Finite Group Databasebeta

← #11803302

Subgroups — #11803302

Order 1152.

1759 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#937C211yesmaximal, characteristic
2C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
3C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
4#10592919C211yesmaximal, characteristic, complemented
5#10591719C211yesmaximal, characteristic, complemented
6#10591710C212yesmaximal, complemented
7#10591707C212yesmaximal, complemented
8#10591706C211yesmaximal, characteristic, complemented
9Dic3×#217C211yesmaximal, characteristic, complemented
10#10591307C212yesmaximal, complemented
11#10591305C212yesmaximal, complemented
12#82578—31nomaximal
13#82395—31nomaximal
14C24×C3×D3C2211yescharacteristic
15C22×C32×D4C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C22×C3×#67C2212yes—
18C23×C3×Dic3C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic, complemented
20C2×#3757C2211yescharacteristic
21C2×#3757C2212yescomplemented
22C2×C3×#217C2211yescharacteristic
23C2×C3×#217C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic, complemented
25C3×#937C418yescomplemented
26C3×D4×Dic3—24no—
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
29C2×C3×C4×Dic3C2211yescharacteristic, complemented
30C2×Dic3⋊Dic3C2212yescomplemented
31C2×(C2×D3)⋊Dic3—24no—
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×Dic32C2212yescomplemented
37#63658C2212yescomplemented
38#63579C2212yescomplemented
39#63579C2212yescomplemented
40C2×C3×#120—31no—
41C2×C3×C4×D4—31no—
42C22×#217—31no—
43C2×#937D311yescharacteristic
44C2×D4×Dic3D311yescharacteristic, complemented
45C22×(C2×D3)⋊C4—31no—
46#5247—31no—
47#5221—32no—
48#5220—31no—
49#5220—31no—
50#5220—32no—
51#5220—61no—
52#5213—32no—
53C4×#217—31no—
54#4990—32no—
55#4957—32no—
56#4955—31no—
57#4951—32no—
58#4951—32no—
59#4950—31no—
60#4946—31no—
61Dic3×C22⋊C4—31no—
62#4940—32no—
63C24×C32C2311yescharacteristic
64C24×C32C2311yescharacteristic
65C23×C3×D3—22no—
66C23×C3×D3—22no—
67C23×C3×D3—42no—
68C23×C3×D3—42no—
69C23×C3×D3C2×C414yescomplemented
70C23×C3×D3C2312yes—
71C2×C32×D4—22no—
72C2×C32×D4—22no—
73C2×C32×D4C2×C414yes—
74C22×C32×C4C2311yescharacteristic
75C22×C3⋊Dic3—22no—
76C22×C3⋊Dic3—42no—
77C22×C3⋊Dic3C2312yes—
78C22×C3⋊Dic3C2312yes—
79C2×C3×#67—42no—
80C2×C3×#67—42no—
81C2×C3×#67C2×C418yescomplemented
82C22×C3×Dic3—22no—
83C22×C3×Dic3—42no—
84C22×C3×Dic3—42no—
85C22×C3×Dic3D414yescomplemented
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2311yescharacteristic
91#3757—22no—
92#3757—42no—
93C3×#217—22no—
94C3×#217—22no—
95C3×#217C2×C414yescomplemented
96C3×(C2×D3)⋊C4C2×C418yescomplemented
97C3×C4⋊Dic3—22no—
98C3×C4×Dic3—22no—
