Finite Group Databasebeta

← C3×#672 #13175122

Subgroups — C3×#672 #13175122

Order 1728.

2448 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×#67C212yesmaximal, complemented
2C2×C3×D3×#67C212yesmaximal, complemented
3C3×#64162C211yesmaximal, characteristic, complemented
4C3×#63983C211yesmaximal, characteristic, complemented
5C3×#63979C211yesmaximal, characteristic, complemented
6C3×#63978C212yesmaximal, complemented
7C3×#63976C212yesmaximal, complemented
8C3×Dic3×#67C212yesmaximal, complemented
9C3×#63970C212yesmaximal, complemented
10C3×D4×#67—32nomaximal
11#672C311yesmaximal, characteristic, direct product factor
12C24×C33C2211yescharacteristic, complemented
13C23×C32×D3C2212yescomplemented
14C22×C3×D32C2211yescharacteristic, complemented
15C2×C3×#638C2212yescomplemented
16C2×C3×#638C2211yescharacteristic, complemented
17C2×C32×#67—28no—
18C2×C32×#67C2212yes—
19C2×C32×#67C2212yescomplemented
20C2×C32×#67C2212yescomplemented
21C2×C32×#67C2212yescomplemented
22C22×C32×Dic3C2212yescomplemented
23C3×D3×#67—28no—
24C2×C3×#626C2212yescomplemented
25C2×C3×#625C2212yescomplemented
26C2×C3×#625C2211yescharacteristic, complemented
27C2×C3×D3×Dic3C2212yescomplemented
28C3×#3757C2211yescharacteristic, complemented
29C3×#3757C2212yescomplemented
30C3×Dic3⋊Dic3C2212yescomplemented
31C3×#3722C2211yescharacteristic, complemented
32C3×(C2×D3)⋊Dic3C2212yescomplemented
33C3×(C2×D3)⋊Dic3C2212yescomplemented
34C3×Dic32C2211yescharacteristic, complemented
35C22×C32×D4—32no—
36C22×C3×#67—22no—
37C22×C3×#67—32no—
38C22×C3×#67D312yescomplemented
39C22×C3×#67C2×C312yescomplemented
40C2×C3×D3×D4—32no—
41C2×D3×#67C2×C312yescomplemented
42#64162C2×C311yescharacteristic, complemented
43C3×#953—32no—
44C3×#953—32no—
45C3×#953—61no—
46C3×#940—32no—
47C3×#939—32no—
48C3×#939—32no—
49C3×#938—32no—
50C3×#937—32no—
51C3×#937—32no—
52C3×D4×Dic3—32no—
53C3×#930—32no—
54C3×C4×#67—32no—
55#63983C2×C311yescharacteristic, complemented
56#63979C2×C311yescharacteristic, complemented
57#63978C2×C312yescomplemented
58#63976C2×C312yescomplemented
59Dic3×#67C2×C312yescomplemented
60#63970C2×C312yescomplemented
61C23×C33—24no—
62C23×C33—41no—
63C23×C33C2311yescharacteristic
64C23×C33C2312yes—
65C22×C3×C3⋊D3C2311yescharacteristic
66C22×C32×D3—24no—
67C22×C32×D3—24no—
68C22×C32×D3—42no—
69C22×C32×D3C2312yes—
70C22×C32×D3C2312yes—
71C2×C3×D32—24no—
72C2×C3×D32—41no—
73C3×#638—24no—
74C3×#638—41no—
75C2×C3×C3⋊Dic3C2312yes—
76C2×C3×C3⋊Dic3C2311yescharacteristic
77C32×#67—24no—
78C32×#67—24no—
79C32×#67—24no—
80C32×#67D418yescomplemented
81C2×C32×Dic3—24no—
