Finite Group Databasebeta

← #11805174

Subgroups — #11805174

Order 1152.

1373 conjugacy classes of subgroups.

The subgroup lattice has 599 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64135C211yesmaximal, characteristic
2C22×C3×Dic3⋊C4C211yesmaximal, characteristic
3C2×#63955C211yesmaximal, characteristic
4C3×#5211C211yesmaximal, characteristic
5#10591716C211yesmaximal, characteristic
6Dic3×#217C211yesmaximal, characteristic
7#10591696C211yesmaximal, characteristic
8#10591272C212yesmaximal, complemented
9#10591268C212yesmaximal, complemented
10#10591241C212yesmaximal, complemented
11#10591192C212yesmaximal, complemented
12#82159—31nomaximal
13#74060—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×#3757C2211yescharacteristic
18C2×#3757C2211yescharacteristic
19#64135—24no—
20C2×C4⋊(C3⋊Dic3)C2212yes—
21C2×C4×C3⋊Dic3C2212yes—
22C2×C3×#217C2211yescharacteristic
23C2×C3×#217C2211yescharacteristic
24C2×C3×Dic3⋊C4C418yescomplemented
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic3⋊Dic3C2212yes—
31#63955—24no—
32C2×Dic32C2212yes—
33C2×Dic32C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C22×C3×C4⋊C4—31no—
41C2×#926—31no—
42C2×#926—31no—
43C2×#926—31no—
44C2×#926—61no—
45C22×Dic3⋊C4D311yescharacteristic
46C2×#877—31no—
47C3×#381—31no—
48#5212—31no—
49#5211—31no—
50#5211D311yescharacteristic
51C4×#217—31no—
52#4984—32no—
53#4980—32no—
54#4980—32no—
55Dic3×C4⋊C4—32no—
56#4943—31no—
57#4942—31no—
58Dic3×C22⋊C4—31no—
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⋊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×Dic3C2312yes—
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2311yescharacteristic
82#3757—22no—
83#3757D414yes—
84C4⋊(C3⋊Dic3)—24no—
85C4×C3⋊Dic3—24no—
86C3×#217—22no—
87C3×#217—22no—
88C3×Dic3⋊C4C2×C414yes—
89C3×Dic3⋊C4C2×C414yes—
90C3×Dic3⋊C4C2×C414yes—
91C3×Dic3⋊C4C2×C414yes—
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
104C2×C3×C4⋊C4—38no—
105C2×C3×C4⋊C4—31no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C4⋊C4—31no—
108C2×C3×C4⋊C4—31no—
109C2×C3×C22⋊C4—31no—
110C2×C3×C22⋊C4—31no—
111C2×#217—31no—
112C2×#217—31no—
113C2×#217—31no—
114C2×#217—31no—
115C2×#217—61no—
116C2×#217—61no—
117C2×#217C2×D311yescharacteristic
118C2×#217C2×D311yescharacteristic
119#926—64no—
120#926—64no—
121#926—64no—
122#926—68no—
123C2×C4⋊Dic3—32no—
124C2×C4⋊Dic3—32no—
125C2×C4⋊Dic3—32no—
126C2×C4⋊Dic3—32no—
127C2×C4⋊Dic3—62no—
128C2×Dic3⋊C4—32no—
129C2×Dic3⋊C4—32no—
130C2×Dic3⋊C4Dic318yescomplemented
131C2×Dic3⋊C4C2×D311yescharacteristic
132C2×Dic3⋊C4C2×D311yescharacteristic
133C2×Dic3⋊C4C2×D311yescharacteristic
134C2×Dic3⋊C4C2×D311yescharacteristic
135C2×C4×Dic3—32no—
136C2×C4×Dic3—32no—
137C2×C4×Dic3—32no—
138C2×C4×Dic3—32no—
139C2×C4×Dic3—32no—
140C2×C4×Dic3—32no—
141C2×C4×Dic3—62no—
142#877—64no—
