Finite Group Databasebeta

← #11805383

Subgroups — #11805383

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×C3×#892C211yesmaximal, characteristic
2C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
4#10591357C211yesmaximal, characteristic, complemented
5#10591352C211yesmaximal, characteristic, complemented
6C4×Dic3⋊Dic3C212yesmaximal, complemented
7#10591313C211yesmaximal, characteristic
8#10591305C212yesmaximal
9#10591286C212yesmaximal
10C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic
11#10591223C212yesmaximal, complemented
12#82240—31nomaximal
13#73634—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C4×C3⋊Dic3C2212yes—
19C2×C3×(C2×D3)⋊C4C2212yes—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2212yes—
24C2×C3×C4×Dic3C2212yes—
25C3×#892C418yescomplemented
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic3⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2211yescharacteristic
29C2×(C2×D3)⋊Dic3C2211yescharacteristic
30C2×(C2×D3)⋊Dic3C2212yes—
31#63658C2212yes—
32C3×C3⋊#95C2212yes—
33#63579C2211yescharacteristic
34#63579C2211yescharacteristic
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×C3×#117—31no—
39C2×#892D311yescharacteristic
40C3×C4×C4⋊C4—31no—
41#5212—31no—
42C4×#217—31no—
43#4987—31no—
44#4984—31no—
45#4984—31no—
46Dic3×C4⋊C4—31no—
47Dic3×C4⋊C4—31no—
48Dic3×C4⋊C4—61no—
49Dic3×C4⋊C4D311yescharacteristic, complemented
50#4972—31no—
51#4951—32no—
52#4951—32no—
53#4940—32no—
54C4×(C2×D3)⋊C4—31no—
55#4937—32no—
56C4×C4⋊Dic3—32no—
57C4×Dic3⋊C4—32no—
58#4928—31no—
59#4669—32no—
60#4651—32no—
61C23×C3×D3C2311yescharacteristic
62C22×C32×C4C2312yes—
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3C2311yescharacteristic
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2311yescharacteristic
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2311yescharacteristic
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3C2×C414yes—
75C32×C4⋊C4C2×C414yes—
76C4⋊(C3⋊Dic3)—22no—
77C4×C3⋊Dic3—22no—
78C4×C3⋊Dic3—42no—
79C3×(C2×D3)⋊C4C2×C418yes—
80C3×C4⋊Dic3—22no—
81C3×C4⋊Dic3C2×C414yes—
82C3×C4×Dic3—22no—
83C3×C4×Dic3—42no—
84C3×C4×Dic3C2×C418yes—
85Dic3⋊Dic3—24no—
86Dic3⋊Dic3—24no—
87(C2×D3)⋊Dic3—22no—
88(C2×D3)⋊Dic3—22no—
89(C2×D3)⋊Dic3—42no—
90#2347—91noSylow
91C23×C3×C4—31no—
92C22×C4×D3C2×D311yescharacteristic
93C3×#117—38no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4C2×D311yescharacteristic
98C2×C3×C4⋊C4C2×D311yescharacteristic
99C2×C3×C22⋊C4—32no—
100C2×C3×C42—32no—
101C2×C3×C42—31no—
102C2×C3×C42—32no—
103C2×#217—31no—
104C2×#217—31no—
105C2×#217—32no—
106C2×(C2×D3)⋊C4—31no—
107C2×(C2×D3)⋊C4—31no—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4C2×D312yes—
110C2×C4⋊Dic3—31no—
111C2×C4⋊Dic3—31no—
112C2×C4⋊Dic3—32no—
113C2×C4⋊Dic3—32no—
114C2×C4⋊Dic3—61no—
115C2×C4⋊Dic3C2×D311yescharacteristic
116C2×C4⋊Dic3C2×D311yescharacteristic
