Finite Group Databasebeta

← #11787537

Subgroups — #11787537

Order 1152.

935 conjugacy classes of subgroups.

The subgroup lattice has 639 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63898C211yesmaximal, characteristic, complemented
2C22×#3713C211yesmaximal, characteristic
3C2×C3×#821C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic, complemented
5#10591323C211yesmaximal, characteristic, complemented
6#10589416C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#70208—31nomaximal
9#70172—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×D3×Dic3—21no—
13C22×C32×C8C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×(C2×D3)⋊Dic3—21no—
19C2×(C2×D3)⋊Dic3—21no—
20C2×(C2×D3)⋊Dic3—21no—
21#63898—22no—
22#63898—22no—
23C2×#3713—22no—
24C2×#3713—22no—
25C2×#3713C414yescomplemented
26C3×#821—22no—
27C3×#821—22no—
28C2×D4×Dic3—31no—
29C22×#213—31no—
30C22×#213—31no—
31C2×#893—31no—
32C2×C3×#102—31no—
33C2×C3×#102—31no—
34#5221—31no—
35C2×#821D311yescharacteristic, complemented
36C2×#821D311yescharacteristic, complemented
37#4988—31no—
38#4550—31no—
39#4550—31no—
40#4550—61no—
41#4529—31no—
42#4529—31no—
43C23×C3×D3—21no—
44C23×C3×D3—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C22×C3⋊Dic3D411yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12C2×C412yes—
59C2×C3×D12C2×C412yescomplemented
60C2×C3×D12D412yes—
61C2×C3×D12D412yes—
62C2×D3×Dic3—24no—
63C2×D3×Dic3—42no—
64C2×D3×Dic3—42no—
65C2×C32×C8—21no—
66C2×C32×C8—21no—
67C2×C32×C8—21no—
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C2×C3⋊(C3⋊C8)C2×C412yescomplemented
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3D412yes—
77(C2×D3)⋊Dic3—24no—
78(C2×D3)⋊Dic3—42no—
79(C2×D3)⋊Dic3—42no—
80#3713—28no—
81#1879—91noSylow
82C22×C3×D4—31no—
83C22×C3×D4—31no—
84C23×Dic3—61no—
85C22×D12C2×D311yescharacteristic
86C22×D12C2×D311yescharacteristic
87C22×C4×D3—61no—
88C22×C3×C8—21no—
89C22×C3×C8C2×D311yescharacteristic
90C22×C3×C8C2×D311yescharacteristic
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4—31no—
93C2×#217—61no—
94C2×#217—61no—
95C2×#217—61no—
96D4×Dic3—62no—
97D4×Dic3—62no—
98C2×#213—34no—
99C2×#213—34no—
100C2×#213—62no—
101C2×#213—62no—
102C2×#213—62no—
103C2×#213—62no—
104C2×(C2×D3)⋊C4—61no—
105C2×(C2×D3)⋊C4—61no—
106C2×(C2×D3)⋊C4—61no—
107C2×C4⋊Dic3C2×D311yescharacteristic
108C2×C4⋊Dic3C2×D311yescharacteristic
109C2×C4×Dic3—31no—
110C2×C4×Dic3—31no—
111C2×C4×Dic3—61no—
112C22×C3⋊C8—31no—
113C22×C3⋊C8—31no—
114C22×C3⋊C8—61no—
115#893—62no—
116#893—62no—
117C3×#102—62no—
118C3×#102—62no—
119#821—22no—
120#821—22no—
121C23×C32C2×D411yescharacteristic
122C22×C3×D3—22no—
123C22×C3×D3—22no—
124C22×C3×D3—22no—
125C22×C3×D3—22no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C22×C3×D3—41no—
133C22×C3×D3—41no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C2×C32×C4C22×C411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3D812yescomplemented
148C2×C3×Dic3—22no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C3×D12—22no—
155C3×D12—22no—
156C3×D12—22no—
157C3×D12—22no—
158C3×D12—22no—
159C3×D12—41no—
160C3×D12—41no—
161C3×D12C22⋊C414yescomplemented
162D3×Dic3—48no—
163C32×C8—41no—
164C3⋊(C3⋊C8)—22no—
165C22×D8—91no—
166C2×C4×D4—91no—
167C2×#102—31no—
168C2×#102—31no—
