Finite Group Databasebeta

← C3×#10591214 #13158298

Subgroups — C3×#10591214 #13158298

Order 1728.

914 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4⋊Dic3C211yesmaximal, characteristic
2C2×C32×Dic3⋊C4C211yesmaximal, characteristic
3C2×C3×#3724C212yesmaximal
4C3×#63658C211yesmaximal, characteristic
5C3×#63579C212yesmaximal
6C3×#4983—31nomaximal
7C3×#4981—31nomaximal
8#10591214C311yesmaximal, characteristic, direct product factor
9C22×C33×C4C2211yescharacteristic
10C22×C3×C3⋊Dic3C2212yes—
11C22×C32×Dic3C2211yescharacteristic
12C22×C32×Dic3C2212yes—
13C22×C32×Dic3C2211yescharacteristic
14C32×C4⋊Dic3—22no—
15C32×Dic3⋊C4—22no—
16C3×#3724—24no—
17C2×C32×C4⋊C4—31no—
18C2×C32×C4⋊C4—31no—
19C2×C3×C4⋊Dic3—21no—
20C2×C3×C4⋊Dic3D311yescharacteristic
21C2×C3×C4⋊Dic3C2×C311yescharacteristic
22C2×C3×Dic3⋊C4—21no—
23C2×C3×Dic3⋊C4—32no—
24C2×C3×Dic3⋊C4—32no—
25C2×C3×Dic3⋊C4D311yescharacteristic
26C2×C3×Dic3⋊C4C2×C311yescharacteristic
27C2×#3724C2×C312yes—
28#63658C2×C311yescharacteristic
29C3×C3⋊#95—31no—
30C3×C3⋊#95—31no—
31C3×C3⋊#95—32no—
32C3×C3⋊#95—32no—
33C3×C3⋊#95—61no—
34#63579C2×C312yes—
35C23×C33C2311yescharacteristic
36C2×C33×C4—22no—
37C2×C33×C4D412yes—
38C2×C3×C3⋊Dic3—22no—
39C2×C3×C3⋊Dic3—22no—
40C2×C3×C3⋊Dic3Q814yes—
41C2×C32×Dic3—21no—
42C2×C32×Dic3—21no—
43C2×C32×Dic3—21no—
44C2×C32×Dic3—22no—
45C2×C32×Dic3—22no—
46C2×C32×Dic3—22no—
47C2×C32×Dic3—22no—
48C2×C32×Dic3D412yes—
49C3×#398—91no—
50#4983—31no—
51#4981—31no—
52C22×C32×C4—21no—
53C22×C32×C4—21no—
54C22×C32×C4—21no—
55C22×C32×C4—31no—
56C22×C32×C4—32no—
57C22×C32×C4—31no—
58C22×C32×C4—41no—
59C22×C32×C4C2×D311yescharacteristic
60C22×C32×C4C2×D311yescharacteristic
61C22×C32×C4C22×C311yescharacteristic
62C22×C3⋊Dic3C22×C312yes—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65C22×C3×Dic3—22no—
66C22×C3×Dic3—32no—
67C22×C3×Dic3—32no—
68C22×C3×Dic3—62no—
69C22×C3×Dic3C2×D312yes—
70C22×C3×Dic3C2×D311yescharacteristic
71C22×C3×Dic3C2×D311yescharacteristic
72C22×C3×Dic3C22×C311yescharacteristic
73C22×C3×Dic3C22×C312yes—
74C22×C3×Dic3C22×C311yescharacteristic
75C32×C4⋊C4—62no—
76C32×C4⋊C4—62no—
77C3×C4⋊Dic3—24no—
78C3×C4⋊Dic3—22no—
79C3×C4⋊Dic3—22no—
80C3×Dic3⋊C4—24no—
81C3×Dic3⋊C4—22no—
82C3×Dic3⋊C4—22no—
83C3×Dic3⋊C4—64no—
84C3×Dic3⋊C4—64no—
85#3724—24no—
86C22×C33C2×D411yescharacteristic
87C22×C33C2×D411yescharacteristic
88C22×C33C2×Q812yes—
89C22×C33#4111yescharacteristic
90C22×C33#4112yes—
91C33×C4—22no—
92C3×C3⋊Dic3—24no—
93C32×Dic3—22no—
94C32×Dic3—42no—
95C32×Dic3—41no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C4⋊C4—61no—
101C2×C3×C4⋊C4—61no—
102C2×C3×C4⋊C4—92no—
103C2×C4⋊Dic3C3×D311yescharacteristic
104C2×Dic3⋊C4—32no—
105C2×Dic3⋊C4—32no—
106C2×Dic3⋊C4C3×D311yescharacteristic
107C3×#95—92no—
108C3×#95—91no—
109C3⋊#95—31no—
110C3⋊#95—31no—
111C3⋊#95—32no—
112C3⋊#95—32no—
113C3⋊#95—61no—
114C23×C32—21no—
115C23×C32—21no—
116C23×C32—21no—
117C23×C32—41no—
118C23×C32C22×D311yescharacteristic
