Finite Group Databasebeta

← C3×#69978 #11775295

Subgroups — C3×#69978 #11775295

Order 1152.

747 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#930C211yesmaximal, characteristic
2C32×#407C211yesmaximal, characteristic, complemented
3C3×#5211C211yesmaximal, characteristic, complemented
4C3×#4470C214yesmaximal, complemented
5C3×#1510—31nomaximal
6#69978C311yesmaximal, characteristic, direct product factor
7C23×C32×C4C2211yescharacteristic
8C22×C3×#67—21no—
9C22×C3×D12C411yescharacteristic, complemented
10C2×C32×M16—21no—
11C2×C3×#217—21no—
12C3×#930—21no—
13C3×#930—21no—
14C3×#930C412yescomplemented
15C3×#930C2212yes—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3C411yescharacteristic, complemented
18C32×C22⋊C8—21no—
19C32×C22⋊C8C2212yescomplemented
20C3×C3⋊#95—21no—
21C3×C3⋊#95C2212yescomplemented
22C2×C3×#121—31no—
23C2×#930C2×C311yescharacteristic
24C3×#407—21no—
25C3×#407D311yescharacteristic, complemented
26C3×#407C2×C311yescharacteristic, complemented
27C3×#381—31no—
28#5211C2×C311yescharacteristic, complemented
29C3×#327—34no—
30#4470C2×C314yescomplemented
31C24×C32D411yescharacteristic
32C23×C3×D3—21no—
33C22×C32×C4—42no—
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4C2311yescharacteristic
40C2×C3×#67—22no—
41C2×C3×#67—22no—
42C2×C3×#67—44no—
43C22×C3×Dic3—21no—
44C22×C3×Dic3—22no—
45C2×C3×D12—21no—
46C2×C3×D12—42no—
47C2×C3×D12C2×C412yes—
48C32×M16—42no—
49C2×C32×C8—22no—
50C3×#217—42no—
51C3×(C2×D3)⋊C4—22no—
52C3×(C2×D3)⋊C4—22no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3C2×C412yes—
55#1510—31noSylow
56C22×C3×D4—31no—
57C22×C3×D4—61no—
58C23×C3×C4—21no—
59C23×C3×C4C2×D311yescharacteristic
60C23×C3×C4C22×C311yescharacteristic
61C22×#67—21no—
62C22×D12C3×C411yescharacteristic, complemented
63C2×C3×M16—22no—
64C2×C3×M16—21no—
65C2×C3×M16—21no—
66C3×#121—32no—
67C3×#121—32no—
68C3×#121—61no—
69C3×#121—61no—
70C2×C3×C4⋊C4—31no—
71C2×C3×C22⋊C4—61no—
72C2×C3×C22⋊C4—61no—
73C2×#217—21no—
74#930—21no—
75#930—21no—
76#930C3×C412yescomplemented
77#930C22×C312yes—
78C2×(C2×D3)⋊C4—21no—
79C2×C4⋊Dic3C3×C411yescharacteristic, complemented
80C3×C22⋊C8—22no—
81C3×C22⋊C8—21no—
82C3×C22⋊C8—21no—
83C3×C22⋊C8—22no—
84C3×C22⋊C8C2×D312yescomplemented
85C3×C22⋊C8C22×C312yescomplemented
86C3×#95—32no—
87C3×#95—61no—
88C3⋊#95—21no—
89C3⋊#95C22×C312yescomplemented
90C23×C32—22no—
91C23×C32—22no—
92C23×C32—41no—
93C23×C32C22⋊C411yescharacteristic
94C23×C32C22⋊C411yescharacteristic
95C23×C32C2×D411yescharacteristic
96C22×C3×D3—22no—
97C22×C3×D3—42no—
98C22×C3×D3—42no—
99C22×C3×D3—42no—
100C2×C32×C4—22no—
101C2×C32×C4—22no—
102C2×C32×C4—41no—
103C2×C32×C4—41no—
104C2×C32×C4—41no—
105C2×C32×C4—41no—
106C2×C32×C4C22⋊C411yescharacteristic
107C2×C32×C4C22⋊C411yescharacteristic
108C2×C32×C4C22×C411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C3×#67—44no—
111C3×#67—44no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—42no—
114C2×C3×Dic3—42no—
115C2×C3×Dic3—42no—
116C2×C3×Dic3—42no—
117C3×D12—42no—
118C3×D12—42no—
119C32×C8—42no—
120C2×#121—31no—
121#407C3×D311yescharacteristic, complemented
122#381—31no—
123#327—34no—
124C24×C3—21no—
125C24×C3—61no—
126C24×C3D1211yescharacteristic
127C24×C3C3×D411yescharacteristic
128C23×D3—21no—
129C2×C3×D4—32no—
130C2×C3×D4—62no—
131C2×C3×D4—62no—
132C2×C3×D4—61no—
133C2×C3×D4—122no—
134C2×C3×D4—124no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—42no—
142C22×C3×C4—42no—
143C22×C3×C4—44no—
144C22×C3×C4—61no—
145C22×C3×C4—62no—
