Finite Group Databasebeta

← C2×#10591428 #11865445

Subgroups — C2×#10591428 #11865445

Order 1152.

1397 conjugacy classes of subgroups.

The subgroup lattice has 585 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic, complemented
3C2×Dic3×D12C211yesmaximal, characteristic, complemented
4C22×#3713C211yesmaximal, characteristic, complemented
5C2×#63659C211yesmaximal, characteristic, complemented
6#10591428C218yesmaximal, direct product factor
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C2×#63563C211yesmaximal, characteristic, complemented
9C2×#5150—31nomaximal
10C2×#5072—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C3×#67—21no—
13C22×C3×#67—21no—
14C22×C3×D12C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×D3×Dic3—21no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×#940—22no—
20C3×#940C2214yescomplemented
21C2×C3×#213—24no—
22C2×C3×#213C2214yescomplemented
23C2×C3×C4×Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×(C2×D3)⋊Dic3—21no—
26Dic3×D12—22no—
27Dic3×D12C2214yescomplemented
28C2×#3713—24no—
29C2×#3713C2214yescomplemented
30#63659C2214yescomplemented
31Dic3⋊(C3⋊C8)C2214yescomplemented
32#63563C2214yescomplemented
33C22×C3×D8—31no—
34C2×C3×#127—31no—
35C2×#940D311yescharacteristic, complemented
36C2×D4×Dic3—31no—
37C22×#213—31no—
38C22×#213—31no—
39C22×#213D311yescharacteristic, complemented
40C2×C4×D12—31no—
41C2×#832—31no—
42C2×#832—31no—
43C2×#832—31no—
44C2×#832—61no—
45#5150—38no—
46C2×#821—31no—
47C2×Dic3⋊C8—31no—
48#5072—38no—
49C2×C4⋊(C3⋊C8)—31no—
50C24×C32—21no—
51C23×C3×D3—21no—
52C23×C3×D3—21no—
53C2×C32×D4—22no—
54C2×C32×D4—21no—
55C2×C32×D4—22no—
56C2×C32×D4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3—21no—
59C2×C3×#67—24no—
60C2×C3×#67—24no—
61C2×C3×#67—44no—
62C2×C3×#67—44no—
63C22×C3×Dic3D411yescharacteristic
64C22×C3×Dic3D411yescharacteristic
65C2×C3×D12—21no—
66C2×C3×D12—22no—
67C2×C3×D12—22no—
68C2×C3×D12—22no—
69C2×C3×D12—21no—
70C2×C3×D12D414yescomplemented
71C2×C3×D12C2312yes—
72C2×C3×D12C2312yes—
73C2×D3×Dic3—24no—
74C2×D3×Dic3—44no—
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)C2312yes—
77C2×C3⋊(C3⋊C8)—22no—
78C2×C3⋊(C3⋊C8)C2312yes—
79C3×#213—28no—
80C3×C4×Dic3D412yes—
81C3×C4×Dic3C2312yes—
82C2×C3×C3⋊C8—22no—
83C2×C3×C3⋊C8C2312yes—
84(C2×D3)⋊Dic3—24no—
85#3713—28no—
86C2×#459—91noSylow
87C22×C3×D4—21no—
88C22×C3×D4—31no—
89C22×C3×D4—31no—
90C22×C3×D4—61no—
91C22×C3×D4—61no—
92C22×C3×D4C2×D311yescharacteristic
93C22×C3×D4C2×D311yescharacteristic
94C22×#67—21no—
95C22×#67—21no—
96C23×Dic3—61no—
97C22×D12C2×D311yescharacteristic
98C22×D12C2×D311yescharacteristic
