Finite Group Databasebeta

← C3×#10590272 #13157286

Subgroups — C3×#10590272 #13157286

Order 1728.

662 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
1C3×#64078C211yesmaximal, characteristic, complemented
2C32×C4×D12C211yesmaximal, characteristic
3C32×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4C3×#63575C212yesmaximal, complemented
5C3×#63563C212yesmaximal
6C3×#5007—31nomaximal
7C3×#4846—31nomaximal
8#10590272C311yesmaximal, characteristic, direct product factor
9C2×C3×#634—21no—
10C2×C32×D12C2211yescharacteristic
11C2×C32×C4×D3—21no—
12C33×C42C2211yescharacteristic
13C3×C4⋊(C3⋊Dic3)—21no—
14C3×C4⋊(C3⋊Dic3)C2212yes—
15C32×(C2×D3)⋊C4—21no—
16C32×C4⋊Dic3C2211yescharacteristic
17C2×C32×C3⋊C8C2212yes—
18C32×C4×D4—31no—
19#64078C2×C311yescharacteristic, complemented
20C3×C4×D12—21no—
21C3×C4×D12D311yescharacteristic
22C3×C4×D12C2×C311yescharacteristic
23C3×#869—31no—
24C3×#869—31no—
25C3×#869—61no—
26C32×C4⋊C8—31no—
27C3×#832—32no—
28C3×#821—32no—
29C3×#818—32no—
30C3×#807—32no—
31C3×C4⋊(C3⋊C8)—21no—
32C3×C4⋊(C3⋊C8)D311yescharacteristic, complemented
33C3×C4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
34#63575C2×C312yescomplemented
35#63563C2×C312yes—
36C22×C32×D3—21no—
37C2×C33×C4D411yescharacteristic
38C2×C33×C4D411yescharacteristic
39C2×C33×C4C2311yescharacteristic
40C2×C3×C3⋊Dic3—22no—
41C3×#634—42no—
42C2×C32×Dic3—21no—
43C32×D12—21no—
44C32×D12Q812yescomplemented
45C32×C4×D3—42no—
46C32×C3⋊C8—22no—
47C3×#474—91no—
48#5007—31no—
49#4846—31no—
50C2×C32×D4—31no—
51C22×C32×C4—61no—
52C2×#634—21no—
53C2×C3×D12—21no—
54C2×C3×D12C2×D311yescharacteristic
55C2×C3×D12C22×C311yescharacteristic
56C2×C3×C4×D3—22no—
57C2×C3×C4×D3—21no—
58C2×C3×C4×D3—21no—
59C2×C3×Dic6—62no—
60C2×C3×Dic6—61no—
61C2×C3×Dic6—61no—
62C2×C32×C8—32no—
63C32×C4⋊C4—31no—
64C32×C22⋊C4—61no—
65C32×C42—21no—
66C32×C42—21no—
67C32×C42—21no—
68C32×C42—41no—
69C32×C42C2×D311yescharacteristic
70C32×C42C2×D311yescharacteristic
71C32×C42C22×C311yescharacteristic
72C4⋊(C3⋊Dic3)—21no—
73C4⋊(C3⋊Dic3)C22×C312yes—
74C3×(C2×D3)⋊C4—22no—
75C3×(C2×D3)⋊C4—21no—
76C3×(C2×D3)⋊C4—21no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3—32no—
79C3×C4⋊Dic3—32no—
80C3×C4⋊Dic3—62no—
81C3×C4⋊Dic3—62no—
82C3×C4⋊Dic3—61no—
83C3×C4⋊Dic3—61no—
84C3×C4⋊Dic3C2×D311yescharacteristic
85C3×C4⋊Dic3C22×C311yescharacteristic
86C2×C3×C3⋊C8—22no—
87C2×C3×C3⋊C8C2×D312yes—
88C2×C3×C3⋊C8C22×C312yes—
89C22×C33C2×D411yescharacteristic
90C2×C32×D3—22no—
91C2×C32×D3—41no—
92C2×C32×D3—41no—
93C33×C4—21no—
94C33×C4D812yes—
95C33×C4C2×Q811yescharacteristic
96C33×C4#4111yescharacteristic
97C3×C3⋊Dic3—42no—
98C32×Dic3—41no—
99C3×C4⋊Q8—91no—
100C3×C4×D4—31no—
101C3×C4×D4—31no—
102C3×C4×D4—61no—
103C4×D12C3×D311yescharacteristic
104#869—31no—
105#869—31no—
106#869—61no—
107C3×#107—92no—
108C3×C4⋊C8—31no—
109C3×C4⋊C8—31no—
110C3×C4⋊C8—61no—
