Finite Group Databasebeta

← C3×#69515 #11788059

Subgroups — C3×#69515 #11788059

Order 1152.

981 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#930C211yesmaximal, characteristic
2C23×C3×C3⋊C8C211yesmaximal, characteristic, complemented
3C32×#380C211yesmaximal, characteristic, complemented
4C2×C3×#809C212yesmaximal, complemented
5C3×#4529C212yesmaximal, complemented
6C3×#1893—31nomaximal
7#69515C311yesmaximal, 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
17C22×C3×C3⋊C8—22no—
18C22×C3×C3⋊C8—24no—
19C22×C3×C3⋊C8C2212yes—
20C32×#95—21no—
21C3×#809—24no—
22C23×C3×C8—31no—
23C2×C3×#121—31no—
24C2×#930C2×C311yescharacteristic
25C23×C3⋊C8C2×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—42no—
44C2×C3×#67—42no—
45C22×C3×Dic3—21no—
46C2×C3×D12—22no—
47C2×C3×D12—22no—
48C2×C3×D12—21no—
49C2×C3×D12C2×C412yes—
50C32×C4⋊C4—22no—
51C32×C4⋊C4—22no—
52C32×C22⋊C4—42no—
53C3×(C2×D3)⋊C4—24no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3C2×C412yes—
56C2×C3×C3⋊C8—28no—
57C2×C3×C3⋊C8—22no—
58C2×C3×C3⋊C8—22no—
59C2×C3×C3⋊C8D414yescomplemented
60#1893—31noSylow
61C22×C3×D4—31no—
62C22×C3×D4—61no—
63C23×C3×C4—21no—
64C23×C3×C4C2×D311yescharacteristic
65C23×C3×C4C22×C311yescharacteristic
66C22×#67—21no—
67C22×D12C22×C311yescharacteristic
68C22×C3×C8—32no—
69C22×C3×C8—64no—
70C22×C3×C8—62no—
71C3×#121—34no—
72C3×#121—62no—
73C2×C3×C4⋊C4—22no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C4⋊C4C2×D312yes—
76C2×C3×C4⋊C4C22×C312yes—
77C2×C3×C22⋊C4—22no—
78C2×C3×C22⋊C4—21no—
79C2×C3×C22⋊C4—21no—
80C2×C3×C22⋊C4—61no—
81#930—22no—
82#930C3×C414yescomplemented
83C2×(C2×D3)⋊C4—21no—
84C2×C4⋊Dic3C22×C311yescharacteristic
85C22×C3⋊C8—22no—
86C22×C3⋊C8—24no—
87C22×C3⋊C8C22×C312yes—
88C3×#102—64no—
89C3×#95—22no—
90C3×#95—21no—
91C3×#95—21no—
92#809—24no—
93C23×C32—22no—
94C23×C32—22no—
95C23×C32C22⋊C412yes—
96C23×C32D812yes—
97C23×C32SD1612yes—
98C23×C32C2×D411yescharacteristic
99C22×C3×D3—22no—
100C22×C3×D3—42no—
101C22×C3×D3—41no—
102C22×C3×D3—41no—
103C22×C3×D3—42no—
104C2×C32×C4—22no—
105C2×C32×C4—24no—
106C2×C32×C4—22no—
107C2×C32×C4—22no—
108C2×C32×C4—42no—
109C2×C32×C4—42no—
110C2×C32×C4—42no—
111C2×C32×C4C22⋊C412yes—
112C2×C32×C4C22×C411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D412yes—
115C2×C32×C4#4112yes—
116C3×#67—48no—
117C2×C3×Dic3—22no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—41no—
120C3×D12—24no—
121C3×D12—41no—
122C3×D12—41no—
123C3×C3⋊C8—24no—
124C23×C8—31no—
125C2×#121—31no—
126C2×#102—32no—
127#380C3×D311yescharacteristic, complemented
128#340—32no—
129C24×C3—21no—
130C24×C3—61no—
131C24×C3#6711yescharacteristic
132C24×C3C3×D411yescharacteristic
133C23×D3—21no—
134C2×C3×D4—32no—
135C2×C3×D4—64no—
136C2×C3×D4—61no—
137C2×C3×D4—62no—
138C2×C3×D4—62no—
139C2×C3×D4—122no—
140C2×C3×D4—122no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—22no—
144C22×C3×C4—22no—
145C22×C3×C4—24no—
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—22no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—42no—
153C22×C3×C4—42no—
154C22×C3×C4—61no—
155C22×C3×C4C4×D312yes—
156C22×C3×C4D1212yes—
157C22×C3×C4#6711yescharacteristic
158C22×C3×C4C2×C3×C412yes—
159C22×C3×C4C3×D412yes—
160C22×C3×C4C3×D411yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C23×C311yescharacteristic
163C2×#67—24no—
164C2×#67—42no—
165C2×#67—42no—
166C22×Dic3—21no—
167C2×D12—22no—
168C2×D12—22no—
169C2×D12—21no—
170C2×D12C2×C3×C412yes—
171C2×C3×C8—34no—
172C2×C3×C8—68no—
