Finite Group Databasebeta

← C3×#68666 #11786355

Subgroups — C3×#68666 #11786355

Order 1152.

755 conjugacy classes of subgroups.

The subgroup lattice has 555 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×C8C211yesmaximal, characteristic
2C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
3C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
4C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
5C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C32×#336C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8C3×#1850—31nomaximal
9#68666C311yesmaximal, characteristic, direct product factor
10C22×C3×C4×D3C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4C411yescharacteristic
15C2×C3×(C2×D3)⋊C4C411yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×C3×D3×C8—22no—
20C2×C3×D3×C8—22no—
21C2×C3×D3×C8—22no—
22C3×C3⋊#95C411yescharacteristic
23C3×C3⋊#95C411yescharacteristic
24C3×(C2×D3)⋊C8—22no—
25C3×Dic3⋊C8—22no—
26C3×C4⋊(C3⋊C8)—22no—
27C23×C3×C8—31no—
28C22×D3×C8C2×C311yescharacteristic
29C2×C3×C4⋊C8—31no—
30C2×C3×C4⋊C8—31no—
31C2×C3×C22⋊C8—31no—
32C3×C4×C22⋊C4—31no—
33C2×(C2×D3)⋊C8C2×C311yescharacteristic
34C2×Dic3⋊C8C2×C311yescharacteristic, complemented
35C4×(C2×D3)⋊C4C2×C311yescharacteristic
36C2×C4⋊(C3⋊C8)C2×C311yescharacteristic, complemented
37C3×#336—21no—
38C3×#336—31no—
39C3×#336D311yescharacteristic, complemented
40C3×#336C2×C311yescharacteristic, complemented
41#4550C2×C311yescharacteristic, complemented
42C23×C3×D3C2×C411yescharacteristic
43C22×C32×C4C2×C411yescharacteristic
44C22×C32×C4C2×C411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3×Dic3C2×C411yescharacteristic
47C22×C3×Dic3C2×C411yescharacteristic
48C22×C3×Dic3C2×C411yescharacteristic
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3—21no—
53C2×C3×C4×D3D412yes—
54C2×C3×C4×D3Q812yes—
55C2×C32×C8—21no—
56C2×C32×C8—21no—
57C2×C32×C8—21no—
58C2×C32×C8—21no—
59C2×C32×C8—21no—
60C2×C32×C8D412yes—
61C32×C42—21no—
62C32×C42—21no—
63C3×(C2×D3)⋊C4—22no—
64C3×(C2×D3)⋊C4C814yescomplemented
65C3×C4×Dic3—21no—
66C3×C4×Dic3—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8D412yes—
73C3×D3×C8—28no—
74#1850—31noSylow
75C23×C3×C4—31no—
76C22×C4×D3C22×C311yescharacteristic
77C22×C3×C8—21no—
78C22×C3×C8—21no—
79C22×C3×C8—31no—
80C22×C3×C8—31no—
81C22×C3×C8—62no—
82C22×C3×C8—62no—
83C22×C3×C8—62no—
84C22×C3×C8C2×D311yescharacteristic
85C22×C3×C8C2×D311yescharacteristic
86C22×C3×C8C22×C311yescharacteristic
87C22×C3×C8C22×C311yescharacteristic
88C2×C3×C22⋊C4—31no—
89C2×C3×C22⋊C4—31no—
90C2×C3×C42—21no—
91C2×C3×C42—31no—
92C2×C3×C42C2×D311yescharacteristic
93C2×C3×C42C22×C311yescharacteristic
94C2×(C2×D3)⋊C4C3×C411yescharacteristic
95C2×(C2×D3)⋊C4C3×C411yescharacteristic
96C2×C4×Dic3C22×C311yescharacteristic
97C22×C3⋊C8C22×C311yescharacteristic
98C22×C3⋊C8C22×C311yescharacteristic
99C2×D3×C8—22no—
100C2×D3×C8—22no—
101C2×D3×C8—22no—
102C3×C4⋊C8—62no—
103C3×C4⋊C8—62no—
104C3×C22⋊C8—62no—
105C3×#95—31no—
106C3×#95—31no—
107C3⋊#95C3×C411yescharacteristic
108C3⋊#95C3×C411yescharacteristic
109(C2×D3)⋊C8—22no—
110Dic3⋊C8—22no—
111C4⋊(C3⋊C8)—22no—
112C23×C32C22×C411yescharacteristic
113C22×C3×D3—21no—
114C22×C3×D3—21no—
115C22×C3×D3—21no—
116C22×C3×D3—21no—
117C22×C3×D3C4⋊C412yes—
118C22×C3×D3C2×C812yes—
119C22×C3×D3M1612yes—
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4—21no—
125C2×C32×C4C2×C812yescomplemented
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×Q811yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3C4⋊C412yes—
140C2×C3×Dic3C2×C812yescomplemented
141C3×C4×D3—22no—
142C3×C4×D3—22no—
143C3×C4×D3—22no—
144C3×C4×D3—22no—
145C32×C8—22no—
146C32×C8—41no—
147C3×C3⋊C8—22no—
148C3×C3⋊C8—41no—
149C23×C8—31no—
150C2×C4⋊C8—31no—
151C2×C4⋊C8—31no—
152C2×C22⋊C8—31no—
153C4×C22⋊C4—31no—
154#336—31no—
155#336C3×D311yescharacteristic, complemented
156C24×C3—31no—
157C23×D3C2×C3×C411yescharacteristic
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—31no—
162C22×C3×C4—31no—
163C22×C3×C4—32no—
164C22×C3×C4—32no—
165C22×C3×C4—31no—
166C22×C3×C4—61no—
167C22×C3×C4—61no—
168C22×C3×C4—61no—
169C22×C3×C4—61no—
