Finite Group Databasebeta

← C3×#69517 #11788126

Subgroups — C3×#69517 #11788126

Order 1152.

941 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#930C211yesmaximal, characteristic
2C22×C3×#208C211yesmaximal, characteristic, complemented
3C32×#380C211yesmaximal, characteristic, complemented
4C2×C3×#809C212yesmaximal, complemented
5C3×#4529C212yesmaximal, complemented
6C3×#1895—31nomaximal
7#69517C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2211yescharacteristic
9C22×C3×#67—21no—
10C22×C3×D12C2211yescharacteristic
11C2×C32×C4⋊C4C2212yes—
12C2×C32×C22⋊C4—21no—
13C3×#930—22no—
14C3×#930C414yescomplemented
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×#208—22no—
18C2×C3×#208—24no—
19C22×C3×C3⋊C8C2212yes—
20C32×#95—21no—
21C3×#809—24no—
22C22×C3×M16—31no—
23C2×C3×#121—31no—
24C2×#930C2×C311yescharacteristic
25C22×#208C2×C311yescharacteristic, complemented
26C2×C3×#102—32no—
27C3×#380—21no—
28C3×#380D311yescharacteristic, complemented
29C3×#380C2×C311yescharacteristic, complemented
30C2×#809C2×C312yescomplemented
31C3×#340—32no—
32#4529C2×C312yescomplemented
33C24×C32D411yescharacteristic
34C23×C3×D3—21no—
35C22×C32×C4—22no—
36C22×C32×C4—22no—
37C22×C32×C4—22no—
38C22×C32×C4C2×C412yes—
39C22×C32×C4D411yescharacteristic
40C22×C32×C4D412yes—
41C22×C32×C4C2311yescharacteristic
42C2×C3×#67—24no—
43C2×C3×#67—44no—
44C22×C3×Dic3—21no—
45C2×C3×D12—22no—
46C2×C3×D12—22no—
47C2×C3×D12—21no—
48C2×C3×D12C2×C412yes—
49C32×C4⋊C4—22no—
50C32×C4⋊C4—22no—
51C32×C22⋊C4—42no—
52C3×(C2×D3)⋊C4—24no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3C2×C412yes—
55C3×#208—28no—
56C2×C3×C3⋊C8—22no—
57C2×C3×C3⋊C8—22no—
58C2×C3×C3⋊C8D414yescomplemented
59#1895—31noSylow
60C22×C3×D4—31no—
61C22×C3×D4—61no—
62C23×C3×C4—21no—
63C23×C3×C4C2×D311yescharacteristic
64C23×C3×C4C22×C311yescharacteristic
65C22×#67—21no—
66C22×D12C22×C311yescharacteristic
67C2×C3×M16—64no—
68C2×C3×M16—62no—
69C22×C3×C8—32no—
70C3×#121—34no—
71C3×#121—62no—
72C2×C3×C4⋊C4—22no—
73C2×C3×C4⋊C4—31no—
74C2×C3×C4⋊C4C2×D312yes—
75C2×C3×C4⋊C4C22×C312yes—
76C2×C3×C22⋊C4—22no—
77C2×C3×C22⋊C4—21no—
78C2×C3×C22⋊C4—21no—
79C2×C3×C22⋊C4—61no—
80#930—22no—
81#930C3×C414yescomplemented
82C2×(C2×D3)⋊C4—21no—
83C2×C4⋊Dic3C22×C311yescharacteristic
84C2×#208—22no—
85C2×#208—24no—
86C22×C3⋊C8C22×C312yes—
87C3×#102—64no—
88C3×#95—22no—
89C3×#95—21no—
90C3×#95—21no—
91#809—24no—
92C23×C32—21no—
93C23×C32—21no—
94C23×C32—22no—
95C23×C32—22no—
96C23×C32C22⋊C412yes—
97C23×C32C2×D411yescharacteristic
98C22×C3×D3—22no—
99C22×C3×D3—42no—
100C22×C3×D3—41no—
101C22×C3×D3—42no—
102C22×C3×D3—41no—
103C2×C32×C4—22no—
104C2×C32×C4—24no—
105C2×C32×C4—22no—
106C2×C32×C4—22no—
107C2×C32×C4—42no—
108C2×C32×C4—42no—
109C2×C32×C4—42no—
110C2×C32×C4C22⋊C412yes—
