Finite Group Databasebeta

← D3×#63980 #13172691

Subgroups — D3×#63980 #13172691

Order 1728.

2182 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×D3×#67C212yesmaximal, complemented
3C2×D3×#625C211yesmaximal, characteristic, complemented
4#11723717C211yesmaximal, characteristic, complemented
5#11723637C212yesmaximal, complemented
6C3×#63980C211yesmaximal, characteristic, complemented
7#11722955C211yesmaximal, characteristic, complemented
8#11722954C212yesmaximal, complemented
9#11722953C211yesmaximal, characteristic, complemented
10D3×#3724C211yesmaximal, characteristic, complemented
11D3×(C2×D3)⋊Dic3C212yesmaximal, complemented
12C2×#63980—31nomaximal
13D3×#939—32nomaximal
14C23×C32×D3C2211yescharacteristic
15C22×C3×D32C2212yes—
16C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
17C2×C3×#638C2212yescomplemented
18C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
19C2×C32×#67C2212yescomplemented
20C2×#6295C2211yescharacteristic, complemented
21C2×#6290C2212yescomplemented
22C2×D3×C3⋊Dic3—24no—
23C2×D3×C3⋊Dic3C2211yescharacteristic
24C2×D3×C3⋊Dic3C2211yescharacteristic
25C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
26C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
27C3×D3×#67—28no—
28C2×C3×#626C2212yescomplemented
29C2×C3×#625C2212yescomplemented
30C2×C3×#625C2211yescharacteristic, complemented
31C2×C3×D3×Dic3C2212yes—
32D3×#625—24no—
33#88815C2211yescharacteristic, complemented
34#88814C2212yescomplemented
35#88806C2212yescomplemented
36#88803C2212yescomplemented
37(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
38C3×#3724C2211yescharacteristic, complemented
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C23×C3⋊Dic3—31no—
41C22×C3×#67—32no—
42C2×C3×D3×D4—32no—
43C2×D3×#67—32no—
44C2×D3×#67D312yescomplemented
45C22×#625—31no—
46C22×D3×Dic3—32no—
47C22×D3×Dic3—61no—
48#64148—32no—
49C3×#939—32no—
50#63980—31no—
51#63980—32no—
52#63980—32no—
53#63980—31no—
54#63980—31no—
55#63980—32no—
56#63980—62no—
57#63980D311yescharacteristic, direct product factor
58#63978—32no—
59#63971—32no—
60#63970—32no—
61D3×#217—32no—
62C2×#3724—31no—
63C2×(C2×D3)⋊Dic3—32no—
64D3×(C2×D3)⋊C4—32no—
65#63886—32no—
66#63885—32no—
67D3×Dic3⋊C4—32no—
68C23×C33C2311yescharacteristic
69C22×C3×C3⋊D3C2312yes—
70C22×C32×D3—22no—
71C22×C32×D3—22no—
72C22×C32×D3D414yescomplemented
73C22×C32×D3C2312yes—
74C22×C32×D3C2311yescharacteristic
75C22×C32×D3C2311yescharacteristic
76C2×C3×D32—24no—
77C2×C3×D32—24no—
