Finite Group Databasebeta

← #11824456

Subgroups — #11824456

Order 1152.

1993 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#874C211yesmaximal, characteristic, complemented
2C2×#63914C211yesmaximal, characteristic, complemented
3C2×#63914C211yesmaximal, characteristic, complemented
4C2×#63898C211yesmaximal, characteristic, complemented
5C2×#63885C214yesmaximal, complemented
6C4×#3750C211yesmaximal, characteristic, complemented
7C3×#4939C211yesmaximal, characteristic, complemented
8#10591389C214yesmaximal, complemented
9#10591323C211yesmaximal, characteristic, complemented
10#83177—31nomaximal
11#76348—31nomaximal
12C22×C3×D12C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×D12C2214yes—
15C22×C3×D12C2211yescharacteristic
16C22×#625C2212yes—
17C22×#625C2214yes—
18C22×#625C2212yes—
19C22×D3×Dic3C2212yes—
20C2×C32×C42C2211yescharacteristic
21C2×#3750C2212yes—
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2214yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C3×#874—24no—
27C2×(C2×D3)⋊Dic3C2214yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29#63914—24no—
30#63914—24no—
31#63898—24no—
32#63885—216no—
33#63658C2212yes—
34C2×C3×#127—31no—
35C2×#940—31no—
36C2×#940—31no—
37C2×#940—31no—
38C2×#940—31no—
39C2×#939—34no—
40C2×D4×Dic3—31no—
41C2×#893—31no—
42C2×#884—34no—
43C2×#874D311yescharacteristic, complemented
44C3×#390—31no—
45#5223—34no—
46#5221—31no—
47#4988—31no—
48#4960—34no—
49#4939D311yescharacteristic, complemented
50C4×Dic3⋊C4—31no—
51C4×Dic3⋊C4—31no—
52C4×Dic3⋊C4—61no—
53C23×C3×D3C2312yes—
54C23×C3×D3C2312yes—
55C23×C3×D3C2312yes—
56C22×C32×C4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3C2312yes—
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3×Dic3C2312yes—
62C2×C3×D12—22no—
63C2×C3×D12—22no—
64C2×C3×D12—28no—
65C2×C3×D12—28no—
66C2×C3×D12—22no—
67C2×C3×D12—22no—
68C2×C3×D12—22no—
69C2×C3×D12—22no—
70C2×C3×D12—22no—
71C2×C3×D12—22no—
72C2×C3×D12—44no—
73C2×C3×D12D414yescomplemented
74C2×#625—28no—
75C2×#625—28no—
76C2×#625—28no—
77C2×#625—24no—
78C2×#625—24no—
79C2×#625—44no—
80C2×#625—44no—
81C2×D3×Dic3—28no—
82C2×D3×Dic3—24no—
83C32×C42—22no—
84#3750D418yescomplemented
85C4×C3⋊Dic3—22no—
86C4×C3⋊Dic3D414yescomplemented
87C3×(C2×D3)⋊C4—28no—
88C3×C4⋊Dic3—22no—
89(C2×D3)⋊Dic3—28no—
90(C2×D3)⋊Dic3—24no—
91#2541—91noSylow
92C22×C3×D4—31no—
93C22×C3×D4—31no—
94C22×C3×D4—31no—
95C22×C3×D4—34no—
96C22×#67—32no—
97C22×#67—32no—
98C22×#67—34no—
99C22×#67—34no—
100C22×#67—32no—
101C22×#67—32no—
102C23×Dic3—32no—
103C22×D12C2×D311yescharacteristic
104C22×D12C2×D311yescharacteristic
105C22×D12C2×D314yes—
106C22×D12C2×D311yescharacteristic
107C22×C4×D3—32no—
108C3×#127—64no—
109C2×C3×C4⋊C4—31no—
110C2×C3×C22⋊C4—34no—
111C2×C3×C42—21no—
112C2×C3×C42C2×D311yescharacteristic
113C2×C3×C42C2×D311yescharacteristic
114C2×#217—34no—
115C2×#217—32no—
116#940—64no—
117#940—64no—
118#940—64no—
119#940—64no—
120#939—616no—
121D4×Dic3—64no—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4—34no—
124C2×(C2×D3)⋊C4C2×D314yes—
125C2×C4⋊Dic3C2×D311yescharacteristic
126C2×Dic3⋊C4—32no—
127C2×Dic3⋊C4—32no—
128C2×Dic3⋊C4—62no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—31no—
131C2×C4×Dic3—31no—
