Finite Group Databasebeta

← #11805249

Subgroups — #11805249

Order 1152.

1181 conjugacy classes of subgroups.

The subgroup lattice has 611 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊Dic3C211yesmaximal, characteristic
2#10592627C211yesmaximal, characteristic, complemented
3C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
4C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
5#10591369C212yesmaximal
6Dic3×(C2×D3)⋊C4C212yesmaximal
7#10591331C212yesmaximal, complemented
8#10591313C211yesmaximal, characteristic
9Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
10#10591251C212yesmaximal, complemented
11#10591212C211yesmaximal, characteristic, complemented
12#73768—31nomaximal
13#73457—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×D3×Dic3C2212yes—
16C2×C32×C42C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×#3750C2212yes—
20C2×C3×(C2×D3)⋊C4C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2212yes—
26C2×#3724C2212yes—
27C2×Dic3⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×Dic32C2212yes—
30D3×C4⋊Dic3C418yescomplemented
31#63658C2212yes—
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2211yescharacteristic
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C22×C4⋊Dic3—31no—
39C2×D3×C4⋊C4—31no—
40C3×C4×C4⋊C4—31no—
41C3×C4×C22⋊C4—31no—
42#5212—31no—
43#4987—31no—
44Dic3×C4⋊C4—31no—
45#4972—31no—
46#4942—32no—
47Dic3×C22⋊C4—32no—
48C4×(C2×D3)⋊C4—32no—
49C4×(C2×D3)⋊C4D311yescharacteristic
50C4×C4⋊Dic3—31no—
51C4×C4⋊Dic3D311yescharacteristic, complemented
52#4933—32no—
53#4928—31no—
54#4928—31no—
55#4928—31no—
56#4928—61no—
57#4667—32no—
58#4654—32no—
59#4654—32no—
60#4652—32no—
61C23×C3×D3C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2311yescharacteristic
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3C2×C414yes—
75C2×D3×Dic3—42no—
76C2×D3×Dic3—42no—
77C2×D3×Dic3C2×C418yes—
78C32×C42—22no—
79C4⋊(C3⋊Dic3)—22no—
80C4⋊(C3⋊Dic3)C2×C414yes—
81#3750—42no—
82C3×(C2×D3)⋊C4—22no—
83C3×(C2×D3)⋊C4Q814yes—
84C3×C4⋊Dic3—22no—
85C3×C4⋊Dic3C2×C414yes—
86C3×C4×Dic3—22no—
87C3×C4×Dic3—42no—
88#3724—42no—
89Dic3⋊Dic3C2×C418yes—
90(C2×D3)⋊Dic3—24no—
91Dic32—42no—
92#2345—91noSylow
93C23×C3×C4—31no—
94C23×Dic3—32no—
95C22×C4×D3—32no—
96C22×C4×D3C2×D311yescharacteristic
97C2×C3×C4⋊C4—31no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C22⋊C4—31no—
100C2×C3×C22⋊C4—31no—
101C2×C3×C42—21no—
102C2×C3×C42—31no—
103C2×C3×C42—32no—
104C2×C3×C42C2×D311yescharacteristic
105C2×C3×C42C2×D311yescharacteristic
106C2×#217—32no—
107C2×(C2×D3)⋊C4—32no—
108C2×(C2×D3)⋊C4C2×D311yescharacteristic
109C2×(C2×D3)⋊C4C2×D311yescharacteristic
110C2×C4⋊Dic3—31no—
111C2×C4⋊Dic3—31no—
112C2×C4⋊Dic3—32no—
113C2×C4⋊Dic3—38no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—61no—
117C2×C4⋊Dic3—61no—
118C2×C4⋊Dic3C2×D311yescharacteristic
119C2×C4⋊Dic3C2×D311yescharacteristic
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—62no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3C2×D311yescharacteristic
129C2×C4×Dic3C2×D312yes—
130D3×C4⋊C4—38no—
131C3×#95—32no—
132C3×#95—31no—
