Finite Group Databasebeta

← C3×#73392 #11805293

Subgroups — C3×#73392 #11805293

Order 1152.

1097 conjugacy classes of subgroups.

The subgroup lattice has 535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#872C211yesmaximal, characteristic
2C32×#376C211yesmaximal, characteristic, complemented
3C3×#4940C212yesmaximal
4C3×#4936C211yesmaximal, characteristic, complemented
5C3×C4×Dic3⋊C4C212yesmaximal, complemented
6C3×#4670C212yesmaximal
7C3×#4667C211yesmaximal, characteristic
8C3×#4666C211yesmaximal, characteristic
9C3×#4650C211yesmaximal, characteristic, complemented
10C3×#4648C211yesmaximal, characteristic, complemented
11C3×#4647C212yesmaximal, complemented
12C3×#2346—31nomaximal
13#73392C311yesmaximal, characteristic, direct product factor
14C22×C3×C4×D3C2211yescharacteristic
15C2×C32×C42C2212yes—
16C2×C32×C42C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4C2212yes—
18C2×C3×(C2×D3)⋊C4C2212yes—
19C2×C3×(C2×D3)⋊C4C2211yescharacteristic
20C2×C3×(C2×D3)⋊C4C2211yescharacteristic
21C2×C3×C4⋊Dic3C2212yes—
22C2×C3×Dic3⋊C4C2212yes—
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×C4×Dic3C2212yes—
27C2×C3×C4×Dic3C2212yes—
28C2×C3×C4×Dic3C2211yescharacteristic
29C3×#872C418yescomplemented
30C32×#95C2212yes—
31C32×#95C2211yescharacteristic
32C32×#95C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C2×C3×#117—31no—
39C2×#872C2×C311yescharacteristic
40C3×#389—32no—
41C3×#388—32no—
42C3×#388—32no—
43C3×#382—31no—
44C3×#382—31no—
45C3×#380—31no—
46C3×C4×C4⋊C4—32no—
47C3×C4×C22⋊C4—31no—
48C3×#376—21no—
49C3×#376—31no—
50C3×#376D311yescharacteristic, complemented
51C3×#376C2×C311yescharacteristic, complemented
52#4940C2×C312yes—
53#4936C2×C311yescharacteristic, complemented
54C4×Dic3⋊C4C2×C312yescomplemented
55#4670C2×C312yes—
56#4667C2×C311yescharacteristic
57#4666C2×C311yescharacteristic
58#4650C2×C311yescharacteristic, complemented
59#4648C2×C311yescharacteristic, complemented
60#4647C2×C312yescomplemented
61C23×C3×D3C2311yescharacteristic
62C22×C32×C4C2312yes—
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2312yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C2×C3×C4×D3—24no—
73C2×C3×C4×D3C2×C414yes—
74C32×C42—24no—
75C32×C42C2×C414yes—
76C3×(C2×D3)⋊C4—24no—
77C3×(C2×D3)⋊C4—42no—
78C3×(C2×D3)⋊C4C2×C414yes—
79C3×(C2×D3)⋊C4C2×C414yes—
80C3×C4⋊Dic3—42no—
81C3×Dic3⋊C4—24no—
82C3×Dic3⋊C4—42no—
83C3×Dic3⋊C4C2×C414yes—
84C3×Dic3⋊C4C2×C414yes—
85C3×C4×Dic3—24no—
86C3×C4×Dic3—24no—
87C3×C4×Dic3C2×C414yes—
88#2346—31noSylow
89C23×C3×C4—31no—
90C22×C4×D3C22×C311yescharacteristic
91C3×#117—38no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4—32no—
95C2×C3×C4⋊C4—32no—
96C2×C3×C4⋊C4—32no—
97C2×C3×C22⋊C4—31no—
98C2×C3×C22⋊C4—31no—
99C2×C3×C22⋊C4—32no—
100C2×C3×C22⋊C4—32no—
101C2×C3×C42—22no—
102C2×C3×C42—21no—
103C2×C3×C42—31no—
104C2×C3×C42—32no—
105C2×C3×C42—32no—
106C2×C3×C42C2×D312yes—
107C2×C3×C42C2×D311yescharacteristic
108C2×C3×C42C22×C312yes—
109C2×C3×C42C22×C311yescharacteristic
110C2×(C2×D3)⋊C4C22×C312yes—
