Finite Group Databasebeta

← C3×#68312 #11775348

Subgroups — C3×#68312 #11775348

Order 1152.

484 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5624C211yesmaximal, characteristic
2C3×#4719C211yesmaximal, characteristic, complemented
3C3×#4650C211yesmaximal, characteristic, complemented
4C32×#328C211yesmaximal, characteristic, complemented
5C3×#4538C211yesmaximal, characteristic, complemented
6C3×#4470C211yesmaximal, characteristic
7C3×#4451C211yesmaximal, characteristic
8C3×#1512—31nomaximal
9#68312C311yesmaximal, characteristic, direct product factor
10C32×C22⋊Q8C2211yescharacteristic
11C3×#947C411yescharacteristic, complemented
12C3×Q8×Dic3C411yescharacteristic, complemented
13C3×#930C2211yescharacteristic
14C2×C3×Dic3⋊C4—21no—
15C2×C3×C4×Dic3C2211yescharacteristic
16C3×#898—21no—
17C3×#893C411yescharacteristic, complemented
18C3×#892—21no—
19C3×#890C411yescharacteristic, complemented
20C3×#886—21no—
21C3×#67⋊C4—21no—
22C32×C22⋊C8C2211yescharacteristic
23C32×#95C2211yescharacteristic
24C3×C3⋊#95—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#815—21no—
28C3×Dic3⋊C8—21no—
29C3×#529—31no—
30#5624C2×C311yescharacteristic
31C3×#432—31no—
32C3×#382—31no—
33#4719C2×C311yescharacteristic, complemented
34#4650C2×C311yescharacteristic, complemented
35C3×#328—21no—
36C3×#328—31no—
37C3×#328D311yescharacteristic, complemented
38C3×#328C2×C311yescharacteristic, complemented
39C3×#327—31no—
40C3×#327—31no—
41#4538C2×C311yescharacteristic, complemented
42#4470C2×C311yescharacteristic
43#4451C2×C311yescharacteristic
44C2×C32×Q8C2×C411yescharacteristic
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12C2×C411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C32×C8—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4C2×C411yescharacteristic
56C32×C22⋊C4—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3C2×C411yescharacteristic
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—42no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3C2×C411yescharacteristic
68C3×C4×Dic3C2×C411yescharacteristic
69C3×C4×Dic3D411yescharacteristic
70C3×C4×Dic3D411yescharacteristic
71C2×C3×C3⋊C8—21no—
72#1512—31noSylow
73C3×#126—61no—
74C3×#125—31no—
75C3×#124—31no—
76C3×#123—61no—
77C3×C22⋊Q8—21no—
78C3×C22⋊Q8C2×D311yescharacteristic
79C3×C22⋊Q8C22×C311yescharacteristic
80C3×#121—31no—
81C3×C4×Q8—31no—
82C3×C4×D4—31no—
83C3×C4×D4—61no—
84C3×#117—61no—
85C2×C3×C4⋊C4—61no—
86C2×C3×C42—31no—
87#947C3×C411yescharacteristic, complemented
88Q8×Dic3C3×C411yescharacteristic, complemented
89#930C22×C311yescharacteristic
90C2×Dic3⋊C4—21no—
91C2×C4×Dic3C22×C311yescharacteristic
92#898—21no—
93#893C3×C411yescharacteristic, complemented
94#892—21no—
95#890C3×C411yescharacteristic, complemented
96#886—21no—
97#67⋊C4—21no—
98C3×C4⋊C8—61no—
99C3×C22⋊C8—21no—
100C3×C22⋊C8—31no—
101C3×C22⋊C8C2×D311yescharacteristic
102C3×C22⋊C8C22×C311yescharacteristic
103C3×#97—61no—
104C3×#95—21no—
105C3×#95—31no—
106C3×#95—61no—
107C3×#95C2×D311yescharacteristic
108C3×#95C22×C311yescharacteristic
109C3⋊#95—21no—
110C3⋊#95C22×C311yescharacteristic
111#830C22×C311yescharacteristic
112#815—21no—
113Dic3⋊C8—21no—
114C23×C32C2×D411yescharacteristic
115C22×C3×D3—21no—
116C32×Q8—41no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4—41no—
120C2×C32×C4—41no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C3×#67—41no—
126C3×#67—41no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3C22⋊C411yescharacteristic
135C2×C3×Dic3C22⋊C411yescharacteristic
136C2×C3×Dic3C22⋊C411yescharacteristic
137C2×C3×Dic3C22⋊C411yescharacteristic
138C3×D12—41no—
139C3×C4×D3—42no—
140C32×C8—41no—
141C3×C3⋊C8—41no—
142#529—31no—