82C2×C32×Dic3C2312yes—
83C2×C32×Dic3C2312yes—
84C3×#626—24no—
85C3×#625—24no—
86C3×#625—41no—
87C3×D3×Dic3—24no—
88C3×D42—91no—
89D4×#67—32no—
90C24×C32—22no—
91C24×C32—21no—
92C24×C32—32no—
93C24×C32—41no—
94C24×C32C2×D312yescomplemented
95C24×C32C22×C311yescharacteristic, complemented
96C23×C3×D3—22no—
97C23×C3×D3—32no—
98C23×C3×D3C2×D312yescomplemented
99C23×C3×D3C22×C312yescomplemented
100C22×D32C22×C311yescharacteristic, complemented
101C2×C32×D4—32no—
102C2×C32×D4—32no—
103C2×C32×D4—32no—
104C2×C32×D4—32no—
105C2×C32×D4—68no—
106C22×C32×C4—32no—
107C2×#638C22×C312yescomplemented
108C2×#638C22×C311yescharacteristic, complemented
109C2×C3×#67—216no—
110C2×C3×#67—22no—
111C2×C3×#67—22no—
112C2×C3×#67—22no—
113C2×C3×#67—22no—
114C2×C3×#67—28no—
115C2×C3×#67—28no—
116C2×C3×#67—32no—
117C2×C3×#67—32no—
118C2×C3×#67—32no—
119C2×C3×#67—32no—
120C2×C3×#67—32no—
121C2×C3×#67—32no—
122C2×C3×#67—32no—
123C2×C3×#67—68no—
124C2×C3×#67—62no—
125C2×C3×#67—61no—
126C2×C3×#67C2×D312yes—
127C2×C3×#67C2×D312yescomplemented
128C2×C3×#67C2×D312yescomplemented
129C2×C3×#67C2×D312yescomplemented
130C2×C3×#67C22×C312yes—
131C2×C3×#67C22×C312yescomplemented
132C2×C3×#67C22×C312yescomplemented
133C2×C3×#67C22×C312yescomplemented
134C22×C3×Dic3—22no—
135C22×C3×Dic3—32no—
136C22×C3×Dic3C2×D312yescomplemented
137C22×C3×Dic3C22×C312yescomplemented
138C3×D3×D4—68no—
139C2×C3×D12—32no—
140C2×C3×C4×D3—32no—
141D3×#67—28no—
142C2×#626C22×C312yescomplemented
143C2×#625C22×C312yescomplemented
144C2×#625C22×C311yescharacteristic, complemented
145C2×D3×Dic3C22×C312yescomplemented
146#3757C22×C311yescharacteristic, complemented
147#3757C22×C312yescomplemented
148C3×#217—32no—
149C3×#217—32no—
150C3×#217—32no—
151C3×#217—32no—
152C3×#217—32no—
153C3×#217—62no—
154C3×#217—61no—
155C3×(C2×D3)⋊C4—32no—
156C3×(C2×D3)⋊C4—32no—
157C3×(C2×D3)⋊C4—32no—
158C3×C4⋊Dic3—32no—
159C3×Dic3⋊C4—32no—
160C3×C4×Dic3—32no—
161Dic3⋊Dic3C22×C312yescomplemented
162#3722C22×C311yescharacteristic, complemented
163(C2×D3)⋊Dic3C22×C312yescomplemented
164(C2×D3)⋊Dic3C22×C312yescomplemented
165Dic32C22×C311yescharacteristic, complemented
166C22×C33—22no—
167C22×C33—22no—
168C22×C33—22no—
169C22×C33—21no—
170C22×C33—44no—
171C22×C33C2×D414yescomplemented
172C22×C33C2411yescharacteristic
173C2×C3×C3⋊D3—22no—
174C2×C3×C3⋊D3—21no—
175C2×C32×D3—22no—
176C2×C32×D3—22no—
177C2×C32×D3—22no—
178C2×C32×D3—22no—
179C2×C32×D3—22no—
180C2×C32×D3—48no—
181C2×C32×D3C2×D414yescomplemented
182C3×D32—44no—
183C3×C3⋊Dic3—22no—
184C3×C3⋊Dic3—21no—
185C32×Dic3—22no—