99C22×C4×D3—61no—
100C2×C3×D8—34no—
101C2×C3×D8—64no—
102C22×C3×C8—31no—
103C3×#127—34no—
104C3×#127—62no—
105C2×C3×C42—31no—
106C2×#217—61no—
107#940—22no—
108#940C2×D314yescomplemented
109D4×Dic3—34no—
110D4×Dic3—62no—
111C2×#213—24no—
112C2×#213—34no—
113C2×#213—34no—
114C2×#213—64no—
115C2×#213—64no—
116C2×#213C2×D314yescomplemented
117C2×(C2×D3)⋊C4—61no—
118C2×C4⋊Dic3—31no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—61no—
121C2×C4×Dic3C2×D311yescharacteristic
122C22×C3⋊C8—31no—
123C22×C3⋊C8—31no—
124C22×C3⋊C8—61no—
125C22×C3⋊C8C2×D311yescharacteristic
126C4×D12—34no—
127C4×D12—62no—
128#832—34no—
129#832—34no—
130#832—34no—
131#832—64no—
132#821—34no—
133Dic3⋊C8—34no—
134C4⋊(C3⋊C8)—34no—
135C23×C32—22no—
136C23×C32—42no—
137C23×C32—42no—
138C23×C32—42no—
139C23×C32C2×D411yescharacteristic
140C22×C3×D3—24no—
141C22×C3×D3—22no—
142C22×C3×D3—22no—
143C22×C3×D3—42no—
144C22×C3×D3—42no—
145C22×C3×D3—42no—
146C22×C3×D3—42no—
147C22×C3×D3—42no—
148C32×D4—22no—
149C32×D4—22no—
150C32×D4—42no—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D412yes—
153C2×C32×C4#4112yes—
154C2×C32×C4C2411yescharacteristic
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—42no—
157C3×#67—48no—
158C3×#67—48no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3D814yescomplemented
161C2×C3×Dic3C2×D412yes—
162C2×C3×Dic3C2×D412yes—
163C3×D12—24no—
164C3×D12—22no—
165C3×D12—22no—
166C3×D12—22no—
167C3×D12—42no—
168C3×D12C2×D414yescomplemented
169D3×Dic3—48no—
170C3⋊(C3⋊C8)—22no—
171C3×C3⋊C8—22no—
172C22×D8—31no—
173C22×D8—91no—
174C2×#127—31no—
175C2×C4×D4—91no—
176#459—98no—
177C2×C4⋊C8—91no—
178C2×#102—91no—
179C2×#102—91no—
180C24×C3—21no—
181C24×C3—21no—
182C24×C3—41no—
183C24×C3—61no—
184C24×C3—61no—
185C23×D3—21no—
186C23×D3—21no—
187C2×C3×D4—24no—
188C2×C3×D4—22no—
189C2×C3×D4—21no—
190C2×C3×D4—22no—
191C2×C3×D4—22no—
192C2×C3×D4—22no—
193C2×C3×D4—21no—
194C2×C3×D4—22no—
195C2×C3×D4—34no—
196C2×C3×D4—32no—
197C2×C3×D4—32no—
198C2×C3×D4—42no—
199C2×C3×D4—41no—
200C2×C3×D4—64no—
201C2×C3×D4—64no—
202C2×C3×D4—61no—
203C2×C3×D4—62no—
204C2×C3×D4—62no—
205C2×C3×D4—61no—
206C2×C3×D4—62no—
207C2×C3×D4—124no—
208C2×C3×D4—124no—
209C2×C3×D4C22×D312yes—
210C2×C3×D4C22×D312yes—
211C22×C3×C4—21no—
212C22×C3×C4—31no—
213C22×C3×C4—31no—
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C2×#67—24no—
217C2×#67—24no—
218C2×#67—44no—
219C2×#67—44no—
220C22×Dic3—61no—
221C22×Dic3—61no—
222C22×Dic3—64no—
223C22×Dic3—121no—
224C22×Dic3—124no—
225C22×Dic3#6711yescharacteristic
226C22×Dic3#6711yescharacteristic
227C2×D12—21no—
228C2×D12—22no—
229C2×D12—22no—
230C2×D12—22no—
