Finite Group Databasebeta

← C3×#73620 #11801916

Subgroups — C3×#73620 #11801916

Order 1152.

1145 conjugacy classes of subgroups.

The subgroup lattice has 549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#872C211yesmaximal, characteristic
2C32×C4×C4⋊C4C211yesmaximal, characteristic, complemented
3C3×#4990C212yesmaximal
4C3×#4978C212yesmaximal, complemented
5C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
6C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
7C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
8C3×#4932C211yesmaximal, characteristic, complemented
9C3×C42×Dic3C211yesmaximal, characteristic, complemented
10C3×#4670C212yesmaximal
11C3×#4655C212yesmaximal, complemented
12C3×#2298—31nomaximal
13#73620C311yesmaximal, characteristic, direct product factor
14C22×C3×C4×D3C2211yescharacteristic
15C2×C32×C4⋊C4C2212yes—
16C2×C32×C42C2211yescharacteristic
17C2×C32×C42C2211yescharacteristic
18C2×C32×C42C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2212yes—
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×(C2×D3)⋊C4C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×C4×Dic3C2212yes—
27C2×C3×C4×Dic3C2212yes—
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C3×#872C418yescomplemented
32C32×#95C2212yes—
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C2×C3×#117—31no—
39C2×#872C2×C311yescharacteristic
40C3×#388—32no—
41C3×#388—32no—
42C3×#387—32no—
43C3×#387—32no—
44C3×C4×C4⋊C4—21no—
45C3×C4×C4⋊C4—31no—
46C3×C4×C4⋊C4D311yescharacteristic, complemented
47C3×C4×C4⋊C4C2×C311yescharacteristic, complemented
48C3×C4×C22⋊C4—31no—
49C3×C4×C22⋊C4—31no—
50C3×#376—31no—
51C3×C43—31no—
52#4990C2×C312yes—
53#4978C2×C312yescomplemented
54C4×(C2×D3)⋊C4C2×C311yescharacteristic
55C4×(C2×D3)⋊C4C2×C311yescharacteristic
56C4×C4⋊Dic3C2×C311yescharacteristic, complemented
57#4932C2×C311yescharacteristic, complemented
58C42×Dic3C2×C311yescharacteristic, complemented
59#4670C2×C312yes—
60#4655C2×C312yescomplemented
61C23×C3×D3C2311yescharacteristic
62C22×C32×C4C2312yes—
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2311yescharacteristic
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3C2×C414yes—
75C32×C4⋊C4—24no—
76C32×C42—22no—
77C32×C42—22no—
78C32×C42C2×C414yes—
79C3×(C2×D3)⋊C4—24no—
80C3×(C2×D3)⋊C4—24no—
81C3×(C2×D3)⋊C4C2×C414yes—
82C3×(C2×D3)⋊C4C2×C414yes—
83C3×C4⋊Dic3—24no—
84C3×Dic3⋊C4C2×C414yes—
85C3×Dic3⋊C4C2×C414yes—
86C3×C4×Dic3—24no—
87C3×C4×Dic3—22no—
88C3×C4×Dic3—22no—
89C3×C4×Dic3—24no—
90C3×C4×Dic3C2×C414yes—
91#2298—31noSylow
92C23×C3×C4—31no—
93C22×C4×D3C22×C311yescharacteristic
94C3×#117—38no—
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C4⋊C4—32no—
99C2×C3×C4⋊C4C2×D312yes—
100C2×C3×C4⋊C4C22×C312yes—
101C2×C3×C22⋊C4—31no—
102C2×C3×C22⋊C4—31no—
103C2×C3×C22⋊C4—32no—
104C2×C3×C22⋊C4—32no—
105C2×C3×C42—21no—
106C2×C3×C42—21no—
107C2×C3×C42—21no—
108C2×C3×C42—31no—
109C2×C3×C42—32no—
110C2×C3×C42—32no—
111C2×C3×C42—31no—
112C2×C3×C42—31no—
113C2×C3×C42C2×D311yescharacteristic
114C2×C3×C42C2×D311yescharacteristic
115C2×C3×C42C2×D311yescharacteristic
116C2×C3×C42C22×C311yescharacteristic