143#432—31no—
144#382—31no—
145#328—31no—
146#328C3×D311yescharacteristic, complemented
147#327—31no—
148#327—31no—
149C2×C3×Q8—21no—
150C2×C3×Q8C4×D311yescharacteristic
151C2×C3×Q8C2×C3×C411yescharacteristic
152C2×C3×D4—31no—
153C2×C3×D4—61no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—31no—
158C22×C3×C4—31no—
159C22×C3×C4—41no—
160C22×C3×C4—61no—
161C22×C3×C4—61no—
162C22×C3×C4C22×D311yescharacteristic
163C22×C3×C4C23×C311yescharacteristic
164C2×#67—21no—
165C22×Dic3—21no—
166C22×Dic3C3×D411yescharacteristic
167C22×Dic3C3×D411yescharacteristic
168C2×D12C2×C3×C411yescharacteristic
169C2×C4×D3—21no—
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C2×C3×C8—41no—
173C2×C3×C8—61no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—21no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—31no—
178C3×C4⋊C4—41no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—122no—
183C3×C4⋊C4C4×D311yescharacteristic
184C3×C4⋊C4C2×C3×C411yescharacteristic
185C3×C22⋊C4—21no—
186C3×C22⋊C4—21no—
187C3×C22⋊C4—41no—
188C3×C22⋊C4—61no—
189C3×C22⋊C4—61no—
190C3×C22⋊C4—61no—
191C3×C22⋊C4—61no—
192C3×C42—31no—
193C3×C42—31no—
194C3×C42—31no—
195C3×C42—31no—
196C3×C42—61no—
197(C2×D3)⋊C4—21no—
198(C2×D3)⋊C4—21no—
199(C2×D3)⋊C4—21no—
200(C2×D3)⋊C4—21no—
201C4⋊Dic3—21no—
202C4⋊Dic3—21no—
203C4⋊Dic3C2×C3×C411yescharacteristic
204Dic3⋊C4—21no—
205Dic3⋊C4—42no—
206C4×Dic3—21no—
207C4×Dic3C2×C3×C411yescharacteristic
208C4×Dic3C2×C3×C411yescharacteristic
209C4×Dic3C3×D411yescharacteristic
210C4×Dic3C3×D411yescharacteristic
211C2×C3⋊C8—21no—
212C22×C32—21no—
213C22×C32—21no—
214C22×C32C2×C22⋊C411yescharacteristic
215C22×C32AGL(1,ℤ/8)11yescharacteristic
216C22×C32#13711yescharacteristic
217C2×C3×D3—41no—
218C2×C3×D3—41no—
219C2×C3×D3—41no—
220C32×C4—21no—
221C32×C4—21no—
222C32×C4—41no—
223C32×C4—41no—
224C32×C4—81no—
225C3×Dic3—21no—
226C3×Dic3—21no—
227C3×Dic3—21no—
228C3×Dic3—21no—
229C3×Dic3—41no—
230C3×Dic3—81no—
231#126—61no—
232#125—31no—
233#124—31no—
234#123—61no—
235C22⋊Q8C2×C3×D311yescharacteristic
236#121—31no—
237C4×Q8—31no—
238C4×D4—31no—
239C4×D4—61no—
240#117—61no—
241C2×C4⋊C4—61no—
242C2×C42—31no—
243C4⋊C8—61no—
244C22⋊C8—31no—
245C22⋊C8C2×C3×D311yescharacteristic
246#97—61no—
247#95—31no—
248#95—61no—
249#95C2×C3×D311yescharacteristic
250C23×C3—21no—
251C23×C3—61no—
252C23×C3D3×D411yescharacteristic
253C23×C3C2×C3×D411yescharacteristic
254C22×D3—21no—
255C3×Q8—41no—
256C3×Q8—41no—
257C3×Q8—81no—
258C3×D4—121no—
259C3×D4—121no—
260C3×D4—121no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—31no—
268C2×C3×C4—31no—
269C2×C3×C4—31no—
270C2×C3×C4—31no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—42no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—61no—
283C2×C3×C4—61no—
284C2×C3×C4—61no—
285C2×C3×C4—81no—
286C2×C3×C4—81no—
287C2×C3×C4—81no—
288C2×C3×C4—122no—
289C2×C3×C4—121no—
290C2×C3×C4—121no—
291C2×C3×C4—121no—
292C2×C3×C4—121no—
293C2×C3×C4C2×C4×D311yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4C22×C3×C411yescharacteristic
296C2×C3×C4C2×C3×D411yescharacteristic
297#67—41no—
298#67—41no—
299C2×Dic3—21no—
300C2×Dic3—21no—
301C2×Dic3—21no—
302C2×Dic3—41no—
303C2×Dic3—41no—
304C2×Dic3—41no—
305C2×Dic3—41no—
306C2×Dic3C3×C22⋊C411yescharacteristic
307C2×Dic3C3×C22⋊C411yescharacteristic
308C2×Dic3C3×C22⋊C411yescharacteristic
309C2×Dic3C3×C22⋊C411yescharacteristic
310D12—41no—
311C4×D3—42no—
312C3×C8—41no—
313C3×C8—41no—
314C3×C8—81no—
315C3×C8—121no—
316C3⋊C8—41no—
317C2×C32—21no—
318C2×C32—21no—
319C2×C32#41011yescharacteristic
320C2×C32#41711yescharacteristic
321C2×C32#42111yescharacteristic
322C3×D3—81no—
323C2×Q8C3×C4×D311yescharacteristic
