Finite Group Databasebeta

← #11856274

Subgroups — #11856274

Order 1152.

2375 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D3C211yesmaximal, characteristic, complemented
2C2×#64138C211yesmaximal, characteristic, complemented
3C2×#63977C211yesmaximal, characteristic
4C2×#63966C211yesmaximal, characteristic, complemented
5C3×#5211C211yesmaximal, characteristic, complemented
6#10591706C211yesmaximal, characteristic, complemented
7#10591696C211yesmaximal, characteristic, complemented
8#10591382C214yesmaximal, complemented
9#10591278C214yesmaximal, complemented
10#84033—31nomaximal
11#74146—31nomaximal
12C24×C3×D3C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C22×#638C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C22×C3×C4×D3—24no—
17C22×C3×C4×D3—24no—
18C22×C3×C4×D3—24no—
19C22×C3×C4×D3C2214yes—
20C22×#626C2212yes—
21C2×#3757C2211yescharacteristic
22#64138—24no—
23C2×#3752C2212yescomplemented
24C2×#3750C2212yescomplemented
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27#63977—24no—
28#63966—24no—
29C2×Dic3⋊Dic3C2212yescomplemented
30C2×#3722C2212yescomplemented
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×(C2×D3)⋊Dic3C2214yes—
33C3×C3⋊#95C2214yescomplemented
34#63579C2214yescomplemented
35C24×C3×C4—31no—
36C23×C4×D3D311yescharacteristic, complemented
37C2×#953—31no—
38C2×#929—31no—
39C2×#929—31no—
40C2×#929—31no—
41C2×#929—61no—
42C2×#886—31no—
43C2×#882—31no—
44C3×#381—31no—
45#5247—31no—
46#5213—34no—
47#5211—31no—
48#5211D311yescharacteristic, complemented
49#5210—34no—
50#4955—31no—
51#4943—31no—
52#4668—34no—
53#4665—34no—
54C24×C32C2311yescharacteristic
55C23×C3⋊D3C2311yescharacteristic
56C23×C3×D3—22no—
57C23×C3×D3—22no—
58C23×C3×D3—28no—
59C23×C3×D3D414yes—
60C23×C3×D3C2312yes—
61C22×C32×C4—22no—
62C22×C32×C4—22no—
63C22×C32×C4D414yescomplemented
64C22×C32×C4C2312yes—
65C2×#638—22no—
66C2×#638—22no—
67C2×#638—22no—
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3×Dic3—22no—
71C22×C3×Dic3—22no—
72C22×C3×Dic3D414yescomplemented
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C2×C3×C4×D3—232no—
77C2×C3×C4×D3—28no—
78C2×C3×C4×D3—28no—
79C2×C3×C4×D3—28no—
80C2×#626—24no—
81C2×#626—28no—
82#3757—22no—
83#3752—24no—
84#3750—24no—
85C3×#217—22no—
86C3×#217—22no—
87Dic3⋊Dic3—24no—
88#3722—24no—
89(C2×D3)⋊Dic3—24no—
90(C2×D3)⋊Dic3—28no—
91#2849—91noSylow
92C25×C3—31no—
93C24×D3C2×D311yescharacteristic
94C23×C3×C4—21no—
95C23×C3×C4—31no—
96C23×C3×C4—34no—
97C23×C3×C4—64no—
98C23×C3×C4—64no—
99C23×C3×C4—64no—
100C23×C3×C4C2×D311yescharacteristic
101C23×C3×C4C2×D311yescharacteristic
102C22×#67—31no—
