Finite Group Databasebeta

← #11836029

Subgroups — #11836029

Order 1152.

2796 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#120C211yesmaximal, characteristic, complemented
2C2×#64162C212yesmaximal, complemented
3C2×#64149C211yesmaximal, characteristic, complemented
4C2×#64148C212yesmaximal, complemented
5#10592922C212yesmaximal, complemented
6#10592919C211yesmaximal, characteristic, complemented
7#10592659C212yesmaximal, complemented
8#10592658C212yesmaximal, complemented
9#10592643C212yesmaximal, complemented
10#82594—34nomaximal
11C25×C32C2211yescharacteristic
12C22×C32×D4C2212yes—
13C22×C32×D4C2211yescharacteristic
14C22×#638C2212yes—
15C22×#638C2212yes—
16C22×#638C2212yes—
17C22×#638C2212yescomplemented
18C23×C3⋊Dic3C2211yescharacteristic, complemented
19C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
20C32×#120—24no—
21C2×C32×C22⋊C4C2212yes—
22C2×C32×C22⋊C4C2211yescharacteristic
23#64162—28no—
24C2×#3757C2212yes—
25C2×#3757C2212yes—
26C2×#3757C2212yes—
27C2×#3757C2211yescharacteristic, complemented
28#64149—24no—
29#64148—28no—
30C2×#3752C2212yescomplemented
31C2×#3752C2212yescomplemented
32C2×#3750C2212yescomplemented
33C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
34#63658C2212yescomplemented
35#63658C2212yescomplemented
36C2×C3×#120D314yescomplemented
37C2×#953—38no—
38C2×#940—34no—
39C2×#939—38no—
40#5223—38no—
41#5220—34no—
42#4960—38no—
43#4959—38no—
44#4944—38no—
45C24×C32—24no—
46C24×C32—22no—
47C24×C32—42no—
48C24×C32—41no—
49C24×C32—41no—
50C24×C32C2311yescharacteristic
51C24×C32C2311yescharacteristic
52C24×C32C2312yes—
53C23×C3⋊D3C2312yes—
54C2×C32×D4—24no—
55C2×C32×D4—24no—
56C2×C32×D4—41no—
57C2×C32×D4—41no—
58C2×C32×D4—42no—
59C2×C32×D4D414yescomplemented
60C22×C32×C4C2312yes—
61C22×C32×C4C2311yescharacteristic
62C2×#638—24no—
63C2×#638—24no—
64C2×#638—24no—
65C2×#638—24no—
66C2×#638—24no—
67C2×#638—24no—
68C2×#638—24no—
69C2×#638—42no—
70C2×#638—42no—
71C2×#638—42no—
72C2×#638—42no—
73C2×#638—42no—
74C22×C3⋊Dic3—24no—
75C22×C3⋊Dic3—41no—
76C22×C3⋊Dic3C2312yes—
77C22×C3⋊Dic3C2312yes—
78C22×C3⋊Dic3C2312yes—
79C2×C4⋊(C3⋊D3)—22no—
80C2×C4⋊(C3⋊D3)—41no—
81C2×C4⋊(C3⋊D3)—41no—
82C32×C22⋊C4—22no—
83C32×C22⋊C4—24no—
84#3757—24no—
85#3757—24no—
86#3757—41no—
87#3757D418yescomplemented
88#3752—24no—
89#3752—42no—
90#3750—24no—
91C4×C3⋊Dic3—22no—
92#2669—91noSylow
93C25×C3C2×D314yes—
94C22×C3×D4C2×D318yes—
95C22×C3×D4C2×D314yes—
96C22×#67—38no—
97C22×#67—38no—
98C22×#67—38no—
99C22×#67—38no—
100C23×Dic3—34no—
101C22×D12—34no—
102C3×#120—216no—
103C2×C3×C22⋊C4C2×D318yes—
104C2×C3×C22⋊C4C2×D314yes—
105#953—632no—
106C2×#217—38no—
107C2×#217—38no—
108C2×#217—38no—
109C2×#217—34no—
110#940—616no—
111#939—632no—
112C2×(C2×D3)⋊C4—38no—
113C2×(C2×D3)⋊C4—38no—
114C2×Dic3⋊C4—38no—