173C2×C3×C8—62no—
174C2×C3×C8—62no—
175C3×C4⋊C4—22no—
176C3×C4⋊C4—22no—
177C3×C4⋊C4—22no—
178C3×C4⋊C4—22no—
179C3×C4⋊C4—32no—
180C3×C4⋊C4—42no—
181C3×C4⋊C4—42no—
182C3×C4⋊C4—61no—
183C3×C22⋊C4—44no—
184C3×C22⋊C4—42no—
185C3×C22⋊C4—42no—
186C3×C22⋊C4—64no—
187(C2×D3)⋊C4—24no—
188C4⋊Dic3—21no—
189C4⋊Dic3C2×C3×C412yes—
190C2×C3⋊C8—28no—
191C2×C3⋊C8—22no—
192C2×C3⋊C8—22no—
193C2×C3⋊C8C3×D414yescomplemented
194C22×C32—22no—
195C22×C32—22no—
196C22×C32—24no—
197C22×C32—24no—
198C22×C32#10214yescomplemented
199C22×C32C2×C22⋊C411yescharacteristic
200C22×C32#12112yes—
201C22×C32C2×D811yescharacteristic
202C22×C32C2×SD1611yescharacteristic
203C22×C32#13512yes—
204C2×C3×D3—42no—
205C2×C3×D3—42no—
206C2×C3×D3—42no—
207C2×C3×D3—82no—
208C2×C3×D3—82no—
209C32×C4—22no—
210C32×C4—82no—
211C32×C4C4×D412yes—
212C32×C4#12011yescharacteristic
213C32×C4#12311yescharacteristic
214C3×Dic3—42no—
215C22×D4—31no—
216C22×D4—61no—
217C23×C4C2×C3×D311yescharacteristic
218C22×C8—32no—
219C22×C8—64no—
220C22×C8—62no—
221#121—34no—
222#121—62no—
223C2×C4⋊C4—31no—
224C2×C4⋊C4C2×C3×D312yes—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—61no—
227#102—64no—
228#95—21no—
229C23×C3—22no—
230C23×C3—22no—
231C23×C3—22no—
232C23×C3—22no—
233C23×C3—22no—
234C23×C3—22no—
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×C3#21312yes—
246C23×C3#21512yes—
247C23×C3C3×C22⋊C412yes—
248C23×C3C3×D812yes—
249C23×C3C3×SD1612yes—
250C23×C3C2×#6711yescharacteristic
251C23×C3C2×C3×D411yescharacteristic
252C22×D3—22no—
253C22×D3—42no—
254C22×D3—41no—
255C22×D3—41no—
256C22×D3—42no—
257C3×D4—64no—
258C3×D4—128no—
259C3×D4—121no—
260C3×D4—121no—
261C2×C3×C4—22no—
262C2×C3×C4—22no—
263C2×C3×C4—24no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—24no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—44no—
275C2×C3×C4—42no—
276C2×C3×C4—42no—
277C2×C3×C4—42no—
278C2×C3×C4—44no—
279C2×C3×C4—44no—
280C2×C3×C4—44no—
281C2×C3×C4—42no—
282C2×C3×C4—42no—
283C2×C3×C4—42no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—62no—
288C2×C3×C4—121no—
289C2×C3×C4—121no—
290C2×C3×C4(C2×D3)⋊C412yes—
291C2×C3×C4C3×C22⋊C412yes—
292C2×C3×C4C2×C4×D311yescharacteristic
293C2×C3×C4C2×D1211yescharacteristic
294C2×C3×C4D3×D412yes—
295C2×C3×C4#23712yes—
296C2×C3×C4C22×C3×C411yescharacteristic
297C2×C3×C4C2×C3×D411yescharacteristic
298C2×C3×C4C2×C3×D412yes—
299C2×C3×C4C3×#4112yes—
300#67—48no—
301C2×Dic3—22no—
302C2×Dic3—41no—
303C2×Dic3—41no—
304D12—24no—
305D12—41no—
306D12—41no—
307C3×C8—64no—
308C3⋊C8—24no—
309C2×C32—24no—
310C2×C32#38611yescharacteristic
311C2×C32C2×#10211yescharacteristic
312C2×C32#41611yescharacteristic
313C2×C32#46512yes—
314C2×C32#46612yes—
315C3×D3—82no—
316C24—61no—
317C24C3×#6711yescharacteristic
318C2×D4—32no—
319C2×D4—64no—
320C2×D4—61no—
321C2×D4—62no—
322C2×D4—62no—
323C2×D4—122no—
324C2×D4—122no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—61no—
329C22×C4C3×C4×D312yes—
330C22×C4C3×D1212yes—
331C22×C4C3×#6711yescharacteristic
332C22×C4C22×C3×D311yescharacteristic
333C2×C8—34no—
334C2×C8—68no—
335C2×C8—62no—
336C2×C8—62no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—32no—
340C4⋊C4—61no—
341C22⋊C4—42no—
342C22⋊C4—64no—
343C22×C3—22no—
344C22×C3—22no—
345C22×C3—22no—
346C22×C3—22no—
347C22×C3—24no—
348C22×C3—24no—
349C22×C3—24no—
350C22×C3—24no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—22no—
354C22×C3—21no—
355C22×C3—22no—
356C22×C3—24no—
357C22×C3—42no—
358C22×C3—42no—
