Finite Group Databasebeta

← #11824449

Subgroups — #11824449

Order 1152.

2109 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic, complemented
2C2×C3×#930C212yesmaximal, complemented
3C2×#63979C212yesmaximal, complemented
4C2×#63916C212yesmaximal, complemented
5C2×#63914C211yesmaximal, characteristic, complemented
6#10591723C212yesmaximal, complemented
7#10591393C212yesmaximal, complemented
8#10591386C212yesmaximal, complemented
9#10591274C211yesmaximal, characteristic, complemented
10#82669—32nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#638C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C3×#67C2214yes—
15C22×C3×D12C2212yes—
16C22×#626C2214yes—
17C22×#625C2212yes—
18C22×#625C2212yes—
19C2×#3757C2211yescharacteristic
20C4×#638—24no—
21C2×#3752C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C3×#930—28no—
25C2×C3×(C2×D3)⋊C4C2214yes—
26C2×C3×C4⋊Dic3C2212yes—
27#63979—28no—
28C2×(C2×D3)⋊Dic3C2214yes—
29C2×Dic32C2212yes—
30#63916—28no—
31#63914—24no—
32#63579C2212yes—
33C2×C3×#121—32no—
34C2×#940—34no—
35C2×#940—32no—
36C2×#938—32no—
37C2×#930D312yescomplemented
38C2×C4×#67—32no—
39C2×C4×#67—61no—
40C2×#895—32no—
41#5223—34no—
42Dic3×C4⋊C4—32no—
43#4960—34no—
44#4957—34no—
45C24×C32C2311yescharacteristic
46C23×C3⋊D3C2311yescharacteristic
47C23×C3×D3C2314yes—
48C22×C32×C4—22no—
49C22×C32×C4—24no—
50C22×C32×C4C2311yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C2×#638—22no—
53C2×#638—22no—
54C2×#638D414yescomplemented
55C22×C3⋊Dic3C2311yescharacteristic
56C22×C3⋊Dic3C2311yescharacteristic
57C22×C3⋊Dic3C2311yescharacteristic
58C2×C4×C3⋊D3—22no—
59C2×C4×C3⋊D3—24no—
60C2×C3×#67—28no—
61C2×C3×#67—28no—
62C2×C3×#67—44no—
63C22×C3×Dic3C2314yes—
64C2×C3×D12—24no—
65C2×C3×D12—24no—
66C2×C3×D12—24no—
67C2×#626—28no—
68C2×#626—28no—
69C2×#626—44no—
70C2×#625—24no—
71C2×#625—24no—
72C2×#625—24no—
73C2×#625—24no—
74C2×#625—44no—
75#3757—22no—
76#3752—22no—
77#3750—22no—
78C4×C3⋊Dic3D414yescomplemented
79C3×(C2×D3)⋊C4—28no—
80C3×C4⋊Dic3D418yescomplemented
81(C2×D3)⋊Dic3—28no—
82Dic32—24no—
83#2541—91noSylow
84C22×C3×D4—34no—
85C22×C3×D4—32no—
86C23×C3×C4—21no—
87C23×C3×C4C2×D312yes—
88C22×#67—32no—
89C22×#67—34no—
90C22×#67—34no—
91C22×#67—34no—
92C22×#67—61no—
93C22×#67C2×D314yes—
94C22×D12—34no—
95C22×D12C2×D312yes—
96C22×C4×D3—32no—
97C22×C4×D3—61no—
98C3×#121—68no—
99C2×C3×C4⋊C4—32no—
100C2×C3×C22⋊C4—34no—
101C2×#217—32no—
102C2×#217—34no—
103C2×#217—61no—
104#940—68no—
105#940—616no—
106#938—68no—
107#930—28no—
108C4×#67—68no—
109C4×#67—68no—
110C2×(C2×D3)⋊C4—34no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—61no—
113C2×(C2×D3)⋊C4C2×D314yes—
114C2×C4⋊Dic3C2×D312yes—
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4—61no—
117C2×C4×Dic3—32no—
118C2×C4×Dic3—34no—
119C2×C4×Dic3—61no—
120#895—68no—
121C3⋊#95—34no—
122C23×C32—21no—
123C23×C32—21no—
124C23×C32—22no—
125C23×C32—22no—
