Finite Group Databasebeta

← C3×#79027 #11882237

Subgroups — C3×#79027 #11882237

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5477C211yesmaximal, characteristic
2C3×#5470C211yesmaximal, characteristic, complemented
3C2×C32×C4⋊C8C211yesmaximal, characteristic, complemented
4C3×#5114C214yesmaximal, complemented
5C3×#4851C212yesmaximal, complemented
6C3×#4848C212yesmaximal, complemented
7C3×#4842C212yesmaximal, complemented
8C3×#4841C212yesmaximal, complemented
9C3×#3246—31nomaximal
10#79027C311yesmaximal, characteristic, direct product factor
11C2×C3×#235—21no—
12C22×C32×C8C2212yes—
13C2×C32×C42C2211yescharacteristic
14C3×#930—21no—
15C3×#930C2212yes—
16C3×#926—21no—
17C3×#924—21no—
18C3×#924C2212yes—
19C2×C3×#204C2214yes—
20C3×#875—21no—
21C3×#874C2211yescharacteristic
22C3×C4×D12—21no—
23C3×C4×D12C2212yes—
24C3×#870—21no—
25C3×#869C2211yescharacteristic
26C3×#869C2211yescharacteristic
27C3×#869C2211yescharacteristic
28C3×C4×Dic6—21no—
29C3×C4×Dic6C2212yes—
30C32×C4⋊C8C2212yes—
31C32×C4⋊C8C2212yes—
32C3×#821C2214yes—
33C3×#817C2214yes—
34C3×#816C2214yes—
35C3×#533—31no—
36C3×#532—31no—
37#5477C2×C311yescharacteristic
38#5470C2×C311yescharacteristic, complemented
39C3×#476—32no—
40C3×#475—32no—
41C3×#465—34no—
42C3×#461—32no—
43C3×#460—32no—
44C2×C3×C4⋊C8—21no—
45C2×C3×C4⋊C8D311yescharacteristic, complemented
46C2×C3×C4⋊C8C2×C311yescharacteristic, complemented
47#5114C2×C314yescomplemented
48#4851C2×C312yescomplemented
49#4848C2×C312yescomplemented
50#4842C2×C312yescomplemented
51#4841C2×C312yescomplemented
52C22×C32×C4D411yescharacteristic
53C22×C32×C4D411yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C2×C3×#67—22no—
56C3×#235—44no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12C2312yes—
60C2×C3×C4×D3—22no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6C2312yes—
64C2×C32×C8—42no—
65C2×C32×C8C2314yes—
66C32×C42D411yescharacteristic
67C32×C42D411yescharacteristic
68C32×C42C2311yescharacteristic
69C32×C42C2311yescharacteristic
70C3×#217—22no—
71C3×(C2×D3)⋊C4—22no—
72C3×(C2×D3)⋊C4—22no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3C2312yes—
78C3×C4⋊Dic3C2312yes—
79C3×Dic3⋊C4—22no—
80C3×Dic3⋊C4—22no—
81C3×C4×Dic3—22no—
82C3×#204—44no—
83#3246—31noSylow
84C2×C3×#41—61no—
85C2×#235—21no—
86C2×C3×SD16—34no—
87C22×C3×C8—22no—
88C22×C3×C8C2×D312yes—
89C22×C3×C8C22×C312yes—
90C3×C4⋊Q8—31no—
91C3×C4⋊Q8—31no—
92C3×C4⋊Q8—31no—
93C3×#127—31no—
94C3×#125—61no—
95C3×#124—61no—
96C3×C22⋊Q8—32no—
97C3×C22⋊Q8—61no—
98C3×#121—32no—
99C3×#121—61no—
100C3×C4×Q8—32no—
101C3×C4×Q8—61no—
102C3×C4×D4—32no—
103C3×C4×D4—61no—
104C3×#117—61no—
105C2×C3×C42—21no—
106C2×C3×C42C2×D311yescharacteristic
107C2×C3×C42C22×C311yescharacteristic
108#930—21no—
109#930C22×C312yes—
110#926—21no—
111#924—21no—
112#924C22×C312yes—
113C2×#204C22×C314yes—
114#875—21no—
115#874C22×C311yescharacteristic