324C2×D4—31no—
325C2×D4—61no—
326C22×C4—21no—
327C22×C4—31no—
328C22×C4—31no—
329C22×C4—61no—
330C22×C4—61no—
331C22×C4C22×C3×D311yescharacteristic
332C2×C8—21no—
333C2×C8—61no—
334C4⋊C4—21no—
335C4⋊C4—31no—
336C4⋊C4—61no—
337C4⋊C4—61no—
338C4⋊C4—61no—
339C4⋊C4—122no—
340C4⋊C4C3×C4×D311yescharacteristic
341C22⋊C4—21no—
342C22⋊C4—61no—
343C22⋊C4—61no—
344C22⋊C4—61no—
345C22⋊C4—61no—
346C42—31no—
347C42—31no—
348C42—31no—
349C42—31no—
350C42—61no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3—121no—
361C22×C3—121no—
362C22×C3—121no—
363C22×C3D3×C22⋊C411yescharacteristic
364C22×C3#91411yescharacteristic
365C22×C3#91811yescharacteristic
366C22×C3C2×C3×C22⋊C411yescharacteristic
367C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
368C22×C3C3×#13711yescharacteristic
369C2×D3—41no—
370C2×D3—41no—
371C2×D3—41no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—41no—
377C3×C4—41no—
378C3×C4—41no—
379C3×C4—41no—
380C3×C4—41no—
381C3×C4—41no—
382C3×C4—61no—
383C3×C4—61no—
384C3×C4—61no—
385C3×C4—61no—
386C3×C4—81no—
387C3×C4—81no—
388C3×C4—81no—
389C3×C4—81no—
390C3×C4—82no—
391C3×C4—121no—
392C3×C4—241no—
393Dic3—21no—
394Dic3—21no—
395Dic3—21no—
396Dic3—21no—
397Dic3—41no—
398Dic3—81no—
399C32#151211yescharacteristic, complemented, Sylow
400C23—61no—
401C23C3×D3×D411yescharacteristic
402Q8—41no—
403D4—121no—
404D4—121no—
405D4—121no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—31no—
409C2×C4—31no—
410C2×C4—31no—
411C2×C4—31no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—61no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—122no—
420C2×C4—121no—
421C2×C4—121no—
422C2×C4—121no—
423C2×C4—121no—
424C2×C4C2×C3×C4×D311yescharacteristic
425C2×C4C3×D3×D411yescharacteristic
426C8—41no—
427C8—121no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—41no—
436C2×C3—41no—
437C2×C3—241no—
438C2×C3#474011yescharacteristic
439C2×C3#480311yescharacteristic
440C2×C3#482111yescharacteristic
441C2×C3C3×#41011yescharacteristic
442C2×C3C3×#41711yescharacteristic
443C2×C3C3×#42111yescharacteristic
444D3—81no—
445C22—21no—
446C22—21no—
447C22—121no—
448C22—121no—
449C22—121no—
450C22C3×D3×C22⋊C411yescharacteristic
451C22C3×#91411yescharacteristic
452C22C3×#91811yescharacteristic
453C4—21no—
454C4—21no—
455C4—41no—
456C4—41no—
457C4—61no—
458C4—61no—
459C4—61no—
460C4—61no—
461C4—81no—
462C4—121no—
463C4—241no—
464C3—21no—
465C3#6831211yescharacteristic, direct product factor
466C3C3×#151211yescharacteristic, complemented
467C2—21no—
468C2—21no—
469C2—241no—
470C2C3×#474011yescharacteristic
471C2C3×#480311yescharacteristic
472C2C3×#482111yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#328C2
socleC22×C32C2×C22⋊C4
prime radicalC3×#930C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#328D3
hypocenterC3C3×#1512
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#328

Complements

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

NH ≅ G/Ntype
2. C3×#4719C2semidirect
3. C3×#4650C2semidirect
4. C32×#328C2semidirect
5. C3×#4538C2semidirect
9. #68312C3direct (N × H)
11. C3×#947C4semidirect
12. C3×Q8×Dic3C4semidirect
17. C3×#893C4semidirect
19. C3×#890C4semidirect
33. #4719C2×C3semidirect
34. #4650C2×C3semidirect
37. C3×#328D3semidirect
38. C3×#328C2×C3semidirect
41. #4538C2×C3semidirect
87. #947C3×C4semidirect
88. Q8×Dic3C3×C4semidirect
93. #893C3×C4semidirect
95. #890C3×C4semidirect
146. #328C3×D3semidirect
399. C32#1512semidirect
465. C3#68312direct (N × H)
466. C3C3×#1512semidirect

Maximal subgroups

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

subgroupindex
C3×#56242
C3×#47192
C3×#46502
C32×#3282
C3×#45382
C3×#44702
C3×#44512
C3×#15123
#683123