Finite Group Databasebeta

← C3×#71646 #11785309

Subgroups — C3×#71646 #11785309

Order 1152.

779 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×#41C211yesmaximal, characteristic
2C2×C3×#837C212yesmaximal
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#4924C211yesmaximal, characteristic, complemented
5C3×#4532C212yesmaximal, complemented
6C3×#1806—31nomaximal
7#71646C311yesmaximal, characteristic, direct product factor
8C2×C32×#41C2211yescharacteristic
9C32×C4×Q8C411yescharacteristic, complemented
10C32×C4×Q8C411yescharacteristic, complemented
11C32×C4×D4—21no—
12C32×C4×D4—21no—
13C32×C4×D4C411yescharacteristic, complemented
14C32×C4×D4C411yescharacteristic, complemented
15C32×#117—21no—
16C32×#117C2211yescharacteristic
17C2×C32×C42—21no—
18C2×C32×C42C2211yescharacteristic
19C2×C3×C4⋊Dic3—21no—
20C2×C3×C4×Dic3C2212yes—
21C2×C3×#208C2212yes—
22C3×#837—24no—
23C3×C3⋊#95—21no—
24C3×C4⋊(C3⋊C8)—21no—
25C3×C4⋊(C3⋊C8)—21no—
26C3×C4×#41—21no—
27C3×C4×#41D311yescharacteristic
28C3×C4×#41C2×C311yescharacteristic
29C3×#423—31no—
30C2×C3×#104—32no—
31C3×C4×C4⋊C4—31no—
32C2×#837C2×C312yes—
33C4×C4⋊Dic3C2×C311yescharacteristic, complemented
34#4924C2×C311yescharacteristic, complemented
35C3×#339—32no—
36#4532C2×C312yescomplemented
37C32×#41—21no—
38C32×#41—21no—
39C32×#41D412yes—
40C32×#41Q812yes—
41C2×C32×Q8C2×C411yescharacteristic
42C2×C32×D4—21no—
43C2×C32×D4C2×C411yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4—21no—
47C22×C32×C4D411yescharacteristic
48C22×C32×C4D411yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C22×C3×Dic3—22no—
51C32×C4⋊C4—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4C2×C411yescharacteristic
54C32×C4⋊C4C2×C411yescharacteristic
55C32×C22⋊C4—21no—
56C32×C22⋊C4—21no—
57C32×C22⋊C4—21no—
58C32×C42—21no—
59C32×C42—21no—
60C32×C42—21no—
61C32×C42C2×C411yescharacteristic
62C32×C42C2×C411yescharacteristic
63C32×C42D411yescharacteristic
64C32×C42D411yescharacteristic
65C3×C4⋊Dic3—24no—
66C3×C4×Dic3—22no—
67C3×C4×Dic3—22no—
68C3×#208—22no—
69C3×#208—22no—
70C2×C3×C3⋊C8—22no—
71#1806—31noSylow
72C2×C3×#41—21no—
73C2×C3×#41C2×D311yescharacteristic
74C2×C3×#41C22×C311yescharacteristic
75C2×C3×M16—32no—
76C3×C4×Q8—21no—
77C3×C4×Q8—21no—
78C3×C4×Q8Dic311yescharacteristic, complemented
79C3×C4×Q8Dic311yescharacteristic, complemented
80C3×C4×Q8C3×C411yescharacteristic, complemented
81C3×C4×Q8C3×C411yescharacteristic, complemented
82C3×C4×D4—22no—
83C3×C4×D4—22no—
84C3×C4×D4—21no—
85C3×C4×D4—21no—
86C3×C4×D4—21no—
87C3×C4×D4—21no—
88C3×C4×D4—21no—
89C3×C4×D4—21no—
90C3×C4×D4Dic311yescharacteristic, complemented
91C3×C4×D4Dic311yescharacteristic, complemented
92C3×C4×D4C3×C411yescharacteristic, complemented
93C3×C4×D4C3×C411yescharacteristic, complemented
94C3×#117—22no—
95C3×#117—21no—
96C3×#117—21no—
97C3×#117—21no—
98C3×#117C2×D311yescharacteristic
99C3×#117C22×C311yescharacteristic
100C2×C3×C4⋊C4—61no—
101C2×C3×C42—22no—
102C2×C3×C42—21no—
103C2×C3×C42—21no—
104C2×C3×C42—21no—
105C2×C3×C42—32no—
106C2×C3×C42C2×D311yescharacteristic
107C2×C3×C42C22×C311yescharacteristic
108C2×C4⋊Dic3—21no—
109C2×C4×Dic3C22×C312yes—
110C2×#208C22×C312yes—
111C3×C4⋊C8—61no—
