Finite Group Databasebeta

← #11856270

Subgroups — #11856270

Order 1152.

2313 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#882C211yesmaximal, characteristic
3C2×#63962C211yesmaximal, characteristic, complemented
4C2×#63961C211yesmaximal, characteristic, complemented
5#10592642C211yesmaximal, characteristic, complemented
6C3×#4943C211yesmaximal, characteristic, complemented
7#10591706C211yesmaximal, characteristic, complemented
8#10591376C214yesmaximal, complemented
9#10591373C214yesmaximal, complemented
10#82602—31nomaximal
11#74146—31nomaximal
12C24×C3×D3C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C22×C3×#67C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C22×C3×D12C2212yes—
17C22×D3×Dic3—24no—
18C22×D3×Dic3—24no—
19C22×D3×Dic3—24no—
20C22×D3×Dic3C2214yes—
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×#3757C2211yescharacteristic
23C2×C3×#217C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2212yes—
25C3×#882—24no—
26C2×#3724C2212yescomplemented
27C2×Dic3⋊Dic3C2212yescomplemented
28#63962—24no—
29#63961—24no—
30C2×(C2×D3)⋊Dic3C2214yes—
31C2×(C2×D3)⋊Dic3C2212yescomplemented
32C2×(C2×D3)⋊Dic3C2212yescomplemented
33#63658C2214yescomplemented
34C3×C3⋊#95C2214yescomplemented
35C24×Dic3—31no—
36C23×C4×D3—31no—
37C2×C3×#120—31no—
38C2×#935—31no—
39C2×#935—31no—
40C2×#929—31no—
41C2×#886—31no—
42C2×#882D311yescharacteristic
43C3×#381—31no—
44#5247—31no—
45#5220—34no—
46#4955—31no—
47#4946—34no—
48#4943—31no—
49#4943—31no—
50#4943—61no—
51#4943D311yescharacteristic, complemented
52#4668—34no—
53#4665—34no—
54C24×C32C2311yescharacteristic
55C23×C3×D3—22no—
56C23×C3×D3—22no—
57C23×C3×D3—28no—
58C23×C3×D3D414yes—
59C23×C3×D3C2311yescharacteristic
60C23×C3×D3C2312yes—
61C22×C32×C4C2312yes—
62C22×C3⋊Dic3—22no—
63C22×C3⋊Dic3—22no—
64C22×C3⋊Dic3D414yescomplemented
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2312yes—
67C2×C3×#67—22no—
68C2×C3×#67—22no—
69C2×C3×#67—22no—
70C22×C3×Dic3—22no—
71C22×C3×Dic3—22no—
72C22×C3×Dic3D414yescomplemented
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C2×C3×D12—24no—
77C2×C3×D12—28no—
78C2×D3×Dic3—232no—
79C2×D3×Dic3—28no—
80C2×D3×Dic3—28no—
81C2×D3×Dic3—28no—
82C32×C22⋊C4—22no—
83#3757—22no—
84C3×#217—22no—
85C3×(C2×D3)⋊C4—24no—
86#3724—24no—
87Dic3⋊Dic3—24no—
88(C2×D3)⋊Dic3—28no—
89(C2×D3)⋊Dic3—24no—
90(C2×D3)⋊Dic3—24no—
91#2849—91noSylow
92C25×C3—31no—
93C24×D3C2×D311yescharacteristic
94C22×C3×D4—31no—
95C22×C3×D4—32no—
96C23×C3×C4—31no—
97C22×#67C2×D311yescharacteristic
98C23×Dic3—31no—
99C23×Dic3—31no—