126C23×C32C2×D412yes—
127C23×C32C2411yescharacteristic
128C22×C3⋊D3—21no—
129C22×C3⋊D3—21no—
130C22×C3⋊D3—22no—
131C22×C3⋊D3—22no—
132C22×C3⋊D3C2×D412yes—
133C22×C3×D3—24no—
134C22×C3×D3—24no—
135C22×C3×D3—24no—
136C22×C3×D3—24no—
137C22×C3×D3—24no—
138C22×C3×D3—24no—
139C22×C3×D3—24no—
140C2×C32×C4—21no—
141C2×C32×C4—22no—
142C2×C32×C4—44no—
143C2×C32×C4C2×D412yes—
144C2×C32×C4C2×D414yes—
145#638—28no—
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3C2×D412yes—
150C2×C3⋊Dic3C2×D412yes—
151C2×C3⋊Dic3C2×D412yes—
152C2×C3⋊Dic3#4112yes—
153C4×C3⋊D3—44no—
154C3×#67—416no—
155C2×C3×Dic3—24no—
156C2×C3×Dic3—24no—
157C2×C3×Dic3C2×D418yes—
158C3×D12—48no—
159#626—416no—
160#625—48no—
161#625—48no—
162C2×#127—91no—
163C2×#127—92no—
164C2×#121—32no—
165C2×#121—92no—
166C2×C4×D4—91no—
167#392—92no—
168#392—92no—
169#390—92no—
170C4×C4⋊C4—91no—
171C24×C3—21no—
172C24×C3—34no—
173C24×C3C22×D312yes—
174C23×D3—32no—
175C23×D3—61no—
176C23×D3C22×D314yes—
177C2×C3×D4—68no—
178C2×C3×D4—68no—
179C2×C3×D4—64no—
180C2×C3×D4—64no—
181C2×C3×D4—64no—
182C2×C3×D4—124no—
183C22×C3×C4—24no—
184C22×C3×C4—24no—
185C22×C3×C4—24no—
186C22×C3×C4—24no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—34no—
190C22×C3×C4—44no—
191C22×C3×C4C22×D312yes—
192C22×C3×C4C22×D312yes—
193C2×#67—28no—
194C2×#67—28no—
195C2×#67—38no—
196C2×#67—44no—
197C2×#67—64no—
198C2×#67—68no—
199C2×#67—64no—
200C2×#67—64no—
201C2×#67—68no—
202C2×#67—68no—
203C2×#67—68no—
204C2×#67—68no—
205C2×#67—64no—
206C2×#67—64no—
207C2×#67—68no—
208C2×#67—124no—
209C2×#67—124no—
210C2×#67—124no—
211C22×Dic3—32no—
212C22×Dic3—32no—
213C22×Dic3—32no—
214C22×Dic3—61no—
215C22×Dic3—61no—
216C22×Dic3—61no—
217C22×Dic3C22×D314yes—
218C2×D12—24no—
219C2×D12—24no—
220C2×D12—24no—
221C2×D12—68no—
222C2×D12—68no—
223C2×D12—124no—
224C2×C4×D3—64no—
225C2×C4×D3—64no—
226C2×C4×D3—64no—
227C2×C4×D3—64no—
228C2×C4×D3—124no—
229C3×C4⋊C4—38no—
230C3×C22⋊C4—68no—
231#217—64no—
232#217—64no—
233#217—68no—
234(C2×D3)⋊C4—28no—
235(C2×D3)⋊C4—64no—
236(C2×D3)⋊C4—64no—
237(C2×D3)⋊C4—68no—
238C4⋊Dic3#6718yescomplemented
239Dic3⋊C4—64no—
240Dic3⋊C4—64no—
241C4×Dic3—38no—
242C4×Dic3—64no—
243C4×Dic3—68no—
244C22×C32—22no—
245C22×C32—24no—
246C22×C32—41no—
247C22×C32—41no—
248C22×C32—42no—
249C22×C32C22×D411yescharacteristic
250C22×C32C22×D411yescharacteristic
251C22×C32C22×D412yes—
252C22×C32C2×#4111yescharacteristic
253C22×C32H(5,𝔽2)12yes—
254C2×C3⋊D3—22no—
255C2×C3⋊D3—24no—
256C2×C3⋊D3—41no—
257C2×C3⋊D3—41no—
258C2×C3⋊D3—42no—
259C2×C3×D3—44no—
260C2×C3×D3—44no—
261C2×C3×D3—44no—
262C2×C3×D3—44no—
263C2×C3×D3—44no—
264C2×C3×D3—44no—
265C2×C3×D3—44no—
266C32×C4—41no—
267C32×C4#12714yescomplemented
268C3⋊Dic3—22no—
269C3⋊Dic3—41no—
270C3⋊Dic3#12114yescomplemented
271C3×Dic3—28no—
272C22×D4—34no—
273C22×D4—32no—
274C22×D4—94no—
275C22×D4—91no—
276C22×D4—92no—
277C22×D4—92no—
278C23×C4—91no—
