharacteristic
28C22×C4⋊Dic3C2×C311yescharacteristic, complemented
29C3×#480—38no—
30C2×C3×#107—32no—
31C2×C3×#102—32no—
32C2×C3×C22⋊C8—21no—
33C2×C3×C22⋊C8D311yescharacteristic, complemented
34C2×C3×C22⋊C8C2×C311yescharacteristic, complemented
35C2×#821C2×C312yescomplemented
36C2×#818C2×C312yescomplemented
37#4736C2×C318yesdirect product factor
38C24×C32D411yescharacteristic
39C23×C3×D3—21no—
40C22×C32×C4—24no—
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D412yes—
43C22×C32×C4C2312yes—
44C22×C32×C4C2311yescharacteristic
45C2×C3×#67—24no—
46C2×C3×#67—44no—
47C22×C3×Dic3—22no—
48C22×C3×Dic3—24no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3—44no—
51C2×C3×D12—24no—
52C2×C3×D12—21no—
53C2×C3×D12C2312yes—
54C2×C32×C8—24no—
55C2×C32×C8C2314yes—
56C3×(C2×D3)⋊C4—24no—
57C3×C4⋊Dic3—22no—
58C3×C4⋊Dic3—24no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3C2314yes—
61C3×C4⋊Dic3C2312yes—
62C2×#480—31noSylow
63C22×C3×D4—31no—
64C22×C3×D4—61no—
65C23×C3×C4—21no—
66C23×C3×C4—61no—
67C23×C3×C4C2×D311yescharacteristic
68C23×C3×C4C22×C311yescharacteristic
69C22×#67—21no—
70C23×Dic3—21no—
71C22×D12C22×C311yescharacteristic
72C22×C3×C8—22no—
73C22×C3×C8C2×D312yes—
74C22×C3×C8C22×C312yes—
75C3×#121—34no—
76C3×#121—62no—
77C2×C3×C4⋊C4—32no—
78C2×C3×C4⋊C4—31no—
79C2×C3×C4⋊C4—34no—
80C2×C3×C4⋊C4—62no—
81C2×C3×C4⋊C4—61no—
82C2×C3×C22⋊C4—61no—
83#930—22no—
84#930C22×C314yes—
85C2×(C2×D3)⋊C4—21no—
86C2×C4⋊Dic3—22no—
87C2×C4⋊Dic3—21no—
88C2×C4⋊Dic3C22×C312yes—
89C2×C4⋊Dic3C22×C311yescharacteristic
90C2×C4⋊Dic3C22×C314yescomplemented
91C3×#107—38no—
92C3×#102—38no—
93C3×C22⋊C8—24no—
94C3×C22⋊C8C2×D314yescomplemented
95C3×C22⋊C8C22×C314yescomplemented
96#821C22×C318yescomplemented
97#818C22×C318yescomplemented
98C23×C32—22no—
99C23×C32—22no—
100C23×C32D814yes—
101C23×C32C2×D412yes—
102C23×C32C2×D411yescharacteristic
103C22×C3×D3—22no—
104C22×C3×D3—42no—
105C22×C3×D3—42no—
106C22×C3×D3—42no—
107C2×C32×C4—22no—
108C2×C32×C4—24no—
109C2×C32×C4—24no—
110C2×C32×C4C2×D412yes—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4#4114yes—
113C2×C32×C4C2411yescharacteristic
114C3×#67—48no—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—48no—
118C2×C3×Dic3—44no—
119C2×C3×Dic3—42no—
120C3×D12—24no—
121C3×D12—42no—
122C32×C8—24no—
123C2×#121—31no—
124C22×C4⋊C4—31no—
125#480—38no—
126C2×#107—32no—
127C2×#102—32no—
128C2×C22⋊C8C3×D311yescharacteristic, complemented
129C24×C3—21no—
130C24×C3—61no—
