Finite Group Databasebeta

← C3×#72044 #11792428

Subgroups — C3×#72044 #11792428

Order 1152.

1189 conjugacy classes of subgroups.

The subgroup lattice has 655 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×D8C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic, complemented
3C22×C3×#213C211yesmaximal, characteristic, complemented
4C3×#5221C211yesmaximal, characteristic, complemented
5C2×C3×#832C211yesmaximal, characteristic, complemented
6C2×C3×#821C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8C3×#2011—31nomaximal
9#72044C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C22×C32×D4C2211yescharacteristic
12C22×C3×#67—22no—
13C22×C3×D12C2211yescharacteristic
14C2×C32×D8—22no—
15C2×C32×D8—22no—
16C2×C32×D8—22no—
17C22×C32×C8C2211yescharacteristic
18C2×C3×#217—22no—
19C3×#940—22no—
20C3×#940—22no—
21C2×C3×#213—22no—
22C2×C3×#213—22no—
23C2×C3×#213—22no—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C3×#832—22no—
28C3×#821—22no—
29C22×C3×D8—21no—
30C22×C3×D8—31no—
31C22×C3×D8D311yescharacteristic, complemented
32C22×C3×D8C2×C311yescharacteristic, complemented
33C2×C3×#127—31no—
34C2×#940C2×C311yescharacteristic, complemented
35C22×#213C2×C311yescharacteristic, complemented
36C2×C3×#102—31no—
37C2×C3×#102—31no—
38C3×#390—31no—
39#5221C2×C311yescharacteristic, complemented
40C2×#832C2×C311yescharacteristic, complemented
41C2×#821C2×C311yescharacteristic, complemented
42C3×#336—31no—
43#4550C2×C311yescharacteristic, complemented
44C24×C32—21no—
45C24×C32—21no—
46C23×C3×D3—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4—21no—
51C2×C32×D4—21no—
52C2×C32×D4—21no—
53C2×C32×D4—21no—
54C2×C32×D4—21no—
55C2×C32×D4—21no—
56C2×C32×D4—21no—
57C2×C32×D4D412yes—
58C2×C32×D4D412yescomplemented
59C22×C32×C4C2311yescharacteristic
60C2×C3×#67—28no—
61C2×C3×#67—44no—
62C2×C3×#67—44no—
63C22×C3×Dic3—21no—
64C22×C3×Dic3D412yes—
65C2×C3×D12—21no—
66C2×C3×D12—21no—
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12D412yes—
71C32×D8—28no—
72C2×C32×C8—21no—
73C2×C32×C8—21no—
74C2×C32×C8D412yescomplemented
75C3×#217—44no—
76C3×#213—28no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3—21no—
79C3×C4×Dic3—21no—
80C3×C4×Dic3—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8—21no—
83C2×C3×C3⋊C8D412yescomplemented
84#2011—31noSylow
85C22×C3×D4—21no—
86C22×C3×D4—21no—
87C22×C3×D4—31no—
88C22×C3×D4—62no—
89C22×C3×D4C2×D311yescharacteristic
90C22×C3×D4C2×D311yescharacteristic
91C22×C3×D4C22×C311yescharacteristic
92C22×C3×D4C22×C311yescharacteristic
93C22×#67—22no—
94C22×D12C22×C311yescharacteristic
95C2×C3×D8—24no—
96C2×C3×D8—24no—
97C2×C3×D8—24no—
98C2×C3×D8—22no—
99C2×C3×D8—22no—
100C2×C3×D8—22no—
101C2×C3×D8—22no—
102C2×C3×D8—22no—
103C2×C3×D8—22no—
104C2×C3×D8—62no—
105C2×C3×D8—62no—
106C2×C3×D8—62no—
107C22×C3×C8—21no—
108C22×C3×C8—31no—
109C22×C3×C8C2×D311yescharacteristic
110C22×C3×C8C22×C311yescharacteristic
111C3×#127—62no—
112C3×#127—62no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C22⋊C4—62no—
115C2×C3×C42—31no—
116C2×#217—22no—
117#940—22no—
118#940—22no—
119C2×#213—22no—
120C2×#213—22no—
121C2×#213—22no—
122C2×C4⋊Dic3C22×C311yescharacteristic
123C2×C4×Dic3C22×C311yescharacteristic
124C22×C3⋊C8C22×C311yescharacteristic
125C3×#102—62no—
126C3×#102—62no—
