Finite Group Databasebeta

← #11805173

Subgroups — #11805173

Order 1152.

1417 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3750C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic
3C2×#63957C211yesmaximal, characteristic
4C3×#5211C211yesmaximal, characteristic
5#10591720C211yesmaximal, characteristic
6#10591705C211yesmaximal, characteristic
7#10591697C211yesmaximal, characteristic
8#10591264C212yesmaximal, complemented
9#10591263C212yesmaximal, complemented
10#10591243C212yesmaximal, complemented
11#10591197C212yesmaximal, complemented
12#82238—31nomaximal
13#74060—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C2×#3750C418yescomplemented
18C2×#3750C2211yescharacteristic
19C2×#3750C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×C3×#217C2211yescharacteristic
23C2×C3×#217C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C3×#926—24no—
27C2×C3×C4⋊Dic3C2212yes—
28C2×C3×C4×Dic3C2212yes—
29C2×#3724C2212yes—
30C2×#3724C2212yes—
31#63957—24no—
32C2×Dic32C2212yes—
33C2×Dic32C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×#117—31no—
41C2×#926D311yescharacteristic
42C22×Dic3⋊C4—31no—
43C22×Dic3⋊C4—31no—
44C22×Dic3⋊C4—61no—
45C2×#877—31no—
46C2×#877—31no—
47C3×#381—31no—
48#5211D311yescharacteristic
49#4978—32no—
50#4976—32no—
51#4943—31no—
52#4943—31no—
53#4942—31no—
54#4942—31no—
55Dic3×C22⋊C4—31no—
56Dic3×C22⋊C4—31no—
57#4933—32no—
58C4×Dic3⋊C4—32no—
59#4655—32no—
60#4652—32no—
61#4649—32no—
62#4647—32no—
63C24×C32C2311yescharacteristic
64C22×C32×C4—22no—
65C22×C32×C4—22no—
66C22×C32×C4C2×C414yes—
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3—22no—
70C22×C3⋊Dic3—22no—
71C22×C3⋊Dic3—24no—
72C22×C3⋊Dic3C2×C414yes—
73C22×C3⋊Dic3C2×C414yes—
74C22×C3⋊Dic3C2311yescharacteristic
75C22×C3⋊Dic3C2311yescharacteristic
76C22×C3⋊Dic3C2311yescharacteristic
77C22×C3⋊Dic3C2311yescharacteristic
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82#3750C2×C414yes—
83#3750C2×C414yes—
84#3750C2×C414yes—
85#3750C2×C414yes—
86C3×#217—22no—
87C3×#217—22no—
88C3×#217—22no—
89C3×#217D414yes—
90C3×C4⋊Dic3—24no—
91C3×C4×Dic3—24no—
92#3724—24no—
93#3724—24no—
94Dic32—24no—
95Dic32—24no—
96#2344—91noSylow
97C23×C3×C4—21no—
98C23×C3×C4C2×D311yescharacteristic
99C23×C3×C4C2×D311yescharacteristic
100C23×Dic3—31no—
101C23×Dic3—31no—
102C23×Dic3—31no—
103C23×Dic3—31no—
104C23×Dic3—61no—
105C23×Dic3—61no—
106C3×#117—64no—
107C2×C3×C4⋊C4—32no—
108C2×C3×C22⋊C4—31no—
109C2×C3×C22⋊C4—31no—
110C2×C3×C22⋊C4—31no—
111C2×C3×C22⋊C4—31no—
112C2×C3×C42—32no—
113C2×#217C2×D311yescharacteristic
114C2×#217C2×D311yescharacteristic
115C2×#217C2×D311yescharacteristic
116C2×#217C2×D311yescharacteristic
117#926—24no—
118C2×C4⋊Dic3C2×D312yes—
119C2×Dic3⋊C4—38no—
120C2×Dic3⋊C4—38no—
121C2×Dic3⋊C4—31no—
122C2×Dic3⋊C4—31no—
123C2×Dic3⋊C4—31no—
124C2×Dic3⋊C4—31no—
125C2×Dic3⋊C4—31no—
126C2×Dic3⋊C4—31no—
127C2×Dic3⋊C4—31no—
128C2×Dic3⋊C4—31no—
129C2×Dic3⋊C4—32no—
130C2×Dic3⋊C4—32no—
