Finite Group Databasebeta

← #11836007

Subgroups — #11836007

Order 1152.

1725 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×#63922C212yesmaximal, complemented
2C2×#63908C212yesmaximal, complemented
3#10592376C211yesmaximal, characteristic, complemented
4C3×#4665C212yesmaximal, complemented
5#10591399C211yesmaximal, characteristic, complemented
6#10591394C212yesmaximal, complemented
7#10591393C211yesmaximal, characteristic, complemented
8#10591382C212yesmaximal, complemented
9#10591315C212yesmaximal, complemented
10#74910—32nomaximal
11C23×D32C2211yescharacteristic
12C22×C3×D12C2212yes—
13C22×C3×C4×D3C2212yescomplemented
14C22×#626C2212yes—
15C22×#625C2212yes—
16C22×#625C2211yescharacteristic, complemented
17C2×#3752C2212yes—
18C2×#3752C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2212yescomplemented
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×(C2×D3)⋊C4C2212yescomplemented
24C2×#3722C2211yescharacteristic
25C2×(C2×D3)⋊Dic3C2212yes—
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2212yescomplemented
28#63922—28no—
29#63908—28no—
30C32×#95C2211yescharacteristic, complemented
31C3×C3⋊#95C2212yescomplemented
32#63579C2211yescharacteristic, complemented
33#63579C2212yescomplemented
34C2×#938—32no—
35C2×#937—32no—
36C2×#930—32no—
37C2×#882—32no—
38C3×#386—32no—
39#5213—32no—
40#4961—32no—
41#4961—32no—
42#4960—32no—
43#4955—32no—
44#4953—32no—
45#4677—32no—
46#4677—61no—
47#4674—32no—
48#4665—32no—
49#4665D312yescomplemented
50C23×C3⋊D3C2311yescharacteristic
51C23×C3×D3C2312yes—
52C23×C3×D3C2312yes—
53C22×D32—22no—
54C22×D32—24no—
55C22×D32—41no—
56C22×D32—42no—
57C22×D32—41no—
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2312yes—
60C22×C3⋊Dic3C2312yes—
61C22×C3⋊Dic3C2311yescharacteristic
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C2×C3×D12—42no—
65C2×C3×D12—42no—
66C2×C3×D12D418yescomplemented
67C2×C3×C4×D3—24no—
68C2×C3×C4×D3—42no—
69C2×C3×C4×D3—42no—
70C2×#626—24no—
71C2×#626—24no—
72C2×#626—42no—
73C2×#625—24no—
74C2×#625—24no—
75C2×#625—24no—
76C2×#625—42no—
77C2×#625—41no—
78#3752—24no—
79#3752—41no—
80C4⋊(C3⋊Dic3)—24no—
81C4⋊(C3⋊Dic3)—41no—
82C3×(C2×D3)⋊C4—24no—
83C3×(C2×D3)⋊C4—42no—
84C3×(C2×D3)⋊C4—42no—
85#3722—41no—
86(C2×D3)⋊Dic3—24no—
87(C2×D3)⋊Dic3—24no—
88(C2×D3)⋊Dic3—24no—
89#2668—91noSylow
90C24×D3—32no—
91C22×C3×D4—32no—
92C23×C3×C4—32no—
93C22×#67—32no—
94C22×#67—32no—
95C22×#67—32no—
96C22×#67—32no—
97C22×D12—32no—
98C22×D12C2×D312yes—
99C22×C4×D3C2×D312yescomplemented
100C2×C3×C22⋊C4—32no—
101C2×C3×C22⋊C4—32no—
102C2×C3×C22⋊C4—32no—
103C2×#217—32no—
104C2×#217—32no—
105C2×#217—32no—
106#938—68no—
107#937—68no—
108#930—68no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—62no—
117C2×(C2×D3)⋊C4—61no—
118C2×(C2×D3)⋊C4C2×D312yes—
119C2×(C2×D3)⋊C4C2×D312yes—
120C2×(C2×D3)⋊C4C2×D312yescomplemented
121C2×C4⋊Dic3—32no—
122C2×C4⋊Dic3—32no—
123C2×C4⋊Dic3—32no—
124C2×C4⋊Dic3—62no—
125C2×C4⋊Dic3—61no—
126#882—68no—
127C3×#95—21no—
128C3×#95—32no—
129C3×#95C2×D312yescomplemented
130C3⋊#95—32no—
131C3⋊#95—32no—
132C3⋊#95—32no—