127#832—22no—
128#821—22no—
129C23×C32—22no—
130C23×C32—22no—
131C23×C32—41no—
132C23×C32—41no—
133C23×C32—41no—
134C23×C32—41no—
135C23×C32—42no—
136C23×C32—42no—
137C23×C32—42no—
138C23×C32—42no—
139C23×C32C2×D411yescharacteristic
140C22×C3×D3—22no—
141C22×C3×D3—41no—
142C22×C3×D3—41no—
143C22×C3×D3—42no—
144C22×C3×D3—42no—
145C32×D4—22no—
146C32×D4—22no—
147C32×D4—22no—
148C32×D4—22no—
149C32×D4—41no—
150C32×D4—41no—
151C32×D4—41no—
152C32×D4—41no—
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4#4111yescharacteristic
159C3×#67—416no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—41no—
163C2×C3×Dic3—42no—
164C2×C3×Dic3D814yescomplemented
165C3×D12—22no—
166C3×D12—22no—
167C3×D12—41no—
168C3×D12—41no—
169C32×C8—22no—
170C3×C3⋊C8—22no—
171C22×D8—31no—
172C22×D8C3×D311yescharacteristic, complemented
173C2×#127—31no—
174C2×#102—31no—
175C2×#102—31no—
176#390—31no—
177#336—31no—
178C24×C3—21no—
179C24×C3—21no—
180C24×C3—21no—
181C24×C3—21no—
182C24×C3—41no—
183C24×C3—41no—
184C24×C3—61no—
185C23×D3—21no—
186C2×C3×D4—22no—
187C2×C3×D4—22no—
188C2×C3×D4—22no—
189C2×C3×D4—22no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4—21no—
201C2×C3×D4—21no—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—22no—
211C2×C3×D4—22no—
212C2×C3×D4—32no—
213C2×C3×D4—41no—
214C2×C3×D4—41no—
215C2×C3×D4—41no—
216C2×C3×D4—41no—
217C2×C3×D4—41no—
218C2×C3×D4—41no—
219C2×C3×D4—68no—
220C2×C3×D4—61no—
221C2×C3×D4—61no—
222C2×C3×D4—61no—
223C2×C3×D4—61no—
224C2×C3×D4—61no—
225C2×C3×D4—124no—
226C2×C3×D4—124no—
227C2×C3×D4#6712yes—
228C2×C3×D4#6712yescomplemented
229C2×C3×D4C3×D412yes—
230C2×C3×D4C3×D412yescomplemented
231C22×C3×C4—21no—
232C22×C3×C4—32no—
233C22×C3×C4—61no—
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C23×C311yescharacteristic
236C2×#67—28no—
237C2×#67—44no—
238C2×#67—44no—
239C22×Dic3—21no—
240C22×Dic3C3×D412yes—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12C3×D412yes—
247C3×D8—216no—
248C3×D8—28no—
249C3×D8—28no—
250C3×D8—68no—
251C2×C3×C8—22no—
252C2×C3×C8—22no—
253C2×C3×C8—21no—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—22no—
258C2×C3×C8—32no—
259C2×C3×C8—61no—
260C2×C3×C8—61no—
261C2×C3×C8#6712yescomplemented
262C2×C3×C8C3×D412yescomplemented
263C3×C4⋊C4—61no—
264C3×C4⋊C4—61no—
265C3×C22⋊C4—124no—
266C3×C42—61no—
267C3×C42—61no—
268#217—44no—
269#213—28no—
270C4⋊Dic3—21no—
271C4⋊Dic3—21no—
272C4×Dic3—21no—
273C4×Dic3—21no—
274C2×C3⋊C8—21no—
275C2×C3⋊C8—21no—
276C2×C3⋊C8C3×D412yescomplemented
277C22×C32—42no—
278C22×C32—42no—
279C22×C32—44no—
280C22×C32—44no—
281C22×C32—82no—
282C22×C32—82no—
283C22×C32—81no—
284C22×C32—81no—
285C22×C32—81no—
286C22×C32—81no—
287C22×C32#12011yescharacteristic
288C22×C32#12111yescharacteristic
289C22×C32#12711yescharacteristic
290C22×C32C2×D812yes—
291C22×C32AGL(1,ℤ/8)12yes—
292C2×C3×D3—42no—
293C2×C3×D3—44no—
294C2×C3×D3—82no—
295C2×C3×D3—81no—
296C2×C3×D3—81no—
297C32×C4#12011yescharacteristic
298C32×C4#12011yescharacteristic
299C32×C4#12111yescharacteristic
300C32×C4#12111yescharacteristic
301C3×Dic3—24no—
302C3×Dic3—81no—
303C22×D4—31no—
304C22×D4—62no—
305C22×D4C2×C3×D311yescharacteristic
306C22×D4C2×C3×D311yescharacteristic
307C2×D8—22no—
308C2×D8—22no—
309C2×D8—22no—
310C2×D8—62no—
311C2×D8—62no—