100C23×Dic3—34no—
101C23×Dic3—61no—
102C23×Dic3—64no—
103C23×Dic3—64no—
104C23×Dic3—64no—
105C23×Dic3C2×D311yescharacteristic
106C22×D12C2×D312yes—
107C22×C4×D3—34no—
108C22×C4×D3—64no—
109C22×C4×D3—64no—
110C22×C4×D3—64no—
111C3×#120—64no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—31no—
114C2×C3×C22⋊C4—32no—
115C2×C3×C22⋊C4C2×D311yescharacteristic
116C2×C3×C22⋊C4C2×D311yescharacteristic
117C2×#217—31no—
118C2×#217—31no—
119C2×#217—34no—
120C2×#217—32no—
121C2×#217—32no—
122C2×#217—61no—
123C2×#217C2×D311yescharacteristic
124#935—64no—
125#935—64no—
126#929—64no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—34no—
130C2×(C2×D3)⋊C4C2×D312yes—
131C2×C4⋊Dic3—32no—
132C2×Dic3⋊C4—32no—
133C2×Dic3⋊C4—32no—
134C2×Dic3⋊C4—32no—
135#886—64no—
136#882—24no—
137C3×#95—34no—
138C3⋊#95—34no—
139C3⋊#95—34no—
140C3⋊#95—64no—
141C3⋊#95C2×D314yescomplemented
142C23×C32—24no—
143C23×C32C2×D412yes—
144C23×C32C2×D412yes—
145C23×C32C2×D412yes—
146C23×C32C2411yescharacteristic
147C22×C3×D3—216no—
148C22×C3×D3—216no—
149C22×C3×D3—28no—
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3—24no—
153C22×C3×D3—216no—
154C22×C3×D3—21no—
155C22×C3×D3—21no—
156C22×C3×D3—21no—
157C22×C3×D3—24no—
158C22×C3×D3C2×D414yes—
159C22×C3×D3#4118yes—
160C2×C32×C4—22no—
161C2×C32×C4—24no—
162C2×C3⋊Dic3—28no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—24no—
167C2×C3⋊Dic3C2×D414yes—
168C3×#67—44no—
169C2×C3×Dic3—28no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—24no—
177C2×C3×Dic3C2×D414yes—
178C3×D12—48no—
179D3×Dic3—232no—
180C24×C4—91no—
181C2×#123—91no—
182C2×#123—91no—
183C2×#120—31no—
184#386—94no—
185#385—94no—
186#381—31no—
187#381—91no—
188#379—91no—
189C24×C3—21no—
190C24×C3—32no—
191C24×C3—34no—
192C24×C3—31no—
193C24×C3—68no—
194C24×C3—62no—
195C24×C3—62no—
196C24×C3C22×D311yescharacteristic
197C24×C3C22×D311yescharacteristic
198C23×D3—22no—
199C23×D3—22no—
200C23×D3—28no—
201C23×D3#6714yes—
202C23×D3C22×D311yescharacteristic
203C23×D3C22×D312yes—
204C2×C3×D4—64no—
205C2×C3×D4—68no—
206C2×C3×D4—62no—
207C2×C3×D4—62no—
208C2×C3×D4—62no—
209C22×C3×C4—22no—
210C22×C3×C4—34no—
211C22×C3×C4—32no—
212C22×C3×C4—32no—
213C22×C3×C4—31no—
214C22×C3×C4—62no—
215C22×C3×C4—62no—
216C22×C3×C4C22×D312yes—
217C22×C3×C4C22×D312yes—
218C2×#67—22no—
219C2×#67—22no—
220C2×#67—22no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—34no—
224C22×Dic3—34no—
225C22×Dic3—32no—
226C22×Dic3—32no—
227C22×Dic3—32no—
228C22×Dic3—32no—
229C22×Dic3—62no—
230C22×Dic3—64no—
231C22×Dic3—62no—
232C22×Dic3—68no—
233C22×Dic3—68no—