231C2×D12—21no—
232C2×D12#6714yescomplemented
233C2×D12C22×D312yes—
234C2×D12C22×D312yes—
235C2×C4×D3—64no—
236C2×C4×D3—124no—
237C3×D8—68no—
238C2×C3×C8—32no—
239C2×C3×C8—62no—
240C3×C42—32no—
241C3×C42—32no—
242#217—64no—
243#213—28no—
244#213—68no—
245#213—68no—
246(C2×D3)⋊C4—64no—
247C4⋊Dic3—32no—
248C4⋊Dic3—32no—
249C4⋊Dic3—62no—
250C4⋊Dic3—61no—
251C4⋊Dic3—61no—
252C4⋊Dic3—121no—
253C4×Dic3#6712yes—
254C4×Dic3C22×D312yes—
255C2×C3⋊C8—22no—
256C2×C3⋊C8—32no—
257C2×C3⋊C8—32no—
258C2×C3⋊C8—62no—
259C2×C3⋊C8—62no—
260C2×C3⋊C8—62no—
261C2×C3⋊C8—122no—
262C2×C3⋊C8C22×D312yes—
263C22×C32—42no—
264C22×C32—42no—
265C22×C32—42no—
266C22×C32—84no—
267C22×C32#12112yes—
268C22×C32C2×D812yes—
269C22×C32AGL(1,ℤ/8)12yes—
270C22×C32C22×D411yescharacteristic
271C2×C3×D3—24no—
272C2×C3×D3—42no—
273C2×C3×D3—42no—
274C2×C3×D3—48no—
275C2×C3×D3—42no—
276C2×C3×D3—42no—
277C2×C3×D3—42no—
278C2×C3×D3—84no—
279C32×C4#12112yes—
280C32×C4C22×D411yescharacteristic
281C32×C4C2×#4111yescharacteristic
282C3⋊Dic3—42no—
283C3×Dic3—22no—
284C3×Dic3C2×D814yescomplemented
285C22×D4—31no—
286C22×D4—31no—
287C22×D4—61no—
288C22×D4—61no—
289C22×D4D3211yescharacteristic
290C23×C4—181no—
291C2×D8—34no—
292C2×D8—64no—
293C2×D8—94no—
294C2×D8—184no—
295C22×C8—31no—
296C22×C8—91no—
297#127—34no—
298#127—62no—
299C4×D4—94no—
300C4×D4—182no—
301C2×C4⋊C4—91no—
302C2×C22⋊C4—181no—
303C2×C42—31no—
304C4⋊C8—94no—
305#102—94no—
306#102—94no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—21no—
310C23×C3—42no—
311C23×C3—44no—
312C23×C3—42no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3—42no—
316C23×C3—42no—
317C23×C3—42no—
318C23×C3—64no—
319C23×C3—62no—
320C23×C3—62no—
321C23×C3—82no—
322C23×C3—82no—
323C23×C3—122no—
324C23×C3—122no—
325C23×C3—122no—
326C23×C3—122no—
327C23×C3—122no—
328C23×C3D3×D411yescharacteristic
329C23×C3C2×#6711yescharacteristic
330C22×D3—24no—
331C22×D3—22no—
332C22×D3—22no—
333C22×D3—42no—
334C22×D3—42no—
335C22×D3—42no—
336C22×D3—42no—
337C22×D3—42no—
338C3×D4—24no—
339C3×D4—22no—
340C3×D4—22no—
341C3×D4—22no—
342C3×D4—22no—
343C3×D4—34no—
344C3×D4—42no—
345C3×D4—44no—
346C3×D4—42no—
347C3×D4—42no—
348C3×D4—64no—
349C3×D4—62no—
350C3×D4—62no—
351C3×D4—62no—
352C3×D4—128no—
353C3×D4—128no—
354C3×D4—122no—
355C2×C3×C4—21no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—21no—
359C2×C3×C4—34no—
360C2×C3×C4—32no—
361C2×C3×C4—32no—
362C2×C3×C4—62no—
363C2×C3×C4D3×D412yes—
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4#23712yes—
366C2×C3×C4#23712yes—
367C2×C3×C4C2×#6711yescharacteristic
368C2×C3×C4C2×#6712yes—
369C2×C3×C4C23×D311yescharacteristic
