Finite Group Databasebeta

← C3×#75966 #11802471

Subgroups — C3×#75966 #11802471

Order 1152.

1053 conjugacy classes of subgroups.

The subgroup lattice has 547 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#890C211yesmaximal, characteristic
2C32×#389C211yesmaximal, characteristic
3C3×#4978C212yesmaximal
4C3×#4977C211yesmaximal, characteristic
5C3×Dic3×C4⋊C4C212yesmaximal
6C3×Dic3×C4⋊C4C211yesmaximal, characteristic
7C3×Dic3×C4⋊C4C211yesmaximal, characteristic
8C3×C42×Dic3C211yesmaximal, characteristic
9C3×#4928C211yesmaximal, characteristic
10C3×#4653C212yesmaximal
11C3×#4649C212yesmaximal
12C3×C4×#125—31nomaximal
13#75966C311yesmaximal, characteristic, direct product factor
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C32×C4⋊C4C2212yes—
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C42C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2212yes—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×Dic3⋊C4C2212yes—
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C3×#890C418yescomplemented
32C32×#95C2212yes—
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C2×C3×#125—31no—
39C2×#890C2×C311yescharacteristic
40C3×#389—21no—
41C3×#389—31no—
42C3×#389D311yescharacteristic
43C3×#389C2×C311yescharacteristic
44C3×#387—32no—
45C3×#387—32no—
46C3×#382—31no—
47C3×C4×C4⋊C4—32no—
48C3×C4×C4⋊C4—31no—
49C3×C4×C4⋊C4—31no—
50C3×C4×C4⋊C4—32no—
51C3×C43—31no—
52#4978C2×C312yes—
53#4977C2×C311yescharacteristic
54Dic3×C4⋊C4C2×C312yes—
55Dic3×C4⋊C4C2×C311yescharacteristic
56Dic3×C4⋊C4C2×C311yescharacteristic
57C42×Dic3C2×C311yescharacteristic
58#4928C2×C311yescharacteristic
59#4653C2×C312yes—
60#4649C2×C312yes—
61C22×C32×C4C2312yes—
62C22×C32×C4C2312yes—
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2311yescharacteristic
68C22×C3×Dic3C2311yescharacteristic
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C32×C4⋊C4—24no—
73C32×C4⋊C4—22no—
74C32×C4⋊C4C2×C414yes—
75C32×C42—22no—
76C3×C4⋊Dic3—22no—
77C3×C4⋊Dic3C2×C418yes—
78C3×C4⋊Dic3C2×C414yes—
79C3×Dic3⋊C4—24no—
80C3×Dic3⋊C4C2×C418yes—
81C3×C4×Dic3—22no—
82C3×C4×Dic3—22no—
83C3×C4×Dic3—22no—
84C3×C4×Dic3—22no—
85C3×C4×Dic3—24no—
86C3×C4×Dic3—24no—
87C3×C4×Dic3C2×C414yes—
88C3×C4×Dic3Q814yes—
89C4×#125—31noSylow
90C3×#125—38no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4—22no—
94C2×C3×C4⋊C4—32no—
95C2×C3×C4⋊C4—32no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—32no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4C2×D311yescharacteristic
100C2×C3×C4⋊C4C2×D312yes—
101C2×C3×C4⋊C4C2×D311yescharacteristic
102C2×C3×C4⋊C4C22×C311yescharacteristic
103C2×C3×C4⋊C4C22×C312yes—
104C2×C3×C4⋊C4C22×C311yescharacteristic
105C2×C3×C42—21no—
106C2×C3×C42—31no—
107C2×C3×C42—31no—
108C2×C3×C42—31no—
109C2×C3×C42—31no—
110C2×C3×C42—31no—
111C2×C3×C42—31no—
112C2×C3×C42—32no—
113C2×C3×C42—32no—
114C2×C3×C42C2×D311yescharacteristic
115C2×C3×C42C22×C311yescharacteristic
116C2×C4⋊Dic3C22×C311yescharacteristic
117C2×C4⋊Dic3C22×C312yes—
118C2×C4⋊Dic3C22×C311yescharacteristic
119C2×Dic3⋊C4C22×C312yes—