112C3×C4⋊C8—61no—
113C3×#104—64no—
114C3×#95—61no—
115#837—24no—
116C3⋊#95—21no—
117C4⋊(C3⋊C8)—21no—
118C4⋊(C3⋊C8)—21no—
119C23×C32—21no—
120C23×C32C2×D411yescharacteristic
121C32×Q8—21no—
122C32×Q8C4⋊C412yescomplemented
123C32×D4—22no—
124C32×D4—22no—
125C32×D4—21no—
126C32×D4C4⋊C412yescomplemented
127C2×C32×C4—21no—
128C2×C32×C4—22no—
129C2×C32×C4—22no—
130C2×C32×C4—21no—
131C2×C32×C4—21no—
132C2×C32×C4—22no—
133C2×C32×C4—41no—
134C2×C32×C4—42no—
135C2×C32×C4—42no—
136C2×C32×C4C22⋊C411yescharacteristic
137C2×C32×C4C22⋊C411yescharacteristic
138C2×C32×C4C22⋊C411yescharacteristic
139C2×C32×C4C22⋊C411yescharacteristic
140C2×C32×C4C22×C411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×Q811yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C2×C32×C4#4111yescharacteristic
146C2×C3×Dic3—24no—
147C2×C3×Dic3—42no—
148C2×C3×Dic3—42no—
149C3×C3⋊C8—42no—
150C4×#41C3×D311yescharacteristic
151#423—31no—
152C2×#104—32no—
153C4×C4⋊C4—31no—
154#339—32no—
155C3×#41—22no—
156C3×#41—22no—
157C3×#41—21no—
158C3×#41—21no—
159C3×#41—21no—
160C3×#41—21no—
161C3×#41—22no—
162C3×#41—22no—
163C3×#41Dic612yes—
164C3×#41D1212yes—
165C3×#41C3×D412yes—
166C3×#41C3×Q812yes—
167C2×C3×Q8—21no—
168C2×C3×Q8C2×Dic311yescharacteristic
169C2×C3×Q8C2×C3×C411yescharacteristic
170C2×C3×D4—22no—
171C2×C3×D4—21no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4C2×Dic311yescharacteristic
175C2×C3×D4C2×C3×C411yescharacteristic
176C22×C3×C4—22no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—62no—
189C22×C3×C4#6711yescharacteristic
190C22×C3×C4#6711yescharacteristic
191C22×C3×C4C3×D411yescharacteristic
192C22×C3×C4C3×D411yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C23×C311yescharacteristic
195C22×Dic3—22no—
196C3×M16—62no—
197C3×M16—62no—
198C2×C3×C8—62no—
199C3×C4⋊C4—22no—
200C3×C4⋊C4—22no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—64no—
208C3×C4⋊C4C2×Dic311yescharacteristic
209C3×C4⋊C4C2×Dic311yescharacteristic
210C3×C4⋊C4C2×C3×C411yescharacteristic
211C3×C4⋊C4C2×C3×C411yescharacteristic
212C3×C22⋊C4—22no—
213C3×C22⋊C4—22no—
214C3×C22⋊C4—22no—
215C3×C22⋊C4—21no—
216C3×C22⋊C4—21no—
217C3×C22⋊C4—21no—
218C3×C22⋊C4—21no—
219C3×C22⋊C4—21no—
220C3×C22⋊C4—21no—
221C3×C42—22no—
222C3×C42—22no—
223C3×C42—22no—
224C3×C42—21no—
225C3×C42—21no—
226C3×C42—21no—
227C3×C42—21no—
228C3×C42—21no—
229C3×C42—21no—
230C3×C42—21no—
231C3×C42—21no—
232C3×C42—21no—
233C3×C42—21no—
234C3×C42—62no—
235C3×C42—62no—
236C3×C42C2×Dic311yescharacteristic
237C3×C42C2×Dic311yescharacteristic
238C3×C42#6711yescharacteristic
239C3×C42#6711yescharacteristic
240C3×C42C2×C3×C411yescharacteristic
241C3×C42C2×C3×C411yescharacteristic
242C3×C42C3×D411yescharacteristic
243C3×C42C3×D411yescharacteristic
244C4⋊Dic3—24no—
245C4×Dic3—22no—
246C4×Dic3—22no—
247#208—22no—
248#208—22no—
249C2×C3⋊C8—22no—
250C22×C32—22no—
251C22×C32—21no—
252C22×C32—21no—
253C22×C32—41no—
254C22×C32—41no—
255C22×C32C2×C22⋊C411yescharacteristic
256C22×C32#12111yescharacteristic
257C22×C32C22⋊Q811yescharacteristic
258C32×C4—22no—
259C32×C4—21no—
260C32×C4—21no—
261C32×C4—21no—
262C32×C4—41no—
263C32×C4—41no—
264C32×C4#10412yescomplemented
265C32×C4C2×C4⋊C411yescharacteristic
