Finite Group Databasebeta

← #11802863

Subgroups — #11802863

Order 1152.

1065 conjugacy classes of subgroups.

The subgroup lattice has 603 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#872C211yesmaximal, characteristic
2C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
4#10591349C211yesmaximal, characteristic, complemented
5#10591313C211yesmaximal, characteristic
6#10591313C211yesmaximal, characteristic
7#10591305C212yesmaximal
8#10591286C212yesmaximal
9#10591224C211yesmaximal, characteristic, complemented
10#10591201C212yesmaximal, complemented
11#10591192C212yesmaximal, complemented
12#82231—31nomaximal
13#73760—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4×C3⋊Dic3C2212yes—
19C2×C3×(C2×D3)⋊C4C2211yescharacteristic
20C2×C3×(C2×D3)⋊C4C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×C4×Dic3C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C3×#872C418yescomplemented
28C2×Dic3⋊Dic3C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30C2×(C2×D3)⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2212yes—
32#63658C2212yes—
33C3×C3⋊#95C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×C3×#117—31no—
39C2×#872D311yescharacteristic
40C3×C4×C4⋊C4—31no—
41#5212—31no—
42#5212—31no—
43#4987—31no—
44#4987—31no—
45#4980—32no—
46#4980—32no—
47#4977—31no—
48#4975—31no—
49#4951—32no—
50#4951—32no—
51#4940—32no—
52#4936—31no—
53#4935—31no—
54C4×C4⋊Dic3—31no—
55C4×C4⋊Dic3—31no—
56C4×C4⋊Dic3—61no—
57C4×C4⋊Dic3D311yescharacteristic, complemented
58#4933—32no—
59#4669—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×Dic3C2312yes—
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3C2×C414yes—
75C32×C42C2×C414yes—
76C4⋊(C3⋊Dic3)—22no—
77C4⋊(C3⋊Dic3)—22no—
78C4×C3⋊Dic3—42no—
79C3×(C2×D3)⋊C4C2×C414yes—
80C3×(C2×D3)⋊C4C2×C414yes—
81C3×C4⋊Dic3—22no—
82C3×C4⋊Dic3—22no—
83C3×Dic3⋊C4C2×C414yes—
84C3×Dic3⋊C4C2×C414yes—
85C3×C4×Dic3—42no—
86C3×C4×Dic3C2×C414yes—
87Dic3⋊Dic3—42no—
88Dic3⋊Dic3—42no—
89(C2×D3)⋊Dic3—42no—
90(C2×D3)⋊Dic3—42no—
91#2314—91noSylow
92C23×C3×C4—31no—
93C22×C4×D3C2×D311yescharacteristic
94C3×#117—38no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—31no—
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×#217—32no—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4C2×D311yescharacteristic
111C2×(C2×D3)⋊C4C2×D311yescharacteristic
112C2×C4⋊Dic3—31no—
113C2×C4⋊Dic3—31no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—32no—
117C2×C4⋊Dic3—32no—
118C2×C4⋊Dic3—61no—
119C2×C4⋊Dic3—61no—
120C2×C4⋊Dic3C2×D311yescharacteristic
121C2×C4⋊Dic3C2×D311yescharacteristic
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4C2×D311yescharacteristic
125C2×Dic3⋊C4C2×D311yescharacteristic
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—62no—
129C2×C4×Dic3C2×D312yes—
130C2×C4×Dic3C2×D311yescharacteristic
131#872Dic318yescomplemented
132C3×#95—32no—
133C3⋊#95—32no—