120C2×Dic3⋊C4C22×C312yes—
121C2×C4×Dic3C22×C311yescharacteristic
122C2×C4×Dic3C22×C312yes—
123C2×C4×Dic3C22×C312yes—
124C2×C4×Dic3C22×C311yescharacteristic
125C2×C4×Dic3C22×C311yescharacteristic
126C2×C4×Dic3C22×C311yescharacteristic
127C2×C4×Dic3C22×C311yescharacteristic
128C2×C4×Dic3C22×C311yescharacteristic
129#890C3×C418yescomplemented
130C3×#95—22no—
131C3×#95—32no—
132C3×#95—32no—
133C3×#95—32no—
134C3×#95—32no—
135C3×#95—32no—
136C3×#95C2×D312yes—
137C3×#95C22×C312yes—
138C3⋊#95C22×C312yes—
139C3⋊#95C22×C312yes—
140C3⋊#95C22×C312yes—
141C3⋊#95C22×C312yes—
142C3⋊#95C22×C312yes—
143C23×C32C2411yescharacteristic
144C2×C32×C4—22no—
145C2×C32×C4—21no—
146C2×C32×C4—21no—
147C2×C32×C4—21no—
148C2×C32×C4—21no—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4C22×C414yes—
154C2×C32×C4C22×C412yes—
155C2×C32×C4C2×Q812yes—
156C2×C32×C4#4112yes—
157C2×C32×C4#4112yes—
158C2×C32×C4#4112yes—
159C2×C3×Dic3—21no—
160C2×C3×Dic3—21no—
161C2×C3×Dic3—21no—
162C2×C3×Dic3—21no—
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×Dic3C22×C412yes—
171C2×C3×Dic3C22×C412yes—
172C2×C3×Dic3C22×C414yes—
173C2×C3×Dic3C2×Q812yes—
174C2×C3×Dic3C2×Q812yes—
175C2×C3×Dic3#4112yes—
176C2×C3×Dic3#4112yes—
177C2×#125—31no—
178#389—31no—
179#389C3×D311yescharacteristic
180#387—32no—
181#387—32no—
182#382—31no—
183C4×C4⋊C4—32no—
184C4×C4⋊C4—31no—
185C4×C4⋊C4—31no—
186C4×C4⋊C4—32no—
187C43—31no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—22no—
191C22×C3×C4—21no—
192C22×C3×C4—22no—
193C22×C3×C4—31no—
194C22×C3×C4—31no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—32no—
198C22×C3×C4—32no—
199C22×C3×C4C22×D312yes—
200C22×C3×C4C22×D312yes—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C23×C312yes—
205C22×C3×C4C23×C312yes—
206C22×C3×C4C23×C311yescharacteristic
207C22×C3×C4C23×C311yescharacteristic
208C22×C3×C4C23×C311yescharacteristic
209C22×Dic3C23×C312yes—
210C22×Dic3C23×C311yescharacteristic
211C22×Dic3C23×C311yescharacteristic
212C22×Dic3C23×C312yes—
213C22×Dic3C23×C311yescharacteristic
214C22×Dic3C23×C311yescharacteristic
215C3×C4⋊C4—24no—
216C3×C4⋊C4—22no—
217C3×C4⋊C4—24no—
218C3×C4⋊C4—22no—
219C3×C4⋊C4—24no—
220C3×C4⋊C4—38no—
221C3×C4⋊C4—38no—
222C3×C4⋊C4—34no—
223C3×C4⋊C4—42no—
224C3×C4⋊C4—44no—
225C3×C4⋊C4—62no—
226C3×C4⋊C4—64no—
227C3×C4⋊C4C4×D314yes—
228C3×C4⋊C4C2×C3×C414yes—
229C3×C42—22no—
230C3×C42—22no—
231C3×C42—34no—
232C3×C42—34no—
233C3×C42—42no—
234C3×C42—62no—
235C3×C42—62no—
236C3×C42—64no—
237C3×C42—64no—
238C3×C42—62no—
239C3×C42—62no—
240C4⋊Dic3—22no—
241C4⋊Dic3C2×C3×C418yes—
242C4⋊Dic3C2×C3×C414yes—
243Dic3⋊C4—24no—
244Dic3⋊C4C2×C3×C418yes—
245C4×Dic3—22no—
246C4×Dic3—22no—
247C4×Dic3—22no—
248C4×Dic3—22no—
249C4×Dic3—24no—
250C4×Dic3—24no—
251C4×Dic3C2×C3×C414yes—
252C4×Dic3C3×Q814yes—
253C22×C32C23×C411yescharacteristic
254C22×C32C22×Q811yescharacteristic
255C22×C32C2×#4111yescharacteristic
256C22×C32C2×#4111yescharacteristic
257C22×C32C2×#4111yescharacteristic
258C22×C32C2×#4111yescharacteristic
259C22×C32C2×#4111yescharacteristic