266C32×C4#11711yescharacteristic
267C32×C4#12111yescharacteristic
268C32×C4C22⋊Q811yescharacteristic
269C3×Dic3—44no—
270C2×#41C2×C3×D311yescharacteristic
271C2×M16—32no—
272C4×Q8C3×Dic311yescharacteristic, complemented
273C4×Q8C3×Dic311yescharacteristic, complemented
274C4×D4—21no—
275C4×D4—21no—
276C4×D4C3×Dic311yescharacteristic, complemented
277C4×D4C3×Dic311yescharacteristic, complemented
278#117—21no—
279#117C2×C3×D311yescharacteristic
280C2×C4⋊C4—61no—
281C2×C42—21no—
282C2×C42—32no—
283C2×C42C2×C3×D311yescharacteristic
284C4⋊C8—61no—
285C4⋊C8—61no—
286#104—64no—
287#95—61no—
288C23×C3—22no—
289C23×C3—21no—
290C23×C3—21no—
291C23×C3—21no—
292C23×C3C2×#6711yescharacteristic
293C23×C3C2×C3×D411yescharacteristic
294C3×Q8—22no—
295C3×Q8—21no—
296C3×Q8—21no—
297C3×Q8—22no—
298C3×Q8C4⋊Dic312yescomplemented
299C3×Q8C3×C4⋊C412yescomplemented
300C3×D4—24no—
301C3×D4—24no—
302C3×D4—22no—
303C3×D4—22no—
304C3×D4—22no—
305C3×D4—22no—
306C3×D4—22no—
307C3×D4—21no—
308C3×D4—21no—
309C3×D4—22no—
310C3×D4C4⋊Dic312yescomplemented
311C3×D4C3×C4⋊C412yescomplemented
312C2×C3×C4—22no—
313C2×C3×C4—24no—
314C2×C3×C4—24no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
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—22no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—42no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—42no—
343C2×C3×C4—44no—
344C2×C3×C4—42no—
345C2×C3×C4—42no—
346C2×C3×C4—44no—
347C2×C3×C4—42no—
348C2×C3×C4—42no—
349C2×C3×C4—64no—
350C2×C3×C4—122no—
351C2×C3×C4—122no—
352C2×C3×C4#21711yescharacteristic
353C2×C3×C4#21711yescharacteristic
354C2×C3×C4#21711yescharacteristic
355C2×C3×C4#21711yescharacteristic
356C2×C3×C4C3×C22⋊C411yescharacteristic
357C2×C3×C4C3×C22⋊C411yescharacteristic
358C2×C3×C4C3×C22⋊C411yescharacteristic
359C2×C3×C4C3×C22⋊C411yescharacteristic
360C2×C3×C4C2×Dic611yescharacteristic
361C2×C3×C4C2×D1211yescharacteristic
362C2×C3×C4#23511yescharacteristic
363C2×C3×C4#23511yescharacteristic
364C2×C3×C4C22×Dic311yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C22×C3×C411yescharacteristic
367C2×C3×C4C2×C3×D411yescharacteristic
368C2×C3×C4C2×C3×D411yescharacteristic
369C2×C3×C4C2×C3×Q811yescharacteristic
370C2×C3×C4C3×#4111yescharacteristic
371C2×C3×C4C3×#4111yescharacteristic
372C2×Dic3—24no—
373C2×Dic3—42no—
374C2×Dic3—42no—
375C3×C8—122no—
376C3⋊C8—42no—
377C2×C32—21no—
378C2×C32—21no—
379C2×C32—42no—
380C2×C32#38011yescharacteristic
381C2×C32C2×#10411yescharacteristic
382C2×C32#42111yescharacteristic
383#41—21no—
384#41—21no—
385#41C3×Dic612yes—
386#41C3×D1212yes—
387C2×Q8C2×C3×Dic311yescharacteristic
388C2×D4—21no—
389C2×D4C2×C3×Dic311yescharacteristic
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—62no—
394C22×C4C3×#6711yescharacteristic
395C22×C4C3×#6711yescharacteristic
396C22×C4C22×C3×D311yescharacteristic
397M16—62no—
398M16—62no—
399C2×C8—62no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—64no—
403C4⋊C4C2×C3×Dic311yescharacteristic
404C4⋊C4C2×C3×Dic311yescharacteristic
405C22⋊C4—21no—
406C22⋊C4—21no—
407C22⋊C4—21no—
408C42—21no—
409C42—21no—
410C42—21no—
411C42—62no—
412C42—62no—
413C42C2×C3×Dic311yescharacteristic
