Finite Group Databasebeta

← #11805172

Subgroups — #11805172

Order 1152.

1317 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#926C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic
3C2×#63955C211yesmaximal, characteristic
4#10592910C211yesmaximal, characteristic
5#10591716C211yesmaximal, characteristic
6Dic3×#217C211yesmaximal, characteristic
7#10591696C211yesmaximal, characteristic
8#10591265C212yesmaximal, complemented
9#10591262C212yesmaximal, complemented
10Dic3×Dic3⋊C4C212yesmaximal, complemented
11#10591201C212yesmaximal, complemented
12#82238—31nomaximal
13#82159—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×#3757C2211yescharacteristic
18C2×#3757C2211yescharacteristic
19C2×C3×#217C2211yescharacteristic
20C2×C3×#217C2211yescharacteristic
21C3×#926—24no—
22C2×C3×C4⋊Dic3C2212yes—
23C2×C3×Dic3⋊C4C418yescomplemented
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×C4×Dic3C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic3⋊Dic3C2212yes—
31#63955—24no—
32C2×Dic32C2212yes—
33C2×Dic32C2212yes—
34#63658C2212yes—
35#63658C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×#117—31no—
41C22×C3×C4⋊C4—31no—
42C2×#926—31no—
43C2×#926D311yescharacteristic
44C22×Dic3⋊C4D311yescharacteristic
45C2×#877—31no—
46#5212—31no—
47#5211—31no—
48#5211—31no—
49#5211—31no—
50#5211—61no—
51C4×#217—31no—
52#4984—32no—
53#4980—32no—
54#4980—32no—
55#4978—32no—
56#4976—32no—
57Dic3×C4⋊C4—32no—
58#4943—31no—
59#4942—31no—
60Dic3×C22⋊C4—31no—
61#4933—32no—
62C4×Dic3⋊C4—32no—
63C24×C32C2311yescharacteristic
64C22×C32×C4—22no—
65C22×C32×C4—22no—
66C22×C32×C4C2×C414yes—
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3C2312yes—
70C22×C3⋊Dic3C2312yes—
71C22×C3×Dic3—22no—
72C22×C3×Dic3—22no—
73C22×C3×Dic3—24no—
74C22×C3×Dic3C2×C414yes—
75C22×C3×Dic3C2×C414yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2311yescharacteristic
82#3757—22no—
83#3757—22no—
84C3×#217—22no—
85C3×#217D414yes—
86C3×C4⋊Dic3—24no—
87C3×Dic3⋊C4C2×C414yes—
88C3×Dic3⋊C4C2×C414yes—
89C3×Dic3⋊C4C2×C414yes—
90C3×Dic3⋊C4C2×C414yes—
91C3×C4×Dic3—24no—
92Dic3⋊Dic3—24no—
93Dic3⋊Dic3—24no—
94Dic32—24no—
95Dic32—24no—
96#2344—91noSylow
97C23×C3×C4—21no—
98C23×C3×C4—31no—
99C23×C3×C4—31no—
100C23×C3×C4C2×D311yescharacteristic
101C23×C3×C4C2×D311yescharacteristic
102C23×Dic3C2×D311yescharacteristic
103C23×Dic3C2×D311yescharacteristic
104C3×#117—64no—
105C2×C3×C4⋊C4—38no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C4⋊C4—31no—
108C2×C3×C4⋊C4—31no—
109C2×C3×C4⋊C4—31no—
110C2×C3×C4⋊C4—32no—
111C2×C3×C22⋊C4—31no—
112C2×C3×C22⋊C4—31no—
113C2×C3×C42—32no—
114C2×#217—31no—
115C2×#217—31no—
116C2×#217—31no—
117C2×#217—31no—
118C2×#217—61no—
119C2×#217—61no—
120C2×#217C2×D311yescharacteristic
121C2×#217C2×D311yescharacteristic
122#926—24no—
123#926—64no—
124C2×C4⋊Dic3—32no—
125C2×C4⋊Dic3—32no—
126C2×C4⋊Dic3C2×D312yes—
127C2×Dic3⋊C4—32no—
128C2×Dic3⋊C4—32no—
129C2×Dic3⋊C4Dic318yescomplemented