370C2×C3×C4C23×D311yescharacteristic
371#67—48no—
372#67—48no—
373C2×Dic3—22no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—122no—
377C2×Dic3—122no—
378C2×Dic3—122no—
379C2×Dic3—128no—
380C2×Dic3—242no—
381C2×Dic3#21314yescomplemented
382C2×Dic3C2×#6712yes—
383C2×Dic3C2×#6712yes—
384D12—24no—
385D12—22no—
386D12—22no—
387D12—22no—
388D12—42no—
389D12C2×#6714yescomplemented
390C4×D3—128no—
391C3×C8—62no—
392C3⋊C8—22no—
393C3⋊C8—62no—
394C3⋊C8—62no—
395C3⋊C8—122no—
396C2×C32—82no—
397C2×C32#45914yescomplemented
398C2×C32C2×#12111yescharacteristic
399C2×C32C22×D811yescharacteristic
400C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
401C3×D3—44no—
402C3×D3—82no—
403C24—21no—
404C24—61no—
405C24—61no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—21no—
409C2×D4—32no—
410C2×D4—32no—
411C2×D4—34no—
412C2×D4—64no—
413C2×D4—64no—
414C2×D4—62no—
415C2×D4—62no—
416C2×D4—61no—
417C2×D4—62no—
418C2×D4—61no—
419C2×D4—124no—
420C2×D4—124no—
421C2×D4C2×D3212yes—
422C22×C4—31no—
423C22×C4—31no—
424C22×C4—184no—
425C22×C4—181no—
426C22×C4—364no—
427C22×C4C2×D3211yescharacteristic
428D8—68no—
429D8—188no—
430C2×C8—32no—
431C2×C8—62no—
432C2×C8—92no—
433C2×C8—182no—
434C4⋊C4—92no—
435C4⋊C4—181no—
436C22⋊C4—184no—
437C42—32no—
438C42—32no—
439C22×C3—21no—
440C22×C3—22no—
441C22×C3—22no—
442C22×C3—22no—
443C22×C3—44no—
444C22×C3—42no—
445C22×C3—42no—
446C22×C3—42no—
447C22×C3—42no—
448C22×C3—42no—
449C22×C3—42no—
450C22×C3—64no—
451C22×C3—82no—
452C22×C3—82no—
453C22×C3—88no—
454C22×C3—84no—
455C22×C3—84no—
456C22×C3—122no—
457C22×C3—122no—
458C22×C3—128no—
459C22×C3—122no—
460C22×C3—122no—
461C22×C3—122no—
462C22×C3—244no—
463C22×C3D3×D812yes—
464C22×C3#91112yes—
465C22×C3C2×#21312yes—
466C22×C3#93212yes—
467C22×C3#93812yes—
468C22×C3#93912yes—
469C22×C3C2×D3×D411yescharacteristic
470C22×C3C22×#6711yescharacteristic
471C2×D3—24no—
472C2×D3—48no—
473C2×D3—42no—
474C2×D3—42no—
475C2×D3—42no—
476C2×D3—42no—
477C2×D3—42no—
478C2×D3—84no—
479C3×C4—21no—
480C3×C4—21no—
481C3×C4—22no—
482C3×C4—34no—
483C3×C4—62no—
484C3×C4#93812yes—
485C3×C4#93912yes—
486C3×C4C2×D3×D411yescharacteristic
487C3×C4C2×#23711yescharacteristic
488C3×C4C2×#23711yescharacteristic
489C3×C4C22×#6711yescharacteristic
490Dic3—22no—
491Dic3—122no—
492Dic3—122no—
493Dic3—242no—
494Dic3C2×#21314yescomplemented
495C32C2×#45911yescharacteristic, complemented, Sylow
496C23—22no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—62no—
501C23—64no—
502C23—62no—
503C23—122no—
504C23—122no—
505C23—122no—
506C23—122no—
507C23—122no—
508C23D3×#6711yescharacteristic
509D4—22no—
510D4—22no—