414C42C2×C3×Dic311yescharacteristic
415C42C3×#6711yescharacteristic
416C42C3×#6711yescharacteristic
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—24no—
422C22×C3—22no—
423C22×C3—22no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—41no—
428C22×C3—41no—
429C22×C3—42no—
430C22×C3—42no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3#92411yescharacteristic
436C22×C3#93011yescharacteristic
437C22×C3C2×#21711yescharacteristic
438C22×C3C2×C3×C22⋊C411yescharacteristic
439C22×C3C3×#12111yescharacteristic
440C22×C3C3×C22⋊Q811yescharacteristic
441C3×C4—24no—
442C3×C4—22no—
443C3×C4—22no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—22no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—22no—
456C3×C4—41no—
457C3×C4—41no—
458C3×C4—42no—
459C3×C4—42no—
460C3×C4—41no—
461C3×C4—41no—
462C3×C4—41no—
463C3×C4—41no—
464C3×C4—124no—
465C3×C4#83712yescomplemented
466C3×C4C3×#10412yescomplemented
467C3×C4#92411yescharacteristic
468C3×C4C2×C4⋊Dic311yescharacteristic
469C3×C4#92611yescharacteristic
470C3×C4#93011yescharacteristic
471C3×C4C2×C3×C4⋊C411yescharacteristic
472C3×C4C3×#11711yescharacteristic
473C3×C4C3×#12111yescharacteristic
474C3×C4C3×C22⋊Q811yescharacteristic
475Dic3—44no—
476C32#180611yescharacteristic, complemented, Sylow
477C23—21no—
478C23C2×C3×#6711yescharacteristic
479Q8—21no—
480Q8C3×C4⋊Dic312yescomplemented
481D4—22no—
482D4—22no—
483D4—21no—
484D4C3×C4⋊Dic312yescomplemented
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—64no—
495C2×C4—122no—
496C2×C4—122no—
497C2×C4C3×#21711yescharacteristic
498C2×C4C3×#21711yescharacteristic
499C2×C4C3×#21711yescharacteristic
500C2×C4C3×#21711yescharacteristic
501C2×C4C2×C3×Dic611yescharacteristic
502C2×C4C2×C3×D1211yescharacteristic
503C2×C4C3×#23511yescharacteristic
504C2×C4C3×#23511yescharacteristic
505C2×C4C22×C3×Dic311yescharacteristic
506C2×C4C2×C3×#6711yescharacteristic
507C8—122no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—41no—
516C2×C3—41no—
517C2×C3—44no—
518C2×C3—42no—
519C2×C3—42no—
520C2×C3#521211yescharacteristic
521C2×C3C2×#83711yescharacteristic
522C2×C3#523611yescharacteristic
523C2×C3C3×#38011yescharacteristic
524C2×C3C2×C3×#10411yescharacteristic
525C2×C3C3×#42111yescharacteristic
526C22—21no—
527C22—21no—
528C22—22no—
529C22—41no—
530C22—41no—
531C22C3×#92411yescharacteristic
532C22C3×#93011yescharacteristic
533C22C2×C3×#21711yescharacteristic
534C4—22no—
535C4—21no—
536C4—21no—
537C4—21no—
538C4—41no—
539C4—41no—
540C4—124no—
541C4C3×#83712yescomplemented
542C4C3×#92411yescharacteristic
543C4C2×C3×C4⋊Dic311yescharacteristic
544C4C3×#92611yescharacteristic
545C4C3×#93011yescharacteristic
546C3—21no—
547C3#7164611yescharacteristic, direct product factor
548C3C3×#180611yescharacteristic, complemented
549C2—21no—
550C2—21no—
551C2—42no—
552C2C3×#521211yescharacteristic
553C2C2×C3×#83711yescharacteristic
554C2C3×#523611yescharacteristic
subgroupG/H
centerC2×C3×C4C2×#67
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×C4×#41C2
socleC22×C32C2×C22⋊C4
prime radicalC2×C32×#41C22
cosocleC22×C3×C4C23×C3
hypercenterC3×C4×#41D3
hypocenterC3C3×#1806
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×C4×#41