99Dic3⋊Dic3—42no—
100(C2×D3)⋊Dic3—24no—
101(C2×D3)⋊Dic3—24no—
102(C2×D3)⋊Dic3—42no—
103(C2×D3)⋊Dic3—42no—
104Dic32—42no—
105#2321—91noSylow
106C25×C3—31no—
107C24×D3C2×D311yescharacteristic
108C22×C3×D4—21no—
109C22×C3×D4—32no—
110C22×C3×D4C2×D311yescharacteristic
111C22×C3×D4C2×D311yescharacteristic
112C23×C3×C4—31no—
113C23×C3×C4—31no—
114C22×#67C2×D312yes—
115C23×Dic3—31no—
116C23×Dic3—31no—
117C23×Dic3—61no—
118C23×Dic3C2×D311yescharacteristic
119C23×Dic3C2×D311yescharacteristic, complemented
120C3×#120—38no—
121C3×C4×D4—64no—
122C2×C3×C4⋊C4—31no—
123C2×C3×C22⋊C4—31no—
124C2×C3×C22⋊C4—32no—
125C2×C3×C22⋊C4—31no—
126C2×C3×C22⋊C4—31no—
127C2×C3×C42—31no—
128C2×#217—31no—
129C2×#217—31no—
130C2×#217—32no—
131C2×#217—32no—
132C2×#217—32no—
133C2×#217—32no—
134C2×#217—32no—
135C2×#217—32no—
136C2×#217—61no—
137C2×#217—62no—
138C2×#217—64no—
139C2×#217C2×D311yescharacteristic
140C2×#217C2×D311yescharacteristic
141C2×#217C2×D311yescharacteristic, complemented
142#937Dic318yescomplemented
143D4×Dic3—24no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4—32no—
148C2×(C2×D3)⋊C4—64no—
149C2×(C2×D3)⋊C4C2×D312yes—
150C2×C4⋊Dic3—32no—
151C2×C4⋊Dic3C2×D311yescharacteristic, complemented
152C2×Dic3⋊C4—32no—
153C2×C4×Dic3—32no—
154C2×C4×Dic3—32no—
155C2×C4×Dic3C2×D311yescharacteristic, complemented
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95—32no—
159C3⋊#95—32no—
160C3⋊#95—32no—
161C3⋊#95—32no—
162C3⋊#95—62no—
163C23×C32—22no—
164C23×C32—22no—
165C23×C32—21no—
166C23×C32—21no—
167C23×C32—22no—
168C23×C32—22no—
169C23×C32C22×C412yes—
170C23×C32C22×C412yes—
171C23×C32C2×D412yes—
172C23×C32#4112yes—
173C23×C32C2411yescharacteristic
174C22×C3×D3—28no—
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3—22no—
179C22×C3×D3—22no—
180C22×C3×D3—22no—
181C22×C3×D3—48no—
182C22×C3×D3—44no—
183C22×C3×D3—44no—
184C22×C3×D3—48no—
185C22×C3×D3C22×C414yes—
186C32×D4—28no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4C22×C412yes—
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3—22no—
192C2×C3⋊Dic3—22no—
193C2×C3⋊Dic3—22no—
194C2×C3⋊Dic3—22no—
195C2×C3⋊Dic3—22no—
196C2×C3⋊Dic3—44no—
197C3×#67—48no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—44no—
207C2×C3×Dic3—44no—
208C2×C3×Dic3C22×C414yes—
209C2×C3×Dic3C2×D412yes—
210C2×C3×Dic3C2×D412yes—
211C2×#120—31no—
212C2×C4×D4—31no—
213C22×C22⋊C4—91no—
214#390—92no—
215#388—92no—
216#388—92no—
217#386—92no—
218#386—91no—
219#385—91no—
220#379—91no—
221C4×C22⋊C4—91no—
222C24×C3—21no—
223C24×C3—21no—
224C24×C3—32no—
225C24×C3—34no—
226C24×C3—62no—
227C24×C3—62no—
228C24×C3—122no—
229C24×C3—122no—
230C24×C3C22×D311yescharacteristic
231C24×C3C22×D311yescharacteristic
