Finite Group Databasebeta

← C2×#10590547 #11865454

Subgroups — C2×#10590547 #11865454

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×#893C211yesmaximal, characteristic, complemented
2C2×#63911C211yesmaximal, characteristic, complemented
3C22×#3714C211yesmaximal, characteristic, complemented
4C22×#3713C211yesmaximal, characteristic, complemented
5C2×#63636C211yesmaximal, characteristic, complemented
6C2×C3×#809C211yesmaximal, characteristic, complemented
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590547C218yesmaximal, direct product factor
9C2×#5015—31nomaximal
10C2×#4786—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3—21no—
15C22×#626—21no—
16C22×#626—21no—
17C2×C32×C4⋊C4C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4—21no—
20C2×C3×C4×Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#893—22no—
23C3×#893C2214yescomplemented
24#63911—22no—
25#63911C2214yescomplemented
26C2×#3714—24no—
27C2×#3714C2214yescomplemented
28C2×#3713—24no—
29C2×#3713C2214yescomplemented
30#63636C2214yescomplemented
31C3×#809C2214yescomplemented
32Dic3⋊(C3⋊C8)C2214yescomplemented
33C2×C3×C4×D4—31no—
34C2×#940—31no—
35C22×#213—31no—
36C22×#213—31no—
37C22×#213—31no—
38C22×D24—31no—
39C2×#893D311yescharacteristic, complemented
40C2×#874—31no—
41C2×C3×#102—31no—
42C2×Dic3⋊C8—31no—
43#5015—38no—
44C2×#809—31no—
45C2×#809—31no—
46C2×#809—61no—
47C2×#809D311yescharacteristic, complemented
48C2×C4⋊(C3⋊C8)—31no—
49#4786—38no—
50C23×C3⋊D3—21no—
51C23×C3×D3—21no—
52C23×C3×D3—21no—
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C2×C4⋊(C3⋊D3)—22no—
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)C2312yes—
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
61C2×C3×D12—21no—
62C2×C3×D12—22no—
63C2×C3×D12—22no—
64C2×C3×D12—22no—
65C2×C3×D12—21no—
66C2×C3×D12D414yescomplemented
67C2×C3×D12C2312yes—
68C2×C3×D12C2312yes—
69C2×C3×C4×D3—24no—
70C2×C3×C4×D3—44no—
71C2×#626—24no—
72C2×#626—24no—
73C2×#626—44no—
74C2×#626—44no—
75C32×C4⋊C4—21no—
76C32×C4⋊C4C2312yes—
77C2×C3⋊(C3⋊C8)—22no—
78C2×C3⋊(C3⋊C8)C2312yes—
79C3×(C2×D3)⋊C4—24no—
80C3×C4×Dic3D412yes—
81C3×C4×Dic3C2312yes—
82C2×C3×C3⋊C8—22no—
83C2×C3×C3⋊C8C2312yes—
84#3714—28no—
85#3713—28no—
86C2×#459—91noSylow
87C22×C3×D4—31no—
88C22×C3×D4—31no—
89C23×C3×C4—61no—
90C22×#67—61no—
91C22×#67—61no—
92C22×D12—31no—
93C22×D12—31no—
94C22×D12—61no—
95C22×D12—61no—
96C22×D12—61no—
97C22×D12C2×D311yescharacteristic
98C22×D12C2×D311yescharacteristic
99C22×C4×D3—21no—
100C22×C3×C8—31no—
101C3×C4×D4—34no—
102C3×C4×D4—62no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4C2×D311yescharacteristic
105C2×C3×C4⋊C4C2×D311yescharacteristic
106C2×C3×C22⋊C4—61no—
107C2×C3×C42—31no—
108#940—34no—
109#940—62no—
110C2×#213—34no—
111C2×#213—34no—
112C2×#213—34no—
113C2×#213—64no—
114C2×#213—64no—
115C2×#213—64no—
116C2×(C2×D3)⋊C4—21no—
117C2×C4×Dic3C2×D311yescharacteristic
118C22×C3⋊C8—31no—
119C22×C3⋊C8—31no—
120C22×C3⋊C8—61no—
121C22×C3⋊C8C2×D311yescharacteristic
122C2×D24—34no—
123C2×D24—64no—
124#893—22no—
125#893C2×D314yescomplemented
126#874—34no—
127#874—62no—
128C3×#102—34no—
129Dic3⋊C8—34no—
130#809—34no—
131#809—34no—