132C2×C4×Dic3—31no—
133C2×C4×Dic3—61no—
134C2×C4×Dic3—61no—
135#893—64no—
136#884—616no—
137#874—24no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—62no—
141C23×C32C2411yescharacteristic
142C22×C3×D3—22no—
143C22×C3×D3—24no—
144C22×C3×D3—22no—
145C22×C3×D3—24no—
146C22×C3×D3—24no—
147C22×C3×D3—24no—
148C22×C3×D3—22no—
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3—24no—
155C22×C3×D3—24no—
156C22×C3×D3C2×D414yes—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4C2×D414yes—
160C2×C32×C4C2×D412yes—
161C2×C32×C4C2×D412yes—
162C2×C32×C4#4112yes—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3C2×D412yes—
167C2×C3⋊Dic3C2×D414yes—
168C2×C3⋊Dic3C2×D412yes—
169C2×C3⋊Dic3C2×D414yes—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—24no—
172C3×D12—28no—
173C3×D12—416no—
174C3×D12—44no—
175C3×D12—44no—
176#625—416no—
177#625—48no—
178#625—48no—
179D3×Dic3—48no—
180C2×#127—31no—
181C2×#127—91no—
182C2×#127—91no—
183C2×#121—94no—
184C2×C4×D4—91no—
185#392—94no—
186#390—31no—
187#390—91no—
188C4×C4⋊C4—91no—
189C24×C3—32no—
190C24×C3—32no—
191C24×C3—32no—
192C23×D3C22×D312yes—
193C23×D3C22×D312yes—
194C23×D3C22×D312yes—
195C2×C3×D4—34no—
196C2×C3×D4—68no—
197C2×C3×D4—62no—
198C2×C3×D4—62no—
199C2×C3×D4—62no—
200C2×C3×D4—68no—
201C2×C3×D4—62no—
202C2×C3×D4—62no—
203C2×C3×D4—62no—
204C2×C3×D4—62no—
205C2×C3×D4—62no—
206C2×C3×D4—124no—
207C22×C3×C4—21no—
208C22×C3×C4—22no—
209C22×C3×C4—32no—
210C22×C3×C4C22×D312yes—
211C22×C3×C4C22×D312yes—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C2×#67—68no—
215C2×#67—68no—
216C2×#67—68no—
217C2×#67—68no—
218C2×#67—64no—
219C2×#67—64no—
220C2×#67—64no—
221C2×#67—64no—
222C2×#67—68no—
223C2×#67—68no—
224C2×#67—124no—
225C2×#67—124no—
226C2×#67—124no—
227C2×#67—124no—
228C22×Dic3—31no—
229C22×Dic3—31no—
230C22×Dic3—31no—
231C22×Dic3—31no—
232C22×Dic3—32no—
233C22×Dic3—32no—
234C22×Dic3—61no—
235C22×Dic3—61no—
236C22×Dic3—62no—
237C22×Dic3—64no—
238C22×Dic3—68no—
239C22×Dic3C22×D312yes—
240C2×D12—22no—
241C2×D12—22no—
242C2×D12—28no—
243C2×D12—22no—
244C2×D12—28no—
245C2×D12—22no—
246C2×D12—22no—
247C2×D12—22no—
248C2×D12—22no—
249C2×D12—22no—
250C2×D12—44no—
251C2×D12#6714yescomplemented
252C2×C4×D3—68no—
253C2×C4×D3—64no—
254C3×C4⋊C4—62no—
255C3×C22⋊C4—68no—
256C3×C42—22no—
257C3×C42—22no—
258C3×C42—42no—
259#217—64no—
260#217—68no—
261(C2×D3)⋊C4—28no—
262(C2×D3)⋊C4—68no—
263(C2×D3)⋊C4—64no—
264C4⋊Dic3—22no—
265Dic3⋊C4—38no—
266Dic3⋊C4—38no—
267Dic3⋊C4—68no—
268C4×Dic3—34no—
269C4×Dic3—34no—
270C4×Dic3—64no—
271C4×Dic3—62no—
272C4×Dic3—62no—
273C4×Dic3—122no—
274C22×C32C22×D411yescharacteristic
275C22×C32C22×D412yes—
276C22×C32C22×D411yescharacteristic
277C22×C32C2×#4111yescharacteristic
278C22×C32H(5,𝔽2)12yes—
279C2×C3×D3—24no—
280C2×C3×D3—28no—
281C2×C3×D3—42no—
282C2×C3×D3—42no—
283C2×C3×D3—44no—
284C2×C3×D3—42no—
285C2×C3×D3—42no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C2×C3×D3—42no—
290C2×C3×D3—44no—
291C2×C3×D3—44no—
292C2×C3×D3—44no—
293C2×C3×D3—44no—
294C32×C4—24no—
295C32×C4#12114yescomplemented
296C3⋊Dic3—22no—
297C3⋊Dic3—24no—
298C3⋊Dic3#12714yescomplemented
299C3×Dic3—42no—
300C22×D4—31no—
301C22×D4—31no—
302C22×D4—31no—
303C22×D4—34no—