130C2×Dic3⋊C4C2×D311yescharacteristic
131C2×Dic3⋊C4C2×D311yescharacteristic
132C2×Dic3⋊C4C2×D311yescharacteristic
133C2×Dic3⋊C4C2×D311yescharacteristic
134C2×C4×Dic3—32no—
135C2×C4×Dic3—32no—
136C2×C4×Dic3—32no—
137C2×C4×Dic3—32no—
138C2×C4×Dic3C2×D312yes—
139#877—64no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—62no—
153C3⋊#95—62no—
154C23×C32—22no—
155C23×C32—22no—
156C23×C32C22×C412yes—
157C23×C32C2×D412yes—
158C23×C32#4112yes—
159C23×C32C2411yescharacteristic
160C2×C32×C4—28no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4C22×C412yes—
166C2×C32×C4C22×C412yes—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—22no—
173C2×C3×Dic3—28no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—28no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3C22×C412yes—
186C2×C3×Dic3C22×C412yes—
187C2×C3×Dic3C22×C412yes—
188C2×C3×Dic3C22×C412yes—
189C2×C3×Dic3C2×D414yes—
190C2×C3×Dic3#4114yes—
191C2×#117—31no—
192C2×#117—91no—
193C22×C4⋊C4—31no—
194#389—92no—
195#387—92no—
196#387—92no—
197#381—91no—
198#381—91no—
199#380—91no—
200C4×C4⋊C4—92no—
201C4×C22⋊C4—91no—
202C24×C3—21no—
203C24×C3C22×D311yescharacteristic
204C24×C3C22×D311yescharacteristic
205C22×C3×C4—22no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—24no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—31no—
213C22×C3×C4—34no—
214C22×C3×C4—34no—
215C22×C3×C4—31no—
216C22×C3×C4—31no—
217C22×C3×C4—31no—
218C22×C3×C4—32no—
219C22×C3×C4—32no—
220C22×C3×C4—42no—
221C22×C3×C4—42no—
222C22×C3×C4—64no—
223C22×C3×C4—62no—
224C22×C3×C4—62no—
225C22×C3×C4C4×D314yes—
226C22×C3×C4C2×Dic314yes—
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—24no—
234C22×Dic3—32no—
235C22×Dic3—32no—
236C22×Dic3—32no—
237C22×Dic3—32no—
238C22×Dic3—62no—
239C22×Dic3—62no—
240C22×Dic3C2×Dic314yes—
241C22×Dic3C2×Dic314yes—
242C22×Dic3C22×D312yes—
243C22×Dic3C22×D311yescharacteristic
244C22×Dic3C22×D311yescharacteristic
245C22×Dic3C22×D311yescharacteristic
246C22×Dic3C22×D312yes—
247C22×Dic3C22×D311yescharacteristic
248C3×C4⋊C4—34no—
249C3×C4⋊C4—34no—
250C3×C4⋊C4—34no—
251C3×C4⋊C4—34no—
252C3×C4⋊C4—64no—
253C3×C22⋊C4—34no—
254C3×C22⋊C4—62no—
255C3×C42—64no—
256#217—22no—
257#217—62no—
258#217—62no—
259#217—62no—
260#217—62no—
261#217—122no—
262#217—122no—
263#217#6714yes—
264C4⋊Dic3—24no—
265C4⋊Dic3—64no—
266C4⋊Dic3—64no—
267Dic3⋊C4—64no—
268Dic3⋊C4—64no—
269Dic3⋊C4C2×Dic314yes—
270Dic3⋊C4C2×Dic314yes—
271Dic3⋊C4C2×Dic314yes—
272Dic3⋊C4C2×Dic314yes—
273C4×Dic3—24no—
274C4×Dic3—64no—
275C4×Dic3—64no—
276C4×Dic3—64no—
277C4×Dic3—64no—
278C22×C32—22no—
279C22×C32—22no—
280C22×C32—24no—
281C22×C32—24no—
282C22×C32C4×D414yes—
283C22×C32C23×C411yescharacteristic
284C22×C32C22×D411yescharacteristic
285C22×C32C2×#4111yescharacteristic
286C22×C32C2×#4112yes—
287C22×C322−1+412yes—
288C32×C4—22no—
289C32×C4—22no—
290C3⋊Dic3—42no—
291C3⋊Dic3—42no—
292C3×Dic3—22no—
293C3×Dic3—22no—
294C3×Dic3—22no—
295C3×Dic3—24no—
