Finite Group Databasebeta

← C3×#73335 #11805051

Subgroups — C3×#73335 #11805051

Order 1152.

1229 conjugacy classes of subgroups.

The subgroup lattice has 551 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#926C211yesmaximal, characteristic
2C2×C32×#95C211yesmaximal, characteristic
3C3×#5211C211yesmaximal, characteristic
4C3×#5210C212yesmaximal
5C3×C4×#217C212yesmaximal
6C3×#4654C212yesmaximal, complemented
7C3×#4653C212yesmaximal, complemented
8C3×#4651C211yesmaximal, characteristic, complemented
9C3×#4650C211yesmaximal, characteristic, complemented
10C3×#4649C211yesmaximal, characteristic, complemented
11C3×#4648C211yesmaximal, characteristic, complemented
12C3×#2343—31nomaximal
13#73335C311yesmaximal, characteristic, direct product factor
14C23×C32×C4C2212yes—
15C23×C32×C4C2211yescharacteristic
16C2×C3×#217C2212yes—
17C2×C3×#217C2211yescharacteristic
18C2×C3×#217C2211yescharacteristic
19C3×#926C418yescomplemented
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×Dic3⋊C4C2212yes—
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×C4×Dic3C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
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×#926C2×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—31no—
49C2×C3×#95—21no—
50C2×C3×#95D311yescharacteristic
51C2×C3×#95C2×C311yescharacteristic
52#5211C2×C311yescharacteristic
53#5210C2×C312yes—
54C4×#217C2×C312yes—
55#4654C2×C312yescomplemented
56#4653C2×C312yescomplemented
57#4651C2×C311yescharacteristic, complemented
58#4650C2×C311yescharacteristic, complemented
59#4649C2×C311yescharacteristic, complemented
60#4648C2×C311yescharacteristic, complemented
61C24×C32C2311yescharacteristic
62C22×C32×C4—24no—
63C22×C32×C4—24no—
64C22×C32×C4—24no—
65C22×C32×C4—42no—
66C22×C32×C4C2×C414yes—
67C22×C32×C4C2312yes—
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C3×#217—24no—
78C3×#217C2×C414yes—
79C3×#217C2×C414yes—
80C3×C4⋊Dic3C2×C414yescomplemented
81C3×C4⋊Dic3C2×C414yescomplemented
82C3×Dic3⋊C4—24no—
83C3×Dic3⋊C4—42no—
84C3×C4×Dic3—24no—
85C3×C4×Dic3—42no—
86C3×C4×Dic3C2×C414yescomplemented
87C3×C4×Dic3C2×C414yescomplemented
88#2343—31noSylow
89C23×C3×C4—22no—
90C23×C3×C4—21no—
91C23×C3×C4C2×D312yes—
92C23×C3×C4C2×D311yescharacteristic
93C23×C3×C4C22×C312yes—
94C23×C3×C4C22×C311yescharacteristic
95C3×#117—38no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C4⋊C4—32no—
99C2×C3×C4⋊C4—32no—
100C2×C3×C22⋊C4—31no—
101C2×C3×C22⋊C4—31no—
102C2×C3×C22⋊C4—32no—
103C2×C3×C42—31no—
104C2×C3×C42—31no—
105C2×C3×C42—32no—
106C2×C3×C42—32no—
107C2×#217C22×C312yes—
108C2×#217C22×C311yescharacteristic
109C2×#217C22×C311yescharacteristic
110#926C3×C418yescomplemented
111C2×C4⋊Dic3C22×C311yescharacteristic
112C2×C4⋊Dic3C22×C311yescharacteristic
113C2×Dic3⋊C4C22×C312yes—
114C2×Dic3⋊C4C22×C312yes—
115C2×C4×Dic3C22×C312yes—
116C2×C4×Dic3C22×C312yes—
117C2×C4×Dic3C22×C311yescharacteristic
118C2×C4×Dic3C22×C311yescharacteristic
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×C32—22no—
143C23×C32—21no—
144C23×C32—21no—
145C23×C32C22×C412yes—
146C23×C32#4114yes—
147C23×C32C2411yescharacteristic
148C2×C32×C4—22no—
149C2×C32×C4—28no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4—22no—
155C2×C32×C4—22no—
156C2×C32×C4—48no—
157C2×C32×C4C22×C412yes—
158C2×C32×C4C22×C412yes—
159C2×C32×C4#4114yes—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3C22×C412yes—
173C2×C3×Dic3C22×C412yes—
174C2×C3×Dic3C22×C412yes—
175C2×C3×Dic3C22×C412yes—