78C2×C3×D32—24no—
79C2×C3⋊(C3⋊Dic3)—22no—
80C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
81C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
82C3×#638—24no—
83C2×C3×C3⋊Dic3—22no—
84C2×C3×C3⋊Dic3C2312yes—
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C2×C3×C3⋊Dic3C2311yescharacteristic
87C32×#67—24no—
88C2×C32×Dic3C2312yes—
89#6295—22no—
90#6290—24no—
91D3×C3⋊Dic3—22no—
92D3×C3⋊Dic3—22no—
93D3×C3⋊Dic3—22no—
94D3×C3⋊Dic3D414yescomplemented
95C3×#626—24no—
96C3×#625—24no—
97C3×#625—22no—
98C3×D3×Dic3—24no—
99C2×#939—92no—
100D3×#121—91no—
101C24×C32—31no—
102C23×C3×D3—21no—
103C23×C3×D3—32no—
104C23×C3×D3—32no—
105C23×C3×D3C2×D312yes—
106C22×D32C2×D312yes—
107C2×C32×D4—32no—
108C2×#638—32no—
109C2×#638C2×D312yescomplemented
110C22×C3⋊Dic3—31no—
111C22×C3⋊Dic3—32no—
112C22×C3⋊Dic3—31no—
113C22×C3⋊Dic3—31no—
114C22×C3⋊Dic3—31no—
115C22×C3⋊Dic3—31no—
116C22×C3⋊Dic3—64no—
117C22×C3⋊Dic3—61no—
118C22×C3⋊Dic3—62no—
119C22×C3⋊Dic3—121no—
120C22×C3⋊Dic3C2×D311yescharacteristic, complemented
121C2×C3×#67—22no—
122C2×C3×#67—32no—
123C2×C3×#67—32no—
124C2×C3×#67—32no—
125C2×C3×#67—32no—
126C2×C3×#67—32no—
127C2×C3×#67—32no—
128C2×C3×#67—68no—
129C2×C3×#67—62no—
130C2×C3×#67C2×D312yescomplemented
131C2×C3×#67C2×D312yescomplemented
132C22×C3×Dic3—32no—
133C22×C3×Dic3—32no—
134C22×C3×Dic3—61no—
135C3×D3×D4—68no—
136C2×C3×D12—32no—
137C2×C3×C4×D3—32no—
138D3×#67—28no—
139D3×#67—68no—
140C2×#626—32no—
141C2×#626C2×D312yescomplemented
142C2×#625—32no—
143C2×#625—32no—
144C2×#625—31no—
145C2×#625—64no—
146C2×#625—62no—
147C2×#625C2×D311yescharacteristic, complemented
148C2×#625C2×D312yescomplemented
149C2×D3×Dic3—32no—
150C2×D3×Dic3—32no—
151C2×D3×Dic3—32no—
152C2×D3×Dic3—32no—
153C2×D3×Dic3—68no—
154C2×D3×Dic3—61no—
155C2×D3×Dic3—61no—
156C2×D3×Dic3—61no—
157C2×D3×Dic3—61no—
158C2×D3×Dic3—68no—
159C2×D3×Dic3C2×D312yes—
160#3757—32no—
161#3752—32no—
162#3750—32no—
163C3×#217—32no—
164C3×(C2×D3)⋊C4—32no—
165C3×Dic3⋊C4—32no—
166#3724—31no—
167#3724—32no—
168#3724—32no—
169#3724—62no—
170#3724C2×D311yescharacteristic, complemented
171Dic3⋊Dic3—32no—
172#3722—32no—
173(C2×D3)⋊Dic3—32no—
174(C2×D3)⋊Dic3—32no—
175(C2×D3)⋊Dic3—32no—
176(C2×D3)⋊Dic3—32no—
177(C2×D3)⋊Dic3—32no—
178(C2×D3)⋊Dic3—32no—
179(C2×D3)⋊Dic3—62no—
180(C2×D3)⋊Dic3—62no—
181(C2×D3)⋊Dic3C2×D312yescomplemented
182C22×C33—21no—
183C22×C33—21no—
184C22×C33C2×D412yescomplemented
185C22×C33C2411yescharacteristic
186C2×C3×C3⋊D3—22no—
187C2×C3×C3⋊D3—22no—
188C2×C3×C3⋊D3—22no—