111C2×C32×C4C22×C411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D412yes—
114C2×C32×C4#4112yes—
115C3×#67—48no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—42no—
118C3×D12—24no—
119C3×D12—41no—
120C3×D12—41no—
121C3×C3⋊C8—24no—
122C22×M16—31no—
123C2×#121—31no—
124C2×#102—32no—
125#380C3×D311yescharacteristic, complemented
126#340—32no—
127C24×C3—21no—
128C24×C3—61no—
129C24×C3#6711yescharacteristic
130C24×C3C3×D411yescharacteristic
131C23×D3—21no—
132C2×C3×D4—32no—
133C2×C3×D4—64no—
134C2×C3×D4—61no—
135C2×C3×D4—62no—
136C2×C3×D4—62no—
137C2×C3×D4—124no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—22no—
141C22×C3×C4—22no—
142C22×C3×C4—24no—
143C22×C3×C4—22no—
144C22×C3×C4—22no—
145C22×C3×C4—22no—
146C22×C3×C4—22no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—42no—
150C22×C3×C4—42no—
151C22×C3×C4—61no—
152C22×C3×C4C4×D312yes—
153C22×C3×C4D1212yes—
154C22×C3×C4#6711yescharacteristic
155C22×C3×C4C2×C3×C412yes—
156C22×C3×C4C3×D412yes—
157C22×C3×C4C3×D411yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C23×C311yescharacteristic
160C2×#67—24no—
161C2×#67—44no—
162C22×Dic3—21no—
163C2×D12—22no—
164C2×D12—22no—
165C2×D12—21no—
166C2×D12C2×C3×C412yes—
167C3×M16—68no—
168C2×C3×C8—34no—
169C2×C3×C8—62no—
170C2×C3×C8—62no—
171C3×C4⋊C4—22no—
172C3×C4⋊C4—22no—
173C3×C4⋊C4—22no—
174C3×C4⋊C4—22no—
175C3×C4⋊C4—32no—
176C3×C4⋊C4—42no—
177C3×C4⋊C4—42no—
178C3×C4⋊C4—61no—
179C3×C22⋊C4—44no—
180C3×C22⋊C4—42no—
181C3×C22⋊C4—42no—
182C3×C22⋊C4—64no—
183(C2×D3)⋊C4—24no—
184C4⋊Dic3—21no—
185C4⋊Dic3C2×C3×C412yes—
186#208—28no—
187C2×C3⋊C8—22no—
188C2×C3⋊C8—22no—
189C2×C3⋊C8C3×D414yescomplemented
190C22×C32—22no—
191C22×C32—22no—
192C22×C32—22no—
193C22×C32—42no—
194C22×C32—42no—
195C22×C32C2×C22⋊C411yescharacteristic
196C22×C32#12112yes—
197C22×C32AGL(1,ℤ/8)11yescharacteristic
198C22×C32AGL(1,ℤ/8)12yes—
199C22×C32#13711yescharacteristic
200C2×C3×D3—42no—
201C2×C3×D3—42no—
202C2×C3×D3—42no—
203C2×C3×D3—82no—
204C2×C3×D3—82no—
205C32×C4—22no—
206C32×C4—82no—
207C32×C4C4×D412yes—
208C32×C4#12011yescharacteristic
209C32×C4#12311yescharacteristic
210C3×Dic3—42no—
211C22×D4—31no—
212C22×D4—61no—
213C23×C4C2×C3×D311yescharacteristic
214C2×M16—64no—
215C2×M16—62no—
216C22×C8—32no—
217#121—34no—
218#121—62no—
219C2×C4⋊C4—31no—
220C2×C4⋊C4C2×C3×D312yes—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—61no—
223#102—64no—
224#95—21no—
225C23×C3—22no—
226C23×C3—22no—
227C23×C3—21no—
228C23×C3—22no—
229C23×C3—21no—
230C23×C3—22no—
231C23×C3—22no—
232C23×C3—21no—
233C23×C3—22no—
234C23×C3—21no—
235C23×C3—22no—
236C23×C3—21no—
237C23×C3—42no—
238C23×C3—42no—
239C23×C3—62no—
240C23×C3—121no—
241C23×C3—122no—
242C23×C3—121no—
243C23×C3—122no—
244C23×C3(C2×D3)⋊C412yes—
