Finite Group Databasebeta

← #11792448

Subgroups — #11792448

Order 1152.

1079 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D24C211yesmaximal, characteristic, complemented
2C2×#63914C211yesmaximal, characteristic, complemented
3C22×#3713C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic, complemented
5#10591323C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic, complemented
7#10589416C211yesmaximal, characteristic, complemented
8#72044—31nomaximal
9#70209—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×#625—22no—
14C22×C32×C8C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×D24—22no—
19C2×C3×D24—22no—
20C2×C3×D24—22no—
21C2×(C2×D3)⋊Dic3—22no—
22#63914—22no—
23#63914—22no—
24C2×#3713—22no—
25C2×#3713—22no—
26C2×#3713—22no—
27C3×#821—22no—
28#63562—22no—
29C22×C3×D8—31no—
30C2×#940—31no—
31C2×#940—31no—
32C22×#213—31no—
33C22×#213—31no—
34C22×D24D311yescharacteristic, complemented
35C2×C3×#102—31no—
36#5221—31no—
37C2×#832—31no—
38C2×#821D311yescharacteristic, complemented
39#4988—31no—
40C2×#809—31no—
41#4550—31no—
42#4550—31no—
43#4550—61no—
44C23×C3×D3—21no—
45C23×C3×D3—21no—
46C23×C3×D3—21no—
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3D412yes—
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×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12—21no—
63C2×C3×D12—21no—
64C2×C3×D12—21no—
65C2×C3×D12D412yes—
66C2×C3×D12D412yes—
67C2×C3×D12D412yescomplemented
68C2×#625—28no—
69C2×#625—44no—
70C2×#625—44no—
71C2×C32×C8—21no—
72C2×C32×C8—21no—
73C2×C32×C8D412yescomplemented
74C4×C3⋊Dic3—21no—
75C4×C3⋊Dic3—21no—
76C2×C3⋊(C3⋊C8)—21no—
77C2×C3⋊(C3⋊C8)—21no—
78C2×C3⋊(C3⋊C8)D412yescomplemented
79C3×C4⋊Dic3—21no—
80C3×C4⋊Dic3—21no—
81C3×D24—28no—
82(C2×D3)⋊Dic3—44no—
83#3713—28no—
84#2011—91noSylow
85C22×C3×D4—31no—
86C22×C3×D4—31no—
87C22×C3×D4—31no—
88C22×#67—62no—
89C22×#67—62no—
90C22×D12C2×D311yescharacteristic
91C22×D12C2×D311yescharacteristic
92C22×D12C2×D311yescharacteristic
93C2×C3×D8—62no—
94C2×C3×D8—62no—
95C2×C3×D8—62no—
96C22×C3×C8—21no—
97C22×C3×C8C2×D311yescharacteristic
98C22×C3×C8C2×D311yescharacteristic
99C2×C3×C4⋊C4—31no—
100C2×#217—62no—
101#940—62no—
102#940—62no—
103#940—62no—
104#940—62no—
105C2×#213—62no—
106C2×#213—62no—
107C2×#213—62no—
108C2×#213—62no—
109C2×#213—62no—
110C2×#213—62no—
111C2×(C2×D3)⋊C4—62no—
112C2×C4⋊Dic3C2×D311yescharacteristic
113C2×C4×Dic3—31no—
114C2×C4×Dic3—31no—
115C2×C4×Dic3—61no—
116C22×C3⋊C8—31no—
117C22×C3⋊C8—31no—
118C22×C3⋊C8—61no—
119C2×D24—22no—
120C2×D24—22no—
121C2×D24—22no—
122C3×#102—62no—
123#832—62no—
124#821—22no—
125#809—62no—
126C23×C32C2×D411yescharacteristic
127C22×C3×D3—22no—
128C22×C3×D3—22no—
129C22×C3×D3—22no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C22×C3×D3—41no—
133C22×C3×D3—41no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C22×C3×D3—42no—
137C22×C3×D3—42no—
138C22×C3×D3—42no—
139C22×C3×D3—42no—
140C22×C3×D3—42no—
141C22×C3×D3—42no—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4#4111yescharacteristic
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3D814yescomplemented
151C2×C3×Dic3—41no—
