Finite Group Databasebeta

← C3×#70833 #11775262

Subgroups — C3×#70833 #11775262

Order 1152.

539 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5479C211yesmaximal, characteristic
2C32×#432C211yesmaximal, characteristic, complemented
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#4470C212yesmaximal
5C3×#4467C212yesmaximal, complemented
6C3×#1509—31nomaximal
7#70833C311yesmaximal, characteristic, direct product factor
8C2×C32×C42C2211yescharacteristic
9C3×#930C2211yescharacteristic
10C3×#929—21no—
11C3×C4×#67—21no—
12C2×C3×C4⋊Dic3—21no—
13C3×#924C2211yescharacteristic
14C2×C3×C4×Dic3—21no—
15C3×#876—21no—
16C3×#875C411yescharacteristic, complemented
17C3×C4×D12C411yescharacteristic, complemented
18C3×#872—21no—
19C3×#870C411yescharacteristic, complemented
20C3×C4×Dic6C411yescharacteristic, complemented
21C32×C4⋊C8—21no—
22C32×C22⋊C8C2212yes—
23C32×#97—21no—
24C3×C3⋊#95C2212yes—
25C3×#529—31no—
26#5479C2×C311yescharacteristic
27C3×#432—21no—
28C3×#432D311yescharacteristic, complemented
29C3×#432C2×C311yescharacteristic, complemented
30C3×C4×C4⋊C4—31no—
31C4×C4⋊Dic3C2×C311yescharacteristic, complemented
32C3×#328—32no—
33C3×#327—32no—
34#4470C2×C312yes—
35#4467C2×C312yescomplemented
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4C2311yescharacteristic
39C2×C3×#67—21no—
40C22×C3×Dic3—22no—
41C2×C3×D12C2×C411yescharacteristic
42C2×C3×C4×D3—21no—
43C2×C3×Dic6C2×C411yescharacteristic
44C2×C32×C8—22no—
45C32×C42C2×C411yescharacteristic
46C32×C42C2×C411yescharacteristic
47C32×C42D411yescharacteristic
48C32×C42D411yescharacteristic
49C3×#217—21no—
50C3×(C2×D3)⋊C4—21no—
51C3×(C2×D3)⋊C4—21no—
52C3×(C2×D3)⋊C4—21no—
53C3×(C2×D3)⋊C4—21no—
54C3×C4⋊Dic3—24no—
55C3×C4⋊Dic3C2×C411yescharacteristic
56C3×C4⋊Dic3C2×C411yescharacteristic
57C3×Dic3⋊C4—21no—
58C3×Dic3⋊C4—21no—
59C3×Dic3⋊C4—21no—
60C3×Dic3⋊C4—21no—
61C3×C4×Dic3—21no—
62C3×C4×Dic3—42no—
63#1509—31noSylow
64C3×#126—61no—
65C3×#125—31no—
66C3×#124—31no—
67C3×#123—61no—
68C3×C22⋊Q8—31no—
69C3×#121—31no—
70C3×C4×Q8—31no—
71C3×C4×D4—31no—
72C3×C4×D4—61no—
73C3×#117—61no—
74C2×C3×C4⋊C4—61no—
75C2×C3×C42—21no—
76C2×C3×C42—61no—
77C2×C3×C42C2×D311yescharacteristic
78C2×C3×C42C22×C311yescharacteristic
79#930C22×C311yescharacteristic
80#929—21no—
81C4×#67—21no—
82C2×C4⋊Dic3—21no—
83#924C22×C311yescharacteristic
84C2×C4×Dic3—21no—
85#876—21no—
86#875C3×C411yescharacteristic, complemented
87C4×D12C3×C411yescharacteristic, complemented
88#872—21no—
89#870C3×C411yescharacteristic, complemented
90C4×Dic6C3×C411yescharacteristic, complemented
91C3×C4⋊C8—22no—
92C3×C4⋊C8—21no—
93C3×C4⋊C8—21no—
94C3×C22⋊C8—22no—
95C3×C22⋊C8C2×D312yes—
96C3×C22⋊C8C22×C312yes—
97C3×#97—22no—
98C3×#97—21no—
99C3×#97—21no—
100C3×#95—32no—
101C3⋊#95C22×C312yes—
102C23×C32C2×D411yescharacteristic
103C22×C3×D3—21no—
104C2×C32×C4—21no—
105C2×C32×C4—21no—
106C2×C32×C4—22no—
107C2×C32×C4—41no—
108C2×C32×C4C22⋊C411yescharacteristic
109C2×C32×C4C22⋊C411yescharacteristic
110C2×C32×C4C22⋊C411yescharacteristic
111C2×C32×C4C22⋊C411yescharacteristic
112C2×C32×C4C22×C411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C3×#67—41no—
115C3×#67—41no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—42no—
121C2×C3×Dic3—42no—
122C3×D12—41no—
123C3×C4×D3—42no—
124C3×Dic6—41no—
125C32×C8—42no—
126#529—31no—
127#432C3×D311yescharacteristic, complemented
128C4×C4⋊C4—31no—
129#328—32no—
130#327—32no—
131C2×C3×Q8—31no—
132C2×C3×D4—31no—
133C2×C3×D4—61no—
134C22×C3×C4—21no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—62no—