170C22×C3×C4C4×D311yescharacteristic
171C22×C3×C4C4×D311yescharacteristic
172C22×C3×C4C2×C3×C411yescharacteristic
173C22×C3×C4C2×C3×C411yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C23×C311yescharacteristic
176C22×Dic3C2×C3×C411yescharacteristic
177C22×Dic3C2×C3×C411yescharacteristic
178C22×Dic3C2×C3×C411yescharacteristic
179C2×C4×D3—21no—
180C2×C4×D3—21no—
181C2×C4×D3—21no—
182C2×C4×D3—21no—
183C2×C4×D3C3×D412yes—
184C2×C4×D3C3×Q812yes—
185C2×C3×C8—21no—
186C2×C3×C8—21no—
187C2×C3×C8—21no—
188C2×C3×C8—21no—
189C2×C3×C8—22no—
190C2×C3×C8—21no—
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C2×C3×C8—21no—
195C2×C3×C8—21no—
196C2×C3×C8—22no—
197C2×C3×C8—32no—
198C2×C3×C8—41no—
199C2×C3×C8—41no—
200C2×C3×C8—41no—
201C2×C3×C8—41no—
202C2×C3×C8—68no—
203C2×C3×C8—61no—
204C2×C3×C8—61no—
205C2×C3×C8—61no—
206C2×C3×C8—61no—
207C2×C3×C8—61no—
208C2×C3×C8D1212yes—
209C2×C3×C8C3×D412yes—
210C3×C22⋊C4—34no—
211C3×C22⋊C4—62no—
212C3×C42—21no—
213C3×C42—21no—
214C3×C42—21no—
215C3×C42—21no—
216C3×C42—41no—
217C3×C42—41no—
218C3×C42—61no—
219C3×C42—61no—
220(C2×D3)⋊C4—22no—
221(C2×D3)⋊C4C3×C814yescomplemented
222C4×Dic3—21no—
223C4×Dic3—21no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—21no—
229C2×C3⋊C8C3×D412yes—
230D3×C8—28no—
231C22×C32C2×C4⋊C411yescharacteristic
232C22×C32C4×D411yescharacteristic
233C22×C32C4×D411yescharacteristic
234C22×C32C22×C811yescharacteristic
235C22×C32C2×M1611yescharacteristic
236C22×C32#13111yescharacteristic
237C22×C32#13111yescharacteristic
238C2×C3×D3—22no—
239C2×C3×D3—22no—
240C2×C3×D3—22no—
241C2×C3×D3—22no—
242C2×C3×D3—22no—
243C2×C3×D3—22no—
244C2×C3×D3C4⋊C814yescomplemented
245C32×C4—22no—
246C32×C4—41no—
247C32×C4#12011yescharacteristic
248C32×C4C22⋊Q811yescharacteristic
249C32×C4C22⋊Q811yescharacteristic
250C32×C4#12311yescharacteristic
251C3×Dic3—22no—
252C3×Dic3—22no—
253C3×Dic3—41no—
254C23×C4—31no—
255C22×C8—31no—
256C22×C8—31no—
257C22×C8—62no—
258C22×C8—62no—
259C22×C8—62no—
260C22×C8C2×C3×D311yescharacteristic
261C22×C8C2×C3×D311yescharacteristic
262C2×C22⋊C4—31no—
263C2×C22⋊C4—31no—
264C2×C42—31no—
265C2×C42C2×C3×D311yescharacteristic
266C4⋊C8—62no—
267C4⋊C8—62no—
268C22⋊C8—62no—
269#95—31no—
270#95—31no—
271C23×C3—21no—
272C23×C3—32no—
273C23×C3—32no—
274C23×C3—32no—
275C23×C3—61no—
276C23×C3—61no—
277C23×C3—61no—
278C23×C3—61no—
279C23×C3C2×C4×D311yescharacteristic
280C23×C3C22×C3×C411yescharacteristic
281C22×D3—21no—
282C22×D3—21no—
283C22×D3—21no—
284C22×D3—21no—
285C22×D3C3×C4⋊C412yes—
286C22×D3C2×C3×C812yes—
287C22×D3C3×M1612yes—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—22no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—32no—
307C2×C3×C4—32no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—61no—
313C2×C3×C4—61no—
314C2×C3×C4—61no—
315C2×C3×C4—61no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—61no—
321C2×C3×C4—61no—
322C2×C3×C4—61no—
323C2×C3×C4D3×C812yescomplemented
324C2×C3×C4C2×C3×C812yescomplemented
325C2×C3×C4C2×D1211yescharacteristic
326C2×C3×C4#23511yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4#23711yescharacteristic
330C2×C3×C4D3×Q811yescharacteristic
331C2×C3×C4C2×C3×D411yescharacteristic
332C2×C3×C4C2×C3×D411yescharacteristic
333C2×C3×C4C2×C3×D411yescharacteristic
334C2×C3×C4C2×C3×Q811yescharacteristic
335C2×C3×C4C3×#4111yescharacteristic
336C2×C3×C4C3×#4111yescharacteristic
337C2×Dic3—21no—
338C2×Dic3—21no—
339C2×Dic3—21no—
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3C3×C4⋊C412yes—
345C2×Dic3C2×C3×C812yescomplemented
346C4×D3—22no—
347C4×D3—22no—
348C4×D3—22no—
349C4×D3—22no—
350C3×C8—22no—
351C3×C8—22no—
352C3×C8—42no—
353C3×C8—42no—
354C3×C8—41no—
355C3×C8—41no—
356C3×C8—62no—
357C3×C8—121no—
358C3⋊C8—22no—
359C3⋊C8—41no—
360C2×C32#38511yescharacteristic
361C2×C32C2×C4⋊C811yescharacteristic
362C2×C32#42411yescharacteristic
363C2×C32C8×D411yescharacteristic
364C2×C32C8×D411yescharacteristic
365C2×C32#43511yescharacteristic
366C2×C32#43511yescharacteristic
367C3×D3—24no—
368C24—31no—
369C22×C4—31no—
370C22×C4—31no—
371C22×C4—32no—
372C22×C4—32no—
373C22×C4—31no—
374C22×C4—61no—
375C22×C4—61no—