232C24×C3C22×D311yescharacteristic
233C24×C3C22×D311yescharacteristic
234C23×D3—22no—
235C23×D3—22no—
236C23×D3—42no—
237C23×D3—42no—
238C23×D3C2×Dic314yescomplemented
239C23×D3C22×D312yes—
240C2×C3×D4—22no—
241C2×C3×D4—22no—
242C2×C3×D4—22no—
243C2×C3×D4—22no—
244C2×C3×D4—24no—
245C2×C3×D4—38no—
246C2×C3×D4—42no—
247C2×C3×D4—42no—
248C2×C3×D4—122no—
249C2×C3×D4—122no—
250C2×C3×D4C4×D314yes—
251C2×C3×D4C2×Dic314yes—
252C22×C3×C4—21no—
253C22×C3×C4—32no—
254C22×C3×C4—31no—
255C22×C3×C4—31no—
256C22×C3×C4—34no—
257C22×C3×C4—31no—
258C22×C3×C4—31no—
259C22×C3×C4—62no—
260C22×C3×C4—122no—
261C22×C3×C4—122no—
262C22×C3×C4C22×D311yescharacteristic
263C22×C3×C4C22×D311yescharacteristic
264C2×#67—42no—
265C2×#67—42no—
266C2×#67C2×Dic318yescomplemented
267C22×Dic3—22no—
268C22×Dic3—32no—
269C22×Dic3—32no—
270C22×Dic3—32no—
271C22×Dic3—32no—
272C22×Dic3—42no—
273C22×Dic3—42no—
274C22×Dic3—62no—
275C22×Dic3—62no—
276C22×Dic3—62no—
277C22×Dic3—62no—
278C22×Dic3—122no—
279C22×Dic3—122no—
280C22×Dic3—122no—
281C22×Dic3—124no—
282C22×Dic3#6714yescomplemented
283C22×Dic3C22×D311yescharacteristic
284C22×Dic3C22×D311yescharacteristic
285C22×Dic3C22×D312yes—
286C22×Dic3C22×D311yescharacteristic
287C22×Dic3C22×D311yescharacteristic
288C3×C4⋊C4—62no—
289C3×C22⋊C4—34no—
290C3×C22⋊C4—38no—
291C3×C22⋊C4—62no—
292C3×C22⋊C4—62no—
293C3×C42—62no—
294#217—22no—
295#217—22no—
296#217—62no—
297#217—62no—
298#217—64no—
299#217—64no—
300#217—122no—
301#217—122no—
302#217—122no—
303#217—122no—
304#217—122no—
305#217—124no—
306#217C2×Dic314yescomplemented
307(C2×D3)⋊C4—64no—
308(C2×D3)⋊C4—64no—
309(C2×D3)⋊C4—122no—
310(C2×D3)⋊C4—122no—
311(C2×D3)⋊C4C2×Dic318yescomplemented
312C4⋊Dic3—22no—
313C4⋊Dic3—122no—
314Dic3⋊C4—122no—
315C4×Dic3—22no—
316C4×Dic3—122no—
317C4×Dic3—122no—
318C22×C32—24no—
319C22×C32—22no—
320C22×C32—22no—
321C22×C32—24no—
322C22×C32—22no—
323C22×C32—24no—
324C22×C32—41no—
325C22×C32—41no—
326C22×C32—42no—
327C22×C32C4×D414yes—
328C22×C32C23×C411yescharacteristic
329C22×C32C22×D411yescharacteristic
330C22×C32C2×#4111yescharacteristic
331C22×C32H(5,𝔽2)12yes—
332C22×C32H(5,𝔽2)12yes—
333C2×C3×D3—24no—
334C2×C3×D3—24no—
335C2×C3×D3—24no—
336C2×C3×D3—416no—
337C2×C3×D3—42no—
338C2×C3×D3—42no—
339C2×C3×D3—42no—
340C2×C3×D3—42no—
341C32×C4—22no—
342C3⋊Dic3—42no—
343C3⋊Dic3—42no—
344C3×Dic3—24no—
345C3×Dic3—22no—
346C3×Dic3—22no—
347C3×Dic3—41no—
348C3×Dic3—41no—
349C25—31no—
350C22×D4—32no—
351C22×D4D3211yescharacteristic
352C23×C4—31no—
353C23×C4—31no—
354C23×C4—91no—
355#120—38no—
356C4×D4—64no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—92no—
359C2×C22⋊C4—31no—
360C2×C22⋊C4—32no—
361C2×C22⋊C4—31no—