Complements

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

NH ≅ G/Ntype
3. C3×C4×C4⋊Dic3C2semidirect
4. C3×#4924C2semidirect
5. C3×#4532C2semidirect
7. #71646C3direct (N × H)
9. C32×C4×Q8C4semidirect
10. C32×C4×Q8C4semidirect
13. C32×C4×D4C4semidirect
14. C32×C4×D4C4semidirect
33. C4×C4⋊Dic3C2×C3semidirect
34. #4924C2×C3semidirect
36. #4532C2×C3semidirect
78. C3×C4×Q8Dic3semidirect
79. C3×C4×Q8Dic3semidirect
80. C3×C4×Q8C3×C4semidirect
81. C3×C4×Q8C3×C4semidirect
90. C3×C4×D4Dic3semidirect
91. C3×C4×D4Dic3semidirect
92. C3×C4×D4C3×C4semidirect
93. C3×C4×D4C3×C4semidirect
122. C32×Q8C4⋊C4semidirect
126. C32×D4C4⋊C4semidirect
264. C32×C4#104semidirect
272. C4×Q8C3×Dic3semidirect
273. C4×Q8C3×Dic3semidirect
276. C4×D4C3×Dic3semidirect
277. C4×D4C3×Dic3semidirect
298. C3×Q8C4⋊Dic3semidirect
299. C3×Q8C3×C4⋊C4semidirect
310. C3×D4C4⋊Dic3semidirect
311. C3×D4C3×C4⋊C4semidirect
465. C3×C4#837semidirect
466. C3×C4C3×#104semidirect
476. C32#1806semidirect
480. Q8C3×C4⋊Dic3semidirect
484. D4C3×C4⋊Dic3semidirect
541. C4C3×#837semidirect
547. C3#71646direct (N × H)
548. C3C3×#1806semidirect

Maximal subgroups

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

subgroupindex
C32×C4×#412
C2×C3×#8372
C3×C4×C4⋊Dic32
C3×#49242
C3×#45322
C3×#18063
#716463