115C2×C4×Dic3—34no—
116C3⋊#95—38no—
117C3⋊#95—38no—
118C23×C32—22no—
119C23×C32—22no—
120C23×C32—22no—
121C23×C32—22no—
122C23×C32—22no—
123C23×C32—22no—
124C23×C32—22no—
125C23×C32—22no—
126C23×C32—21no—
127C23×C32—21no—
128C23×C32—22no—
129C23×C32—21no—
130C23×C32—21no—
131C23×C32—22no—
132C23×C32—44no—
133C23×C32—48no—
134C23×C32—44no—
135C23×C32—48no—
136C23×C32—44no—
137C23×C32C2×D414yes—
138C23×C32C2×D412yes—
139C23×C32C2×D412yes—
140C23×C32C2411yescharacteristic
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—
148C32×D4—44no—
149C32×D4—48no—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4—22no—
155C2×C32×C4C2×D412yes—
156#638—48no—
157#638—48no—
158#638—48no—
159#638—48no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—44no—
168C2×C3⋊Dic3C2×D414yes—
169C2×C3⋊Dic3C2×D414yes—
170C4⋊(C3⋊D3)—44no—
171C2×#127—91no—
172C2×#121—92no—
173C2×#120—92no—
174C2×#120C3⋊D311yescharacteristic, complemented
175#394—92no—
176#392—92no—
177#392—92no—
178#388—92no—
179#386—91no—
180C24×C3—216no—
181C24×C3—28no—
182C24×C3—48no—
183C24×C3—44no—
184C24×C3—44no—
185C24×C3C22×D318yes—
186C24×C3C22×D314yes—
187C24×C3C22×D314yes—
188C23×D3—38no—
189C2×C3×D4—216no—
190C2×C3×D4—216no—
191C2×C3×D4—44no—
192C2×C3×D4—44no—
193C2×C3×D4—48no—
194C2×C3×D4#67116yescomplemented
195C22×C3×C4C22×D318yes—
196C22×C3×C4C22×D314yes—
197C2×#67—616no—
198C2×#67—616no—
199C2×#67—616no—
200C2×#67—616no—
201C2×#67—616no—
202C2×#67—616no—
203C2×#67—616no—
204C2×#67—128no—
205C2×#67—128no—
206C2×#67—128no—
207C2×#67—128no—
208C2×#67—128no—
209C22×Dic3—38no—
210C22×Dic3—38no—
211C22×Dic3—38no—
212C22×Dic3—616no—
213C22×Dic3—124no—
214C2×D12—68no—
215C2×D12—124no—
216C2×D12—124no—
217C3×C22⋊C4—28no—
218C3×C22⋊C4—216no—
219#217—332no—
220#217—616no—
221#217—616no—
222#217—124no—
223(C2×D3)⋊C4—616no—
224(C2×D3)⋊C4—128no—
225Dic3⋊C4—616no—
226C4×Dic3—68no—
227C22×C32—22no—
228C22×C32—22no—
229C22×C32—24no—
230C22×C32—24no—
231C22×C32—24no—
232C22×C32—24no—
233C22×C32—24no—
234C22×C32—416no—
235C22×C32—42no—
236C22×C32—42no—
237C22×C32—42no—
238C22×C32—42no—
239C22×C32—41no—
240C22×C32—42no—
241C22×C32—41no—
242C22×C32—41no—
243C22×C32—41no—
244C22×C32—42no—
245C22×C32C22×D412yes—
246C22×C32C22×D411yescharacteristic
247C22×C32H(5,𝔽2)11yescharacteristic
248C22×C32H(5,𝔽2)11yescharacteristic
249C22×C32H(5,𝔽2)12yes—
250C2×C3⋊D3—42no—
251C2×C3⋊D3—42no—
252C2×C3⋊D3—42no—
253C2×C3⋊D3—42no—
254C2×C3⋊D3—42no—
255C2×C3⋊D3—42no—
256C2×C3⋊D3—42no—
257C32×C4—22no—
258C32×C4—42no—
259C3⋊Dic3—24no—
260C3⋊Dic3—24no—
261C3⋊Dic3—42no—
262C25C2×C3⋊D311yescharacteristic
263C22×D4—92no—
264C22×D4—92no—
265C22×D4—92no—
266C22×D4—92no—
267C22×D4—91no—
268C22×D4C2×C3⋊D312yes—
269C22×D4C2×C3⋊D311yescharacteristic
270C23×C4—91no—
271#127—184no—
272#121—188no—