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—32no—
143C3⋊#95—62no—
144C3⋊#95C2×D312yes—
145C23×C32C2411yescharacteristic
146C22×C3×D3—21no—
147C22×C3×D3—21no—
148C22×C3×D3—21no—
149C22×C3×D3—21no—
150C22×C3×D3—21no—
151C22×C3×D3—21no—
152C22×C3×D3C22×C412yes—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4C22×C412yes—
158C2×C32×C4C22×C412yes—
159C2×C32×C4C22×C412yes—
160C2×C32×C4#4112yes—
161C2×C32×C4#4112yes—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3C22×C412yes—
181C2×C3×Dic3C22×C412yes—
182C2×C3×Dic3C22×C412yes—
183C3×C4×D3—28no—
184C2×#117—31no—
185#388—92no—
186#388—92no—
187#387—92no—
188#387—92no—
189#384—91no—
190#382—91no—
191#380—91no—
192#380—91no—
193C4×C4⋊C4—31no—
194C4×C4⋊C4—91no—
195C24×C3—31no—
196C23×D3C22×D311yescharacteristic
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—31no—
201C22×C3×C4—31no—
202C22×C3×C4—31no—
203C22×C3×C4—34no—
204C22×C3×C4—32no—
205C22×C3×C4—32no—
206C22×C3×C4—62no—
207C22×C3×C4—62no—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×Dic3—32no—
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—32no—
218C22×Dic3—62no—
219C22×Dic3—62no—
220C22×Dic3C22×D312yes—
221C22×Dic3C22×D312yes—
222C22×Dic3C22×D311yescharacteristic
223C22×Dic3C22×D311yescharacteristic
224C22×Dic3C22×D311yescharacteristic
225C2×C4×D3—22no—
226C2×C4×D3—22no—
227C2×C4×D3C2×Dic314yes—
228C3×C4⋊C4—34no—
229C3×C4⋊C4—34no—
230C3×C4⋊C4—62no—
231C3×C4⋊C4—62no—
232C3×C22⋊C4—34no—
233C3×C22⋊C4—34no—
234C3×C42—24no—
235C3×C42—34no—
236C3×C42—122no—
237C3×C42C4×D314yes—
238C3×C42C2×Dic314yes—
239#217—122no—
240#217—122no—
241(C2×D3)⋊C4—122no—
242(C2×D3)⋊C4—122no—
243(C2×D3)⋊C4C2×Dic314yes—
244(C2×D3)⋊C4C2×Dic314yes—
245C4⋊Dic3—22no—
246C4⋊Dic3—22no—
247C4⋊Dic3—64no—
248C4⋊Dic3—64no—
249C4⋊Dic3—62no—
250C4⋊Dic3—62no—
251C4⋊Dic3—62no—
252C4⋊Dic3—62no—
253C4⋊Dic3—122no—
254C4⋊Dic3—122no—
255Dic3⋊C4—122no—
256Dic3⋊C4—122no—
257Dic3⋊C4C2×Dic314yes—
258Dic3⋊C4C2×Dic314yes—
259C4×Dic3—42no—
260C4×Dic3—122no—
261C4×Dic3—122no—
262C4×Dic3—124no—
263C4×Dic3C2×Dic314yes—
264C22×C32C23×C411yescharacteristic
265C22×C32C2×#4111yescharacteristic
266C22×C32C2×#4111yescharacteristic
267C22×C32H(5,𝔽2)11yescharacteristic
268C22×C32H(5,𝔽2)11yescharacteristic
269C22×C322−1+411yescharacteristic
270C22×C322−1+411yescharacteristic
271C2×C3×D3—22no—
272C2×C3×D3—22no—
273C2×C3×D3—22no—
274C2×C3×D3—41no—
275C2×C3×D3—41no—
276C2×C3×D3—41no—
277C2×C3×D3—41no—
278C32×C4—22no—
279C32×C4—22no—
280C32×C4#11714yes—
281C3⋊Dic3—42no—
282C3⋊Dic3—42no—
283C3×Dic3—22no—
284C3×Dic3—22no—
285C3×Dic3—22no—
286C3×Dic3—42no—
287C3×Dic3—42no—
288C23×C4—31no—
289#117—38no—
290C2×C4⋊C4—31no—
291C2×C4⋊C4—31no—
292C2×C4⋊C4—31no—
293C2×C4⋊C4—31no—
294C2×C4⋊C4—91no—
295C2×C4⋊C4—91no—
296C2×C4⋊C4—92no—
297C2×C4⋊C4—92no—
298C2×C22⋊C4—31no—
299C2×C22⋊C4—31no—
300C2×C22⋊C4—92no—
301C2×C22⋊C4—92no—
302C2×C42—31no—
303C2×C42—32no—
304C2×C42—92no—
305C2×C42D3211yescharacteristic