186C32×Dic3C2×D414yescomplemented
187C22×C3×D4—32no—
188C22×C3×D4—32no—
189C22×C3×D4—62no—
190C22×C3×D4—92no—
191C22×#67—32no—
192C22×#67C3×D312yescomplemented
193C2×D3×D4—32no—
194C3×#127—91no—
195C3×#121—92no—
196C3×#121—92no—
197C3×#120—91no—
198C3×#120—92no—
199C3×#120—91no—
200C3×C4×D4—92no—
201#953—32no—
202#953—32no—
203#953—61no—
204#940—32no—
205#939—32no—
206#939—32no—
207#938—32no—
208#937—32no—
209#937—32no—
210D4×Dic3—32no—
211#930—32no—
212C4×#67—32no—
213C23×C32—24no—
214C23×C32—28no—
215C23×C32—24no—
216C23×C32—24no—
217C23×C32—21no—
218C23×C32—22no—
219C23×C32—22no—
220C23×C32—22no—
221C23×C32—22no—
222C23×C32—32no—
223C23×C32—32no—
224C23×C32—42no—
225C23×C32—41no—
226C23×C32—44no—
227C23×C32—44no—
228C23×C32—48no—
229C23×C32—42no—
230C23×C32—41no—
231C23×C32—42no—
232C23×C32—44no—
233C23×C32—44no—
234C23×C32—64no—
235C23×C32—64no—
236C23×C32—122no—
237C23×C32C22×D312yes—
238C23×C32C22×D312yes—
239C23×C32C22×D312yes—
240C23×C32C23×C311yescharacteristic
241C23×C32C23×C312yes—
242C22×C3⋊D3C23×C311yescharacteristic
243C22×C3×D3—28no—
244C22×C3×D3—24no—
245C22×C3×D3—24no—
246C22×C3×D3—24no—
247C22×C3×D3—24no—
248C22×C3×D3—22no—
249C22×C3×D3—22no—
250C22×C3×D3—32no—
251C22×C3×D3—44no—
252C22×C3×D3—42no—
253C22×C3×D3—42no—
254C22×C3×D3—44no—
255C22×C3×D3—61no—
256C22×C3×D3—64no—
257C22×C3×D3—64no—
258C22×C3×D3—122no—
259C22×C3×D3C22×D312yes—
260C22×C3×D3C22×D312yes—
261C22×C3×D3C23×C312yes—
262C22×C3×D3C23×C312yes—
263C2×D32—24no—
264C2×D32—41no—
265C32×D4—38no—
266C32×D4—64no—
267C32×D4—64no—
268C32×D4—64no—
269C2×C32×C4—32no—
270C2×C32×C4—32no—
271C2×C32×C4—64no—
272#638—24no—
273#638—41no—
274C2×C3⋊Dic3C23×C311yescharacteristic
275C2×C3⋊Dic3C23×C312yes—
276C3×#67—28no—
277C3×#67—28no—
278C3×#67—28no—
279C3×#67—24no—
280C3×#67—24no—
281C3×#67—24no—
282C3×#67—24no—
283C3×#67—24no—
284C3×#67—24no—
285C3×#67—28no—
286C3×#67—64no—
287C3×#67—64no—
288C3×#67—64no—
289C3×#67—64no—
290C3×#67—64no—
291C3×#67—124no—
292C3×#67—122no—
293C3×#67—122no—
294C3×#67—122no—
295C3×#67#6718yesdirect product factor
296C3×#67C3×D418yescomplemented
297C2×C3×Dic3—28no—
298C2×C3×Dic3—24no—
299C2×C3×Dic3—24no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—32no—
303C2×C3×Dic3—32no—
304C2×C3×Dic3—32no—
305C2×C3×Dic3—61no—
306C2×C3×Dic3—62no—
307C2×C3×Dic3—64no—
308C2×C3×Dic3C22×D312yes—
309C2×C3×Dic3C22×D312yes—
310C2×C3×Dic3C23×C312yes—
311C2×C3×Dic3C23×C312yes—
312C3×D12—64no—
313C3×C4×D3—64no—
314#626—24no—
315#625—24no—
316#625—41no—
317D3×Dic3—24no—
318D42—91noSylow
319C2×C33—24no—
320C2×C33—41no—
321C2×C33C22×D412yes—