273#120—24no—
274#120—188no—
275C2×C4⋊C4—92no—
276C2×C22⋊C4—92no—
277C2×C22⋊C4—92no—
278C2×C22⋊C4—92no—
279C2×C22⋊C4—92no—
280C2×C22⋊C4—91no—
281C2×C22⋊C4—92no—
282C2×C22⋊C4C2×C3⋊D312yes—
283C2×C22⋊C4C2×C3⋊D311yescharacteristic
284C2×C42—91no—
285#95—92no—
286#95—92no—
287C23×C3—28no—
288C23×C3—28no—
289C23×C3—28no—
290C23×C3—24no—
291C23×C3—24no—
292C23×C3—28no—
293C23×C3—28no—
294C23×C3—28no—
295C23×C3—28no—
296C23×C3—28no—
297C23×C3—28no—
298C23×C3—24no—
299C23×C3—24no—
300C23×C3—28no—
301C23×C3—432no—
302C23×C3—416no—
303C23×C3—416no—
304C23×C3—432no—
305C23×C3—416no—
306C23×C3D3×D4116yes—
307C23×C3C2×#6718yes—
308C23×C3C2×#6718yes—
309C23×C3C23×D314yes—
310C22×D3—68no—
311C22×D3—68no—
312C22×D3—68no—
313C22×D3—68no—
314C22×D3—68no—
315C22×D3—68no—
316C22×D3—68no—
317C3×D4—416no—
318C3×D4—432no—
319C2×C3×C4—24no—
320C2×C3×C4—24no—
321C2×C3×C4—28no—
322C2×C3×C4—28no—
323C2×C3×C4—28no—
324C2×C3×C4C2×#6718yes—
325#67—1232no—
326#67—1232no—
327#67—1232no—
328#67—1232no—
329C2×Dic3—316no—
330C2×Dic3—316no—
331C2×Dic3—68no—
332C2×Dic3—68no—
333C2×Dic3—68no—
334C2×Dic3—68no—
335C2×Dic3—68no—
336C2×Dic3—68no—
337C2×Dic3—68no—
338C2×Dic3—1216no—
339D12—1216no—
340C2×C32—42no—
341C2×C32—42no—
342C2×C32—44no—
343C2×C32#53411yescharacteristic
344C2×C32#53512yes—
345C2×C32D4212yes—
346C2×C32D4211yescharacteristic
347C2×C32#56011yescharacteristic
348C3⋊D3—82no—
349C24—24no—
350C24—22no—
351C24—42no—
352C24—41no—
353C24—41no—
354C24—92no—
355C24C22×C3⋊D312yes—
356C24C22×C3⋊D311yescharacteristic
357C24C22×C3⋊D311yescharacteristic
358C2×D4—24no—
359C2×D4—24no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—42no—
363C2×D4—184no—
364C2×D4—184no—
365C2×D4—184no—
366C2×D4—184no—
367C2×D4—184no—
368C2×D4—184no—
369C2×D4—184no—
370C2×D4—182no—
371C2×D4—361no—
372C2×D4—361no—
373C2×D4—362no—
374C2×D4—362no—
375C2×D4—362no—
376C2×D4—362no—
377C2×D4—362no—
378C2×D4#63814yescomplemented
379C22×C4—92no—
380C22×C4—92no—
381C22×C4—92no—
382C22×C4—184no—
383C22×C4—361no—
384C22×C4C22×C3⋊D312yes—
385C22×C4C22×C3⋊D311yescharacteristic
386C4⋊C4—184no—
387C22⋊C4—22no—
388C22⋊C4—24no—
389C22⋊C4—98no—
390C22⋊C4—184no—
391C22⋊C4—184no—
392C22⋊C4—184no—
393C22⋊C4—362no—
394C22⋊C4—361no—
395C42—182no—
396C22×C3—216no—
397C22×C3—216no—
398C22×C3—216no—
399C22×C3—28no—
400C22×C3—28no—
401C22×C3—216no—
402C22×C3—216no—
403C22×C3—464no—
404C22×C3—48no—
405C22×C3—48no—
406C22×C3—44no—
407C22×C3—44no—
408C22×C3—48no—
409C22×C3—48no—
410C22×C3—48no—
411C22×C3—44no—
412C22×C3—48no—
413C22×C3—44no—
414C22×C3C2×D3×D418yes—
415C22×C3#100418yes—
416C22×C3#100414yes—
417C22×C3#100414yes—
418C22×C3C22×#6714yes—
419C2×D3—128no—
420C2×D3—128no—
421C2×D3—128no—
422C2×D3—128no—
423C2×D3—128no—
424C2×D3—128no—
425C2×D3—128no—
426C3×C4—28no—
427C3×C4—48no—