132#809—64no—
133#809C2×D314yescomplemented
134C4⋊(C3⋊C8)—34no—
135C23×C32C2×D411yescharacteristic
136C22×C3⋊D3—22no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—42no—
139C22×C3⋊D3—42no—
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—
148C2×C32×C4—22no—
149C2×C32×C4—42no—
150C2×C32×C4C2×D412yes—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4#4112yes—
153C2×C32×C4C2411yescharacteristic
154C4⋊(C3⋊D3)—22no—
155C4⋊(C3⋊D3)—22no—
156C4⋊(C3⋊D3)—42no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3D814yescomplemented
159C2×C3×Dic3C2×D412yes—
160C2×C3×Dic3C2×D412yes—
161C3×D12—24no—
162C3×D12—22no—
163C3×D12—22no—
164C3×D12—22no—
165C3×D12—42no—
166C3×D12C2×D414yescomplemented
167C3×C4×D3—48no—
168#626—48no—
169#626—48no—
170C3⋊(C3⋊C8)—22no—
171C3×C3⋊C8—22no—
172C22×D8—91no—
173C22×D8—91no—
174C2×#127—91no—
175C2×C4×D4—31no—
176#459—98no—
177C2×C4⋊C8—91no—
178C2×#102—31no—
179C2×#102—91no—
180C24×C3—61no—
181C24×C3—61no—
182C23×D3—21no—
183C23×D3—21no—
184C23×D3—61no—
185C23×D3—61no—
186C23×D3—121no—
187C2×C3×D4—34no—
188C2×C3×D4—32no—
189C2×C3×D4—32no—
190C2×C3×D4—62no—
191C2×C3×D4—62no—
192C2×C3×D4—62no—
193C2×C3×D4—61no—
194C2×C3×D4—61no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—31no—
199C22×C3×C4—31no—
200C22×C3×C4—41no—
201C22×C3×C4—64no—
202C22×C3×C4—124no—
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C2×#67—64no—
206C2×#67—64no—
207C2×#67—124no—
208C2×#67—124no—
209C22×Dic3#6711yescharacteristic
210C22×Dic3#6711yescharacteristic
211C2×D12—22no—
212C2×D12—21no—
213C2×D12—22no—
214C2×D12—22no—
215C2×D12—21no—
216C2×D12—32no—
217C2×D12—32no—
218C2×D12—62no—
219C2×D12—64no—
220C2×D12—62no—
221C2×D12—62no—
222C2×D12—62no—
223C2×D12—62no—
224C2×D12—64no—
225C2×D12—64no—
226C2×D12—61no—
227C2×D12—61no—
228C2×D12—122no—
229C2×D12—121no—
230C2×D12—124no—
231C2×D12—124no—
232C2×D12D1214yescomplemented
233C2×D12C22×D312yes—
234C2×D12C22×D312yes—
235C2×C4×D3—24no—
236C2×C4×D3—44no—
237C2×C3×C8—32no—
238C2×C3×C8—62no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—22no—
242C3×C4⋊C4—41no—
243C3×C4⋊C4C22×D312yes—
244C3×C4⋊C4C22×D312yes—
245C3×C22⋊C4—64no—
246C3×C42—32no—
247C3×C42—32no—
248#213—68no—
249#213—68no—
250#213—68no—
251(C2×D3)⋊C4—24no—
252C4×Dic3#6712yes—
253C4×Dic3C22×D312yes—
254C2×C3⋊C8—22no—
255C2×C3⋊C8—32no—
256C2×C3⋊C8—32no—
257C2×C3⋊C8—62no—
258C2×C3⋊C8—62no—
259C2×C3⋊C8—62no—
260C2×C3⋊C8—122no—
261C2×C3⋊C8C22×D312yes—
262D24—68no—
263C22×C32#12112yes—
264C22×C32C2×D812yes—
265C22×C32AGL(1,ℤ/8)12yes—
266C22×C32C22×D411yescharacteristic
267C2×C3⋊D3—42no—
268C2×C3⋊D3—42no—
269C2×C3⋊D3—42no—
270C2×C3⋊D3—84no—
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—42no—
280C32×C4#12112yes—
281C32×C4C22×D411yescharacteristic
282C32×C4C2×#4111yescharacteristic
283C3×Dic3—22no—
284C3×Dic3C2×D814yescomplemented
285C22×D4—31no—
286C22×D4—31no—
287C22×D4—91no—
288C22×D4—181no—
289C22×D4—181no—
290C23×C4—61no—
291C2×D8—94no—
292C2×D8—94no—
293C2×D8—184no—
294C2×D8—184no—
295C22×C8—31no—
296C22×C8—91no—
297#127—94no—
298#127—182no—
299C4×D4—34no—
300C4×D4—62no—
301C2×C4⋊C4D3211yescharacteristic
302C2×C22⋊C4—61no—
303C2×C42—31no—
