Finite Group Databasebeta

← C2×C3×#4477 #11796452

Subgroups — C2×C3×#4477 #11796452

Order 1152.

593 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#947C211yesmaximal, characteristic
2C2×C32×#101C211yesmaximal, characteristic, complemented
3C2×C3×#836C211yesmaximal, characteristic, complemented
4C3×#4477C214yesmaximal, direct product factor
5C2×C3×#355—31nomaximal
6C2×#4477C311yesmaximal, characteristic, direct product factor
7C22×C32×Q8C2211yescharacteristic
8C22×C3×D12C411yescharacteristic
9C2×C32×M16—21no—
10C3×#947—21no—
11C3×#947—21no—
12C3×#947C412yes—
13C3×#947C2212yes—
14C2×C3×(C2×D3)⋊C4—21no—
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×C4×Dic3C411yescharacteristic
17C2×C3×#208—21no—
18C32×#101—21no—
19C32×#101C2212yescomplemented
20C3×#836—21no—
21C3×#836C2212yescomplemented
22C2×C3×#124—31no—
23C2×#947C2×C311yescharacteristic
24C2×C3×#101—21no—
25C2×C3×#101—31no—
26C2×C3×#101D311yescharacteristic, complemented
27C2×C3×#101C2×C311yescharacteristic, complemented
28C2×#836C2×C311yescharacteristic, complemented
29C3×#355—34no—
30#4477C2×C314yesdirect product factor
31C23×C3×D3—21no—
32C2×C32×Q8—41no—
33C2×C32×Q8—41no—
34C2×C32×Q8C2×C411yescharacteristic
35C2×C32×Q8D411yescharacteristic
36C2×C32×Q8D411yescharacteristic
37C2×C32×Q8C2311yescharacteristic
38C22×C32×C4C2×C411yescharacteristic
39C22×C32×C4D411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C22×C3×Dic3—21no—
42C2×C3×D12—21no—
43C2×C3×D12—41no—
44C2×C3×D12—41no—
45C2×C3×D12C2×C412yes—
46C32×M16—22no—
47C32×M16—41no—
48C2×C32×C8—41no—
49C3×(C2×D3)⋊C4—22no—
50C3×(C2×D3)⋊C4—22no—
51C3×(C2×D3)⋊C4—22no—
52C3×(C2×D3)⋊C4—22no—
53C3×C4×Dic3—21no—
54C3×C4×Dic3C2×C412yes—
55C3×#208—22no—
56C3×#208—41no—
57C2×C3×C3⋊C8—41no—
58C2×#355—31noSylow
59C22×C3×Q8—21no—
60C22×C3×Q8C2×D311yescharacteristic
61C22×C3×Q8C22×C311yescharacteristic
62C22×C3×D4—31no—
63C22×D12C3×C411yescharacteristic
64C2×C3×M16—22no—
65C2×C3×M16—21no—
66C2×C3×M16—21no—
67C2×C3×M16—61no—
68C3×#124—32no—
69C3×#124—32no—
70C3×#124—61no—
71C3×#124—61no—
72C2×C3×C22⋊C4—61no—
73C2×C3×C22⋊C4—61no—
74C2×C3×C42—31no—
75#947—21no—
76#947—21no—
77#947C3×C412yes—
78#947C22×C312yes—
79C2×(C2×D3)⋊C4—21no—
80C2×(C2×D3)⋊C4—21no—
81C2×C4×Dic3C3×C411yescharacteristic
82C2×#208—21no—
83C3×#101—22no—
84C3×#101—21no—
85C3×#101—21no—
86C3×#101—22no—
87C3×#101—32no—
88C3×#101—61no—
89C3×#101C2×D312yescomplemented
90C3×#101C22×C312yescomplemented
91#836—21no—
92#836C22×C312yescomplemented
93C23×C32C22⋊C411yescharacteristic
94C22×C3×D3—22no—
95C22×C3×D3—44no—
96C22×C3×D3—41no—
97C22×C3×D3—41no—
98C32×Q8—41no—
99C32×Q8—41no—
100C32×Q8—41no—
101C32×Q8—41no—
102C2×C32×C4—21no—
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4—21no—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4C22⋊C411yescharacteristic
109C2×C32×C4C22⋊C411yescharacteristic
110C2×C32×C4C22⋊C411yescharacteristic
111C2×C32×C4C22×C411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C3×Dic3—22no—
115C2×C3×Dic3—42no—
116C3×D12—42no—
117C3×D12—42no—
118C32×C8—42no—
119C3×C3⋊C8—42no—
120C2×#124—31no—
121C2×#101—31no—
122C2×#101C3×D311yescharacteristic, complemented
123#355—34no—
124C24×C3—61no—
125C23×D3—21no—
126C2×C3×Q8—21no—
127C2×C3×Q8—21no—
128C2×C3×Q8—21no—
129C2×C3×Q8—21no—
130C2×C3×Q8—41no—
131C2×C3×Q8—41no—
132C2×C3×Q8—41no—
133C2×C3×Q8—41no—
134C2×C3×Q8—42no—