131C2×Dic3⋊C4—32no—
132C2×Dic3⋊C4—32no—
133C2×Dic3⋊C4—68no—
134C2×Dic3⋊C4—61no—
135C2×Dic3⋊C4—61no—
136C2×Dic3⋊C4—61no—
137C2×Dic3⋊C4—61no—
138C2×C4×Dic3—32no—
139C2×C4×Dic3—32no—
140C2×C4×Dic3—32no—
141C2×C4×Dic3—32no—
142C2×C4×Dic3C2×D312yes—
143#877—64no—
144#877—64no—
145C3×#95—32no—
146C3×#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95C2×D312yes—
156C3⋊#95C2×D312yes—
157C23×C32—22no—
158C23×C32—22no—
159C23×C32C22×C412yes—
160C23×C32C2×D412yes—
161C23×C32#4112yes—
162C23×C32C2411yescharacteristic
163C2×C32×C4—28no—
164C2×C32×C4—21no—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4C22×C412yes—
169C2×C32×C4C22×C412yes—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—28no—
172C2×C3⋊Dic3—28no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3C22×C412yes—
178C2×C3⋊Dic3C22×C412yes—
179C2×C3⋊Dic3C22×C412yes—
180C2×C3⋊Dic3C22×C412yes—
181C2×C3⋊Dic3#4114yes—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3C2×D414yes—
194C2×#117—31no—
195C2×#117—91no—
196C22×C4⋊C4—91no—
197#389—92no—
198#387—92no—
199#387—92no—
200#381—31no—
201#381—91no—
202#380—91no—
203C4×C4⋊C4—92no—
204C4×C22⋊C4—91no—
205C24×C3—21no—
206C24×C3C22×D311yescharacteristic
207C24×C3C22×D311yescharacteristic
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—24no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—32no—
216C22×C3×C4—32no—
217C22×C3×C4—32no—
218C22×C3×C4—32no—
219C22×C3×C4—42no—
220C22×C3×C4—42no—
221C22×C3×C4C4×D314yes—
222C22×C3×C4C4×D314yes—
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C22×Dic3—31no—
228C22×Dic3—31no—
229C22×Dic3—34no—
230C22×Dic3—34no—
231C22×Dic3—34no—
232C22×Dic3—34no—
233C22×Dic3—31no—
234C22×Dic3—31no—
235C22×Dic3—31no—
236C22×Dic3—31no—
237C22×Dic3—31no—
238C22×Dic3—31no—
239C22×Dic3—64no—
240C22×Dic3—61no—
241C22×Dic3—61no—
242C22×Dic3—64no—
243C22×Dic3—61no—
244C22×Dic3—61no—
245C22×Dic3—64no—
246C22×Dic3—64no—
247C22×Dic3—68no—
248C22×Dic3—62no—
249C22×Dic3—62no—
250C22×Dic3—62no—
251C22×Dic3—62no—
252C22×Dic3—122no—
253C22×Dic3—122no—
254C22×Dic3C22×D312yes—
255C22×Dic3C22×D312yes—
256C22×Dic3C22×D312yes—
257C22×Dic3C22×D312yes—
258C3×C4⋊C4—64no—
259C3×C22⋊C4—34no—
260C3×C22⋊C4—62no—
261C3×C22⋊C4—62no—
262C3×C22⋊C4—62no—
263C3×C42—64no—
264#217—22no—
265#217—22no—
266#217—22no—
267#217#6714yes—
268C4⋊Dic3—24no—
269Dic3⋊C4—34no—
270Dic3⋊C4—34no—
271Dic3⋊C4—34no—
272Dic3⋊C4—34no—
273Dic3⋊C4—34no—
274Dic3⋊C4—34no—
275Dic3⋊C4—34no—
276Dic3⋊C4—34no—
277Dic3⋊C4—64no—
278Dic3⋊C4—64no—
279Dic3⋊C4—64no—
280Dic3⋊C4—64no—
281Dic3⋊C4—64no—
282Dic3⋊C4—64no—
283Dic3⋊C4—64no—
284Dic3⋊C4—64no—
285C4×Dic3—24no—
286C4×Dic3—64no—
287C4×Dic3—64no—
288C4×Dic3—64no—
289C4×Dic3—64no—
290C22×C32—22no—
291C22×C32—22no—
292C22×C32—24no—
293C22×C32—24no—
294C22×C32C4×D414yes—
295C22×C32C23×C411yescharacteristic
296C22×C32C22×D411yescharacteristic
297C22×C32C2×#4111yescharacteristic
298C22×C32C2×#4112yes—
299C22×C322−1+412yes—
300C32×C4—22no—
