Finite Group Databasebeta

← C3×#73416 #11805066

Subgroups — C3×#73416 #11805066

Order 1152.

1153 conjugacy classes of subgroups.

The subgroup lattice has 539 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×C4×(C2×D3)⋊C4C212yesmaximal
4C3×#4936C211yesmaximal, characteristic, complemented
5C3×#4933C212yesmaximal, complemented
6C3×#4668C212yesmaximal
7C3×#4664C211yesmaximal, characteristic
8C3×D3×#95C211yesmaximal, characteristic
9C3×#4655C212yesmaximal, complemented
10C3×#4651C211yesmaximal, characteristic, complemented
11C3×#4649C211yesmaximal, characteristic, complemented
12C3×#2343—31nomaximal
13#73416C311yesmaximal, characteristic, direct product factor
14C22×C3×C4×D3C2212yes—
15C22×C3×C4×D3C2211yescharacteristic
16C2×C32×C42C2212yes—
17C2×C32×C42C2211yescharacteristic
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⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×C4×Dic3C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C3×#872C418yescomplemented
28C32×#95C2211yescharacteristic
29C32×#95C2211yescharacteristic
30C32×#95C2212yes—
31C3×C3⋊#95C2211yescharacteristic
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C2×C3×#117—31no—
39C2×#872C2×C311yescharacteristic
40C3×#387—32no—
41C3×#387—32no—
42C3×#385—32no—
43C3×#383—31no—
44C3×#382—31no—
45C3×#381—31no—
46C3×C4×C4⋊C4—31no—
47C3×C4×C22⋊C4—32no—
48C3×#376—21no—
49C3×#376D311yescharacteristic, complemented
50C3×#376C2×C311yescharacteristic, complemented
51C2×C3×#95—31no—
52C4×(C2×D3)⋊C4C2×C312yes—
53#4936C2×C311yescharacteristic, complemented
54#4933C2×C312yescomplemented
55#4668C2×C312yes—
56#4664C2×C311yescharacteristic
57D3×#95C2×C311yescharacteristic
58#4655C2×C312yescomplemented
59#4651C2×C311yescharacteristic, complemented
60#4649C2×C311yescharacteristic, complemented
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×D3—24no—
74C2×C3×C4×D3—24no—
75C2×C3×C4×D3—42no—
76C2×C3×C4×D3C2×C414yes—
77C32×C42—24no—
78C32×C42C2×C414yescomplemented
79C3×(C2×D3)⋊C4—24no—
80C3×(C2×D3)⋊C4C2×C414yes—
81C3×(C2×D3)⋊C4C2×C414yes—
82C3×C4⋊Dic3—42no—
83C3×Dic3⋊C4—24no—
84C3×Dic3⋊C4C2×C414yescomplemented
85C3×Dic3⋊C4C2×C414yescomplemented
86C3×C4×Dic3—42no—
87C3×C4×Dic3C2×C414yescomplemented
88#2343—31noSylow
89C23×C3×C4—31no—
90C23×C3×C4—32no—
91C22×C4×D3C22×C312yes—
92C22×C4×D3C22×C311yescharacteristic
93C3×#117—38no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—32no—
97C2×C3×C4⋊C4—32no—
98C2×C3×C22⋊C4—31no—
99C2×C3×C22⋊C4—31no—
100C2×C3×C22⋊C4—32no—
101C2×C3×C42—22no—
102C2×C3×C42—21no—
103C2×C3×C42—31no—
104C2×C3×C42—32no—
105C2×C3×C42C2×D312yes—
106C2×C3×C42C2×D311yescharacteristic
107C2×C3×C42C22×C312yes—
108C2×C3×C42C22×C311yescharacteristic
109C2×(C2×D3)⋊C4C22×C312yes—
110C2×(C2×D3)⋊C4C22×C311yescharacteristic
111C2×(C2×D3)⋊C4C22×C311yescharacteristic
112C2×C4⋊Dic3C22×C312yes—
113C2×Dic3⋊C4C22×C312yes—
114C2×Dic3⋊C4C22×C311yescharacteristic