111C3×#102—92no—
112#832—32no—
113#821—32no—
114#818—32no—
115#807—32no—
116C4⋊(C3⋊C8)C3×D311yescharacteristic, complemented
117C23×C32—61no—
118C22×C3×D3—22no—
119C22×C3×D3—21no—
120C22×C3×D3—21no—
121C32×D4—32no—
122C32×D4—61no—
123C2×C32×C4—21no—
124C2×C32×C4—21no—
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4—21no—
129C2×C32×C4—21no—
130C2×C32×C4—21no—
131C2×C32×C4—21no—
132C2×C32×C4—41no—
133C2×C32×C4—41no—
134C2×C32×C4—41no—
135C2×C32×C4—61no—
136C2×C32×C4—122no—
137C2×C32×C4D1211yescharacteristic
138C2×C32×C4D1211yescharacteristic
139C2×C32×C4#6711yescharacteristic
140C2×C32×C4#6711yescharacteristic
141C2×C32×C4C3×D411yescharacteristic
142C2×C32×C4C3×D411yescharacteristic
143C2×C32×C4C22×D311yescharacteristic
144C2×C32×C4C22×D311yescharacteristic
145C2×C32×C4C23×C311yescharacteristic
146C2×C3⋊Dic3—22no—
147#634—42no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—64no—
152C2×C3×Dic3—62no—
153C2×C3×Dic3—62no—
154C3×D12—22no—
155C3×D12—21no—
156C3×D12—21no—
157C3×D12—22no—
158C3×D12Dic612yescomplemented
159C3×D12C3×Q812yescomplemented
160C3×C4×D3—44no—
161C3×C4×D3—42no—
162C3×C4×D3—42no—
163C3×Dic6—124no—
164C3×Dic6—122no—
165C3×Dic6—122no—
166C32×C8—62no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8—22no—
169C3×C3⋊C8—42no—
170#474—91noSylow
171C2×C33C22⋊Q811yescharacteristic
172C2×C33C2×D811yescharacteristic
173C2×C33#13711yescharacteristic
174C32×D3—42no—
175C2×C3×Q8—181no—
176C2×C3×D4—31no—
177C2×C3×D4—31no—
178C2×C3×D4—61no—
179C22×C3×C4—62no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C2×D12C2×C3×D311yescharacteristic
183C2×C4×D3—21no—
184C2×Dic6—62no—
185C2×Dic6—61no—
186C2×Dic6—61no—
187C2×C3×C8—32no—
188C2×C3×C8—32no—
189C2×C3×C8—62no—
190C3×C4⋊C4—31no—
191C3×C4⋊C4—31no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—92no—
194C3×C4⋊C4—181no—
195C3×C22⋊C4—62no—
196C3×C22⋊C4—61no—
197C3×C22⋊C4—61no—
198C3×C42—21no—
199C3×C42—21no—
200C3×C42—21no—
201C3×C42—41no—
202C3×C42D3211yescharacteristic
203C3×C42C2×C3×D311yescharacteristic
204C3×C42C2×C3×D311yescharacteristic
205(C2×D3)⋊C4—21no—
206C4⋊Dic3—32no—
207C4⋊Dic3—32no—
208C4⋊Dic3—62no—
209C4⋊Dic3—62no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3C2×C3×D311yescharacteristic
213C2×C3⋊C8C2×C3×D312yes—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32—21no—
217C22×C32—41no—
218C22×C32—62no—
219C22×C32—121no—
220C22×C32—121no—
221C22×C32C2×D1211yescharacteristic
222C22×C32C2×#6711yescharacteristic
223C22×C32C2×C3×D411yescharacteristic
224C2×C3×D3—24no—
225C2×C3×D3—22no—
226C2×C3×D3—22no—
227C2×C3×D3—42no—
228C2×C3×D3—42no—
229C2×C3×D3—41no—
230C2×C3×D3—41no—
231C2×C3×D3—41no—
232C2×C3×D3—41no—
233C32×C4—21no—
234C32×C4—22no—
235C32×C4—21no—
236C32×C4—21no—
237C32×C4—22no—
238C32×C4—22no—
239C32×C4—22no—
240C32×C4—21no—
241C32×C4—21no—
242C32×C4—21no—
243C32×C4—21no—
244C32×C4—21no—