234C22×Dic3—632no—
235C22×Dic3—62no—
236C22×Dic3—62no—
237C22×Dic3—62no—
238C22×Dic3—62no—
239C22×Dic3—68no—
240C22×Dic3—122no—
241C22×Dic3—122no—
242C22×Dic3D1214yescomplemented
243C22×Dic3C22×D312yes—
244C22×Dic3C22×D311yescharacteristic
245C22×Dic3C22×D312yes—
246C2×D12—28no—
247C2×D12—24no—
248C2×C4×D3—68no—
249C2×C4×D3—68no—
250C2×C4×D3—632no—
251C2×C4×D3—68no—
252C3×C22⋊C4—22no—
253C3×C22⋊C4—22no—
254C3×C22⋊C4—42no—
255C3×C22⋊C4—64no—
256C3×C22⋊C4—62no—
257#217—22no—
258#217—64no—
259#217—68no—
260#217—62no—
261#217—62no—
262#217—64no—
263#217—122no—
264(C2×D3)⋊C4—24no—
265(C2×D3)⋊C4—64no—
266(C2×D3)⋊C4—64no—
267(C2×D3)⋊C4—68no—
268C4⋊Dic3—64no—
269Dic3⋊C4—64no—
270Dic3⋊C4—64no—
271Dic3⋊C4—64no—
272C22×C32—24no—
273C22×C32—24no—
274C22×C32—24no—
275C22×C32#12014yes—
276C22×C32C22×D411yescharacteristic
277C22×C32C22×D411yescharacteristic
278C22×C32C22×D411yescharacteristic
279C22×C32C2×#4114yes—
280C2×C3×D3—232no—
281C2×C3×D3—24no—
282C2×C3×D3—24no—
283C2×C3×D3—28no—
284C2×C3×D3—28no—
285C2×C3×D3—41no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C2×C3×D3#12318yescomplemented
290C32×C4—42no—
291C3⋊Dic3—24no—
292C3⋊Dic3—42no—
293C3×Dic3—24no—
294C3×Dic3—41no—
295C3×Dic3—42no—
296C25—31no—
297C22×D4—31no—
298C22×D4—32no—
299C23×C4—31no—
300C23×C4—94no—
301C23×C4—91no—
302C23×C4—184no—
303C23×C4—184no—
304C23×C4—184no—
305#123—184no—
306#123—184no—
307#120—64no—
308C2×C4⋊C4—92no—
309C2×C4⋊C4—92no—
310C2×C22⋊C4—31no—
311C2×C22⋊C4—32no—
312C2×C22⋊C4—92no—
313C2×C22⋊C4—92no—
314C2×C22⋊C4—94no—
315C2×C22⋊C4—91no—
316C2×C22⋊C4D3211yescharacteristic
317#95—34no—
318#95—94no—
319C23×C3—24no—
320C23×C3—24no—
321C23×C3—21no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—34no—
326C23×C3—38no—
327C23×C3—44no—
328C23×C3—616no—
329C23×C3—616no—
330C23×C3—616no—
331C23×C3—68no—
332C23×C3—62no—
333C23×C3—62no—
334C23×C3—64no—
335C23×C3—61no—
336C23×C3—61no—
337C23×C3—61no—
338C23×C3—64no—
339C23×C3C2×D1212yes—
340C23×C3D3×D412yes—
341C23×C3D3×D412yes—
342C23×C3D3×D412yes—
343C23×C3D3×D412yes—
344C23×C3C2×#6712yes—
345C23×C3C23×D311yescharacteristic
346C23×C3C23×D311yescharacteristic
347C22×D3—216no—
348C22×D3—216no—
349C22×D3—28no—
350C22×D3—22no—
351C22×D3—22no—
352C22×D3—24no—
353C22×D3—216no—
354C22×D3—21no—
355C22×D3—21no—
356C22×D3—24no—
357C22×D3—21no—
358C22×D3#23718yes—
359C22×D3C2×#6714yes—
360C3×D4—128no—
361C3×D4—124no—
362C2×C3×C4—22no—
363C2×C3×C4—24no—
364C2×C3×C4—24no—
365C2×C3×C4—22no—
366C2×C3×C4—34no—
367C2×C3×C4—42no—
368C2×C3×C4—44no—
369C2×C3×C4—68no—
370C2×C3×C4—62no—