115C2×Dic3⋊C4C22×C311yescharacteristic
116C2×C4×Dic3C22×C312yes—
117C2×C4×Dic3C22×C311yescharacteristic
118#872C3×C418yescomplemented
119C3×#95—21no—
120C3×#95—21no—
121C3×#95—22no—
122C3×#95—31no—
123C3×#95—32no—
124C3×#95—32no—
125C3×#95—32no—
126C3×#95—31no—
127C3×#95—32no—
128C3×#95—32no—
129C3×#95C2×D311yescharacteristic
130C3×#95C2×D311yescharacteristic
131C3×#95C2×D312yes—
132C3×#95C22×C311yescharacteristic
133C3×#95C22×C311yescharacteristic
134C3×#95C22×C312yes—
135C3⋊#95C22×C311yescharacteristic
136C3⋊#95C22×C312yes—
137C3⋊#95C22×C311yescharacteristic
138C3⋊#95C22×C312yes—
139C3⋊#95C22×C312yes—
140C3⋊#95C22×C312yes—
141C3⋊#95C22×C312yes—
142C23×C32C2411yescharacteristic
143C22×C3×D3—22no—
144C22×C3×D3—21no—
145C22×C3×D3—21no—
146C22×C3×D3C22×C412yes—
147C22×C3×D3#4114yes—
148C2×C32×C4—22no—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
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—22no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3C22×C412yes—
172C2×C3×Dic3C22×C412yes—
173C2×C3×Dic3C22×C412yes—
174C3×C4×D3—28no—
175C3×C4×D3—48no—
176C2×#117—31no—
177#387—32no—
178#387—32no—
179#385—32no—
180#383—31no—
181#382—31no—
182#381—31no—
183C4×C4⋊C4—31no—
184C4×C22⋊C4—32no—
185#376C3×D311yescharacteristic, complemented
186C2×#95—31no—
187C24×C3—31no—
188C23×D3C23×C311yescharacteristic
189C22×C3×C4—21no—
190C22×C3×C4—22no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—22no—
194C22×C3×C4—31no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—34no—
198C22×C3×C4—32no—
199C22×C3×C4—32no—
200C22×C3×C4—64no—
201C22×C3×C4—64no—
202C22×C3×C4—64no—
203C22×C3×C4—122no—
204C22×C3×C4C22×D312yes—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D312yes—
209C22×C3×C4C23×C312yes—
210C22×C3×C4C23×C311yescharacteristic
211C22×C3×C4C23×C311yescharacteristic
212C22×C3×C4C23×C311yescharacteristic
213C22×C3×C4C23×C312yes—
214C22×Dic3C23×C312yes—
215C22×Dic3C23×C312yes—
216C22×Dic3C23×C311yescharacteristic
217C22×Dic3C23×C311yescharacteristic
218C22×Dic3C23×C311yescharacteristic
219C2×C4×D3—24no—
220C2×C4×D3—24no—
221C2×C4×D3—24no—
222C2×C4×D3—42no—
223C2×C4×D3C2×C3×C414yes—
224C3×C4⋊C4—34no—
225C3×C4⋊C4—34no—
226C3×C4⋊C4—64no—
227C3×C4⋊C4—122no—
228C3×C22⋊C4—34no—
229C3×C22⋊C4—34no—
230C3×C22⋊C4—64no—
231C3×C42—28no—
232C3×C42—24no—
233C3×C42—24no—
234C3×C42—24no—
235C3×C42—34no—
236C3×C42—122no—
237C3×C42C4×D314yescomplemented
238C3×C42C2×C3×C414yescomplemented
239(C2×D3)⋊C4—24no—
240(C2×D3)⋊C4C2×C3×C414yes—
241(C2×D3)⋊C4C2×C3×C414yes—
242C4⋊Dic3—42no—
243Dic3⋊C4—24no—
244Dic3⋊C4C2×C3×C414yescomplemented
245Dic3⋊C4C2×C3×C414yescomplemented
246C4×Dic3—42no—
247C4×Dic3C2×C3×C414yescomplemented
248C22×C32C23×C411yescharacteristic
249C22×C32C2×#4112yes—
250C22×C32C2×#4112yes—
251C22×C32H(5,𝔽2)11yescharacteristic
252C22×C322−1+411yescharacteristic
253C2×C3×D3—22no—
254C2×C3×D3—22no—
255C2×C3×D3—24no—
256C2×C3×D3—24no—
257C2×C3×D3#11714yes—