189C2×C32×D3—21no—
190C2×C32×D3—21no—
191C2×C32×D3—28no—
192C2×C32×D3—22no—
193C2×C32×D3—22no—
194C2×C32×D3—22no—
195C2×C32×D3C2×D412yes—
196C2×C32×D3C2×D412yes—
197C2×C32×D3C2×D412yescomplemented
198C2×C32×D3#4112yes—
199C3×D32—48no—
200C3⋊(C3⋊Dic3)—21no—
201C3⋊(C3⋊Dic3)C2×D412yescomplemented
202C3×C3⋊Dic3—21no—
203C3×C3⋊Dic3—22no—
204C3×C3⋊Dic3C2×D412yescomplemented
205C32×Dic3—22no—
206C22×C3×D4—92no—
207C22×#67—32no—
208C22×#67—92no—
209C23×Dic3—92no—
210C23×Dic3—181no—
211C2×D3×D4—32no—
212C2×D3×D4—91no—
213C22×C4×D3—91no—
214C3×#121—91no—
215C2×#217—92no—
216#939—32no—
217#939—92no—
218#939—92no—
219#939—92no—
220#939—92no—
221#939—92no—
222#939—92no—
223#939—92no—
224#939—92no—
225#939—182no—
226#938—91no—
227#930—91no—
228C2×(C2×D3)⋊C4—92no—
229C2×Dic3⋊C4—92no—
230#895—91no—
231D3×C4⋊C4—91no—
232#884—92no—
233D3×C22⋊C4—92no—
234C23×C32—21no—
235C23×C32—22no—
236C23×C32—31no—
237C23×C32—34no—
238C23×C32—31no—
239C23×C32—32no—
240C23×C32—41no—
241C23×C32—62no—
242C23×C32—62no—
243C23×C32C22×D311yescharacteristic
244C23×C32C22×D312yes—
245C22×C3⋊D3C22×D312yes—
246C22×C3×D3—24no—
247C22×C3×D3—24no—
248C22×C3×D3—24no—
249C22×C3×D3—24no—
250C22×C3×D3—24no—
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—22no—
254C22×C3×D3—32no—
255C22×C3×D3—32no—
256C22×C3×D3—62no—
257C22×C3×D3—64no—
258C22×C3×D3—64no—
259C22×C3×D3—64no—
260C22×C3×D3—64no—
261C22×C3×D3—64no—
262C22×C3×D3—64no—
263C22×C3×D3#6718yescomplemented
264C22×C3×D3C22×D312yes—
265C22×C3×D3C22×D312yes—
266C22×C3×D3C22×D312yes—
267C22×C3×D3C22×D312yes—
268C2×D32—24no—
269C2×D32—24no—
270C2×D32—24no—
271C32×D4—64no—
272C2×C32×C4—32no—
273#638—24no—
274#638—64no—
275C2×C3⋊Dic3—22no—
276C2×C3⋊Dic3—31no—
277C2×C3⋊Dic3—32no—
278C2×C3⋊Dic3—34no—
279C2×C3⋊Dic3—31no—
280C2×C3⋊Dic3—32no—
281C2×C3⋊Dic3—62no—
282C2×C3⋊Dic3—61no—
283C2×C3⋊Dic3—61no—
284C2×C3⋊Dic3—62no—
285C2×C3⋊Dic3—62no—
286C2×C3⋊Dic3—62no—
287C2×C3⋊Dic3—62no—
288C2×C3⋊Dic3—62no—
289C2×C3⋊Dic3—64no—
290C2×C3⋊Dic3—64no—
291C2×C3⋊Dic3—121no—
292C2×C3⋊Dic3—121no—
293C2×C3⋊Dic3—124no—
294C2×C3⋊Dic3—124no—
295C2×C3⋊Dic3C22×D311yescharacteristic
296C2×C3⋊Dic3C22×D312yes—
297C2×C3⋊Dic3C22×D311yescharacteristic
298C3×#67—24no—
299C3×#67—24no—
300C3×#67—44no—
301C3×#67—64no—
302C3×#67—64no—
303C3×#67—64no—
304C3×#67—64no—
305C3×#67—64no—
306C3×#67—64no—
307C3×#67—124no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—32no—
310C2×C3×Dic3—32no—
311C2×C3×Dic3—32no—
312C2×C3×Dic3—32no—
313C2×C3×Dic3—61no—