111C2×(C2×D3)⋊C4C22×C312yes—
112C2×(C2×D3)⋊C4C22×C311yescharacteristic
113C2×(C2×D3)⋊C4C22×C311yescharacteristic
114C2×C4⋊Dic3C22×C312yes—
115C2×Dic3⋊C4C22×C312yes—
116C2×Dic3⋊C4C22×C312yes—
117C2×Dic3⋊C4C22×C311yescharacteristic
118C2×Dic3⋊C4C22×C311yescharacteristic
119C2×C4×Dic3C22×C312yes—
120C2×C4×Dic3C22×C312yes—
121C2×C4×Dic3C22×C311yescharacteristic
122#872C3×C418yescomplemented
123C3×#95—21no—
124C3×#95—21no—
125C3×#95—22no—
126C3×#95—31no—
127C3×#95—32no—
128C3×#95—31no—
129C3×#95—32no—
130C3×#95—32no—
131C3×#95C2×D311yescharacteristic
132C3×#95C2×D311yescharacteristic
133C3×#95C2×D312yes—
134C3×#95C22×C312yes—
135C3×#95C22×C311yescharacteristic
136C3×#95C22×C311yescharacteristic
137C3⋊#95C22×C312yes—
138C3⋊#95C22×C311yescharacteristic
139C3⋊#95C22×C311yescharacteristic
140C3⋊#95C22×C312yes—
141C3⋊#95C22×C312yes—
142C23×C32C2411yescharacteristic
143C22×C3×D3—22no—
144C22×C3×D3—22no—
145C22×C3×D3—21no—
146C22×C3×D3—21no—
147C22×C3×D3C22×C412yes—
148C2×C32×C4—22no—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4—21no—
153C2×C32×C4—21no—
154C2×C32×C4—22no—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4C22×C412yes—
158C2×C32×C4C22×C412yes—
159C2×C32×C4C22×C412yes—
160C2×C32×C4#4114yes—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3C22×C412yes—
171C2×C3×Dic3C22×C412yes—
172C2×C3×Dic3C22×C412yes—
173C2×C3×Dic3#4114yes—
174C3×C4×D3—28no—
175C2×#117—31no—
176#389—32no—
177#388—32no—
178#388—32no—
179#382—31no—
180#382—31no—
181#380—31no—
182C4×C4⋊C4—32no—
183C4×C22⋊C4—31no—
184#376—31no—
185#376C3×D311yescharacteristic, complemented
186C24×C3—31no—
187C23×D3C23×C311yescharacteristic
188C22×C3×C4—21no—
189C22×C3×C4—22no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—22no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—31no—
196C22×C3×C4—34no—
197C22×C3×C4—32no—
198C22×C3×C4—32no—
199C22×C3×C4—64no—
200C22×C3×C4C22×D312yes—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D312yes—
205C22×C3×C4C23×C312yes—
206C22×C3×C4C23×C311yescharacteristic
207C22×C3×C4C23×C311yescharacteristic
208C22×C3×C4C23×C311yescharacteristic
209C22×C3×C4C23×C312yes—
210C22×Dic3C23×C312yes—
211C22×Dic3C23×C312yes—
212C22×Dic3C23×C311yescharacteristic
213C22×Dic3C23×C311yescharacteristic
214C22×Dic3C23×C311yescharacteristic
215C2×C4×D3—24no—
216C2×C4×D3C2×C3×C414yes—
217C3×C4⋊C4—34no—
218C3×C4⋊C4—34no—
219C3×C4⋊C4—64no—
220C3×C4⋊C4—122no—
221C3×C4⋊C4—122no—
222C3×C22⋊C4—34no—
223C3×C22⋊C4—34no—
224C3×C22⋊C4—64no—
225C3×C22⋊C4—122no—
226C3×C42—28no—
227C3×C42—24no—
228C3×C42—24no—
229C3×C42—24no—
230C3×C42—34no—
231C3×C42—64no—
232C3×C42—64no—
233C3×C42C4×D314yes—
234C3×C42C2×C3×C414yes—
235(C2×D3)⋊C4—24no—
236(C2×D3)⋊C4—42no—
237(C2×D3)⋊C4C2×C3×C414yes—
238(C2×D3)⋊C4C2×C3×C414yes—
239C4⋊Dic3—42no—
240Dic3⋊C4—24no—
241Dic3⋊C4—42no—
242Dic3⋊C4C2×C3×C414yes—
243Dic3⋊C4C2×C3×C414yes—
244C4×Dic3—24no—
245C4×Dic3—24no—
246C4×Dic3C2×C3×C414yes—
247C22×C32C23×C411yescharacteristic
248C22×C32C2×#4112yes—
249C22×C32C2×#4112yes—