117C2×Dic3⋊C4—32no—
118C2×Dic3⋊C4—32no—
119C2×C4×Dic3—31no—
120C2×C4×Dic3—31no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—61no—
124C2×C4×Dic3—62no—
125C2×C4×Dic3C2×D311yescharacteristic
126C2×C4×Dic3C2×D312yes—
127C2×C4×Dic3C2×D312yes—
128#892Dic318yescomplemented
129C3×#95—32no—
130C3⋊#95—32no—
131C3⋊#95—32no—
132C3⋊#95—31no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—31no—
137C3⋊#95—31no—
138C3⋊#95—32no—
139C3⋊#95—31no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—62no—
143C3⋊#95C2×D312yes—
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—22no—
153C2×C32×C4—22no—
154C2×C32×C4C22×C414yes—
155C2×C32×C4C22×C412yes—
156C2×C32×C4#4112yes—
157C2×C32×C4#4112yes—
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3#4112yes—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
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—21no—
176C2×C3×Dic3—22no—
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—31no—
184#389—91no—
185#389—91no—
186#388—92no—
187#388—92no—
188#383—92no—
189#380—91no—
190C4×C4⋊C4—31no—
191C4×C4⋊C4—92no—
192C4×C4⋊C4—91no—
193C4×C22⋊C4—91no—
194C24×C3—31no—
195C23×D3C22×D311yescharacteristic
196C22×C3×C4—21no—
197C22×C3×C4—22no—
198C22×C3×C4—31no—
199C22×C3×C4—32no—
200C22×C3×C4—31no—
201C22×C3×C4—34no—
202C22×C3×C4—31no—
203C22×C3×C4—32no—
204C22×C3×C4—62no—
205C22×C3×C4—62no—
206C22×C3×C4C22×D312yes—
207C22×C3×C4C22×D312yes—
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C22×Dic3—31no—
211C22×Dic3—31no—
212C22×Dic3—31no—
213C22×Dic3—31no—
214C22×Dic3—32no—
215C22×Dic3—32no—
216C22×Dic3—61no—
217C22×Dic3—61no—
218C22×Dic3—62no—
219C22×Dic3C22×D311yescharacteristic
220C22×Dic3C22×D312yes—
221C22×Dic3C22×D311yescharacteristic
222C22×Dic3C22×D311yescharacteristic
223C22×Dic3C22×D312yes—
224C2×C4×D3—22no—
225C2×C4×D3—22no—
226C2×C4×D3C2×Dic314yes—
227C3×C4⋊C4—24no—
228C3×C4⋊C4—34no—
229C3×C4⋊C4—62no—
230C3×C4⋊C4C4×D314yes—
231C3×C4⋊C4C2×Dic314yes—
232C3×C22⋊C4—38no—
233C3×C42—38no—
234C3×C42—62no—
235C3×C42—122no—
236#217—62no—
237#217—62no—
238#217—122no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—122no—
242(C2×D3)⋊C4C2×Dic318yes—
243C4⋊Dic3—22no—
244C4⋊Dic3—64no—
245C4⋊Dic3—64no—
246C4⋊Dic3—62no—
247C4⋊Dic3—62no—
248C4⋊Dic3—64no—
249C4⋊Dic3C2×Dic314yes—
250Dic3⋊C4—64no—
251Dic3⋊C4—64no—
252C4×Dic3—22no—
253C4×Dic3—42no—
254C4×Dic3—64no—
255C4×Dic3—62no—
256C4×Dic3—62no—
257C4×Dic3—122no—
258C4×Dic3—122no—
259C4×Dic3—124no—
260C4×Dic3C2×Dic318yes—
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—24no—
276C32×C4#11714yes—
277C3⋊Dic3—22no—
278C3⋊Dic3—42no—
279C3⋊Dic3—41no—
280C3×Dic3—22no—
281C3×Dic3—24no—
282C3×Dic3—22no—
283C3×Dic3—42no—
284C3×Dic3—41no—
285C23×C4—31no—
286#117—38no—
287C2×C4⋊C4—31no—
288C2×C4⋊C4—31no—
289C2×C4⋊C4—92no—
290C2×C4⋊C4—92no—
291C2×C4⋊C4—91no—
292C2×C4⋊C4D3211yescharacteristic