304C22×D4—92no—
305C22×D4—94no—
306C22×D4—92no—
307C23×C4—92no—
308#127—64no—
309#127—184no—
310#127—184no—
311#121—1816no—
312C4×D4—184no—
313C2×C4⋊C4—31no—
314C2×C4⋊C4—92no—
315C2×C22⋊C4—34no—
316C2×C22⋊C4—92no—
317C2×C22⋊C4—94no—
318C2×C42—91no—
319C2×C42—91no—
320C2×C42D3211yescharacteristic
321#95—92no—
322C23×C3—21no—
323C23×C3—34no—
324C23×C3—62no—
325C23×C3—62no—
326C23×C3—64no—
327C23×C3—64no—
328C23×C3—62no—
329C23×C3—64no—
330C23×C3—64no—
331C23×C3—62no—
332C23×C3—62no—
333C23×C3—62no—
334C23×C3—62no—
335C23×C3—64no—
336C23×C3—64no—
337C23×C3—62no—
338C23×C3C23×D311yescharacteristic
339C23×C3C23×D311yescharacteristic
340C22×D3—22no—
341C22×D3—24no—
342C22×D3—22no—
343C22×D3—24no—
344C22×D3—22no—
345C22×D3—24no—
346C22×D3—24no—
347C22×D3—22no—
348C22×D3—22no—
349C22×D3—22no—
350C22×D3—22no—
351C22×D3—24no—
352C22×D3—24no—
353C22×D3—22no—
354C22×D3C2×#6714yes—
355C3×D4—68no—
356C3×D4—1216no—
357C3×D4—124no—
358C3×D4—124no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—24no—
366C2×C3×C4—22no—
367C2×C3×C4—42no—
368C2×C3×C4—42no—
369C2×C3×C4—64no—
370C2×C3×C4—62no—
371C2×C3×C4#23512yes—
372C2×C3×C4D3×D414yes—
373C2×C3×C4D3×D414yes—
374C2×C3×C4D3×D412yes—
375C2×C3×C4D3×D412yes—
376C2×C3×C4D3×D412yes—
377C2×C3×C4#23712yes—
378C2×C3×C4C2×#6712yes—
379#67—128no—
380#67—128no—
381#67—1216no—
382#67—1216no—
383#67—128no—
384#67—128no—
385C2×Dic3—22no—
386C2×Dic3—24no—
387C2×Dic3—32no—
388C2×Dic3—32no—
389C2×Dic3—34no—
390C2×Dic3—34no—
391C2×Dic3—32no—
392C2×Dic3—32no—
393C2×Dic3—34no—
394C2×Dic3—34no—
395C2×Dic3—62no—
396C2×Dic3—64no—
397C2×Dic3—62no—
398C2×Dic3—64no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—122no—
406C2×Dic3—122no—
407C2×Dic3—122no—
408C2×Dic3—128no—
409D12—28no—
410D12—416no—
411D12—44no—
412D12—44no—
413C4×D3—128no—
414C2×C32C2×#12111yescharacteristic
415C2×C32C2×#12711yescharacteristic
416C2×C32#53511yescharacteristic
417C2×C32D4212yes—
418C2×C32#55012yes—
419C3×D3—44no—
420C3×D3—82no—
421C3×D3—82no—
422C24—32no—
423C24—32no—
424C24—32no—
425C2×D4—34no—
426C2×D4—68no—
427C2×D4—62no—
428C2×D4—62no—
429C2×D4—62no—
430C2×D4—62no—
431C2×D4—68no—
432C2×D4—62no—
433C2×D4—62no—
434C2×D4—62no—
435C2×D4—62no—
436C2×D4—124no—
437C2×D4—188no—
438C2×D4—188no—
439C2×D4—184no—
440C2×D4—184no—
441C2×D4—188no—
442C2×D4—364no—
443C2×D4—364no—
444C22×C4—32no—
445C22×C4—91no—
446C22×C4—91no—
447C22×C4—92no—
448C22×C4—184no—
449C22×C4—188no—
450C22×C4C2×D3212yes—
451C22×C4C2×D3211yescharacteristic
452C4⋊C4—62no—
453C4⋊C4—98no—
454C22⋊C4—68no—
455C22⋊C4—184no—
456C22⋊C4—188no—
457C42—22no—
458C42—94no—
459C42—182no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—21no—
465C22×C3—64no—
466C22×C3—68no—
467C22×C3—122no—
468C22×C3—122no—
469C22×C3—124no—
470C22×C3—122no—
471C22×C3—122no—
472C22×C3—122no—
473C22×C3—122no—
474C22×C3—124no—
475C22×C3—122no—
476C22×C3—124no—
477C22×C3—122no—
478C22×C3—124no—
479C22×C3—124no—
480C22×C3C2×#23511yescharacteristic
481C22×C3C2×D3×D411yescharacteristic
482C22×C3C2×D3×D411yescharacteristic
483C22×C3C2×D3×D412yes—
484C22×C3C2×D3×D412yes—
485C22×C3C2×D3×D411yescharacteristic
486C22×C3C2×#23711yescharacteristic
487C22×C3#100412yes—
488C22×C3#100912yes—