103C22×#67—31no—
104C22×#67—32no—
105C22×#67—61no—
106C23×Dic3C2×D311yescharacteristic
107C22×D12—32no—
108C22×C4×D3—24no—
109C22×C4×D3—24no—
110C22×C4×D3—24no—
111C22×C4×D3C2×D314yes—
112C2×C3×C22⋊C4—31no—
113C2×C3×C22⋊C4—31no—
114#953—64no—
115C2×#217—31no—
116C2×#217—31no—
117C2×#217—32no—
118C2×#217—34no—
119C2×#217—61no—
120C2×#217C2×D311yescharacteristic
121C2×#217C2×D311yescharacteristic
122#929—64no—
123#929—68no—
124#929—64no—
125#929—64no—
126C2×(C2×D3)⋊C4—34no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—62no—
133C2×C4⋊Dic3—32no—
134C2×Dic3⋊C4—32no—
135C2×Dic3⋊C4—32no—
136C2×Dic3⋊C4—32no—
137C2×Dic3⋊C4—62no—
138#886—64no—
139#882—64no—
140C3×#95—34no—
141C3⋊#95—34no—
142C3⋊#95—34no—
143C3⋊#95C2×D314yescomplemented
144C23×C32—24no—
145C23×C32C2×D412yes—
146C23×C32C2×D412yes—
147C23×C32C2×D412yes—
148C23×C32C2411yescharacteristic
149C22×C3⋊D3—21no—
150C22×C3⋊D3—21no—
151C22×C3⋊D3—21no—
152C22×C3⋊D3—24no—
153C22×C3×D3—216no—
154C22×C3×D3—216no—
155C22×C3×D3—28no—
156C22×C3×D3—22no—
157C22×C3×D3—22no—
158C22×C3×D3—24no—
159C22×C3×D3—216no—
160C22×C3×D3C2×D414yes—
161C22×C3×D3#4118yes—
162C2×C32×C4—28no—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4C2×D414yes—
166#638—44no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—24no—
172C2×C3×Dic3—28no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—24no—
178C2×C3×Dic3—24no—
179C2×C3×Dic3C2×D414yes—
180C3×C4×D3—232no—
181#626—48no—
182C24×C4—31no—
183C2×#123—91no—
184C2×#123—91no—
185C2×#120—91no—
186#386—94no—
187#385—94no—
188#381—31no—
189#381—91no—
190#379—91no—
191C24×C3—21no—
192C24×C3—32no—
193C24×C3—34no—
194C24×C3—68no—
195C24×C3—62no—
196C24×C3—62no—
197C24×C3C22×D311yescharacteristic
198C24×C3C22×D311yescharacteristic
199C23×D3—22no—
200C23×D3—22no—
201C23×D3—28no—
202C23×D3—31no—
203C23×D3—31no—
204C23×D3—61no—
205C23×D3#6714yes—
206C23×D3C22×D312yes—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—24no—
212C22×C3×C4—22no—
213C22×C3×C4—34no—
214C22×C3×C4—32no—
215C22×C3×C4—32no—
216C22×C3×C4—32no—
217C22×C3×C4—42no—
218C22×C3×C4—42no—
219C22×C3×C4—68no—
220C22×C3×C4—68no—
221C22×C3×C4—632no—
222C22×C3×C4—62no—
223C22×C3×C4—62no—
224C22×C3×C4—68no—
225C22×C3×C4D1214yescomplemented
226C22×C3×C4#6714yescomplemented
227C22×C3×C4C22×D312yes—
228C22×C3×C4C22×D312yes—
229C2×#67—64no—
230C2×#67—68no—
231C2×#67—64no—
232C2×#67—62no—
233C2×#67—62no—
234C2×#67—62no—
235C2×#67—62no—
236C2×#67—62no—
237C2×#67—62no—
238C2×#67—122no—
239C2×#67—122no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—32no—
243C22×Dic3—32no—
244C22×Dic3—31no—
245C22×Dic3—31no—
246C22×Dic3—61no—