169#390—91no—
170#340—91no—
171#336—91no—
172C24×C3—61no—
173C24×C3—61no—
174C23×D3—21no—
175C23×D3—21no—
176C2×C3×D4—32no—
177C2×C3×D4—32no—
178C2×C3×D4—32no—
179C2×C3×D4—32no—
180C2×C3×D4—61no—
181C2×C3×D4—61no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C2×C3×D4—61no—
188C22×C3×C4—21no—
189C22×C3×C4—61no—
190C22×C3×C4—61no—
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C22×Dic3—21no—
194C22×Dic3—21no—
195C22×Dic3—31no—
196C22×Dic3—31no—
197C22×Dic3—31no—
198C22×Dic3—31no—
199C22×Dic3—61no—
200C22×Dic3—61no—
201C22×Dic3—64no—
202C22×Dic3—122no—
203C22×Dic3—122no—
204C2×D12—21no—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12—21no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12C4×D312yes—
213C2×D12C4×D312yescomplemented
214C2×D12D1212yes—
215C2×D12#6712yes—
216C2×C4×D3—64no—
217C2×C4×D3—122no—
218C2×C4×D3—122no—
219C2×C3×C8—22no—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—21no—
226C2×C3×C8—41no—
227C2×C3×C8—41no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—61no—
232#217—64no—
233#217—122no—
234#217—122no—
235#213—68no—
236#213—68no—
237(C2×D3)⋊C4—64no—
238(C2×D3)⋊C4—122no—
239(C2×D3)⋊C4—122no—
240C4⋊Dic3—21no—
241C4⋊Dic3—21no—
242C4⋊Dic3—21no—
243C4⋊Dic3#6712yes—
244C4×Dic3—61no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247C4×Dic3—61no—
248C4×Dic3—121no—
249C4×Dic3—121no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—62no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—121no—
258C2×C3⋊C8—121no—
259C22×C32C4×D411yescharacteristic
260C22×C32#12011yescharacteristic
261C22×C32#12111yescharacteristic
262C22×C32C2×D811yescharacteristic
263C22×C32#13511yescharacteristic
264C22×C32AGL(1,ℤ/8)11yescharacteristic
265C22×C32AGL(1,ℤ/8)11yescharacteristic
266C2×C3×D3—24no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C2×C3×D3—42no—
275C2×C3×D3—42no—
276C2×C3×D3—81no—
277C2×C3×D3—81no—
278C2×C3×D3—81no—
279C2×C3×D3—81no—
280C32×C4C2×C22⋊C411yescharacteristic
281C32×C4C4×D411yescharacteristic
282C32×C4#12111yescharacteristic
283C32×C4#12311yescharacteristic
284C3⋊Dic3—22no—
285C3⋊Dic3—41no—
286C3×Dic3—42no—
287C3×Dic3—81no—
288C22×D4—31no—
289C22×D4—31no—
290C23×C4—181no—
291C2×D8—94no—
292C2×D8—182no—
293C2×D8—182no—
294C22×C8—91no—
295C22×C8D3211yescharacteristic
296C4×D4—182no—
297C4×D4—182no—
298C2×C4⋊C4—31no—
299C2×C4⋊C4—31no—
300C2×C22⋊C4—181no—
301C2×C22⋊C4—181no—
302C2×C22⋊C4—181no—
303C2×C42—91no—
304#102—62no—
305#102—62no—
306C23×C3—21no—
307C23×C3—62no—
308C23×C3—62no—
309C23×C3—62no—
310C23×C3—62no—
311C23×C3—121no—
312C23×C3—121no—
313C23×C3—121no—
314C23×C3—121no—
315C23×C3—121no—
316C23×C3—121no—
317C23×C3—121no—
318C23×C3—121no—
319C23×C3—121no—
320C23×C3—121no—
321C23×C3D3×D411yescharacteristic
322C23×C3D3×D411yescharacteristic
323C22×D3—22no—
324C22×D3—22no—
325C22×D3—22no—
326C22×D3—22no—
327C22×D3—41no—
328C22×D3—41no—
329C22×D3—41no—
330C22×D3—41no—
331C22×D3—41no—
332C22×D3—41no—
333C22×D3—41no—
334C22×D3—41no—
335C22×D3—41no—
336C22×D3—41no—
337C3×D4—34no—
338C3×D4—62no—
339C3×D4—62no—
340C3×D4—62no—
341C3×D4—62no—
342C3×D4—62no—
343C3×D4—121no—
344C3×D4—121no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—62no—
352C2×C3×C4—121no—
353C2×C3×C4—121no—
354C2×C3×C4—121no—