296C3×Dic3—42no—
297C3×Dic3#11714yescomplemented
298C23×C4—31no—
299C23×C4—31no—
300C23×C4D3211yescharacteristic
301#117—64no—
302#117—184no—
303C2×C4⋊C4—38no—
304C2×C4⋊C4—31no—
305C2×C4⋊C4—31no—
306C2×C4⋊C4—31no—
307C2×C4⋊C4—31no—
308C2×C4⋊C4—32no—
309C2×C4⋊C4—92no—
310C2×C4⋊C4—92no—
311C2×C22⋊C4—31no—
312C2×C22⋊C4—31no—
313C2×C22⋊C4—91no—
314C2×C22⋊C4—91no—
315C2×C42—32no—
316C2×C42—92no—
317C2×C42—92no—
318#95—92no—
319#95—92no—
320#95—92no—
321#95—92no—
322#95—92no—
323#95—92no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—21no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3C2×C4×D312yes—
335C23×C3#23512yes—
336C23×C3D3×D412yes—
337C23×C3#23712yes—
338C23×C3C22×Dic312yes—
339C23×C3C2×#6712yes—
340C23×C3C23×D311yescharacteristic
341C23×C3C23×D311yescharacteristic
342C2×C3×C4—28no—
343C2×C3×C4—28no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—32no—
355C2×C3×C4—34no—
356C2×C3×C4—32no—
357C2×C3×C4—32no—
358C2×C3×C4—32no—
359C2×C3×C4—34no—
360C2×C3×C4—41no—
361C2×C3×C4—41no—
362C2×C3×C4—41no—
363C2×C3×C4—41no—
364C2×C3×C4—48no—
365C2×C3×C4—68no—
366C2×C3×C4—68no—
367C2×C3×C4—62no—
368C2×C3×C4—61no—
369C2×C3×C4—61no—
370C2×C3×C4—62no—
371C2×C3×C4—62no—
372C2×C3×C4—61no—
373C2×C3×C4—61no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4C2×C4×D312yes—
378C2×C3×C4C2×C4×D312yes—
379C2×C3×C4C22×Dic312yes—
380C2×C3×C4C22×Dic312yes—
381C2×Dic3—28no—
382C2×Dic3—22no—
383C2×Dic3—21no—
384C2×Dic3—21no—
385C2×Dic3—21no—
386C2×Dic3—21no—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—28no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—122no—
406C2×Dic3—122no—
407C2×Dic3—122no—
408C2×Dic3—122no—
409C2×Dic3—122no—
410C2×Dic3—122no—
411C2×Dic3#23514yes—
412C2×Dic3C22×Dic312yes—
413C2×Dic3C22×Dic312yes—
414C2×Dic3C22×Dic312yes—
415C2×Dic3C22×Dic312yes—
416C2×Dic3C2×#6714yes—
417C2×C32—24no—
418C2×C32C2×#11711yescharacteristic
419C2×C32C2×C4×D411yescharacteristic
420C2×C32#51911yescharacteristic
421C2×C32#54712yes—
422C2×C32#55212yes—
423C24C2×D3211yescharacteristic
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—31no—
427C22×C4—31no—
428C22×C4—31no—
429C22×C4—31no—
430C22×C4—32no—
431C22×C4—34no—
432C22×C4—34no—
433C22×C4—32no—
434C22×C4—64no—
435C22×C4—62no—
436C22×C4—62no—
437C22×C4—92no—
438C22×C4—92no—
439C22×C4D3×Dic314yes—
440C22×C4C2×D3211yescharacteristic
441C22×C4C2×D3211yescharacteristic
442C4⋊C4—34no—
443C4⋊C4—34no—
444C4⋊C4—34no—
445C4⋊C4—34no—
446C4⋊C4—64no—
447C4⋊C4—184no—
448C4⋊C4—184no—
449C22⋊C4—34no—
450C22⋊C4—62no—
451C22⋊C4—182no—
452C22⋊C4—182no—
453C42—64no—
454C42—184no—
455C42—184no—
456C22×C3—24no—
457C22×C3—24no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—22no—
461C22×C3—24no—
462C22×C3—22no—
463C22×C3—24no—
464C22×C3—22no—
465C22×C3—22no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—24no—
470C22×C3—42no—
471C22×C3—44no—
472C22×C3—42no—
473C22×C3—44no—
474C22×C3C4×#6714yes—
475C22×C3D4×Dic314yes—