131C24×C3D1211yescharacteristic
132C24×C3C3×D411yescharacteristic
133C23×D3—21no—
134C2×C3×D4—32no—
135C2×C3×D4—64no—
136C2×C3×D4—61no—
137C2×C3×D4—64no—
138C2×C3×D4—124no—
139C22×C3×C4—24no—
140C22×C3×C4—24no—
141C22×C3×C4—21no—
142C22×C3×C4—22no—
143C22×C3×C4—21no—
144C22×C3×C4—22no—
145C22×C3×C4—44no—
146C22×C3×C4—64no—
147C22×C3×C4—61no—
148C22×C3×C4—62no—
149C22×C3×C4—124no—
150C22×C3×C4D1212yes—
151C22×C3×C4D1211yescharacteristic
152C22×C3×C4C3×D411yescharacteristic
153C22×C3×C4C3×D412yes—
154C22×C3×C4C22×D312yes—
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C23×C312yes—
157C22×C3×C4C23×C311yescharacteristic
158C2×#67—24no—
159C2×#67—44no—
160C22×Dic3—22no—
161C22×Dic3—24no—
162C22×Dic3—21no—
163C22×Dic3—44no—
164C2×D12—24no—
165C2×D12—21no—
166C2×D12C23×C312yes—
167C2×C3×C8—24no—
168C2×C3×C8—24no—
169C2×C3×C8—24no—
170C2×C3×C8—44no—
171C2×C3×C8C22×D314yes—
172C2×C3×C8C23×C314yes—
173C3×C4⋊C4—34no—
174C3×C4⋊C4—32no—
175C3×C4⋊C4—64no—
176C3×C4⋊C4—62no—
177C3×C4⋊C4—61no—
178C3×C22⋊C4—64no—
179(C2×D3)⋊C4—24no—
180C4⋊Dic3—22no—
181C4⋊Dic3—24no—
182C4⋊Dic3—21no—
183C4⋊Dic3C23×C312yes—
184C4⋊Dic3C23×C314yes—
185C22×C32—22no—
186C22×C32—22no—
187C22×C32—28no—
188C22×C32#12312yes—
189C22×C32C2×D814yes—
190C22×C32C2×D812yes—
191C22×C32#13712yes—
192C22×C32C22×D411yescharacteristic
193C2×C3×D3—42no—
194C2×C3×D3—42no—
195C2×C3×D3—42no—
196C2×C3×D3—84no—
197C32×C4—22no—
198C32×C4#12312yes—
199C32×C4C2×#4112yes—
200C3×Dic3—44no—
201C3×Dic3—42no—
202C22×D4—31no—
203C22×D4—61no—
204C23×C4—61no—
205C23×C4C2×C3×D311yescharacteristic
206C22×C8C2×C3×D312yes—
207#121—34no—
208#121—62no—
209C2×C4⋊C4—32no—
210C2×C4⋊C4—34no—
211C2×C4⋊C4—31no—
212C2×C4⋊C4—61no—
213C2×C4⋊C4—62no—
214C2×C22⋊C4—61no—
215#107—38no—
216#102—38no—
217C22⋊C8C2×C3×D314yescomplemented
218C23×C3—22no—
219C23×C3—22no—
220C23×C3—22no—
221C23×C3—22no—
222C23×C3—24no—
223C23×C3—21no—
224C23×C3—22no—
225C23×C3—42no—
226C23×C3—42no—
227C23×C3—62no—
228C23×C3—122no—
229C23×C3—122no—
230C23×C3—122no—
231C23×C3D2414yes—
232C23×C3C3×D814yes—
233C23×C3C2×D1212yes—
234C23×C3C2×D1211yescharacteristic
235C23×C3C2×C3×D412yes—
236C23×C3C2×C3×D411yescharacteristic
237C22×D3—22no—
238C22×D3—42no—
239C22×D3—42no—
240C22×D3—42no—
241C3×D4—64no—
242C3×D4—128no—
243C3×D4—122no—
244C2×C3×C4—22no—
245C2×C3×C4—22no—
246C2×C3×C4—24no—
247C2×C3×C4—24no—
248C2×C3×C4—24no—
249C2×C3×C4—24no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—22no—
