Finite Group Databasebeta

← C3×#76779 #11808763

Subgroups — C3×#76779 #11808763

Order 1152.

1237 conjugacy classes of subgroups.

The subgroup lattice has 609 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#67⋊C4C211yesmaximal, characteristic
3C32×#393C211yesmaximal, characteristic, complemented
4C3×#5231C211yesmaximal, characteristic, complemented
5C3×#4961C212yesmaximal
6C3×#4953C211yesmaximal, characteristic, complemented
7C3×Dic3×C22⋊C4C212yesmaximal, complemented
8C3×#4674C211yesmaximal, characteristic, complemented
9C3×#4666C212yesmaximal, complemented
10C3×#4660C212yesmaximal, complemented
11C3×#4648C211yesmaximal, characteristic, complemented
12C3×#2398—31nomaximal
13#76779C311yesmaximal, characteristic, direct product factor
14C22×C32×Q8C2211yescharacteristic
15C22×C3×#67C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C2×C32×C22⋊C4C2212yes—
19C2×C32×C22⋊C4C2211yescharacteristic
20C2×C3×#217C2212yes—
21C3×Q8×Dic3—24no—
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×C4⋊Dic3C2212yes—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×C4×Dic3C2212yes—
29C2×C3×C4×Dic3C2212yes—
30C2×C3×C4×Dic3C2211yescharacteristic
31C3×#67⋊C4—24no—
32C32×#95C2211yescharacteristic
33C32×#95C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39C2×C3×C4×Q8—31no—
40C2×C3×C4×D4—31no—
41C2×Q8×Dic3C2×C311yescharacteristic, complemented
42C2×#67⋊C4C2×C311yescharacteristic
43C3×#400—32no—
44C3×#397—31no—
45C3×#397—31no—
46C3×#394—32no—
47C3×#393—21no—
48C3×#393—31no—
49C3×#393D311yescharacteristic, complemented
50C3×#393C2×C311yescharacteristic, complemented
51C3×C4×C22⋊C4—32no—
52C3×C4×C22⋊C4—32no—
53C3×#376—31no—
54#5231C2×C311yescharacteristic, complemented
55#4961C2×C312yes—
56#4953C2×C311yescharacteristic, complemented
57Dic3×C22⋊C4C2×C312yescomplemented
58#4674C2×C311yescharacteristic, complemented
59#4666C2×C312yescomplemented
60#4660C2×C312yescomplemented
61#4648C2×C311yescharacteristic, complemented
62C24×C32C2311yescharacteristic
63C23×C3×D3C2311yescharacteristic
64C2×C32×Q8—22no—
65C2×C32×Q8—24no—
66C22×C32×C4C2312yes—
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2312yes—
70C2×C3×#67—22no—
71C2×C3×#67—22no—
72C2×C3×#67—22no—
73C22×C3×Dic3—22no—
74C22×C3×Dic3—24no—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2311yescharacteristic
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3—24no—
82C32×C22⋊C4—22no—
83C32×C22⋊C4—24no—
84C3×#217—24no—
85C3×(C2×D3)⋊C4—24no—
86C3×(C2×D3)⋊C4—22no—
87C3×(C2×D3)⋊C4—24no—
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3—24no—
90C3×Dic3⋊C4—22no—
91C3×C4×Dic3—24no—
92C3×C4×Dic3—24no—
93C3×C4×Dic3D414yes—
94#2398—31noSylow
95C22×C3×Q8—21no—
