Finite Group Databasebeta

← #11803402

Subgroups — #11803402

Order 1152.

1407 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#935C211yesmaximal, characteristic
2C2×C3×D4×Dic3C211yesmaximal, characteristic
3C22×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
4#10592919C211yesmaximal, characteristic
5#10591719C211yesmaximal, characteristic, complemented
6#10591718C212yesmaximal, complemented
7#10591702C212yesmaximal, complemented
8Dic3×#217C211yesmaximal, characteristic, complemented
9#10591696C211yesmaximal, characteristic, complemented
10#10591265C212yesmaximal, complemented
11#10591201C212yesmaximal, complemented
12#82836—31nomaximal
13#82326—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C23×C3×Dic3C2211yescharacteristic
19C2×#3757C2211yescharacteristic
20C2×#3757C2212yes—
21C2×C3×#217C2211yescharacteristic
22C2×C3×#217C2211yescharacteristic
23C2×C3×#217C2211yescharacteristic
24C2×C3×#217C2212yes—
25C3×#935C418yescomplemented
26C3×D4×Dic3—24no—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2212yes—
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×Dic3⋊Dic3—24no—
31C2×Dic3⋊Dic3C2212yes—
32C2×Dic3⋊Dic3C2212yes—
33C2×Dic3⋊Dic3C2212yes—
34C2×Dic32C2212yes—
35#63658C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×#123—31no—
41C2×C3×C4×D4—31no—
42C2×#935D311yescharacteristic
43C2×D4×Dic3D311yescharacteristic
44C22×C4⋊Dic3—31no—
45C22×Dic3⋊C4—31no—
46#5220—31no—
47#5220—31no—
48#5220—61no—
49#5211—31no—
50#5210—32no—
51C4×#217—31no—
52#4984—32no—
53#4980—32no—
54#4976—32no—
55#4951—32no—
56#4950—32no—
57#4950—31no—
58#4946—31no—
59#4945—32no—
60#4943—31no—
61Dic3×C22⋊C4—31no—
62#4933—32no—
63C24×C32C2311yescharacteristic
64C24×C32C2311yescharacteristic
65C2×C32×D4—22no—
66C2×C32×D4—22no—
67C2×C32×D4C2×C414yes—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3—22no—
70C22×C3⋊Dic3—42no—
71C22×C3⋊Dic3C2312yes—
72C22×C3⋊Dic3C2312yes—
73C22×C3×Dic3—22no—
74C22×C3×Dic3—22no—
75C22×C3×Dic3—22no—
76C22×C3×Dic3—42no—
77C22×C3×Dic3—42no—
78C22×C3×Dic3C2×C414yescomplemented
79C22×C3×Dic3D414yes—
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86#3757—22no—
87#3757—42no—
88C3×#217—22no—
89C3×#217—22no—
90C3×#217C2×C414yescomplemented
91C3×#217C2×C418yescomplemented
92C3×C4⋊Dic3—22no—
93C3×Dic3⋊C4C2×C418yescomplemented
94C3×C4×Dic3—22no—
95Dic3⋊Dic3—24no—
96Dic3⋊Dic3—24no—
97Dic3⋊Dic3—42no—
98Dic32—42no—
99#2322—91noSylow
100C22×C3×D4—21no—
101C22×C3×D4C2×D311yescharacteristic
102C22×C3×D4C2×D311yescharacteristic
103C23×C3×C4—31no—
104C23×C3×C4—31no—
105C23×C3×C4—31no—
106C23×Dic3—31no—
107C23×Dic3—31no—
108C23×Dic3—61no—
109C23×Dic3C2×D311yescharacteristic
110C23×Dic3C2×D311yescharacteristic
111C23×Dic3C2×D311yescharacteristic
112C3×#123—38no—
113C3×C4×D4—64no—
114C2×C3×C4⋊C4—32no—
115C2×C3×C4⋊C4—31no—
116C2×C3×C22⋊C4—31no—
117C2×C3×C22⋊C4—32no—
118C2×C3×C22⋊C4—31no—
119C2×C3×C22⋊C4—31no—
120C2×C3×C42—31no—
121C2×#217—31no—
122C2×#217—31no—
123C2×#217—32no—
124C2×#217—32no—
125C2×#217—61no—
126C2×#217—62no—
127C2×#217C2×D311yescharacteristic
128C2×#217C2×D311yescharacteristic
129C2×#217C2×D312yes—
130C2×#217C2×D311yescharacteristic
131#935Dic318yescomplemented
132D4×Dic3—24no—
133C2×C4⋊Dic3—32no—
134C2×C4⋊Dic3—32no—
135C2×C4⋊Dic3—32no—
136C2×C4⋊Dic3—64no—
