Finite Group Databasebeta

← C3×#69505 #11786451

Subgroups — C3×#69505 #11786451

Order 1152.

837 conjugacy classes of subgroups.

The subgroup lattice has 457 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊Dic3C211yesmaximal, characteristic
2C32×#380C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4C2×C3×#808C212yesmaximal, complemented
5C3×#4529C212yesmaximal, complemented
6C3×#1853—31nomaximal
7#69505C311yesmaximal, characteristic, direct product factor
8C23×C32×C4C2211yescharacteristic
9C23×C3×Dic3—21no—
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C22⋊C4—21no—
13C2×C3×C4⋊Dic3—21no—
14C2×C3×C4⋊Dic3—24no—
15C2×C3×C4⋊Dic3C2212yes—
16C22×C3×C3⋊C8C2212yes—
17C32×#95—21no—
18C3×#830C414yescomplemented
19C3×#808—24no—
20C22×C3×C4⋊C4—31no—
21C22×C4⋊Dic3C2×C311yescharacteristic
22C2×C3×#106—32no—
23C2×C3×C22⋊C8—31no—
24C3×#380—21no—
25C3×#380D311yescharacteristic
26C3×#380C2×C311yescharacteristic
27C2×#830C2×C311yescharacteristic
28C2×#808C2×C312yescomplemented
29C3×#340—32no—
30#4529C2×C312yescomplemented
31C24×C32D411yescharacteristic
32C22×C32×C4—22no—
33C22×C32×C4—22no—
34C22×C32×C4—21no—
35C22×C32×C4—21no—
36C22×C32×C4C2×C412yes—
37C22×C32×C4D411yescharacteristic
38C22×C32×C4Q812yes—
39C22×C32×C4C2311yescharacteristic
40C22×C3×Dic3—24no—
41C22×C3×Dic3—22no—
42C22×C3×Dic3—42no—
43C22×C3×Dic3—42no—
44C32×C4⋊C4—22no—
45C32×C4⋊C4—22no—
46C32×C22⋊C4—42no—
47C3×C4⋊Dic3—24no—
48C3×C4⋊Dic3—22no—
49C3×C4⋊Dic3D414yes—
50C2×C3×C3⋊C8—22no—
51C2×C3×C3⋊C8—22no—
52C2×C3×C3⋊C8C2×C414yescomplemented
53#1853—31noSylow
54C23×C3×C4—21no—
55C23×C3×C4—61no—
56C23×C3×C4C2×D311yescharacteristic
57C23×C3×C4C22×C311yescharacteristic
58C23×Dic3—21no—
59C22×C3×C8—32no—
60C2×C3×C4⋊C4—21no—
61C2×C3×C4⋊C4—21no—
62C2×C3×C4⋊C4—32no—
63C2×C3×C4⋊C4—64no—
64C2×C3×C4⋊C4—61no—
65C2×C3×C4⋊C4C2×D311yescharacteristic
66C2×C3×C4⋊C4C2×D311yescharacteristic
67C2×C3×C4⋊C4C22×C311yescharacteristic
68C2×C3×C4⋊C4C22×C311yescharacteristic
69C2×C3×C22⋊C4—22no—
70C2×C3×C22⋊C4—21no—
71C2×C3×C22⋊C4—21no—
72C2×C4⋊Dic3—21no—
73C2×C4⋊Dic3—24no—
74C2×C4⋊Dic3C22×C312yes—
75C22×C3⋊C8C22×C312yes—
76C3×#106—64no—
77C3×C22⋊C8—34no—
78C3×#95—22no—
79C3×#95—21no—
80C3×#95—21no—
81#830C3×C414yescomplemented
82#808—24no—
83C23×C32—21no—
84C23×C32—21no—
85C23×C32—21no—
86C23×C32—21no—
87C23×C32C4⋊C412yes—
88C23×C32SD1612yes—
89C23×C32SD1612yes—
90C23×C32C2×D411yescharacteristic
91C2×C32×C4—21no—
92C2×C32×C4—21no—
93C2×C32×C4—24no—
94C2×C32×C4—24no—
95C2×C32×C4—41no—
96C2×C32×C4—41no—
97C2×C32×C4—41no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4—41no—
101C2×C32×C4C4⋊C412yes—
102C2×C32×C4C22×C411yescharacteristic
103C2×C32×C4C2×D412yes—
104C2×C32×C4C2×Q811yescharacteristic