362C2×C22⋊C4—31no—
363C2×C22⋊C4—92no—
364C2×C22⋊C4—92no—
365C2×C22⋊C4—91no—
366C2×C22⋊C4—92no—
367C2×C22⋊C4—92no—
368C2×C22⋊C4—92no—
369C2×C22⋊C4—184no—
370C2×C42—31no—
371C2×C42—92no—
372#95—92no—
373#95—92no—
374#95—92no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—34no—
393C23×C3—42no—
394C23×C3—42no—
395C23×C3—42no—
396C23×C3—41no—
397C23×C3—41no—
398C23×C3—42no—
399C23×C3—68no—
400C23×C3—62no—
401C23×C3—62no—
402C23×C3—62no—
403C23×C3—62no—
404C23×C3—62no—
405C23×C3—62no—
406C23×C3—128no—
407C23×C3—124no—
408C23×C3—128no—
409C23×C3—124no—
410C23×C3C2×C4×D312yes—
411C23×C3C2×C4×D312yes—
412C23×C3#23512yes—
413C23×C3D3×D412yes—
414C23×C3#23712yes—
415C23×C3C22×Dic312yes—
416C23×C3C22×Dic312yes—
417C23×C3C2×#6712yes—
418C23×C3C23×D311yescharacteristic
419C23×C3C23×D311yescharacteristic
420C22×D3—28no—
421C22×D3—22no—
422C22×D3—22no—
423C22×D3—22no—
424C22×D3—22no—
425C22×D3—22no—
426C22×D3—22no—
427C22×D3—48no—
428C22×D3—44no—
429C22×D3—44no—
430C22×D3—48no—
431C22×D3C22×Dic314yes—
432C3×D4—28no—
433C3×D4—28no—
434C3×D4—48no—
435C3×D4—128no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—22no—
441C2×C3×C4—34no—
442C2×C3×C4—32no—
443C2×C3×C4—32no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—62no—
447C2×C3×C4—62no—
448C2×C3×C4—62no—
449C2×C3×C4—62no—
450C2×C3×C4—61no—
451C2×C3×C4—61no—
452C2×C3×C4—62no—
453C2×C3×C4—62no—
454C2×C3×C4—124no—
455C2×C3×C4—124no—
456C2×C3×C4C2×C4×D312yes—
457C2×C3×C4C22×Dic312yes—
458#67—48no—
459C2×Dic3—22no—
460C2×Dic3—22no—
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3—22no—
464C2×Dic3—22no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—44no—
468C2×Dic3—44no—
469C2×Dic3—64no—
470C2×Dic3—62no—
471C2×Dic3—62no—
472C2×Dic3—62no—
473C2×Dic3—62no—
474C2×Dic3—62no—
475C2×Dic3—62no—
476C2×Dic3—62no—
477C2×Dic3—62no—
478C2×Dic3—62no—
479C2×Dic3—62no—
480C2×Dic3—62no—
481C2×Dic3—62no—
482C2×Dic3—122no—
483C2×Dic3—122no—
484C2×Dic3—122no—
485C2×Dic3—122no—
486C2×Dic3—122no—
487C2×Dic3—124no—
488C2×Dic3—124no—
489C2×Dic3—128no—
490C2×Dic3C22×Dic314yes—
491C2×Dic3C2×#6712yes—
492C2×Dic3C2×#6712yes—
493C2×C32—24no—
494C2×C32—42no—
495C2×C32C2×C4×D411yescharacteristic
496C2×C32#51812yes—
497C2×C32#53411yescharacteristic
498C2×C32#53511yescharacteristic
499C2×C32#53812yes—
500C3×D3—44no—
501C24—32no—
502C24—34no—
503C24—62no—
504C24—62no—
505C24—122no—
506C24—122no—
507C24C2×D3211yescharacteristic
508C24C2×D3211yescharacteristic
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—38no—
512C2×D4—122no—
513C2×D4—122no—
514C2×D4D3×Dic314yes—
515C22×C4—31no—
516C22×C4—32no—
517C22×C4—31no—
518C22×C4—34no—
519C22×C4—31no—
520C22×C4—31no—
521C22×C4—62no—
