Finite Group Databasebeta

← C3×#10592855 #13163194

Subgroups — C3×#10592855 #13163194

Order 1728.

1492 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C33×D8C211yesmaximal, characteristic, complemented
3C3×#64147C211yesmaximal, characteristic, complemented
4C2×C3×#3753C211yesmaximal, characteristic, complemented
5C3×#63659C211yesmaximal, characteristic, complemented
6C3×#63648C211yesmaximal, characteristic, complemented
7C3×#63647C211yesmaximal, characteristic, complemented
8#10592855C311yesmaximal, characteristic, direct product factor
9C3×#5156—34nomaximal
10C23×C3×C3⋊D3—21no—
11C2×C33×D4C2211yescharacteristic
12C2×C33×D4C2211yescharacteristic, complemented
13C2×C3×#638—21no—
14C2×C3×#638—21no—
15C3×D4×C3⋊D3—22no—
16C3×D4×C3⋊D3—22no—
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C3×C4×C3⋊D3C2211yescharacteristic
19C33×D8—22no—
20C2×C33×C8C2211yescharacteristic, complemented
21C3×#3757—21no—
22C3×#3753—22no—
23C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
24C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
25C2×D4×C3⋊D3C2×C311yescharacteristic, complemented
26C2×C3×D3×D4—34no—
27C2×C32×D8—24no—
28C2×C32×D8D314yescomplemented
29C2×C32×D8C2×C311yescharacteristic, complemented
30#64147C2×C311yescharacteristic, complemented
31C2×#3753C2×C311yescharacteristic, complemented
32C3×#938—34no—
33C2×C3×#213—34no—
34#63659C2×C311yescharacteristic, complemented
35#63648C2×C311yescharacteristic, complemented
36#63647C2×C311yescharacteristic, complemented
37C3×#832—34no—
38C3×#821—34no—
39C3×(C2×D3)⋊C8—34no—
40C23×C33—21no—
41C23×C33—21no—
42C22×C3×C3⋊D3—24no—
43C22×C3×C3⋊D3—21no—
44C22×C3×C3⋊D3—42no—
45C22×C3×C3⋊D3—42no—
46C22×C3×C3⋊D3D411yescharacteristic
47C33×D4—21no—
48C33×D4—21no—
49C33×D4—21no—
50C33×D4D412yescomplemented
51C2×C33×C4C2311yescharacteristic
52C3×#638—24no—
53C3×#638—42no—
54C2×C3×C3⋊Dic3—21no—
55C2×C3×C3⋊Dic3D411yescharacteristic
56C3×C4⋊(C3⋊D3)—21no—
57C3×C4⋊(C3⋊D3)D412yescomplemented
58C3×C4×C3⋊D3—21no—
59C3×C4×C3⋊D3—21no—
60C33×C8—21no—
61C3×C3⋊(C3⋊C8)—21no—
62C3×#447—91no—
63#5156—34no—
64C23×C3⋊D3—21no—
65C23×C3×D3—64no—
66C2×C32×D4—24no—
67C2×C32×D4—24no—
68C2×C32×D4C2×D314yes—
69C2×C32×D4C2×D314yescomplemented
70C2×C32×D4C22×C311yescharacteristic
71C2×C32×D4C22×C311yescharacteristic, complemented
72C2×#638—21no—
73C2×#638—21no—
74D4×C3⋊D3—22no—
75D4×C3⋊D3—22no—
76C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
77C2×C4×C3⋊D3C22×C311yescharacteristic