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#376—31no—
186C2×#95C3×D311yescharacteristic
187C24×C3—21no—
188C24×C3C22×D311yescharacteristic
189C24×C3C23×C311yescharacteristic
190C22×C3×C4—24no—
191C22×C3×C4—24no—
192C22×C3×C4—28no—
193C22×C3×C4—24no—
194C22×C3×C4—24no—
195C22×C3×C4—24no—
196C22×C3×C4—24no—
197C22×C3×C4—24no—
198C22×C3×C4—22no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—22no—
202C22×C3×C4—31no—
203C22×C3×C4—31no—
204C22×C3×C4—31no—
205C22×C3×C4—31no—
206C22×C3×C4—32no—
207C22×C3×C4—32no—
208C22×C3×C4—44no—
209C22×C3×C4—44no—
210C22×C3×C4—42no—
211C22×C3×C4—42no—
212C22×C3×C4—44no—
213C22×C3×C4C4×D314yes—
214C22×C3×C4C2×C3×C414yes—
215C22×C3×C4C22×D312yes—
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D312yes—
219C22×C3×C4C23×C312yes—
220C22×C3×C4C23×C311yescharacteristic
221C22×C3×C4C23×C311yescharacteristic
222C22×C3×C4C23×C312yes—
223C22×Dic3C23×C312yes—
224C22×Dic3C23×C312yes—
225C22×Dic3C23×C311yescharacteristic
226C22×Dic3C23×C311yescharacteristic
227C22×Dic3C23×C311yescharacteristic
228C22×Dic3C23×C311yescharacteristic
229C3×C4⋊C4—34no—
230C3×C4⋊C4—34no—
231C3×C4⋊C4—64no—
232C3×C4⋊C4—122no—
233C3×C22⋊C4—34no—
234C3×C22⋊C4—34no—
235C3×C22⋊C4—64no—
236C3×C42—34no—
237C3×C42—34no—
238C3×C42—64no—
239C3×C42—122no—
240#217—24no—
241#217C2×C3×C414yes—
242#217C2×C3×C414yes—
243C4⋊Dic3C2×C3×C414yescomplemented
244C4⋊Dic3C2×C3×C414yescomplemented
245Dic3⋊C4—24no—
246Dic3⋊C4—42no—
247C4×Dic3—24no—
248C4×Dic3—42no—
249C4×Dic3C2×C3×C414yescomplemented
250C4×Dic3C2×C3×C414yescomplemented
251C22×C32—22no—
252C22×C32—22no—
253C22×C32—24no—
254C22×C32—24no—
255C22×C32#11714yes—
256C22×C32C23×C411yescharacteristic
257C22×C32C2×#4112yes—
258C22×C32C2×#4112yes—
259C22×C32H(5,𝔽2)11yescharacteristic
260C22×C322−1+411yescharacteristic
261C32×C4—22no—
262C32×C4—22no—
263C32×C4—24no—
264C32×C4—42no—
265C3×Dic3—22no—
266C3×Dic3—22no—
267C3×Dic3—22no—
268C3×Dic3—22no—
269C3×Dic3—42no—
270C3×Dic3—42no—
271C23×C4C2×C3×D312yes—
272C23×C4C2×C3×D311yescharacteristic
273#117—38no—
274C2×C4⋊C4—31no—
275C2×C4⋊C4—31no—
276C2×C4⋊C4—32no—
277C2×C4⋊C4—32no—
278C2×C22⋊C4—31no—
279C2×C22⋊C4—31no—
280C2×C22⋊C4—32no—
281C2×C42—31no—
282C2×C42—31no—
283C2×C42—32no—
284C2×C42—32no—
285#95—31no—
286#95—32no—
287#95—32no—
288#95—32no—
289#95—31no—
290#95—32no—
291#95—32no—
292#95C2×C3×D311yescharacteristic
293#95C2×C3×D311yescharacteristic
294#95C2×C3×D312yes—
295C23×C3—24no—
296C23×C3—22no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—22no—
302C23×C3—21no—
303C23×C3—21no—
304C23×C3—21no—
305C23×C3—22no—
306C23×C3—24no—
307C23×C3C2×C4×D312yes—
308C23×C3#23714yes—
309C23×C3C22×C3×C412yes—
310C23×C3C3×#4114yes—
311C23×C3C23×D311yescharacteristic
312C23×C3C24×C311yescharacteristic
313C2×C3×C4—28no—
314C2×C3×C4—28no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—24no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—24no—
333C2×C3×C4—32no—
334C2×C3×C4—32no—
335C2×C3×C4—32no—
336C2×C3×C4—32no—
337C2×C3×C4—48no—
338C2×C3×C4—42no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—48no—
345C2×C3×C4—48no—
346C2×C3×C4—416no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—61no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4C2×C4×D312yes—
360C2×C3×C4C2×C4×D312yes—
361C2×C3×C4#23514yes—
362C2×C3×C4C22×C3×C412yes—
363C2×C3×C4C22×C3×C412yes—
364C2×C3×C4C3×#4114yes—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3C22×C3×C412yes—
378C2×Dic3C22×C3×C412yes—
379C2×Dic3C22×C3×C412yes—