279C23×C4D3211yescharacteristic
280#127—184no—
281#127—188no—
282#121—68no—
283#121—188no—
284C4×D4—184no—
285C2×C4⋊C4—32no—
286C2×C4⋊C4—91no—
287C2×C22⋊C4—34no—
288C2×C22⋊C4—94no—
289C2×C22⋊C4—91no—
290C2×C22⋊C4—91no—
291C2×C42—91no—
292C2×C42—92no—
293#95—92no—
294C23×C3—22no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—22no—
301C23×C3—22no—
302C23×C3—21no—
303C23×C3—22no—
304C23×C3—42no—
305C23×C3—42no—
306C23×C3—64no—
307C23×C3—64no—
308C23×C3—64no—
309C23×C3—64no—
310C23×C3—64no—
311C23×C3—64no—
312C23×C3—64no—
313C23×C3D3×D414yes—
314C23×C3C23×D312yes—
315C22×D3—24no—
316C22×D3—24no—
317C22×D3—24no—
318C22×D3—24no—
319C22×D3—24no—
320C22×D3—24no—
321C22×D3—24no—
322C22×D3—34no—
323C22×D3—62no—
324C22×D3—62no—
325C22×D3—62no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—122no—
333C22×D3—122no—
334C3×D4—1216no—
335C3×D4—128no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—24no—
341C2×C3×C4—22no—
342C2×C3×C4—38no—
343C2×C3×C4—42no—
344C2×C3×C4—48no—
345C2×C3×C4—48no—
346C2×C3×C4—64no—
347C2×C3×C4—64no—
348C2×C3×C4D3×D414yes—
349C2×C3×C4D3×D414yes—
350C2×C3×C4C2×#6714yes—
351#67—416no—
352#67—616no—
353#67—616no—
354#67—1216no—
355#67—1216no—
356#67—1216no—
357C2×Dic3—24no—
358C2×Dic3—24no—
359C2×Dic3—34no—
360C2×Dic3—34no—
361C2×Dic3—34no—
362C2×Dic3—34no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—122no—
374C2×Dic3—122no—
375C2×Dic3C2×#6718yes—
376D12—48no—
377D12—1216no—
378C4×D3—128no—
379C4×D3—128no—
380C2×C32—42no—
381C2×C32C2×#12111yescharacteristic
382C2×C32C2×#12711yescharacteristic
383C2×C32#53511yescharacteristic
384C2×C32D4212yes—
385C2×C32#55012yes—
386C3⋊D3—42no—
387C3×D3—84no—
388C24—34no—
389C24—91no—
390C24C2×D3211yescharacteristic
391C2×D4—68no—
392C2×D4—68no—
393C2×D4—64no—
394C2×D4—64no—
395C2×D4—64no—
396C2×D4—94no—
397C2×D4—124no—
398C2×D4—188no—
399C2×D4—188no—
400C2×D4—182no—
401C2×D4—182no—
402C2×D4—184no—
403C2×D4—184no—
404C2×D4—184no—
405C2×D4—184no—
406C2×D4—364no—
407C2×D4—364no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—34no—
411C22×C4—91no—
412C22×C4—91no—
413C22×C4—91no—
414C22×C4—184no—
415C22×C4—182no—
416C22×C4C2×D3211yescharacteristic
417C22×C4C2×D3211yescharacteristic
418C4⋊C4—38no—
419C4⋊C4—182no—
420C22⋊C4—68no—
421C22⋊C4—182no—
422C22⋊C4—188no—
423C22⋊C4—182no—
424C42—94no—
425C42—184no—
426C22×C3—24no—
427C22×C3—24no—
428C22×C3—24no—
429C22×C3—24no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—21no—
435C22×C3—44no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—44no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—124no—
444C22×C3—124no—
445C22×C3—124no—
446C22×C3—124no—
447C22×C3—124no—
448C22×C3—124no—
449C22×C3—124no—
450C22×C3C2×D3×D412yes—
451C22×C3C2×D3×D412yes—
452C22×C3C2×D3×D412yes—
453C22×C3#100412yes—
454C22×C3D3×#4112yes—
455C22×C3#100912yes—
456C22×C3C22×#6712yes—
457C2×D3—44no—
458C2×D3—44no—
459C2×D3—44no—
460C2×D3—44no—
