Finite Group Databasebeta

← #11805314

Subgroups — #11805314

Order 1152.

1105 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×#63841C211yesmaximal, characteristic
2C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
3C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
4C3×#4928C211yesmaximal, characteristic, complemented
5#10591352C211yesmaximal, characteristic, complemented
6#10591313C211yesmaximal, characteristic
7#10591287C212yesmaximal
8#10591285C212yesmaximal
9Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
10#10591252C212yesmaximal, complemented
11#10591245C212yesmaximal, complemented
12#75979—31nomaximal
13#73459—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⋊C4C2212yes—
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×Dic3⋊Dic3C2212yes—
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×Dic32C2212yes—
29C2×Dic32C2212yes—
30#63841C418yescomplemented
31#63658C2212yes—
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×#926—31no—
39C2×#892—31no—
40C3×#389—31no—
41C3×C4×C22⋊C4—31no—
42#5212—31no—
43#4990—32no—
44#4987—31no—
45#4984—31no—
46#4977—32no—
47Dic3×C4⋊C4—31no—
48#4944—32no—
49#4944—32no—
50C4×(C2×D3)⋊C4D311yescharacteristic
51C4×C4⋊Dic3—31no—
52C4×C4⋊Dic3—31no—
53C4×C4⋊Dic3—31no—
54C4×C4⋊Dic3—61no—
55#4928—31no—
56#4928D311yescharacteristic, complemented
57#4670—32no—
58#4650—32no—
59#4648—32no—
60#4648—32no—
61C23×C3×D3C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2312yes—
67C22×C3×Dic3C2311yescharacteristic
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3C2×C414yes—
75C32×C42—22no—
76C4⋊(C3⋊Dic3)—22no—
77C4⋊(C3⋊Dic3)C2×C414yes—
78C4×C3⋊Dic3—24no—
79C3×(C2×D3)⋊C4—22no—
80C3×(C2×D3)⋊C4—22no—
81C3×C4⋊Dic3—22no—
82C3×C4⋊Dic3C2×C414yes—
83C3×Dic3⋊C4—42no—
84C3×C4×Dic3—22no—
85Dic3⋊Dic3—42no—
86(C2×D3)⋊Dic3—42no—
87(C2×D3)⋊Dic3C2×C418yes—
88Dic32—24no—
89Dic32C2×C418yes—
90#2346—91noSylow
91C23×C3×C4—31no—
92C22×C4×D3C2×D311yescharacteristic
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C4⋊C4—32no—
96C2×C3×C22⋊C4—31no—
97C2×C3×C22⋊C4—31no—
98C2×C3×C42—21no—
99C2×C3×C42—31no—
100C2×C3×C42C2×D311yescharacteristic
101C2×C3×C42C2×D311yescharacteristic
102C2×#217—32no—
103C2×#217—32no—
104C2×(C2×D3)⋊C4—32no—
105C2×(C2×D3)⋊C4—32no—
106C2×(C2×D3)⋊C4C2×D311yescharacteristic
107C2×(C2×D3)⋊C4C2×D311yescharacteristic
108#926—38no—
109C2×C4⋊Dic3—31no—
110C2×C4⋊Dic3—31no—
111C2×C4⋊Dic3—31no—
112C2×C4⋊Dic3—31no—
113C2×C4⋊Dic3—32no—
114C2×C4⋊Dic3—61no—
115C2×C4⋊Dic3—61no—
116C2×C4⋊Dic3C2×D311yescharacteristic
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4C2×D312yes—
120C2×C4×Dic3—32no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—32no—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—62no—
127C2×C4×Dic3C2×D311yescharacteristic
128#892—38no—
129C3×#95—31no—
130C3×#95—32no—
131C3×#95—31no—
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—62no—
141C3⋊#95C2×D311yescharacteristic
142C3⋊#95C2×D312yes—