105C2×C32×C4#4112yes—
106C2×C3×Dic3—24no—
107C2×C3×Dic3—48no—
108C2×C3×Dic3—42no—
109C2×C3×Dic3—42no—
110C3×C3⋊C8—24no—
111C22×C4⋊C4—31no—
112C2×#106—32no—
113C2×C22⋊C8—31no—
114#380C3×D311yescharacteristic
115#340—32no—
116C24×C3—21no—
117C24×C3#6711yescharacteristic
118C24×C3C3×D411yescharacteristic
119C22×C3×C4—22no—
120C22×C3×C4—22no—
121C22×C3×C4—22no—
122C22×C3×C4—22no—
123C22×C3×C4—22no—
124C22×C3×C4—22no—
125C22×C3×C4—21no—
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—22no—
130C22×C3×C4—22no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—42no—
134C22×C3×C4—42no—
135C22×C3×C4—64no—
136C22×C3×C4—62no—
137C22×C3×C4—122no—
138C22×C3×C4—122no—
139C22×C3×C4Dic612yes—
140C22×C3×C4C4×D312yes—
141C22×C3×C4#6711yescharacteristic
142C22×C3×C4C2×C3×C412yes—
143C22×C3×C4C3×D411yescharacteristic
144C22×C3×C4C3×Q812yes—
145C22×C3×C4C22×D311yescharacteristic
146C22×C3×C4C23×C311yescharacteristic
147C22×Dic3—24no—
148C22×Dic3—22no—
149C22×Dic3—42no—
150C22×Dic3—42no—
151C2×C3×C8—34no—
152C2×C3×C8—62no—
153C2×C3×C8—62no—
154C3×C4⋊C4—22no—
155C3×C4⋊C4—22no—
156C3×C4⋊C4—22no—
157C3×C4⋊C4—22no—
158C3×C4⋊C4—34no—
159C3×C4⋊C4—42no—
160C3×C4⋊C4—42no—
161C3×C4⋊C4—64no—
162C3×C4⋊C4—62no—
163C3×C22⋊C4—44no—
164C3×C22⋊C4—42no—
165C3×C22⋊C4—42no—
166C4⋊Dic3—24no—
167C4⋊Dic3—22no—
168C4⋊Dic3C3×D414yes—
169C2×C3⋊C8—22no—
170C2×C3⋊C8—22no—
171C2×C3⋊C8C2×C3×C414yescomplemented
172C22×C32—22no—
173C22×C32—22no—
174C22×C32—22no—
175C22×C32—22no—
176C22×C32—22no—
177C22×C32—22no—
178C22×C32#10614yescomplemented
179C22×C32C2×C4⋊C411yescharacteristic
180C22×C32#12011yescharacteristic
181C22×C32#12311yescharacteristic
182C22×C32C2×SD1611yescharacteristic
183C22×C32C2×SD1611yescharacteristic
184C22×C32AGL(1,ℤ/8)11yescharacteristic
185C22×C32#13711yescharacteristic
186C32×C4—22no—
187C32×C4—81no—
188C32×C4—81no—
189C32×C4C4×D412yes—
190C32×C4C22⋊Q812yes—
191C3×Dic3—44no—
192C23×C4—61no—
193C23×C4C2×C3×D311yescharacteristic
194C22×C8—32no—
195C2×C4⋊C4—32no—
196C2×C4⋊C4—64no—
197C2×C4⋊C4—61no—
198C2×C4⋊C4C2×C3×D311yescharacteristic
199C2×C4⋊C4C2×C3×D311yescharacteristic
200C2×C22⋊C4—21no—
201#106—64no—
202C22⋊C8—34no—
203#95—21no—
204C23×C3—21no—
205C23×C3—21no—
206C23×C3—21no—
207C23×C3—21no—
208C23×C3—21no—
209C23×C3—21no—
210C23×C3—21no—
211C23×C3—21no—
212C23×C3—22no—
213C23×C3—22no—
214C23×C3—22no—
215C23×C3—21no—
216C23×C3—41no—
217C23×C3—41no—
218C23×C3—41no—
219C23×C3—41no—
220C23×C3Dic3⋊C412yes—
221C23×C3#21412yes—
222C23×C3#21512yes—
223C23×C3C3×C4⋊C412yes—
224C23×C3C3×SD1612yes—
225C23×C3C3×SD1612yes—
226C23×C3C2×#6711yescharacteristic
227C23×C3C2×C3×D411yescharacteristic
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—24no—