380C2×Dic3C22×C3×C412yes—
381C2×C32—24no—
382C2×C32C2×#11711yescharacteristic
383C2×C32C4×#4111yescharacteristic
384C2×C32#52011yescharacteristic
385C2×C32#55112yes—
386C2×C32#55212yes—
387C24C22×C3×D311yescharacteristic
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—31no—
392C22×C4—31no—
393C22×C4—31no—
394C22×C4—31no—
395C22×C4—32no—
396C22×C4—32no—
397C22×C4—42no—
398C22×C4C3×C4×D314yes—
399C22×C4C22×C3×D312yes—
400C22×C4C22×C3×D311yescharacteristic
401C22×C4C22×C3×D311yescharacteristic
402C22×C4C22×C3×D312yes—
403C4⋊C4—34no—
404C4⋊C4—34no—
405C4⋊C4—64no—
406C4⋊C4—122no—
407C22⋊C4—34no—
408C22⋊C4—34no—
409C22⋊C4—64no—
410C42—34no—
411C42—34no—
412C42—64no—
413C42—122no—
414C22×C3—28no—
415C22×C3—24no—
416C22×C3—28no—
417C22×C3—24no—
418C22×C3—22no—
419C22×C3—24no—
420C22×C3—22no—
421C22×C3—24no—
422C22×C3—22no—
423C22×C3—22no—
424C22×C3—24no—
425C22×C3—24no—
426C22×C3—24no—
427C22×C3—21no—
428C22×C3—22no—
429C22×C3—22no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3#87714yes—
433C22×C3C3×#11714yes—
434C22×C3C22×C4×D311yescharacteristic
435C22×C3C2×#23512yes—
436C22×C3C2×#23712yes—
437C22×C3#100411yescharacteristic
438C22×C3#100711yescharacteristic
439C22×C3C23×C3×C411yescharacteristic
440C22×C3C2×C3×#4112yes—
441C22×C3C2×C3×#4112yes—
442C22×C3C3×H(5,𝔽2)11yescharacteristic
443C22×C3C3×2−1+411yescharacteristic
444C3×C4—22no—
445C3×C4—22no—
446C3×C4—24no—
447C3×C4—22no—
448C3×C4—22no—
449C3×C4—24no—
450C3×C4—44no—
451C3×C4—42no—
452C3×C4—42no—
453C3×C4—44no—
454C3×C4—42no—
455C3×C4—42no—
456C3×C4—62no—
457C3×C4—62no—
458C3×C4—62no—
459C3×C4—62no—
460C3×C4—122no—
461C3×C4—122no—
462Dic3—22no—
463Dic3—22no—
464Dic3—22no—
465Dic3—22no—
466Dic3—42no—
467Dic3—42no—
468C32#234311yescharacteristic, complemented, Sylow
469C23—22no—
470C23—21no—
471C23—21no—
472C23C2×C3×C4×D312yes—
473C23C3×#23714yes—
474C23C23×C3×D311yescharacteristic
475C2×C4—28no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—32no—
484C2×C4—32no—
485C2×C4—32no—
486C2×C4—32no—
487C2×C4—48no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—61no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4C2×C3×C4×D312yes—
501C2×C4C2×C3×C4×D312yes—
502C2×C4C3×#23514yes—
503C2×C3—28no—
504C2×C3—24no—
505C2×C3—24no—
506C2×C3—22no—
507C2×C3—21no—
508C2×C3—22no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3C4×#23511yescharacteristic
512C2×C3C2×#87711yescharacteristic
513C2×C3#549512yes—
514C2×C3#550411yescharacteristic
515C2×C3#551312yes—
516C2×C3C2×C3×#11711yescharacteristic
517C2×C3C3×C4×#4111yescharacteristic
518C2×C3C3×#52011yescharacteristic
519C2×C3C3×#55112yes—
520C2×C3C3×#55212yes—
521C22—24no—
522C22—22no—
523C22—24no—
524C22—22no—
525C22C3×#87714yes—
526C22C22×C3×C4×D311yescharacteristic
527C22C2×C3×#23512yes—
528C22C2×C3×#23712yes—
529C22C3×#100411yescharacteristic
530C22C3×#100711yescharacteristic
531C4—24no—
532C4—22no—
533C4—22no—
534C4—42no—
535C4—62no—
536C4—62no—
537C4—62no—
538C4—62no—
539C4—122no—
540C4—122no—
541C3—21no—
542C3#7333511yescharacteristic, direct product factor
543C3C3×#234311yescharacteristic, complemented
544C2—24no—
545C2C3×C4×#23511yescharacteristic
546C2C2×C3×#87711yescharacteristic
547C2C3×#549512yes—
548C2C3×#550411yescharacteristic
549C2C3×#551312yes—
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×#95C2
socleC23×C32C24
prime radicalC24×C32C23
cosocleC23×C3C24×C3
hypercenterC2×C3×#95D3
hypocenterC3C3×#2343
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#95