301C32×C4—22no—
302C3⋊Dic3—22no—
303C3⋊Dic3—22no—
304C3⋊Dic3—22no—
305C3⋊Dic3#11714yescomplemented
306C3×Dic3—24no—
307C3×Dic3—42no—
308C3×Dic3—42no—
309C3×Dic3—42no—
310C23×C4—91no—
311C23×C4—91no—
312C23×C4D3211yescharacteristic
313#117—64no—
314#117—184no—
315C2×C4⋊C4—32no—
316C2×C4⋊C4—98no—
317C2×C4⋊C4—91no—
318C2×C4⋊C4—91no—
319C2×C4⋊C4—91no—
320C2×C4⋊C4—91no—
321C2×C4⋊C4—92no—
322C2×C4⋊C4—92no—
323C2×C22⋊C4—31no—
324C2×C22⋊C4—31no—
325C2×C22⋊C4—31no—
326C2×C22⋊C4—31no—
327C2×C42—32no—
328C2×C42—92no—
329C2×C42—92no—
330#95—32no—
331#95—32no—
332#95—92no—
333#95—92no—
334#95—92no—
335#95—92no—
336C23×C3—24no—
337C23×C3—24no—
338C23×C3—22no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—22no—
342C23×C3—21no—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3C2×C4×D312yes—
347C23×C3C2×C4×D312yes—
348C23×C3#23512yes—
349C23×C3D3×D412yes—
350C23×C3#23712yes—
351C23×C3C2×#6712yes—
352C23×C3C23×D311yescharacteristic
353C23×C3C23×D311yescharacteristic
354C2×C3×C4—28no—
355C2×C3×C4—28no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—34no—
367C2×C3×C4—41no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—48no—
372C2×C3×C4—62no—
373C2×C3×C4—62no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4C2×C4×D312yes—
384C2×C3×C4C2×C4×D312yes—
385C2×C3×C4C2×C4×D312yes—
386C2×C3×C4C2×C4×D312yes—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—32no—
399C2×Dic3—32no—
400C2×Dic3—34no—
401C2×Dic3—34no—
402C2×Dic3—32no—
403C2×Dic3—32no—
404C2×Dic3—32no—
405C2×Dic3—32no—
406C2×Dic3—32no—
407C2×Dic3—32no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—64no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—68no—
414C2×Dic3—68no—
415C2×Dic3—616no—
416C2×Dic3—64no—
417C2×Dic3—68no—
418C2×Dic3—68no—
419C2×Dic3—61no—
420C2×Dic3—61no—
421C2×Dic3—61no—
422C2×Dic3—61no—
423C2×Dic3—61no—
424C2×Dic3—61no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—61no—
428C2×Dic3—61no—
429C2×Dic3—121no—
430C2×Dic3—121no—
431C2×Dic3—121no—
432C2×Dic3—121no—
433C2×Dic3—128no—
434C2×Dic3C2×#6714yes—
435C2×C32—24no—
436C2×C32C2×#11711yescharacteristic
437C2×C32C2×C4×D411yescharacteristic
438C2×C32#51911yescharacteristic
439C2×C32#54712yes—
440C2×C32#55212yes—
441C24C2×D3211yescharacteristic
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—32no—
445C22×C4—32no—
446C22×C4—32no—
447C22×C4—32no—
448C22×C4—91no—
449C22×C4—91no—
450C22×C4—91no—
451C22×C4—91no—
452C22×C4—94no—
453C22×C4—94no—
454C22×C4—184no—
455C22×C4—182no—
456C22×C4—182no—
457C22×C4#62414yes—
458C22×C4C2×D3211yescharacteristic
459C22×C4C2×D3211yescharacteristic
460C4⋊C4—64no—
461C4⋊C4—94no—
462C4⋊C4—94no—
463C4⋊C4—94no—
464C4⋊C4—94no—
465C4⋊C4—184no—
466C4⋊C4—184no—
467C22⋊C4—34no—
468C22⋊C4—62no—
469C22⋊C4—62no—
470C22⋊C4—62no—
471C42—64no—
472C42—184no—
473C42—184no—
474C22×C3—24no—
475C22×C3—24no—
476C22×C3—28no—
477C22×C3—28no—
478C22×C3—24no—
479C22×C3—24no—
480C22×C3—22no—
481C22×C3—22no—
482C22×C3—22no—
