Finite Group Databasebeta

← C3×#79087 #11866249

Subgroups — C3×#79087 #11866249

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C211yesmaximal, characteristic
2C22×C3×#204C211yesmaximal, characteristic, complemented
3C3×#5526C211yesmaximal, characteristic, complemented
4C3×#5521C211yesmaximal, characteristic, complemented
5C32×#424C211yesmaximal, characteristic, complemented
6C3×#5120C211yesmaximal, characteristic, complemented
7C3×#5113C211yesmaximal, characteristic, complemented
8C3×#4844C214yesmaximal, complemented
9C3×#4841C214yesmaximal, complemented
10C3×#3042—31nomaximal
11#79087C311yesmaximal, characteristic, direct product factor
12C2×C3×#235C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C22×C32×C8C2211yescharacteristic
17C32×#117C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C3×#908—24no—
20C2×C3×D24C2212yes—
21C2×C3×#204—24no—
22C2×C3×#204C2212yes—
23C2×C3×#204C2214yes—
24C3×#897—22no—
25C3×#893—22no—
26C3×#886—22no—
27C3×D3×C22⋊C4—22no—
28C3×#875C2212yescomplemented
29C3×C4×D12C2214yes—
30C3×#869C2212yescomplemented
31C32×C4⋊C8C2214yescomplemented
32C3×#821C2212yescomplemented
33C3×#816C2212yescomplemented
34C3×#816C2214yescomplemented
35C2×C3×AGL(1,ℤ/8)—31no—
36C22×C3×SD16—31no—
37C3×#536—31no—
38C3×#518—31no—
39C2×#908C2×C311yescharacteristic
40C22×#204C2×C311yescharacteristic, complemented
41#5526C2×C311yescharacteristic, complemented
42#5521C2×C311yescharacteristic, complemented
43C3×#463—34no—
44C3×#461—34no—
45C3×#424—21no—
46C3×#424D311yescharacteristic, complemented
47C3×#424C2×C311yescharacteristic, complemented
48C3×#419—31no—
49C3×#416—31no—
50#5120C2×C311yescharacteristic, complemented
51#5113C2×C311yescharacteristic, complemented
52#4844C2×C314yescomplemented
53#4841C2×C314yescomplemented
54C23×C3×D3—21no—
55C22×C32×C4C2311yescharacteristic
56C2×C3×#67—21no—
57C22×C3×Dic3—21no—
58C3×#235—22no—
59C3×#235—22no—
60C2×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12D414yes—
63C2×C3×D12C2311yescharacteristic
64C2×C3×D12C2312yes—
65C2×C3×C4×D3—21no—
66C2×C3×C4×D3—24no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C2×C3×Dic6C2311yescharacteristic
72C32×M16—22no—
73C2×C32×C8—22no—
74C2×C32×C8C2312yes—
75C2×C32×C8C2312yes—
76C32×C4⋊C4D412yes—
77C32×C22⋊C4D412yes—
78C32×C42C2312yes—
79C3×#217—21no—
80C3×(C2×D3)⋊C4—24no—
81C3×(C2×D3)⋊C4—24no—
82C3×C4⋊Dic3—24no—
83C3×C4⋊Dic3C2312yes—
84C3×C4×Dic3—21no—
85C3×D24—24no—
86C3×#204—28no—
87C3×#204—24no—
88#3042—31noSylow
89C2×C3×#41—31no—
90C22×C3×Q8—31no—
91C22×C3×D4—31no—
92C2×#235C22×C311yescharacteristic
93C22×D12C22×C311yescharacteristic
94C22×Dic6C22×C311yescharacteristic
95C3×AGL(1,ℤ/8)—64no—
96C2×C3×SD16—34no—
97C2×C3×SD16—32no—
98C2×C3×SD16—64no—
99C2×C3×D8—32no—
100C2×C3×M16—21no—
101C2×C3×M16C2×D311yescharacteristic
102C2×C3×M16C22×C311yescharacteristic
103C22×C3×C8—21no—
104C22×C3×C8C2×D311yescharacteristic
105C22×C3×C8C22×C311yescharacteristic
106C3×C4⋊Q8—32no—
107C3×#124—32no—
108C3×#123—62no—
109C3×C22⋊Q8—62no—