260C32×C4—24no—
261C32×C4—22no—
262C32×C4—22no—
263C32×C4—42no—
264C32×C4C4×Q814yes—
265C3×Dic3—22no—
266C3×Dic3—22no—
267C3×Dic3—24no—
268C3×Dic3—22no—
269C3×Dic3—42no—
270C3×Dic3#12514yescomplemented
271#125—38no—
272C2×C4⋊C4—32no—
273C2×C4⋊C4—32no—
274C2×C4⋊C4—31no—
275C2×C4⋊C4—31no—
276C2×C4⋊C4—32no—
277C2×C4⋊C4C2×C3×D311yescharacteristic
278C2×C4⋊C4C2×C3×D312yes—
279C2×C4⋊C4C2×C3×D311yescharacteristic
280C2×C42—31no—
281C2×C42—31no—
282C2×C42—31no—
283C2×C42—31no—
284C2×C42—31no—
285C2×C42—31no—
286C2×C42—32no—
287C2×C42—32no—
288C2×C42C2×C3×D311yescharacteristic
289#95—32no—
290#95—32no—
291#95—32no—
292#95—32no—
293#95—32no—
294#95C2×C3×D312yes—
295C23×C3—21no—
296C23×C3C23×D311yescharacteristic
297C23×C3C24×C311yescharacteristic
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
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—32no—
323C2×C3×C4—32no—
324C2×C3×C4—32no—
325C2×C3×C4—32no—
326C2×C3×C4—32no—
327C2×C3×C4—34no—
328C2×C3×C4—32no—
329C2×C3×C4—41no—
330C2×C3×C4—41no—
331C2×C3×C4—42no—
332C2×C3×C4—41no—
333C2×C3×C4—42no—
334C2×C3×C4—41no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
337C2×C3×C4—42no—
338C2×C3×C4—61no—
339C2×C3×C4—61no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—62no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4C2×C4×D314yes—
350C2×C3×C4C2×C4×D312yes—
351C2×C3×C4#23712yes—
352C2×C3×C4#23712yes—
353C2×C3×C4D3×Q812yes—
354C2×C3×C4#23912yes—
355C2×C3×C4C22×C3×C414yes—
356C2×C3×C4C22×C3×C412yes—
357C2×C3×C4C2×C3×Q812yes—
358C2×C3×C4C3×#4112yes—
359C2×C3×C4C3×#4112yes—
360C2×C3×C4C3×#4112yes—
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—21no—
366C2×Dic3—21no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3C22×C3×C412yes—
373C2×Dic3C22×C3×C412yes—
374C2×Dic3C22×C3×C414yes—
375C2×Dic3C2×C3×Q812yes—
376C2×Dic3C2×C3×Q812yes—
377C2×Dic3C3×#4112yes—
378C2×Dic3C3×#4112yes—
379C2×C32C2×C4×Q811yescharacteristic
380C2×C32C4×#4111yescharacteristic
381C2×C32C4×#4111yescharacteristic
382C2×C32C2×#12511yescharacteristic
383C2×C32#52911yescharacteristic
384C2×C32#52911yescharacteristic
385C2×C32#53311yescharacteristic
386C22×C4—31no—
387C22×C4—31no—
388C22×C4—31no—
389C22×C4—31no—
390C22×C4—32no—
391C22×C4—32no—
392C22×C4C22×C3×D312yes—
393C22×C4C22×C3×D312yes—
394C22×C4C22×C3×D311yescharacteristic
395C22×C4C22×C3×D311yescharacteristic
396C22×C4C22×C3×D311yescharacteristic
397C4⋊C4—24no—
398C4⋊C4—22no—
399C4⋊C4—38no—
400C4⋊C4—38no—
401C4⋊C4—34no—
402C4⋊C4—62no—
403C4⋊C4—64no—
404C4⋊C4C3×C4×D314yes—
405C42—22no—
406C42—34no—
407C42—34no—
408C42—62no—
409C42—62no—
410C42—64no—
411C42—64no—
412C42—62no—
413C42—62no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3C22×C4×D311yescharacteristic
422C22×C3C2×#23711yescharacteristic
423C22×C3C2×#23711yescharacteristic
424C22×C3C2×D3×Q811yescharacteristic
425C22×C3C2×#23911yescharacteristic
426C22×C3D3×#4111yescharacteristic
427C22×C3D3×#4111yescharacteristic
428C22×C3C23×C3×C411yescharacteristic
429C22×C3C22×C3×Q811yescharacteristic
430C22×C3C2×C3×#4111yescharacteristic