117C2×C3×C42C22×C311yescharacteristic
118C2×C3×C42C22×C311yescharacteristic
119C2×(C2×D3)⋊C4C22×C312yes—
120C2×(C2×D3)⋊C4C22×C312yes—
121C2×(C2×D3)⋊C4C22×C311yescharacteristic
122C2×(C2×D3)⋊C4C22×C311yescharacteristic
123C2×C4⋊Dic3C22×C312yes—
124C2×Dic3⋊C4C22×C311yescharacteristic
125C2×Dic3⋊C4C22×C311yescharacteristic
126C2×C4×Dic3C22×C312yes—
127C2×C4×Dic3C22×C312yes—
128C2×C4×Dic3C22×C311yescharacteristic
129C2×C4×Dic3C22×C311yescharacteristic
130C2×C4×Dic3C22×C311yescharacteristic
131#872C3×C418yescomplemented
132C3×#95—22no—
133C3×#95—32no—
134C3×#95—32no—
135C3×#95—32no—
136C3×#95—32no—
137C3×#95—32no—
138C3×#95C2×D312yes—
139C3×#95C22×C312yes—
140C3⋊#95C22×C312yes—
141C3⋊#95C22×C312yes—
142C3⋊#95C22×C312yes—
143C3⋊#95C22×C312yes—
144C3⋊#95C22×C312yes—
145C23×C32C2411yescharacteristic
146C22×C3×D3—22no—
147C22×C3×D3—22no—
148C22×C3×D3—21no—
149C22×C3×D3—21no—
150C22×C3×D3C22×C412yes—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4—22no—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4C22×C412yes—
159C2×C32×C4C22×C412yes—
160C2×C32×C4C22×C412yes—
161C2×C32×C4#4114yes—
162C2×C32×C4#4112yes—
163C2×C32×C4#4112yes—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3C22×C412yes—
174C2×C3×Dic3C22×C412yes—
175C2×C3×Dic3C22×C412yes—
176C2×C3×Dic3#4114yes—
177C3×C4×D3—28no—
178C2×#117—31no—
179#388—32no—
180#388—32no—
181#387—32no—
182#387—32no—
183C4×C4⋊C4—31no—
184C4×C4⋊C4C3×D311yescharacteristic, complemented
185C4×C22⋊C4—31no—
186C4×C22⋊C4—31no—
187#376—31no—
188C43—31no—
189C24×C3—31no—
190C23×D3C23×C311yescharacteristic
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—31no—
197C22×C3×C4—31no—
198C22×C3×C4—31no—
199C22×C3×C4—32no—
200C22×C3×C4—34no—
201C22×C3×C4—32no—
202C22×C3×C4—62no—
203C22×C3×C4—62no—
204C22×C3×C4C22×D312yes—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D312yes—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C23×C312yes—
210C22×C3×C4C23×C311yescharacteristic
211C22×C3×C4C23×C311yescharacteristic
212C22×C3×C4C23×C312yes—
213C22×C3×C4C23×C311yescharacteristic
214C22×Dic3C23×C312yes—
215C22×Dic3C23×C311yescharacteristic
216C22×Dic3C23×C311yescharacteristic
217C22×Dic3C23×C311yescharacteristic
218C22×Dic3C23×C312yes—
219C2×C4×D3—22no—
220C2×C4×D3—22no—
221C2×C4×D3C2×C3×C414yes—
222C3×C4⋊C4—28no—
223C3×C4⋊C4—24no—
224C3×C4⋊C4—24no—
225C3×C4⋊C4—34no—
226C3×C4⋊C4—34no—
227C3×C4⋊C4—64no—
228C3×C22⋊C4—34no—
229C3×C22⋊C4—34no—
230C3×C22⋊C4—64no—
231C3×C22⋊C4—64no—
232C3×C42—22no—
233C3×C42—22no—
234C3×C42—22no—
235C3×C42—22no—
236C3×C42—24no—
237C3×C42—34no—
238C3×C42—42no—
239C3×C42—42no—
240C3×C42—64no—
241C3×C42—64no—
242C3×C42—62no—
243C3×C42—62no—
244C3×C42C4×D314yes—
245C3×C42C2×C3×C414yes—
246(C2×D3)⋊C4—24no—
247(C2×D3)⋊C4—24no—
248(C2×D3)⋊C4C2×C3×C414yes—
249(C2×D3)⋊C4C2×C3×C414yes—
250C4⋊Dic3—24no—
251Dic3⋊C4C2×C3×C414yes—
252Dic3⋊C4C2×C3×C414yes—
253C4×Dic3—24no—
254C4×Dic3—22no—
255C4×Dic3—22no—
256C4×Dic3—24no—
257C4×Dic3C2×C3×C414yes—
258C22×C32C23×C411yescharacteristic
259C22×C32C2×#4112yes—
260C22×C32C2×#4111yescharacteristic
261C22×C32C2×#4111yescharacteristic
262C22×C32C2×#4112yes—
263C2×C3×D3—22no—
264C2×C3×D3—22no—