253C2×C3×C4—24no—
254C2×C3×C4—44no—
255C2×C3×C4—44no—
256C2×C3×C4—42no—
257C2×C3×C4—62no—
258C2×C3×C4—64no—
259C2×C3×C4—128no—
260C2×C3×C4—124no—
261C2×C3×C4—122no—
262C2×C3×C4C2×D1212yes—
263C2×C3×C4C2×D1211yescharacteristic
264C2×C3×C4#23714yes—
265C2×C3×C4C2×C3×D412yes—
266C2×C3×C4C2×C3×D411yescharacteristic
267C2×C3×C4C3×#4114yes—
268C2×C3×C4C23×D311yescharacteristic
269C2×C3×C4C24×C311yescharacteristic
270#67—48no—
271C2×Dic3—24no—
272C2×Dic3—22no—
273C2×Dic3—48no—
274C2×Dic3—44no—
275C2×Dic3—42no—
276D12—24no—
277D12—42no—
278C3×C8—24no—
279C3×C8—24no—
280C3×C8—44no—
281C2×C32—24no—
282C2×C32#48014yescomplemented
283C2×C32C2×#12311yescharacteristic
284C2×C32C22×D811yescharacteristic
285C2×C32C2×#13711yescharacteristic
286C3×D3—82no—
287C24—61no—
288C24C3×D1211yescharacteristic
289C2×D4—32no—
290C2×D4—64no—
291C2×D4—61no—
292C2×D4—64no—
293C2×D4—124no—
294C22×C4—24no—
295C22×C4—61no—
296C22×C4—64no—
297C22×C4—62no—
298C22×C4—124no—
299C22×C4C3×D1211yescharacteristic
300C22×C4C3×D1212yes—
301C22×C4C22×C3×D312yes—
302C22×C4C22×C3×D311yescharacteristic
303C2×C8—24no—
304C2×C8C22×C3×D314yes—
305C4⋊C4—34no—
306C4⋊C4—32no—
307C4⋊C4—64no—
308C4⋊C4—62no—
309C4⋊C4—61no—
310C22⋊C4—64no—
311C22×C3—22no—
312C22×C3—22no—
313C22×C3—22no—
314C22×C3—28no—
315C22×C3—22no—
316C22×C3—28no—
317C22×C3—22no—
318C22×C3—22no—
319C22×C3—24no—
320C22×C3—22no—
321C22×C3—21no—
322C22×C3—42no—
323C22×C3—42no—
324C22×C3—48no—
325C22×C3—122no—
326C22×C3—122no—
327C22×C3—122no—
328C22×C3—244no—
329C22×C3#88612yes—
330C22×C3C2×D2414yes—
331C22×C3C2×D2412yes—
332C22×C3#90912yes—
333C22×C3C3×#12312yes—
334C22×C3C2×C3×D814yes—
335C22×C3C2×C3×D812yes—
336C22×C3C3×#13712yes—
337C22×C3C22×D1211yescharacteristic
338C22×C3C22×C3×D411yescharacteristic
339C2×D3—42no—
340C2×D3—42no—
341C2×D3—42no—
342C2×D3—84no—
343C3×C4—22no—
344C3×C4—22no—
345C3×C4—22no—
346C3×C4—22no—
347C3×C4—42no—
348C3×C4—124no—
349C3×C4—122no—
350C3×C4#88612yes—
351C3×C4C3×#12312yes—
352C3×C4C2×#23712yes—
353C3×C4C2×C3×#4112yes—
354Dic3—44no—
355Dic3—42no—
356C32C2×#48011yescharacteristic, complemented, Sylow
357C23—22no—
358C23—22no—
359C23—62no—
360C23—122no—
361C23—122no—
362C23—122no—
363C23C3×D2414yes—
364C23C2×C3×D1212yes—
365C23C2×C3×D1211yescharacteristic
366D4—64no—
367D4—128no—
368D4—122no—
369C2×C4—22no—
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—62no—
373C2×C4—64no—
374C2×C4—128no—
375C2×C4—124no—
376C2×C4—122no—