110C3×C4×D4—34no—
111C3×C4×D4—62no—
112C3×#117—21no—
113C3×#117—31no—
114C3×#117C2×D311yescharacteristic
115C3×#117C22×C311yescharacteristic
116C2×C3×C22⋊C4—62no—
117#926C22×C311yescharacteristic
118#908—24no—
119C2×D24C22×C312yes—
120C2×#204—24no—
121C2×#204C22×C314yes—
122C2×#204C22×C312yes—
123#897—22no—
124#893—22no—
125#886—22no—
126D3×C22⋊C4—22no—
127#875C22×C312yescomplemented
128C4×D12C22×C314yes—
129#869C22×C312yescomplemented
130C3×C4⋊C8—24no—
131C3×C4⋊C8C2×D314yescomplemented
132C3×C4⋊C8C22×C314yescomplemented
133C3×#103—32no—
134C3×#103—34no—
135C3×#102—32no—
136#821C22×C312yescomplemented
137#816C22×C314yescomplemented
138#816C22×C312yescomplemented
139C23×C32C2×D411yescharacteristic
140C22×C3×D3—22no—
141C22×C3×D3—24no—
142C22×C3×D3—21no—
143C22×C3×D3—82no—
144C2×C32×C4C2×D414yes—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D412yes—
147C2×C32×C4#4112yes—
148C2×C32×C4C2411yescharacteristic
149C3×#67—42no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—42no—
154C3×D12—24no—
155C3×D12—21no—
156C3×D12—22no—
157C3×D12—21no—
158C3×D12C2×D414yes—
159C3×C4×D3—42no—
160C3×C4×D3—84no—
161C3×Dic6—22no—
162C3×Dic6—21no—
163C3×Dic6—22no—
164C3×Dic6—21no—
165C3×Dic6—42no—
166C32×C8—22no—
167C32×C8—22no—
168C2×AGL(1,ℤ/8)—31no—
169C22×SD16—31no—
170#536—31no—
171#518—31no—
172#463—34no—
173#461—34no—
174#424C3×D311yescharacteristic, complemented
175#419—31no—
176#416—31no—
177C24×C3—61no—
178C23×D3—21no—
179C3×#41—62no—
180C3×#41—62no—
181C2×C3×Q8—32no—
182C2×C3×Q8—31no—
183C2×C3×Q8—61no—
184C2×C3×Q8—62no—
185C2×C3×Q8—62no—
186C2×C3×D4—34no—
187C2×C3×D4—32no—
188C2×C3×D4—31no—
189C2×C3×D4—61no—
190C2×C3×D4—61no—
191C2×C3×D4—62no—
192C22×C3×C4—21no—
193C22×C3×C4—61no—
194C22×C3×C4—61no—
195C22×C3×C4—64no—
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C23×C311yescharacteristic
198C2×#67—21no—
199C22×Dic3—21no—
200#235—22no—
201#235—22no—
202C2×D12—21no—
203C2×D12—22no—
204C2×D12C3×D414yes—
205C2×D12C23×C311yescharacteristic
206C2×D12C23×C312yes—
207C2×C4×D3—21no—
208C2×C4×D3—24no—
209C2×Dic6—22no—
210C2×Dic6—22no—
211C2×Dic6—21no—
212C2×Dic6C23×C311yescharacteristic
213C2×Dic6C23×C312yes—
214C3×SD16—68no—
215C3×SD16—64no—
216C3×D8—64no—
217C3×M16—22no—
218C3×M16—22no—
219C3×M16—42no—
220C2×C3×C8—22no—
221C2×C3×C8—22no—
222C2×C3×C8—22no—
223C2×C3×C8—22no—
224C2×C3×C8—42no—
225C2×C3×C8C22×D312yes—
226C2×C3×C8C22×D312yes—
227C2×C3×C8C23×C312yes—
228C2×C3×C8C23×C312yes—
229C3×C4⋊C4—22no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—64no—
232C3×C4⋊C4D1212yes—
233C3×C4⋊C4C3×D412yes—
234C3×C22⋊C4—22no—
235C3×C22⋊C4—61no—
236C3×C22⋊C4—64no—
237C3×C22⋊C4—64no—
238C3×C22⋊C4D1212yes—
239C3×C22⋊C4C3×D412yes—
240C3×C42—22no—
241C3×C42—61no—
242C3×C42C22×D312yes—
243C3×C42C23×C312yes—
244#217—21no—
245(C2×D3)⋊C4—24no—
246(C2×D3)⋊C4—24no—
247C4⋊Dic3—24no—
248C4⋊Dic3C23×C312yes—
249C4×Dic3—21no—
250D24—24no—
251#204—28no—
252#204—24no—
253C22×C32—22no—
254C22×C32#12112yes—
255C22×C32C22×D411yescharacteristic