322C2×C33H(5,𝔽2)11yescharacteristic
323C3×C3⋊D3—41no—
324C32×D3—24no—
325C32×D3—42no—
326C24×C3—22no—
327C24×C3—21no—
328C24×C3—32no—
329C24×C3—32no—
330C24×C3—41no—
331C24×C3—62no—
332C24×C3—91no—
333C24×C3D3211yescharacteristic, complemented
334C24×C3C2×C3×D312yescomplemented
335C23×D3—32no—
336C23×D3C2×C3×D312yescomplemented
337C2×C3×D4—32no—
338C2×C3×D4—32no—
339C2×C3×D4—32no—
340C2×C3×D4—32no—
341C2×C3×D4—32no—
342C2×C3×D4—32no—
343C2×C3×D4—32no—
344C2×C3×D4—32no—
345C2×C3×D4—62no—
346C2×C3×D4—62no—
347C2×C3×D4—62no—
348C2×C3×D4—62no—
349C2×C3×D4—68no—
350C2×C3×D4—68no—
351C2×C3×D4—616no—
352C2×C3×D4—92no—
353C2×C3×D4—92no—
354C2×C3×D4—92no—
355C2×C3×D4—91no—
356C2×C3×D4—91no—
357C2×C3×D4—188no—
358C22×C3×C4—32no—
359C22×C3×C4—32no—
360C22×C3×C4—62no—
361C22×C3×C4—92no—
362C2×#67—28no—
363C2×#67—32no—
364C2×#67—32no—
365C2×#67—32no—
366C2×#67—32no—
367C2×#67—32no—
368C2×#67—32no—
369C2×#67—32no—
370C2×#67—62no—
371C2×#67—61no—
372C2×#67—68no—
373C2×#67C2×C3×D312yes—
374C2×#67C2×C3×D312yescomplemented
375C2×#67C2×C3×D312yescomplemented
376C2×#67C2×C3×D312yescomplemented
377C22×Dic3—32no—
378C22×Dic3C2×C3×D312yescomplemented
379D3×D4—68no—
380C2×D12—32no—
381C2×C4×D3—32no—
382C3×C4⋊C4—92no—
383C3×C22⋊C4—91no—
384C3×C22⋊C4—92no—
385C3×C22⋊C4—92no—
386C3×C22⋊C4—92no—
387C3×C22⋊C4—91no—
388C3×C42—91no—
389#217—32no—
390#217—32no—
391#217—32no—
392#217—32no—
393#217—32no—
394#217—62no—
395#217—61no—
396(C2×D3)⋊C4—32no—
397(C2×D3)⋊C4—32no—
398(C2×D3)⋊C4—32no—
399C4⋊Dic3—32no—
400Dic3⋊C4—32no—
401C4×Dic3—32no—
402C22×C32—22no—
403C22×C32—22no—
404C22×C32—22no—
405C22×C32—21no—
406C22×C32—24no—
407C22×C32—24no—
408C22×C32—22no—
409C22×C32—22no—
410C22×C32—22no—
411C22×C32—22no—
412C22×C32—24no—
413C22×C32—22no—
414C22×C32—22no—
415C22×C32—22no—
416C22×C32—22no—
417C22×C32—21no—
418C22×C32—22no—
419C22×C32—24no—
420C22×C32—24no—
421C22×C32—24no—
422C22×C32—34no—
423C22×C32—44no—
424C22×C32—41no—
425C22×C32—42no—
426C22×C32—42no—
427C22×C32—42no—
428C22×C32—42no—
429C22×C32—42no—
430C22×C32—42no—
431C22×C32—42no—
432C22×C32—44no—
433C22×C32—44no—
434C22×C32—42no—
435C22×C32—44no—
436C22×C32—48no—
437C22×C32—44no—
438C22×C32—416no—
439C22×C32—48no—
440C22×C32—416no—
441C22×C32—62no—
442C22×C32—62no—
443C22×C32—62no—
444C22×C32—62no—
445C22×C32—62no—
446C22×C32—128no—
447C22×C32D3×D414yescomplemented
448C22×C32C2×#6714yescomplemented
449C22×C32C2×C3×D414yescomplemented
450C22×C32C23×D312yes—
451C22×C32C24×C311yescharacteristic
452C2×C3⋊D3—22no—
453C2×C3⋊D3—21no—
454C2×C3×D3—22no—