135C2×C3×Q8—42no—
136C2×C3×Q8C4×D311yescharacteristic
137C2×C3×Q8D1211yescharacteristic
138C2×C3×Q8#6711yescharacteristic
139C2×C3×Q8C2×C3×C411yescharacteristic
140C2×C3×Q8C3×D411yescharacteristic
141C2×C3×Q8C3×D411yescharacteristic
142C2×C3×Q8C22×D311yescharacteristic
143C2×C3×Q8C23×C311yescharacteristic
144C2×C3×D4—32no—
145C2×C3×D4—61no—
146C2×C3×D4—121no—
147C2×C3×D4—121no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—61no—
152C22×C3×C4C4×D311yescharacteristic
153C22×C3×C4D1211yescharacteristic
154C22×C3×C4#6711yescharacteristic
155C22×C3×C4C2×C3×C411yescharacteristic
156C22×C3×C4C3×D411yescharacteristic
157C22×C3×C4C3×D411yescharacteristic
158C22×Dic3—21no—
159C2×D12—21no—
160C2×D12—41no—
161C2×D12—41no—
162C2×D12C2×C3×C412yes—
163C3×M16—24no—
164C3×M16—22no—
165C3×M16—22no—
166C3×M16—42no—
167C3×M16—41no—
168C3×M16—41no—
169C3×M16—62no—
170C3×M16—121no—
171C2×C3×C8—42no—
172C2×C3×C8—41no—
173C2×C3×C8—41no—
174C2×C3×C8—121no—
175C3×C22⋊C4—62no—
176C3×C22⋊C4—62no—
177C3×C22⋊C4—62no—
178C3×C22⋊C4—62no—
179C3×C42—32no—
180C3×C42—61no—
181(C2×D3)⋊C4—22no—
182(C2×D3)⋊C4—22no—
183(C2×D3)⋊C4—22no—
184(C2×D3)⋊C4—22no—
185C4×Dic3—21no—
186C4×Dic3C2×C3×C412yes—
187#208—22no—
188#208—41no—
189C2×C3⋊C8—41no—
190C22×C32—22no—
191C22×C32#9911yescharacteristic
192C22×C32#9911yescharacteristic
193C22×C32C2×C22⋊C411yescharacteristic
194C2×C3×D3—44no—
195C2×C3×D3—42no—
196C2×C3×D3—82no—
197C2×C3×D3—82no—
198C32×C4—21no—
199C32×C4—21no—
200C32×C4—21no—
201C32×C4—21no—
202C32×C4—21no—
203C32×C4—21no—
204C3×Dic3—42no—
205C22×Q8C2×C3×D311yescharacteristic
206C22×D4—31no—
207C2×M16—21no—
208C2×M16—61no—
209#124—32no—
210#124—32no—
211#124—61no—
212#124—61no—
213C2×C22⋊C4—61no—
214C2×C22⋊C4—61no—
215C2×C42—31no—
216#101—21no—
217#101—32no—
218#101—61no—
219#101C2×C3×D312yescomplemented
220C23×C3—21no—
221C23×C3—62no—
222C23×C3—124no—
223C23×C3—121no—
224C23×C3—121no—
225C23×C3(C2×D3)⋊C411yescharacteristic
226C23×C3C3×C22⋊C411yescharacteristic
227C22×D3—22no—
228C22×D3—44no—
229C22×D3—41no—
230C22×D3—41no—
231C3×Q8—41no—
232C3×Q8—41no—
233C3×Q8—41no—
234C3×Q8—41no—
235C3×Q8—41no—
236C3×Q8—41no—
237C3×Q8—41no—
238C3×Q8—41no—
239C3×Q8—42no—
240C3×Q8—42no—
241C3×Q8—42no—
242C3×Q8—42no—
243C3×D4—122no—
244C3×D4—122no—
245C2×C3×C4—22no—
246C2×C3×C4—22no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—62no—
270C2×C3×C4—122no—
271C2×C3×C4(C2×D3)⋊C411yescharacteristic
272C2×C3×C4(C2×D3)⋊C411yescharacteristic
273C2×C3×C4(C2×D3)⋊C411yescharacteristic
274C2×C3×C4C3×C22⋊C411yescharacteristic
275C2×C3×C4C3×C22⋊C411yescharacteristic
276C2×C3×C4C3×C22⋊C411yescharacteristic
277C2×C3×C4C2×C4×D311yescharacteristic
278C2×C3×C4C2×D1211yescharacteristic
279C2×C3×C4C2×#6711yescharacteristic
280C2×C3×C4C22×C3×C411yescharacteristic
281C2×C3×C4C2×C3×D411yescharacteristic
282C2×C3×C4C2×C3×D411yescharacteristic
283C2×Dic3—22no—
284C2×Dic3—42no—
285D12—42no—
286D12—42no—
287C3×C8—44no—
288C3×C8—42no—
289C3×C8—42no—
290C3×C8—122no—
291C3⋊C8—42no—
292C2×C32—21no—
293C2×C32—21no—
294C2×C32#35512yescomplemented
295C2×C32C2×#9911yescharacteristic
296C3×D3—82no—
297C24—61no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8C3×C4×D311yescharacteristic
301C2×Q8C3×D1211yescharacteristic
302C2×Q8C3×#6711yescharacteristic
303C2×Q8C22×C3×D311yescharacteristic
304C2×D4—32no—
305C2×D4—61no—
306C2×D4—121no—