371C2×C3×C4—62no—
372C2×C3×C4—61no—
373C2×C3×C4—61no—
374C2×C3×C4—62no—
375C2×C3×C4—61no—
376C2×C3×C4—64no—
377#67—44no—
378C2×Dic3—28no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—21no—
382C2×Dic3—22no—
383C2×Dic3—21no—
384C2×Dic3—24no—
385C2×Dic3—21no—
386C2×Dic3—34no—
387C2×Dic3—34no—
388C2×Dic3—64no—
389C2×Dic3—632no—
390C2×Dic3—68no—
391C2×Dic3—68no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—64no—
399C2×Dic3—64no—
400C2×Dic3—122no—
401C2×Dic3—122no—
402C2×Dic3—128no—
403C2×Dic3—122no—
404C2×Dic3—124no—
405C2×Dic3C2×D1214yes—
406D12—48no—
407C4×D3—632no—
408C2×C32—24no—
409C2×C32C2×#12011yescharacteristic
410C2×C32C2×#12312yes—
411C2×C32#52512yes—
412C2×C32#52512yes—
413C3×D3—28no—
414C3×D3—81no—
415C24—32no—
416C24—34no—
417C24—31no—
418C24—68no—
419C24—62no—
420C24—62no—
421C24C2×D3211yescharacteristic
422C2×D4—64no—
423C2×D4—68no—
424C2×D4—62no—
425C2×D4—62no—
426C2×D4—62no—
427C22×C4—32no—
428C22×C4—34no—
429C22×C4—32no—
430C22×C4—31no—
431C22×C4—62no—
432C22×C4—62no—
433C22×C4—92no—
434C22×C4—94no—
435C22×C4—92no—
436C22×C4—188no—
437C22×C4—188no—
438C22×C4—188no—
439C22×C4—1832no—
440C22×C4—182no—
441C22×C4—182no—
442C22×C4C2×D3212yes—
443C4⋊C4—184no—
444C4⋊C4—184no—
445C22⋊C4—22no—
446C22⋊C4—64no—
447C22⋊C4—62no—
448C22⋊C4—184no—
449C22⋊C4—184no—
450C22⋊C4—188no—
451C22⋊C4—182no—
452C22×C3—24no—
453C22×C3—24no—
454C22×C3—24no—
455C22×C3—24no—
456C22×C3—24no—
457C22×C3—24no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—24no—
461C22×C3—21no—
462C22×C3—24no—
463C22×C3—38no—
464C22×C3—44no—
465C22×C3—44no—
466C22×C3—44no—
467C22×C3—632no—
468C22×C3—64no—
469C22×C3—68no—
470C22×C3—64no—
471C22×C3—68no—
472C22×C3—122no—
473C22×C3—122no—
474C22×C3—121no—
475C22×C3—122no—
476C22×C3#88214yes—
477C22×C3#93714yes—
478C22×C3C22×D1211yescharacteristic
479C22×C3C2×D3×D411yescharacteristic
480C22×C3C2×D3×D411yescharacteristic
481C22×C3C2×D3×D411yescharacteristic
482C22×C3C2×D3×D411yescharacteristic
483C22×C3C2×#23714yes—
484C22×C3D3×#4114yes—
485C22×C3C22×#6711yescharacteristic
486C2×D3—232no—
487C2×D3—24no—
488C2×D3—24no—
489C2×D3—28no—
490C2×D3—28no—
491C2×D3—42no—
492C2×D3—41no—
493C2×D3—42no—
494C2×D3—42no—
495C2×D3#93518yescomplemented
496C3×C4—42no—
497C3×C4—42no—
498C3×C4—64no—
499C3×C4—82no—
500C3×C4—121no—
501C3×C4—122no—
502Dic3—24no—
503Dic3—42no—
504Dic3—41no—
505Dic3—64no—
506Dic3—64no—
507Dic3—124no—
508Dic3—122no—
509Dic3—122no—
510Dic3—242no—
511C32#284911yescharacteristic, complemented, Sylow
512C23—24no—
513C23—38no—
514C23—34no—
515C23—616no—