116C4×D12—21no—
117C4×D12C22×C312yes—
118#870—21no—
119#869C22×C311yescharacteristic
120#869C22×C311yescharacteristic
121#869C22×C311yescharacteristic
122C4×Dic6—21no—
123C4×Dic6C22×C312yes—
124C3×#106—34no—
125C3×C4⋊C8—22no—
126C3×C4⋊C8—22no—
127C3×C4⋊C8C2×D312yes—
128C3×C4⋊C8C2×D312yes—
129C3×C4⋊C8C22×C312yes—
130C3×C4⋊C8C22×C312yes—
131C3×#103—34no—
132C3×#102—34no—
133#821C22×C314yes—
134#817C22×C314yes—
135#816C22×C314yes—
136C23×C32C2×D411yescharacteristic
137C22×C3×D3—22no—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4—41no—
141C2×C32×C4SD1614yescomplemented
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2411yescharacteristic
148C3×#67—44no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C3×D12—22no—
153C3×D12—22no—
154C3×D12—42no—
155C3×D12—42no—
156C3×C4×D3—44no—
157C3×Dic6—22no—
158C3×Dic6—22no—
159C3×Dic6—42no—
160C3×Dic6—42no—
161C32×C8—24no—
162#533—31no—
163#532—31no—
164#476—32no—
165#475—32no—
166#465—34no—
167#461—32no—
168#460—32no—
169C2×C4⋊C8C3×D311yescharacteristic, complemented
170C3×#41—124no—
171C2×C3×Q8—32no—
172C2×C3×Q8—61no—
173C2×C3×Q8—61no—
174C2×C3×D4—32no—
175C2×C3×D4—62no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—62no—
182C22×C3×C4D1211yescharacteristic
183C22×C3×C4D1211yescharacteristic
184C22×C3×C4C3×D411yescharacteristic
185C22×C3×C4C3×D411yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C23×C311yescharacteristic
188C2×#67—22no—
189#235—44no—
190C2×D12—21no—
191C2×D12—21no—
192C2×D12C23×C312yes—
193C2×C4×D3—22no—
194C2×Dic6—21no—
195C2×Dic6—21no—
196C2×Dic6C23×C312yes—
197C3×SD16—124no—
198C2×C3×C8—24no—
199C2×C3×C8—42no—
200C2×C3×C8—42no—
201C2×C3×C8—44no—
202C2×C3×C8C22×D314yes—
203C2×C3×C8C23×C314yes—
204C3×C4⋊C4—32no—
205C3×C4⋊C4—32no—
206C3×C4⋊C4—62no—
207C3×C4⋊C4—62no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4—61no—
211C3×C4⋊C4—61no—
212C3×C22⋊C4—62no—
213C3×C22⋊C4—62no—
214C3×C22⋊C4—62no—
215C3×C42—21no—
216C3×C42—21no—
217C3×C42—21no—
218C3×C42—21no—
219C3×C42—62no—
220C3×C42D1211yescharacteristic
221C3×C42D1211yescharacteristic
222C3×C42C3×D411yescharacteristic
223C3×C42C3×D411yescharacteristic
224C3×C42C22×D311yescharacteristic
225C3×C42C22×D311yescharacteristic
226C3×C42C23×C311yescharacteristic
227C3×C42C23×C311yescharacteristic
228#217—22no—
229(C2×D3)⋊C4—22no—
230(C2×D3)⋊C4—22no—
231C4⋊Dic3—21no—
232C4⋊Dic3—21no—
233C4⋊Dic3—21no—
234C4⋊Dic3—21no—
235C4⋊Dic3C23×C312yes—
236C4⋊Dic3C23×C312yes—
237Dic3⋊C4—22no—
238Dic3⋊C4—22no—
239C4×Dic3—22no—
240#204—44no—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32C2×SD1612yes—
244C22×C32C22×D411yescharacteristic
245C2×C3×D3—42no—
246C2×C3×D3—42no—
247C2×C3×D3—42no—
248C32×C4—21no—
249C32×C4—21no—
250C32×C4—21no—
251C32×C4C2×SD1612yes—
252C32×C4C2×SD1612yes—
253C32×C4H(5,𝔽2)11yescharacteristic
254C32×C42−1+411yescharacteristic
255C3×Dic3—42no—