233C2×C3×C4—24no—
234C2×C3×C4—24no—
235C2×C3×C4—24no—
236C2×C3×C4—22no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—44no—
242C2×C3×C4—44no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—42no—
246C2×C3×C4—42no—
247C2×C3×C4—42no—
248C2×C3×C4—42no—
249C2×C3×C4—42no—
250C2×C3×C4—42no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—64no—
264C2×C3×C4—128no—
265C2×C3×C4—122no—
266C2×C3×C4—122no—
267C2×C3×C4Dic3⋊C412yes—
268C2×C3×C4C3×C4⋊C412yes—
269C2×C3×C4C2×Dic611yescharacteristic
270C2×C3×C4C2×C4×D311yescharacteristic
271C2×C3×C4D3×D412yes—
272C2×C3×C4#23712yes—
273C2×C3×C4C22×C3×C411yescharacteristic
274C2×C3×C4C2×C3×D412yes—
275C2×C3×C4C2×C3×Q811yescharacteristic
276C2×C3×C4C3×#4112yes—
277C2×Dic3—24no—
278C2×Dic3—48no—
279C2×Dic3—42no—
280C2×Dic3—42no—
281C3×C8—64no—
282C3⋊C8—24no—
283C2×C32—24no—
284C2×C32#38511yescharacteristic
285C2×C32C2×#10611yescharacteristic
286C2×C32#42811yescharacteristic
287C2×C32#44811yescharacteristic
288C2×C32#45011yescharacteristic
289C2×C32#48111yescharacteristic
290C2×C32#48311yescharacteristic
291C24C3×#6711yescharacteristic
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—64no—
297C22×C4—62no—
298C22×C4—122no—
299C22×C4—122no—
300C22×C4C3×Dic612yes—
301C22×C4C3×C4×D312yes—
302C22×C4C3×#6711yescharacteristic
303C22×C4C22×C3×D311yescharacteristic
304C2×C8—34no—
305C2×C8—62no—
306C2×C8—62no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—34no—
310C4⋊C4—64no—
311C4⋊C4—62no—
312C22⋊C4—42no—
313C22×C3—22no—
314C22×C3—22no—
315C22×C3—22no—
316C22×C3—22no—
317C22×C3—22no—
318C22×C3—22no—
319C22×C3—22no—
320C22×C3—22no—
321C22×C3—22no—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—22no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—24no—
333C22×C3—42no—
334C22×C3—42no—
335C22×C3—42no—
336C22×C3—42no—
337C22×C3—42no—
338C22×C3—42no—
339C22×C3#80814yescomplemented
340C22×C3C3×#10614yescomplemented
341C22×C3C2×Dic3⋊C411yescharacteristic
342C22×C3C2×#21411yescharacteristic
343C22×C3#93511yescharacteristic
344C22×C3#93711yescharacteristic
345C22×C3C2×#21511yescharacteristic
346C22×C3#94911yescharacteristic
347C22×C3#95111yescharacteristic
348C22×C3C2×C3×C4⋊C411yescharacteristic
349C22×C3C3×#12011yescharacteristic
350C22×C3C3×#12311yescharacteristic
351C22×C3C2×C3×SD1611yescharacteristic
352C22×C3C2×C3×SD1611yescharacteristic
353C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
354C22×C3C3×#13711yescharacteristic
355C3×C4—22no—
356C3×C4—22no—
357C3×C4—22no—
358C3×C4—22no—
359C3×C4—42no—
360C3×C4—82no—
361C3×C4—82no—
362C3×C4—81no—
363C3×C4—81no—
364C3×C4—81no—
365C3×C4—81no—
366C3×C4—124no—
367C3×C4#87812yes—
368C3×C4#67⋊C412yes—
369C3×C4C3×C4×D412yes—
370C3×C4C3×C22⋊Q812yes—