96C22×C3×Q8C2×D311yescharacteristic
97C22×C3×Q8C22×C311yescharacteristic
98C22×C3×D4—31no—
99C23×C3×C4—31no—
100C23×C3×C4—31no—
101C22×#67C22×C311yescharacteristic
102C23×Dic3C22×C311yescharacteristic
103C22×C4×D3C22×C311yescharacteristic
104C3×C4×Q8—64no—
105C3×C4×D4—64no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C4⋊C4—32no—
108C2×C3×C4⋊C4—31no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—32no—
112C2×C3×C22⋊C4—32no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C22⋊C4—31no—
115C2×C3×C22⋊C4C2×D312yes—
116C2×C3×C22⋊C4C2×D311yescharacteristic
117C2×C3×C22⋊C4C22×C312yes—
118C2×C3×C22⋊C4C22×C311yescharacteristic
119C2×C3×C42—31no—
120C2×C3×C42—32no—
121C2×C3×C42—32no—
122C2×#217C22×C312yes—
123Q8×Dic3—24no—
124C2×(C2×D3)⋊C4C22×C312yes—
125C2×(C2×D3)⋊C4C22×C312yes—
126C2×(C2×D3)⋊C4C22×C311yescharacteristic
127C2×C4⋊Dic3C22×C312yes—
128C2×C4⋊Dic3C22×C311yescharacteristic
129C2×Dic3⋊C4C22×C311yescharacteristic
130C2×C4×Dic3C22×C312yes—
131C2×C4×Dic3C22×C312yes—
132C2×C4×Dic3C22×C311yescharacteristic
133#67⋊C4—24no—
134C3×#95—21no—
135C3×#95—22no—
136C3×#95—31no—
137C3×#95—32no—
138C3×#95—32no—
139C3×#95—32no—
140C3×#95—32no—
141C3×#95C2×D311yescharacteristic
142C3×#95C2×D312yes—
143C3×#95C22×C311yescharacteristic
144C3×#95C22×C312yes—
145C3⋊#95C22×C312yes—
146C3⋊#95C22×C311yescharacteristic
147C3⋊#95C22×C312yes—
148C3⋊#95C22×C312yes—
149C3⋊#95C22×C312yes—
150C23×C32—21no—
151C23×C32—22no—
152C23×C32—22no—
153C23×C32—21no—
154C23×C32#4112yes—
155C23×C32C2411yescharacteristic
156C22×C3×D3—21no—
157C22×C3×D3—22no—
158C22×C3×D3—22no—
159C22×C3×D3—21no—
160C22×C3×D3#4112yes—
161C32×Q8—28no—
162C2×C32×C4—22no—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4—21no—
166C2×C32×C4—22no—
167C2×C32×C4—22no—
168C2×C32×C4—22no—
169C2×C32×C4—22no—
170C2×C32×C4C2×D412yes—
171C2×C32×C4#4114yes—
172C3×#67—28no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—44no—
184C2×C3×Dic3C2×D412yes—
185C2×C3×Dic3C2×D412yes—
186C2×C3×Dic3#4114yes—
187C3×C4×D3—44no—
188C2×C4×Q8—31no—
189C2×C4×D4—31no—
190#400—32no—
191#397—31no—
192#397—31no—
193#394—32no—
194#393—31no—
195#393C3×D311yescharacteristic, complemented
196C4×C22⋊C4—32no—
197C4×C22⋊C4—32no—
198#376—31no—
199C24×C3—21no—
200C24×C3—31no—
201C24×C3C22×D311yescharacteristic
202C24×C3C23×C311yescharacteristic
203C23×D3C23×C311yescharacteristic
204C2×C3×Q8—22no—
205C2×C3×Q8—24no—
206C2×C3×Q8—22no—
207C2×C3×Q8—24no—
208C2×C3×Q8—42no—
209C2×C3×Q8—44no—
210C2×C3×D4—62no—
211C2×C3×D4—62no—
212C2×C3×D4—62no—
213C22×C3×C4—21no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—21no—
217C22×C3×C4—31no—
218C22×C3×C4—31no—
219C22×C3×C4—32no—
220C22×C3×C4—31no—
221C22×C3×C4—32no—