314C2×C3×Dic3—61no—
315C2×C3×Dic3—62no—
316C2×C3×Dic3—64no—
317C2×C3×Dic3—64no—
318C2×C3×Dic3—64no—
319C2×C3×Dic3C22×D312yes—
320C2×C3×Dic3C22×D312yes—
321C3×D12—64no—
322C3×C4×D3—64no—
323#626—24no—
324#626—64no—
325#625—24no—
326#625—22no—
327#625—64no—
328#625—64no—
329#625—62no—
330#625—124no—
331D3×Dic3—24no—
332D3×Dic3—38no—
333D3×Dic3—64no—
334D3×Dic3—64no—
335D3×Dic3—64no—
336D3×Dic3—64no—
337D3×Dic3—64no—
338D3×Dic3—64no—
339D3×Dic3—64no—
340C2×#121—271noSylow
341C2×C33—22no—
342C2×C33C22×D411yescharacteristic
343C2×C33C22×D411yescharacteristic
344C2×C33C2×#4111yescharacteristic
345C3×C3⋊D3—42no—
346C32×D3—22no—
347C32×D3—42no—
348C32×D3#12114yescomplemented
349C24×C3—32no—
350C24×C3—61no—
351C24×C3—92no—
352C23×D3—32no—
353C23×D3—32no—
354C23×D3D3211yescharacteristic
355C2×C3×D4—32no—
356C2×C3×D4—32no—
357C2×C3×D4—62no—
358C2×C3×D4—92no—
359C2×C3×D4—91no—
360C2×C3×D4—92no—
361C2×C3×D4—92no—
362C2×C3×D4—188no—
363C22×C3×C4—92no—
364C22×C3×C4—91no—
365C2×#67—32no—
366C2×#67—32no—
367C2×#67—32no—
368C2×#67—32no—
369C2×#67—32no—
370C2×#67—32no—
371C2×#67—62no—
372C2×#67—68no—
373C2×#67—92no—
374C2×#67—92no—
375C2×#67—92no—
376C2×#67—92no—
377C2×#67—182no—
378C2×#67—188no—
379C2×#67D3212yescomplemented
380C22×Dic3—32no—
381C22×Dic3—32no—
382C22×Dic3—61no—
383C22×Dic3—92no—
384C22×Dic3—92no—
385C22×Dic3—92no—
386C22×Dic3—92no—
387C22×Dic3—91no—
388C22×Dic3—92no—
389C22×Dic3—181no—
390C22×Dic3—181no—
391C22×Dic3—181no—
392C22×Dic3—181no—
393C22×Dic3—181no—
394C22×Dic3—182no—
395C22×Dic3—188no—
396C22×Dic3—188no—
397C22×Dic3—361no—
398D3×D4—68no—
399D3×D4—184no—
400C2×D12—32no—
401C2×D12—91no—
402C2×C4×D3—32no—
403C2×C4×D3—91no—
404C2×C4×D3—91no—
405C2×C4×D3—91no—
406C2×C4×D3—91no—
407C2×C4×D3—184no—
408C3×C4⋊C4—91no—
409C3×C22⋊C4—92no—
410#217—32no—
411#217—92no—
412#217—92no—
413#217—92no—
414#217—92no—
415#217—182no—
416(C2×D3)⋊C4—32no—
417(C2×D3)⋊C4—92no—
418(C2×D3)⋊C4—92no—
419(C2×D3)⋊C4—92no—
420(C2×D3)⋊C4—92no—
421(C2×D3)⋊C4—92no—
422(C2×D3)⋊C4—182no—
423C4⋊Dic3—91no—
424Dic3⋊C4—32no—
425Dic3⋊C4—92no—
426Dic3⋊C4—92no—
427Dic3⋊C4—92no—
428Dic3⋊C4—92no—
429Dic3⋊C4—182no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—22no—
433C22×C32—22no—
434C22×C32—22no—
435C22×C32—22no—
436C22×C32—22no—
437C22×C32—21no—
438C22×C32—22no—
439C22×C32—24no—
440C22×C32—32no—
441C22×C32—32no—
442C22×C32—32no—
443C22×C32—32no—
444C22×C32—42no—
445C22×C32—41no—
446C22×C32—42no—
447C22×C32—42no—
448C22×C32—42no—
449C22×C32—42no—