476C22×C3C22×C4×D311yescharacteristic
477C22×C3C2×#23512yes—
478C22×C3C2×#23511yescharacteristic
479C22×C3C2×D3×D411yescharacteristic
480C22×C3C2×#23711yescharacteristic
481C22×C3#100712yes—
482C22×C3D3×#4112yes—
483C22×C3#101012yes—
484C22×C3C23×Dic311yescharacteristic
485C22×C3C22×#6711yescharacteristic
486C3×C4—22no—
487C3×C4—22no—
488C3×C4—22no—
489C3×C4—22no—
490C3×C4—34no—
491C3×C4—42no—
492C3×C4—42no—
493C3×C4—64no—
494C3×C4—62no—
495C3×C4—62no—
496C3×C4—62no—
497C3×C4—122no—
498Dic3—22no—
499Dic3—22no—
500Dic3—22no—
501Dic3—24no—
502Dic3—42no—
503Dic3—122no—
504Dic3—122no—
505Dic3—122no—
506Dic3—122no—
507Dic3—242no—
508Dic3—242no—
509Dic3#92614yescomplemented
510C32#234411yescharacteristic, complemented, Sylow
511C23—22no—
512C23—22no—
513C23C2×D3×Dic312yes—
514C23#380412yes—
515C23D3×#6712yes—
516C23C22×D3211yescharacteristic
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—28no—
522C2×C4—34no—
523C2×C4—32no—
524C2×C4—32no—
525C2×C4—32no—
526C2×C4—32no—
527C2×C4—34no—
528C2×C4—68no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—61no—
533C2×C4—61no—
534C2×C4—61no—
535C2×C4—61no—
536C2×C4—68no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—182no—
541C2×C4—182no—
542C2×C4—182no—
543C2×C4—182no—
544C2×C4—182no—
545C2×C4—182no—
546C2×C4C2×D3×Dic312yes—
547C2×C4C2×D3×Dic312yes—
548C2×C3—24no—
549C2×C3—24no—
550C2×C3—21no—
551C2×C3—22no—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—22no—
555C2×C3—44no—
556C2×C3#550712yes—
557C2×C3#551312yes—
558C2×C3#551611yescharacteristic
559C2×C3D3×#11711yescharacteristic
560C2×C3#553112yes—
561C2×C3C2×#92611yescharacteristic
562C2×C3C2×C4×#6711yescharacteristic
563C2×C3C2×D4×Dic311yescharacteristic
564C2×C3#581211yescharacteristic
565C2×C3#582412yes—
566C22—22no—
567C22—24no—
568C22—22no—
569C22—24no—
570C22Dic3×#6714yes—
571C22#6429712yes—
572C22D3×#23512yes—
573C22C22×D3×Dic311yescharacteristic
574C22C2×#380411yescharacteristic
575C22C2×D3×#6711yescharacteristic
576C4—22no—
577C4—22no—
578C4—34no—
579C4—64no—
580C4—62no—
581C4—62no—
582C4—62no—
583C4—122no—
584C4—362no—
585C4—362no—
586C3—21no—
587C3#8215911yescharacteristic, complemented
588C3#8223811yescharacteristic, complemented
589C2—24no—
590C2#1059480712yes—
591C2#1059481811yescharacteristic
592C2#1059488512yes—
593C2D3×#92611yescharacteristic
594C2C2×Dic3×#6711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2344
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
8. #10591265C2semidirect
9. #10591262C2semidirect
10. Dic3×Dic3⋊C4C2semidirect
11. #10591201C2semidirect
23. C2×C3×Dic3⋊C4C4semidirect
129. C2×Dic3⋊C4Dic3semidirect
297. C3×Dic3#117semidirect
509. Dic3#926semidirect
510. C32#2344semidirect
587. C3#82159semidirect
588. C3#82238semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9262
C22×C3×Dic3⋊C42
C2×#639552
#105929102
#105917162
Dic3×#2172
#105916962
#105912652
#105912622
Dic3×Dic3⋊C42
#105912012
#822383
#821593