Finite Group Databasebeta

← C2×#10591453 #11866970

Subgroups — C2×#10591453 #11866970

Order 1152.

1361 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3753C211yesmaximal, characteristic, complemented
2C2×C3×#938C211yesmaximal, characteristic, complemented
3C2×#63909C211yesmaximal, characteristic, complemented
4C22×#3711C211yesmaximal, characteristic, complemented
5C2×C3×#832C211yesmaximal, characteristic, complemented
6#10591453C218yesmaximal, direct product factor
7C2×#63574C211yesmaximal, characteristic, complemented
8C2×#63564C211yesmaximal, characteristic, complemented
9C2×#5039—31nomaximal
10C2×#4782—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×#67—21no—
14C22×C3×C4×D3C2211yescharacteristic
15C22×#626—21no—
16C2×#3753—24no—
17C2×#3753C2214yescomplemented
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C2×C3×#217—21no—
20C3×#938—22no—
21C3×#938C2214yescomplemented
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×#3722—21no—
26#63909—22no—
27#63909C2214yescomplemented
28C2×#3711—24no—
29C2×#3711C2214yescomplemented
30C3×#832C2214yescomplemented
31#63574C2214yescomplemented
32#63564C2214yescomplemented
33C2×C3×#121—31no—
34C2×#938D311yescharacteristic, complemented
35C22×#213—31no—
36C22×#213—31no—
37C22×#213—61no—
38C2×#930—31no—
39C22×#208—31no—
40C22×ΓL(1,𝔽25)—31no—
41C2×#895—31no—
42C2×C3×#102—31no—
43C2×#832D311yescharacteristic, complemented
44C2×#821—31no—
45#5039—38no—
46C2×#809—31no—
47C2×#808—31no—
48C2×#808—31no—
49#4782—38no—
50C24×C32—21no—
51C23×C3⋊D3—21no—
52C23×C3×D3D411yescharacteristic
53C2×C32×D4—22no—
54C2×C32×D4—21no—
55C2×C32×D4—22no—
56C2×C32×D4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)C2312yes—
62C2×C3×#67—24no—
63C2×C3×#67—44no—
64C22×C3×Dic3—21no—
65C22×C3×Dic3—21no—
66C22×C3×Dic3D411yescharacteristic
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3D412yes—
70C2×C3×C4×D3C2312yes—
71C2×#626—24no—
72C2×#626—44no—
73#3753—28no—
74C2×C3⋊(C3⋊C8)D414yescomplemented
75C2×C3⋊(C3⋊C8)C2312yes—
76C3×#217—24no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3—21no—
79C3×C4⋊Dic3C2312yes—
80C3×C4⋊Dic3C2312yes—
81C2×C3×C3⋊C8—22no—
82C2×C3×C3⋊C8C2312yes—
83#3722—24no—
84#3711—28no—
85C2×#469—91noSylow
86C22×C3×D4—21no—
87C22×C3×D4—61no—
88C22×C3×D4C2×D311yescharacteristic
89C22×C3×D4C2×D311yescharacteristic
90C23×C3×C4—31no—
91C22×#67—21no—
92C22×#67—61no—
93C22×D12—31no—
94C22×D12—31no—
95C22×D12—61no—
96C22×D12—61no—
97C22×C4×D3C2×D311yescharacteristic
98C22×C3×C8—31no—
99C3×#121—34no—
100C3×#121—62no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C22⋊C4—61no—
104C2×#217—21no—
105#938—22no—
106#938C2×D314yescomplemented
107C2×#213—34no—
108C2×#213—34no—
109C2×#213—64no—
110C2×#213—64no—
111C2×#213—64no—