489C22×C3C22×#6711yescharacteristic
490C2×D3—28no—
491C2×D3—24no—
492C2×D3—42no—
493C2×D3—42no—
494C2×D3—44no—
495C2×D3—42no—
496C2×D3—42no—
497C2×D3—42no—
498C2×D3—42no—
499C2×D3—44no—
500C2×D3—42no—
501C2×D3—44no—
502C2×D3—42no—
503C2×D3—44no—
504C2×D3—44no—
505C3×C4—24no—
506C3×C4—24no—
507C3×C4—24no—
508C3×C4—44no—
509C3×C4—122no—
510C3×C4#88414yescomplemented
511C3×C4#93914yescomplemented
512Dic3—34no—
513Dic3—34no—
514Dic3—42no—
515Dic3—64no—
516Dic3—62no—
517Dic3—62no—
518Dic3—64no—
519Dic3—64no—
520Dic3—122no—
521Dic3—124no—
522C32#254111yescharacteristic, complemented, Sylow
523C23—34no—
524C23—62no—
525C23—62no—
526C23—64no—
527C23—64no—
528C23—62no—
529C23—62no—
530C23—64no—
531C23—64no—
532C23—62no—
533C23—62no—
534C23—64no—
535C23—64no—
536C23—62no—
537C23—62no—
538C23C22×D3211yescharacteristic
539D4—68no—
540D4—1216no—
541D4—124no—
542D4—124no—
543D4—368no—
544D4—3616no—
545D4—368no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—64no—
549C2×C4—62no—
550C2×C4—92no—
551C2×C4—94no—
552C2×C4—92no—
553C2×C4—94no—
554C2×C4—182no—
555C2×C4—182no—
556C2×C4—182no—
557C2×C4—368no—
558C2×C4#379512yes—
559C2×C4#380214yes—
560C2×C4#380212yes—
561C2×C4D3×#6712yes—
562C2×C3—21no—
563C2×C3—22no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—22no—
567C2×C3—124no—
568C2×C3—242no—
569C2×C3—242no—
570C2×C3C2×#88411yescharacteristic
571C2×C3#555312yes—
572C2×C3#560912yes—
573C2×C3#567411yescharacteristic
574C2×C3D3×#12711yescharacteristic
575C2×C3D3×#12711yescharacteristic
576C2×C3#571511yescharacteristic
577C2×C3#571812yes—
578C2×C3D4×#6712yes—
579C2×C3C2×#93911yescharacteristic
580D3—44no—
581D3—82no—
582D3—82no—
583C22—64no—
584C22—68no—
585C22—124no—
586C22—122no—
587C22—122no—
588C22—122no—
589C22—122no—
590C22—124no—
591C22—124no—
592C22—122no—
593C22—122no—
594C22—122no—
595C22—122no—
596C22—124no—
597C22—124no—
598C22C2×#379511yescharacteristic
599C22C2×#380211yescharacteristic
600C22C2×#380212yes—
601C22#6430712yes—
602C22C2×D3×#6711yescharacteristic
603C4—24no—
604C4—94no—
605C4—122no—
606C4—182no—
607C4—184no—
608C4#6388514yescomplemented
609C3—21no—
610C3#7634811yescharacteristic, complemented
611C3#8317711yescharacteristic, complemented
612C2—124no—
613C2—242no—
614C2—242no—
615C2#1059390612yes—
616C2#1059400811yescharacteristic
617C2#1059401011yescharacteristic
618C2C2×#6388511yescharacteristic
619C2#1059506912yes—
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#2541
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C3×#874C2semidirect
2. C2×#63914C2semidirect
3. C2×#63914C2semidirect
4. C2×#63898C2semidirect
5. C2×#63885C2semidirect
6. C4×#3750C2semidirect
7. C3×#4939C2semidirect
8. #10591389C2semidirect
9. #10591323C2semidirect
43. C2×#874D3semidirect
49. #4939D3semidirect
73. C2×C3×D12D4semidirect
84. #3750D4semidirect
86. C4×C3⋊Dic3D4semidirect
251. C2×D12#67semidirect
295. C32×C4#121semidirect
298. C3⋊Dic3#127semidirect
510. C3×C4#884semidirect
511. C3×C4#939semidirect
522. C32#2541semidirect
608. C4#63885semidirect
610. C3#76348semidirect
611. C3#83177semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8742
C2×#639142
C2×#638982
C2×#638852
C4×#37502
C3×#49392
#105913892
#105913232
#831773
#763483