483C22×C3—22no—
484C22×C3—24no—
485C22×C3—24no—
486C22×C3—22no—
487C22×C3—22no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—24no—
492C22×C3#67⋊C414yes—
493C22×C3C4×#6714yes—
494C22×C3C22×C4×D311yescharacteristic
495C22×C3C22×C4×D311yescharacteristic
496C22×C3C2×#23511yescharacteristic
497C22×C3C2×D3×D411yescharacteristic
498C22×C3C2×#23711yescharacteristic
499C22×C3D3×#4112yes—
500C22×C3D3×#4112yes—
501C22×C3#101012yes—
502C22×C3#101012yes—
503C22×C3C22×#6711yescharacteristic
504C3×C4—22no—
505C3×C4—22no—
506C3×C4—22no—
507C3×C4—22no—
508C3×C4—42no—
509C3×C4—42no—
510C3×C4—64no—
511C3×C4—122no—
512C3×C4—122no—
513C3×C4—122no—
514Dic3—24no—
515Dic3—34no—
516Dic3—34no—
517Dic3—42no—
518Dic3—42no—
519Dic3—42no—
520Dic3—64no—
521Dic3—64no—
522Dic3—62no—
523Dic3—62no—
524Dic3—62no—
525Dic3—62no—
526Dic3—62no—
527Dic3—62no—
528Dic3—122no—
529Dic3—122no—
530C32#234411yescharacteristic, complemented, Sylow
531C23—22no—
532C23—22no—
533C23#380412yes—
534C23C2×#62412yes—
535C23D3×#6712yes—
536C23C22×D3211yescharacteristic
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—28no—
542C2×C4—34no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—94no—
555C2×C4—92no—
556C2×C4—92no—
557C2×C4—92no—
558C2×C4—92no—
559C2×C4—188no—
560C2×C4—182no—
561C2×C4—181no—
562C2×C4—181no—
563C2×C4—181no—
564C2×C4—181no—
565C2×C4—188no—
566C2×C4C2×#62412yes—
567C2×C4C2×#62412yes—
568C2×C3—28no—
569C2×C3—24no—
570C2×C3—24no—
571C2×C3—21no—
572C2×C3—22no—
573C2×C3—22no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3C2×#67⋊C411yescharacteristic
577C2×C3#551611yescharacteristic
578C2×C3#551611yescharacteristic
579C2×C3D3×#11711yescharacteristic
580C2×C3D3×#11711yescharacteristic
581C2×C3#553112yes—
582C2×C3#565012yes—
583C2×C3#565512yes—
584C2×C3C2×C4×#6711yescharacteristic
585C2×C3#582412yes—
586C22—22no—
587C22—24no—
588C22—24no—
589C22—22no—
590C22#6395214yes—
591C22#6429812yes—
592C22#6430612yes—
593C22C2×#380411yescharacteristic
594C22C22×#62411yescharacteristic
595C22C2×D3×#6711yescharacteristic
596C4—22no—
597C4—22no—
598C4—64no—
599C4—94no—
600C4—122no—
601C4—122no—
602C4—122no—
603C4—182no—
604C4—182no—
605C4—182no—
606C3—21no—
607C3#7406011yescharacteristic, complemented
608C3#8223811yescharacteristic, complemented
609C2—24no—
610C2#1059482811yescharacteristic
611C2#1059488812yes—
612C2#1059496012yes—
613C2#1059496911yescharacteristic
614C2C2×#6395211yescharacteristic
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. #10591264C2semidirect
9. #10591263C2semidirect
10. #10591243C2semidirect
11. #10591197C2semidirect
17. C2×#3750C4semidirect
305. C3⋊Dic3#117semidirect
530. C32#2344semidirect
607. C3#74060semidirect
608. C3#82238semidirect

Maximal subgroups

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

subgroupindex
C22×#37502
C2×C3×#9262
C2×#639572
C3×#52112
#105917202
#105917052
#105916972
#105912642
#105912632
#105912432
#105911972
#822383
#740603