376C22×C4—61no—
377C22×C4—61no—
378C22×C4C3×C4×D311yescharacteristic
379C22×C4C3×C4×D311yescharacteristic
380C22×C4C22×C3×D311yescharacteristic
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—32no—
387C2×C8—68no—
388C2×C8—61no—
389C2×C8—61no—
390C2×C8—61no—
391C2×C8—61no—
392C2×C8—61no—
393C2×C8C3×D1212yes—
394C22⋊C4—34no—
395C22⋊C4—62no—
396C42—21no—
397C42—21no—
398C42—61no—
399C42—61no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—34no—
408C22×C3—62no—
409C22×C3—62no—
410C22×C3—62no—
411C22×C3—62no—
412C22×C3—62no—
413C22×C3—62no—
414C22×C3C4×D1211yescharacteristic
415C22×C3#67⋊C411yescharacteristic
416C22×C3D3×C4⋊C411yescharacteristic
417C22×C3C2×D3×C811yescharacteristic
418C22×C3#90111yescharacteristic
419C22×C3D3×M1611yescharacteristic
420C22×C3#90711yescharacteristic
421C22×C3C2×C3×C4⋊C411yescharacteristic
422C22×C3C3×C4×D411yescharacteristic
423C22×C3C3×C4×D411yescharacteristic
424C22×C3C22×C3×C811yescharacteristic
425C22×C3C2×C3×M1611yescharacteristic
426C22×C3C3×#13111yescharacteristic
427C22×C3C3×#13111yescharacteristic
428C2×D3—22no—
429C2×D3—22no—
430C2×D3—22no—
431C2×D3—22no—
432C2×D3—22no—
433C2×D3—22no—
434C2×D3C3×C4⋊C814yescomplemented
435C3×C4—22no—
436C3×C4—22no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—42no—
442C3×C4—42no—
443C3×C4—41no—
444C3×C4—41no—
445C3×C4—62no—
446C3×C4—62no—
447C3×C4—121no—
448C3×C4#88211yescharacteristic
449C3×C4#88311yescharacteristic
450C3×C4#89611yescharacteristic
451C3×C4#89711yescharacteristic
452C3×C4C3×#12011yescharacteristic
453C3×C4C3×C22⋊Q811yescharacteristic
454C3×C4C3×C22⋊Q811yescharacteristic
455C3×C4C3×#12311yescharacteristic
456Dic3—22no—
457Dic3—22no—
458Dic3—41no—
459C32#185011yescharacteristic, complemented, Sylow
460C23—32no—
461C23—32no—
462C23—32no—
463C23—61no—
464C23—61no—
465C23—61no—
466C23—61no—
467C23C2×C3×C4×D311yescharacteristic
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—32no—
474C2×C4—32no—
475C2×C4—61no—
476C2×C4—61no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—61no—
484C2×C4—61no—
485C2×C4—61no—
486C2×C4C3×D3×C812yescomplemented
487C2×C4C2×C3×D1211yescharacteristic
488C2×C4C3×#23511yescharacteristic
489C2×C4C3×D3×D411yescharacteristic
490C2×C4C3×D3×D411yescharacteristic
491C2×C4C3×#23711yescharacteristic
492C2×C4C3×D3×Q811yescharacteristic
493C8—22no—
494C8—41no—
495C8—62no—
496C8—121no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—64no—
505C2×C3#466811yescharacteristic
506C2×C3C8×D1211yescharacteristic
507C2×C3#470611yescharacteristic
508C2×C3#67⋊C811yescharacteristic
509C2×C3#472811yescharacteristic
510C2×C3D3×C4⋊C811yescharacteristic
511C2×C3#483911yescharacteristic
512C2×C3C3×#38511yescharacteristic
513C2×C3C2×C3×C4⋊C811yescharacteristic
514C2×C3C3×#42411yescharacteristic
515C2×C3C3×C8×D411yescharacteristic
516C2×C3C3×C8×D411yescharacteristic
517C2×C3C3×#43511yescharacteristic
518C2×C3C3×#43511yescharacteristic
519D3—24no—
520C22—34no—
521C22—62no—
522C22—62no—
523C22—62no—
524C22—62no—
525C22—62no—
526C22—62no—
527C22C3×C4×D1211yescharacteristic
528C22C3×#67⋊C411yescharacteristic
529C22C3×D3×C4⋊C411yescharacteristic
530C22C2×C3×D3×C811yescharacteristic
531C22C3×#90111yescharacteristic
532C22C3×D3×M1611yescharacteristic
533C22C3×#90711yescharacteristic
534C4—22no—
535C4—41no—
536C4—62no—
537C4—62no—
538C4—121no—
539C4C3×#88211yescharacteristic
540C4C3×#88311yescharacteristic
541C4C3×#89611yescharacteristic
542C4C3×#89711yescharacteristic
543C3—21no—
544C3#6866611yescharacteristic, direct product factor
545C3C3×#185011yescharacteristic, complemented
546C2—64no—
547C2C3×#466811yescharacteristic
548C2C3×C8×D1211yescharacteristic
549C2C3×#470611yescharacteristic
550C2C3×#67⋊C811yescharacteristic
551C2C3×#472811yescharacteristic
552C2C3×D3×C4⋊C811yescharacteristic
553C2C3×#483911yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D3
commutatorC22×C3C22×C3×C8
FrattiniC22×C4C22×C3×D3
FittingC32×#336C2
socleC23×C32C22×C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C3×C4C23×C3
hypercenterC3×#336D3
hypocenterC3C3×#1850
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×#336