222C22×C3×C4—62no—
223C22×C3×C4—64no—
224C22×C3×C4—62no—
225C22×C3×C4—64no—
226C22×C3×C4C22×D312yes—
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D312yes—
230C22×C3×C4C23×C312yes—
231C22×C3×C4C23×C311yescharacteristic
232C22×C3×C4C23×C311yescharacteristic
233C22×C3×C4C23×C312yes—
234C2×#67—22no—
235C2×#67—22no—
236C2×#67—22no—
237C22×Dic3—22no—
238C22×Dic3—24no—
239C22×Dic3C23×C312yes—
240C22×Dic3C23×C311yescharacteristic
241C22×Dic3C23×C312yes—
242C22×Dic3C23×C311yescharacteristic
243C22×Dic3C23×C311yescharacteristic
244C2×C4×D3—22no—
245C2×C4×D3—24no—
246C3×C4⋊C4—62no—
247C3×C4⋊C4—64no—
248C3×C4⋊C4—62no—
249C3×C22⋊C4—22no—
250C3×C22⋊C4—24no—
251C3×C22⋊C4—22no—
252C3×C22⋊C4—24no—
253C3×C22⋊C4—42no—
254C3×C22⋊C4—44no—
255C3×C22⋊C4—64no—
256C3×C22⋊C4—64no—
257C3×C22⋊C4—62no—
258C3×C22⋊C4—64no—
259C3×C42—34no—
260C3×C42—64no—
261C3×C42—64no—
262#217—24no—
263(C2×D3)⋊C4—24no—
264(C2×D3)⋊C4—22no—
265(C2×D3)⋊C4—24no—
266C4⋊Dic3—22no—
267C4⋊Dic3—24no—
268Dic3⋊C4—22no—
269C4×Dic3—24no—
270C4×Dic3—24no—
271C4×Dic3C3×D414yes—
272C22×C32—22no—
273C22×C32—24no—
274C22×C32—41no—
275C22×C32—41no—
276C22×C32—42no—
277C22×C32C22×D411yescharacteristic
278C22×C32C2×#4112yes—
279C22×C32C2×#4111yescharacteristic
280C22×C32C2×#4111yescharacteristic
281C22×C32C2×#4112yes—
282C2×C3×D3—22no—
283C2×C3×D3—24no—
284C2×C3×D3—41no—
285C2×C3×D3—41no—
286C2×C3×D3—42no—
287C32×C4—22no—
288C32×C4—24no—
289C32×C4—41no—
290C32×C4—42no—
291C3×Dic3—22no—
292C3×Dic3—42no—
293C3×Dic3—41no—
294C3×Dic3—42no—
295C3×Dic3#12414yes—
296C22×Q8C2×C3×D311yescharacteristic
297C22×D4—31no—
298C23×C4—31no—
299C23×C4—31no—
300C4×Q8—64no—
301C4×D4—64no—
302C2×C4⋊C4—31no—
303C2×C4⋊C4—32no—
304C2×C4⋊C4—31no—
305C2×C22⋊C4—32no—
306C2×C22⋊C4—31no—
307C2×C22⋊C4—32no—
308C2×C22⋊C4—32no—
309C2×C22⋊C4C2×C3×D311yescharacteristic
310C2×C22⋊C4C2×C3×D312yes—
311C2×C42—31no—
312C2×C42—32no—
313C2×C42—32no—
314#95—31no—
315#95—32no—
316#95—32no—
317#95—32no—
318#95—32no—
319#95C2×C3×D311yescharacteristic
320#95C2×C3×D312yes—
321C23×C3—21no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—21no—
325C23×C3—21no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—22no—
331C23×C3—32no—
332C23×C3—41no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—41no—
336C23×C3—61no—
337C23×C3—62no—
338C23×C3—61no—
339C23×C3—62no—
340C23×C3#23912yes—
341C23×C3C3×#4112yes—
342C23×C3C23×D311yescharacteristic
343C23×C3C24×C311yescharacteristic
344C22×D3—21no—
345C22×D3—22no—
346C22×D3—22no—
347C22×D3—21no—
348C22×D3C3×#4112yes—
349C3×Q8—28no—
350C3×Q8—28no—
351C3×Q8—48no—
352C3×D4—68no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—21no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—21no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—24no—