304C4⋊C8—94no—
305#102—34no—
306#102—94no—
307C23×C3—21no—
308C23×C3—64no—
309C23×C3—62no—
310C23×C3—62no—
311C23×C3—122no—
312C23×C3—122no—
313C23×C3—122no—
314C23×C3—122no—
315C23×C3—122no—
316C23×C3D3×D411yescharacteristic
317C23×C3C2×#6711yescharacteristic
318C22×D3—24no—
319C22×D3—22no—
320C22×D3—22no—
321C22×D3—42no—
322C22×D3—42no—
323C22×D3—42no—
324C22×D3—42no—
325C22×D3—42no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—122no—
329C22×D3—124no—
330C22×D3—122no—
331C22×D3—122no—
332C22×D3—122no—
333C22×D3—122no—
334C22×D3—122no—
335C22×D3—122no—
336C22×D3—242no—
337C22×D3—242no—
338C3×D4—34no—
339C3×D4—64no—
340C3×D4—62no—
341C3×D4—62no—
342C3×D4—62no—
343C3×D4—122no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—21no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—21no—
350C2×C3×C4—34no—
351C2×C3×C4—32no—
352C2×C3×C4—32no—
353C2×C3×C4—42no—
354C2×C3×C4—42no—
355C2×C3×C4—42no—
356C2×C3×C4—62no—
357C2×C3×C4—82no—
358C2×C3×C4—128no—
359C2×C3×C4C2×D1212yes—
360C2×C3×C4#23512yes—
361C2×C3×C4#23512yes—
362C2×C3×C4D3×D412yes—
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367#67—128no—
368#67—128no—
369C2×Dic3—22no—
370C2×Dic3#21314yescomplemented
371C2×Dic3C2×#6712yes—
372C2×Dic3C2×#6712yes—
373D12—24no—
374D12—22no—
375D12—22no—
376D12—22no—
377D12—42no—
378D12—64no—
379D12—62no—
380D12—62no—
381D12—62no—
382D12—62no—
383D12—122no—
384D12—124no—
385D12—128no—
386D12—128no—
387D12—122no—
388D12—122no—
389D12C2×D1214yescomplemented
390C4×D3—48no—
391C3×C8—62no—
392C3⋊C8—22no—
393C3⋊C8—62no—
394C3⋊C8—62no—
395C3⋊C8—122no—
396C2×C32#45914yescomplemented
397C2×C32C2×#12111yescharacteristic
398C2×C32C22×D811yescharacteristic
399C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
400C3⋊D3—82no—
401C3×D3—44no—
402C3×D3—82no—
403C24—61no—
404C24—61no—
405C24—181no—
406C2×D4—32no—
407C2×D4—32no—
408C2×D4—34no—
409C2×D4—62no—
410C2×D4—62no—
411C2×D4—62no—
412C2×D4—61no—
413C2×D4—61no—
414C2×D4—92no—
415C2×D4—184no—
416C2×D4—184no—
417C2×D4—182no—
418C2×D4—182no—
419C2×D4—181no—
420C2×D4—364no—
421C2×D4—364no—
422C22×C4—21no—
423C22×C4—31no—
424C22×C4—31no—
425C22×C4—64no—
426C22×C4—124no—
427C22×C4C2×D3211yescharacteristic
428D8—188no—
429D8—188no—
430C2×C8—32no—
431C2×C8—62no—
432C2×C8—92no—
433C2×C8—182no—
434C4⋊C4—21no—
435C4⋊C4C2×D3212yes—
436C22⋊C4—64no—
437C42—32no—
438C42—32no—
439C22×C3—21no—
440C22×C3—22no—
441C22×C3—22no—
442C22×C3—22no—
443C22×C3—64no—
444C22×C3—122no—
445C22×C3—122no—
446C22×C3—128no—
447C22×C3—122no—
448C22×C3—122no—
449C22×C3—122no—
450C22×C3—244no—
451C22×C3#88412yes—
452C22×C3D3×D812yes—
453C22×C3#91412yes—
454C22×C3#93012yes—
455C22×C3C2×#21312yes—
456C22×C3#94912yes—
457C22×C3C2×D3×D411yescharacteristic
458C22×C3C22×#6711yescharacteristic
459C2×D3—24no—
460C2×D3—48no—
461C2×D3—42no—
462C2×D3—42no—
463C2×D3—42no—
464C2×D3—42no—
465C2×D3—42no—
466C2×D3—84no—
467C2×D3—124no—
468C2×D3—122no—
469C2×D3—122no—
470C2×D3—122no—
471C2×D3—122no—
472C2×D3—122no—
473C2×D3—122no—
474C2×D3—242no—
475C2×D3—242no—
476C2×D3—248no—
477C2×D3—244no—
478C2×D3—244no—
479C3×C4—21no—
480C3×C4—21no—
481C3×C4—22no—
482C3×C4—34no—
483C3×C4—42no—