522C22×C4—92no—
523C22×C4—92no—
524C22×C4—122no—
525C22×C4—122no—
526C22×C4—182no—
527C22×C4—362no—
528C22×C4C2×D3211yescharacteristic
529C4⋊C4—62no—
530C4⋊C4—362no—
531C22⋊C4—34no—
532C22⋊C4—38no—
533C22⋊C4—62no—
534C22⋊C4—62no—
535C22⋊C4—184no—
536C22⋊C4—184no—
537C22⋊C4—182no—
538C22⋊C4—362no—
539C22⋊C4—362no—
540C22⋊C4—362no—
541C42—62no—
542C42—362no—
543C22×C3—24no—
544C22×C3—24no—
545C22×C3—22no—
546C22×C3—24no—
547C22×C3—22no—
548C22×C3—22no—
549C22×C3—22no—
550C22×C3—24no—
551C22×C3—22no—
552C22×C3—22no—
553C22×C3—24no—
554C22×C3—24no—
555C22×C3—22no—
556C22×C3—22no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—24no—
561C22×C3—42no—
562C22×C3—44no—
563C22×C3—44no—
564C22×C3—42no—
565C22×C3—42no—
566C22×C3—44no—
567C22×C3—41no—
568C22×C3—42no—
569C22×C3—41no—
570C22×C3—41no—
571C22×C3—41no—
572C22×C3—42no—
573C22×C3—64no—
574C22×C3—64no—
575C22×C3—64no—
576C22×C3—82no—
577C22×C3—81no—
578C22×C3—81no—
579C22×C3—1216no—
580C22×C3—122no—
581C22×C3—122no—
582C22×C3—122no—
583C22×C3—122no—
584C22×C3C4×#6714yes—
585C22×C3D4×Dic314yes—
586C22×C3C22×C4×D311yescharacteristic
587C22×C3C2×#23511yescharacteristic
588C22×C3C2×D3×D411yescharacteristic
589C22×C3C2×#23711yescharacteristic
590C22×C3#100412yes—
591C22×C3#100412yes—
592C22×C3#100412yes—
593C22×C3#100912yes—
594C22×C3C23×Dic311yescharacteristic
595C22×C3C22×#6711yescharacteristic
596C2×D3—24no—
597C2×D3—24no—
598C2×D3—24no—
599C2×D3—416no—
600C2×D3—42no—
601C2×D3—42no—
602C2×D3—42no—
603C2×D3—42no—
604C3×C4—22no—
605C3×C4—22no—
606C3×C4—42no—
607C3×C4—64no—
608C3×C4—62no—
609C3×C4—62no—
610C3×C4—121no—
611C3×C4—121no—
612Dic3—24no—
613Dic3—22no—
614Dic3—22no—
615Dic3—41no—
616Dic3—41no—
617Dic3—124no—
618Dic3—122no—
619Dic3—122no—
620Dic3—122no—
621Dic3—122no—
622Dic3—242no—
623C32#232111yescharacteristic, complemented, Sylow
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—21no—
629C23—21no—
630C23—34no—
631C23—62no—
632C23—62no—
633C23—62no—
634C23—62no—
635C23—62no—
636C23—62no—
637C23—68no—
638C23—128no—
639C23—128no—
640C23—124no—
641C23—124no—
642C23C2×D3×Dic312yes—
643C23C2×D3×Dic312yes—
644C23#380412yes—
645C23D3×#6712yes—
646C23C22×D3211yescharacteristic
647D4—28no—
648D4—128no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—34no—
652C2×C4—32no—
653C2×C4—32no—
654C2×C4—62no—
655C2×C4—62no—
656C2×C4—62no—
657C2×C4—62no—
658C2×C4—62no—
659C2×C4—62no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—124no—
663C2×C4—124no—
664C2×C4—182no—
665C2×C4—182no—
666C2×C4—182no—
667C2×C4—182no—
668C2×C4—182no—
669C2×C4—182no—
670C2×C4—364no—
671C2×C4C2×D3×Dic312yes—
672C2×C3—24no—
673C2×C3—24no—
674C2×C3—22no—