371C2×C3×C4—32no—
372C2×C3×C4—34no—
373C2×C3×C4—32no—
374C2×C3×C4—42no—
375C2×C3×C4—42no—
376C2×C3×C4—42no—
377C2×C3×C4—41no—
378C2×C3×C4—42no—
379C2×C3×C4—42no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—61no—
383C2×C3×C4—61no—
384C2×C3×C4—62no—
385C2×C3×C4—61no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4—124no—
393C2×C3×C4—124no—
394C2×C3×C4D3×D412yes—
395C2×C3×C4#23714yes—
396C2×C3×C4C2×C3×D412yes—
397C2×C3×C4C3×#4114yes—
398#67—28no—
399C2×Dic3—21no—
400C2×Dic3—21no—
401C2×Dic3—22no—
402C2×Dic3—21no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—44no—
410C2×Dic3C2×C3×D412yes—
411C2×Dic3C2×C3×D412yes—
412C2×Dic3C3×#4114yes—
413C4×D3—44no—
414C2×C32—42no—
415C2×C32#52511yescharacteristic
416C2×C32#52511yescharacteristic
417C2×C32C2×#12411yescharacteristic
418C2×C32#52912yes—
419C2×C32#52912yes—
420C3×D3—42no—
421C24—31no—
422C24C22×C3×D311yescharacteristic
423C2×Q8—22no—
424C2×Q8—24no—
425C2×D4—62no—
426C2×D4—62no—
427C2×D4—62no—
428C22×C4—31no—
429C22×C4—31no—
430C22×C4—32no—
431C22×C4—31no—
432C22×C4—32no—
433C22×C4—62no—
434C22×C4—64no—
435C22×C4—62no—
436C22×C4—64no—
437C22×C4C22×C3×D312yes—
438C22×C4C22×C3×D311yescharacteristic
439C22×C4C22×C3×D311yescharacteristic
440C22×C4C22×C3×D312yes—
441C4⋊C4—62no—
442C4⋊C4—64no—
443C4⋊C4—62no—
444C22⋊C4—22no—
445C22⋊C4—24no—
446C22⋊C4—64no—
447C22⋊C4—64no—
448C22⋊C4—62no—
449C22⋊C4—64no—
450C42—34no—
451C42—64no—
452C42—64no—
453C22×C3—22no—
454C22×C3—24no—
455C22×C3—24no—
456C22×C3—22no—
457C22×C3—21no—
458C22×C3—22no—
459C22×C3—21no—
460C22×C3—22no—
461C22×C3—21no—
462C22×C3—44no—
463C22×C3—42no—
464C22×C3—41no—
465C22×C3—42no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3—42no—
470C22×C3—64no—
471C22×C3—62no—
472C22×C3—81no—
473C22×C3—81no—
474C22×C3—82no—
475C22×C3—121no—
476C22×C3—121no—
477C22×C3—122no—
478C22×C3C2×D3×D411yescharacteristic
479C22×C3C2×#23712yes—
480C22×C3C2×#23911yescharacteristic
481C22×C3D3×#4112yes—
482C22×C3D3×#4111yescharacteristic
483C22×C3C22×C3×D411yescharacteristic
484C22×C3C2×C3×#4112yes—
485C22×C3C2×C3×#4111yescharacteristic
486C22×C3C2×C3×#4111yescharacteristic
487C22×C3C2×C3×#4112yes—
488C2×D3—22no—
489C2×D3—24no—
490C2×D3—41no—
491C2×D3—41no—
492C2×D3—42no—
493C3×C4—22no—
494C3×C4—24no—
495C3×C4—22no—
496C3×C4—24no—
497C3×C4—34no—
498C3×C4—42no—
499C3×C4—44no—
500C3×C4—41no—
501C3×C4—42no—
502C3×C4—41no—
503C3×C4—42no—
504C3×C4—62no—
505C3×C4—81no—
506C3×C4—82no—
507C3×C4—121no—
508C3×C4—122no—
509C3×C4—122no—
510Dic3—22no—
511Dic3—42no—
512Dic3—41no—
513Dic3—42no—
514Dic3C3×#12414yes—
515C32#239811yescharacteristic, complemented, Sylow