484C3×C4—42no—
485C3×C4—62no—
486C3×C4—82no—
487C3×C4#88412yes—
488C3×C4#93012yes—
489C3×C4C22×D1211yescharacteristic
490C3×C4C2×#23511yescharacteristic
491C3×C4C2×#23511yescharacteristic
492C3×C4C2×D3×D411yescharacteristic
493Dic3—22no—
494Dic3C2×#21314yescomplemented
495C32C2×#45911yescharacteristic, complemented, Sylow
496C23—62no—
497C23—64no—
498C23—62no—
499C23—122no—
500C23—122no—
501C23—122no—
502C23—122no—
503C23—122no—
504C23—182no—
505C23—362no—
506C23—362no—
507C23—362no—
508C23D3×#6711yescharacteristic
509D4—34no—
510D4—62no—
511D4—62no—
512D4—62no—
513D4—64no—
514D4—122no—
515D4—182no—
516D4—182no—
517D4—368no—
518D4—368no—
519D4—362no—
520C2×C4—22no—
521C2×C4—32no—
522C2×C4—34no—
523C2×C4—32no—
524C2×C4—42no—
525C2×C4—62no—
526C2×C4—128no—
527C2×C4#379812yes—
528C2×C4D3×D1212yes—
529C2×C4D3×#6711yescharacteristic
530C2×C4C22×D3211yescharacteristic
531C8—62no—
532C8—182no—
533C2×C3—21no—
534C2×C3—24no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—124no—
538C2×C3—242no—
539C2×C3#478614yescomplemented
540C2×C3#501514yescomplemented
541C2×C3C2×#88411yescharacteristic
542C2×C3C2×D3×D811yescharacteristic
543C2×C3C2×#91411yescharacteristic
544C2×C3C2×#93011yescharacteristic
545C2×C3C22×#21311yescharacteristic
546C2×C3C2×#94911yescharacteristic
547D3—44no—
548D3—82no—
549D3—244no—
550D3—242no—
551D3—242no—
552C22—64no—
553C22—122no—
554C22—128no—
555C22—122no—
556C22—122no—
557C22—122no—
558C22—122no—
559C22—244no—
560C22—362no—
561C22—362no—
562C22—362no—
563C22—724no—
564C22#6390612yes—
565C22D3×#21312yes—
566C22#6393912yes—
567C22C2×D3×#6711yescharacteristic
568C4—34no—
569C4—42no—
570C4—62no—
571C4#6390612yes—
572C4C2×#379811yescharacteristic
573C4C2×D3×D1211yescharacteristic
574C3—21no—
575C3C2×#478611yescharacteristic, complemented
576C3C2×#501511yescharacteristic, complemented
577C2—124no—
578C2—242no—
579C2—722no—
580C2#1059054714yesdirect product factor
581C2C2×#6390611yescharacteristic
582C2C2×D3×#21311yescharacteristic
583C2C2×#6393911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#459
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#893C2semidirect
2. C2×#63911C2semidirect
3. C22×#3714C2semidirect
4. C22×#3713C2semidirect
5. C2×#63636C2semidirect
6. C2×C3×#809C2semidirect
7. C2×Dic3⋊(C3⋊C8)C2semidirect
8. #10590547C2direct (N × H)
23. C3×#893C22semidirect
25. #63911C22semidirect
27. C2×#3714C22semidirect
29. C2×#3713C22semidirect
30. #63636C22semidirect
31. C3×#809C22semidirect
32. Dic3⋊(C3⋊C8)C22semidirect
39. C2×#893D3semidirect
47. C2×#809D3semidirect
66. C2×C3×D12D4semidirect
125. #893C2×D3semidirect
133. #809C2×D3semidirect
158. C2×C3×Dic3D8semidirect
166. C3×D12C2×D4semidirect
232. C2×D12D12semidirect
284. C3×Dic3C2×D8semidirect
370. C2×Dic3#213semidirect
389. D12C2×D12semidirect
396. C2×C32#459semidirect
494. Dic3C2×#213semidirect
495. C32C2×#459semidirect
539. C2×C3#4786semidirect
540. C2×C3#5015semidirect
575. C3C2×#4786semidirect
576. C3C2×#5015semidirect
580. C2#10590547direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×#639112
C22×#37142
C22×#37132
C2×#636362
C2×C3×#8092
C2×Dic3⋊(C3⋊C8)2
#105905472
C2×#50153
C2×#47863