306#95—32no—
307#95—92no—
308#95—92no—
309#95—92no—
310#95—92no—
311#95—92no—
312C23×C3—21no—
313C23×C3—32no—
314C23×C3—61no—
315C23×C3—61no—
316C23×C3—61no—
317C23×C3—61no—
318C23×C3—61no—
319C23×C3—61no—
320C23×C3C23×D311yescharacteristic
321C23×C3C23×D311yescharacteristic
322C22×D3—21no—
323C22×D3—21no—
324C22×D3—21no—
325C22×D3—21no—
326C22×D3—21no—
327C22×D3—21no—
328C22×D3C22×Dic312yes—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—32no—
345C2×C3×C4—32no—
346C2×C3×C4—32no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—61no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—61no—
355C2×C3×C4—68no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4C2×C4×D312yes—
363C2×C3×C4C2×C4×D312yes—
364C2×C3×C4C2×C4×D312yes—
365C2×C3×C4#23512yes—
366C2×C3×C4#23512yes—
367C2×C3×C4#23512yes—
368C2×C3×C4#23512yes—
369C2×C3×C4C22×Dic312yes—
370C2×C3×C4C22×Dic312yes—
371C2×C3×C4C22×Dic312yes—
372C2×Dic3—21no—
373C2×Dic3—21no—
374C2×Dic3—21no—
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—21no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—64no—
385C2×Dic3—64no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—122no—
399C2×Dic3—122no—
400C2×Dic3—122no—
401C2×Dic3—122no—
402C2×Dic3C22×Dic312yes—
403C2×Dic3C22×Dic312yes—
404C2×Dic3C22×Dic312yes—
405C4×D3—28no—
406C2×C32C2×#11711yescharacteristic
407C2×C32#52011yescharacteristic
408C2×C32#52011yescharacteristic
409C2×C32#54011yescharacteristic
410C2×C32#54111yescharacteristic
411C2×C32#54211yescharacteristic
412C2×C32#54211yescharacteristic
413C3×D3—42no—
414C24—31no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—31no—
418C22×C4—34no—
419C22×C4—32no—
420C22×C4—32no—
421C22×C4—62no—
422C22×C4—62no—
423C22×C4—92no—
424C22×C4—92no—
425C22×C4C2×D3211yescharacteristic
426C22×C4C2×D3211yescharacteristic
427C22×C4C2×D3211yescharacteristic
428C4⋊C4—34no—
429C4⋊C4—34no—
430C4⋊C4—62no—
431C4⋊C4—62no—
432C4⋊C4—182no—
433C4⋊C4—182no—
434C4⋊C4—362no—
435C4⋊C4—362no—
436C22⋊C4—34no—
437C22⋊C4—34no—
438C22⋊C4—362no—
439C22⋊C4—362no—
440C42—34no—
441C42—122no—
442C42—362no—
443C42D3×Dic314yes—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—62no—
452C22×C3—62no—
453C22×C3—62no—
454C22×C3—121no—
455C22×C3—121no—
456C22×C3—121no—
457C22×C3—121no—
458C22×C3C22×C4×D311yescharacteristic
459C22×C3C2×#23511yescharacteristic
460C22×C3C2×#23511yescharacteristic
461C22×C3C2×#23511yescharacteristic
462C22×C3C2×#23511yescharacteristic
463C22×C3#100411yescharacteristic
464C22×C3#100711yescharacteristic
465C22×C3#100911yescharacteristic
466C22×C3#100911yescharacteristic
467C22×C3#100911yescharacteristic
468C22×C3#101011yescharacteristic
469C22×C3#101011yescharacteristic
470C22×C3#101011yescharacteristic
471C22×C3C23×Dic311yescharacteristic
472C2×D3—22no—
473C2×D3—22no—
474C2×D3—22no—
475C2×D3—41no—
476C2×D3—41no—
477C2×D3—41no—
478C2×D3—41no—
479C3×C4—24no—
480C3×C4—22no—
481C3×C4—22no—