78C2×C3×#67—64no—
79C2×C3×#67—64no—
80C3×D3×D4—68no—
81C3×D3×D4—68no—
82C2×C3×D12—34no—
83C2×C3×C4×D3—34no—
84C32×D8—216no—
85C32×D8—28no—
86C32×D8—22no—
87C2×C32×C8—24no—
88C2×C32×C8C2×D314yescomplemented
89C2×C32×C8C22×C311yescharacteristic, complemented
90#3757—21no—
91#3753—22no—
92C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
93C2×C3⋊(C3⋊C8)C22×C311yescharacteristic, complemented
94C3×#217—64no—
95C3×#213—68no—
96C3×C4⋊Dic3—34no—
97C2×C3×C3⋊C8—34no—
98C22×C33—22no—
99C22×C33—41no—
100C22×C33—41no—
101C22×C33—41no—
102C22×C33—41no—
103C22×C33—41no—
104C22×C33C2×D411yescharacteristic
105C2×C3×C3⋊D3—21no—
106C2×C3×C3⋊D3—21no—
107C2×C3×C3⋊D3—22no—
108C2×C3×C3⋊D3—48no—
109C2×C3×C3⋊D3—41no—
110C2×C3×C3⋊D3—41no—
111C2×C3×C3⋊D3D812yescomplemented
112C33×C4C2×D411yescharacteristic
113C33×C4C2×D411yescharacteristic
114C3×C3⋊Dic3—21no—
115C3×C3⋊Dic3—41no—
116C22×C3×D4—91no—
117C2×D3×D4—34no—
118C2×C3×D8—24no—
119C2×C3×D8—91no—
120C2×C3×D8C3×D314yescomplemented
121C2×C3×D8C3⋊D311yescharacteristic, complemented
122C3×#121—91no—
123#938—34no—
124C2×#213—34no—
125C3×#102—91no—
126C3×#102—91no—
127C3×C22⋊C8—91no—
128#832—34no—
129#821—34no—
130(C2×D3)⋊C8—34no—
131C23×C32—21no—
132C23×C32—21no—
133C23×C32—24no—
134C23×C32—24no—
135C23×C32—44no—
136C23×C32—44no—
137C22×C3⋊D3—24no—
138C22×C3⋊D3—21no—
139C22×C3⋊D3—42no—
140C22×C3⋊D3—42no—
141C22×C3⋊D3C3×D411yescharacteristic
142C22×C3×D3—34no—
143C22×C3×D3—616no—
144C22×C3×D3—64no—
145C22×C3×D3—128no—
146C22×C3×D3—128no—
147C32×D4—28no—
148C32×D4—24no—
149C32×D4—21no—
150C32×D4—21no—
151C32×D4—21no—
152C32×D4—28no—
153C32×D4—24no—
154C32×D4—24no—
155C32×D4—44no—
156C32×D4—44no—
157C32×D4#6718yescomplemented
158C32×D4C3×D412yescomplemented
159C2×C32×C4—24no—
160C2×C32×C4C22×D314yes—
161C2×C32×C4C23×C311yescharacteristic
162#638—24no—
163#638—42no—
164C2×C3⋊Dic3—21no—
165C2×C3⋊Dic3C3×D411yescharacteristic
166C4⋊(C3⋊D3)—21no—
167C4⋊(C3⋊D3)C3×D412yescomplemented
168C4×C3⋊D3—21no—
169C4×C3⋊D3—21no—
170C3×#67—616no—
171C3×#67—128no—
172C2×C3×Dic3—34no—
173C2×C3×Dic3—64no—
174C3×D12—38no—
175C3×D12—64no—
176C3×C4×D3—64no—
177C3×C4×D3—64no—
178C32×C8—28no—
179C32×C8—24no—
180C32×C8—21no—
181C3⋊(C3⋊C8)—21no—
182C3×C3⋊C8—64no—
183#447—91noSylow
184C2×C33—42no—
185C2×C33—81no—
186C2×C33#12011yescharacteristic
187C2×C33C2×D811yescharacteristic
188C2×C33AGL(1,ℤ/8)11yescharacteristic
189C3×C3⋊D3—22no—
190C3×C3⋊D3—42no—
191C24×C3—181no—
192C23×D3—64no—
193C2×C3×D4—24no—
194C2×C3×D4—24no—