675C2×C3—22no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—44no—
680C2×C3—42no—
681C2×C3—42no—
682C2×C3—82no—
683C2×C3—124no—
684C2×C3#554512yes—
685C2×C3#556012yes—
686C2×C3#558911yescharacteristic
687C2×C3#559211yescharacteristic
688C2×C3#559312yes—
689C2×C3C2×C4×#6711yescharacteristic
690C2×C3C2×D4×Dic311yescharacteristic
691C2×C3#579812yes—
692C2×C3#580411yescharacteristic
693C2×C3#583011yescharacteristic
694D3—44no—
695C22—24no—
696C22—24no—
697C22—22no—
698C22—22no—
699C22—24no—
700C22—22no—
701C22—42no—
702C22—41no—
703C22—41no—
704C22—64no—
705C22—64no—
706C22—64no—
707C22—1216no—
708C22—122no—
709C22—122no—
710C22—122no—
711C22—122no—
712C22Dic3×#6714yes—
713C22#6431312yes—
714C22#6431412yes—
715C22C22×D3×Dic311yescharacteristic
716C22C2×#380411yescharacteristic
717C22C2×D3×#6711yescharacteristic
718C4—22no—
719C4—64no—
720C4—62no—
721C4—62no—
722C4—121no—
723C4—121no—
724C4—362no—
725C4—362no—
726C3—21no—
727C3#8239511yescharacteristic, complemented
728C3#8257811yescharacteristic, complemented
729C2—24no—
730C2—42no—
731C2—124no—
732C2#1059512312yes—
733C2#1059521512yes—
734C2#1059523011yescharacteristic
735C2#1059523811yescharacteristic
736C2C2×Dic3×#6711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×D4C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#937C2
hypercenterC22×D4D32
hypocenterC32#2321
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D4×Dic3C2semidirect
3. C22×(C2×D3)⋊Dic3C2semidirect
4. #10592919C2semidirect
5. #10591719C2semidirect
6. #10591710C2semidirect
7. #10591707C2semidirect
8. #10591706C2semidirect
9. Dic3×#217C2semidirect
10. #10591307C2semidirect
11. #10591305C2semidirect
19. C23×C3×Dic3C22semidirect
21. C2×#3757C22semidirect
24. C2×C3×#217C22semidirect
25. C3×#937C4semidirect
28. C2×C3×C4⋊Dic3C22semidirect
29. C2×C3×C4×Dic3C22semidirect
30. C2×Dic3⋊Dic3C22semidirect
36. C2×Dic32C22semidirect
37. #63658C22semidirect
38. #63579C22semidirect
39. #63579C22semidirect
44. C2×D4×Dic3D3semidirect
69. C23×C3×D3C2×C4semidirect
81. C2×C3×#67C2×C4semidirect
85. C22×C3×Dic3D4semidirect
95. C3×#217C2×C4semidirect
96. C3×(C2×D3)⋊C4C2×C4semidirect
119. C23×Dic3C2×D3semidirect
141. C2×#217C2×D3semidirect
142. #937Dic3semidirect
151. C2×C4⋊Dic3C2×D3semidirect
155. C2×C4×Dic3C2×D3semidirect
238. C23×D3C2×Dic3semidirect
266. C2×#67C2×Dic3semidirect
282. C22×Dic3#67semidirect
306. #217C2×Dic3semidirect
311. (C2×D3)⋊C4C2×Dic3semidirect
623. C32#2321semidirect
727. C3#82395semidirect
728. C3#82578semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9372
C2×C3×D4×Dic32
C22×(C2×D3)⋊Dic32
#105929192
#105917192
#105917102
#105917072
#105917062
Dic3×#2172
#105913072
#105913052
#825783
#823953