265C2×C3×D3—22no—
266C2×C3×D3—42no—
267C2×C3×D3—42no—
268C32×C4—22no—
269C32×C4—22no—
270C32×C4—24no—
271C32×C4—42no—
272C32×C4#11714yes—
273C3×Dic3—22no—
274C3×Dic3—22no—
275C3×Dic3—22no—
276C3×Dic3—24no—
277C3×Dic3—42no—
278C23×C4—31no—
279#117—38no—
280C2×C4⋊C4—31no—
281C2×C4⋊C4—31no—
282C2×C4⋊C4—32no—
283C2×C4⋊C4C2×C3×D312yes—
284C2×C22⋊C4—31no—
285C2×C22⋊C4—31no—
286C2×C22⋊C4—32no—
287C2×C22⋊C4—32no—
288C2×C42—31no—
289C2×C42—31no—
290C2×C42—32no—
291C2×C42—32no—
292C2×C42—31no—
293C2×C42C2×C3×D311yescharacteristic
294C2×C42C2×C3×D311yescharacteristic
295C2×C42C2×C3×D311yescharacteristic
296#95—32no—
297#95—32no—
298#95—32no—
299#95—32no—
300#95—32no—
301#95C2×C3×D312yes—
302C23×C3—21no—
303C23×C3—32no—
304C23×C3—62no—
305C23×C3—61no—
306C23×C3—61no—
307C23×C3—62no—
308C23×C3C23×D311yescharacteristic
309C23×C3C24×C311yescharacteristic
310C22×D3—22no—
311C22×D3—22no—
312C22×D3—21no—
313C22×D3—21no—
314C22×D3C22×C3×C412yes—
315C2×C3×C4—24no—
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—22no—
324C2×C3×C4—24no—
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—22no—
333C2×C3×C4—22no—
334C2×C3×C4—24no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—32no—
338C2×C3×C4—32no—
339C2×C3×C4—32no—
340C2×C3×C4—34no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—42no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—61no—
349C2×C3×C4—62no—
350C2×C3×C4—61no—
351C2×C3×C4—62no—
352C2×C3×C4—68no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4C2×C4×D312yes—
357C2×C3×C4C2×C4×D312yes—
358C2×C3×C4C2×C4×D312yes—
359C2×C3×C4#23514yes—
360C2×C3×C4#23712yes—
361C2×C3×C4#23912yes—
362C2×C3×C4C22×C3×C412yes—
363C2×C3×C4C22×C3×C412yes—
364C2×C3×C4C22×C3×C412yes—
365C2×C3×C4C3×#4114yes—
366C2×C3×C4C3×#4112yes—
367C2×C3×C4C3×#4112yes—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—21no—
373C2×Dic3—21no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3C22×C3×C412yes—
378C2×Dic3C22×C3×C412yes—
379C2×Dic3C22×C3×C412yes—
380C2×Dic3C3×#4114yes—
381C4×D3—28no—
382C2×C32C2×#11711yescharacteristic
383C2×C32C4×#4111yescharacteristic
384C2×C32C4×#4111yescharacteristic
385C2×C32#52912yes—
386C2×C32#52912yes—
387C3×D3—42no—
388C24—31no—
389C22×C4—31no—
390C22×C4—31no—
391C22×C4—31no—
392C22×C4—32no—
393C22×C4—34no—
394C22×C4—32no—
395C22×C4—62no—
396C22×C4—62no—
397C22×C4C22×C3×D312yes—
398C22×C4C22×C3×D311yescharacteristic
399C22×C4C22×C3×D311yescharacteristic
400C22×C4C22×C3×D312yes—
401C22×C4C22×C3×D311yescharacteristic
402C4⋊C4—24no—
403C4⋊C4—34no—
404C4⋊C4—34no—
405C4⋊C4—64no—
406C22⋊C4—34no—
407C22⋊C4—34no—
408C22⋊C4—64no—
409C22⋊C4—64no—
410C42—22no—
411C42—22no—
412C42—34no—
413C42—64no—
414C42—64no—
415C42—62no—
416C42—62no—
417C42C3×C4×D314yes—
418C22×C3—21no—
419C22×C3—22no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—22no—
423C22×C3—62no—
424C22×C3—62no—
425C22×C3—62no—
426C22×C3—122no—
427C22×C3—122no—
428C22×C3C22×C4×D311yescharacteristic
429C22×C3C2×#23512yes—
430C22×C3C2×#23711yescharacteristic
431C22×C3C2×#23911yescharacteristic
432C22×C3D3×#4112yes—
433C22×C3C23×C3×C411yescharacteristic
434C22×C3C2×C3×#4112yes—