152C2×C3×Dic3—42no—
153C3×D12—22no—
154C3×D12—22no—
155C3×D12—22no—
156C3×D12—22no—
157C3×D12—22no—
158C3×D12—22no—
159C3×D12—41no—
160C3×D12—41no—
161C3×D12—41no—
162C3×D12—41no—
163C3×D12—41no—
164C3×D12—41no—
165#625—416no—
166C32×C8—22no—
167C3⋊(C3⋊C8)—22no—
168C22×D8—31no—
169C22×D8—91no—
170C2×#127—91no—
171C2×#102—31no—
172C2×#102—91no—
173#390—91no—
174#336—91no—
175C24×C3—61no—
176C24×C3—61no—
177C24×C3—61no—
178C23×D3—21no—
179C23×D3—21no—
180C23×D3—21no—
181C2×C3×D4—32no—
182C2×C3×D4—32no—
183C2×C3×D4—32no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C2×C3×D4—61no—
187C2×C3×D4—61no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C2×C3×D4—61no—
195C2×C3×D4—61no—
196C2×C3×D4—61no—
197C2×C3×D4—61no—
198C2×C3×D4—61no—
199C22×C3×C4—21no—
200C22×C3×C4—61no—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C2×#67—68no—
204C2×#67—68no—
205C2×#67—124no—
206C2×#67—124no—
207C2×#67—124no—
208C2×#67—124no—
209C22×Dic3—21no—
210C22×Dic3—32no—
211C22×Dic3—32no—
212C22×Dic3—62no—
213C2×D12—21no—
214C2×D12—21no—
215C2×D12—21no—
216C2×D12—21no—
217C2×D12—21no—
218C2×D12—21no—
219C2×D12—21no—
220C2×D12—21no—
221C2×D12—21no—
222C2×D12—21no—
223C2×D12—21no—
224C2×D12—21no—
225C2×D12—21no—
226C2×D12—21no—
227C2×D12—21no—
228C2×D12D1212yes—
229C2×D12#6712yes—
230C2×D12#6712yescomplemented
231C3×D8—68no—
232C2×C3×C8—21no—
233C2×C3×C8—21no—
234C2×C3×C8—21no—
235C2×C3×C8—21no—
236C2×C3×C8—22no—
237C2×C3×C8—41no—
238C2×C3×C8—41no—
239C2×C3×C8#6712yescomplemented
240C2×C3×C8#6712yescomplemented
241C3×C4⋊C4—61no—
242C3×C4⋊C4—61no—
243#217—124no—
244#213—68no—
245#213—68no—
246(C2×D3)⋊C4—124no—
247C4⋊Dic3—21no—
248C4⋊Dic3—21no—
249C4×Dic3—61no—
250C4×Dic3—61no—
251C4×Dic3—61no—
252C4×Dic3—61no—
253C4×Dic3—121no—
254C4×Dic3—121no—
255C2×C3⋊C8—32no—
256C2×C3⋊C8—32no—
257C2×C3⋊C8—62no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—61no—
260C2×C3⋊C8—61no—
261C2×C3⋊C8—61no—
262C2×C3⋊C8—121no—
263C2×C3⋊C8—121no—
264D24—28no—
265C22×C32#12011yescharacteristic
266C22×C32#12111yescharacteristic
267C22×C32#12711yescharacteristic
268C22×C32C2×D812yes—
269C22×C32AGL(1,ℤ/8)12yes—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C2×C3×D3—44no—
274C2×C3×D3—44no—
275C2×C3×D3—44no—
276C2×C3×D3—82no—
277C2×C3×D3—82no—
278C2×C3×D3—82no—
279C2×C3×D3—81no—
280C2×C3×D3—81no—
281C2×C3×D3—81no—
282C2×C3×D3—81no—
283C2×C3×D3—81no—
284C2×C3×D3—81no—
285C32×C4#12011yescharacteristic
286C32×C4#12011yescharacteristic
287C32×C4#12111yescharacteristic
288C32×C4#12111yescharacteristic
289C3⋊Dic3—24no—
290C3×Dic3—81no—
291C22×D4—31no—
292C22×D4—31no—
293C22×D4—31no—
294C22×D4—182no—
295C2×D8—62no—
296C2×D8—62no—
297C2×D8—62no—
298C2×D8—182no—
299C2×D8—182no—
300C2×D8—182no—
301C22×C8—91no—
302C22×C8D3211yescharacteristic
303#127—182no—
304#127—182no—
305C2×C4⋊C4—31no—
306C2×C22⋊C4—182no—
307C2×C42—91no—
308#102—62no—
309#102—182no—
310C23×C3—21no—
311C23×C3—62no—
312C23×C3—62no—
313C23×C3—62no—
314C23×C3—121no—
315C23×C3—121no—
316C23×C3—122no—
317C23×C3—122no—
318C23×C3—122no—
319C23×C3—122no—
320C23×C3—122no—
321C23×C3—122no—
322C23×C3—121no—
323C23×C3—121no—