455C2×C3×D3—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—24no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—24no—
466C2×C3×D3—42no—
467C2×C3×D3—42no—
468C2×C3×D3—42no—
469C2×C3×D3—42no—
470C2×C3×D3—48no—
471C2×C3×D3—48no—
472C2×C3×D3—416no—
473C2×C3×D3—62no—
474C2×C3×D3—62no—
475C2×C3×D3—62no—
476C2×C3×D3—122no—
477C2×C3×D3—121no—
478C2×C3×D3—128no—
479C2×C3×D3C2×#6714yescomplemented
480C2×C3×D3C2×C3×D414yescomplemented
481D32—44no—
482C32×C4—34no—
483C32×C4—62no—
484C3⋊Dic3—22no—
485C3⋊Dic3—21no—
486C3×Dic3—24no—
487C3×Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—24no—
490C3×Dic3—62no—
491C3×Dic3—62no—
492C3×Dic3—62no—
493C3×Dic3—122no—
494C3×Dic3—121no—
495C3×Dic3C2×#6714yescomplemented
496C3×Dic3C2×C3×D414yescomplemented
497C22×D4—32no—
498C22×D4—92no—
499#127—91no—
500#121—92no—
501#121—92no—
502#120—91no—
503#120—92no—
504#120—91no—
505C4×D4—92no—
506C33D4211yescharacteristic, complemented, Sylow
507C23×C3—28no—
508C23×C3—24no—
509C23×C3—24no—
510C23×C3—24no—
511C23×C3—22no—
512C23×C3—22no—
513C23×C3—22no—
514C23×C3—21no—
515C23×C3—22no—
516C23×C3—32no—
517C23×C3—32no—
518C23×C3—32no—
519C23×C3—32no—
520C23×C3—44no—
521C23×C3—44no—
522C23×C3—48no—
523C23×C3—41no—
524C23×C3—42no—
525C23×C3—44no—
526C23×C3—42no—
527C23×C3—44no—
528C23×C3—41no—
529C23×C3—42no—
530C23×C3—62no—
531C23×C3—62no—
532C23×C3—64no—
533C23×C3—64no—
534C23×C3—68no—
535C23×C3—64no—
536C23×C3—64no—
537C23×C3—91no—
538C23×C3—124no—
539C23×C3—122no—
540C23×C3—122no—
541C23×C3—124no—
542C23×C3—184no—
543C23×C3—361no—
544C23×C3C2×D3211yescharacteristic
545C23×C3C2×D3212yes—
546C23×C3C22×C3×D312yes—
547C23×C3C22×C3×D312yes—
548C23×C3C22×C3×D312yes—
549C22×D3—24no—
550C22×D3—24no—
551C22×D3—32no—
552C22×D3—42no—
553C22×D3—61no—
554C22×D3—64no—
555C22×D3—64no—
556C22×D3—122no—
557C22×D3C22×C3×D312yes—
558C22×D3C22×C3×D312yes—
559C3×D4—38no—
560C3×D4—38no—
561C3×D4—68no—
562C3×D4—64no—
563C3×D4—64no—
564C3×D4—64no—
565C3×D4—64no—
566C3×D4—68no—
567C3×D4—68no—
568C3×D4—68no—
569C3×D4—64no—
570C3×D4—64no—
571C3×D4—184no—
572C3×D4—184no—
573C3×D4—184no—
574C3×D4—361no—
575C3×D4—361no—
576C2×C3×C4—32no—
577C2×C3×C4—32no—
578C2×C3×C4—32no—
579C2×C3×C4—32no—
580C2×C3×C4—62no—
581C2×C3×C4—62no—
582C2×C3×C4—64no—
583C2×C3×C4—64no—
584C2×C3×C4—68no—
585C2×C3×C4—91no—
586C2×C3×C4—92no—
587C2×C3×C4—184no—
588#67—24no—
589#67—24no—
590#67—24no—
591#67—64no—
592#67—64no—
593#67—64no—
594#67—64no—
595#67—64no—
596#67—124no—
597#67—122no—
598#67—122no—
599#67—122no—
600#67C3×#6718yesdirect product factor
601C2×Dic3—24no—
602C2×Dic3—32no—
603C2×Dic3—32no—
604C2×Dic3—32no—