250C22×C32H(5,𝔽2)11yescharacteristic
251C22×C322−1+411yescharacteristic
252C2×C3×D3—22no—
253C2×C3×D3—22no—
254C2×C3×D3—22no—
255C2×C3×D3—42no—
256C2×C3×D3—42no—
257C32×C4—22no—
258C32×C4—22no—
259C32×C4—22no—
260C32×C4—24no—
261C32×C4—42no—
262C3×Dic3—22no—
263C3×Dic3—22no—
264C3×Dic3—42no—
265C3×Dic3—42no—
266C3×Dic3#11714yes—
267C23×C4—31no—
268#117—38no—
269C2×C4⋊C4—31no—
270C2×C4⋊C4—31no—
271C2×C4⋊C4—32no—
272C2×C4⋊C4—32no—
273C2×C4⋊C4—32no—
274C2×C22⋊C4—31no—
275C2×C22⋊C4—31no—
276C2×C22⋊C4—32no—
277C2×C22⋊C4—32no—
278C2×C42—31no—
279C2×C42—32no—
280C2×C42—32no—
281C2×C42C2×C3×D312yes—
282C2×C42C2×C3×D311yescharacteristic
283#95—31no—
284#95—32no—
285#95—31no—
286#95—32no—
287#95—32no—
288#95C2×C3×D311yescharacteristic
289#95C2×C3×D311yescharacteristic
290#95C2×C3×D312yes—
291C23×C3—21no—
292C23×C3—32no—
293C23×C3—62no—
294C23×C3—62no—
295C23×C3—61no—
296C23×C3—61no—
297C23×C3C23×D311yescharacteristic
298C23×C3C24×C311yescharacteristic
299C22×D3—22no—
300C22×D3—22no—
301C22×D3—21no—
302C22×D3—21no—
303C22×D3C22×C3×C412yes—
304C2×C3×C4—24no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—22no—
317C2×C3×C4—24no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—24no—
328C2×C3×C4—32no—
329C2×C3×C4—34no—
330C2×C3×C4—32no—
331C2×C3×C4—32no—
332C2×C3×C4—42no—
333C2×C3×C4—42no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—42no—
337C2×C3×C4—42no—
338C2×C3×C4—42no—
339C2×C3×C4—68no—
340C2×C3×C4—62no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4C2×C4×D312yes—
350C2×C3×C4C2×C4×D312yes—
351C2×C3×C4C2×C4×D312yes—
352C2×C3×C4#23514yes—
353C2×C3×C4C22×C3×C412yes—
354C2×C3×C4C22×C3×C412yes—
355C2×C3×C4C22×C3×C412yes—
356C2×C3×C4C3×#4114yes—
357C2×Dic3—22no—
358C2×Dic3—21no—
359C2×Dic3—21no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3C22×C3×C412yes—
367C2×Dic3C22×C3×C412yes—
368C2×Dic3C22×C3×C412yes—
369C2×Dic3C3×#4114yes—
370C4×D3—28no—
371C2×C32C2×#11711yescharacteristic
372C2×C32C4×#4111yescharacteristic
373C2×C32#52011yescharacteristic
374C2×C32#55212yes—
375C2×C32#55512yes—
376C3×D3—42no—
377C24—31no—
378C22×C4—31no—
379C22×C4—31no—
380C22×C4—31no—
381C22×C4—34no—
382C22×C4—32no—
383C22×C4—32no—
384C22×C4—64no—
385C22×C4C22×C3×D312yes—
386C22×C4C22×C3×D311yescharacteristic
387C22×C4C22×C3×D311yescharacteristic
388C22×C4C22×C3×D311yescharacteristic
389C22×C4C22×C3×D312yes—
390C4⋊C4—34no—
391C4⋊C4—34no—
392C4⋊C4—64no—
393C4⋊C4—122no—
394C4⋊C4—122no—
395C22⋊C4—34no—
396C22⋊C4—34no—
397C22⋊C4—64no—
398C22⋊C4—122no—
399C42—24no—
400C42—34no—
401C42—64no—
402C42—64no—
403C42C3×C4×D314yes—
404C22×C3—21no—
405C22×C3—22no—
406C22×C3—22no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—62no—
410C22×C3—62no—
411C22×C3—62no—
412C22×C3—122no—
413C22×C3—122no—
414C22×C3C22×C4×D311yescharacteristic
415C22×C3C2×#23512yes—
416C22×C3D3×#4112yes—
417C22×C3#100911yescharacteristic
418C22×C3#101011yescharacteristic
419C22×C3C23×C3×C411yescharacteristic
420C22×C3C2×C3×#4112yes—
421C22×C3C2×C3×#4112yes—