133C3⋊#95C2×D312yescomplemented
134C23×C32C2411yescharacteristic
135C22×C3⋊D3—22no—
136C22×C3⋊D3—21no—
137C22×C3⋊D3—21no—
138C22×C3⋊D3—22no—
139C22×C3⋊D3#4112yes—
140C22×C3×D3—22no—
141C22×C3×D3—22no—
142C22×C3×D3—22no—
143C22×C3×D3—22no—
144C22×C3×D3—22no—
145C22×C3×D3—22no—
146C22×C3×D3—22no—
147C22×C3×D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3C2×D414yes—
153C22×C3×D3C2×D414yes—
154C2×D32—44no—
155C2×D32—48no—
156C2×D32—48no—
157C2×D32—44no—
158C2×D32—44no—
159C2×C32×C4—21no—
160C2×C32×C4—22no—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4C2×D414yes—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—21no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C3×D12—48no—
176C3×C4×D3—48no—
177#626—48no—
178#625—44no—
179#625—48no—
180C2×#121—92no—
181C2×#120—92no—
182#399—91no—
183#397—92no—
184#394—92no—
185#392—91no—
186#386—32no—
187#386—92no—
188#379—91no—
189C24×C3—32no—
190C24×C3—32no—
191C23×D3—32no—
192C23×D3—61no—
193C23×D3—64no—
194C23×D3—64no—
195C23×D3—64no—
196C23×D3—122no—
197C23×D3—122no—
198C23×D3—122no—
199C23×D3—122no—
200C23×D3C22×D312yes—
201C23×D3C22×D312yes—
202C2×C3×D4—38no—
203C2×C3×D4—122no—
204C2×C3×D4—122no—
205C22×C3×C4—21no—
206C22×C3×C4—22no—
207C22×C3×C4—32no—
208C22×C3×C4—32no—
209C22×C3×C4—64no—
210C22×C3×C4—122no—
211C22×C3×C4—122no—
212C22×C3×C4C22×D312yes—
213C22×C3×C4C22×D312yes—
214C22×C3×C4C22×D312yes—
215C2×#67—64no—
216C2×#67—64no—
217C2×#67—64no—
218C2×#67—64no—
219C2×#67—64no—
220C2×#67—64no—
221C2×#67—64no—
222C2×#67—64no—
223C2×#67—122no—
224C2×#67—122no—
225C2×#67—122no—
226C2×#67—122no—
227C22×Dic3—32no—
228C22×Dic3—32no—
229C22×Dic3—32no—
230C22×Dic3—62no—
231C22×Dic3—61no—
232C22×Dic3C22×D312yes—
233C22×Dic3C22×D312yes—
234C2×D12—42no—
235C2×D12—42no—
236C2×D12—64no—
237C2×D12—64no—
238C2×D12—122no—
239C2×D12D1218yescomplemented
240C2×C4×D3—24no—
241C2×C4×D3—42no—
242C2×C4×D3—42no—
243C3×C22⋊C4—64no—
244C3×C22⋊C4—122no—
245C3×C22⋊C4—122no—
246#217—64no—
247#217—64no—
248#217—64no—
249(C2×D3)⋊C4—24no—
250(C2×D3)⋊C4—42no—
251(C2×D3)⋊C4—42no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—124no—
258(C2×D3)⋊C4—122no—
259(C2×D3)⋊C4—122no—
260(C2×D3)⋊C4—122no—
261C4⋊Dic3—64no—
262C4⋊Dic3—64no—
263C4⋊Dic3—124no—
264C4⋊Dic3—122no—
265C4⋊Dic3—122no—
266C22×C32C22×D412yes—
267C22×C32C2×#4111yescharacteristic
268C22×C32H(5,𝔽2)11yescharacteristic
269C22×C32H(5,𝔽2)12yes—
270C22×C32H(5,𝔽2)11yescharacteristic
271C2×C3⋊D3—22no—
272C2×C3⋊D3—24no—
273C2×C3⋊D3—42no—
274C2×C3⋊D3—41no—
275C2×C3⋊D3—41no—
276C2×C3×D3—24no—
277C2×C3×D3—24no—
278C2×C3×D3—24no—
279C2×C3×D3—24no—
280C2×C3×D3—24no—
281C2×C3×D3—24no—
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C2×C3×D3—42no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C2×C3×D3—42no—
290D32—416no—
291C32×C4—24no—
292C32×C4—41no—
293C3⋊Dic3—41no—
294C3⋊Dic3—42no—
295C3×Dic3—42no—
296C3×Dic3—42no—
297C25—91no—
298C22×D4—32no—
299C22×D4—92no—
300C22×D4—92no—
301C22×D4—91no—
302C23×C4—32no—
303#121—188no—
304#120—188no—
305C2×C4⋊C4—92no—
306C2×C4⋊C4—91no—
307C2×C22⋊C4—32no—
308C2×C22⋊C4—32no—
309C2×C22⋊C4—32no—