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—32no—
153C3⋊#95C2×D312yes—
154C3⋊#95C2×D312yes—
155C23×C32—22no—
156C23×C32—22no—
157C23×C32C22×C412yes—
158C23×C32C2×D412yes—
159C23×C32#4112yes—
160C23×C32C2411yescharacteristic
161C2×C32×C4—28no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4—21no—
166C2×C32×C4C22×C412yes—
167C2×C32×C4C22×C412yes—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3C2×D414yes—
174C2×C3×Dic3—28no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—28no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3C22×C412yes—
188C2×C3×Dic3C22×C412yes—
189C2×C3×Dic3C22×C412yes—
190C2×C3×Dic3C22×C412yes—
191C2×C3×Dic3#4114yes—
192C2×#117—91no—
193C2×#117—91no—
194C22×C4⋊C4—31no—
195#389—92no—
196#387—92no—
197#387—92no—
198#381—31no—
199#381—91no—
200#380—91no—
201C4×C4⋊C4—92no—
202C4×C22⋊C4—91no—
203C24×C3—21no—
204C24×C3C22×D311yescharacteristic
205C24×C3C22×D311yescharacteristic
206C22×C3×C4—24no—
207C22×C3×C4—24no—
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—31no—
216C22×C3×C4—34no—
217C22×C3×C4—34no—
218C22×C3×C4—31no—
219C22×C3×C4—31no—
220C22×C3×C4—31no—
221C22×C3×C4—32no—
222C22×C3×C4—32no—
223C22×C3×C4—64no—
224C22×C3×C4—62no—
225C22×C3×C4—62no—
226C22×C3×C4C4×D314yes—
227C22×C3×C4C2×Dic314yes—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—24no—
235C22×Dic3—32no—
236C22×Dic3—32no—
237C22×Dic3—32no—
238C22×Dic3—32no—
239C22×Dic3—62no—
240C22×Dic3—62no—
241C22×Dic3C2×Dic314yes—
242C22×Dic3C2×Dic314yes—
243C22×Dic3C22×D312yes—
244C22×Dic3C22×D312yes—
245C22×Dic3C22×D311yescharacteristic
246C22×Dic3C22×D311yescharacteristic
247C22×Dic3C22×D311yescharacteristic
248C22×Dic3C22×D311yescharacteristic
249C3×C4⋊C4—34no—
250C3×C4⋊C4—34no—
251C3×C4⋊C4—34no—
252C3×C4⋊C4—34no—
253C3×C22⋊C4—62no—
254C3×C22⋊C4—62no—
255#217—22no—
256#217—22no—
257#217—34no—
258#217—34no—
259#217—64no—
260#217—64no—
261#217—62no—
262#217—62no—
263C4⋊Dic3—64no—
264C4⋊Dic3—64no—
265C4⋊Dic3—64no—
266C4⋊Dic3—64no—
267C4⋊Dic3—68no—
268Dic3⋊C4—64no—
269Dic3⋊C4—64no—
270Dic3⋊C4C2×Dic314yes—
271Dic3⋊C4C2×Dic314yes—
272Dic3⋊C4C2×Dic314yes—
273Dic3⋊C4C2×Dic314yes—
274C4×Dic3—64no—
275C4×Dic3—64no—
276C4×Dic3—64no—
277C4×Dic3—64no—
278C4×Dic3—64no—
279C4×Dic3—68no—
280C4×Dic3—64no—
281C22×C32—22no—
282C22×C32—22no—
283C22×C32—24no—
284C22×C32—24no—
285C22×C32C4×D414yes—
286C22×C32C23×C411yescharacteristic
287C22×C32C22×D411yescharacteristic
288C22×C32C2×#4112yes—
289C22×C32C2×#4111yescharacteristic
290C22×C322−1+412yes—
291C32×C4—22no—
292C32×C4—22no—
293C3⋊Dic3—24no—
294C3⋊Dic3—42no—
295C3×Dic3—22no—
296C3×Dic3—22no—
297C3×Dic3—22no—
298C3×Dic3—42no—
299C3×Dic3—42no—
300C3×Dic3#11714yescomplemented
301C23×C4—31no—
302C23×C4—31no—
303C23×C4D3211yescharacteristic
304#117—184no—
305#117—184no—
306C2×C4⋊C4—38no—