482C3×C4—22no—
483C3×C4—22no—
484C3×C4—24no—
485C3×C4—42no—
486C3×C4—62no—
487C3×C4—62no—
488C3×C4—62no—
489C3×C4—122no—
490C3×C4—122no—
491C3×C4#87214yes—
492C3×C4#92614yes—
493Dic3—22no—
494Dic3—22no—
495Dic3—22no—
496Dic3—42no—
497Dic3—42no—
498Dic3—124no—
499Dic3—124no—
500Dic3—122no—
501Dic3—122no—
502Dic3—122no—
503Dic3—122no—
504C32#231411yescharacteristic, complemented, Sylow
505C23—32no—
506C23—61no—
507C23—61no—
508C23—61no—
509C23—61no—
510C23—61no—
511C23—61no—
512C23C22×D3211yescharacteristic
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—32no—
518C2×C4—32no—
519C2×C4—32no—
520C2×C4—61no—
521C2×C4—61no—
522C2×C4—61no—
523C2×C4—61no—
524C2×C4—61no—
525C2×C4—61no—
526C2×C4—68no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—182no—
534C2×C4—182no—
535C2×C4—182no—
536C2×C4—182no—
537C2×C4—182no—
538C2×C4—182no—
539C2×C4#379812yes—
540C2×C4#379812yes—
541C2×C4C2×D3×Dic312yes—
542C2×C4C2×D3×Dic312yes—
543C2×C4C2×D3×Dic312yes—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—122no—
552C2×C3C2×#87211yescharacteristic
553C2×C3#550411yescharacteristic
554C2×C3#551811yescharacteristic
555C2×C3#552311yescharacteristic
556C2×C3#553411yescharacteristic
557C2×C3#553411yescharacteristic
558C2×C3#553511yescharacteristic
559C2×C3#556111yescharacteristic
560C2×C3#556211yescharacteristic
561C2×C3#558211yescharacteristic
562C2×C3#558311yescharacteristic
563C2×C3C2×#92611yescharacteristic
564C2×C3#582711yescharacteristic
565C2×C3#582711yescharacteristic
566D3—42no—
567C22—62no—
568C22—62no—
569C22—62no—
570C22—121no—
571C22—121no—
572C22—121no—
573C22—121no—
574C22#6429711yescharacteristic
575C22#6429811yescharacteristic
576C22C2×#379811yescharacteristic
577C22C2×#379811yescharacteristic
578C22#6430711yescharacteristic
579C22#6430811yescharacteristic
580C22C22×D3×Dic311yescharacteristic
581C4—22no—
582C4—22no—
583C4—62no—
584C4—62no—
585C4—62no—
586C4—122no—
587C4—122no—
588C4—362no—
589C4—362no—
590C4#6385514yes—
591C3—21no—
592C3#7376011yescharacteristic, complemented
593C3#8223111yescharacteristic, complemented
594C2—122no—
595C2#1059387811yescharacteristic
596C2#1059388011yescharacteristic
597C2#1059398311yescharacteristic
598C2#1059398611yescharacteristic
599C2C2×#6385511yescharacteristic
600C2#1059498611yescharacteristic
601C2#1059499211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2314
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊(C3⋊Dic3)C2semidirect
3. C3×C4×C4⋊Dic3C2semidirect
4. #10591349C2semidirect
9. #10591224C2semidirect
10. #10591201C2semidirect
11. #10591192C2semidirect
27. C3×#872C4semidirect
57. C4×C4⋊Dic3D3semidirect
131. #872Dic3semidirect
504. C32#2314semidirect
592. C3#73760semidirect
593. C3#82231semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8722
C4×C4⋊(C3⋊Dic3)2
C3×C4×C4⋊Dic32
#105913492
#105913132
#105913052
#105912862
#105912242
#105912012
#105911922
#822313
#737603