112C2×#213—68no—
113#930—34no—
114#930—62no—
115C2×(C2×D3)⋊C4—61no—
116C2×(C2×D3)⋊C4—61no—
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×C4⋊Dic3C2×D311yescharacteristic
119C2×#208—34no—
120C2×#208—64no—
121C22×C3⋊C8—31no—
122C22×C3⋊C8—31no—
123C22×C3⋊C8—61no—
124C22×C3⋊C8C2×D311yescharacteristic
125C2×ΓL(1,𝔽25)—34no—
126C2×ΓL(1,𝔽25)—64no—
127#895—34no—
128#895—62no—
129C3×#102—34no—
130#832C2×D314yescomplemented
131#821—34no—
132#809—34no—
133#808—34no—
134#808—34no—
135C23×C32—22no—
136C23×C32—42no—
137C23×C32—42no—
138C23×C32—42no—
139C23×C32C2×D411yescharacteristic
140C22×C3⋊D3—22no—
141C22×C3⋊D3—42no—
142C22×C3⋊D3—42no—
143C22×C3⋊D3—42no—
144C22×C3×D3—22no—
145C22×C3×D3—22no—
146C22×C3×D3—22no—
147C22×C3×D3C2×D412yes—
148C32×D4—22no—
149C32×D4—22no—
150C32×D4—42no—
151C2×C32×C4C2×D412yes—
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4#4112yes—
154C2×C32×C4C2411yescharacteristic
155C4⋊(C3⋊D3)—22no—
156C4⋊(C3⋊D3)—22no—
157C4⋊(C3⋊D3)—42no—
158C3×#67—48no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—42no—
163C2×C3×Dic3—42no—
164C2×C3×Dic3C2×D412yes—
165C3×C4×D3—24no—
166C3×C4×D3—22no—
167C3×C4×D3—22no—
168#626—48no—
169C3⋊(C3⋊C8)C2×D414yescomplemented
170C3×C3⋊C8—22no—
171C22×D8—91no—
172C22×M16—91no—
173C2×#121—31no—
174C2×#121—91no—
175#469—98no—
176C2×#106—91no—
177C2×#102—31no—
178C2×#102—91no—
179C24×C3—21no—
180C24×C3—21no—
181C24×C3—31no—
182C24×C3—41no—
183C23×D3—61no—
184C23×D3—61no—
185C23×D3—121no—
186C23×D3#6711yescharacteristic
187C2×C3×D4—24no—
188C2×C3×D4—22no—
189C2×C3×D4—22no—
190C2×C3×D4—22no—
191C2×C3×D4—21no—
192C2×C3×D4—22no—
193C2×C3×D4—21no—
194C2×C3×D4—22no—
195C2×C3×D4—42no—
196C2×C3×D4—41no—
197C2×C3×D4—64no—
198C2×C3×D4—124no—
199C2×C3×D4C22×D312yes—
200C2×C3×D4C22×D312yes—
201C22×C3×C4—21no—
202C22×C3×C4—31no—
203C22×C3×C4—32no—
204C22×C3×C4—32no—
205C22×C3×C4—62no—
206C22×C3×C4—62no—
207C22×C3×C4—61no—
208C22×C3×C4—61no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C2×#67—24no—
212C2×#67—44no—
213C2×#67—64no—
214C2×#67—124no—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3#6711yescharacteristic
218C2×D12—32no—
219C2×D12—32no—
220C2×D12—62no—
221C2×D12—64no—
222C2×D12—62no—
223C2×D12—62no—
224C2×D12—62no—
225C2×D12—62no—
226C2×D12—64no—
227C2×D12—61no—
228C2×D12—61no—
229C2×D12—122no—
230C2×D12—121no—
231C2×D12—124no—
232C2×C4×D3—22no—
233C2×C4×D3—22no—
234C2×C4×D3#6712yes—
235C2×C4×D3C22×D312yes—
236C2×C3×C8—32no—
237C2×C3×C8—62no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4—61no—
242C3×C22⋊C4—64no—
243#217—24no—
244#213—68no—
245#213—68no—
246#213—616no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249C4⋊Dic3—21no—
250C4⋊Dic3—21no—
251C4⋊Dic3C22×D312yes—
252C4⋊Dic3C22×D312yes—
253#208—68no—