307C2×C4⋊C4—31no—
308C2×C4⋊C4—31no—
309C2×C4⋊C4—31no—
310C2×C4⋊C4—31no—
311C2×C4⋊C4—92no—
312C2×C4⋊C4—92no—
313C2×C4⋊C4—92no—
314C2×C22⋊C4—31no—
315C2×C22⋊C4—31no—
316C2×C22⋊C4—91no—
317C2×C22⋊C4—91no—
318C2×C42—92no—
319C2×C42—92no—
320C2×C42—92no—
321#95—32no—
322#95—32no—
323#95—92no—
324#95—92no—
325#95—92no—
326#95—92no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—21no—
332C23×C3—22no—
333C23×C3—22no—
334C23×C3—22no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3C2×C4×D312yes—
338C23×C3D3×D412yes—
339C23×C3D3×D412yes—
340C23×C3#23712yes—
341C23×C3#23712yes—
342C23×C3C22×Dic312yes—
343C23×C3C23×D311yescharacteristic
344C23×C3C23×D311yescharacteristic
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—216no—
350C2×C3×C4—28no—
351C2×C3×C4—28no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—32no—
363C2×C3×C4—34no—
364C2×C3×C4—32no—
365C2×C3×C4—32no—
366C2×C3×C4—32no—
367C2×C3×C4—68no—
368C2×C3×C4—68no—
369C2×C3×C4—61no—
370C2×C3×C4—61no—
371C2×C3×C4—61no—
372C2×C3×C4—61no—
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×C4C2×C4×D312yes—
381C2×C3×C4C2×C4×D312yes—
382C2×C3×C4C22×Dic312yes—
383C2×C3×C4C22×Dic312yes—
384C2×Dic3—28no—
385C2×Dic3—22no—
386C2×Dic3—21no—
387C2×Dic3—21no—
388C2×Dic3—21no—
389C2×Dic3—21no—
390C2×Dic3—28no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—34no—
398C2×Dic3—34no—
399C2×Dic3—64no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—64no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—122no—
412C2×Dic3—122no—
413C2×Dic3—122no—
414C2×Dic3—122no—
415C2×Dic3#23514yes—
416C2×Dic3C22×Dic312yes—
417C2×Dic3C22×Dic312yes—
418C2×Dic3C22×Dic312yes—
419C2×Dic3C22×Dic312yes—
420C2×C32—24no—
421C2×C32C2×#11711yescharacteristic
422C2×C32C2×C4×D411yescharacteristic
423C2×C32#51911yescharacteristic
424C2×C32#54712yes—
425C2×C32#55212yes—
426C24C2×D3211yescharacteristic
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—31no—
430C22×C4—31no—
431C22×C4—31no—
432C22×C4—31no—
433C22×C4—34no—
434C22×C4—34no—
435C22×C4—32no—
436C22×C4—32no—
437C22×C4—64no—
438C22×C4—62no—
439C22×C4—62no—
440C22×C4—92no—
441C22×C4—92no—
442C22×C4D3×Dic314yes—
443C22×C4C2×D3211yescharacteristic
444C22×C4C2×D3211yescharacteristic
445C4⋊C4—34no—
446C4⋊C4—34no—
447C4⋊C4—34no—
448C4⋊C4—34no—
449C4⋊C4—184no—
450C4⋊C4—184no—
451C4⋊C4—184no—
452C22⋊C4—62no—
453C22⋊C4—62no—
454C22⋊C4—94no—
455C22⋊C4—182no—
456C42—184no—
457C42—184no—
458C42—184no—
459C22×C3—24no—
460C22×C3—24no—
461C22×C3—24no—
462C22×C3—24no—
463C22×C3—22no—
464C22×C3—22no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—22no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—24no—
473C22×C3—42no—
474C22×C3—44no—
475C22×C3—42no—
476C22×C3—44no—
477C22×C3#67⋊C414yes—
478C22×C3D4×Dic314yes—
479C22×C3C22×C4×D311yescharacteristic