143C3⋊#95C2×D311yescharacteristic
144C23×C32C2411yescharacteristic
145C22×C3×D3—21no—
146C22×C3×D3—21no—
147C22×C3×D3—21no—
148C22×C3×D3—21no—
149C22×C3×D3—21no—
150C22×C3×D3—21no—
151C22×C3×D3C22×C412yes—
152C2×C32×C4—21no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4C22×C412yes—
158C2×C32×C4#4112yes—
159C2×C32×C4#4112yes—
160C2×C32×C4#4112yes—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3C22×C414yes—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3C22×C412yes—
180C2×C3×Dic3C22×C414yes—
181C2×C3×Dic3#4112yes—
182C3×C4×D3—28no—
183C2×#117—91no—
184#389—31no—
185#389—91no—
186#388—92no—
187#388—92no—
188#382—92no—
189#380—91no—
190C4×C4⋊C4—91no—
191C4×C4⋊C4—91no—
192C4×C22⋊C4—31no—
193#376—92no—
194C24×C3—31no—
195C23×D3C22×D311yescharacteristic
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—31no—
200C22×C3×C4—31no—
201C22×C3×C4—32no—
202C22×C3×C4—34no—
203C22×C3×C4—32no—
204C22×C3×C4—31no—
205C22×C3×C4—62no—
206C22×C3×C4—62no—
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×Dic3—32no—
214C22×Dic3—32no—
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—62no—
218C22×Dic3—62no—
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D311yescharacteristic
221C22×Dic3C22×D311yescharacteristic
222C22×Dic3C22×D312yes—
223C22×Dic3C22×D311yescharacteristic
224C2×C4×D3—22no—
225C2×C4×D3—22no—
226C2×C4×D3C4×D314yes—
227C3×C4⋊C4—34no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4—122no—
230C3×C22⋊C4—62no—
231C3×C22⋊C4—62no—
232C3×C42—24no—
233C3×C42—22no—
234C3×C42—22no—
235C3×C42—62no—
236#217—38no—
237#217—122no—
238(C2×D3)⋊C4—22no—
239(C2×D3)⋊C4—22no—
240(C2×D3)⋊C4—38no—
241(C2×D3)⋊C4—122no—
242C4⋊Dic3—22no—
243C4⋊Dic3—34no—
244C4⋊Dic3—34no—
245C4⋊Dic3—64no—
246C4⋊Dic3—64no—
247C4⋊Dic3—62no—
248C4⋊Dic3—62no—
249C4⋊Dic3—122no—
250C4⋊Dic3C4×D314yes—
251Dic3⋊C4—42no—
252Dic3⋊C4—122no—
253C4×Dic3—22no—
254C4×Dic3—38no—
255C4×Dic3—38no—
256C4×Dic3—64no—
257C4×Dic3—64no—
258C4×Dic3—64no—
259C4×Dic3—64no—
260C4×Dic3—124no—
261C22×C32C23×C411yescharacteristic
262C22×C32C2×#4111yescharacteristic
263C22×C32C2×#4111yescharacteristic
264C22×C32C2×#4111yescharacteristic
265C22×C32C2×#4111yescharacteristic
266C22×C32H(5,𝔽2)11yescharacteristic
267C22×C322−1+411yescharacteristic
268C2×C3×D3—22no—
269C2×C3×D3—22no—
270C2×C3×D3—22no—
271C2×C3×D3—41no—
272C2×C3×D3—41no—
273C2×C3×D3—41no—
274C2×C3×D3—41no—
275C32×C4—22no—
276C32×C4—41no—
277C32×C4#11714yes—
278C3⋊Dic3—24no—
279C3⋊Dic3—42no—
280C3×Dic3—22no—
281C3×Dic3—24no—
282C3×Dic3—22no—
283C3×Dic3—41no—
284C3×Dic3—42no—
285C23×C4—31no—
286#117—98no—
287C2×C4⋊C4—31no—
288C2×C4⋊C4—31no—
289C2×C4⋊C4—32no—
290C2×C4⋊C4—91no—
291C2×C4⋊C4—91no—
292C2×C4⋊C4—92no—
293C2×C22⋊C4—31no—
294C2×C22⋊C4—31no—
295C2×C22⋊C4—92no—
296C2×C22⋊C4—92no—
297C2×C42—31no—
298C2×C42—92no—
299C2×C42—92no—
300C2×C42—92no—
301C2×C42D3211yescharacteristic
302#95—31no—
303#95—32no—
304#95—31no—
305#95—92no—
306#95—92no—
307#95—92no—
308#95—92no—
309C23×C3—21no—