138C22×C3×C4—61no—
139C22×C3×C4D1211yescharacteristic
140C22×C3×C4D1211yescharacteristic
141C22×C3×C4C3×D411yescharacteristic
142C22×C3×C4C3×D411yescharacteristic
143C22×C3×C4C22×D311yescharacteristic
144C22×C3×C4C23×C311yescharacteristic
145C2×#67—21no—
146C22×Dic3—22no—
147C2×D12C2×C3×C411yescharacteristic
148C2×C4×D3—21no—
149C2×Dic6C2×C3×C411yescharacteristic
150C2×C3×C8—24no—
151C2×C3×C8—22no—
152C2×C3×C8—22no—
153C3×C4⋊C4—31no—
154C3×C4⋊C4—31no—
155C3×C4⋊C4—64no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4—61no—
160C3×C22⋊C4—61no—
161C3×C22⋊C4—61no—
162C3×C22⋊C4—61no—
163C3×C22⋊C4—61no—
164C3×C22⋊C4—61no—
165C3×C42—21no—
166C3×C42—21no—
167C3×C42—21no—
168C3×C42—21no—
169C3×C42—61no—
170C3×C42—122no—
171C3×C42C4×D311yescharacteristic
172C3×C42C4×D311yescharacteristic
173C3×C42#6711yescharacteristic
174C3×C42#6711yescharacteristic
175C3×C42C2×C3×C411yescharacteristic
176C3×C42C2×C3×C411yescharacteristic
177C3×C42C3×D411yescharacteristic
178C3×C42C3×D411yescharacteristic
179#217—21no—
180(C2×D3)⋊C4—21no—
181(C2×D3)⋊C4—21no—
182(C2×D3)⋊C4—21no—
183(C2×D3)⋊C4—21no—
184C4⋊Dic3—24no—
185C4⋊Dic3C2×C3×C411yescharacteristic
186C4⋊Dic3C2×C3×C411yescharacteristic
187Dic3⋊C4—21no—
188Dic3⋊C4—21no—
189Dic3⋊C4—21no—
190Dic3⋊C4—21no—
191C4×Dic3—21no—
192C4×Dic3—42no—
193C22×C32—21no—
194C22×C32—21no—
195C22×C32C2×C22⋊C411yescharacteristic
196C22×C32AGL(1,ℤ/8)11yescharacteristic
197C22×C32#13711yescharacteristic
198C2×C3×D3—41no—
199C2×C3×D3—41no—
200C2×C3×D3—41no—
201C32×C4—21no—
202C32×C4—21no—
203C32×C4—21no—
204C32×C4—21no—
205C32×C4—21no—
206C32×C4#10412yes—
207C3×Dic3—44no—
208C3×Dic3—41no—
209C3×Dic3—41no—
210C3×Dic3—41no—
211#126—61no—
212#125—31no—
213#124—31no—
214#123—61no—
215C22⋊Q8—31no—
216#121—31no—
217C4×Q8—31no—
218C4×D4—31no—
219C4×D4—61no—
220#117—61no—
221C2×C4⋊C4—61no—
222C2×C42—61no—
223C2×C42C2×C3×D311yescharacteristic
224C4⋊C8—21no—
225C22⋊C8C2×C3×D312yes—
226#97—21no—
227#95—32no—
228C23×C3—21no—
229C23×C3—61no—
230C23×C3C2×D1211yescharacteristic
231C23×C3C2×C3×D411yescharacteristic
232C22×D3—21no—
233C3×Q8—121no—
234C3×D4—121no—
235C3×D4—121no—
236C3×D4—121no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—42no—
250C2×C3×C4—41no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—42no—
255C2×C3×C4—64no—
256C2×C3×C4—61no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4—122no—
260C2×C3×C4—122no—
261C2×C3×C4—122no—
262C2×C3×C4(C2×D3)⋊C411yescharacteristic
263C2×C3×C4(C2×D3)⋊C411yescharacteristic
264C2×C3×C4(C2×D3)⋊C411yescharacteristic
265C2×C3×C4(C2×D3)⋊C411yescharacteristic
266C2×C3×C4C3×C22⋊C411yescharacteristic
267C2×C3×C4C3×C22⋊C411yescharacteristic
268C2×C3×C4C3×C22⋊C411yescharacteristic
269C2×C3×C4C3×C22⋊C411yescharacteristic
270C2×C3×C4C2×C4×D311yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×C3×C4C22×C3×C411yescharacteristic
273C2×C3×C4C2×C3×D411yescharacteristic
274#67—41no—
275#67—41no—
276C2×Dic3—24no—
277C2×Dic3—21no—
278C2×Dic3—21no—
279C2×Dic3—21no—
280C2×Dic3—42no—
281C2×Dic3—42no—
282D12—41no—
283C4×D3—42no—
284Dic6—41no—
285C3×C8—44no—
286C3×C8—42no—
287C3×C8—42no—
288C2×C32—21no—
289C2×C32—21no—
290C2×C32#41011yescharacteristic
291C2×C32#41711yescharacteristic
292C2×C32C2×#10411yescharacteristic
293C3×D3—81no—
294C2×Q8—31no—
295C2×D4—31no—
296C2×D4—61no—
297C22×C4—62no—
298C22×C4—61no—
299C22×C4C3×D1211yescharacteristic
300C22×C4C3×D1211yescharacteristic
301C22×C4C22×C3×D311yescharacteristic
302C2×C8—22no—
303C4⋊C4—31no—