450C22×C32—68no—
451C22×C32—61no—
452C22×C32—61no—
453C22×C32—62no—
454C22×C32—62no—
455C22×C32—62no—
456C22×C32D3×D412yescomplemented
457C22×C32C2×#6714yescomplemented
458C22×C32C23×D311yescharacteristic
459C22×C32C23×D312yes—
460C2×C3⋊D3—22no—
461C2×C3⋊D3—22no—
462C2×C3⋊D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—216no—
466C2×C3×D3—22no—
467C2×C3×D3—22no—
468C2×C3×D3—216no—
469C2×C3×D3—22no—
470C2×C3×D3—22no—
471C2×C3×D3—22no—
472C2×C3×D3—22no—
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—42no—
480C2×C3×D3—42no—
481C2×C3×D3—42no—
482C2×C3×D3—62no—
483C2×C3×D3—62no—
484C2×C3×D3—62no—
485C2×C3×D3—62no—
486C2×C3×D3—62no—
487C2×C3×D3—62no—
488C2×C3×D3—122no—
489C2×C3×D3—122no—
490C2×C3×D3—122no—
491C2×C3×D3—128no—
492C2×C3×D3—128no—
493C2×C3×D3D3×D414yes—
494C2×C3×D3#23714yes—
495C2×C3×D3C2×#6714yes—
496C2×C3×D3C2×#6714yescomplemented
497D32—48no—
498C32×C4—62no—
499C3⋊Dic3—21no—
500C3⋊Dic3—22no—
501C3⋊Dic3—34no—
502C3⋊Dic3—32no—
503C3⋊Dic3—62no—
504C3⋊Dic3—64no—
505C3⋊Dic3—61no—
506C3⋊Dic3—62no—
507C3⋊Dic3—62no—
508C3⋊Dic3—122no—
509C3⋊Dic3—122no—
510C3⋊Dic3—122no—
511C3⋊Dic3D3×D412yescomplemented
512C3×Dic3—22no—
513C3×Dic3—22no—
514C3×Dic3—34no—
515C3×Dic3—42no—
516C3×Dic3—62no—
517C3×Dic3—62no—
518C3×Dic3—62no—
519C3×Dic3—62no—
520C3×Dic3—62no—
521C3×Dic3—122no—
522C22×D4—92no—
523C22×D4—271no—
524C23×C4—271no—
525#121—91no—
526#121—272no—
527#121—271no—
528#121—271no—
529#121—272no—
530#121—271no—
531C2×C4⋊C4—271no—
532C2×C22⋊C4—272no—
533C33C2×#12111yescharacteristic, complemented, Sylow
534C23×C3—21no—
535C23×C3—22no—
536C23×C3—32no—
537C23×C3—32no—
538C23×C3—38no—
539C23×C3—32no—
540C23×C3—32no—
541C23×C3—41no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3—64no—
545C23×C3—62no—
546C23×C3—64no—
547C23×C3—64no—
548C23×C3—64no—
549C23×C3—64no—
550C23×C3—92no—
551C23×C3—184no—
552C23×C3—184no—
553C23×C3—184no—
554C23×C3C2×D3211yescharacteristic
555C23×C3C2×D3212yes—
556C22×D3—22no—
557C22×D3—22no—
558C22×D3—32no—
559C22×D3—32no—
560C22×D3—62no—
561C22×D3—64no—
562C22×D3—64no—
563C22×D3—64no—
564C22×D3—64no—
565C22×D3—64no—
566C22×D3—64no—
567C22×D3#62514yescomplemented
568C22×D3C2×D3212yes—
569C22×D3C2×D3211yescharacteristic
570C22×D3C2×D3211yescharacteristic
571C3×D4—64no—
572C3×D4—64no—
573C3×D4—124no—
574C3×D4—184no—
575C3×D4—182no—
576C3×D4—184no—
577C3×D4—184no—
578C2×C3×C4—32no—
579C2×C3×C4—32no—
580C2×C3×C4—62no—
581C2×C3×C4—91no—
582C2×C3×C4—92no—
583C2×C3×C4—91no—
584C2×C3×C4—184no—