435C22×C3C2×C3×#4111yescharacteristic
436C22×C3C2×C3×#4111yescharacteristic
437C22×C3C2×C3×#4112yes—
438C2×D3—22no—
439C2×D3—22no—
440C2×D3—22no—
441C2×D3—42no—
442C2×D3—42no—
443C3×C4—24no—
444C3×C4—22no—
445C3×C4—22no—
446C3×C4—24no—
447C3×C4—22no—
448C3×C4—22no—
449C3×C4—24no—
450C3×C4—24no—
451C3×C4—42no—
452C3×C4—44no—
453C3×C4—44no—
454C3×C4—42no—
455C3×C4—42no—
456C3×C4—62no—
457C3×C4—62no—
458C3×C4—62no—
459C3×C4—64no—
460C3×C4—122no—
461C3×C4#89214yes—
462C3×C4C3×#11714yes—
463Dic3—22no—
464Dic3—22no—
465Dic3—22no—
466Dic3—24no—
467Dic3—42no—
468C32#229811yescharacteristic, complemented, Sylow
469C23—32no—
470C23—62no—
471C23—61no—
472C23—61no—
473C23—62no—
474C23C23×C3×D311yescharacteristic
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—32no—
483C2×C4—32no—
484C2×C4—32no—
485C2×C4—34no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—61no—
489C2×C4—62no—
490C2×C4—61no—
491C2×C4—62no—
492C2×C4—68no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4C2×C3×C4×D312yes—
497C2×C4C2×C3×C4×D312yes—
498C2×C4C2×C3×C4×D312yes—
499C2×C4C3×#23514yes—
500C2×C4C3×#23712yes—
501C2×C4C3×#23912yes—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—22no—
505C2×C3—22no—
506C2×C3—21no—
507C2×C3—122no—
508C2×C3C4×#23511yescharacteristic
509C2×C3C2×#89211yescharacteristic
510C2×C3#552211yescharacteristic
511C2×C3#553812yes—
512C2×C3#558012yes—
513C2×C3C2×C3×#11711yescharacteristic
514C2×C3C3×C4×#4111yescharacteristic
515C2×C3C3×C4×#4111yescharacteristic
516C2×C3C3×#52912yes—
517C2×C3C3×#52912yes—
518D3—42no—
519C22—62no—
520C22—62no—
521C22—62no—
522C22—122no—
523C22—122no—
524C22C22×C3×C4×D311yescharacteristic
525C22C2×C3×#23512yes—
526C22C2×C3×#23711yescharacteristic
527C22C2×C3×#23911yescharacteristic
528C22C3×D3×#4112yes—
529C4—22no—
530C4—24no—
531C4—22no—
532C4—42no—
533C4—62no—
534C4—62no—
535C4—64no—
536C4—62no—
537C4—122no—
538C4C3×#89214yes—
539C3—21no—
540C3#7362011yescharacteristic, direct product factor
541C3C3×#229811yescharacteristic, complemented
542C2—122no—
543C2C3×C4×#23511yescharacteristic
544C2C2×C3×#89211yescharacteristic
545C2C3×#552211yescharacteristic
546C2C3×#553812yes—
547C2C3×#558012yes—
subgroupG/H
centerC22×C3×C4C22×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×C4×C4⋊C4C2
socleC23×C32C24
prime radicalC23×C3×D3C23
cosocleC23×C3C24×C3
hypercenterC3×C4×C4⋊C4D3
hypocenterC3C3×#2298
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C32×C4×C4⋊C4C2semidirect
4. C3×#4978C2semidirect
7. C3×C4×C4⋊Dic3C2semidirect
8. C3×#4932C2semidirect
9. C3×C42×Dic3C2semidirect
11. C3×#4655C2semidirect
13. #73620C3direct (N × H)
31. C3×#872C4semidirect
46. C3×C4×C4⋊C4D3semidirect
47. C3×C4×C4⋊C4C2×C3semidirect
53. #4978C2×C3semidirect
56. C4×C4⋊Dic3C2×C3semidirect
57. #4932C2×C3semidirect
58. C42×Dic3C2×C3semidirect
60. #4655C2×C3semidirect
131. #872C3×C4semidirect
184. C4×C4⋊C4C3×D3semidirect
468. C32#2298semidirect
540. C3#73620direct (N × H)
541. C3C3×#2298semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8722
C32×C4×C4⋊C42
C3×#49902
C3×#49782
C3×C4×(C2×D3)⋊C42
C3×C4×C4⋊Dic32
C3×#49322
C3×C42×Dic32
C3×#46702
C3×#46552
C3×#22983
#736203