256C3×Dic3—42no—
257C3×Dic3—42no—
258C2×#41—61no—
259C2×SD16—34no—
260C22×C8C2×C3×D312yes—
261C4⋊Q8—31no—
262C4⋊Q8—31no—
263C4⋊Q8—31no—
264#127—31no—
265#125—61no—
266#124—61no—
267C22⋊Q8—32no—
268C22⋊Q8—61no—
269#121—32no—
270#121—61no—
271C4×Q8—32no—
272C4×Q8—61no—
273C4×D4—32no—
274C4×D4—61no—
275#117—61no—
276C2×C42C2×C3×D311yescharacteristic
277#106—34no—
278C4⋊C8C2×C3×D312yes—
279C4⋊C8C2×C3×D312yes—
280#103—34no—
281#102—34no—
282C23×C3—21no—
283C23×C3—62no—
284C23×C3C2×D1211yescharacteristic
285C23×C3C2×C3×D411yescharacteristic
286C22×D3—22no—
287C3×Q8—62no—
288C3×Q8—62no—
289C3×Q8—122no—
290C3×Q8—122no—
291C3×D4—62no—
292C3×D4—62no—
293C3×D4—122no—
294C3×D4—124no—
295C3×D4—122no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—24no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—42no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—124no—
316C2×C3×C4#20414yescomplemented
317C2×C3×C4C3×SD1614yescomplemented
318C2×C3×C4C2×D1211yescharacteristic
319C2×C3×C4C2×D1211yescharacteristic
320C2×C3×C4C2×D1211yescharacteristic
321C2×C3×C4C2×D1211yescharacteristic
322C2×C3×C4C2×D1211yescharacteristic
323C2×C3×C4C2×C3×D411yescharacteristic
324C2×C3×C4C2×C3×D411yescharacteristic
325C2×C3×C4C2×C3×D411yescharacteristic
326C2×C3×C4C2×C3×D411yescharacteristic
327C2×C3×C4C2×C3×D411yescharacteristic
328C2×C3×C4C23×D311yescharacteristic
329C2×C3×C4C24×C311yescharacteristic
330#67—44no—
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334D12—22no—
335D12—22no—
336D12—42no—
337D12—42no—
338C4×D3—44no—
339Dic6—22no—
340Dic6—22no—
341Dic6—42no—
342Dic6—42no—
343C3×C8—24no—
344C3×C8—24no—
345C3×C8—44no—
346C2×C32—22no—
347C2×C32#53711yescharacteristic
348C2×C32C22×SD1611yescharacteristic
349C2×C32#57511yescharacteristic
350C3×D3—82no—
351#41—124no—
352C2×Q8—32no—
353C2×Q8—61no—
354C2×Q8—61no—
355C2×D4—32no—
356C2×D4—62no—
357C2×D4—61no—
358C2×D4—61no—
359C22×C4—62no—
360C22×C4C3×D1211yescharacteristic
361C22×C4C3×D1211yescharacteristic
362C22×C4C22×C3×D311yescharacteristic
363SD16—124no—
364C2×C8—42no—
365C2×C8C22×C3×D314yes—
366C4⋊C4—32no—
367C4⋊C4—32no—
368C4⋊C4—61no—
369C4⋊C4—61no—
370C4⋊C4—61no—
371C4⋊C4—62no—
372C4⋊C4—62no—
373C4⋊C4—61no—
374C22⋊C4—62no—
375C22⋊C4—62no—
376C22⋊C4—62no—
377C42—62no—
378C42C3×D1211yescharacteristic
379C42C3×D1211yescharacteristic
380C42C22×C3×D311yescharacteristic
381C42C22×C3×D311yescharacteristic
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—22no—
389C22×C3—21no—
390C22×C3—122no—
391C22×C3—122no—
392C22×C3—122no—
393C22×C3C2×#20412yes—
394C22×C3C2×C3×SD1612yes—
395C22×C3C22×D1211yescharacteristic
396C22×C3C22×C3×D411yescharacteristic
397C2×D3—42no—
398C2×D3—42no—
399C2×D3—42no—
400C3×C4—22no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—22no—
408C3×C4—22no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—41no—
412C3×C4—41no—
413C3×C4—122no—