310C2×C22⋊C4—92no—
311C2×C22⋊C4—92no—
312C2×C22⋊C4—92no—
313C2×C22⋊C4—92no—
314C2×C22⋊C4—91no—
315C2×C22⋊C4—91no—
316#95—32no—
317#95—92no—
318#95—91no—
319#95D3211yescharacteristic, complemented
320C23×C3—21no—
321C23×C3—34no—
322C23×C3—34no—
323C23×C3—62no—
324C23×C3—62no—
325C23×C3—62no—
326C23×C3—62no—
327C23×C3—62no—
328C23×C3—62no—
329C23×C3—62no—
330C23×C3—62no—
331C23×C3—62no—
332C23×C3—62no—
333C23×C3—62no—
334C23×C3—62no—
335C23×C3C23×D312yes—
336C22×D3—22no—
337C22×D3—22no—
338C22×D3—22no—
339C22×D3—22no—
340C22×D3—22no—
341C22×D3—22no—
342C22×D3—22no—
343C22×D3—22no—
344C22×D3—22no—
345C22×D3—22no—
346C22×D3—22no—
347C22×D3—22no—
348C22×D3—34no—
349C22×D3—62no—
350C22×D3—62no—
351C22×D3—62no—
352C22×D3—62no—
353C22×D3—62no—
354C22×D3—62no—
355C22×D3—62no—
356C22×D3—122no—
357C22×D3—121no—
358C22×D3—121no—
359C22×D3—122no—
360C22×D3—128no—
361C22×D3—128no—
362C22×D3—128no—
363C22×D3—128no—
364C22×D3—128no—
365C22×D3—128no—
366C22×D3—128no—
367C22×D3C2×D1214yes—
368C22×D3C2×D1214yes—
369C3×D4—128no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—24no—
379C2×C3×C4—42no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4—128no—
389C2×C3×C4C2×D1214yes—
390C2×C3×C4D3×D414yes—
391#67—128no—
392#67—128no—
393#67—128no—
394#67—128no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—122no—
411C2×Dic3—122no—
412C2×Dic3—122no—
413C2×Dic3—122no—
414C2×Dic3—121no—
415D12—48no—
416D12—128no—
417C4×D3—48no—
418C2×C32#53412yes—
419C2×C32#53811yescharacteristic
420C2×C32D4211yescharacteristic
421C2×C32#54612yes—
422C2×C32#56011yescharacteristic
423C3⋊D3—42no—
424C3×D3—44no—
425C3×D3—44no—
426C24—32no—
427C24—32no—
428C24—91no—
429C24—184no—
430C24—182no—
431C24—361no—
432C24—362no—
433C24—361no—
434C2×D4—38no—
435C2×D4—122no—
436C2×D4—122no—
437C2×D4—184no—
438C2×D4—184no—
439C2×D4—184no—
440C2×D4—184no—
441C2×D4—184no—
442C2×D4—362no—
443C2×D4—361no—
444C2×D4—362no—
445C22×C4—32no—
446C22×C4—32no—
447C22×C4—64no—
448C22×C4—92no—
449C22×C4—91no—
450C22×C4—122no—
451C22×C4—122no—
452C22×C4C2×D3211yescharacteristic
453C22×C4C2×D3212yes—
454C4⋊C4—184no—
455C4⋊C4—361no—
456C22⋊C4—64no—
457C22⋊C4—122no—
458C22⋊C4—122no—
459C22⋊C4—184no—
460C22⋊C4—184no—
461C22⋊C4—184no—
462C22⋊C4—184no—
463C22⋊C4—361no—
464C22⋊C4—361no—
465C22×C3—22no—
466C22×C3—21no—
467C22×C3—22no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—64no—
471C22×C3—64no—
472C22×C3—64no—
473C22×C3—64no—
474C22×C3—64no—
475C22×C3—64no—
476C22×C3—122no—
477C22×C3—122no—
478C22×C3—122no—
479C22×C3—122no—
480C22×C3—122no—
481C22×C3—122no—
482C22×C3—122no—
483C22×C3—122no—
484C22×C3C22×D1212yes—
485C22×C3C2×D3×D412yes—
486C22×C3#100412yes—
487C22×C3#100412yes—
488C22×C3#100412yes—
489C22×C3D3×#4112yes—
490C22×C3#100912yes—
491C2×D3—24no—
492C2×D3—24no—
493C2×D3—24no—
494C2×D3—24no—
495C2×D3—24no—
496C2×D3—24no—
497C2×D3—42no—
498C2×D3—42no—
499C2×D3—42no—
500C2×D3—42no—
501C2×D3—42no—
502C2×D3—42no—
503C2×D3—42no—
504C2×D3—42no—
505C2×D3—64no—
506C2×D3—64no—
507C2×D3—64no—
508C2×D3—124no—
509C2×D3—122no—
510C2×D3—1232no—
511C2×D3—122no—