Complements

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

NH ≅ G/Ntype
6. C3×#4654C2semidirect
7. C3×#4653C2semidirect
8. C3×#4651C2semidirect
9. C3×#4650C2semidirect
10. C3×#4649C2semidirect
11. C3×#4648C2semidirect
13. #73335C3direct (N × H)
19. C3×#926C4semidirect
55. #4654C2×C3semidirect
56. #4653C2×C3semidirect
57. #4651C2×C3semidirect
58. #4650C2×C3semidirect
59. #4649C2×C3semidirect
60. #4648C2×C3semidirect
80. C3×C4⋊Dic3C2×C4semidirect
81. C3×C4⋊Dic3C2×C4semidirect
86. C3×C4×Dic3C2×C4semidirect
87. C3×C4×Dic3C2×C4semidirect
110. #926C3×C4semidirect
243. C4⋊Dic3C2×C3×C4semidirect
244. C4⋊Dic3C2×C3×C4semidirect
249. C4×Dic3C2×C3×C4semidirect
250. C4×Dic3C2×C3×C4semidirect
468. C32#2343semidirect
542. C3#73335direct (N × H)
543. C3C3×#2343semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9262
C2×C32×#952
C3×#52112
C3×#52102
C3×C4×#2172
C3×#46542
C3×#46532
C3×#46512
C3×#46502
C3×#46492
C3×#46482
C3×#23433
#733353