195C2×C3×D4—91no—
196C2×C3×D4—181no—
197C2×C3×D4—182no—
198C2×C3×D4—182no—
199C2×C3×D4—181no—
200C2×C3×D4C2×C3×D314yes—
201C2×C3×D4C2×C3×D314yescomplemented
202C2×C3×D4C2×C3⋊D311yescharacteristic
203C2×C3×D4C2×C3⋊D311yescharacteristic, complemented
204C22×C3×C4—91no—
205C2×#67—64no—
206C2×#67—64no—
207D3×D4—68no—
208D3×D4—68no—
209C2×D12—34no—
210C2×C4×D3—34no—
211C3×D8—216no—
212C3×D8—28no—
213C3×D8—22no—
214C3×D8—182no—
215C2×C3×C8—24no—
216C2×C3×C8—91no—
217C2×C3×C8C2×C3×D314yescomplemented
218C2×C3×C8C2×C3⋊D311yescharacteristic, complemented
219C3×C4⋊C4—91no—
220C3×C22⋊C4—181no—
221#217—64no—
222#213—68no—
223C4⋊Dic3—34no—
224C2×C3⋊C8—34no—
225C22×C32—22no—
226C22×C32—24no—
227C22×C32—28no—
228C22×C32—48no—
229C22×C32—48no—
230C22×C32—41no—
231C22×C32—41no—
232C22×C32—44no—
233C22×C32—41no—
234C22×C32—41no—
235C22×C32—41no—
236C22×C32—44no—
237C22×C32—44no—
238C22×C32—44no—
239C22×C32—44no—
240C22×C32—84no—
241C22×C32—84no—
242C22×C32—84no—
243C22×C32—84no—
244C22×C32D3×D414yes—
245C22×C32C2×C3×D411yescharacteristic
246C2×C3⋊D3—21no—
247C2×C3⋊D3—21no—
248C2×C3⋊D3—22no—
249C2×C3⋊D3—48no—
250C2×C3⋊D3—41no—
251C2×C3⋊D3—41no—
252C2×C3⋊D3C3×D812yescomplemented
253C2×C3×D3—38no—
254C2×C3×D3—64no—
255C2×C3×D3—64no—
256C2×C3×D3—68no—
257C2×C3×D3—1232no—
258C2×C3×D3—124no—
259C2×C3×D3—124no—
260C32×C4—24no—
261C32×C4—24no—
262C32×C4D3×D414yes—
263C32×C4C2×#6714yes—
264C32×C4C2×C3×D411yescharacteristic
265C32×C4C2×C3×D411yescharacteristic
266C3⋊Dic3—21no—
267C3⋊Dic3—41no—
268C3×Dic3—64no—
269C3×Dic3—124no—
270C22×D4—91no—
271C2×D8—91no—
272C2×D8C3×C3⋊D311yescharacteristic, complemented
273#121—91no—
274#102—91no—
275#102—91no—
276C22⋊C8—91no—
277C33#44711yescharacteristic, complemented, Sylow
278C23×C3—24no—
279C23×C3—21no—
280C23×C3—24no—
281C23×C3—21no—
282C23×C3—44no—
283C23×C3—44no—
284C23×C3—91no—
285C23×C3—184no—
286C23×C3—181no—
287C23×C3—362no—
288C23×C3—362no—
289C22×D3—34no—
290C22×D3—616no—
291C22×D3—64no—
292C22×D3—128no—
293C22×D3—128no—
294C3×D4—28no—
295C3×D4—24no—
296C3×D4—24no—
297C3×D4—24no—
298C3×D4—21no—
299C3×D4—21no—
300C3×D4—21no—
301C3×D4—28no—
302C3×D4—44no—
303C3×D4—44no—
304C3×D4—92no—
305C3×D4—184no—
306C3×D4—181no—
307C3×D4—362no—
308C3×D4C3×#6718yescomplemented
309C3×D4#63812yescomplemented
310C2×C3×C4—24no—
311C2×C3×C4—91no—
312C2×C3×C4—181no—
313C2×C3×C4—181no—
314C2×C3×C4—181no—
315C2×C3×C4C22×C3×D314yes—
316C2×C3×C4C22×C3⋊D311yescharacteristic
317#67—616no—
318#67—128no—