371Dic3—44no—
372C32#185311yescharacteristic, complemented, Sylow
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23C3×Dic3⋊C412yes—
378C23C3×#21412yes—
379C23C3×#21512yes—
380C23C2×C3×#6711yescharacteristic
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—24no—
384C2×C4—24no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—64no—
392C2×C4—128no—
393C2×C4—122no—
394C2×C4—122no—
395C2×C4C3×Dic3⋊C412yes—
396C2×C4C2×C3×Dic611yescharacteristic
397C2×C4C2×C3×C4×D311yescharacteristic
398C2×C4C3×D3×D412yes—
399C2×C4C3×#23712yes—
400C8—64no—
401C2×C3—24no—
402C2×C3—24no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—44no—
411C2×C3#494611yescharacteristic
412C2×C3C2×#80811yescharacteristic
413C2×C3#499511yescharacteristic
414C2×C3#503411yescharacteristic
415C2×C3#504011yescharacteristic
416C2×C3#504311yescharacteristic
417C2×C3#504611yescharacteristic
418C2×C3C3×#38511yescharacteristic
419C2×C3C2×C3×#10611yescharacteristic
420C2×C3C3×#42811yescharacteristic
421C2×C3C3×#44811yescharacteristic
422C2×C3C3×#45011yescharacteristic
423C2×C3C3×#48111yescharacteristic
424C2×C3C3×#48311yescharacteristic
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22C3×#80814yescomplemented
432C22C2×C3×Dic3⋊C411yescharacteristic
433C22C2×C3×#21411yescharacteristic
434C22C3×#93511yescharacteristic
435C22C3×#93711yescharacteristic
436C22C2×C3×#21511yescharacteristic
437C22C3×#94911yescharacteristic
438C22C3×#95111yescharacteristic
439C4—22no—
440C4—81no—
441C4—81no—
442C4—124no—
443C4C3×#87812yes—
444C4C3×#67⋊C412yes—
445C3—21no—
446C3#6950511yescharacteristic, direct product factor
447C3C3×#185311yescharacteristic, complemented
448C2—24no—
449C2C3×#494611yescharacteristic
450C2C2×C3×#80811yescharacteristic
451C2C3×#499511yescharacteristic
452C2C3×#503411yescharacteristic
453C2C3×#504011yescharacteristic
454C2C3×#504311yescharacteristic
455C2C3×#504611yescharacteristic
subgroupG/H
centerC23×C3C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#380C2
socleC23×C32C2×D4
prime radicalC24×C32D4
cosocleC22×C3×C4C23×C3
hypercenterC3×#380D3
hypocenterC3C3×#1853
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
4. C2×C3×#808C2semidirect
5. C3×#4529C2semidirect
7. #69505C3direct (N × H)
18. C3×#830C4semidirect
28. C2×#808C2×C3semidirect
30. #4529C2×C3semidirect
52. C2×C3×C3⋊C8C2×C4semidirect
81. #830C3×C4semidirect
171. C2×C3⋊C8C2×C3×C4semidirect
178. C22×C32#106semidirect
339. C22×C3#808semidirect
340. C22×C3C3×#106semidirect
372. C32#1853semidirect
431. C22C3×#808semidirect
446. C3#69505direct (N × H)
447. C3C3×#1853semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊Dic32
C32×#3802
C2×C3×#8302
C2×C3×#8082
C3×#45292
C3×#18533
#695053