Finite Group Databasebeta

← C3×#80966 #11868777

Subgroups — C3×#80966 #11868777

Order 1152.

886 conjugacy classes of subgroups.

The subgroup lattice has 593 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2C3×C4×#237C211yesmaximal, characteristic
3C32×#474C211yesmaximal, characteristic, complemented
4C3×#5094C211yesmaximal, characteristic, complemented
5C3×#5007C211yesmaximal, characteristic, complemented
6C3×#4881C212yesmaximal, complemented
7C3×#4875C212yesmaximal, complemented
8C3×#4851C211yesmaximal, characteristic, complemented
9C3×#4837C211yesmaximal, characteristic, complemented
10C3×#4771C212yesmaximal
11C3×#4761C212yesmaximal, complemented
12C3×#3079—31nomaximal
13#80966C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8—21no—
15C2×C3×#237C2211yescharacteristic
16C32×C4⋊Q8C2211yescharacteristic
17C32×C4×D4C2211yescharacteristic
18C3×#944—21no—
19C3×D4×Dic3C2211yescharacteristic
20C3×C4×#67—21no—
21C2×C3×C4×Dic3—21no—
22C2×C3×ΓL(1,𝔽25)C2212yes—
23C3×#892C2211yescharacteristic
24C3×D3×C4⋊C4—21no—
25C3×D3×C4⋊C4C2212yes—
26C3×#888—21no—
27C3×#888C2212yes—
28C3×#887C2211yescharacteristic
29C3×#67⋊C4—21no—
30C3×#877—21no—
31C3×C42×D3C2211yescharacteristic
32C3×#869C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34C32×#107C2212yes—
35C32×C4⋊C8C2211yescharacteristic
36C32×#102C2212yes—
37C3×#832C2212yes—
38C3×#817C2212yes—
39C3×#816C2212yes—
40C3×Dic3⋊C8C2212yes—
41C3×#810C2212yes—
42C3×#808C2212yes—
43C3×#807C2212yes—
44C3×C4⋊(C3⋊C8)C2211yescharacteristic
45C2×C3×C4⋊Q8—31no—
46C3×C4×#41—31no—
47D3×C4⋊Q8C2×C311yescharacteristic, complemented
48C4×#237C2×C311yescharacteristic
49C3×#477—32no—
50C3×#476—32no—
51C3×#475—31no—
52C3×#475—31no—
53C3×#474—21no—
54C3×#474—31no—
55C3×#474D311yescharacteristic, complemented
56C3×#474C2×C311yescharacteristic, complemented
57C3×#428—32no—
58C3×#423—31no—
59C3×#417—32no—
60#5094C2×C311yescharacteristic, complemented
61#5007C2×C311yescharacteristic, complemented
62#4881C2×C312yescomplemented
63#4875C2×C312yescomplemented
64#4851C2×C311yescharacteristic, complemented
65#4837C2×C311yescharacteristic, complemented
66#4771C2×C312yes—
67#4761C2×C312yescomplemented
68C2×C32×Q8—21no—
69C2×C32×D4C2311yescharacteristic
70C22×C32×C4—21no—
71C2×C3×#67—21no—
72C22×C3×Dic3—21no—
73C22×C3×Dic3—21no—
74C3×D3×Q8—44no—
75C3×#237—22no—
76C3×#237Q814yescomplemented
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3D411yescharacteristic
79C2×C3×C4×D3D411yescharacteristic
80C2×C3×C4×D3C2311yescharacteristic
81C2×C3×Dic6—21no—
82C2×C3×Dic6—22no—
83C2×C3×Dic6C2311yescharacteristic
84C2×C32×C8C2312yes—
85C32×C4⋊C4—21no—
86C32×C4⋊C4C2311yescharacteristic
87C32×C4⋊C4C2312yes—
88C32×C22⋊C4—21no—
89C32×C42C2311yescharacteristic
90C3×#217—21no—
91C3×(C2×D3)⋊C4—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2312yes—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×Dic3⋊C4—21no—