319C2×Dic3—34no—
320C2×Dic3—64no—
321D12—38no—
322D12—64no—
323C4×D3—64no—
324C4×D3—64no—
325C3×C8—28no—
326C3×C8—24no—
327C3×C8—21no—
328C3×C8—181no—
329C3⋊C8—64no—
330C2×C32—24no—
331C2×C32—24no—
332C2×C32—24no—
333C2×C32—42no—
334C2×C32—48no—
335C2×C32—88no—
336C2×C32—88no—
337C2×C32—84no—
338C2×C32—81no—
339C2×C32D3×D814yes—
340C2×C32#91114yes—
341C2×C32#93714yes—
342C2×C32C3×#12011yescharacteristic
343C2×C32C2×C3×D811yescharacteristic
344C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
345C3⋊D3—22no—
346C3⋊D3—42no—
347C3×D3—68no—
348C3×D3—128no—
349C24—181no—
350C2×D4—91no—
351C2×D4—181no—
352C2×D4—182no—
353C2×D4—182no—
354C2×D4—181no—
355C2×D4C2×C3×C3⋊D311yescharacteristic
356C2×D4C2×C3×C3⋊D311yescharacteristic, complemented
357C22×C4—91no—
358D8—22no—
359D8—182no—
360C2×C8—91no—
361C2×C8C2×C3×C3⋊D311yescharacteristic, complemented
362C4⋊C4—91no—
363C22⋊C4—181no—
364C22×C3—28no—
365C22×C3—22no—
366C22×C3—24no—
367C22×C3—48no—
368C22×C3—48no—
369C22×C3—44no—
370C22×C3—44no—
371C22×C3—41no—
372C22×C3—41no—
373C22×C3—44no—
374C22×C3—44no—
375C22×C3—44no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—84no—
380C22×C3—84no—
381C22×C3—84no—
382C22×C3—84no—
383C22×C3—92no—
384C22×C3—181no—
385C22×C3—181no—
386C22×C3—182no—
387C22×C3—368no—
388C22×C3—361no—
389C22×C3—361no—
390C22×C3C3×D3×D414yes—
391C22×C3D4×C3⋊D311yescharacteristic
392C2×D3—38no—
393C2×D3—64no—
394C2×D3—64no—
395C2×D3—68no—
396C2×D3—1232no—
397C2×D3—124no—
398C2×D3—124no—
399C3×C4—24no—
400C3×C4—24no—
401C3×C4—181no—
402C3×C4—361no—
403C3×C4C3×D3×D414yes—
404C3×C4C2×C3×#6714yes—
405C3×C4D4×C3⋊D311yescharacteristic
406C3×C4C2×#63811yescharacteristic
407Dic3—64no—
408Dic3—124no—
409C32—24no—
410C32#515614yescomplemented
411C32C3×#44711yescharacteristic, complemented
412C23—21no—
413C23—21no—
414C23—91no—
415C23—184no—
416C23—181no—
417C23—362no—
418C23—362no—
419D4—21no—
420D4—21no—
421D4—21no—
422D4—92no—
423D4—184no—
424D4—181no—
425D4—362no—
426D4C3×#63812yescomplemented
427C2×C4—91no—
428C2×C4—181no—
429C2×C4—181no—
430C2×C4—181no—
431C2×C4C22×C3×C3⋊D311yescharacteristic
432C8—21no—
433C8—181no—
434C2×C3—24no—
435C2×C3—24no—
436C2×C3—24no—
437C2×C3—42no—
438C2×C3—48no—
439C2×C3—88no—
440C2×C3—88no—
441C2×C3—81no—
442C2×C3—84no—
443C2×C3—182no—
444C2×C3—362no—
445C2×C3C3×D3×D814yes—
446C2×C3C3×#91114yes—
447C2×C3C3×#93714yes—
448C2×C3D8×C3⋊D311yescharacteristic
449C2×C3#6412011yescharacteristic
450C2×C3#6414611yescharacteristic