605C2×Dic3—61no—
606C2×Dic3—62no—
607C2×Dic3—64no—
608C2×Dic3C22×C3×D312yes—
609C2×Dic3C22×C3×D312yes—
610D12—64no—
611C4×D3—64no—
612C2×C32—24no—
613C2×C32—28no—
614C2×C32—24no—
615C2×C32—24no—
616C2×C32—22no—
617C2×C32—21no—
618C2×C32—22no—
619C2×C32—22no—
620C2×C32—22no—
621C2×C32—42no—
622C2×C32—41no—
623C2×C32—44no—
624C2×C32—44no—
625C2×C32—48no—
626C2×C32—44no—
627C2×C32—42no—
628C2×C32—44no—
629C2×C32—42no—
630C2×C32—41no—
631C2×C32—64no—
632C2×C32—122no—
633C2×C32C2×D3×D412yes—
634C2×C32#100412yes—
635C2×C32C22×#6712yes—
636C2×C32C22×C3×D412yes—
637C2×C32C3×H(5,𝔽2)11yescharacteristic
638C3⋊D3—41no—
639C3×D3—24no—
640C3×D3—24no—
641C3×D3—44no—
642C3×D3—44no—
643C3×D3—42no—
644C3×D3—42no—
645C3×D3—122no—
646C3×D3—241no—
647C24—32no—
648C24—91no—
649C24C3×D3211yescharacteristic, complemented
650C2×D4—32no—
651C2×D4—32no—
652C2×D4—32no—
653C2×D4—32no—
654C2×D4—68no—
655C2×D4—92no—
656C2×D4—92no—
657C2×D4—92no—
658C2×D4—91no—
659C2×D4—91no—
660C2×D4—188no—
661C22×C4—32no—
662C22×C4—92no—
663C4⋊C4—92no—
664C22⋊C4—91no—
665C22⋊C4—92no—
666C22⋊C4—92no—
667C22⋊C4—92no—
668C22⋊C4—91no—
669C42—91no—
670C22×C3—24no—
671C22×C3—24no—
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—22no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—24no—
680C22×C3—22no—
681C22×C3—21no—
682C22×C3—22no—
683C22×C3—22no—
684C22×C3—22no—
685C22×C3—21no—
686C22×C3—22no—
687C22×C3—24no—
688C22×C3—24no—
689C22×C3—24no—
690C22×C3—34no—
691C22×C3—34no—
692C22×C3—42no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3—42no—
698C22×C3—42no—
699C22×C3—44no—
700C22×C3—44no—
701C22×C3—44no—
702C22×C3—42no—
703C22×C3—48no—
704C22×C3—44no—
705C22×C3—416no—
706C22×C3—48no—
707C22×C3—416no—
708C22×C3—41no—
709C22×C3—44no—
710C22×C3—64no—
711C22×C3—64no—
712C22×C3—62no—
713C22×C3—62no—
714C22×C3—62no—
715C22×C3—62no—
716C22×C3—62no—
717C22×C3—62no—
718C22×C3—62no—
719C22×C3—62no—
720C22×C3—62no—
721C22×C3—62no—
722C22×C3—122no—
723C22×C3—122no—
724C22×C3—122no—
725C22×C3—122no—
726C22×C3—128no—
727C22×C3—128no—
728C22×C3—1216no—
729C22×C3—182no—
730C22×C3—181no—
731C22×C3—364no—
732C22×C3D3×#6714yescomplemented
733C22×C3C3×D3×D414yescomplemented
734C22×C3C2×C3×#6714yescomplemented
735C22×C3C22×D3211yescharacteristic
736C22×C3C23×C3×D312yes—
737C2×D3—22no—
738C2×D3—22no—
739C2×D3—22no—
740C2×D3—22no—
741C2×D3—22no—
742C2×D3—48no—
743C2×D3—62no—
744C2×D3—62no—
745C2×D3—62no—
746C2×D3—122no—
747C2×D3—121no—
748C2×D3—128no—
749C2×D3C2×C3×#6714yescomplemented
750C3×C4—34no—
751C3×C4—34no—
752C3×C4—64no—
753C3×C4—64no—
754C3×C4—62no—