146C22×C3×C4C4×D311yescharacteristic
147C22×C3×C4C4×D311yescharacteristic
148C22×C3×C4D1211yescharacteristic
149C22×C3×C4#6711yescharacteristic
150C22×C3×C4#6711yescharacteristic
151C22×C3×C4C2×C3×C411yescharacteristic
152C22×C3×C4C2×C3×C411yescharacteristic
153C22×C3×C4C3×D411yescharacteristic
154C22×C3×C4C3×D411yescharacteristic
155C22×C3×C4C3×D411yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C23×C311yescharacteristic
158C2×#67—22no—
159C2×#67—22no—
160C2×#67—44no—
161C22×Dic3—21no—
162C22×Dic3—22no—
163C2×D12—21no—
164C2×D12—42no—
165C2×D12C2×C3×C412yes—
166C3×M16—44no—
167C3×M16—42no—
168C3×M16—42no—
169C2×C3×C8—24no—
170C2×C3×C8—22no—
171C2×C3×C8—22no—
172C3×C4⋊C4—32no—
173C3×C4⋊C4—61no—
174C3×C22⋊C4—62no—
175C3×C22⋊C4—62no—
176C3×C22⋊C4—122no—
177#217—42no—
178(C2×D3)⋊C4—22no—
179(C2×D3)⋊C4—22no—
180C4⋊Dic3—21no—
181C4⋊Dic3C2×C3×C412yes—
182C22×C32—21no—
183C22×C32—21no—
184C22×C32—21no—
185C22×C32—21no—
186C22×C32—21no—
187C22×C32—21no—
188C22×C32—21no—
189C22×C32—44no—
190C22×C32#9912yes—
191C22×C32C2×C22⋊C411yescharacteristic
192C22×C32AGL(1,ℤ/8)12yes—
193C2×C3×D3—42no—
194C2×C3×D3—42no—
195C2×C3×D3—42no—
196C2×C3×D3—84no—
197C32×C4—21no—
198C32×C4—21no—
199C32×C4—21no—
200C32×C4—21no—
201C3×Dic3—42no—
202C3×Dic3—82no—
203C22×D4—31no—
204C22×D4—61no—
205C23×C4C2×C3×D311yescharacteristic
206C2×M16—21no—
207#121—32no—
208#121—32no—
209#121—61no—
210#121—61no—
211C2×C4⋊C4—31no—
212C2×C22⋊C4—61no—
213C2×C22⋊C4—61no—
214C22⋊C8—21no—
215C22⋊C8C2×C3×D312yescomplemented
216#95—32no—
217#95—61no—
218C23×C3—22no—
219C23×C3—22no—
220C23×C3—22no—
221C23×C3—22no—
222C23×C3—21no—
223C23×C3—21no—
224C23×C3—21no—
225C23×C3—42no—
226C23×C3—42no—
227C23×C3—41no—
228C23×C3—41no—
229C23×C3—42no—
230C23×C3—62no—
231C23×C3—122no—
232C23×C3—122no—
233C23×C3—122no—
234C23×C3(C2×D3)⋊C411yescharacteristic
235C23×C3(C2×D3)⋊C411yescharacteristic
236C23×C3C3×C22⋊C411yescharacteristic
237C23×C3C3×C22⋊C411yescharacteristic
238C23×C3C2×D1211yescharacteristic
239C23×C3C2×C3×D411yescharacteristic
240C22×D3—22no—
241C22×D3—42no—
242C22×D3—42no—
243C22×D3—42no—
244C3×D4—122no—
245C3×D4—122no—
246C3×D4—124no—
247C3×D4—124no—
248C2×C3×C4—24no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—42no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—42no—
267C2×C3×C4—42no—
268C2×C3×C4—42no—
269C2×C3×C4—42no—
270C2×C3×C4—62no—
271C2×C3×C4—122no—
272C2×C3×C4—122no—
273C2×C3×C4—122no—
274C2×C3×C4—122no—
275C2×C3×C4(C2×D3)⋊C411yescharacteristic
276C2×C3×C4(C2×D3)⋊C411yescharacteristic
277C2×C3×C4C3×C22⋊C411yescharacteristic
278C2×C3×C4C3×C22⋊C411yescharacteristic
279C2×C3×C4C2×C4×D311yescharacteristic
280C2×C3×C4C2×#6711yescharacteristic
281C2×C3×C4C22×C3×C411yescharacteristic
282C2×C3×C4C2×C3×D411yescharacteristic
283#67—44no—
284#67—44no—
285C2×Dic3—22no—
286C2×Dic3—42no—
287C2×Dic3—42no—
288C2×Dic3—42no—
289C2×Dic3—42no—
290D12—42no—
291D12—42no—
292C3×C8—44no—
293C3×C8—42no—
294C3×C8—42no—
295C2×C32—22no—
296C2×C32—22no—
297C2×C32—41no—
298C2×C32C2×#9911yescharacteristic
299C2×C32#41811yescharacteristic
300C2×C32#42111yescharacteristic
301C3×D3—82no—
302C24—61no—
303C24C3×D1211yescharacteristic
304C2×D4—32no—
305C2×D4—62no—
306C2×D4—62no—
307C2×D4—61no—
308C2×D4—122no—
309C2×D4—124no—
310C22×C4—42no—
311C22×C4—61no—
312C22×C4—62no—
313C22×C4C3×C4×D311yescharacteristic
314C22×C4C3×C4×D311yescharacteristic
315C22×C4C3×D1211yescharacteristic
316C22×C4C3×#6711yescharacteristic
317C22×C4C3×#6711yescharacteristic