585C2×C3×C4—182no—
586#67—24no—
587#67—64no—
588#67—64no—
589#67—64no—
590#67—64no—
591#67—64no—
592#67—64no—
593#67—124no—
594#67—184no—
595#67—184no—
596#67—184no—
597#67—184no—
598#67—364no—
599C2×Dic3—32no—
600C2×Dic3—32no—
601C2×Dic3—32no—
602C2×Dic3—32no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—62no—
606C2×Dic3—64no—
607C2×Dic3—64no—
608C2×Dic3—64no—
609C2×Dic3—98no—
610C2×Dic3—91no—
611C2×Dic3—92no—
612C2×Dic3—91no—
613C2×Dic3—92no—
614C2×Dic3—184no—
615C2×Dic3—182no—
616C2×Dic3—181no—
617C2×Dic3—181no—
618C2×Dic3—182no—
619C2×Dic3—184no—
620C2×Dic3—184no—
621C2×Dic3—184no—
622C2×Dic3—184no—
623C2×Dic3—184no—
624C2×Dic3—184no—
625C2×Dic3—182no—
626C2×Dic3—184no—
627C2×Dic3—184no—
628C2×Dic3—361no—
629C2×Dic3—361no—
630C2×Dic3—364no—
631C2×Dic3—364no—
632C2×Dic3C2×D3212yes—
633D12—64no—
634D12—182no—
635C4×D3—64no—
636C4×D3—94no—
637C4×D3—182no—
638C4×D3—182no—
639C4×D3—182no—
640C2×C32—22no—
641C2×C32—24no—
642C2×C32—24no—
643C2×C32—22no—
644C2×C32—22no—
645C2×C32—21no—
646C2×C32—21no—
647C2×C32—22no—
648C2×C32—21no—
649C2×C32—34no—
650C2×C32—41no—
651C2×C32—41no—
652C2×C32—41no—
653C2×C32—44no—
654C2×C32—44no—
655C2×C32—62no—
656C2×C32—122no—
657C2×C32C2×D3×D411yescharacteristic
658C2×C32C2×D3×D412yes—
659C2×C32C2×D3×D411yescharacteristic
660C2×C32C2×#23712yes—
661C2×C32D3×#4111yescharacteristic
662C2×C32C22×#6712yes—
663C3⋊D3—42no—
664C3×D3—24no—
665C3×D3—24no—
666C3×D3—24no—
667C3×D3—42no—
668C3×D3—42no—
669C3×D3—82no—
670C3×D3—122no—
671C3×D3—122no—
672C3×D3—242no—
673C3×D3#93918yescomplemented
674C24—31no—
675C24—92no—
676C2×D4—32no—
677C2×D4—92no—
678C2×D4—91no—
679C2×D4—92no—
680C2×D4—92no—
681C2×D4—188no—
682C2×D4—271no—
683C2×D4—272no—
684C2×D4—544no—
685C22×C4—92no—
686C22×C4—91no—
687C22×C4—271no—
688C22×C4—271no—
689C22×C4—271no—
690C22×C4—271no—
691C22×C4—271no—
692C22×C4—544no—
693C4⋊C4—91no—
694C4⋊C4—272no—
695C4⋊C4—271no—
696C22⋊C4—92no—
697C22⋊C4—272no—
698C22⋊C4—272no—
699C22⋊C4—272no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—22no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—24no—
710C22×C3—34no—
711C22×C3—34no—
712C22×C3—34no—
713C22×C3—34no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3—42no—
718C22×C3—41no—
719C22×C3—42no—
720C22×C3—62no—
721C22×C3—62no—
722C22×C3—62no—
723C22×C3—62no—
724C22×C3—616no—
725C22×C3—62no—
726C22×C3—616no—
727C22×C3—62no—
728C22×C3—62no—
729C22×C3—62no—
730C22×C3—62no—
731C22×C3—62no—
732C22×C3—62no—
733C22×C3—62no—
734C22×C3—62no—