245C32×C4—21no—
246C32×C4—42no—
247C32×C4—41no—
248C32×C4—41no—
249C32×C4—41no—
250C32×C4—41no—
251C32×C4—42no—
252C32×C4—121no—
253C32×C4D2412yes—
254C32×C4#21312yes—
255C32×C4C3×D812yes—
256C32×C4C2×Dic611yescharacteristic
257C32×C4#23511yescharacteristic
258C32×C4#23711yescharacteristic
259C32×C4D3×Q811yescharacteristic
260C32×C4C2×C3×Q811yescharacteristic
261C32×C4C3×#4111yescharacteristic
262C3⋊Dic3—42no—
263C3×Dic3—42no—
264C3×Dic3—41no—
265C3×Dic3—41no—
266C3×Dic3—124no—
267C3×Dic3—122no—
268C3×Dic3—122no—
269C4⋊Q8—91no—
270C4×D4—31no—
271#107—92no—
272C4⋊C8—31no—
273#102—92no—
274C33#47411yescharacteristic, complemented, Sylow
275C23×C3—62no—
276C23×C3—61no—
277C23×C3—61no—
278C22×D3—21no—
279C3×Q8—362no—
280C3×D4—32no—
281C3×D4—32no—
282C3×D4—62no—
283C3×D4—62no—
284C3×D4—61no—
285C3×D4—61no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—62no—
299C2×C3×C4—61no—
300C2×C3×C4—61no—
301C2×C3×C4—124no—
302C2×C3×C4—122no—
303C2×C3×C4—122no—
304C2×C3×C4—182no—
305C2×C3×C4#62611yescharacteristic
306C2×C3×C4#62611yescharacteristic
307C2×C3×C4C3×D1211yescharacteristic
308C2×C3×C4C3×D1211yescharacteristic
309C2×C3×C4C3×#6711yescharacteristic
310C2×C3×C4C3×#6711yescharacteristic
311C2×C3×C4C2×D3211yescharacteristic
312C2×C3×C4C22×C3×D311yescharacteristic
313C2×C3×C4C22×C3×D311yescharacteristic
314C2×Dic3—21no—
315C2×Dic3—64no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318D12—21no—
319D12C3×Dic612yescomplemented
320C4×D3—42no—
321Dic6—124no—
322Dic6—122no—
323Dic6—122no—
324C3×C8—62no—
325C3×C8—62no—
326C3×C8—122no—
327C3⋊C8—22no—
328C2×C32—21no—
329C2×C32—21no—
330C2×C32—21no—
331C2×C32—21no—
332C2×C32—21no—
333C2×C32—21no—
334C2×C32—21no—
335C2×C32—21no—
336C2×C32—21no—
337C2×C32—41no—
338C2×C32—41no—
339C2×C32—41no—
340C2×C32—122no—
341C2×C32#89711yescharacteristic
342C2×C32C2×D2411yescharacteristic
343C2×C32#90911yescharacteristic
344C2×C32#92411yescharacteristic
345C2×C32C2×#21311yescharacteristic
346C2×C32#95111yescharacteristic
347C2×C32C3×C22⋊Q811yescharacteristic
348C2×C32C2×C3×D811yescharacteristic
349C2×C32C3×#13711yescharacteristic
350C3×D3—44no—
351C3×D3—42no—
352C3×D3—42no—
353C2×Q8—181no—
354C2×D4—31no—
355C22×C4—61no—
356C2×C8—32no—
357C4⋊C4—31no—
358C4⋊C4—92no—
359C4⋊C4—181no—
360C22⋊C4—61no—
361C42C3×D3211yescharacteristic
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—41no—
366C22×C3—64no—
367C22×C3—62no—
368C22×C3—62no—
369C22×C3—122no—
370C22×C3—122no—
371C22×C3—121no—
372C22×C3—121no—
373C22×C3—121no—
374C22×C3—121no—
375C22×C3C2×#62611yescharacteristic
376C22×C3C2×C3×D1211yescharacteristic
377C22×C3C2×C3×#6711yescharacteristic
378C2×D3—22no—
379C2×D3—41no—
380C2×D3—41no—
381C3×C4—22no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—22no—
392C3×C4—22no—
393C3×C4—22no—
394C3×C4—41no—
395C3×C4—41no—
396C3×C4—42no—
397C3×C4—41no—
398C3×C4—41no—