461C2×D3—44no—
462C2×D3—44no—
463C2×D3—44no—
464C2×D3—64no—
465C2×D3—64no—
466C2×D3—64no—
467C2×D3—64no—
468C2×D3—124no—
469C2×D3—122no—
470C2×D3—122no—
471C2×D3—124no—
472C2×D3—122no—
473C2×D3—122no—
474C2×D3—122no—
475C2×D3—122no—
476C3×C4—24no—
477C3×C4—42no—
478C3×C4—42no—
479C3×C4—68no—
480C3×C4#94018yescomplemented
481Dic3—28no—
482Dic3—38no—
483Dic3—64no—
484Dic3—64no—
485Dic3—122no—
486Dic3—122no—
487Dic3—122no—
488C32#254111yescharacteristic, complemented, Sylow
489C23—21no—
490C23—22no—
491C23—22no—
492C23—21no—
493C23—64no—
494C23—64no—
495C23—64no—
496C23—64no—
497C23—64no—
498C23—64no—
499C23—64no—
500C23—92no—
501C23—181no—
502C23—182no—
503C23—182no—
504C23—181no—
505C23#380212yes—
506C23C22×D3211yescharacteristic
507D4—1216no—
508D4—128no—
509D4—188no—
510D4—3616no—
511D4—368no—
512D4—368no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—38no—
516C2×C4—44no—
517C2×C4—64no—
518C2×C4—64no—
519C2×C4—92no—
520C2×C4—92no—
521C2×C4—92no—
522C2×C4—92no—
523C2×C4—182no—
524C2×C4—182no—
525C2×C4—181no—
526C2×C4—364no—
527C2×C4D3×#6714yes—
528C2×C4#381112yes—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—22no—
533C2×C3—22no—
534C2×C3—44no—
535C2×C3—44no—
536C2×C3—244no—
537C2×C3#559912yes—
538C2×C3D3×#12112yes—
539C2×C3#560712yes—
540C2×C3#560912yes—
541C2×C3D4×#6712yes—
542C2×C3C2×#94012yes—
543C2×C3#583412yes—
544D3—84no—
545D3—124no—
546D3—124no—
547C22—22no—
548C22—24no—
549C22—41no—
550C22—41no—
551C22—42no—
552C22—124no—
553C22—124no—
554C22—124no—
555C22—124no—
556C22—124no—
557C22—124no—
558C22—124no—
559C22—182no—
560C22—184no—
561C22—361no—
562C22—361no—
563C22—362no—
564C22C2×#380211yescharacteristic
565C22#6430611yescharacteristic
566C22#6430712yes—
567C22C2×D3×#6712yes—
568C22C2×#381111yescharacteristic
569C4—41no—
570C4—68no—
571C4—94no—
572C4—182no—
573C4—361no—
574C4#6397914yescomplemented
575C3—21no—
576C3#8266912yescomplemented
577C2—42no—
578C2—244no—
579C2—362no—
580C2#1059500612yes—
581C2#1059506912yes—
582C2#1059508111yescharacteristic
583C2#1059508211yescharacteristic
584C2C2×#6397911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC23×C32×C4C22
hypercenterC23×C4D32
hypocenterC32#2541
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×#638C2semidirect
2. C2×C3×#930C2semidirect
3. C2×#63979C2semidirect
4. C2×#63916C2semidirect
5. C2×#63914C2semidirect
6. #10591723C2semidirect
7. #10591393C2semidirect
8. #10591386C2semidirect
9. #10591274C2semidirect
37. C2×#930D3semidirect
54. C2×#638D4semidirect
78. C4×C3⋊Dic3D4semidirect
80. C3×C4⋊Dic3D4semidirect
238. C4⋊Dic3#67semidirect
267. C32×C4#127semidirect
270. C3⋊Dic3#121semidirect
480. C3×C4#940semidirect
488. C32#2541semidirect
574. C4#63979semidirect
576. C3#82669semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C2×C3×#9302
C2×#639792
C2×#639162
C2×#639142
#105917232
#105913932
#105913862
#105912742
#826693