735C22×C3—62no—
736C22×C3—122no—
737C22×C3—122no—
738C22×C3—122no—
739C22×C3—182no—
740C22×C3—182no—
741C22×C3—182no—
742C22×C3—368no—
743C22×C3C2×#62512yescomplemented
744C22×C3D3×#6714yescomplemented
745C22×C3C22×D3212yes—
746C22×C3C22×D3211yescharacteristic
747C2×D3—21no—
748C2×D3—21no—
749C2×D3—28no—
750C2×D3—22no—
751C2×D3—22no—
752C2×D3—22no—
753C2×D3—62no—
754C2×D3—62no—
755C2×D3—62no—
756C2×D3—62no—
757C2×D3—62no—
758C2×D3—62no—
759C2×D3—122no—
760C2×D3—122no—
761C2×D3—122no—
762C2×D3—128no—
763C2×D3—128no—
764C2×D3#380512yes—
765C2×D3C2×#62512yes—
766C2×D3C2×#62512yescomplemented
767C2×D3#381112yes—
768C3×C4—62no—
769C3×C4—62no—
770C3×C4—92no—
771C3×C4—122no—
772C3×C4—182no—
773C3×C4—181no—
774Dic3—22no—
775Dic3—34no—
776Dic3—62no—
777Dic3—62no—
778Dic3—62no—
779Dic3—62no—
780Dic3—62no—
781Dic3—94no—
782Dic3—92no—
783Dic3—122no—
784Dic3—182no—
785Dic3—184no—
786Dic3—182no—
787Dic3—182no—
788Dic3—181no—
789Dic3—362no—
790Dic3—362no—
791Dic3—362no—
792C32—21no—
793C32—22no—
794C32—41no—
795C32D3×#12111yescharacteristic, complemented
796C32C2×#93912yescomplemented
797C23—31no—
798C23—31no—
799C23—34no—
800C23—32no—
801C23—62no—
802C23—62no—
803C23—92no—
804C23—184no—
805C23—184no—
806C23—184no—
807C23D3311yescharacteristic
808D4—64no—
809D4—184no—
810D4—182no—
811D4—184no—
812D4—184no—
813D4—542no—
814D4—544no—
815C2×C4—32no—
816C2×C4—91no—
817C2×C4—91no—
818C2×C4—92no—
819C2×C4—184no—
820C2×C4—182no—
821C2×C4—274no—
822C2×C4—271no—
823C2×C4—271no—
824C2×C4—542no—
825C2×C4—542no—
826C2×C4—542no—
827C2×C4—542no—
828C2×C3—24no—
829C2×C3—22no—
830C2×C3—24no—
831C2×C3—22no—
832C2×C3—21no—
833C2×C3—22no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—22no—
837C2×C3—38no—
838C2×C3—44no—
839C2×C3—44no—
840C2×C3—41no—
841C2×C3—41no—
842C2×C3—41no—
843C2×C3—64no—
844C2×C3—64no—
845C2×C3—64no—
846C2×C3—122no—
847C2×C3—122no—
848C2×C3—242no—
849C2×C3—362no—
850C2×C3D32×D412yes—
851C2×C3D3×#23712yes—
852C2×C3C2×#380511yescharacteristic
853C2×C3C22×#62511yescharacteristic
854C2×C3C2×D3×#6712yes—
855C2×C3C2×#381111yescharacteristic
856D3—22no—
857D3—42no—
858D3—122no—
859D3—122no—
860D3—242no—
861D3#6398014yesdirect product factor
862C22—21no—
863C22—21no—
864C22—32no—
865C22—32no—
866C22—32no—
867C22—32no—
868C22—68no—
869C22—61no—
870C22—61no—
871C22—62no—
872C22—62no—
873C22—62no—
874C22—182no—
875C22—182no—
876C22—182no—
877C22—368no—
878C22D3×#62512yescomplemented
879C22C2×D3311yescharacteristic
880C4—62no—
881C4—92no—