359C22×C3—44no—
360C22×C3—44no—
361C22×C3—122no—
362C22×C3—122no—
363C22×C3—122no—
364C22×C3—242no—
365C22×C3—242no—
366C22×C3#80914yescomplemented
367C22×C3C3×#10214yescomplemented
368C22×C3C2×(C2×D3)⋊C411yescharacteristic
369C22×C3C2×#21311yescharacteristic
370C22×C3#93912yes—
371C22×C3C2×#21511yescharacteristic
372C22×C3#95012yes—
373C22×C3C2×C3×C22⋊C411yescharacteristic
374C22×C3C3×#12112yes—
375C22×C3C2×C3×D811yescharacteristic
376C22×C3C2×C3×SD1611yescharacteristic
377C22×C3C3×#13512yes—
378C2×D3—42no—
379C2×D3—42no—
380C2×D3—42no—
381C2×D3—82no—
382C2×D3—82no—
383C3×C4—22no—
384C3×C4—22no—
385C3×C4—22no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—42no—
389C3×C4—84no—
390C3×C4—82no—
391C3×C4—82no—
392C3×C4—122no—
393C3×C4#67⋊C412yes—
394C3×C4#88211yescharacteristic
395C3×C4#88611yescharacteristic
396C3×C4C3×C4×D412yes—
397C3×C4C3×#12011yescharacteristic
398C3×C4C3×#12311yescharacteristic
399Dic3—42no—
400C32#189311yescharacteristic, complemented, Sylow
401C23—22no—
402C23—22no—
403C23—62no—
404C23—121no—
405C23—122no—
406C23—121no—
407C23—122no—
408C23C3×(C2×D3)⋊C412yes—
409C23C3×#21312yes—
410C23C3×#21512yes—
411C23C2×C3×#6711yescharacteristic
412D4—64no—
413D4—128no—
414D4—121no—
415D4—121no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—62no—
424C2×C4—121no—
425C2×C4—121no—
426C2×C4C3×(C2×D3)⋊C412yes—
427C2×C4C2×C3×C4×D311yescharacteristic
428C2×C4C2×C3×D1211yescharacteristic
429C2×C4C3×D3×D412yes—
430C2×C4C3×#23712yes—
431C8—64no—
432C2×C3—24no—
433C2×C3—24no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—22no—
438C2×C3—22no—
439C2×C3—44no—
440C2×C3—242no—
441C2×C3#495811yescharacteristic
442C2×C3C2×#80911yescharacteristic
443C2×C3#500211yescharacteristic
444C2×C3#503812yes—
445C2×C3#504812yes—
446C2×C3C3×#38611yescharacteristic
447C2×C3C2×C3×#10211yescharacteristic
448C2×C3C3×#41611yescharacteristic
449C2×C3C3×#46512yes—
450C2×C3C3×#46612yes—
451D3—82no—
452C22—22no—
453C22—22no—
454C22—24no—
455C22—24no—
456C22—122no—
457C22—122no—
458C22—122no—
459C22—242no—
460C22—242no—
461C22C3×#80914yescomplemented
462C22C2×C3×(C2×D3)⋊C411yescharacteristic
463C22C2×C3×#21311yescharacteristic
464C22C3×#93912yes—
465C22C2×C3×#21511yescharacteristic
466C22C3×#95012yes—
467C4—22no—
468C4—82no—
469C4—122no—
470C4C3×#67⋊C412yes—
471C4C3×#88211yescharacteristic
472C4C3×#88611yescharacteristic
473C3—21no—
474C3#6951511yescharacteristic, direct product factor
475C3C3×#189311yescharacteristic, complemented
476C2—24no—
477C2—242no—
478C2C3×#495811yescharacteristic
479C2C2×C3×#80911yescharacteristic
480C2C3×#500211yescharacteristic
481C2C3×#503812yes—
482C2C3×#504812yes—
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×#1893
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. C23×C3×C3⋊C8C2semidirect
3. C32×#380C2semidirect
4. C2×C3×#809C2semidirect
5. C3×#4529C2semidirect
7. #69515C3direct (N × H)
14. C3×#930C4semidirect
25. C23×C3⋊C8C2×C3semidirect
28. C3×#380D3semidirect
29. C3×#380C2×C3semidirect
30. C2×#809C2×C3semidirect
32. #4529C2×C3semidirect
59. C2×C3×C3⋊C8D4semidirect
82. #930C3×C4semidirect
127. #380C3×D3semidirect
193. C2×C3⋊C8C3×D4semidirect
198. C22×C32#102semidirect
366. C22×C3#809semidirect
367. C22×C3C3×#102semidirect
400. C32#1893semidirect
461. C22C3×#809semidirect
474. C3#69515direct (N × H)
475. C3C3×#1893semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9302
C23×C3×C3⋊C82
C32×#3802
C2×C3×#8092
C3×#45292
C3×#18933
#695153