414C3×C4—122no—
415C3×C4—122no—
416C3×C4C2×#20412yes—
417C3×C4C2×#20412yes—
418C3×C4C2×C3×SD1612yes—
419C3×C4C2×C3×SD1612yes—
420C3×C4#100411yescharacteristic
421C3×C4#100711yescharacteristic
422C3×C4C3×H(5,𝔽2)11yescharacteristic
423C3×C4C3×2−1+411yescharacteristic
424Dic3—42no—
425Dic3—42no—
426Dic3—42no—
427C32#324611yescharacteristic, complemented, Sylow
428C23—62no—
429C23C2×C3×D1211yescharacteristic
430Q8—62no—
431Q8—62no—
432Q8—122no—
433Q8—122no—
434D4—62no—
435D4—62no—
436D4—122no—
437D4—124no—
438D4—122no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—41no—
442C2×C4—62no—
443C2×C4—62no—
444C2×C4—62no—
445C2×C4—124no—
446C2×C4C3×#20414yescomplemented
447C2×C4C2×C3×D1211yescharacteristic
448C2×C4C2×C3×D1211yescharacteristic
449C2×C4C2×C3×D1211yescharacteristic
450C2×C4C2×C3×D1211yescharacteristic
451C2×C4C2×C3×D1211yescharacteristic
452C2×C4C23×C3×D311yescharacteristic
453C8—24no—
454C2×C3—24no—
455C2×C3—22no—
456C2×C3—22no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—242no—
461C2×C3#551011yescharacteristic
462C2×C3C22×#20411yescharacteristic
463C2×C3#574811yescharacteristic
464C2×C3C3×#53711yescharacteristic
465C2×C3C22×C3×SD1611yescharacteristic
466C2×C3C3×#57511yescharacteristic
467D3—82no—
468C22—21no—
469C22—21no—
470C22—122no—
471C22—122no—
472C22—122no—
473C22C2×C3×#20412yes—
474C22C22×C3×D1211yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—122no—
479C4—122no—
480C4—122no—
481C4C2×C3×#20412yes—
482C4C2×C3×#20412yes—
483C4C3×#100411yescharacteristic
484C4C3×#100711yescharacteristic
485C3—21no—
486C3#7902711yescharacteristic, direct product factor
487C3C3×#324611yescharacteristic, complemented
488C2—22no—
489C2—242no—
490C2C3×#551011yescharacteristic
491C2C22×C3×#20411yescharacteristic
492C2C3×#574811yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×C4⋊C8C2
socleC22×C32C22×D4
prime radicalC3×#5477C2
hypercenterC2×C3×C4⋊C8D3
hypocenterC3C3×#3246
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ C2×C3×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#5470C2semidirect
3. C2×C32×C4⋊C8C2semidirect
4. C3×#5114C2semidirect
5. C3×#4851C2semidirect
6. C3×#4848C2semidirect
7. C3×#4842C2semidirect
8. C3×#4841C2semidirect
10. #79027C3direct (N × H)
38. #5470C2×C3semidirect
45. C2×C3×C4⋊C8D3semidirect
46. C2×C3×C4⋊C8C2×C3semidirect
47. #5114C2×C3semidirect
48. #4851C2×C3semidirect
49. #4848C2×C3semidirect
50. #4842C2×C3semidirect
51. #4841C2×C3semidirect
141. C2×C32×C4SD16semidirect
169. C2×C4⋊C8C3×D3semidirect
316. C2×C3×C4#204semidirect
317. C2×C3×C4C3×SD16semidirect
427. C32#3246semidirect
446. C2×C4C3×#204semidirect
486. C3#79027direct (N × H)
487. C3C3×#3246semidirect

Maximal subgroups

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

subgroupindex
C3×#54772
C3×#54702
C2×C32×C4⋊C82
C3×#51142
C3×#48512
C3×#48482
C3×#48422
C3×#48412
C3×#32463
#790273