137C2×C4⋊Dic3C2×D311yescharacteristic
138C2×Dic3⋊C4—32no—
139C2×Dic3⋊C4—32no—
140C2×Dic3⋊C4—32no—
141C2×Dic3⋊C4—64no—
142C2×Dic3⋊C4C2×D312yes—
143C2×C4×Dic3—32no—
144C2×C4×Dic3—32no—
145C2×C4×Dic3C2×D311yescharacteristic
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⋊#95—32no—
156C3⋊#95—62no—
157C23×C32—22no—
158C23×C32—22no—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—22no—
162C23×C32—22no—
163C23×C32C22×C412yes—
164C23×C32C22×C412yes—
165C23×C32C2×D412yes—
166C23×C32#4112yes—
167C23×C32C2411yescharacteristic
168C32×D4—28no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4C22×C412yes—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3—44no—
179C2×C3×Dic3—28no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—44no—
191C2×C3×Dic3—44no—
192C2×C3×Dic3C22×C414yes—
193C2×C3×Dic3C22×C414yes—
194C2×C3×Dic3C2×D412yes—
195C2×C3×Dic3C2×D412yes—
196C2×#123—31no—
197C2×C4×D4—31no—
198C22×C4⋊C4—91no—
199#389—92no—
200#388—92no—
201#387—92no—
202#386—91no—
203#385—91no—
204#385—92no—
205#381—91no—
206C4×C22⋊C4—91no—
207C24×C3—21no—
208C24×C3—21no—
209C24×C3C22×D311yescharacteristic
210C24×C3C22×D311yescharacteristic
211C24×C3C22×D311yescharacteristic
212C24×C3C22×D311yescharacteristic
213C2×C3×D4—22no—
214C2×C3×D4—22no—
215C2×C3×D4—22no—
216C2×C3×D4—22no—
217C2×C3×D4—24no—
218C2×C3×D4—42no—
219C2×C3×D4—42no—
220C2×C3×D4C4×D314yes—
221C2×C3×D4C2×Dic314yes—
222C22×C3×C4—21no—
223C22×C3×C4—34no—
224C22×C3×C4—32no—
225C22×C3×C4—31no—
226C22×C3×C4—32no—
227C22×C3×C4—31no—
228C22×C3×C4—34no—
229C22×C3×C4—31no—
230C22×C3×C4—31no—
231C22×C3×C4—62no—
232C22×C3×C4—62no—
233C22×C3×C4—62no—
234C22×C3×C4—122no—
235C22×C3×C4—122no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C22×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3—22no—
241C22×Dic3—32no—
242C22×Dic3—32no—
243C22×Dic3—32no—
244C22×Dic3—32no—
245C22×Dic3—42no—
246C22×Dic3—42no—
247C22×Dic3—62no—
248C22×Dic3—62no—
249C22×Dic3—62no—
250C22×Dic3—62no—
251C22×Dic3—122no—
252C22×Dic3—122no—
253C22×Dic3—122no—
254C22×Dic3—124no—
255C22×Dic3C2×Dic314yescomplemented
256C22×Dic3#6714yes—
257C22×Dic3C22×D311yescharacteristic
258C22×Dic3C22×D311yescharacteristic
259C22×Dic3C22×D312yes—
260C22×Dic3C22×D312yes—
261C22×Dic3C22×D311yescharacteristic
262C22×Dic3C22×D311yescharacteristic
263C3×C4⋊C4—38no—
264C3×C4⋊C4—62no—
265C3×C22⋊C4—34no—
266C3×C22⋊C4—38no—
267C3×C22⋊C4—62no—
268C3×C22⋊C4—62no—
269C3×C42—62no—
270#217—22no—
271#217—22no—
272#217—62no—
273#217—62no—
274#217—122no—
275#217—122no—
276#217—122no—
277#217—124no—
278#217C2×Dic314yescomplemented
279#217C2×Dic318yescomplemented
280C4⋊Dic3—22no—
281C4⋊Dic3—64no—
282C4⋊Dic3—64no—
283C4⋊Dic3—122no—
284Dic3⋊C4—64no—
285Dic3⋊C4—64no—
286Dic3⋊C4—122no—
287Dic3⋊C4C2×Dic318yescomplemented
288C4×Dic3—22no—
289C4×Dic3—122no—
290C4×Dic3—122no—
291C22×C32—24no—
292C22×C32—22no—
293C22×C32—22no—
294C22×C32—24no—
295C22×C32—22no—
296C22×C32—24no—
297C22×C32—41no—
298C22×C32—41no—
299C22×C32—42no—
300C22×C32C4×D414yes—
301C22×C32C23×C411yescharacteristic
302C22×C32C22×D411yescharacteristic
303C22×C32C2×#4111yescharacteristic
304C22×C32H(5,𝔽2)12yes—
305C22×C322−1+412yes—
306C32×C4—22no—
307C3⋊Dic3—42no—
308C3⋊Dic3—42no—
309C3×Dic3—24no—
310C3×Dic3—24no—
311C3×Dic3—22no—
312C3×Dic3—22no—