258C32×C4—22no—
259C32×C4—22no—
260C32×C4—22no—
261C32×C4—24no—
262C32×C4—42no—
263C3×Dic3—22no—
264C3×Dic3—22no—
265C3×Dic3—22no—
266C3×Dic3—42no—
267C3×Dic3—42no—
268C23×C4—31no—
269C23×C4—32no—
270#117—38no—
271C2×C4⋊C4—31no—
272C2×C4⋊C4—31no—
273C2×C4⋊C4—32no—
274C2×C4⋊C4—32no—
275C2×C22⋊C4—31no—
276C2×C22⋊C4—31no—
277C2×C22⋊C4—32no—
278C2×C42—31no—
279C2×C42—32no—
280C2×C42C2×C3×D312yes—
281C2×C42C2×C3×D311yescharacteristic
282#95—31no—
283#95—32no—
284#95—32no—
285#95—32no—
286#95—31no—
287#95—32no—
288#95—32no—
289#95C2×C3×D311yescharacteristic
290#95C2×C3×D311yescharacteristic
291#95C2×C3×D312yes—
292C23×C3—21no—
293C23×C3—32no—
294C23×C3—34no—
295C23×C3—62no—
296C23×C3—61no—
297C23×C3—61no—
298C23×C3C23×D311yescharacteristic
299C23×C3C24×C311yescharacteristic
300C22×D3—22no—
301C22×D3—21no—
302C22×D3—21no—
303C22×D3C22×C3×C412yes—
304C22×D3C3×#4114yes—
305C2×C3×C4—24no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—24no—
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—22no—
328C2×C3×C4—24no—
329C2×C3×C4—32no—
330C2×C3×C4—32no—
331C2×C3×C4—32no—
332C2×C3×C4—42no—
333C2×C3×C4—42no—
334C2×C3×C4—42no—
335C2×C3×C4—41no—
336C2×C3×C4—41no—
337C2×C3×C4—42no—
338C2×C3×C4—42no—
339C2×C3×C4—68no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—128no—
351C2×C3×C4C2×C4×D312yes—
352C2×C3×C4C2×C4×D312yes—
353C2×C3×C4C2×C4×D312yes—
354C2×C3×C4#23514yes—
355C2×C3×C4C22×C3×C412yes—
356C2×C3×C4C22×C3×C412yes—
357C2×C3×C4C22×C3×C412yes—
358C2×C3×C4C3×#4114yes—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3C22×C3×C412yes—
370C2×Dic3C22×C3×C412yes—
371C2×Dic3C22×C3×C412yes—
372C4×D3—28no—
373C4×D3—48no—
374C2×C32C2×#11711yescharacteristic
375C2×C32C4×#4111yescharacteristic
376C2×C32#52011yescharacteristic
377C2×C32#55112yes—
378C2×C32#55212yes—
379C3×D3—24no—
380C24—31no—
381C22×C4—31no—
382C22×C4—31no—
383C22×C4—31no—
384C22×C4—34no—
385C22×C4—32no—
386C22×C4—32no—
387C22×C4—64no—
388C22×C4—64no—
389C22×C4—64no—
390C22×C4—122no—
391C22×C4C22×C3×D312yes—
392C22×C4C22×C3×D311yescharacteristic
393C22×C4C22×C3×D311yescharacteristic
394C22×C4C22×C3×D311yescharacteristic
395C22×C4C22×C3×D312yes—
396C4⋊C4—34no—
397C4⋊C4—34no—
398C4⋊C4—64no—
399C4⋊C4—122no—
400C22⋊C4—34no—
401C22⋊C4—34no—
402C22⋊C4—64no—
403C42—24no—
404C42—34no—
405C42—122no—
406C42C3×C4×D314yescomplemented
407C22×C3—21no—
408C22×C3—22no—
409C22×C3—22no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—34no—
413C22×C3—62no—
414C22×C3—62no—
415C22×C3—64no—
416C22×C3—64no—
417C22×C3C22×C4×D311yescharacteristic
418C22×C3C2×#23512yes—
419C22×C3D3×#4112yes—
420C22×C3#100911yescharacteristic
421C22×C3#101011yescharacteristic
422C22×C3C23×C3×C411yescharacteristic
423C22×C3C2×C3×#4112yes—
424C22×C3C2×C3×#4112yes—
425C22×C3C3×H(5,𝔽2)11yescharacteristic
426C22×C3C3×2−1+411yescharacteristic
427C2×D3—22no—
428C2×D3—22no—
429C2×D3—24no—
430C2×D3—24no—
431C2×D3C3×#11714yes—
432C3×C4—24no—