422C22×C3C3×H(5,𝔽2)11yescharacteristic
423C22×C3C3×2−1+411yescharacteristic
424C2×D3—22no—
425C2×D3—22no—
426C2×D3—22no—
427C2×D3—42no—
428C2×D3—42no—
429C3×C4—24no—
430C3×C4—22no—
431C3×C4—22no—
432C3×C4—22no—
433C3×C4—24no—
434C3×C4—22no—
435C3×C4—22no—
436C3×C4—22no—
437C3×C4—24no—
438C3×C4—34no—
439C3×C4—42no—
440C3×C4—42no—
441C3×C4—44no—
442C3×C4—44no—
443C3×C4—42no—
444C3×C4—42no—
445C3×C4—62no—
446C3×C4—62no—
447C3×C4—122no—
448C3×C4—122no—
449Dic3—22no—
450Dic3—22no—
451Dic3—42no—
452Dic3—42no—
453Dic3C3×#11714yes—
454C32#234611yescharacteristic, complemented, Sylow
455C23—32no—
456C23—62no—
457C23—62no—
458C23—61no—
459C23—61no—
460C23C23×C3×D311yescharacteristic
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—32no—
471C2×C4—34no—
472C2×C4—32no—
473C2×C4—32no—
474C2×C4—68no—
475C2×C4—62no—
476C2×C4—61no—
477C2×C4—61no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4C2×C3×C4×D312yes—
485C2×C4C2×C3×C4×D312yes—
486C2×C4C2×C3×C4×D312yes—
487C2×C4C3×#23514yes—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—22no—
491C2×C3—22no—
492C2×C3—21no—
493C2×C3—122no—
494C2×C3C4×#23511yescharacteristic
495C2×C3D3×#11711yescharacteristic
496C2×C3#552311yescharacteristic
497C2×C3#553112yes—
498C2×C3#553212yes—
499C2×C3C2×C3×#11711yescharacteristic
500C2×C3C3×C4×#4111yescharacteristic
501C2×C3C3×#52011yescharacteristic
502C2×C3C3×#55212yes—
503C2×C3C3×#55512yes—
504D3—42no—
505C22—62no—
506C22—62no—
507C22—62no—
508C22—122no—
509C22—122no—
510C22C22×C3×C4×D311yescharacteristic
511C22C2×C3×#23512yes—
512C22C3×D3×#4112yes—
513C22C3×#100911yescharacteristic
514C22C3×#101011yescharacteristic
515C4—22no—
516C4—22no—
517C4—24no—
518C4—22no—
519C4—34no—
520C4—42no—
521C4—62no—
522C4—62no—
523C4—122no—
524C4—122no—
525C3—21no—
526C3#7339211yescharacteristic, direct product factor
527C3C3×#234611yescharacteristic, complemented
528C2—122no—
529C2C3×C4×#23511yescharacteristic
530C2C3×D3×#11711yescharacteristic
531C2C3×#552311yescharacteristic
532C2C3×#553112yes—
533C2C3×#553212yes—
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#376C2
socleC23×C32C24
prime radicalC23×C3×D3C23
cosocleC23×C3C24×C3
hypercenterC3×#376D3
hypocenterC3C3×#2346
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#376

Complements

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

NH ≅ G/Ntype
2. C32×#376C2semidirect
4. C3×#4936C2semidirect
5. C3×C4×Dic3⋊C4C2semidirect
9. C3×#4650C2semidirect
10. C3×#4648C2semidirect
11. C3×#4647C2semidirect
13. #73392C3direct (N × H)
29. C3×#872C4semidirect
50. C3×#376D3semidirect
51. C3×#376C2×C3semidirect
53. #4936C2×C3semidirect
54. C4×Dic3⋊C4C2×C3semidirect
58. #4650C2×C3semidirect
59. #4648C2×C3semidirect
60. #4647C2×C3semidirect
122. #872C3×C4semidirect
185. #376C3×D3semidirect
454. C32#2346semidirect
526. C3#73392direct (N × H)
527. C3C3×#2346semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8722
C32×#3762
C3×#49402
C3×#49362
C3×C4×Dic3⋊C42
C3×#46702
C3×#46672
C3×#46662
C3×#46502
C3×#46482
C3×#46472
C3×#23463
#733923