324C23×C3—121no—
325C23×C3—121no—
326C23×C3D3×D411yescharacteristic
327C23×C3D3×D411yescharacteristic
328C22×D3—22no—
329C22×D3—22no—
330C22×D3—22no—
331C22×D3—41no—
332C22×D3—42no—
333C22×D3—42no—
334C22×D3—42no—
335C22×D3—42no—
336C22×D3—42no—
337C22×D3—42no—
338C22×D3—41no—
339C22×D3—41no—
340C22×D3—41no—
341C22×D3—41no—
342C22×D3—41no—
343C3×D4—62no—
344C3×D4—62no—
345C3×D4—62no—
346C3×D4—62no—
347C3×D4—62no—
348C3×D4—62no—
349C3×D4—121no—
350C3×D4—121no—
351C3×D4—121no—
352C3×D4—121no—
353C3×D4—121no—
354C3×D4—121no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—122no—
362C2×C3×C4—121no—
363C2×C3×C4C2×D1211yescharacteristic
364C2×C3×C4#23511yescharacteristic
365C2×C3×C4D3×D411yescharacteristic
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4#23711yescharacteristic
371C2×C3×C4C2×#6711yescharacteristic
372C2×C3×C4C2×#6711yescharacteristic
373C2×C3×C4C2×#6711yescharacteristic
374C2×C3×C4C2×#6711yescharacteristic
375#67—1216no—
376#67—1216no—
377C2×Dic3—34no—
378C2×Dic3—34no—
379C2×Dic3—42no—
380C2×Dic3—41no—
381C2×Dic3—64no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—122no—
387C2×Dic3—122no—
388D12—22no—
389D12—22no—
390D12—22no—
391D12—22no—
392D12—22no—
393D12—22no—
394D12—41no—
395D12—41no—
396D12—41no—
397D12—41no—
398D12—41no—
399D12—41no—
400C3×C8—22no—
401C3×C8—22no—
402C3×C8—42no—
403C3⋊C8—62no—
404C3⋊C8—62no—
405C3⋊C8—122no—
406C2×C32#39211yescharacteristic
407C2×C32#44712yes—
408C2×C32#45912yes—
409C2×C32#49311yescharacteristic
410C2×C32#49611yescharacteristic
411C3×D3—82no—
412C3×D3—82no—
413C3×D3—82no—
414C24—61no—
415C24—61no—
416C24—61no—
417C2×D4—32no—
418C2×D4—32no—
419C2×D4—32no—
420C2×D4—61no—
421C2×D4—61no—
422C2×D4—61no—
423C2×D4—61no—
424C2×D4—61no—
425C2×D4—61no—
426C2×D4—61no—
427C2×D4—61no—
428C2×D4—61no—
429C2×D4—61no—
430C2×D4—61no—
431C2×D4—61no—
432C2×D4—61no—
433C2×D4—61no—
434C2×D4—61no—
435C2×D4—188no—
436C2×D4—364no—
437C2×D4—364no—
438C22×C4—61no—
439C22×C4—92no—
440C22×C4C2×D3211yescharacteristic
441D8—68no—
442D8—188no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—92no—
446C2×C8—181no—
447C2×C8—181no—
448C2×C8#62512yescomplemented
449C4⋊C4—61no—
450C4⋊C4—61no—
451C22⋊C4—364no—
452C42—181no—
453C42—181no—
454C22×C3—22no—
455C22×C3—22no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—124no—
460C22×C3—122no—
461C22×C3—122no—
462C22×C3—122no—
463C22×C3—124no—
464C22×C3—124no—
465C22×C3—242no—
466C22×C3—241no—
467C22×C3—241no—
468C22×C3—241no—
469C22×C3—241no—
470C22×C3—241no—
471C22×C3—241no—
472C22×C3—242no—
473C22×C3—242no—
474C22×C3#88211yescharacteristic
475C22×C3#88411yescharacteristic
476C22×C3D3×D812yes—
477C22×C3D3×D812yes—
478C22×C3#91112yes—
479C22×C3#91412yes—
480C22×C3#93711yescharacteristic
481C22×C3#93911yescharacteristic
482C22×C3#94011yescharacteristic
483C22×C3#94011yescharacteristic
484C2×D3—44no—
485C2×D3—44no—
486C2×D3—42no—
487C2×D3—42no—
488C2×D3—42no—
489C2×D3—44no—
490C2×D3—82no—
491C2×D3—81no—
492C2×D3—81no—
493C2×D3—81no—
494C2×D3—81no—
495C2×D3—81no—
496C2×D3—82no—
497C2×D3—81no—
498C2×D3—82no—
499C3×C4—21no—
500C3×C4—21no—
501C3×C4—21no—
502C3×C4—21no—