313C3×Dic3—41no—
314C3×Dic3—41no—
315C22×D4D3211yescharacteristic
316C23×C4—31no—
317C23×C4—31no—
318C23×C4—31no—
319C23×C4—91no—
320#123—38no—
321C4×D4—64no—
322C2×C4⋊C4—32no—
323C2×C4⋊C4—31no—
324C2×C4⋊C4—92no—
325C2×C4⋊C4—92no—
326C2×C4⋊C4—92no—
327C2×C4⋊C4—184no—
328C2×C22⋊C4—31no—
329C2×C22⋊C4—32no—
330C2×C22⋊C4—31no—
331C2×C22⋊C4—31no—
332C2×C22⋊C4—91no—
333C2×C22⋊C4—92no—
334C2×C42—31no—
335C2×C42—92no—
336#95—92no—
337#95—92no—
338#95—92no—
339#95—92no—
340#95—92no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—21no—
346C23×C3—21no—
347C23×C3—21no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3—42no—
361C23×C3—41no—
362C23×C3—41no—
363C23×C3—42no—
364C23×C3C2×C4×D312yes—
365C23×C3C2×C4×D312yes—
366C23×C3#23512yes—
367C23×C3D3×D412yes—
368C23×C3#23712yes—
369C23×C3C22×Dic312yes—
370C23×C3C22×Dic312yes—
371C23×C3C2×#6712yes—
372C23×C3C23×D311yescharacteristic
373C23×C3C23×D311yescharacteristic
374C3×D4—28no—
375C3×D4—28no—
376C3×D4—48no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—22no—
382C2×C3×C4—34no—
383C2×C3×C4—34no—
384C2×C3×C4—32no—
385C2×C3×C4—32no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—68no—
389C2×C3×C4—62no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4—61no—
396C2×C3×C4—61no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
399C2×C3×C4—124no—
400C2×C3×C4—124no—
401C2×C3×C4C2×C4×D312yes—
402C2×C3×C4C22×Dic312yes—
403C2×Dic3—28no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—21no—
413C2×Dic3—21no—
414C2×Dic3—44no—
415C2×Dic3—44no—
416C2×Dic3—64no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—122no—
430C2×Dic3—122no—
431C2×Dic3—122no—
432C2×Dic3—122no—
433C2×Dic3—122no—
434C2×Dic3—124no—
435C2×Dic3—124no—
436C2×Dic3—128no—
437C2×Dic3C22×Dic314yes—
438C2×Dic3C22×Dic314yes—
439C2×Dic3C2×#6712yes—
440C2×Dic3C2×#6712yes—
441C2×C32—24no—
442C2×C32—42no—
443C2×C32C2×C4×D411yescharacteristic
444C2×C32#52012yes—
445C2×C32#53411yescharacteristic
446C2×C32#53611yescharacteristic
447C2×C32#53912yes—
448C24C2×D3211yescharacteristic
449C24C2×D3211yescharacteristic
450C2×D4—22no—
451C2×D4—22no—
452C2×D4D3×Dic314yes—
453C22×C4—31no—
454C22×C4—32no—
455C22×C4—32no—
456C22×C4—31no—
457C22×C4—34no—
458C22×C4—34no—
459C22×C4—31no—
460C22×C4—31no—
461C22×C4—62no—
462C22×C4—62no—
463C22×C4—62no—
464C22×C4—92no—
465C22×C4—92no—
466C22×C4—122no—
467C22×C4—122no—
468C22×C4—182no—
469C22×C4—362no—
470C22×C4C2×D3211yescharacteristic
471C4⋊C4—38no—
472C4⋊C4—62no—
473C4⋊C4—184no—
474C4⋊C4—184no—
475C4⋊C4—362no—
476C22⋊C4—34no—
477C22⋊C4—38no—
478C22⋊C4—62no—
479C22⋊C4—62no—
480C22⋊C4—182no—
481C22⋊C4—362no—
482C42—62no—
483C42—362no—
484C22×C3—22no—
485C22×C3—22no—
486C22×C3—24no—
487C22×C3—24no—
488C22×C3—22no—
489C22×C3—24no—
490C22×C3—22no—
491C22×C3—24no—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—24no—
495C22×C3—24no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—24no—
502C22×C3—42no—
503C22×C3—44no—
504C22×C3—44no—
505C22×C3—42no—
506C22×C3—42no—
507C22×C3—44no—
508C22×C3—41no—
509C22×C3—41no—
510C22×C3—42no—
511C22×C3—41no—
512C22×C3—42no—
513C22×C3—41no—
514C22×C3—82no—
515C22×C3—81no—
516C22×C3—81no—
517C22×C3C4×#6714yes—
518C22×C3D4×Dic314yes—
519C22×C3C22×C4×D311yescharacteristic
520C22×C3C2×#23511yescharacteristic