399C3×C4—42no—
400C3×C4—122no—
401C3×C4—121no—
402C3×C4—121no—
403C3×C4—362no—
404C3×C4#371412yes—
405C3×C4C3×D2412yes—
406C3×C4C3×#21312yes—
407C3×C4D3×Dic611yescharacteristic
408C3×C4#379511yescharacteristic
409C3×C4C2×C3×Dic611yescharacteristic
410C3×C4C3×#23511yescharacteristic
411C3×C4C3×#23711yescharacteristic
412C3×C4C3×D3×Q811yescharacteristic
413Dic3—41no—
414Dic3—124no—
415Dic3—122no—
416Dic3—122no—
417C32—21no—
418C32—21no—
419C32—21no—
420C32—41no—
421C32#484611yescharacteristic, complemented
422C32#500711yescharacteristic, complemented
423C32C3×#47411yescharacteristic, complemented
424C23—61no—
425Q8—362no—
426D4—32no—
427D4—61no—
428C2×C4—61no—
429C2×C4—122no—
430C2×C4—182no—
431C2×C4C3×#62611yescharacteristic
432C2×C4C3×#62611yescharacteristic
433C2×C4C2×C3×D3211yescharacteristic
434C8—62no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—41no—
445C2×C3—41no—
446C2×C3—41no—
447C2×C3—124no—
448C2×C3—122no—
449C2×C3—122no—
450C2×C3C2×#371411yescharacteristic
451C2×C3#6383111yescharacteristic
452C2×C3#6385711yescharacteristic
453C2×C3C3×#89711yescharacteristic
454C2×C3C2×C3×D2411yescharacteristic
455C2×C3C3×#90911yescharacteristic
456C2×C3C3×#92411yescharacteristic
457C2×C3C2×C3×#21311yescharacteristic
458C2×C3C3×#95111yescharacteristic
459D3—42no—
460C22—62no—
461C22—121no—
462C22—121no—
463C22C2×C3×#62611yescharacteristic
464C4—21no—
465C4—121no—
466C4—362no—
467C4C3×#371412yes—
468C4C3×D3×Dic611yescharacteristic
469C4C3×#379511yescharacteristic
470C3—21no—
471C3—21no—
472C3—21no—
473C3—41no—
474C3#1059027211yescharacteristic, direct product factor
475C3C3×#484611yescharacteristic, complemented
476C3C3×#500711yescharacteristic, complemented
477C2—122no—
478C2C2×C3×#371411yescharacteristic
479C2C3×#6383111yescharacteristic
480C2C3×#6385711yescharacteristic
subgroupG/H
centerC22×C3C2×#626
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC33×C42C22
socleC22×C33C2×D4
prime radicalC2×C32×D12C22
hypercenterC3×C42D32
hypocenterC32C3×#474
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C42

Complements

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

NH ≅ G/Ntype
1. C3×#64078C2semidirect
3. C32×C4⋊(C3⋊C8)C2semidirect
4. C3×#63575C2semidirect
8. #10590272C3direct (N × H)
19. #64078C2×C3semidirect
32. C3×C4⋊(C3⋊C8)D3semidirect
33. C3×C4⋊(C3⋊C8)C2×C3semidirect
34. #63575C2×C3semidirect
44. C32×D12Q8semidirect
116. C4⋊(C3⋊C8)C3×D3semidirect
158. C3×D12Dic6semidirect
159. C3×D12C3×Q8semidirect
274. C33#474semidirect
319. D12C3×Dic6semidirect
421. C32#4846semidirect
422. C32#5007semidirect
423. C32C3×#474semidirect
474. C3#10590272direct (N × H)
475. C3C3×#4846semidirect
476. C3C3×#5007semidirect

Maximal subgroups

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

subgroupindex
C3×#640782
C32×C4×D122
C32×C4⋊(C3⋊C8)2
C3×#635752
C3×#635632
C3×#50073
C3×#48463
#105902723