119C23×C32C22×D311yescharacteristic
120C23×C32C23×C311yescharacteristic
121C2×C32×C4—22no—
122C2×C32×C4—24no—
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4—22no—
127C2×C32×C4—22no—
128C2×C32×C4—32no—
129C2×C32×C4—42no—
130C2×C32×C4—42no—
131C2×C32×C4—42no—
132C2×C32×C4—44no—
133C2×C32×C4—61no—
134C2×C32×C4—61no—
135C2×C32×C4—61no—
136C2×C32×C4—62no—
137C2×C32×C4—62no—
138C2×C32×C4—62no—
139C2×C32×C4—62no—
140C2×C32×C4#6712yes—
141C2×C32×C4#6712yes—
142C2×C32×C4C3×D412yes—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3C3×Q814yes—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—24no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—21no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—21no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—34no—
166C2×C3×Dic3—34no—
167C2×C3×Dic3—42no—
168C2×C3×Dic3—42no—
169C2×C3×Dic3—42no—
170C2×C3×Dic3—64no—
171C2×C3×Dic3—62no—
172C2×C3×Dic3—62no—
173C2×C3×Dic3—62no—
174C2×C3×Dic3—62no—
175C2×C3×Dic3—122no—
176C2×C3×Dic3—122no—
177C2×C3×Dic3D1212yes—
178C2×C3×Dic3C3×D412yes—
179#398—91noSylow
180C2×C33#12111yescharacteristic
181C2×C33C22⋊Q812yes—
182C2×C33#12311yescharacteristic
183C2×C33#12512yes—
184C2×C33C4⋊Q811yescharacteristic
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—31no—
189C22×C3×C4—31no—
190C22×C3×C4—31no—
191C22×C3×C4—32no—
192C22×C3×C4—31no—
193C22×C3×C4—32no—
194C22×C3×C4—41no—
195C22×C3×C4—61no—
196C22×C3×C4—61no—
197C22×C3×C4—62no—
198C22×C3×C4—92no—
199C22×C3×C4D3211yescharacteristic
200C22×C3×C4C2×C3×D311yescharacteristic
201C22×C3×C4C2×C3×D311yescharacteristic
202C22×Dic3—32no—
203C22×Dic3—32no—
204C22×Dic3—62no—
205C22×Dic3C2×C3×D311yescharacteristic
206C22×Dic3C2×C3×D312yes—
207C22×Dic3C2×C3×D311yescharacteristic
208C3×C4⋊C4—64no—
209C3×C4⋊C4—64no—
210C3×C4⋊C4—62no—
211C3×C4⋊C4—62no—
212C3×C4⋊C4—62no—
213C3×C4⋊C4—62no—
214C3×C4⋊C4—184no—
215C4⋊Dic3—22no—
216Dic3⋊C4—22no—
217Dic3⋊C4—64no—
218Dic3⋊C4—64no—
219C22×C32—21no—
220C22×C32—22no—
221C22×C32—21no—
222C22×C32—22no—
223C22×C32—21no—
224C22×C32—21no—
225C22×C32—21no—
226C22×C32—22no—
227C22×C32—21no—
228C22×C32—21no—
229C22×C32—22no—
230C22×C32—22no—
231C22×C32—22no—
232C22×C32—21no—
233C22×C32—21no—
234C22×C32—41no—
235C22×C32—41no—
236C22×C32—42no—
237C22×C32—42no—
238C22×C32—41no—
239C22×C32C2×D1211yescharacteristic
240C22×C32#23511yescharacteristic
241C22×C32#23512yes—
242C22×C32D3×D411yescharacteristic
243C22×C32#23711yescharacteristic
244C22×C32#23712yes—
245C22×C32D3×Q812yes—
246C22×C32D3×Q812yes—
247C22×C32C2×#6711yescharacteristic
248C22×C32C2×#6711yescharacteristic
249C22×C32C2×C3×D411yescharacteristic
250C22×C32C2×C3×D411yescharacteristic
251C22×C32C2×C3×Q812yes—
252C22×C32C3×#4111yescharacteristic
253C22×C32C3×#4112yes—
254C32×C4—22no—
255C32×C4—24no—
256C32×C4—22no—
257C32×C4—22no—
258C32×C4—42no—
259C32×C4—42no—
260C32×C4—44no—
261C32×C4—62no—
262C32×C4—121no—
263C32×C4—122no—
264C3⋊Dic3—24no—