516C23—21no—
517C23—22no—
518C23—22no—
519C23—21no—
520C23—32no—
521C23—61no—
522C23—62no—
523C23—61no—
524C23—62no—
525C23C3×#23912yes—
526C23C23×C3×D311yescharacteristic
527Q8—28no—
528D4—68no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—32no—
538C2×C4—34no—
539C2×C4—32no—
540C2×C4—61no—
541C2×C4—61no—
542C2×C4—62no—
543C2×C4—61no—
544C2×C4—62no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—124no—
551C2×C4—124no—
552C2×C4C3×D3×D412yes—
553C2×C4C3×#23714yes—
554C2×C3—21no—
555C2×C3—22no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—22no—
559C2×C3—42no—
560C2×C3—42no—
561C2×C3—82no—
562C2×C3—122no—
563C2×C3#558611yescharacteristic
564C2×C3#562412yes—
565C2×C3#562711yescharacteristic
566C2×C3D3×#12411yescharacteristic
567C2×C3#568012yes—
568C2×C3C3×#52511yescharacteristic
569C2×C3C3×#52511yescharacteristic
570C2×C3C2×C3×#12411yescharacteristic
571C2×C3C3×#52912yes—
572C2×C3C3×#52912yes—
573D3—42no—
574C22—24no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—42no—
579C22—62no—
580C22—64no—
581C22—121no—
582C22—122no—
583C22—121no—
584C22C2×C3×D3×D411yescharacteristic
585C22C2×C3×#23712yes—
586C22C2×C3×#23911yescharacteristic
587C22C3×D3×#4112yes—
588C22C3×D3×#4111yescharacteristic
589C4—22no—
590C4—24no—
591C4—34no—
592C4—41no—
593C4—42no—
594C4—62no—
595C4—122no—
596C4—122no—
597C4—121no—
598C3—21no—
599C3#7677911yescharacteristic, direct product factor
600C3C3×#239811yescharacteristic, complemented
601C2—42no—
602C2—122no—
603C2C3×#558611yescharacteristic
604C2C3×#562412yes—
605C2C3×#562711yescharacteristic
606C2C3×D3×#12411yescharacteristic
607C2C3×#568012yes—
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#393C2
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC3×#393D3
hypocenterC3C3×#2398
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#393

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×Dic3C2semidirect
3. C32×#393C2semidirect
4. C3×#5231C2semidirect
6. C3×#4953C2semidirect
7. C3×Dic3×C22⋊C4C2semidirect
8. C3×#4674C2semidirect
9. C3×#4666C2semidirect
10. C3×#4660C2semidirect
11. C3×#4648C2semidirect
13. #76779C3direct (N × H)
41. C2×Q8×Dic3C2×C3semidirect
49. C3×#393D3semidirect
50. C3×#393C2×C3semidirect
54. #5231C2×C3semidirect
56. #4953C2×C3semidirect
57. Dic3×C22⋊C4C2×C3semidirect
58. #4674C2×C3semidirect
59. #4666C2×C3semidirect
60. #4660C2×C3semidirect
61. #4648C2×C3semidirect
195. #393C3×D3semidirect
515. C32#2398semidirect
599. C3#76779direct (N × H)
600. C3C3×#2398semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×Dic32
C2×C3×#67⋊C42
C32×#3932
C3×#52312
C3×#49612
C3×#49532
C3×Dic3×C22⋊C42
C3×#46742
C3×#46662
C3×#46602
C3×#46482
C3×#23983
#767793