293C2×C22⋊C4—32no—
294C2×C22⋊C4—91no—
295C2×C22⋊C4—91no—
296C2×C22⋊C4—92no—
297C2×C42—32no—
298C2×C42—31no—
299C2×C42—32no—
300C2×C42—91no—
301C2×C42—92no—
302#95—32no—
303#95—91no—
304#95—91no—
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×D3C22×Dic312yes—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—24no—
334C2×C3×C4—32no—
335C2×C3×C4—34no—
336C2×C3×C4—32no—
337C2×C3×C4—42no—
338C2×C3×C4—42no—
339C2×C3×C4—61no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—61no—
345C2×C3×C4—68no—
346C2×C3×C4—61no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—61no—
350C2×C3×C4—62no—
351C2×C3×C4—61no—
352C2×C3×C4C2×C4×D314yes—
353C2×C3×C4C2×C4×D312yes—
354C2×C3×C4#23512yes—
355C2×C3×C4#23512yes—
356C2×C3×C4#23512yes—
357C2×C3×C4#23512yes—
358C2×C3×C4C22×Dic314yes—
359C2×C3×C4C22×Dic312yes—
360C2×Dic3—21no—
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—21no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—21no—
371C2×Dic3—21no—
372C2×Dic3—32no—
373C2×Dic3—32no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—62no—
382C2×Dic3—64no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—61no—
390C2×Dic3—62no—
391C2×Dic3—61no—
392C2×Dic3—62no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—122no—
396C2×Dic3—121no—
397C2×Dic3—121no—
398C2×Dic3—122no—
399C2×Dic3#23912yes—
400C2×Dic3C22×Dic312yes—
401C2×Dic3C22×Dic314yes—
402C4×D3—28no—
403C2×C32C2×#11711yescharacteristic
404C2×C32C4×#4111yescharacteristic
405C2×C32#52011yescharacteristic
406C2×C32#55311yescharacteristic
407C2×C32#55311yescharacteristic
408C2×C32#55611yescharacteristic
409C2×C32#55611yescharacteristic
410C3×D3—42no—
411C24—31no—
412C22×C4—31no—
413C22×C4—32no—
414C22×C4—31no—
415C22×C4—34no—
416C22×C4—31no—
417C22×C4—32no—
418C22×C4—62no—
419C22×C4—62no—
420C22×C4—91no—
421C22×C4—91no—
422C22×C4—92no—
423C22×C4C2×D3212yes—
424C22×C4C2×D3211yescharacteristic
425C4⋊C4—34no—
426C4⋊C4—62no—
427C4⋊C4—184no—
428C4⋊C4—184no—
429C4⋊C4—182no—
430C4⋊C4D3×Dic314yes—
431C22⋊C4—38no—
432C22⋊C4—182no—
433C22⋊C4—182no—
434C22⋊C4—362no—
435C42—38no—
436C42—62no—
437C42—122no—
438C42—182no—
439C42—362no—
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×C3C2×#23511yescharacteristic
456C22×C3C2×#23511yescharacteristic
457C22×C3C2×#23511yescharacteristic
458C22×C3C2×#23511yescharacteristic
459C22×C3#100411yescharacteristic
460C22×C3C2×#23911yescharacteristic
461C22×C3D3×#4111yescharacteristic
462C22×C3D3×#4111yescharacteristic
463C22×C3D3×#4111yescharacteristic
464C22×C3#100911yescharacteristic
465C22×C3#101011yescharacteristic
466C22×C3#101011yescharacteristic
467C22×C3C23×Dic311yescharacteristic
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—24no—
477C3×C4—24no—
478C3×C4—44no—
479C3×C4—62no—
480C3×C4—62no—
481C3×C4—64no—
482C3×C4—122no—
483C3×C4—121no—
484C3×C4#87214yes—
485C3×C4#92614yes—
486Dic3—22no—