304C4⋊C4—31no—
305C4⋊C4—64no—
306C4⋊C4—61no—
307C4⋊C4—61no—
308C4⋊C4—61no—
309C4⋊C4—61no—
310C22⋊C4—61no—
311C22⋊C4—61no—
312C22⋊C4—61no—
313C22⋊C4—61no—
314C22⋊C4—61no—
315C42—61no—
316C42—122no—
317C42C3×C4×D311yescharacteristic
318C42C3×C4×D311yescharacteristic
319C42C3×#6711yescharacteristic
320C42C3×#6711yescharacteristic
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—121no—
331C22×C3—121no—
332C22×C3—121no—
333C22×C3#90811yescharacteristic
334C22×C3#90911yescharacteristic
335C22×C3C2×(C2×D3)⋊C411yescharacteristic
336C22×C3C2×C3×C22⋊C411yescharacteristic
337C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
338C22×C3C3×#13711yescharacteristic
339C2×D3—41no—
340C2×D3—41no—
341C2×D3—41no—
342C3×C4—22no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—21no—
353C3×C4—22no—
354C3×C4—41no—
355C3×C4—41no—
356C3×C4—41no—
357C3×C4—41no—
358C3×C4—124no—
359C3×C4—121no—
360C3×C4—121no—
361C3×C4—121no—
362C3×C4#82512yes—
363C3×C4C3×#10412yes—
364Dic3—44no—
365Dic3—41no—
366Dic3—41no—
367Dic3—41no—
368C32#150911yescharacteristic, complemented, Sylow
369C23—61no—
370C23C2×C3×D1211yescharacteristic
371Q8—121no—
372D4—121no—
373D4—121no—
374D4—121no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—22no—
378C2×C4—41no—
379C2×C4—64no—
380C2×C4—61no—
381C2×C4—61no—
382C2×C4—61no—
383C2×C4—122no—
384C2×C4—122no—
385C2×C4—122no—
386C2×C4C3×(C2×D3)⋊C411yescharacteristic
387C2×C4C3×(C2×D3)⋊C411yescharacteristic
388C2×C4C3×(C2×D3)⋊C411yescharacteristic
389C2×C4C3×(C2×D3)⋊C411yescharacteristic
390C2×C4C2×C3×C4×D311yescharacteristic
391C2×C4C2×C3×#6711yescharacteristic
392C8—42no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—41no—
401C2×C3—41no—
402C2×C3—241no—
403C2×C3#500611yescharacteristic
404C2×C3#513311yescharacteristic
405C2×C3C2×#82511yescharacteristic
406C2×C3C3×#41011yescharacteristic
407C2×C3C3×#41711yescharacteristic
408C2×C3C2×C3×#10411yescharacteristic
409D3—81no—
410C22—21no—
411C22—21no—
412C22—121no—
413C22—121no—
414C22—121no—
415C22C3×#90811yescharacteristic
416C22C3×#90911yescharacteristic
417C22C2×C3×(C2×D3)⋊C411yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—124no—
424C4—121no—
425C4—121no—
426C4—121no—
427C4C3×#82512yes—
428C3—21no—
429C3#7083311yescharacteristic, direct product factor
430C3C3×#150911yescharacteristic, complemented
431C2—21no—
432C2—21no—
433C2—241no—
434C2C3×#500611yescharacteristic
435C2C3×#513311yescharacteristic
436C2C2×C3×#82511yescharacteristic
subgroupG/H
centerC22×C3C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#432C2
socleC22×C32C2×C22⋊C4
prime radicalC3×#930C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#432D3
hypocenterC3C3×#1509
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C3×#432

Complements

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

NH ≅ G/Ntype
2. C32×#432C2semidirect
3. C3×C4×C4⋊Dic3C2semidirect
5. C3×#4467C2semidirect
7. #70833C3direct (N × H)
16. C3×#875C4semidirect
17. C3×C4×D12C4semidirect
19. C3×#870C4semidirect
20. C3×C4×Dic6C4semidirect
28. C3×#432D3semidirect
29. C3×#432C2×C3semidirect
31. C4×C4⋊Dic3C2×C3semidirect
35. #4467C2×C3semidirect
86. #875C3×C4semidirect
87. C4×D12C3×C4semidirect
89. #870C3×C4semidirect
90. C4×Dic6C3×C4semidirect
127. #432C3×D3semidirect
368. C32#1509semidirect
429. C3#70833direct (N × H)
430. C3C3×#1509semidirect

Maximal subgroups

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

subgroupindex
C3×#54792
C32×#4322
C3×C4×C4⋊Dic32
C3×#44702
C3×#44672
C3×#15093
#708333