516C23—616no—
517C23—616no—
518C23—62no—
519C23—62no—
520C23—64no—
521C23—68no—
522C23—61no—
523C23—61no—
524C23—64no—
525C23—61no—
526C23D3×D1212yes—
527C23#380212yes—
528C23D3×#6712yes—
529C23C22×D3211yescharacteristic
530D4—128no—
531D4—124no—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—34no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—68no—
538C2×C4—61no—
539C2×C4—62no—
540C2×C4—61no—
541C2×C4—64no—
542C2×C4—61no—
543C2×C4—94no—
544C2×C4—1832no—
545C2×C4—182no—
546C2×C4—182no—
547C2×C4—188no—
548C2×C4—182no—
549C2×C4—184no—
550C2×C3—24no—
551C2×C3—24no—
552C2×C3—22no—
553C2×C3—22no—
554C2×C3—22no—
555C2×C3—21no—
556C2×C3—44no—
557C2×C3—68no—
558C2×C3—241no—
559C2×C3C2×#88211yescharacteristic
560C2×C3#552412yes—
561C2×C3#558612yes—
562C2×C3#558612yes—
563C2×C3D3×#12312yes—
564C2×C3#565612yes—
565C2×C3C2×#93512yes—
566C2×C3C2×#93711yescharacteristic
567D3—28no—
568D3—81no—
569C22—24no—
570C22—24no—
571C22—24no—
572C22—38no—
573C22—632no—
574C22—68no—
575C22—68no—
576C22—64no—
577C22—64no—
578C22—122no—
579C22—122no—
580C22—122no—
581C22—121no—
582C22#6392214yes—
583C22C2×D3×D1211yescharacteristic
584C22C2×#380211yescharacteristic
585C22D3×#23714yes—
586C22C2×D3×#6711yescharacteristic
587C4—42no—
588C4—64no—
589C4—122no—
590C4—121no—
591C4—184no—
592C4—362no—
593C3—21no—
594C3#7414611yescharacteristic, complemented
595C3#8260211yescharacteristic, complemented
596C2—24no—
597C2—68no—
598C2—241no—
599C2#1059407812yes—
600C2#1059408212yes—
601C2C2×#6392211yescharacteristic
602C2D3×#93512yes—
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×C3×#882C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2849
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×D3×Dic3C2semidirect
3. C2×#63962C2semidirect
4. C2×#63961C2semidirect
5. #10592642C2semidirect
6. C3×#4943C2semidirect
7. #10591706C2semidirect
8. #10591376C2semidirect
9. #10591373C2semidirect
26. C2×#3724C22semidirect
27. C2×Dic3⋊Dic3C22semidirect
31. C2×(C2×D3)⋊Dic3C22semidirect
32. C2×(C2×D3)⋊Dic3C22semidirect
33. #63658C22semidirect
34. C3×C3⋊#95C22semidirect
51. #4943D3semidirect
64. C22×C3⋊Dic3D4semidirect
72. C22×C3×Dic3D4semidirect
141. C3⋊#95C2×D3semidirect
242. C22×Dic3D12semidirect
289. C2×C3×D3#123semidirect
495. C2×D3#935semidirect
511. C32#2849semidirect
594. C3#74146semidirect
595. C3#82602semidirect

Maximal subgroups

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

subgroupindex
C23×D3×Dic32
C2×C3×#8822
C2×#639622
C2×#639612
#105926422
C3×#49432
#105917062
#105913762
#105913732
#826023
#741463