265C3×Dic3—24no—
266C3×Dic3—22no—
267C3×Dic3—22no—
268C3×Dic3—42no—
269C3×Dic3—44no—
270C3×Dic3—41no—
271C3×Dic3—42no—
272C3×Dic3—42no—
273C3×Dic3—41no—
274C3×Dic3—64no—
275C3×Dic3—64no—
276C3×Dic3—124no—
277C2×C4⋊C4—31no—
278C2×C4⋊C4—31no—
279C2×C4⋊C4—92no—
280#95—92no—
281#95—91no—
282C33#39811yescharacteristic, complemented, Sylow
283C23×C3—21no—
284C23×C3—21no—
285C23×C3—21no—
286C23×C3—41no—
287C23×C3C2×D3211yescharacteristic
288C23×C3C22×C3×D311yescharacteristic
289C23×C3C22×C3×D311yescharacteristic
290C2×C3×C4—24no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—32no—
298C2×C3×C4—32no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—44no—
302C2×C3×C4—42no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4—61no—
307C2×C3×C4—61no—
308C2×C3×C4—61no—
309C2×C3×C4—61no—
310C2×C3×C4—62no—
311C2×C3×C4—64no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—61no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—61no—
321C2×C3×C4—62no—
322C2×C3×C4—94no—
323C2×C3×C4—122no—
324C2×C3×C4—122no—
325C2×C3×C4—122no—
326C2×C3×C4—182no—
327C2×C3×C4—182no—
328C2×C3×C4#62512yes—
329C2×C3×C4C3×#6712yes—
330C2×C3×C4C3×#6712yes—
331C2×Dic3—21no—
332C2×Dic3—21no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—21no—
337C2×Dic3—22no—
338C2×Dic3—34no—
339C2×Dic3—34no—
340C2×Dic3—64no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C2×Dic3—62no—
344C2×Dic3—62no—
345C2×Dic3—122no—
346C2×Dic3—122no—
347C2×Dic3C3×D1212yes—
348C2×C32—22no—
349C2×C32—22no—
350C2×C32—22no—
351C2×C32—22no—
352C2×C32—21no—
353C2×C32—21no—
354C2×C32—21no—
355C2×C32—21no—
356C2×C32—21no—
357C2×C32—21no—
358C2×C32—22no—
359C2×C32—21no—
360C2×C32—22no—
361C2×C32—21no—
362C2×C32—21no—
363C2×C32—41no—
364C2×C32—42no—
365C2×C32—41no—
366C2×C32—42no—
367C2×C32—41no—
368C2×C32#88912yes—
369C2×C32#88912yes—
370C2×C32#89612yes—
371C2×C32#89712yes—
372C2×C32#92911yescharacteristic
373C2×C32#93011yescharacteristic
374C2×C32#93511yescharacteristic
375C2×C32#93811yescharacteristic
376C2×C32#94411yescharacteristic
377C2×C32#94411yescharacteristic
378C2×C32C3×#12111yescharacteristic
379C2×C32C3×C22⋊Q812yes—
380C2×C32C3×#12311yescharacteristic
381C2×C32C3×#12512yes—
382C2×C32C3×C4⋊Q811yescharacteristic
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—32no—
386C22×C4—92no—
387C22×C4C3×D3211yescharacteristic
388C4⋊C4—62no—
389C4⋊C4—62no—
390C4⋊C4—184no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—22no—
395C22×C3—22no—
396C22×C3—22no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—22no—
401C22×C3—22no—
402C22×C3—22no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—41no—
407C22×C3—42no—
408C22×C3—41no—
409C22×C3—42no—
410C22×C3—41no—
411C22×C3#379511yescharacteristic
412C22×C3#379712yes—
413C22×C3D3×D1211yescharacteristic
414C22×C3#380412yes—
415C22×C3C2×#62511yescharacteristic
416C22×C3C2×C3×D1211yescharacteristic
417C22×C3C3×#23511yescharacteristic
418C22×C3C3×#23512yes—