355C2×C3×C4—121no—
356C2×C3×C4—121no—
357C2×C3×C4C2×C4×D311yescharacteristic
358C2×C3×C4C2×C4×D311yescharacteristic
359C2×C3×C4C2×D1211yescharacteristic
360C2×C3×C4#23511yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4#23711yescharacteristic
365C2×C3×C4#23711yescharacteristic
366C2×C3×C4#23711yescharacteristic
367C2×C3×C4C2×#6711yescharacteristic
368C2×C3×C4C2×#6711yescharacteristic
369C2×Dic3—22no—
370C2×Dic3—32no—
371C2×Dic3—32no—
372C2×Dic3—41no—
373C2×Dic3—41no—
374C2×Dic3—41no—
375C2×Dic3—41no—
376C2×Dic3—41no—
377C2×Dic3—62no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—62no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—61no—
389C2×Dic3—121no—
390C2×Dic3—121no—
391C2×Dic3—121no—
392C2×Dic3—121no—
393C2×Dic3—128no—
394D12—22no—
395D12—22no—
396D12—22no—
397D12—22no—
398D12—22no—
399D12—41no—
400D12—41no—
401D12(C2×D3)⋊C414yescomplemented
402C4×D3—128no—
403C3×C8—42no—
404C3×C8—41no—
405C3×C8—41no—
406C3⋊C8—62no—
407C3⋊C8—62no—
408C3⋊C8—122no—
409C2×C32#38611yescharacteristic
410C2×C32C4×D811yescharacteristic
411C2×C32#44211yescharacteristic
412C2×C32#44711yescharacteristic
413C2×C32#44911yescharacteristic
414C2×C32#45911yescharacteristic
415C2×C32#46311yescharacteristic
416C3×D3—44no—
417C3×D3—82no—
418C24—61no—
419C24—61no—
420C2×D4—32no—
421C2×D4—32no—
422C2×D4—32no—
423C2×D4—32no—
424C2×D4—61no—
425C2×D4—61no—
426C2×D4—61no—
427C2×D4—61no—
428C2×D4—61no—
429C2×D4—61no—
430C2×D4—61no—
431C2×D4—61no—
432C22×C4—61no—
433C22×C4—61no—
434C22×C4—91no—
435C22×C4—91no—
436C22×C4—184no—
437C22×C4—362no—
438C22×C4—362no—
439C22×C4C2×D3211yescharacteristic
440D8—188no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—92no—
445C2×C8—181no—
446C2×C8—181no—
447C4⋊C4—32no—
448C4⋊C4—61no—
449C4⋊C4—61no—
450C4⋊C4—61no—
451C22⋊C4—184no—
452C22⋊C4—362no—
453C22⋊C4—362no—
454C42—181no—
455C42—181no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—64no—
464C22×C3—122no—
465C22×C3—122no—
466C22×C3—122no—
467C22×C3—122no—
468C22×C3—122no—
469C22×C3—122no—
470C22×C3—122no—
471C22×C3—122no—
472C22×C3—122no—
473C22×C3—241no—
474C22×C3—241no—
475C22×C3—241no—
476C22×C3—241no—
477C22×C3#67⋊C411yescharacteristic
478C22×C3#67⋊C411yescharacteristic
479C22×C3#88211yescharacteristic
480C22×C3#88411yescharacteristic
481C22×C3D3×D811yescharacteristic
482C22×C3D3×D811yescharacteristic
483C22×C3#91111yescharacteristic
484C22×C3#91111yescharacteristic
485C22×C3#91411yescharacteristic
486C22×C3#91411yescharacteristic
487C22×C3#91611yescharacteristic
488C22×C3#91611yescharacteristic
489C22×C3#93711yescharacteristic
490C22×C3#93911yescharacteristic
491C2×D3—24no—
492C2×D3—42no—
493C2×D3—42no—
494C2×D3—42no—
495C2×D3—42no—
496C2×D3—42no—
497C2×D3—42no—
498C2×D3—42no—
499C2×D3—42no—
500C2×D3—42no—
501C2×D3—81no—
502C2×D3—81no—
503C2×D3—81no—
504C2×D3—81no—
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—21no—
508C3×C4—21no—
509C3×C4—122no—
510C3×C4—241no—
511C3×C4D3×C22⋊C411yescharacteristic
512C3×C4#67⋊C411yescharacteristic
513C3×C4#88311yescharacteristic
514C3×C4#88611yescharacteristic
515C3×C4C2×(C2×D3)⋊C411yescharacteristic
516C3×C4C4×#6711yescharacteristic
517C3×C4#93811yescharacteristic
518C3×C4#93911yescharacteristic
519Dic3—42no—
520Dic3—62no—
521Dic3—62no—
522Dic3—81no—