755C3×C4—62no—
756C3×C4—182no—
757C3×C4—181no—
758Dic3—22no—
759Dic3—62no—
760Dic3—62no—
761Dic3—62no—
762Dic3—122no—
763Dic3—121no—
764Dic3C2×C3×#6714yescomplemented
765C32—22no—
766C32—21no—
767C32—41no—
768C32D4×#6712yescomplemented
769C32C3×D4211yescharacteristic, complemented
770C23—24no—
771C23—32no—
772C23—32no—
773C23—41no—
774C23—64no—
775C23—64no—
776C23—91no—
777C23—122no—
778C23—184no—
779C23—361no—
780C23C2×C3×D3211yescharacteristic
781C23C2×C3×D3212yes—
782D4—38no—
783D4—64no—
784D4—64no—
785D4—64no—
786D4—184no—
787D4—184no—
788D4—184no—
789D4—361no—
790D4—361no—
791C2×C4—32no—
792C2×C4—32no—
793C2×C4—64no—
794C2×C4—91no—
795C2×C4—92no—
796C2×C4—184no—
797C2×C3—28no—
798C2×C3—24no—
799C2×C3—24no—
800C2×C3—24no—
801C2×C3—22no—
802C2×C3—22no—
803C2×C3—22no—
804C2×C3—21no—
805C2×C3—22no—
806C2×C3—44no—
807C2×C3—44no—
808C2×C3—48no—
809C2×C3—42no—
810C2×C3—44no—
811C2×C3—44no—
812C2×C3—42no—
813C2×C3—41no—
814C2×C3—42no—
815C2×C3—41no—
816C2×C3—64no—
817C2×C3—64no—
818C2×C3—124no—
819C2×C3—124no—
820C2×C3—122no—
821C2×C3—122no—
822C2×C3—361no—
823C2×C3C2×D3×#6712yes—
824C2×C3#6433011yescharacteristic
825C2×C3C2×C3×D3×D412yes—
826C2×C3C3×#100412yes—
827C2×C3C22×C3×#6712yes—
828D3—24no—
829D3—42no—
830D3—122no—
831D3—241no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—21no—
836C22—34no—
837C22—44no—
838C22—62no—
839C22—62no—
840C22—62no—
841C22—62no—
842C22—62no—
843C22—128no—
844C22—182no—
845C22—181no—
846C22—364no—
847C22C3×D3×#6714yescomplemented
848C22C22×C3×D3211yescharacteristic
849C4—34no—
850C4—62no—
851C4—182no—
852C4—181no—
853C3—21no—
854C3—22no—
855C3—41no—
856C3#67211yescharacteristic, direct product factor
857C3C3×D4×#6712yescomplemented
858C2—24no—
859C2—41no—
860C2—64no—
861C2—122no—
862C2—361no—
863C2C2×C3×D3×#6712yes—
864C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC24×C33C22
socleC22×C33C24
hypercenterC24×C3D32
hypocenterC32C3×D42
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C24×C3

Complements

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

NH ≅ G/Ntype
1. C22×C32×#67C2semidirect
2. C2×C3×D3×#67C2semidirect
3. C3×#64162C2semidirect
4. C3×#63983C2semidirect
5. C3×#63979C2semidirect
6. C3×#63978C2semidirect
7. C3×#63976C2semidirect
8. C3×Dic3×#67C2semidirect
9. C3×#63970C2semidirect
11. #672C3direct (N × H)
12. C24×C33C22semidirect
13. C23×C32×D3C22semidirect
14. C22×C3×D32C22semidirect
15. C2×C3×#638C22semidirect
16. C2×C3×#638C22semidirect
19. C2×C32×#67C22semidirect
20. C2×C32×#67C22semidirect
21. C2×C32×#67C22semidirect
22. C22×C32×Dic3C22semidirect