312C2×D8—62no—
313C22×C8—31no—
314C22×C8C2×C3×D311yescharacteristic
315#127—62no—
316#127—62no—
317C2×C4⋊C4—31no—
318C2×C22⋊C4—62no—
319C2×C42—31no—
320#102—62no—
321#102—62no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—21no—
327C23×C3—42no—
328C23×C3—42no—
329C23×C3—42no—
330C23×C3—42no—
331C23×C3—42no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—41no—
338C23×C3—41no—
339C23×C3—41no—
340C23×C3—41no—
341C23×C3—41no—
342C23×C3—41no—
343C23×C3—41no—
344C23×C3—41no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—62no—
350C23×C3—82no—
351C23×C3—82no—
352C23×C3—82no—
353C23×C3—82no—
354C23×C3—122no—
355C23×C3—122no—
356C23×C3—121no—
357C23×C3—121no—
358C23×C3D3×D411yescharacteristic
359C23×C3C2×C3×D411yescharacteristic
360C22×D3—22no—
361C22×D3—41no—
362C22×D3—41no—
363C22×D3—42no—
364C22×D3—42no—
365C3×D4—24no—
366C3×D4—24no—
367C3×D4—22no—
368C3×D4—22no—
369C3×D4—22no—
370C3×D4—22no—
371C3×D4—22no—
372C3×D4—22no—
373C3×D4—22no—
374C3×D4—22no—
375C3×D4—42no—
376C3×D4—42no—
377C3×D4—42no—
378C3×D4—42no—
379C3×D4—42no—
380C3×D4—42no—
381C3×D4—41no—
382C3×D4—41no—
383C3×D4—41no—
384C3×D4—41no—
385C3×D4—41no—
386C3×D4—41no—
387C3×D4—41no—
388C3×D4—41no—
389C3×D4—62no—
390C3×D4—62no—
391C3×D4—1216no—
392C3×D4—121no—
393C3×D4—121no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—34no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—122no—
404C2×C3×C4—121no—
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4D3×D411yescharacteristic
407C2×C3×C4#23711yescharacteristic
408C2×C3×C4C2×#6711yescharacteristic
409C2×C3×C4C2×#6711yescharacteristic
410C2×C3×C4C2×#6711yescharacteristic
411C2×C3×C4C2×C3×D411yescharacteristic
412C2×C3×C4C2×C3×D411yescharacteristic
413C2×C3×C4C2×C3×D411yescharacteristic
414C2×C3×C4C2×C3×D411yescharacteristic
415C2×C3×C4C2×C3×D411yescharacteristic
416C2×C3×C4C3×#4111yescharacteristic
417#67—416no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—41no—
421C2×Dic3—42no—
422C2×Dic3C3×D814yescomplemented
423D12—22no—
424D12—22no—
425D12—41no—
426D12—41no—
427C3×C8—24no—
428C3×C8—22no—
429C3×C8—22no—
430C3×C8—62no—
431C3⋊C8—22no—
432C2×C32—82no—
433C2×C32—82no—
434C2×C32#39211yescharacteristic
435C2×C32#44712yes—
436C2×C32#45912yes—
437C2×C32#49311yescharacteristic
438C2×C32#49611yescharacteristic
439C3×D3—82no—
440C24—21no—
441C24—21no—
442C24—61no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—32no—
454C2×D4—68no—
455C2×D4—61no—
456C2×D4—61no—
457C2×D4—61no—
458C2×D4—61no—
459C2×D4—61no—
460C2×D4—124no—
461C2×D4—124no—
462C2×D4C3×#6712yes—
463C2×D4C3×#6712yescomplemented
464C22×C4—32no—
465C22×C4—61no—
466C22×C4C22×C3×D311yescharacteristic
467D8—28no—
468D8—68no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—32no—
472C2×C8—61no—
473C2×C8—61no—
474C2×C8C3×#6712yescomplemented
475C4⋊C4—61no—
476C4⋊C4—61no—
477C22⋊C4—124no—
478C42—61no—
479C42—61no—
480C22×C3—22no—
481C22×C3—22no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—44no—
486C22×C3—44no—
487C22×C3—44no—
488C22×C3—44no—
489C22×C3—42no—
490C22×C3—42no—
491C22×C3—42no—
492C22×C3—42no—
493C22×C3—44no—
494C22×C3—44no—
495C22×C3—84no—
496C22×C3—84no—
497C22×C3—84no—
498C22×C3—82no—
499C22×C3—82no—
500C22×C3—82no—
501C22×C3—82no—
502C22×C3—84no—
503C22×C3—82no—