882C4—182no—
883C4—181no—
884C4—272no—
885C4—541no—
886C3—22no—
887C3—21no—
888C3—41no—
889C3D3×#93912yescomplemented
890C3C2×#6398011yescharacteristic, complemented
891C2—22no—
892C2—34no—
893C2—62no—
894C2—122no—
895C2—362no—
896C2D3×#380511yescharacteristic
897C2C2×D3×#62511yescharacteristic
898C2D3×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33C2×#121
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×D3×C3⋊Dic3C2semidirect
2. C2×C3×D3×#67C2semidirect
3. C2×D3×#625C2semidirect
4. #11723717C2semidirect
5. #11723637C2semidirect
6. C3×#63980C2semidirect
7. #11722955C2semidirect
8. #11722954C2semidirect
9. #11722953C2semidirect
10. D3×#3724C2semidirect
11. D3×(C2×D3)⋊Dic3C2semidirect
16. C22×C3⋊(C3⋊Dic3)C22semidirect
17. C2×C3×#638C22semidirect
18. C22×C3×C3⋊Dic3C22semidirect
19. C2×C32×#67C22semidirect
20. C2×#6295C22semidirect
21. C2×#6290C22semidirect
25. C2×D3×C3⋊Dic3C22semidirect
26. C2×D3×C3⋊Dic3C22semidirect
28. C2×C3×#626C22semidirect
29. C2×C3×#625C22semidirect
30. C2×C3×#625C22semidirect
33. #88815C22semidirect
34. #88814C22semidirect
35. #88806C22semidirect
36. #88803C22semidirect
37. (C2×D3)⋊(C3⋊Dic3)C22semidirect
38. C3×#3724C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
44. C2×D3×#67D3semidirect
57. #63980D3direct (N × H)
72. C22×C32×D3D4semidirect
94. D3×C3⋊Dic3D4semidirect
109. C2×#638C2×D3semidirect
120. C22×C3⋊Dic3C2×D3semidirect
130. C2×C3×#67C2×D3semidirect
131. C2×C3×#67C2×D3semidirect
141. C2×#626C2×D3semidirect
147. C2×#625C2×D3semidirect
148. C2×#625C2×D3semidirect
170. #3724C2×D3semidirect
181. (C2×D3)⋊Dic3C2×D3semidirect
184. C22×C33C2×D4semidirect
197. C2×C32×D3C2×D4semidirect
201. C3⋊(C3⋊Dic3)C2×D4semidirect
204. C3×C3⋊Dic3C2×D4semidirect
263. C22×C3×D3#67semidirect
348. C32×D3#121semidirect
379. C2×#67D32semidirect
456. C22×C32D3×D4semidirect
457. C22×C32C2×#67semidirect
496. C2×C3×D3C2×#67semidirect
511. C3⋊Dic3D3×D4semidirect
533. C33C2×#121semidirect
567. C22×D3#625semidirect
673. C3×D3#939semidirect
743. C22×C3C2×#625semidirect
744. C22×C3D3×#67semidirect
766. C2×D3C2×#625semidirect
795. C32D3×#121semidirect
796. C32C2×#939semidirect
861. D3#63980direct (N × H)
878. C22D3×#625semidirect
889. C3D3×#939semidirect
890. C3C2×#63980semidirect

Maximal subgroups

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

subgroupindex
C22×D3×C3⋊Dic32
C2×C3×D3×#672
C2×D3×#6252
#117237172
#117236372
C3×#639802
#117229552
#117229542
#117229532
D3×#37242
D3×(C2×D3)⋊Dic32
C2×#639803
D3×#9393