Complements

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

NH ≅ G/Ntype
3. C2×C3×Dic3⋊C8C2semidirect
5. C2×C3×C4⋊(C3⋊C8)C2semidirect
6. C32×#336C2semidirect
7. C3×#4550C2semidirect
9. #68666C3direct (N × H)
34. C2×Dic3⋊C8C2×C3semidirect
36. C2×C4⋊(C3⋊C8)C2×C3semidirect
39. C3×#336D3semidirect
40. C3×#336C2×C3semidirect
41. #4550C2×C3semidirect
64. C3×(C2×D3)⋊C4C8semidirect
125. C2×C32×C4C2×C8semidirect
140. C2×C3×Dic3C2×C8semidirect
155. #336C3×D3semidirect
221. (C2×D3)⋊C4C3×C8semidirect
244. C2×C3×D3C4⋊C8semidirect
323. C2×C3×C4D3×C8semidirect
324. C2×C3×C4C2×C3×C8semidirect
345. C2×Dic3C2×C3×C8semidirect
434. C2×D3C3×C4⋊C8semidirect
459. C32#1850semidirect
486. C2×C4C3×D3×C8semidirect
544. C3#68666direct (N × H)
545. C3C3×#1850semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×C82
C2×C3×(C2×D3)⋊C82
C2×C3×Dic3⋊C82
C3×C4×(C2×D3)⋊C42
C2×C3×C4⋊(C3⋊C8)2
C32×#3362
C3×#45502
C3×#18503
#686663