419C22×C3C3×D3×D411yescharacteristic
420C22×C3C3×#23711yescharacteristic
421C22×C3C3×#23712yes—
422C22×C3C3×D3×Q812yes—
423C22×C3C3×D3×Q812yes—
424C22×C3C2×C3×#6711yescharacteristic
425C22×C3C2×C3×#6711yescharacteristic
426C3×C4—24no—
427C3×C4—22no—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—42no—
431C3×C4—42no—
432C3×C4—44no—
433C3×C4—64no—
434C3×C4—62no—
435C3×C4—62no—
436C3×C4—122no—
437C3×C4—124no—
438C3×C4—121no—
439C3×C4—122no—
440C3×C4—122no—
441C3×C4—121no—
442C3×C4—184no—
443Dic3—22no—
444Dic3—41no—
445Dic3—42no—
446Dic3—64no—
447Dic3—64no—
448Dic3—124no—
449C32—21no—
450C32—21no—
451C32—21no—
452C32—41no—
453C32#498111yescharacteristic, complemented
454C32#498311yescharacteristic, complemented
455C32C3×#39811yescharacteristic, complemented
456C23C2×C3×D3211yescharacteristic
457C2×C4—22no—
458C2×C4—32no—
459C2×C4—61no—
460C2×C4—61no—
461C2×C4—62no—
462C2×C4—62no—
463C2×C4—62no—
464C2×C4—61no—
465C2×C4—62no—
466C2×C4—94no—
467C2×C4—182no—
468C2×C4—182no—
469C2×C4C3×#62512yes—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—22no—
474C2×C3—22no—
475C2×C3—22no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—22no—
480C2×C3—22no—
481C2×C3—22no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—41no—
486C2×C3—42no—
487C2×C3—41no—
488C2×C3—42no—
489C2×C3—41no—
490C2×C3#6384712yes—
491C2×C3#6387311yescharacteristic
492C2×C3#6389512yes—
493C2×C3#6390811yescharacteristic
494C2×C3#6396111yescharacteristic
495C2×C3C3×#88912yes—
496C2×C3C3×#88912yes—
497C2×C3C3×#89612yes—
498C2×C3C3×#89712yes—
499C2×C3C3×#92911yescharacteristic
500C2×C3C3×#93011yescharacteristic
501C2×C3C3×#93511yescharacteristic
502C2×C3C3×#93811yescharacteristic
503C2×C3C3×#94411yescharacteristic
504C2×C3C3×#94411yescharacteristic
505C22C3×#379511yescharacteristic
506C22C3×#379712yes—
507C22C3×D3×D1211yescharacteristic
508C22C3×#380412yes—
509C22C2×C3×#62511yescharacteristic
510C4—22no—
511C4—62no—
512C4—121no—
513C4—122no—
514C4—184no—
515C3—21no—
516C3—21no—
517C3—21no—
518C3—41no—
519C3#1059121411yescharacteristic, direct product factor
520C3C3×#498111yescharacteristic, complemented
521C3C3×#498311yescharacteristic, complemented
522C2C3×#6384712yes—
523C2C3×#6387311yescharacteristic
524C2C3×#6389512yes—
525C2C3×#6390811yescharacteristic
526C2C3×#6396111yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC23×C32C23×C3
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socle, prime radicalC23×C33C23
hypercenterC22×C3×C4D32
hypocenterC32C3×#398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
8. #10591214C3direct (N × H)
282. C33#398semidirect
453. C32#4981semidirect
454. C32#4983semidirect
455. C32C3×#398semidirect
519. C3#10591214direct (N × H)
520. C3C3×#4981semidirect
521. C3C3×#4983semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4⋊Dic32
C2×C32×Dic3⋊C42
C2×C3×#37242
C3×#636582
C3×#635792
C3×#49833
C3×#49813
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