133C3×#95—31no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—62no—
143C3⋊#95C2×D311yescharacteristic
144C3⋊#95C2×D312yes—
145C3⋊#95C2×D311yescharacteristic
146C23×C32C2411yescharacteristic
147C22×C3×D3—21no—
148C22×C3×D3—21no—
149C22×C3×D3—21no—
150C22×C3×D3—21no—
151C22×C3×D3C22×C412yes—
152C22×C3×D3C2×Q812yes—
153C22×C3×D3#4112yes—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4C22×C412yes—
160C2×C32×C4C2×Q812yes—
161C2×C32×C4#4112yes—
162C2×C32×C4#4112yes—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3C22×C414yes—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3C22×C412yes—
182C2×C3×Dic3C22×C414yes—
183C2×C3×Dic3C2×Q812yes—
184C3×C4×D3—28no—
185D3×Dic3—48no—
186C22×C4⋊C4—91no—
187#389—91no—
188#389—91no—
189#387—92no—
190#387—92no—
191#380—92no—
192#380—91no—
193C4×C4⋊C4—31no—
194C4×C4⋊C4—91no—
195C4×C22⋊C4—31no—
196C4×C22⋊C4—92no—
197C24×C3—31no—
198C23×D3C22×D311yescharacteristic
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—31no—
203C22×C3×C4—31no—
204C22×C3×C4—32no—
205C22×C3×C4—34no—
206C22×C3×C4—31no—
207C22×C3×C4—32no—
208C22×C3×C4—62no—
209C22×C3×C4—62no—
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C22×Dic3—32no—
217C22×Dic3—32no—
218C22×Dic3—38no—
219C22×Dic3—32no—
220C22×Dic3—32no—
221C22×Dic3—62no—
222C22×Dic3—62no—
223C22×Dic3—122no—
224C22×Dic3—122no—
225C22×Dic3C22×D311yescharacteristic
226C22×Dic3C22×D312yes—
227C22×Dic3C22×D311yescharacteristic
228C22×Dic3C22×D311yescharacteristic
229C22×Dic3C22×D312yes—
230C2×C4×D3—22no—
231C2×C4×D3—22no—
232C2×C4×D3—38no—
233C2×C4×D3—122no—
234C2×C4×D3—122no—
235C2×C4×D3C4×D314yes—
236C3×C4⋊C4—34no—
237C3×C4⋊C4—62no—
238C3×C22⋊C4—34no—
239C3×C22⋊C4—62no—
240C3×C42—22no—
241C3×C42—22no—
242C3×C42—42no—
243C3×C42—62no—
244C3×C42—122no—
245#217—64no—
246(C2×D3)⋊C4—22no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4Dic614yes—
249C4⋊Dic3—22no—
250C4⋊Dic3—34no—
251C4⋊Dic3—34no—
252C4⋊Dic3—38no—
253C4⋊Dic3—64no—
254C4⋊Dic3—62no—
255C4⋊Dic3—62no—
256C4⋊Dic3—122no—
257C4⋊Dic3C4×D314yes—
258Dic3⋊C4—38no—
259Dic3⋊C4—122no—
260Dic3⋊C4—122no—
261Dic3⋊C4—122no—
262Dic3⋊C4—122no—
263Dic3⋊C4—124no—
264C4×Dic3—22no—
265C4×Dic3—42no—
266C4×Dic3—122no—
267C4×Dic3—122no—
268C22×C32C23×C411yescharacteristic
269C22×C32C22×Q811yescharacteristic
270C22×C32C2×#4111yescharacteristic
271C22×C32C2×#4111yescharacteristic
272C22×C32C2×#4111yescharacteristic
273C22×C32H(5,𝔽2)11yescharacteristic
274C22×C32H(5,𝔽2)11yescharacteristic
275C2×C3×D3—22no—
276C2×C3×D3—22no—
277C2×C3×D3—22no—
278C2×C3×D3—22no—
279C2×C3×D3—22no—
280C2×C3×D3—22no—
281C2×C3×D3C4×Q814yes—
282C32×C4—22no—
283C32×C4—41no—
284C32×C4#11714yes—
285C3⋊Dic3—24no—
286C3⋊Dic3—42no—
287C3×Dic3—22no—
288C3×Dic3—24no—
289C3×Dic3—22no—
290C3×Dic3—42no—
291C3×Dic3—41no—
292C23×C4—31no—
293C23×C4—92no—
294C2×C4⋊C4—31no—
295C2×C4⋊C4—31no—
296C2×C4⋊C4—98no—
297C2×C4⋊C4—92no—
298C2×C4⋊C4—91no—
299C2×C4⋊C4—91no—
300C2×C4⋊C4—92no—
301C2×C4⋊C4—92no—
302C2×C22⋊C4—31no—
303C2×C22⋊C4—31no—
304C2×C22⋊C4—92no—
305C2×C42—31no—
306C2×C42—32no—
307C2×C42—92no—
308C2×C42D3211yescharacteristic
309#95—31no—