480C22×C3C2×#23512yes—
481C22×C3C2×D3×D411yescharacteristic
482C22×C3C2×D3×D411yescharacteristic
483C22×C3C2×#23711yescharacteristic
484C22×C3C2×#23711yescharacteristic
485C22×C3#100712yes—
486C22×C3D3×#4112yes—
487C22×C3#101012yes—
488C22×C3C23×Dic311yescharacteristic
489C3×C4—24no—
490C3×C4—24no—
491C3×C4—22no—
492C3×C4—22no—
493C3×C4—22no—
494C3×C4—22no—
495C3×C4—34no—
496C3×C4—62no—
497C3×C4—62no—
498C3×C4—62no—
499C3×C4—122no—
500C3×C4—122no—
501Dic3—22no—
502Dic3—22no—
503Dic3—22no—
504Dic3—42no—
505Dic3—42no—
506Dic3—64no—
507Dic3—64no—
508Dic3—124no—
509Dic3—124no—
510Dic3—122no—
511Dic3—122no—
512Dic3#92614yescomplemented
513C32#234411yescharacteristic, complemented, Sylow
514C23—22no—
515C23—22no—
516C23C2×D3×Dic312yes—
517C23#380512yes—
518C23#381112yes—
519C23C22×D3211yescharacteristic
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—28no—
525C2×C4—34no—
526C2×C4—32no—
527C2×C4—32no—
528C2×C4—32no—
529C2×C4—32no—
530C2×C4—68no—
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—62no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—94no—
544C2×C4—182no—
545C2×C4—182no—
546C2×C4—182no—
547C2×C4—182no—
548C2×C4—182no—
549C2×C4C2×D3×Dic312yes—
550C2×C4C2×D3×Dic312yes—
551C2×C3—24no—
552C2×C3—24no—
553C2×C3—21no—
554C2×C3—22no—
555C2×C3—21no—
556C2×C3—22no—
557C2×C3—21no—
558C2×C3—44no—
559C2×C3C2×#67⋊C411yescharacteristic
560C2×C3#550712yes—
561C2×C3#551312yes—
562C2×C3#551611yescharacteristic
563C2×C3D3×#11711yescharacteristic
564C2×C3#565012yes—
565C2×C3#565512yes—
566C2×C3C2×#92611yescharacteristic
567C2×C3C2×D4×Dic311yescharacteristic
568C2×C3#581211yescharacteristic
569C22—22no—
570C22—24no—
571C22—22no—
572C22—24no—
573C22#67⋊Dic314yes—
574C22#6429712yes—
575C22D3×#23512yes—
576C22C22×D3×Dic311yescharacteristic
577C22C2×#380511yescharacteristic
578C22C2×#381111yescharacteristic
579C4—22no—
580C4—22no—
581C4—34no—
582C4—62no—
583C4—62no—
584C4—62no—
585C4—122no—
586C4—122no—
587C4—184no—
588C4—362no—
589C3—21no—
590C3#7406011yescharacteristic, complemented
591C3#8215911yescharacteristic, complemented
592C2—24no—
593C2#1059481811yescharacteristic
594C2#1059491712yes—
595C2D3×#92611yescharacteristic
596C2#1059495212yes—
597C2C2×#67⋊Dic311yescharacteristic
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. #10591272C2semidirect
9. #10591268C2semidirect
10. #10591241C2semidirect
11. #10591192C2semidirect
24. C2×C3×Dic3⋊C4C4semidirect
130. C2×Dic3⋊C4Dic3semidirect
300. C3×Dic3#117semidirect
512. Dic3#926semidirect
513. C32#2344semidirect
590. C3#74060semidirect
591. C3#82159semidirect

Maximal subgroups

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

subgroupindex
C2×#641352
C22×C3×Dic3⋊C42
C2×#639552
C3×#52112
#105917162
Dic3×#2172
#105916962
#105912722
#105912682
#105912412
#105911922
#821593
#740603