256C2×C3×D3—24no—
257C2×C3×D3—44no—
258C2×C3×D3—41no—
259C2×C3×D3—42no—
260C2×C3×D3—84no—
261C32×C4—24no—
262C32×C4#12112yes—
263C32×C4C22×D411yescharacteristic
264C32×C4C2×#4111yescharacteristic
265C3×Dic3—42no—
266C3×Dic3—41no—
267C3×Dic3—42no—
268C2×#41—31no—
269C22×Q8—31no—
270C22×D4—31no—
271AGL(1,ℤ/8)—64no—
272C2×SD16—34no—
273C2×SD16—32no—
274C2×SD16—64no—
275C2×D8—32no—
276C2×M16C2×C3×D311yescharacteristic
277C22×C8C2×C3×D311yescharacteristic
278C4⋊Q8—32no—
279#124—32no—
280#123—62no—
281C22⋊Q8—62no—
282C4×D4—34no—
283C4×D4—62no—
284#117—31no—
285#117C2×C3×D311yescharacteristic
286C2×C22⋊C4—62no—
287C4⋊C8C2×C3×D314yescomplemented
288#103—32no—
289#103—34no—
290#102—32no—
291C23×C3—21no—
292C23×C3—62no—
293C23×C3—64no—
294C23×C3—61no—
295C23×C3—242no—
296C23×C3C2×D1211yescharacteristic
297C23×C3C2×C3×D411yescharacteristic
298C22×D3—22no—
299C22×D3—24no—
300C22×D3—21no—
301C22×D3—82no—
302C3×Q8—62no—
303C3×Q8—61no—
304C3×Q8—62no—
305C3×Q8—61no—
306C3×Q8—122no—
307C3×D4—34no—
308C3×D4—64no—
309C3×D4—61no—
310C3×D4—62no—
311C3×D4—61no—
312C3×D4—122no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—24no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—61no—
321C2×C3×C4—122no—
322C2×C3×C4—122no—
323C2×C3×C4—244no—
324C2×C3×C4C2×D1214yes—
325C2×C3×C4C2×D1211yescharacteristic
326C2×C3×C4D3×D412yes—
327C2×C3×C4#23912yes—
328C2×C3×C4C2×C3×D414yes—
329C2×C3×C4C2×C3×D411yescharacteristic
330C2×C3×C4C2×C3×D412yes—
331C2×C3×C4C3×#4112yes—
332C2×C3×C4C23×D311yescharacteristic
333C2×C3×C4C24×C311yescharacteristic
334#67—42no—
335C2×Dic3—22no—
336C2×Dic3—21no—
337C2×Dic3—22no—
338C2×Dic3—42no—
339D12—24no—
340D12—21no—
341D12—22no—
342D12—21no—
343D12C2×C3×D414yes—
344C4×D3—42no—
345C4×D3—84no—
346Dic6—22no—
347Dic6—21no—
348Dic6—22no—
349Dic6—21no—
350Dic6—42no—
351C3×C8—22no—
352C3×C8—22no—
353C3×C8—22no—
354C3×C8—22no—
355C3×C8—42no—
356C3×C8—42no—
357C2×C32—22no—
358C2×C32C2×#12111yescharacteristic
359C2×C32#57712yes—
360C3×D3—44no—
361C3×D3—81no—
362C24—61no—
363#41—62no—
364#41—62no—
365C2×Q8—32no—
366C2×Q8—31no—
367C2×Q8—61no—
368C2×Q8—62no—
369C2×Q8—62no—
370C2×D4—32no—
371C2×D4—31no—
372C2×D4—34no—
373C2×D4—61no—
374C2×D4—61no—
375C2×D4—62no—
376C22×C4—61no—
377C22×C4—61no—
378C22×C4—64no—
379C22×C4C22×C3×D311yescharacteristic
380SD16—68no—
381SD16—64no—
382D8—64no—
383M16—22no—
384C2×C8—22no—
385C2×C8C22×C3×D312yes—
386C2×C8C22×C3×D312yes—
387C4⋊C4—32no—
388C4⋊C4—64no—
389C4⋊C4C3×D1212yes—
390C22⋊C4—61no—
391C22⋊C4—64no—
392C22⋊C4—64no—
393C22⋊C4C3×D1212yes—
394C42—61no—
395C42C22×C3×D312yes—
396C22×C3—22no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—21no—
400C22×C3—42no—
401C22×C3—64no—
402C22×C3—124no—
403C22×C3—122no—
404C22×C3—121no—
405C22×C3—244no—
406C22×C3#89512yes—
407C22×C3C3×#12112yes—
408C22×C3C22×D1211yescharacteristic
409C22×C3C22×C3×D411yescharacteristic
410C2×D3—24no—
411C2×D3—44no—
412C2×D3—42no—
413C2×D3—41no—
414C2×D3—84no—
415C3×C4—24no—
416C3×C4—24no—