310C23×C3—32no—
311C23×C3—61no—
312C23×C3—61no—
313C23×C3—61no—
314C23×C3—61no—
315C23×C3—61no—
316C23×C3—61no—
317C23×C3C23×D311yescharacteristic
318C23×C3C23×D311yescharacteristic
319C22×D3—21no—
320C22×D3—21no—
321C22×D3—21no—
322C22×D3—21no—
323C22×D3—21no—
324C22×D3—21no—
325C22×D3C2×C4×D312yes—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—22no—
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—32no—
344C2×C3×C4—34no—
345C2×C3×C4—32no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—61no—
349C2×C3×C4—61no—
350C2×C3×C4—61no—
351C2×C3×C4—62no—
352C2×C3×C4—61no—
353C2×C3×C4—62no—
354C2×C3×C4—68no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—61no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—62no—
361C2×C3×C4C2×C4×D312yes—
362C2×C3×C4C2×C4×D312yes—
363C2×C3×C4#23512yes—
364C2×C3×C4#23712yes—
365C2×C3×C4#23712yes—
366C2×C3×C4#23712yes—
367C2×C3×C4#23912yes—
368C2×C3×C4#23912yes—
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—21no—
372C2×Dic3—22no—
373C2×Dic3—21no—
374C2×Dic3—22no—
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—21no—
381C2×Dic3—34no—
382C2×Dic3—34no—
383C2×Dic3—64no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—64no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—122no—
396C2×Dic3—122no—
397C2×Dic3—122no—
398C2×Dic3—122no—
399C2×Dic3C2×C4×D312yes—
400C2×Dic3C2×C4×D314yes—
401C2×Dic3#23512yes—
402C4×D3—28no—
403C2×C32C2×#11711yescharacteristic
404C2×C32C4×#4111yescharacteristic
405C2×C32#52011yescharacteristic
406C2×C32#55211yescharacteristic
407C2×C32#55211yescharacteristic
408C2×C32#55511yescharacteristic
409C2×C32#55511yescharacteristic
410C3×D3—42no—
411C24—31no—
412C22×C4—31no—
413C22×C4—31no—
414C22×C4—32no—
415C22×C4—34no—
416C22×C4—31no—
417C22×C4—32no—
418C22×C4—62no—
419C22×C4—62no—
420C22×C4—92no—
421C22×C4—92no—
422C22×C4C2×D3211yescharacteristic
423C22×C4C2×D3211yescharacteristic
424C22×C4C2×D3211yescharacteristic
425C4⋊C4—34no—
426C4⋊C4—62no—
427C4⋊C4—94no—
428C4⋊C4—122no—
429C4⋊C4—182no—
430C4⋊C4—362no—
431C22⋊C4—62no—
432C22⋊C4—62no—
433C22⋊C4—98no—
434C22⋊C4—362no—
435C42—22no—
436C42—62no—
437C42—98no—
438C42—184no—
439C42—184no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—62no—
448C22×C3—62no—
449C22×C3—62no—
450C22×C3—121no—
451C22×C3—121no—
452C22×C3—121no—
453C22×C3—121no—
454C22×C3C22×C4×D311yescharacteristic
455C22×C3C22×C4×D311yescharacteristic
456C22×C3C2×#23511yescharacteristic
457C22×C3C2×#23511yescharacteristic
458C22×C3C2×#23711yescharacteristic
459C22×C3C2×#23711yescharacteristic
460C22×C3C2×#23711yescharacteristic
461C22×C3#100411yescharacteristic
462C22×C3C2×#23911yescharacteristic
463C22×C3C2×#23911yescharacteristic
464C22×C3D3×#4111yescharacteristic
465C22×C3#100911yescharacteristic
466C22×C3#101011yescharacteristic
467C22×C3#101011yescharacteristic
468C2×D3—22no—
469C2×D3—22no—
470C2×D3—22no—
471C2×D3—41no—
472C2×D3—41no—
473C2×D3—41no—
474C2×D3—41no—
475C3×C4—24no—