96C3×Dic3⋊C4—21no—
97C3×Dic3⋊C4—22no—
98C3×Dic3⋊C4—22no—
99C3×C4×Dic3—21no—
100C3×C4×Dic3—21no—
101C3×C4×Dic3—21no—
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C2×C3×C3⋊C8C2312yes—
106C3×ΓL(1,𝔽25)—24no—
107#3079—31noSylow
108C2×C3×#41—31no—
109C22×C3×Q8—61no—
110C2×D3×Q8—21no—
111C2×#237C22×C311yescharacteristic
112C2×C3×M16—32no—
113C3×C4⋊Q8—21no—
114C3×C4⋊Q8—32no—
115C3×C4⋊Q8—31no—
116C3×C4⋊Q8—61no—
117C3×C4⋊Q8—61no—
118C3×C4⋊Q8C2×D311yescharacteristic
119C3×C4⋊Q8C22×C311yescharacteristic
120C3×C4×Q8—31no—
121C3×C4×Q8—31no—
122C3×C4×D4—21no—
123C3×C4×D4—31no—
124C3×C4×D4—61no—
125C3×C4×D4—61no—
126C3×C4×D4C2×D311yescharacteristic
127C3×C4×D4C22×C311yescharacteristic
128C3×#117—31no—
129C3×#117—61no—
130C2×C3×C4⋊C4—32no—
131C2×C3×C4⋊C4—61no—
132C2×C3×C42—31no—
133C2×C3×C42—61no—
134#944—21no—
135D4×Dic3C22×C311yescharacteristic
136C4×#67—21no—
137C2×C4×Dic3—21no—
138C2×ΓL(1,𝔽25)C22×C312yes—
139#892C22×C311yescharacteristic
140D3×C4⋊C4—21no—
141D3×C4⋊C4C22×C312yes—
142#888—21no—
143#888C22×C312yes—
144#887C22×C311yescharacteristic
145#67⋊C4—21no—
146#877—21no—
147C42×D3C22×C311yescharacteristic
148#869C22×C311yescharacteristic
149C4×Dic6C22×C311yescharacteristic
150C3×#107—22no—
151C3×#107—32no—
152C3×#107C2×D312yes—
153C3×#107C22×C312yes—
154C3×#106—32no—
155C3×#106—32no—
156C3×C4⋊C8—21no—
157C3×C4⋊C8—32no—
158C3×C4⋊C8—31no—
159C3×C4⋊C8C2×D311yescharacteristic
160C3×C4⋊C8C22×C311yescharacteristic
161C3×#103—32no—
162C3×#103—32no—
163C3×#102—22no—
164C3×#102—32no—
165C3×#102C2×D312yes—
166C3×#102C22×C312yes—
167#832C22×C312yes—
168#817C22×C312yes—
169#816C22×C312yes—
170Dic3⋊C8C22×C312yes—
171#810C22×C312yes—
172#808C22×C312yes—
173#807C22×C312yes—
174C4⋊(C3⋊C8)C22×C311yescharacteristic
175C23×C32—21no—
176C22×C3×D3C2×D411yescharacteristic
177C32×Q8—42no—
178C32×D4—21no—
179C32×D4C2×Q812yescomplemented
180C2×C32×C4—21no—
181C2×C32×C4—22no—
182C2×C32×C4—42no—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186C3×#67—24no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—24no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—42no—
192C2×C3×Dic3C2×D411yescharacteristic
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C3×C4×D3—22no—
196C3×C4×D3—22no—
197C3×C4×D3—44no—
198C3×C4×D3C2×Q812yes—
199C3×C4×D3#4112yes—
200C3×Dic6—21no—
201C3×Dic6—44no—
202C3×Dic6—42no—
203C3×Dic6C2×Q812yescomplemented
204C32×C8—22no—
205C3×C3⋊C8—22no—
206C2×C4⋊Q8—31no—
207C4×#41—31no—
208#477—32no—
209#476—32no—
210#475—31no—
211#475—31no—
212#474—31no—
213#474C3×D311yescharacteristic, complemented
214#428—32no—
215#423—31no—
216#417—32no—
217C3×#41—34no—
218C3×#41—62no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—31no—
222C2×C3×Q8—41no—
223C2×C3×Q8—62no—
224C2×C3×Q8—61no—
225C2×C3×Q8—124no—
226C2×C3×D4—21no—
227C2×C3×D4—61no—
228C2×C3×D4C22×D311yescharacteristic