428Dic3—616no—
429Dic3—616no—
430Dic3—128no—
431C32#266911yescharacteristic, complemented, Sylow
432C23—22no—
433C23—22no—
434C23—22no—
435C23—21no—
436C23—21no—
437C23—22no—
438C23—22no—
439C23—21no—
440C23—21no—
441C23—22no—
442C23—22no—
443C23—22no—
444C23—22no—
445C23—22no—
446C23—48no—
447C23—44no—
448C23—44no—
449C23—48no—
450C23—44no—
451C23—182no—
452C23—182no—
453C23—182no—
454C23—182no—
455C23—182no—
456C23—182no—
457C23—182no—
458C23D4×C3⋊D314yes—
459C23C2×#63812yes—
460C23C2×#63812yes—
461C23C23×C3⋊D311yescharacteristic
462D4—44no—
463D4—48no—
464D4—364no—
465D4—368no—
466D4—368no—
467D4—368no—
468D4—368no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—94no—
475C2×C4—94no—
476C2×C4—182no—
477C2×C4—182no—
478C2×C4—182no—
479C2×C4—182no—
480C2×C4—182no—
481C2×C4—182no—
482C2×C4—182no—
483C2×C4—364no—
484C2×C4C2×#63812yes—
485C2×C3—48no—
486C2×C3—416no—
487C2×C3—48no—
488C2×C3#559014yes—
489C2×C3#559218yes—
490C2×C3#559514yes—
491C2×C3D4×#6718yes—
492C2×C3#580414yes—
493D3—248no—
494C22—24no—
495C22—24no—
496C22—24no—
497C22—22no—
498C22—22no—
499C22—24no—
500C22—24no—
501C22—416no—
502C22—42no—
503C22—42no—
504C22—41no—
505C22—41no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—42no—
510C22—41no—
511C22—41no—
512C22—362no—
513C22—362no—
514C22—362no—
515C22—362no—
516C22—362no—
517C22—362no—
518C22—362no—
519C22C2×D4×C3⋊D312yes—
520C22#6436112yes—
521C22#6436111yescharacteristic
522C22#6436111yescharacteristic
523C22C22×#63811yescharacteristic
524C4—22no—
525C4—42no—
526C4—184no—
527C4—184no—
528C4—362no—
529C3#8259414yescomplemented
530C2—44no—
531C2—42no—
532C2—42no—
533C2—722no—
534C2#1059606111yescharacteristic
535C2#1059606312yes—
536C2#1059606611yescharacteristic
537C2D4×#63812yes—
538C2#1059627511yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC2×C32×#120C2
hypercenterC2×#120C3⋊D3
hypocenterC32#2669
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×C32×#120C2semidirect
2. C2×#64162C2semidirect
3. C2×#64149C2semidirect
4. C2×#64148C2semidirect
5. #10592922C2semidirect
6. #10592919C2semidirect
7. #10592659C2semidirect
8. #10592658C2semidirect
9. #10592643C2semidirect
17. C22×#638C22semidirect
18. C23×C3⋊Dic3C22semidirect
19. C22×C4⋊(C3⋊D3)C22semidirect
27. C2×#3757C22semidirect
30. C2×#3752C22semidirect
31. C2×#3752C22semidirect
32. C2×#3750C22semidirect
33. C2×C4×C3⋊Dic3C22semidirect
34. #63658C22semidirect
35. #63658C22semidirect
36. C2×C3×#120D3semidirect
59. C2×C32×D4D4semidirect
87. #3757D4semidirect
174. C2×#120C3⋊D3semidirect
194. C2×C3×D4#67semidirect
378. C2×D4#638semidirect
431. C32#2669semidirect
529. C3#82594semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1202
C2×#641622
C2×#641492
C2×#641482
#105929222
#105929192
#105926592
#105926582
#105926432
#825943