24. C2×C3×#626C22semidirect
25. C2×C3×#625C22semidirect
26. C2×C3×#625C22semidirect
27. C2×C3×D3×Dic3C22semidirect
28. C3×#3757C22semidirect
29. C3×#3757C22semidirect
30. C3×Dic3⋊Dic3C22semidirect
31. C3×#3722C22semidirect
32. C3×(C2×D3)⋊Dic3C22semidirect
33. C3×(C2×D3)⋊Dic3C22semidirect
34. C3×Dic32C22semidirect
38. C22×C3×#67D3semidirect
39. C22×C3×#67C2×C3semidirect
41. C2×D3×#67C2×C3semidirect
42. #64162C2×C3semidirect
55. #63983C2×C3semidirect
56. #63979C2×C3semidirect
57. #63978C2×C3semidirect
58. #63976C2×C3semidirect
59. Dic3×#67C2×C3semidirect
60. #63970C2×C3semidirect
80. C32×#67D4semidirect
94. C24×C32C2×D3semidirect
95. C24×C32C22×C3semidirect
98. C23×C3×D3C2×D3semidirect
99. C23×C3×D3C22×C3semidirect
100. C22×D32C22×C3semidirect
107. C2×#638C22×C3semidirect
108. C2×#638C22×C3semidirect
127. C2×C3×#67C2×D3semidirect
128. C2×C3×#67C2×D3semidirect
129. C2×C3×#67C2×D3semidirect
131. C2×C3×#67C22×C3semidirect
132. C2×C3×#67C22×C3semidirect
133. C2×C3×#67C22×C3semidirect
136. C22×C3×Dic3C2×D3semidirect
137. C22×C3×Dic3C22×C3semidirect
142. C2×#626C22×C3semidirect
143. C2×#625C22×C3semidirect
144. C2×#625C22×C3semidirect
145. C2×D3×Dic3C22×C3semidirect
146. #3757C22×C3semidirect
147. #3757C22×C3semidirect
161. Dic3⋊Dic3C22×C3semidirect
162. #3722C22×C3semidirect
163. (C2×D3)⋊Dic3C22×C3semidirect
164. (C2×D3)⋊Dic3C22×C3semidirect
165. Dic32C22×C3semidirect
171. C22×C33C2×D4semidirect
181. C2×C32×D3C2×D4semidirect
186. C32×Dic3C2×D4semidirect
192. C22×#67C3×D3semidirect
295. C3×#67#67direct (N × H)
296. C3×#67C3×D4semidirect
333. C24×C3D32semidirect
334. C24×C3C2×C3×D3semidirect
336. C23×D3C2×C3×D3semidirect
374. C2×#67C2×C3×D3semidirect
375. C2×#67C2×C3×D3semidirect
376. C2×#67C2×C3×D3semidirect
378. C22×Dic3C2×C3×D3semidirect
447. C22×C32D3×D4semidirect
448. C22×C32C2×#67semidirect
449. C22×C32C2×C3×D4semidirect
479. C2×C3×D3C2×#67semidirect
480. C2×C3×D3C2×C3×D4semidirect
495. C3×Dic3C2×#67semidirect
496. C3×Dic3C2×C3×D4semidirect
506. C33D42semidirect
600. #67C3×#67direct (N × H)
649. C24C3×D32semidirect
732. C22×C3D3×#67semidirect
733. C22×C3C3×D3×D4semidirect
734. C22×C3C2×C3×#67semidirect
749. C2×D3C2×C3×#67semidirect
764. Dic3C2×C3×#67semidirect
768. C32D4×#67semidirect
769. C32C3×D42semidirect
847. C22C3×D3×#67semidirect
856. C3#672direct (N × H)
857. C3C3×D4×#67semidirect

Maximal subgroups

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

subgroupindex
C22×C32×#672
C2×C3×D3×#672
C3×#641622
C3×#639832
C3×#639792
C3×#639782
C3×#639762
C3×Dic3×#672
C3×#639702
C3×D4×#673
#6723