377C2×C4C2×C3×D1212yes—
378C2×C4C2×C3×D1211yescharacteristic
379C2×C4C3×#23714yes—
380C2×C4C23×C3×D311yescharacteristic
381C8—24no—
382C2×C3—24no—
383C2×C3—24no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—24no—
387C2×C3—21no—
388C2×C3—44no—
389C2×C3—242no—
390C2×C3#473614yesdirect product factor
391C2×C3C3×#48014yescomplemented
392C2×C3C2×#88611yescharacteristic
393C2×C3C22×D2411yescharacteristic
394C2×C3C2×#90911yescharacteristic
395C2×C3C2×C3×#12311yescharacteristic
396C2×C3C22×C3×D811yescharacteristic
397C2×C3C2×C3×#13711yescharacteristic
398D3—82no—
399C22—22no—
400C22—22no—
401C22—28no—
402C22—122no—
403C22—122no—
404C22—122no—
405C22—244no—
406C22C3×#88612yes—
407C22C2×C3×D2414yes—
408C22C2×C3×D2412yes—
409C22C3×#90912yes—
410C22C22×C3×D1211yescharacteristic
411C4—22no—
412C4—124no—
413C4—122no—
414C4C3×#88612yes—
415C4C2×C3×#23712yes—
416C3—21no—
417C3C2×#473611yescharacteristic, direct product factor
418C3C2×C3×#48011yescharacteristic, complemented
419C2—24no—
420C2—242no—
421C2C3×#473614yesdirect product factor
422C2C2×C3×#88611yescharacteristic
423C2C22×C3×D2411yescharacteristic
424C2C2×C3×#90911yescharacteristic
subgroupG/H
centerC23×C3C2×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C22⋊C8C2
socleC23×C32C2×D4
prime radicalC2×C3×#930C2
hypercenterC2×C3×C22⋊C8D3
hypocenterC3C2×C3×#480
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C2×C3×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4⋊Dic3C2semidirect
3. C2×C32×C22⋊C8C2semidirect
4. C2×C3×#821C2semidirect
5. C2×C3×#818C2semidirect
6. C3×#4736C2direct (N × H)
8. C2×#4736C3direct (N × H)
21. C2×C3×C4⋊Dic3C22semidirect
22. C32×C22⋊C8C22semidirect
23. C3×#821C22semidirect
24. C3×#818C22semidirect
28. C22×C4⋊Dic3C2×C3semidirect
33. C2×C3×C22⋊C8D3semidirect
34. C2×C3×C22⋊C8C2×C3semidirect
35. C2×#821C2×C3semidirect
36. C2×#818C2×C3semidirect
37. #4736C2×C3direct (N × H)
90. C2×C4⋊Dic3C22×C3semidirect
94. C3×C22⋊C8C2×D3semidirect
95. C3×C22⋊C8C22×C3semidirect
96. #821C22×C3semidirect
97. #818C22×C3semidirect
128. C2×C22⋊C8C3×D3semidirect
217. C22⋊C8C2×C3×D3semidirect
282. C2×C32#480semidirect
356. C32C2×#480semidirect
390. C2×C3#4736direct (N × H)
391. C2×C3C3×#480semidirect
417. C3C2×#4736direct (N × H)
418. C3C2×C3×#480semidirect
421. C2C3×#4736direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9302
C22×C3×C4⋊Dic32
C2×C32×C22⋊C82
C2×C3×#8212
C2×C3×#8182
C3×#47362
C2×C3×#4803
C2×#47363