318C22×C4C22×C3×D311yescharacteristic
319M16—42no—
320C2×C8—22no—
321C4⋊C4—32no—
322C4⋊C4—61no—
323C22⋊C4—62no—
324C22⋊C4—62no—
325C22⋊C4—122no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—22no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—22no—
342C22×C3—21no—
343C22×C3—22no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3—44no—
351C22×C3—44no—
352C22×C3—48no—
353C22×C3—122no—
354C22×C3—122no—
355C22×C3—122no—
356C22×C3—244no—
357C22×C3#80612yes—
358C22×C3C3×#9912yes—
359C22×C3#90812yes—
360C22×C3C2×(C2×D3)⋊C411yescharacteristic
361C22×C3C2×C3×C22⋊C411yescharacteristic
362C22×C3C3×AGL(1,ℤ/8)12yes—
363C2×D3—42no—
364C2×D3—42no—
365C2×D3—42no—
366C2×D3—84no—
367C3×C4—22no—
368C3×C4—22no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—41no—
378C3×C4—41no—
379C3×C4—122no—
380C3×C4—242no—
381Dic3—42no—
382Dic3—82no—
383C32#151011yescharacteristic, complemented, Sylow
384C23—22no—
385C23—22no—
386C23—41no—
387C23—62no—
388C23—122no—
389C23—122no—
390C23—122no—
391C23C3×(C2×D3)⋊C411yescharacteristic
392C23C3×(C2×D3)⋊C411yescharacteristic
393C23C2×C3×D1211yescharacteristic
394D4—122no—
395D4—122no—
396D4—124no—
397D4—124no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—62no—
405C2×C4—122no—
406C2×C4—122no—
407C2×C4—122no—
408C2×C4—122no—
409C2×C4C3×(C2×D3)⋊C411yescharacteristic
410C2×C4C3×(C2×D3)⋊C411yescharacteristic
411C2×C4C2×C3×C4×D311yescharacteristic
412C2×C4C2×C3×#6711yescharacteristic
413C8—42no—
414C2×C3—22no—
415C2×C3—22no—
416C2×C3—22no—
417C2×C3—22no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—42no—
422C2×C3—42no—
423C2×C3—42no—
424C2×C3—41no—
425C2×C3—41no—
426C2×C3—242no—
427C2×C3C2×#80611yescharacteristic
428C2×C3#513111yescharacteristic
429C2×C3#513911yescharacteristic
430C2×C3C2×C3×#9911yescharacteristic
431C2×C3C3×#41811yescharacteristic
432C2×C3C3×#42111yescharacteristic
433D3—82no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—44no—
442C22—122no—
443C22—122no—
444C22—122no—
445C22—244no—
446C22C3×#80612yes—
447C22C3×#90812yes—
448C22C2×C3×(C2×D3)⋊C411yescharacteristic
449C4—21no—
450C4—21no—
451C4—21no—
452C4—21no—
453C4—122no—
454C4—242no—
455C3—21no—
456C3#6997811yescharacteristic, direct product factor
457C3C3×#151011yescharacteristic, complemented
458C2—22no—
459C2—22no—
460C2—41no—
461C2—242no—
462C2C2×C3×#80611yescharacteristic
463C2C3×#513111yescharacteristic
464C2C3×#513911yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#407C2
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#930C2
cosocleC22×C3×C4C23×C3
hypercenterC3×#407D3
hypocenterC3C3×#1510
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C3×#407

Complements

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

NH ≅ G/Ntype
2. C32×#407C2semidirect
3. C3×#5211C2semidirect
4. C3×#4470C2semidirect
6. #69978C3direct (N × H)
9. C22×C3×D12C4semidirect
14. C3×#930C4semidirect
17. C2×C3×C4⋊Dic3C4semidirect
19. C32×C22⋊C8C22semidirect
21. C3×C3⋊#95C22semidirect
25. C3×#407D3semidirect
26. C3×#407C2×C3semidirect
28. #5211C2×C3semidirect
30. #4470C2×C3semidirect
62. C22×D12C3×C4semidirect
76. #930C3×C4semidirect
79. C2×C4⋊Dic3C3×C4semidirect
84. C3×C22⋊C8C2×D3semidirect
85. C3×C22⋊C8C22×C3semidirect
89. C3⋊#95C22×C3semidirect
121. #407C3×D3semidirect
215. C22⋊C8C2×C3×D3semidirect
383. C32#1510semidirect
456. C3#69978direct (N × H)
457. C3C3×#1510semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9302
C32×#4072
C3×#52112
C3×#44702
C3×#15103
#699783