523Dic3—122no—
524Dic3—122no—
525Dic3—121no—
526Dic3—121no—
527C32#187911yescharacteristic, complemented, Sylow
528C23—62no—
529C23—62no—
530C23—62no—
531C23—62no—
532C23—121no—
533C23—121no—
534C23—121no—
535C23—121no—
536C23—121no—
537C23—121no—
538C23—121no—
539C23—121no—
540C23—121no—
541C23—121no—
542C23#380211yescharacteristic
543D4—34no—
544D4—62no—
545D4—62no—
546D4—62no—
547D4—62no—
548D4—62no—
549D4—121no—
550D4—121no—
551C2×C4—62no—
552C2×C4—92no—
553C2×C4—121no—
554C2×C4—121no—
555C2×C4—121no—
556C2×C4—121no—
557C2×C4—121no—
558C2×C4—181no—
559C2×C4—181no—
560C2×C4—181no—
561C2×C4—181no—
562C2×C4—181no—
563C2×C4—368no—
564C2×C4#379511yescharacteristic
565C2×C4C4×D3211yescharacteristic
566C2×C4D3×D1211yescharacteristic
567C2×C4#380511yescharacteristic
568C2×C4D3×#6711yescharacteristic
569C2×C4D3×#6711yescharacteristic
570C8—41no—
571C8—182no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—124no—
580C2×C3—242no—
581C2×C3#475611yescharacteristic
582C2×C3#475611yescharacteristic
583C2×C3#477311yescharacteristic
584C2×C3#478111yescharacteristic
585C2×C3#478511yescharacteristic
586C2×C3#478511yescharacteristic
587C2×C3#478611yescharacteristic
588C2×C3#478711yescharacteristic
589C2×C3#495611yescharacteristic
590C2×C3#495811yescharacteristic
591C2×C3#515011yescharacteristic
592C2×C3#515611yescharacteristic
593C2×C3#516511yescharacteristic
594C2×C3#517211yescharacteristic
595D3—44no—
596D3—82no—
597C22—64no—
598C22—122no—
599C22—122no—
600C22—122no—
601C22—122no—
602C22—122no—
603C22—122no—
604C22—122no—
605C22—122no—
606C22—122no—
607C22—241no—
608C22—241no—
609C22—241no—
610C22—241no—
611C22#6379711yescharacteristic
612C22#6379811yescharacteristic
613C22#6379811yescharacteristic
614C22#6380911yescharacteristic
615C22#6388511yescharacteristic
616C22#6390211yescharacteristic
617C22#6392211yescharacteristic
618C4—122no—
619C4—182no—
620C4—241no—
621C4—361no—
622C4#6387911yescharacteristic
623C4#6389111yescharacteristic
624C4D3×(C2×D3)⋊C411yescharacteristic
625C4#6397011yescharacteristic
626C3—21no—
627C3#7017211yescharacteristic, complemented
628C3#7020811yescharacteristic, complemented
629C2—124no—
630C2—242no—
631C2#1059074011yescharacteristic
632C2#1059074111yescharacteristic
633C2#1059074911yescharacteristic
634C2#1059075011yescharacteristic
635C2#1059094511yescharacteristic
636C2#1059096411yescharacteristic
637C2#1059136311yescharacteristic
subgroupG/H
centerC23#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×#3713C2
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1879
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#63898C2semidirect
3. C2×C3×#821C2semidirect
4. C2×C3×#821C2semidirect
5. #10591323C2semidirect
6. #10589416C2semidirect
7. #10589163C2semidirect
25. C2×#3713C4semidirect
35. C2×#821D3semidirect
36. C2×#821D3semidirect
59. C2×C3×D12C2×C4semidirect
72. C2×C3⋊(C3⋊C8)C2×C4semidirect
147. C2×C3⋊Dic3D8semidirect
161. C3×D12C22⋊C4semidirect
213. C2×D12C4×D3semidirect
401. D12(C2×D3)⋊C4semidirect
527. C32#1879semidirect
627. C3#70172semidirect
628. C3#70208semidirect

Maximal subgroups

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

subgroupindex
C2×#638982
C22×#37132
C2×C3×#8212
#105913232
#105894162
#105891632
#702083
#701723