431C22×C3C2×C3×#4111yescharacteristic
432C22×C3C2×C3×#4111yescharacteristic
433C22×C3C2×C3×#4111yescharacteristic
434C22×C3C2×C3×#4111yescharacteristic
435C3×C4—24no—
436C3×C4—24no—
437C3×C4—22no—
438C3×C4—22no—
439C3×C4—22no—
440C3×C4—22no—
441C3×C4—24no—
442C3×C4—34no—
443C3×C4—44no—
444C3×C4—42no—
445C3×C4—42no—
446C3×C4—42no—
447C3×C4—42no—
448C3×C4—62no—
449C3×C4—62no—
450C3×C4—62no—
451C3×C4—64no—
452C3×C4—82no—
453C3×C4—122no—
454C3×C4#88714yes—
455C3×C4C3×C4×Q814yes—
456Dic3—22no—
457Dic3—22no—
458Dic3—24no—
459Dic3—22no—
460Dic3—42no—
461Dic3C3×#12514yescomplemented
462C32C4×#12511yescharacteristic, complemented, Sylow
463C23C23×C3×D311yescharacteristic
464C2×C4—21no—
465C2×C4—21no—
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—32no—
477C2×C4—32no—
478C2×C4—34no—
479C2×C4—32no—
480C2×C4—61no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—62no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4C2×C3×C4×D314yes—
492C2×C4C2×C3×C4×D312yes—
493C2×C4C3×#23712yes—
494C2×C4C3×#23712yes—
495C2×C4C3×D3×Q812yes—
496C2×C4C3×#23912yes—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3C2×#88711yescharacteristic
505C2×C3C4×#23711yescharacteristic
506C2×C3C4×#23911yescharacteristic
507C2×C3#560011yescharacteristic
508C2×C3#562411yescharacteristic
509C2×C3D3×#12511yescharacteristic
510C2×C3#572811yescharacteristic
511C2×C3C2×C3×C4×Q811yescharacteristic
512C2×C3C3×C4×#4111yescharacteristic
513C2×C3C3×C4×#4111yescharacteristic
514C2×C3C2×C3×#12511yescharacteristic
515C2×C3C3×#52911yescharacteristic
516C2×C3C3×#52911yescharacteristic
517C2×C3C3×#53311yescharacteristic
518C22C22×C3×C4×D311yescharacteristic
519C22C2×C3×#23711yescharacteristic
520C22C2×C3×#23711yescharacteristic
521C22C2×C3×D3×Q811yescharacteristic
522C22C2×C3×#23911yescharacteristic
523C22C3×D3×#4111yescharacteristic
524C22C3×D3×#4111yescharacteristic
525C4—24no—
526C4—22no—
527C4—22no—
528C4—34no—
529C4—42no—
530C4—62no—
531C4—62no—
532C4—64no—
533C4—62no—
534C4—122no—
535C4C3×#88714yes—
536C3—21no—
537C3#7596611yescharacteristic, direct product factor
538C3C3×C4×#12511yescharacteristic, complemented
539C2C2×C3×#88711yescharacteristic
540C2C3×C4×#23711yescharacteristic
541C2C3×C4×#23911yescharacteristic
542C2C3×#560011yescharacteristic
543C2C3×#562411yescharacteristic
544C2C3×D3×#12511yescharacteristic
545C2C3×#572811yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#389C2
socle, prime radicalC23×C32C24
cosocleC23×C3C24×C3
hypercenterC3×#389D3
hypocenterC3C3×C4×#125
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#389

Complements

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

NH ≅ G/Ntype
13. #75966C3direct (N × H)
31. C3×#890C4semidirect
129. #890C3×C4semidirect
270. C3×Dic3#125semidirect
461. Dic3C3×#125semidirect
462. C32C4×#125semidirect
537. C3#75966direct (N × H)
538. C3C3×C4×#125semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8902
C32×#3892
C3×#49782
C3×#49772
C3×Dic3×C4⋊C42
C3×C42×Dic32
C3×#49282
C3×#46532
C3×#46492
C3×C4×#1253
#759663