417C3×C4—22no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—44no—
421C3×C4—122no—
422C3×C4—121no—
423C3×C4—122no—
424C3×C4#89512yes—
425C3×C4C3×#12112yes—
426C3×C4C2×D3×D411yescharacteristic
427C3×C4C2×#23911yescharacteristic
428C3×C4C22×C3×D411yescharacteristic
429C3×C4C2×C3×#4111yescharacteristic
430Dic3—42no—
431Dic3—42no—
432Dic3—41no—
433C32#304211yescharacteristic, complemented, Sylow
434C23—62no—
435C23—64no—
436C23—61no—
437C23—242no—
438C23C2×C3×D1211yescharacteristic
439Q8—62no—
440Q8—61no—
441Q8—62no—
442Q8—61no—
443Q8—122no—
444D4—34no—
445D4—64no—
446D4—61no—
447D4—62no—
448D4—61no—
449D4—122no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—61no—
453C2×C4—122no—
454C2×C4—122no—
455C2×C4—244no—
456C2×C4C2×C3×D1214yes—
457C2×C4C2×C3×D1211yescharacteristic
458C2×C4C3×D3×D412yes—
459C2×C4C3×#23912yes—
460C2×C4C23×C3×D311yescharacteristic
461C8—22no—
462C8—22no—
463C2×C3—22no—
464C2×C3—22no—
465C2×C3—22no—
466C2×C3—21no—
467C2×C3—42no—
468C2×C3—124no—
469C2×C3—241no—
470C2×C3C2×#89511yescharacteristic
471C2×C3#575112yes—
472C2×C3C2×C3×#12111yescharacteristic
473C2×C3C3×#57712yes—
474D3—44no—
475D3—81no—
476C22—22no—
477C22—64no—
478C22—124no—
479C22—122no—
480C22—121no—
481C22—244no—
482C22C3×#89512yes—
483C22C22×C3×D1211yescharacteristic
484C4—24no—
485C4—122no—
486C4—121no—
487C4—122no—
488C4C3×#89512yes—
489C4C2×C3×D3×D411yescharacteristic
490C4C2×C3×#23911yescharacteristic
491C3—21no—
492C3#7908711yescharacteristic, direct product factor
493C3C3×#304211yescharacteristic, complemented
494C2—22no—
495C2—124no—
496C2—241no—
497C2C2×C3×#89511yescharacteristic
498C2C3×#575112yes—
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#424C2
socleC22×C32C22×D4
prime radicalC2×C3×#908C2
hypercenterC3×#424D3
hypocenterC3C3×#3042
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#424

Complements

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

NH ≅ G/Ntype
2. C22×C3×#204C2semidirect
3. C3×#5526C2semidirect
4. C3×#5521C2semidirect
5. C32×#424C2semidirect
6. C3×#5120C2semidirect
7. C3×#5113C2semidirect
8. C3×#4844C2semidirect
9. C3×#4841C2semidirect
11. #79087C3direct (N × H)
28. C3×#875C22semidirect
30. C3×#869C22semidirect
31. C32×C4⋊C8C22semidirect
32. C3×#821C22semidirect
33. C3×#816C22semidirect
34. C3×#816C22semidirect
40. C22×#204C2×C3semidirect
41. #5526C2×C3semidirect
42. #5521C2×C3semidirect
46. C3×#424D3semidirect
47. C3×#424C2×C3semidirect
50. #5120C2×C3semidirect
51. #5113C2×C3semidirect
52. #4844C2×C3semidirect
53. #4841C2×C3semidirect
127. #875C22×C3semidirect
129. #869C22×C3semidirect
131. C3×C4⋊C8C2×D3semidirect
132. C3×C4⋊C8C22×C3semidirect
136. #821C22×C3semidirect
137. #816C22×C3semidirect
138. #816C22×C3semidirect
174. #424C3×D3semidirect
287. C4⋊C8C2×C3×D3semidirect
433. C32#3042semidirect
492. C3#79087direct (N × H)
493. C3C3×#3042semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9082
C22×C3×#2042
C3×#55262
C3×#55212
C32×#4242
C3×#51202
C3×#51132
C3×#48442
C3×#48412
C3×#30423
#790873