247C22×Dic3—62no—
248C22×Dic3#6714yescomplemented
249C22×Dic3C22×D312yes—
250C22×Dic3C22×D312yes—
251C22×Dic3C22×D312yes—
252C2×D12—68no—
253C2×D12—64no—
254C2×C4×D3—232no—
255C2×C4×D3—28no—
256C2×C4×D3—28no—
257C2×C4×D3—28no—
258C3×C22⋊C4—62no—
259C3×C22⋊C4—62no—
260#217—22no—
261#217—22no—
262#217—68no—
263#217—64no—
264#217—64no—
265#217—62no—
266#217—62no—
267(C2×D3)⋊C4—64no—
268(C2×D3)⋊C4—68no—
269(C2×D3)⋊C4—68no—
270(C2×D3)⋊C4—64no—
271(C2×D3)⋊C4—64no—
272(C2×D3)⋊C4—64no—
273(C2×D3)⋊C4—64no—
274C4⋊Dic3—64no—
275Dic3⋊C4—64no—
276Dic3⋊C4—68no—
277Dic3⋊C4—64no—
278Dic3⋊C4—64no—
279C22×C32—24no—
280C22×C32—24no—
281C22×C32—24no—
282C22×C32#12014yes—
283C22×C32C22×D411yescharacteristic
284C22×C32C22×D411yescharacteristic
285C22×C32C22×D411yescharacteristic
286C22×C32C2×#4114yes—
287C2×C3⋊D3—41no—
288C2×C3⋊D3—42no—
289C2×C3⋊D3—42no—
290C2×C3⋊D3—42no—
291C2×C3×D3—232no—
292C2×C3×D3—24no—
293C2×C3×D3—24no—
294C2×C3×D3—28no—
295C2×C3×D3—28no—
296C2×C3×D3#12318yescomplemented
297C32×C4—24no—
298C3⋊Dic3—41no—
299C3⋊Dic3—42no—
300C3×Dic3—24no—
301C3×Dic3—42no—
302C3×Dic3—42no—
303C25—31no—
304C22×D4—92no—
305C22×D4—91no—
306C23×C4—31no—
307C23×C4—34no—
308C23×C4—64no—
309C23×C4—64no—
310C23×C4—64no—
311C23×C4D3211yescharacteristic
312#123—184no—
313#123—184no—
314#120—184no—
315C2×C4⋊C4—92no—
316C2×C4⋊C4—92no—
317C2×C22⋊C4—31no—
318C2×C22⋊C4—31no—
319C2×C22⋊C4—92no—
320C2×C22⋊C4—92no—
321C2×C22⋊C4—94no—
322C2×C22⋊C4—91no—
323C2×C22⋊C4—92no—
324#95—34no—
325#95—94no—
326C23×C3—24no—
327C23×C3—24no—
328C23×C3—21no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—34no—
333C23×C3—38no—
334C23×C3—44no—
335C23×C3—616no—
336C23×C3—616no—
337C23×C3—616no—
338C23×C3—68no—
339C23×C3—62no—
340C23×C3—62no—
341C23×C3—64no—
342C23×C3C2×D1212yes—
343C23×C3D3×D412yes—
344C23×C3D3×D412yes—
345C23×C3C2×#6712yes—
346C23×C3C2×#6712yes—
347C23×C3C2×#6712yes—
348C23×C3C23×D311yescharacteristic
349C23×C3C23×D311yescharacteristic
350C22×D3—216no—
351C22×D3—216no—
352C22×D3—28no—
353C22×D3—24no—
354C22×D3—22no—
355C22×D3—22no—
356C22×D3—216no—
357C22×D3—62no—
358C22×D3—61no—
359C22×D3—64no—
360C22×D3—61no—
361C22×D3—61no—
362C22×D3—64no—
363C22×D3—61no—
364C22×D3—61no—
365C22×D3—61no—
366C22×D3—121no—
367C22×D3—121no—
368C22×D3—124no—
369C22×D3#23518yes—
370C22×D3C2×#6714yes—
371C2×C3×C4—28no—
372C2×C3×C4—28no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—24no—
378C2×C3×C4—34no—
379C2×C3×C4—42no—
380C2×C3×C4—42no—
381C2×C3×C4—48no—
382C2×C3×C4—632no—
383C2×C3×C4—68no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—64no—
387C2×C3×C4—64no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4C2×D1214yes—