487Dic3—22no—
488Dic3—24no—
489Dic3—41no—
490Dic3—42no—
491Dic3—64no—
492Dic3—62no—
493Dic3—62no—
494Dic3—122no—
495Dic3—124no—
496Dic3—122no—
497Dic3—122no—
498Dic3—121no—
499Dic3—121no—
500C32#234711yescharacteristic, complemented, Sylow
501C23—32no—
502C23—61no—
503C23—61no—
504C23—61no—
505C23—61no—
506C23—61no—
507C23—61no—
508C23C22×D3211yescharacteristic
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—32no—
512C2×C4—32no—
513C2×C4—34no—
514C2×C4—61no—
515C2×C4—61no—
516C2×C4—61no—
517C2×C4—61no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—68no—
521C2×C4—61no—
522C2×C4—62no—
523C2×C4—61no—
524C2×C4—62no—
525C2×C4—61no—
526C2×C4—62no—
527C2×C4—92no—
528C2×C4—181no—
529C2×C4—181no—
530C2×C4—181no—
531C2×C4—182no—
532C2×C4—181no—
533C2×C4—182no—
534C2×C4—181no—
535C2×C4—182no—
536C2×C4#379812yes—
537C2×C4#379812yes—
538C2×C4C2×D3×Dic314yes—
539C2×C4C2×D3×Dic312yes—
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×C3C2×#87211yescharacteristic
549C2×C3#551411yescharacteristic
550C2×C3#553011yescharacteristic
551C2×C3#553011yescharacteristic
552C2×C3#553311yescharacteristic
553C2×C3#553311yescharacteristic
554C2×C3#553311yescharacteristic
555C2×C3#554611yescharacteristic
556C2×C3#555811yescharacteristic
557C2×C3C4×#23911yescharacteristic
558C2×C3#558411yescharacteristic
559C2×C3C2×#92611yescharacteristic
560C2×C3Dic3×#4111yescharacteristic
561C2×C3#582711yescharacteristic
562D3—42no—
563C22—62no—
564C22—62no—
565C22—62no—
566C22—121no—
567C22—121no—
568C22—121no—
569C22—121no—
570C22C2×#379811yescharacteristic
571C22C2×#379811yescharacteristic
572C22#6430911yescharacteristic
573C22#6431411yescharacteristic
574C22D3×#23911yescharacteristic
575C22#6431911yescharacteristic
576C22C22×D3×Dic311yescharacteristic
577C4—24no—
578C4—62no—
579C4—64no—
580C4—62no—
581C4—121no—
582C4—122no—
583C4—182no—
584C4—361no—
585C4—362no—
586C4#6385514yes—
587C3—21no—
588C3#7363411yescharacteristic, complemented
589C3#8224011yescharacteristic, complemented
590C2—122no—
591C2#1059455911yescharacteristic
592C2#1059456511yescharacteristic
593C2#1059458111yescharacteristic
594C2#1059458311yescharacteristic
595C2C2×#6385511yescharacteristic
596C2#1059522211yescharacteristic
597C2Dic3×#23911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2347
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C4⋊C4×C3⋊Dic3C2semidirect
3. C3×Dic3×C4⋊C4C2semidirect
4. #10591357C2semidirect
5. #10591352C2semidirect
6. C4×Dic3⋊Dic3C2semidirect
11. #10591223C2semidirect
25. C3×#892C4semidirect
49. Dic3×C4⋊C4D3semidirect
128. #892Dic3semidirect
500. C32#2347semidirect
588. C3#73634semidirect
589. C3#82240semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8922
C4⋊C4×C3⋊Dic32
C3×Dic3×C4⋊C42
#105913572
#105913522
C4×Dic3⋊Dic32
#105913132
#105913052
#105912862
C4×(C2×D3)⋊Dic32
#105912232
#822403
#736343