503C3×C4—241no—
504C3×C4#88211yescharacteristic
505C3×C4#88411yescharacteristic
506C3×C4#93011yescharacteristic
507C3×C4#93711yescharacteristic
508C3×C4#93711yescharacteristic
509C3×C4#93811yescharacteristic
510C3×C4#93911yescharacteristic
511C3×C4#95311yescharacteristic
512Dic3—64no—
513Dic3—64no—
514Dic3—81no—
515Dic3—124no—
516C32#201111yescharacteristic, complemented, Sylow
517C23—62no—
518C23—62no—
519C23—62no—
520C23—122no—
521C23—122no—
522C23—122no—
523C23—122no—
524C23—122no—
525C23—122no—
526C23—121no—
527C23—121no—
528C23—121no—
529C23—121no—
530C23—121no—
531C23—121no—
532C23#380211yescharacteristic
533D4—62no—
534D4—62no—
535D4—62no—
536D4—62no—
537D4—62no—
538D4—62no—
539D4—121no—
540D4—121no—
541D4—121no—
542D4—121no—
543D4—121no—
544D4—121no—
545D4—3616no—
546C2×C4—94no—
547C2×C4—122no—
548C2×C4—121no—
549C2×C4—182no—
550C2×C4—182no—
551C2×C4#379511yescharacteristic
552C2×C4D3×D1211yescharacteristic
553C2×C4#380211yescharacteristic
554C2×C4C2×#62511yescharacteristic
555C2×C4D3×#6711yescharacteristic
556C2×C4D3×#6711yescharacteristic
557C8—22no—
558C8—182no—
559C2×C3—22no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—22no—
564C2×C3—242no—
565C2×C3—242no—
566C2×C3—242no—
567C2×C3#477312yes—
568C2×C3#478612yes—
569C2×C3#496011yescharacteristic
570C2×C3#515012yes—
571C2×C3#515111yescharacteristic
572C2×C3#515111yescharacteristic
573C2×C3#515411yescharacteristic
574C2×C3#515612yes—
575C2×C3#517611yescharacteristic
576C2×C3#522311yescharacteristic
577D3—82no—
578D3—82no—
579D3—82no—
580C22—124no—
581C22—122no—
582C22—122no—
583C22—122no—
584C22—124no—
585C22—124no—
586C22—242no—
587C22—242no—
588C22—241no—
589C22—241no—
590C22—241no—
591C22—241no—
592C22—241no—
593C22—241no—
594C22—242no—
595C22#6379712yes—
596C22#6379812yes—
597C22#6388511yescharacteristic
598C22#6391411yescharacteristic
599C22#6392211yescharacteristic
600C4—184no—
601C4—241no—
602C4#6388511yescharacteristic
603C4#6390811yescharacteristic
604C4#6392211yescharacteristic
605C4#6397611yescharacteristic
606C3—21no—
607C3#7020911yescharacteristic, complemented
608C3#7204411yescharacteristic, complemented
609C2—242no—
610C2—242no—
611C2—242no—
612C2#1059074912yes—
613C2#1059088611yescharacteristic
614C2#1059088711yescharacteristic
615C2#1059094512yes—
616C2#1059138911yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
hypercenterC22×C8D32
hypocenterC32#2011
LCSG ▷ C22×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. C22×C3×D24C2semidirect
2. C2×#63914C2semidirect
3. C22×#3713C2semidirect
4. C2×C3×#821C2semidirect
5. #10591323C2semidirect
6. C2×#63562C2semidirect
7. #10589416C2semidirect
34. C22×D24D3semidirect
38. C2×#821D3semidirect
67. C2×C3×D12D4semidirect
73. C2×C32×C8D4semidirect
78. C2×C3⋊(C3⋊C8)D4semidirect
150. C2×C3⋊Dic3D8semidirect
230. C2×D12#67semidirect
239. C2×C3×C8#67semidirect
240. C2×C3×C8#67semidirect
448. C2×C8#625semidirect
516. C32#2011semidirect
607. C3#70209semidirect
608. C3#72044semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D242
C2×#639142
C22×#37132
C2×C3×#8212
#105913232
C2×#635622
#105894162
#720443
#702093