391C2×C3×C4C2×#6714yes—
392#67—128no—
393#67—128no—
394#67—124no—
395#67—124no—
396C2×Dic3—28no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—24no—
402C2×Dic3—24no—
403C2×Dic3—62no—
404C2×Dic3—64no—
405C2×Dic3—61no—
406C2×Dic3—62no—
407C2×Dic3—64no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410C2×Dic3—64no—
411C2×Dic3—61no—
412C2×Dic3—62no—
413C2×Dic3—61no—
414C2×Dic3—61no—
415C2×Dic3—124no—
416C2×Dic3—121no—
417C2×Dic3—121no—
418C2×Dic3C2×#6714yes—
419D12—128no—
420C4×D3—232no—
421C2×C32—24no—
422C2×C32C2×#12011yescharacteristic
423C2×C32C2×#12312yes—
424C2×C32#52512yes—
425C2×C32#52512yes—
426C3⋊D3—81no—
427C3×D3—28no—
428C24—32no—
429C24—34no—
430C24—68no—
431C24—62no—
432C24—62no—
433C24—91no—
434C24C2×D3211yescharacteristic
435C2×D4—184no—
436C2×D4—188no—
437C2×D4—182no—
438C2×D4—182no—
439C2×D4—182no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—32no—
443C22×C4—34no—
444C22×C4—32no—
445C22×C4—32no—
446C22×C4—68no—
447C22×C4—68no—
448C22×C4—632no—
449C22×C4—62no—
450C22×C4—62no—
451C22×C4—68no—
452C22×C4—92no—
453C22×C4—91no—
454C22×C4#62614yescomplemented
455C22×C4C2×D3212yes—
456C4⋊C4—184no—
457C4⋊C4—184no—
458C22⋊C4—62no—
459C22⋊C4—62no—
460C22⋊C4—184no—
461C22⋊C4—184no—
462C22⋊C4—188no—
463C22⋊C4—182no—
464C22⋊C4—184no—
465C22×C3—24no—
466C22×C3—24no—
467C22×C3—24no—
468C22×C3—24no—
469C22×C3—24no—
470C22×C3—24no—
471C22×C3—24no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—24no—
476C22×C3—38no—
477C22×C3—44no—
478C22×C3—44no—
479C22×C3—44no—
480C22×C3—632no—
481C22×C3—64no—
482C22×C3—68no—
483C22×C3—64no—
484C22×C3—68no—
485C22×C3#88214yes—
486C22×C3#95314yes—
487C22×C3C22×D1211yescharacteristic
488C22×C3C2×#23514yes—
489C22×C3C2×D3×D411yescharacteristic
490C22×C3C2×D3×D411yescharacteristic
491C22×C3D3×#4114yes—
492C22×C3C22×#6711yescharacteristic
493C22×C3C22×#6711yescharacteristic
494C22×C3C22×#6711yescharacteristic
495C2×D3—232no—
496C2×D3—24no—
497C2×D3—28no—
498C2×D3—28no—
499C2×D3—24no—
500C2×D3—122no—
501C2×D3—124no—
502C2×D3—122no—
503C2×D3—122no—
504C2×D3—121no—
505C2×D3—122no—
506C2×D3—122no—
507C2×D3—122no—
508C2×D3—122no—
509C2×D3—121no—
510C2×D3—242no—
511C2×D3—242no—
512C2×D3#92918yescomplemented
513C3×C4—24no—
514C3×C4—24no—
515C3×C4—44no—
516C3×C4—64no—
517C3×C4—122no—
518C3×C4—122no—
519Dic3—24no—
520Dic3—42no—
521Dic3—42no—
522Dic3—122no—
523Dic3—124no—
524Dic3—121no—
525Dic3—122no—
526Dic3—122no—
527Dic3—121no—
528C32#284911yescharacteristic, complemented, Sylow
529C23—24no—
530C23—38no—
531C23—34no—
532C23—616no—
533C23—616no—
534C23—616no—
535C23—64no—