254C2×C3⋊C8—22no—
255C2×C3⋊C8—34no—
256C2×C3⋊C8—34no—
257C2×C3⋊C8—32no—
258C2×C3⋊C8—32no—
259C2×C3⋊C8—64no—
260C2×C3⋊C8—62no—
261C2×C3⋊C8C22×D312yes—
262ΓL(1,𝔽25)—68no—
263C22×C32—42no—
264C22×C32—42no—
265C22×C32—42no—
266C22×C32—84no—
267C22×C32#12112yes—
268C22×C32AGL(1,ℤ/8)12yes—
269C22×C32AGL(1,ℤ/8)12yes—
270C22×C32C22×D411yescharacteristic
271C2×C3⋊D3—42no—
272C2×C3⋊D3—42no—
273C2×C3⋊D3—42no—
274C2×C3⋊D3—84no—
275C2×C3×D3—22no—
276C2×C3×D3—22no—
277C2×C3×D3—22no—
278C2×C3×D3—44no—
279C32×C4#12112yes—
280C32×C4C22×D411yescharacteristic
281C32×C4C2×#4111yescharacteristic
282C3×Dic3—22no—
283C3×Dic3—42no—
284C3×Dic3—42no—
285C22×D4—61no—
286C22×D4—91no—
287C22×D4—181no—
288C22×D4D3211yescharacteristic
289C23×C4—31no—
290C2×D8—94no—
291C2×D8—184no—
292C2×M16—94no—
293C2×M16—184no—
294C22×C8—31no—
295C22×C8—91no—
296#121—34no—
297#121—62no—
298#121—94no—
299#121—182no—
300C2×C4⋊C4—31no—
301C2×C4⋊C4—31no—
302C2×C22⋊C4—61no—
303C2×C22⋊C4—181no—
304#106—94no—
305#102—34no—
306#102—94no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—21no—
310C23×C3—32no—
311C23×C3—42no—
312C23×C3—44no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3—42no—
316C23×C3—42no—
317C23×C3—42no—
318C23×C3—42no—
319C23×C3—62no—
320C23×C3—62no—
321C23×C3—62no—
322C23×C3—82no—
323C23×C3—82no—
324C23×C3D3×D411yescharacteristic
325C23×C3C2×#6711yescharacteristic
326C22×D3—22no—
327C22×D3—22no—
328C22×D3—22no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—122no—
332C22×D3—124no—
333C22×D3—122no—
334C22×D3—122no—
335C22×D3—122no—
336C22×D3—122no—
337C22×D3—122no—
338C22×D3—122no—
339C22×D3—242no—
340C22×D3—242no—
341C22×D3C2×#6712yes—
342C3×D4—24no—
343C3×D4—22no—
344C3×D4—22no—
345C3×D4—22no—
346C3×D4—22no—
347C3×D4—42no—
348C3×D4—44no—
349C3×D4—42no—
350C3×D4—42no—
351C3×D4—128no—
352C2×C3×C4—21no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—22no—
356C2×C3×C4—32no—
357C2×C3×C4—62no—
358C2×C3×C4—64no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—122no—
364C2×C3×C4—122no—
365C2×C3×C4#23512yes—
366C2×C3×C4D3×D411yescharacteristic
367C2×C3×C4D3×D412yes—
368C2×C3×C4D3×D412yes—
369C2×C3×C4#23712yes—
370C2×C3×C4C2×#6711yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373#67—48no—
374#67—128no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—42no—
379C2×Dic3—42no—
380C2×Dic3C2×#6712yes—
381D12—64no—
382D12—62no—
383D12—62no—
384D12—62no—
385D12—62no—
386D12—122no—
387D12—124no—
388D12—128no—
389D12—122no—
390D12—122no—
391C4×D3—24no—
392C4×D3—22no—
393C4×D3—22no—
394C3×C8—62no—
395C3⋊C8—22no—
396C3⋊C8—34no—
397C3⋊C8—34no—
398C3⋊C8—64no—
399C2×C32—82no—
400C2×C32#46914yescomplemented
401C2×C32C2×#12111yescharacteristic
402C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