504C22×C3—81no—
505C22×C3—81no—
506C22×C3—81no—
507C22×C3—81no—
508C22×C3—82no—
509C22×C3—82no—
510C22×C3—82no—
511C22×C3—81no—
512C22×C3—81no—
513C22×C3—81no—
514C22×C3—81no—
515C22×C3—124no—
516C22×C3—122no—
517C22×C3—242no—
518C22×C3—241no—
519C22×C3—241no—
520C22×C3D3×D812yes—
521C22×C3#91112yes—
522C22×C3#93711yescharacteristic
523C22×C3#93911yescharacteristic
524C22×C3#94011yescharacteristic
525C22×C3C3×#12011yescharacteristic
526C22×C3C3×#12111yescharacteristic
527C22×C3C3×#12711yescharacteristic
528C22×C3C2×C3×D812yes—
529C22×C3C3×AGL(1,ℤ/8)12yes—
530C2×D3—42no—
531C2×D3—44no—
532C2×D3—82no—
533C2×D3—81no—
534C2×D3—81no—
535C3×C4—21no—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—64no—
540C3×C4—241no—
541C3×C4#93711yescharacteristic
542C3×C4#93811yescharacteristic
543C3×C4#93911yescharacteristic
544C3×C4#95311yescharacteristic
545C3×C4C3×#12011yescharacteristic
546C3×C4C3×#12011yescharacteristic
547C3×C4C3×#12111yescharacteristic
548C3×C4C3×#12111yescharacteristic
549Dic3—24no—
550Dic3—81no—
551C32#201111yescharacteristic, complemented, Sylow
552C23—22no—
553C23—22no—
554C23—42no—
555C23—42no—
556C23—42no—
557C23—42no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—62no—
563C23—122no—
564C23—122no—
565C23—121no—
566C23—121no—
567C23C3×D3×D411yescharacteristic
568D4—22no—
569D4—22no—
570D4—22no—
571D4—22no—
572D4—41no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—62no—
577D4—62no—
578D4—1216no—
579D4—121no—
580D4—121no—
581C2×C4—34no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—122no—
585C2×C4—121no—
586C2×C4C3×D3×D411yescharacteristic
587C2×C4C3×D3×D411yescharacteristic
588C2×C4C3×#23711yescharacteristic
589C2×C4C2×C3×#6711yescharacteristic
590C2×C4C2×C3×#6711yescharacteristic
591C2×C4C2×C3×#6711yescharacteristic
592C8—22no—
593C8—62no—
594C2×C3—21no—
595C2×C3—22no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—22no—
599C2×C3—84no—
600C2×C3—84no—
601C2×C3—82no—
602C2×C3—82no—
603C2×C3—82no—
604C2×C3—82no—
605C2×C3—242no—
606C2×C3#515012yes—
607C2×C3#515111yescharacteristic
608C2×C3#515411yescharacteristic
609C2×C3#515612yes—
610C2×C3#522311yescharacteristic
611C2×C3C3×#39211yescharacteristic
612C2×C3C3×#44712yes—
613C2×C3C3×#45912yes—
614C2×C3C3×#49311yescharacteristic
615C2×C3C3×#49611yescharacteristic
616D3—82no—
617C22—42no—
618C22—42no—
619C22—44no—
620C22—44no—
621C22—82no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—82no—
627C22—122no—
628C22—124no—
629C22—242no—
630C22—241no—
631C22—241no—
632C22C3×D3×D812yes—
633C22C3×#91112yes—
634C22C3×#93711yescharacteristic
635C22C3×#93911yescharacteristic
636C22C3×#94011yescharacteristic
637C4—64no—
638C4—241no—
639C4C3×#93711yescharacteristic
640C4C3×#93811yescharacteristic
641C4C3×#93911yescharacteristic
642C4C3×#95311yescharacteristic
643C3—21no—
644C3#7204411yescharacteristic, direct product factor
645C3C3×#201111yescharacteristic, complemented
646C2—82no—
647C2—82no—
648C2—242no—
649C2C3×#515012yes—
650C2C3×#515111yescharacteristic
651C2C3×#515411yescharacteristic
652C2C3×#515612yes—
653C2C3×#522311yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC22×C32×D8C2
socleC23×C32C2×D4
hypercenterC22×C3×D8D3
hypocenterC3C3×#2011
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C22×C3×D8