310#95—31no—
311#95—32no—
312#95—92no—
313#95—92no—
314#95—92no—
315#95—92no—
316C23×C3—21no—
317C23×C3—32no—
318C23×C3—32no—
319C23×C3—32no—
320C23×C3—61no—
321C23×C3—61no—
322C23×C3—61no—
323C23×C3—61no—
324C23×C3C23×D311yescharacteristic
325C23×C3C23×D311yescharacteristic
326C22×D3—21no—
327C22×D3—21no—
328C22×D3—21no—
329C22×D3—21no—
330C22×D3C2×Dic612yes—
331C22×D3C2×C4×D312yes—
332C22×D3#23512yes—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—34no—
349C2×C3×C4—32no—
350C2×C3×C4—32no—
351C2×C3×C4—41no—
352C2×C3×C4—41no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—61no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
358C2×C3×C4—61no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—68no—
362C2×C3×C4—62no—
363C2×C3×C4—61no—
364C2×C3×C4—62no—
365C2×C3×C4—61no—
366C2×C3×C4—61no—
367C2×C3×C4—62no—
368C2×C3×C4C2×Dic612yes—
369C2×C3×C4C2×C4×D312yes—
370C2×C3×C4C2×C4×D312yes—
371C2×C3×C4#23512yes—
372C2×C3×C4#23512yes—
373C2×C3×C4#23712yes—
374C2×C3×C4#23712yes—
375C2×C3×C4D3×Q812yes—
376C2×Dic3—21no—
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—22no—
380C2×Dic3—21no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—21no—
384C2×Dic3—21no—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—21no—
388C2×Dic3—34no—
389C2×Dic3—34no—
390C2×Dic3—64no—
391C2×Dic3—62no—
392C2×Dic3—62no—
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—122no—
402C2×Dic3—122no—
403C2×Dic3—122no—
404C2×Dic3—122no—
405C2×Dic3—122no—
406C2×Dic3—128no—
407C2×Dic3C2×Dic612yes—
408C2×Dic3C2×C4×D312yes—
409C2×Dic3C2×C4×D314yes—
410C4×D3—28no—
411C4×D3—128no—
412C2×C32C2×#11711yescharacteristic
413C2×C32C2×C4×Q811yescharacteristic
414C2×C32#51811yescharacteristic
415C2×C32#55311yescharacteristic
416C2×C32#55311yescharacteristic
417C2×C32#55411yescharacteristic
418C2×C32#55411yescharacteristic
419C3×D3—24no—
420C24—31no—
421C22×C4—31no—
422C22×C4—31no—
423C22×C4—32no—
424C22×C4—34no—
425C22×C4—31no—
426C22×C4—32no—
427C22×C4—62no—
428C22×C4—62no—
429C22×C4—98no—
430C22×C4—92no—
431C22×C4—92no—
432C22×C4—362no—
433C22×C4—362no—
434C22×C4C2×D3211yescharacteristic
435C22×C4C2×D3211yescharacteristic
436C22×C4C2×D3211yescharacteristic
437C4⋊C4—34no—
438C4⋊C4—62no—
439C4⋊C4—98no—
440C4⋊C4—94no—
441C4⋊C4—182no—
442C4⋊C4—362no—
443C4⋊C4—362no—
444C22⋊C4—34no—
445C22⋊C4—62no—
446C22⋊C4—184no—
447C42—22no—
448C42—62no—
449C42—122no—
450C42—362no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—34no—
459C22×C3—62no—
460C22×C3—62no—
461C22×C3—62no—
462C22×C3—62no—
463C22×C3—62no—
464C22×C3—62no—
465C22×C3C22×Dic611yescharacteristic
466C22×C3C22×C4×D311yescharacteristic
467C22×C3C22×C4×D311yescharacteristic
468C22×C3C2×#23511yescharacteristic
469C22×C3C2×#23511yescharacteristic
470C22×C3C2×#23511yescharacteristic
471C22×C3C2×#23711yescharacteristic
472C22×C3C2×#23711yescharacteristic
473C22×C3#100411yescharacteristic
474C22×C3C2×D3×Q811yescharacteristic
475C22×C3D3×#4111yescharacteristic
476C22×C3#100911yescharacteristic
477C22×C3#100911yescharacteristic
478C22×C3#100911yescharacteristic
479C2×D3—22no—