451D3—68no—
452D3—128no—
453C22—22no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—92no—
460C22—181no—
461C22—181no—
462C22—182no—
463C22—368no—
464C22—361no—
465C22—361no—
466C22C3×D4×C3⋊D311yescharacteristic
467C4—181no—
468C4—361no—
469C4C3×D4×C3⋊D311yescharacteristic
470C4C2×C3×#63811yescharacteristic
471C3—24no—
472C3C3×#515614yescomplemented
473C3#1059285511yescharacteristic, direct product factor
474C2—42no—
475C2—81no—
476C2—182no—
477C2—362no—
478C2C3×D8×C3⋊D311yescharacteristic
479C2C3×#6412011yescharacteristic
480C2C3×#6414611yescharacteristic
subgroupG/H
centerC22×C3D4×C3⋊D3
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C22×C3×C3⋊D3
FittingC2×C33×D8C2
socleC22×C33C2×D4
hypercenterC2×C3×D8C3⋊D3
hypocenterC32C3×#447
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×D8

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×C3⋊D3C2semidirect
2. C2×C33×D8C2semidirect
3. C3×#64147C2semidirect
4. C2×C3×#3753C2semidirect
5. C3×#63659C2semidirect
6. C3×#63648C2semidirect
7. C3×#63647C2semidirect
8. #10592855C3direct (N × H)
12. C2×C33×D4C22semidirect
20. C2×C33×C8C22semidirect
23. C3×C4⋊(C3⋊Dic3)C22semidirect
24. C2×C3×C3⋊(C3⋊C8)C22semidirect
25. C2×D4×C3⋊D3C2×C3semidirect
28. C2×C32×D8D3semidirect
29. C2×C32×D8C2×C3semidirect
30. #64147C2×C3semidirect
31. C2×#3753C2×C3semidirect
34. #63659C2×C3semidirect
35. #63648C2×C3semidirect
36. #63647C2×C3semidirect
50. C33×D4D4semidirect
57. C3×C4⋊(C3⋊D3)D4semidirect
69. C2×C32×D4C2×D3semidirect
71. C2×C32×D4C22×C3semidirect
88. C2×C32×C8C2×D3semidirect
89. C2×C32×C8C22×C3semidirect
92. C4⋊(C3⋊Dic3)C22×C3semidirect
93. C2×C3⋊(C3⋊C8)C22×C3semidirect
111. C2×C3×C3⋊D3D8semidirect
120. C2×C3×D8C3×D3semidirect
121. C2×C3×D8C3⋊D3semidirect
157. C32×D4#67semidirect
158. C32×D4C3×D4semidirect
167. C4⋊(C3⋊D3)C3×D4semidirect
201. C2×C3×D4C2×C3×D3semidirect
203. C2×C3×D4C2×C3⋊D3semidirect
217. C2×C3×C8C2×C3×D3semidirect
218. C2×C3×C8C2×C3⋊D3semidirect
252. C2×C3⋊D3C3×D8semidirect
272. C2×D8C3×C3⋊D3semidirect
277. C33#447semidirect
308. C3×D4C3×#67semidirect
309. C3×D4#638semidirect
356. C2×D4C2×C3×C3⋊D3semidirect
361. C2×C8C2×C3×C3⋊D3semidirect
410. C32#5156semidirect
411. C32C3×#447semidirect
426. D4C3×#638semidirect
472. C3C3×#5156semidirect
473. C3#10592855direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×C3⋊D32
C2×C33×D82
C3×#641472
C2×C3×#37532
C3×#636592
C3×#636482
C3×#636472
#105928553
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