229C2×C3×D4C23×C311yescharacteristic
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C22×C3×C4—31no—
235C22×C3×C4—41no—
236C22×C3×C4—62no—
237C22×C3×C4—61no—
238C22×C3×C4—61no—
239C2×#67—21no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242D3×Q8—44no—
243#237—22no—
244#237C3×Q814yescomplemented
245C2×C4×D3—22no—
246C2×C4×D3C3×D411yescharacteristic
247C2×C4×D3C3×D411yescharacteristic
248C2×C4×D3C23×C311yescharacteristic
249C2×Dic6—21no—
250C2×Dic6—22no—
251C2×Dic6C23×C311yescharacteristic
252C3×M16—64no—
253C2×C3×C8—22no—
254C2×C3×C8—32no—
255C2×C3×C8C22×D312yes—
256C2×C3×C8C23×C312yes—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—22no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—32no—
262C3×C4⋊C4—31no—
263C3×C4⋊C4—41no—
264C3×C4⋊C4—62no—
265C3×C4⋊C4—62no—
266C3×C4⋊C4—61no—
267C3×C4⋊C4—61no—
268C3×C4⋊C4—61no—
269C3×C4⋊C4C22×D312yes—
270C3×C4⋊C4C22×D311yescharacteristic
271C3×C4⋊C4C23×C311yescharacteristic
272C3×C4⋊C4C23×C312yes—
273C3×C22⋊C4—21no—
274C3×C22⋊C4—21no—
275C3×C22⋊C4—41no—
276C3×C22⋊C4—61no—
277C3×C22⋊C4—61no—
278C3×C42—21no—
279C3×C42—31no—
280C3×C42—31no—
281C3×C42—31no—
282C3×C42—61no—
283C3×C42—61no—
284C3×C42—61no—
285C3×C42C22×D311yescharacteristic
286C3×C42C23×C311yescharacteristic
287#217—21no—
288(C2×D3)⋊C4—21no—
289C4⋊Dic3—21no—
290C4⋊Dic3C23×C312yes—
291C4⋊Dic3C23×C311yescharacteristic
292Dic3⋊C4—21no—
293Dic3⋊C4—21no—
294Dic3⋊C4—22no—
295Dic3⋊C4—22no—
296C4×Dic3—21no—
297C4×Dic3—21no—
298C4×Dic3—21no—
299C4×Dic3C3×D411yescharacteristic
300C4×Dic3C3×D411yescharacteristic
301C4×Dic3C23×C311yescharacteristic
302C2×C3⋊C8C23×C312yes—
303ΓL(1,𝔽25)—24no—
304C22×C32—22no—
305C22×C32—41no—
306C22×C32—41no—
307C22×C32C22×D411yescharacteristic
308C2×C3×D3—21no—
309C2×C3×D3—21no—
310C2×C3×D3C22⋊Q812yes—
311C32×C4—21no—
312C32×C4—42no—
313C32×C4—41no—
314C32×C4AGL(1,ℤ/8)12yes—
315C32×C4C22×Q811yescharacteristic
316C32×C4C2×#4111yescharacteristic
317C3×Dic3—22no—
318C3×Dic3—21no—
319C3×Dic3—42no—
320C3×Dic3—41no—
321C3×Dic3C22⋊Q812yes—
322C3×Dic3#13712yes—
323C2×#41—31no—
324C22×Q8—61no—
325C2×M16—32no—
326C4⋊Q8—32no—
327C4⋊Q8—31no—
328C4⋊Q8—61no—
329C4⋊Q8—61no—
330C4⋊Q8C2×C3×D311yescharacteristic
331C4×Q8—31no—
332C4×Q8—31no—
333C4×D4—31no—
334C4×D4—61no—
335C4×D4—61no—
336C4×D4C2×C3×D311yescharacteristic
337#117—31no—
338#117—61no—
339C2×C4⋊C4—32no—
340C2×C4⋊C4—61no—
341C2×C42—31no—
342C2×C42—61no—
343#107—32no—
344#107C2×C3×D312yes—
345#106—32no—
346#106—32no—
347C4⋊C8—32no—
348C4⋊C8—31no—
349C4⋊C8C2×C3×D311yescharacteristic
350#103—32no—
351#103—32no—
352#102—32no—
353#102C2×C3×D312yes—
354C23×C3—21no—
355C23×C3—21no—
356C23×C3—31no—
357C23×C3—41no—
358C22×D3C2×C3×D411yescharacteristic
359C3×Q8—32no—
360C3×Q8—42no—
361C3×Q8—42no—
362C3×Q8—61no—
363C3×Q8—82no—
364C3×Q8—124no—
365C3×Q8—122no—
366C3×D4—21no—
367C3×D4—21no—
368C3×D4—22no—
369C3×D4—41no—