480C2×D3—22no—
481C2×D3—22no—
482C2×D3—22no—
483C2×D3—22no—
484C2×D3—22no—
485C2×D3C4×Dic614yes—
486C3×C4—22no—
487C3×C4—22no—
488C3×C4—24no—
489C3×C4—42no—
490C3×C4—42no—
491C3×C4—41no—
492C3×C4—41no—
493C3×C4—62no—
494C3×C4—64no—
495C3×C4—62no—
496C3×C4—121no—
497C3×C4—122no—
498C3×C4#87214yes—
499C3×C4#87714yes—
500Dic3—22no—
501Dic3—22no—
502Dic3—24no—
503Dic3—42no—
504Dic3—41no—
505Dic3—64no—
506Dic3—64no—
507Dic3—124no—
508Dic3—122no—
509Dic3—122no—
510Dic3—242no—
511C32#234511yescharacteristic, complemented, Sylow
512C23—32no—
513C23—32no—
514C23—32no—
515C23—61no—
516C23—61no—
517C23—61no—
518C23—61no—
519C23C22×D3211yescharacteristic
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—32no—
526C2×C4—34no—
527C2×C4—32no—
528C2×C4—61no—
529C2×C4—61no—
530C2×C4—62no—
531C2×C4—61no—
532C2×C4—62no—
533C2×C4—61no—
534C2×C4—68no—
535C2×C4—61no—
536C2×C4—62no—
537C2×C4—61no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—61no—
541C2×C4—94no—
542C2×C4—182no—
543C2×C4—182no—
544C2×C4—182no—
545C2×C4—182no—
546C2×C4—182no—
547C2×C4—368no—
548C2×C4D3×Dic612yes—
549C2×C4#379512yes—
550C2×C4C4×D3212yes—
551C2×C4#380412yes—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—64no—
560C2×C3C2×C4×Dic611yescharacteristic
561C2×C3C2×#87211yescharacteristic
562C2×C3C2×#87711yescharacteristic
563C2×C3#551111yescharacteristic
564C2×C3#552111yescharacteristic
565C2×C3#553011yescharacteristic
566C2×C3#554311yescharacteristic
567C2×C3#554311yescharacteristic
568C2×C3#554511yescharacteristic
569C2×C3#555811yescharacteristic
570C2×C3#556511yescharacteristic
571C2×C3#556511yescharacteristic
572C2×C3C4×D3×Q811yescharacteristic
573C2×C3#557911yescharacteristic
574D3—24no—
575C22—34no—
576C22—62no—
577C22—62no—
578C22—62no—
579C22—62no—
580C22—62no—
581C22—62no—
582C22C2×D3×Dic611yescharacteristic
583C22C2×#379511yescharacteristic
584C22C2×C4×D3211yescharacteristic
585C22D3×#23511yescharacteristic
586C22#6430711yescharacteristic
587C22#6430811yescharacteristic
588C22C2×#380411yescharacteristic
589C4—22no—
590C4—41no—
591C4—62no—
592C4—62no—
593C4—64no—
594C4—121no—
595C4—122no—
596C4—184no—
597C4—362no—
598C4#6387714yes—
599C3—21no—
600C3#7345711yescharacteristic, complemented
601C3#7376811yescharacteristic, complemented
602C2—64no—
603C2C4×D3×Dic611yescharacteristic
604C2#1059392311yescharacteristic
605C2#1059396011yescharacteristic
606C2#1059399411yescharacteristic
607C2C2×#6387711yescharacteristic
608C2#1059494611yescharacteristic
609C2#1059498811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2345
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10592627C2semidirect
4. C3×C4×C4⋊Dic3C2semidirect
7. #10591331C2semidirect
9. Dic3×C4⋊Dic3C2semidirect
10. #10591251C2semidirect
11. #10591212C2semidirect
30. D3×C4⋊Dic3C4semidirect
51. C4×C4⋊Dic3D3semidirect
511. C32#2345semidirect
600. C3#73457semidirect
601. C3#73768semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊Dic32
#105926272
C3×C4×(C2×D3)⋊C42
C3×C4×C4⋊Dic32
#105913692
Dic3×(C2×D3)⋊C42
#105913312
#105913132
Dic3×C4⋊Dic32
#105912512
#105912122
#737683
#734573