476C3×C4—22no—
477C3×C4—22no—
478C3×C4—24no—
479C3×C4—42no—
480C3×C4—41no—
481C3×C4—41no—
482C3×C4—62no—
483C3×C4—62no—
484C3×C4—64no—
485C3×C4—121no—
486C3×C4—122no—
487C3×C4#87714yes—
488C3×C4#89214yes—
489Dic3—22no—
490Dic3—22no—
491Dic3—24no—
492Dic3—41no—
493Dic3—42no—
494Dic3—64no—
495Dic3—64no—
496Dic3—124no—
497Dic3—124no—
498Dic3—122no—
499Dic3—122no—
500C32#234611yescharacteristic, complemented, Sylow
501C23—32no—
502C23—61no—
503C23—61no—
504C23—61no—
505C23—61no—
506C23—61no—
507C23—61no—
508C23C22×D3211yescharacteristic
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—32no—
515C2×C4—34no—
516C2×C4—32no—
517C2×C4—61no—
518C2×C4—61no—
519C2×C4—62no—
520C2×C4—61no—
521C2×C4—62no—
522C2×C4—61no—
523C2×C4—68no—
524C2×C4—61no—
525C2×C4—61no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—61no—
529C2×C4—62no—
530C2×C4—94no—
531C2×C4—182no—
532C2×C4—182no—
533C2×C4—182no—
534C2×C4—182no—
535C2×C4—182no—
536C2×C4#379612yes—
537C2×C4#379912yes—
538C2×C4C4×D3212yes—
539C2×C4#380512yes—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—122no—
548C2×C3C4×#23511yescharacteristic
549C2×C3C2×#87711yescharacteristic
550C2×C3C2×#89211yescharacteristic
551C2×C3#552311yescharacteristic
552C2×C3#554111yescharacteristic
553C2×C3#554111yescharacteristic
554C2×C3#554611yescharacteristic
555C2×C3#556311yescharacteristic
556C2×C3#556311yescharacteristic
557C2×C3C4×#23911yescharacteristic
558C2×C3#561611yescharacteristic
559C2×C3#564211yescharacteristic
560C2×C3#569411yescharacteristic
561C2×C3#573411yescharacteristic
562D3—42no—
563C22—62no—
564C22—62no—
565C22—62no—
566C22—121no—
567C22—121no—
568C22—121no—
569C22—121no—
570C22C2×#379611yescharacteristic
571C22#6429811yescharacteristic
572C22C2×#379911yescharacteristic
573C22C2×C4×D3211yescharacteristic
574C22D3×#23511yescharacteristic
575C22#6430711yescharacteristic
576C22C2×#380511yescharacteristic
577C4—22no—
578C4—41no—
579C4—62no—
580C4—64no—
581C4—62no—
582C4—121no—
583C4—122no—
584C4—184no—
585C4—362no—
586C4#6387814yes—
587C3—21no—
588C3#7345911yescharacteristic, complemented
589C3#7597911yescharacteristic, complemented
590C2—122no—
591C2#1059388711yescharacteristic
592C2#1059392011yescharacteristic
593C2C4×#379911yescharacteristic
594C2#1059398711yescharacteristic
595C2#1059485311yescharacteristic
596C2C2×#6387811yescharacteristic
597C2#1059502611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2346
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
4. C3×#4928C2semidirect
5. #10591352C2semidirect
9. Dic3×C4⋊Dic3C2semidirect
10. #10591252C2semidirect
11. #10591245C2semidirect
30. #63841C4semidirect
56. #4928D3semidirect
500. C32#2346semidirect
588. C3#73459semidirect
589. C3#75979semidirect

Maximal subgroups

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

subgroupindex
C2×#638412
C4×C4⋊(C3⋊Dic3)2
C3×C4×(C2×D3)⋊C42
C3×#49282
#105913522
#105913132
#105912872
#105912852
Dic3×C4⋊Dic32
#105912522
#105912452
#759793
#734593