521C22×C3C2×D3×D411yescharacteristic
522C22×C3C2×#23711yescharacteristic
523C22×C3#100412yes—
524C22×C3#100912yes—
525C22×C3#101012yes—
526C22×C3#101012yes—
527C22×C3C23×Dic311yescharacteristic
528C22×C3C22×#6711yescharacteristic
529C3×C4—22no—
530C3×C4—22no—
531C3×C4—42no—
532C3×C4—62no—
533C3×C4—62no—
534C3×C4—64no—
535C3×C4—64no—
536C3×C4—121no—
537C3×C4—121no—
538Dic3—24no—
539Dic3—22no—
540Dic3—22no—
541Dic3—24no—
542Dic3—41no—
543Dic3—41no—
544Dic3—124no—
545Dic3—122no—
546Dic3—122no—
547Dic3—122no—
548Dic3—122no—
549Dic3—242no—
550C32#232211yescharacteristic, complemented, Sylow
551C23—22no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—21no—
556C23—21no—
557C23C2×D3×Dic312yes—
558C23C2×D3×Dic312yes—
559C23#380412yes—
560C23D3×#6712yes—
561C23C22×D3211yescharacteristic
562D4—28no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—34no—
566C2×C4—34no—
567C2×C4—32no—
568C2×C4—32no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—68no—
576C2×C4—62no—
577C2×C4—62no—
578C2×C4—61no—
579C2×C4—61no—
580C2×C4—124no—
581C2×C4—124no—
582C2×C4—182no—
583C2×C4—182no—
584C2×C4—182no—
585C2×C4—182no—
586C2×C4—182no—
587C2×C4—182no—
588C2×C4—364no—
589C2×C4C2×D3×Dic312yes—
590C2×C3—24no—
591C2×C3—24no—
592C2×C3—22no—
593C2×C3—22no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—44no—
598C2×C3—42no—
599C2×C3—42no—
600C2×C3—82no—
601C2×C3#554612yes—
602C2×C3#556412yes—
603C2×C3#564811yescharacteristic
604C2×C3#565311yescharacteristic
605C2×C3#566512yes—
606C2×C3C2×C4×#6711yescharacteristic
607C2×C3C2×D4×Dic311yescharacteristic
608C2×C3#580411yescharacteristic
609C2×C3#582511yescharacteristic
610C2×C3#582712yes—
611C22—24no—
612C22—24no—
613C22—22no—
614C22—22no—
615C22—24no—
616C22—22no—
617C22—42no—
618C22—41no—
619C22—41no—
620C22Dic3×#6714yes—
621C22#6430912yes—
622C22#6431412yes—
623C22C22×D3×Dic311yescharacteristic
624C22C2×#380411yescharacteristic
625C22C2×D3×#6711yescharacteristic
626C4—22no—
627C4—64no—
628C4—62no—
629C4—62no—
630C4—64no—
631C4—121no—
632C4—121no—
633C4—362no—
634C4—362no—
635C3—21no—
636C3#8232611yescharacteristic, complemented
637C3#8283611yescharacteristic, complemented
638C2—24no—
639C2—42no—
640C2#1059512712yes—
641C2#1059522212yes—
642C2#1059523411yescharacteristic
643C2#1059527011yescharacteristic
644C2C2×Dic3×#6711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
Fitting, prime radicalC22×C32×D4C22
socle, cosocleC23×C32C24
hypercenterC22×D4D32
hypocenterC32#2322
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. C22×Dic3⋊Dic3C2semidirect
5. #10591719C2semidirect
6. #10591718C2semidirect
7. #10591702C2semidirect
8. Dic3×#217C2semidirect
9. #10591696C2semidirect
10. #10591265C2semidirect
11. #10591201C2semidirect
25. C3×#935C4semidirect
78. C22×C3×Dic3C2×C4semidirect
90. C3×#217C2×C4semidirect
91. C3×#217C2×C4semidirect
93. C3×Dic3⋊C4C2×C4semidirect
131. #935Dic3semidirect
255. C22×Dic3C2×Dic3semidirect
278. #217C2×Dic3semidirect
279. #217C2×Dic3semidirect
287. Dic3⋊C4C2×Dic3semidirect
550. C32#2322semidirect
636. C3#82326semidirect
637. C3#82836semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9352
C2×C3×D4×Dic32
C22×Dic3⋊Dic32
#105929192
#105917192
#105917182
#105917022
Dic3×#2172
#105916962
#105912652
#105912012
#828363
#823263