433C3×C4—22no—
434C3×C4—22no—
435C3×C4—22no—
436C3×C4—24no—
437C3×C4—22no—
438C3×C4—22no—
439C3×C4—22no—
440C3×C4—24no—
441C3×C4—42no—
442C3×C4—42no—
443C3×C4—44no—
444C3×C4—44no—
445C3×C4—42no—
446C3×C4—42no—
447C3×C4—62no—
448C3×C4—62no—
449C3×C4—62no—
450C3×C4—122no—
451C3×C4—122no—
452Dic3—22no—
453Dic3—22no—
454Dic3—22no—
455Dic3—42no—
456Dic3—42no—
457C32#234311yescharacteristic, complemented, Sylow
458C23—32no—
459C23—34no—
460C23—62no—
461C23—61no—
462C23—61no—
463C23C23×C3×D311yescharacteristic
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—32no—
474C2×C4—32no—
475C2×C4—32no—
476C2×C4—68no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—61no—
480C2×C4—61no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—128no—
488C2×C4C2×C3×C4×D312yes—
489C2×C4C2×C3×C4×D312yes—
490C2×C4C2×C3×C4×D312yes—
491C2×C4C3×#23514yes—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—22no—
495C2×C3—22no—
496C2×C3—21no—
497C2×C3—64no—
498C2×C3C4×#23511yescharacteristic
499C2×C3D3×#11711yescharacteristic
500C2×C3#552311yescharacteristic
501C2×C3#552712yes—
502C2×C3#552912yes—
503C2×C3C2×C3×#11711yescharacteristic
504C2×C3C3×C4×#4111yescharacteristic
505C2×C3C3×#52011yescharacteristic
506C2×C3C3×#55112yes—
507C2×C3C3×#55212yes—
508D3—24no—
509C22—34no—
510C22—62no—
511C22—64no—
512C22—64no—
513C22—62no—
514C22C22×C3×C4×D311yescharacteristic
515C22C2×C3×#23512yes—
516C22C3×D3×#4112yes—
517C22C3×#100911yescharacteristic
518C22C3×#101011yescharacteristic
519C4—22no—
520C4—22no—
521C4—24no—
522C4—22no—
523C4—42no—
524C4—62no—
525C4—62no—
526C4—62no—
527C4—122no—
528C4—122no—
529C3—21no—
530C3#7341611yescharacteristic, direct product factor
531C3C3×#234311yescharacteristic, complemented
532C2—64no—
533C2C3×C4×#23511yescharacteristic
534C2C3×D3×#11711yescharacteristic
535C2C3×#552311yescharacteristic
536C2C3×#552712yes—
537C2C3×#552912yes—
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×#2343
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×#4933C2semidirect
9. C3×#4655C2semidirect
10. C3×#4651C2semidirect
11. C3×#4649C2semidirect
13. #73416C3direct (N × H)
27. C3×#872C4semidirect
49. C3×#376D3semidirect
50. C3×#376C2×C3semidirect
53. #4936C2×C3semidirect
54. #4933C2×C3semidirect
58. #4655C2×C3semidirect
59. #4651C2×C3semidirect
60. #4649C2×C3semidirect
78. C32×C42C2×C4semidirect
84. C3×Dic3⋊C4C2×C4semidirect
85. C3×Dic3⋊C4C2×C4semidirect
87. C3×C4×Dic3C2×C4semidirect
118. #872C3×C4semidirect
185. #376C3×D3semidirect
237. C3×C42C4×D3semidirect
238. C3×C42C2×C3×C4semidirect
244. Dic3⋊C4C2×C3×C4semidirect
245. Dic3⋊C4C2×C3×C4semidirect
247. C4×Dic3C2×C3×C4semidirect
406. C42C3×C4×D3semidirect
457. C32#2343semidirect
530. C3#73416direct (N × H)
531. C3C3×#2343semidirect

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×C4×(C2×D3)⋊C42
C3×#49362
C3×#49332
C3×#46682
C3×#46642
C3×D3×#952
C3×#46552
C3×#46512
C3×#46492
C3×#23433
#734163