511D4—34no—
512D4—42no—
513D4—62no—
514D4—62no—
515D4—62no—
516D4—64no—
517D4—128no—
518D4—128no—
519D4—122no—
520C2×C4—32no—
521C2×C4—34no—
522C2×C4—32no—
523C2×C4—62no—
524C2×C4—182no—
525C2×C4—368no—
526C2×C4—362no—
527C2×C4#380512yes—
528C2×C4D3×#6712yes—
529C2×C4D3×#6711yescharacteristic
530C2×C4C22×D3211yescharacteristic
531C8—62no—
532C8—182no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—24no—
537C2×C3—84no—
538C2×C3—82no—
539C2×C3—82no—
540C2×C3—124no—
541C2×C3—242no—
542C2×C3#507214yescomplemented
543C2×C3#515014yescomplemented
544C2×C3C2×D3×D811yescharacteristic
545C2×C3C2×#91111yescharacteristic
546C2×C3C22×#21311yescharacteristic
547C2×C3C2×#93211yescharacteristic
548C2×C3C2×#93811yescharacteristic
549C2×C3C2×#93911yescharacteristic
550D3—44no—
551D3—82no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—64no—
556C22—84no—
557C22—122no—
558C22—122no—
559C22—128no—
560C22—122no—
561C22—122no—
562C22—122no—
563C22—244no—
564C22D3×#21312yes—
565C22#6393212yes—
566C22#6397012yes—
567C22C2×D3×#6711yescharacteristic
568C4—34no—
569C4—62no—
570C4—362no—
571C4#6397012yes—
572C4C2×#380511yescharacteristic
573C4C2×D3×#6711yescharacteristic
574C3—21no—
575C3C2×#507211yescharacteristic, complemented
576C3C2×#515011yescharacteristic, complemented
577C2—82no—
578C2—124no—
579C2—242no—
580C2#1059142814yesdirect product factor
581C2C2×D3×#21311yescharacteristic
582C2C2×#6393211yescharacteristic
583C2C2×#6397011yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#459
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#940C2semidirect
2. C22×C3×#213C2semidirect
3. C2×Dic3×D12C2semidirect
4. C22×#3713C2semidirect
5. C2×#63659C2semidirect
6. #10591428C2direct (N × H)
7. C2×Dic3⋊(C3⋊C8)C2semidirect
8. C2×#63563C2semidirect
20. C3×#940C22semidirect
22. C2×C3×#213C22semidirect
27. Dic3×D12C22semidirect
29. C2×#3713C22semidirect
30. #63659C22semidirect
31. Dic3⋊(C3⋊C8)C22semidirect
32. #63563C22semidirect
35. C2×#940D3semidirect
39. C22×#213D3semidirect
70. C2×C3×D12D4semidirect
108. #940C2×D3semidirect
116. C2×#213C2×D3semidirect
160. C2×C3×Dic3D8semidirect
168. C3×D12C2×D4semidirect
232. C2×D12#67semidirect
284. C3×Dic3C2×D8semidirect
381. C2×Dic3#213semidirect
389. D12C2×#67semidirect
397. C2×C32#459semidirect
494. Dic3C2×#213semidirect
495. C32C2×#459semidirect
542. C2×C3#5072semidirect
543. C2×C3#5150semidirect
575. C3C2×#5072semidirect
576. C3C2×#5150semidirect
580. C2#10591428direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9402
C22×C3×#2132
C2×Dic3×D122
C22×#37132
C2×#636592
#105914282
C2×Dic3⋊(C3⋊C8)2
C2×#635632
C2×#51503
C2×#50723