Complements

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

NH ≅ G/Ntype
1. C22×C32×D8C2semidirect
2. C2×C3×#940C2semidirect
3. C22×C3×#213C2semidirect
4. C3×#5221C2semidirect
5. C2×C3×#832C2semidirect
6. C2×C3×#821C2semidirect
7. C3×#4550C2semidirect
9. #72044C3direct (N × H)
31. C22×C3×D8D3semidirect
32. C22×C3×D8C2×C3semidirect
34. C2×#940C2×C3semidirect
35. C22×#213C2×C3semidirect
39. #5221C2×C3semidirect
40. C2×#832C2×C3semidirect
41. C2×#821C2×C3semidirect
43. #4550C2×C3semidirect
58. C2×C32×D4D4semidirect
74. C2×C32×C8D4semidirect
83. C2×C3×C3⋊C8D4semidirect
164. C2×C3×Dic3D8semidirect
172. C22×D8C3×D3semidirect
228. C2×C3×D4#67semidirect
230. C2×C3×D4C3×D4semidirect
261. C2×C3×C8#67semidirect
262. C2×C3×C8C3×D4semidirect
276. C2×C3⋊C8C3×D4semidirect
422. C2×Dic3C3×D8semidirect
463. C2×D4C3×#67semidirect
474. C2×C8C3×#67semidirect
551. C32#2011semidirect
644. C3#72044direct (N × H)
645. C3C3×#2011semidirect

Maximal subgroups

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

subgroupindex
C22×C32×D82
C2×C3×#9402
C22×C3×#2132
C3×#52212
C2×C3×#8322
C2×C3×#8212
C3×#45502
C3×#20113
#720443