370C3×D4—64no—
371C3×D4D3×Q812yescomplemented
372C3×D4C2×C3×Q812yescomplemented
373C2×C3×C4—21no—
374C2×C3×C4—22no—
375C2×C3×C4—21no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—31no—
381C2×C3×C4—31no—
382C2×C3×C4—32no—
383C2×C3×C4—32no—
384C2×C3×C4—31no—
385C2×C3×C4—41no—
386C2×C3×C4—42no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4—62no—
390C2×C3×C4—64no—
391C2×C3×C4—61no—
392C2×C3×C4—62no—
393C2×C3×C4—61no—
394C2×C3×C4—62no—
395C2×C3×C4—82no—
396C2×C3×C4—122no—
397C2×C3×C4—124no—
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4D3×D411yescharacteristic
400C2×C3×C4C2×C3×D411yescharacteristic
401C2×C3×C4C2×C3×D411yescharacteristic
402C2×C3×C4C23×D311yescharacteristic
403C2×C3×C4C24×C311yescharacteristic
404#67—24no—
405C2×Dic3—21no—
406C2×Dic3—24no—
407C2×Dic3—21no—
408C2×Dic3—22no—
409C2×Dic3—42no—
410C2×Dic3C2×C3×D411yescharacteristic
411C2×Dic3C2×C3×D411yescharacteristic
412C2×Dic3C2×C3×D411yescharacteristic
413C4×D3—22no—
414C4×D3—22no—
415C4×D3—44no—
416C4×D3C2×C3×Q812yes—
417C4×D3C3×#4112yes—
418Dic6—21no—
419Dic6—44no—
420Dic6—42no—
421Dic6C2×C3×Q812yescomplemented
422C3×C8—22no—
423C3×C8—22no—
424C3×C8—42no—
425C3×C8—62no—
426C3⋊C8—22no—
427C2×C32—42no—
428C2×C32C2×C22⋊Q811yescharacteristic
429C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
430C2×C32C2×#13711yescharacteristic
431C3×D3—22no—
432#41—34no—
433#41—62no—
434C2×Q8—21no—
435C2×Q8—31no—
436C2×Q8—62no—
437C2×Q8—61no—
438C2×Q8—124no—
439C2×D4—61no—
440C2×D4C22×C3×D311yescharacteristic
441C22×C4—21no—
442C22×C4—31no—
443C22×C4—31no—
444C22×C4—31no—
445C22×C4—62no—
446C22×C4—61no—
447C22×C4—61no—
448M16—64no—
449C2×C8—32no—
450C2×C8C22×C3×D312yes—
451C4⋊C4—21no—
452C4⋊C4—32no—
453C4⋊C4—31no—
454C4⋊C4—62no—
455C4⋊C4—62no—
456C4⋊C4—61no—
457C4⋊C4—61no—
458C4⋊C4—61no—
459C4⋊C4C22×C3×D312yes—
460C4⋊C4C22×C3×D311yescharacteristic
461C22⋊C4—21no—
462C22⋊C4—61no—
463C22⋊C4—61no—
464C42—31no—
465C42—31no—
466C42—31no—
467C42—61no—
468C42—61no—
469C42—61no—
470C42C22×C3×D311yescharacteristic
471C22×C3—22no—
472C22×C3—22no—
473C22×C3—21no—
474C22×C3—32no—
475C22×C3—42no—
476C22×C3—41no—
477C22×C3—41no—
478C22×C3—41no—
479C22×C3—41no—
480C22×C3—61no—
481C22×C3—61no—
482C22×C3—81no—
483C22×C3—81no—
484C22×C3C2×D3×D411yescharacteristic
485C22×C3C22×C3×D411yescharacteristic
486C2×D3—21no—
487C2×D3—21no—
488C2×D3C3×C22⋊Q812yes—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—22no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—32no—
495C3×C4—32no—
496C3×C4—41no—
497C3×C4—42no—
498C3×C4—41no—
499C3×C4—41no—
500C3×C4—42no—
501C3×C4—61no—
502C3×C4—62no—
503C3×C4—81no—
504C3×C4—82no—
505C3×C4—122no—
506C3×C4—121no—
507C3×C4#91112yes—
508C3×C4C3×AGL(1,ℤ/8)12yes—
509C3×C4C2×D3×Q811yescharacteristic
510C3×C4D3×#4111yescharacteristic
511C3×C4C22×C3×Q811yescharacteristic
512C3×C4C2×C3×#4111yescharacteristic