512C2×D3—122no—
513C2×D3—122no—
514C2×D3—122no—
515C2×D3—241no—
516C2×D3—241no—
517C2×D3—242no—
518C3×C4—24no—
519C3×C4—24no—
520C3×C4—44no—
521C3×C4—42no—
522C3×C4—42no—
523C3×C4—122no—
524C3×C4—122no—
525Dic3—42no—
526Dic3—42no—
527Dic3—122no—
528Dic3—122no—
529Dic3—122no—
530Dic3—242no—
531Dic3—241no—
532C32#266811yescharacteristic, complemented, Sylow
533C23—34no—
534C23—34no—
535C23—62no—
536C23—62no—
537C23—62no—
538C23—62no—
539C23—62no—
540C23—62no—
541C23—62no—
542C23—62no—
543C23—62no—
544C23—62no—
545C23—62no—
546C23—62no—
547C23—92no—
548C23—182no—
549C23—181no—
550C23—181no—
551C23—182no—
552C23—364no—
553C23—368no—
554C23—368no—
555C23—364no—
556C23—364no—
557C23C22×D3211yescharacteristic
558D4—128no—
559D4—368no—
560D4—364no—
561D4—368no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—62no—
572C2×C4—128no—
573C2×C4—182no—
574C2×C4—182no—
575C2×C4—182no—
576C2×C4—181no—
577C2×C4—182no—
578C2×C4D3×D1214yes—
579C2×C3—21no—
580C2×C3—22no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—22no—
584C2×C3—124no—
585C2×C3—124no—
586C2×C3#549312yes—
587C2×C3D4×D1212yes—
588C2×C3#555412yes—
589C2×C3#558912yes—
590C2×C3#561212yes—
591C2×C3#562012yes—
592C2×C3#565712yes—
593D3—44no—
594D3—44no—
595D3—124no—
596D3—242no—
597C22—64no—
598C22—64no—
599C22—64no—
600C22—64no—
601C22—64no—
602C22—64no—
603C22—122no—
604C22—122no—
605C22—122no—
606C22—122no—
607C22—122no—
608C22—122no—
609C22—122no—
610C22—122no—
611C22—184no—
612C22—182no—
613C22—3616no—
614C22—361no—
615C22—361no—
616C22—362no—
617C22C2×D3×D1212yes—
618C22#6430811yescharacteristic
619C22#6431312yes—
620C22#6431311yescharacteristic
621C22#6431911yescharacteristic
622C4—24no—
623C4—41no—
624C4—122no—
625C4—122no—
626C4—362no—
627C4—361no—
628C3—21no—
629C3#7491012yescomplemented
630C2—124no—
631C2—124no—
632C2—362no—
633C2D12211yescharacteristic
634C2#1059429012yes—
635C2#1059431011yescharacteristic
636C2#1059463012yes—
637C2#1059465911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
hypercenter#95D32
hypocenterC32#2668
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×#63922C2semidirect
2. C2×#63908C2semidirect
3. #10592376C2semidirect
4. C3×#4665C2semidirect
5. #10591399C2semidirect
6. #10591394C2semidirect
7. #10591393C2semidirect
8. #10591382C2semidirect
9. #10591315C2semidirect
13. C22×C3×C4×D3C22semidirect
16. C22×#625C22semidirect
19. C2×C4⋊(C3⋊Dic3)C22semidirect
20. C2×C4⋊(C3⋊Dic3)C22semidirect
23. C2×C3×(C2×D3)⋊C4C22semidirect
27. C2×(C2×D3)⋊Dic3C22semidirect
30. C32×#95C22semidirect
31. C3×C3⋊#95C22semidirect
32. #63579C22semidirect
33. #63579C22semidirect
49. #4665D3semidirect
66. C2×C3×D12D4semidirect
99. C22×C4×D3C2×D3semidirect
120. C2×(C2×D3)⋊C4C2×D3semidirect
129. C3×#95C2×D3semidirect
133. C3⋊#95C2×D3semidirect
239. C2×D12D12semidirect
319. #95D32semidirect
532. C32#2668semidirect
629. C3#74910semidirect

Maximal subgroups

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

subgroupindex
C2×#639222
C2×#639082
#105923762
C3×#46652
#105913992
#105913942
#105913932
#105913822
#105913152
#749103