245C23×C3C3×C22⋊C412yes—
246C23×C3C2×#6711yescharacteristic
247C23×C3C2×C3×D411yescharacteristic
248C22×D3—22no—
249C22×D3—42no—
250C22×D3—42no—
251C22×D3—41no—
252C22×D3—41no—
253C3×D4—64no—
254C3×D4—128no—
255C3×D4—121no—
256C3×D4—121no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—24no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—24no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—44no—
271C2×C3×C4—42no—
272C2×C3×C4—42no—
273C2×C3×C4—42no—
274C2×C3×C4—44no—
275C2×C3×C4—44no—
276C2×C3×C4—44no—
277C2×C3×C4—42no—
278C2×C3×C4—42no—
279C2×C3×C4—42no—
280C2×C3×C4—42no—
281C2×C3×C4—42no—
282C2×C3×C4—42no—
283C2×C3×C4—62no—
284C2×C3×C4—122no—
285C2×C3×C4(C2×D3)⋊C412yes—
286C2×C3×C4C3×C22⋊C412yes—
287C2×C3×C4C2×C4×D311yescharacteristic
288C2×C3×C4C2×D1211yescharacteristic
289C2×C3×C4D3×D412yes—
290C2×C3×C4#23712yes—
291C2×C3×C4C22×C3×C411yescharacteristic
292C2×C3×C4C2×C3×D411yescharacteristic
293C2×C3×C4C2×C3×D412yes—
294C2×C3×C4C3×#4112yes—
295#67—48no—
296C2×Dic3—22no—
297C2×Dic3—42no—
298D12—24no—
299D12—41no—
300D12—41no—
301C3×C8—64no—
302C3⋊C8—24no—
303C2×C32—42no—
304C2×C32#38611yescharacteristic
305C2×C32#41711yescharacteristic
306C2×C32#41811yescharacteristic
307C2×C32#46812yes—
308C2×C32#46912yes—
309C3×D3—82no—
310C24—61no—
311C24C3×#6711yescharacteristic
312C2×D4—32no—
313C2×D4—64no—
314C2×D4—61no—
315C2×D4—62no—
316C2×D4—62no—
317C2×D4—124no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—61no—
322C22×C4C3×C4×D312yes—
323C22×C4C3×D1212yes—
324C22×C4C3×#6711yescharacteristic
325C22×C4C22×C3×D311yescharacteristic
326M16—68no—
327C2×C8—34no—
328C2×C8—62no—
329C2×C8—62no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—32no—
333C4⋊C4—61no—
334C22⋊C4—42no—
335C22⋊C4—64no—
336C22×C3—24no—
337C22×C3—22no—
338C22×C3—22no—
339C22×C3—22no—
340C22×C3—22no—
341C22×C3—22no—
342C22×C3—22no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—22no—
346C22×C3—21no—
347C22×C3—22no—
348C22×C3—42no—
349C22×C3—42no—
350C22×C3—44no—
351C22×C3—44no—
352C22×C3—42no—
353C22×C3—42no—
354C22×C3—42no—
355C22×C3—42no—
356C22×C3—122no—
357C22×C3—122no—
358C22×C3—122no—
359C22×C3—242no—
360C22×C3—242no—
361C22×C3C2×(C2×D3)⋊C411yescharacteristic
362C22×C3#93211yescharacteristic
363C22×C3#93912yes—
364C22×C3#94211yescharacteristic
365C22×C3#94912yes—
366C22×C3C2×C3×C22⋊C411yescharacteristic
367C22×C3C3×#12112yes—
368C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
369C22×C3C3×AGL(1,ℤ/8)12yes—
370C22×C3C3×#13711yescharacteristic
371C2×D3—42no—
372C2×D3—42no—
373C2×D3—42no—
374C2×D3—82no—
375C2×D3—82no—
376C3×C4—22no—
377C3×C4—22no—
378C3×C4—22no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—42no—
382C3×C4—84no—
383C3×C4—82no—
384C3×C4—82no—
385C3×C4—122no—
386C3×C4#67⋊C412yes—