307C2×D4—121no—
308C22×C4—61no—
309C22×C4C3×C4×D311yescharacteristic
310C22×C4C3×D1211yescharacteristic
311C22×C4C3×#6711yescharacteristic
312M16—22no—
313M16—41no—
314M16—62no—
315M16—121no—
316C2×C8—41no—
317C2×C8—121no—
318C22⋊C4—62no—
319C22⋊C4—62no—
320C22⋊C4—62no—
321C22⋊C4—62no—
322C42—32no—
323C42—61no—
324C22×C3—22no—
325C22×C3—22no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—42no—
330C22×C3—124no—
331C22×C3—122no—
332C22×C3—242no—
333C22×C3—242no—
334C22×C3#80611yescharacteristic
335C22×C3#80611yescharacteristic
336C22×C3C3×#9911yescharacteristic
337C22×C3C3×#9911yescharacteristic
338C22×C3C2×(C2×D3)⋊C411yescharacteristic
339C22×C3C2×C3×C22⋊C411yescharacteristic
340C2×D3—44no—
341C2×D3—42no—
342C2×D3—82no—
343C2×D3—82no—
344C3×C4—22no—
345C3×C4—22no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—41no—
359C3×C4—41no—
360C3×C4—41no—
361C3×C4—41no—
362C3×C4—122no—
363Dic3—42no—
364C32C2×#35511yescharacteristic, complemented, Sylow
365C23—62no—
366C23—124no—
367C23—121no—
368C23—121no—
369C23C3×(C2×D3)⋊C411yescharacteristic
370Q8—41no—
371Q8—41no—
372Q8—41no—
373Q8—41no—
374D4—122no—
375D4—122no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—62no—
383C2×C4—122no—
384C2×C4C3×(C2×D3)⋊C411yescharacteristic
385C2×C4C3×(C2×D3)⋊C411yescharacteristic
386C2×C4C3×(C2×D3)⋊C411yescharacteristic
387C2×C4C2×C3×C4×D311yescharacteristic
388C2×C4C2×C3×D1211yescharacteristic
389C2×C4C2×C3×#6711yescharacteristic
390C8—42no—
391C8—122no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—22no—
397C2×C3—21no—
398C2×C3—41no—
399C2×C3—41no—
400C2×C3—242no—
401C2×C3#447712yesdirect product factor
402C2×C3C3×#35512yescomplemented
403C2×C3C2×#80611yescharacteristic
404C2×C3C2×C3×#9911yescharacteristic
405D3—82no—
406C22—22no—
407C22—124no—
408C22—122no—
409C22—242no—
410C22—242no—
411C22C3×#80611yescharacteristic
412C22C3×#80611yescharacteristic
413C22C2×C3×(C2×D3)⋊C411yescharacteristic
414C4—21no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—21no—
419C4—21no—
420C4—122no—
421C3—21no—
422C3C2×#447711yescharacteristic, direct product factor
423C3C2×C3×#35511yescharacteristic, complemented
424C2—21no—
425C2—21no—
426C2—242no—
427C2C3×#447712yesdirect product factor
428C2C2×C3×#80611yescharacteristic
subgroupG/H
centerC22×C3#806
commutatorC2×C3×C4C22×C3×C4
FrattiniC2×Q8C22×C3×D3
FittingC2×C32×#101C2
socleC22×C32#99
prime radicalC22×C3×D12C4
cosocleC2×C3×Q8C23×C3
hypercenterC2×C3×#101D3
hypocenterC3C2×C3×#355
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3 ◁ C22×C3×Q8 ◁ C2×C3×#101

Complements

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

NH ≅ G/Ntype
2. C2×C32×#101C2semidirect
3. C2×C3×#836C2semidirect
4. C3×#4477C2direct (N × H)
6. C2×#4477C3direct (N × H)
19. C32×#101C22semidirect
21. C3×#836C22semidirect
26. C2×C3×#101D3semidirect
27. C2×C3×#101C2×C3semidirect
28. C2×#836C2×C3semidirect
30. #4477C2×C3direct (N × H)
89. C3×#101C2×D3semidirect
90. C3×#101C22×C3semidirect
92. #836C22×C3semidirect
122. C2×#101C3×D3semidirect
219. #101C2×C3×D3semidirect
294. C2×C32#355semidirect
364. C32C2×#355semidirect
401. C2×C3#4477direct (N × H)
402. C2×C3C3×#355semidirect
422. C3C2×#4477direct (N × H)
423. C3C2×C3×#355semidirect
427. C2C3×#4477direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9472
C2×C32×#1012
C2×C3×#8362
C3×#44772
C2×C3×#3553
C2×#44773