513Dic3—21no—
514Dic3—22no—
515Dic3—42no—
516Dic3—41no—
517Dic3C3×C22⋊Q812yes—
518Dic3C3×#13712yes—
519C32#307911yescharacteristic, complemented, Sylow
520C23—21no—
521C23—31no—
522Q8—32no—
523Q8—42no—
524Q8—61no—
525Q8—124no—
526Q8—122no—
527D4—21no—
528D4—64no—
529D4C3×D3×Q812yescomplemented
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—31no—
533C2×C4—31no—
534C2×C4—32no—
535C2×C4—32no—
536C2×C4—31no—
537C2×C4—42no—
538C2×C4—62no—
539C2×C4—64no—
540C2×C4—61no—
541C2×C4—62no—
542C2×C4—61no—
543C2×C4—62no—
544C2×C4—122no—
545C2×C4—124no—
546C2×C4C3×D3×D411yescharacteristic
547C2×C4C3×D3×D411yescharacteristic
548C2×C4C23×C3×D311yescharacteristic
549C8—22no—
550C8—62no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—42no—
555C2×C3—42no—
556C2×C3—62no—
557C2×C3—82no—
558C2×C3D3×C22⋊Q811yescharacteristic
559C2×C3C2×#91111yescharacteristic
560C2×C3D3×#13711yescharacteristic
561C2×C3C2×C3×C22⋊Q811yescharacteristic
562C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
563C2×C3C2×C3×#13711yescharacteristic
564D3—22no—
565C22—22no—
566C22—32no—
567C22—41no—
568C22—41no—
569C22—61no—
570C22—61no—
571C22C2×C3×D3×D411yescharacteristic
572C4—21no—
573C4—32no—
574C4—32no—
575C4—41no—
576C4—42no—
577C4—61no—
578C4—62no—
579C4—122no—
580C4—121no—
581C4C3×#91112yes—
582C4C2×C3×D3×Q811yescharacteristic
583C4C3×D3×#4111yescharacteristic
584C3—21no—
585C3#8096611yescharacteristic, direct product factor
586C3C3×#307911yescharacteristic, complemented
587C2—42no—
588C2—62no—
589C2C3×D3×C22⋊Q811yescharacteristic
590C2C2×C3×#91111yescharacteristic
591C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#474C2
socleC22×C32C22×D4
prime radicalC2×C3×#237C22
hypercenterC3×#474D3
hypocenterC3C3×#3079
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#474

Complements

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

NH ≅ G/Ntype
1. C3×D3×C4⋊Q8C2semidirect
3. C32×#474C2semidirect
4. C3×#5094C2semidirect
5. C3×#5007C2semidirect
6. C3×#4881C2semidirect
7. C3×#4875C2semidirect
8. C3×#4851C2semidirect
9. C3×#4837C2semidirect
11. C3×#4761C2semidirect
13. #80966C3direct (N × H)
47. D3×C4⋊Q8C2×C3semidirect
55. C3×#474D3semidirect
56. C3×#474C2×C3semidirect
60. #5094C2×C3semidirect
61. #5007C2×C3semidirect
62. #4881C2×C3semidirect
63. #4875C2×C3semidirect
64. #4851C2×C3semidirect
65. #4837C2×C3semidirect
67. #4761C2×C3semidirect
76. C3×#237Q8semidirect
179. C32×D4C2×Q8semidirect
203. C3×Dic6C2×Q8semidirect
213. #474C3×D3semidirect
244. #237C3×Q8semidirect
371. C3×D4D3×Q8semidirect
372. C3×D4C2×C3×Q8semidirect
421. Dic6C2×C3×Q8semidirect
519. C32#3079semidirect
529. D4C3×D3×Q8semidirect
585. C3#80966direct (N × H)
586. C3C3×#3079semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
C3×C4×#2372
C32×#4742
C3×#50942
C3×#50072
C3×#48812
C3×#48752
C3×#48512
C3×#48372
C3×#47712
C3×#47612
C3×#30793
#809663