536C23—62no—
537C23—62no—
538C23—68no—
539C23—184no—
540C23—181no—
541C23—181no—
542C23—181no—
543C23C2×#62612yes—
544C23D3×#6712yes—
545C23D3×#6712yes—
546C23C22×D3211yescharacteristic
547D4—368no—
548D4—364no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—28no—
552C2×C4—34no—
553C2×C4—632no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—68no—
557C2×C4—64no—
558C2×C4—64no—
559C2×C4—62no—
560C2×C4—62no—
561C2×C4—184no—
562C2×C4—182no—
563C2×C4—181no—
564C2×C4—181no—
565C2×C4—181no—
566C2×C4C2×#62614yes—
567C2×C3—24no—
568C2×C3—24no—
569C2×C3—22no—
570C2×C3—21no—
571C2×C3—22no—
572C2×C3—22no—
573C2×C3—44no—
574C2×C3—68no—
575C2×C3C2×#88211yescharacteristic
576C2×C3#552412yes—
577C2×C3D3×#12312yes—
578C2×C3#565612yes—
579C2×C3C2×#92912yes—
580C2×C3#579112yes—
581C2×C3#579112yes—
582C2×C3C2×#95311yescharacteristic
583D3—28no—
584D3—242no—
585D3—241no—
586D3—241no—
587C22—24no—
588C22—24no—
589C22—24no—
590C22—38no—
591C22—632no—
592C22—68no—
593C22—64no—
594C22—68no—
595C22—64no—
596C22—362no—
597C22—361no—
598C22—362no—
599C22—362no—
600C22#6397714yes—
601C22D3×#23514yes—
602C22C22×#62611yescharacteristic
603C22C2×D3×#6711yescharacteristic
604C22C2×D3×#6711yescharacteristic
605C4—24no—
606C4—64no—
607C4—122no—
608C4—122no—
609C4—361no—
610C4—362no—
611C3—21no—
612C3#7414611yescharacteristic, complemented
613C3#8403311yescharacteristic, complemented
614C2—24no—
615C2—68no—
616C2—721no—
617C2#1059489612yes—
618C2#1059502312yes—
619C2D3×#92912yes—
620C2C2×#6397711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC23×C32×C4C22
prime radicalC2×#63977C2
hypercenterC23×C4D32
hypocenterC32#2849
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C3×C4×D3C2semidirect
2. C2×#64138C2semidirect
4. C2×#63966C2semidirect
5. C3×#5211C2semidirect
6. #10591706C2semidirect
7. #10591696C2semidirect
8. #10591382C2semidirect
9. #10591278C2semidirect
23. C2×#3752C22semidirect
24. C2×#3750C22semidirect
29. C2×Dic3⋊Dic3C22semidirect
30. C2×#3722C22semidirect
33. C3×C3⋊#95C22semidirect
34. #63579C22semidirect
36. C23×C4×D3D3semidirect
48. #5211D3semidirect
63. C22×C32×C4D4semidirect
72. C22×C3×Dic3D4semidirect
143. C3⋊#95C2×D3semidirect
225. C22×C3×C4D12semidirect
226. C22×C3×C4#67semidirect
248. C22×Dic3#67semidirect
296. C2×C3×D3#123semidirect
454. C22×C4#626semidirect
512. C2×D3#929semidirect
528. C32#2849semidirect
612. C3#74146semidirect
613. C3#84033semidirect

Maximal subgroups

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

subgroupindex
C23×C3×C4×D32
C2×#641382
C2×#639772
C2×#639662
C3×#52112
#105917062
#105916962
#105913822
#105912782
#840333
#741463