387C3×C4#88211yescharacteristic
388C3×C4#88611yescharacteristic
389C3×C4C3×C4×D412yes—
390C3×C4C3×#12011yescharacteristic
391C3×C4C3×#12311yescharacteristic
392Dic3—42no—
393C32#189511yescharacteristic, complemented, Sylow
394C23—21no—
395C23—22no—
396C23—21no—
397C23—22no—
398C23—62no—
399C23—121no—
400C23—122no—
401C23—121no—
402C23—122no—
403C23C3×(C2×D3)⋊C412yes—
404C23C2×C3×#6711yescharacteristic
405D4—64no—
406D4—128no—
407D4—121no—
408D4—121no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—62no—
417C2×C4—122no—
418C2×C4C3×(C2×D3)⋊C412yes—
419C2×C4C2×C3×C4×D311yescharacteristic
420C2×C4C2×C3×D1211yescharacteristic
421C2×C4C3×D3×D412yes—
422C2×C4C3×#23712yes—
423C8—64no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—22no—
428C2×C3—22no—
429C2×C3—44no—
430C2×C3—42no—
431C2×C3—42no—
432C2×C3—242no—
433C2×C3#495811yescharacteristic
434C2×C3#496611yescharacteristic
435C2×C3#500111yescharacteristic
436C2×C3#503912yes—
437C2×C3#504912yes—
438C2×C3C3×#38611yescharacteristic
439C2×C3C3×#41711yescharacteristic
440C2×C3C3×#41811yescharacteristic
441C2×C3C3×#46812yes—
442C2×C3C3×#46912yes—
443D3—82no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—42no—
448C22—42no—
449C22—122no—
450C22—122no—
451C22—122no—
452C22—242no—
453C22—242no—
454C22C2×C3×(C2×D3)⋊C411yescharacteristic
455C22C3×#93211yescharacteristic
456C22C3×#93912yes—
457C22C3×#94211yescharacteristic
458C22C3×#94912yes—
459C4—22no—
460C4—82no—
461C4—122no—
462C4C3×#67⋊C412yes—
463C4C3×#88211yescharacteristic
464C4C3×#88611yescharacteristic
465C3—21no—
466C3#6951711yescharacteristic, direct product factor
467C3C3×#189511yescharacteristic, complemented
468C2—42no—
469C2—242no—
470C2C3×#495811yescharacteristic
471C2C3×#496611yescharacteristic
472C2C3×#500111yescharacteristic
473C2C3×#503912yes—
474C2C3×#504912yes—
subgroupG/H
centerC23×C3C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#380C2
socleC23×C32C2×D4
prime radicalC2×C3×#930C2
cosocleC22×C3×C4C23×C3
hypercenterC3×#380D3
hypocenterC3C3×#1895
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C3×#380

Complements

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

NH ≅ G/Ntype
2. C22×C3×#208C2semidirect
3. C32×#380C2semidirect
4. C2×C3×#809C2semidirect
5. C3×#4529C2semidirect
7. #69517C3direct (N × H)
14. C3×#930C4semidirect
25. C22×#208C2×C3semidirect
28. C3×#380D3semidirect
29. C3×#380C2×C3semidirect
30. C2×#809C2×C3semidirect
32. #4529C2×C3semidirect
58. C2×C3×C3⋊C8D4semidirect
81. #930C3×C4semidirect
125. #380C3×D3semidirect
189. C2×C3⋊C8C3×D4semidirect
393. C32#1895semidirect
466. C3#69517direct (N × H)
467. C3C3×#1895semidirect

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×#2082
C32×#3802
C2×C3×#8092
C3×#45292
C3×#18953
#695173