403C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
404C3⋊D3—82no—
405C3×D3—42no—
406C24—21no—
407C24—31no—
408C24—181no—
409C2×D4—22no—
410C2×D4—21no—
411C2×D4—22no—
412C2×D4—64no—
413C2×D4—92no—
414C2×D4—124no—
415C2×D4—184no—
416C2×D4—182no—
417C2×D4—181no—
418C2×D4—182no—
419C2×D4—364no—
420C2×D4C2×D3212yes—
421C22×C4—31no—
422C22×C4—32no—
423C22×C4—32no—
424C22×C4—62no—
425C22×C4—62no—
426C22×C4—61no—
427C22×C4—61no—
428C22×C4C2×D3211yescharacteristic
429D8—188no—
430M16—188no—
431C2×C8—32no—
432C2×C8—62no—
433C2×C8—92no—
434C2×C8—94no—
435C4⋊C4—32no—
436C4⋊C4—32no—
437C4⋊C4—61no—
438C4⋊C4—61no—
439C22⋊C4—64no—
440C22⋊C4—184no—
441C22×C3—21no—
442C22×C3—22no—
443C22×C3—22no—
444C22×C3—22no—
445C22×C3—44no—
446C22×C3—42no—
447C22×C3—42no—
448C22×C3—42no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—42no—
452C22×C3—62no—
453C22×C3—62no—
454C22×C3—62no—
455C22×C3—82no—
456C22×C3—82no—
457C22×C3—88no—
458C22×C3—84no—
459C22×C3—84no—
460C22×C3—124no—
461C22×C3#88412yes—
462C22×C3#91112yes—
463C22×C3#91412yes—
464C22×C3#93212yes—
465C22×C3#93912yes—
466C22×C3#94912yes—
467C22×C3C2×D3×D411yescharacteristic
468C22×C3C22×#6711yescharacteristic
469C2×D3—22no—
470C2×D3—22no—
471C2×D3—22no—
472C2×D3—44no—
473C2×D3—124no—
474C2×D3—122no—
475C2×D3—122no—
476C2×D3—122no—
477C2×D3—122no—
478C2×D3—122no—
479C2×D3—122no—
480C2×D3—242no—
481C2×D3—242no—
482C2×D3—248no—
483C2×D3—244no—
484C2×D3—244no—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—22no—
488C3×C4—62no—
489C3×C4—122no—
490C3×C4—122no—
491C3×C4#88412yes—
492C3×C4#93912yes—
493C3×C4C2×#23511yescharacteristic
494C3×C4C2×D3×D411yescharacteristic
495C3×C4C2×D3×D411yescharacteristic
496C3×C4C2×#23711yescharacteristic
497Dic3—22no—
498Dic3—42no—
499Dic3—42no—
500C32C2×#46911yescharacteristic, complemented, Sylow
501C23—22no—
502C23—32no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—62no—
507C23—62no—
508C23—62no—
509C23—182no—
510C23—362no—
511C23—362no—
512C23—362no—
513C23D3×#6711yescharacteristic
514D4—22no—
515D4—22no—
516D4—42no—
517D4—128no—
518D4—182no—
519D4—182no—
520D4—368no—
521D4—362no—
522C2×C4—32no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—64no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—122no—
530C2×C4—122no—
531C2×C4#380412yes—
532C2×C4D3×#6711yescharacteristic
533C2×C4#381112yes—
534C2×C4C22×D3211yescharacteristic
535C8—62no—
536C8—94no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—24no—
541C2×C3—84no—
542C2×C3—82no—
543C2×C3—82no—
544C2×C3—122no—
545C2×C3#478214yescomplemented
546C2×C3#503914yescomplemented
547C2×C3C2×#88411yescharacteristic
548C2×C3C2×#91111yescharacteristic
549C2×C3C2×#91411yescharacteristic
550C2×C3C2×#93211yescharacteristic
551C2×C3C2×#93911yescharacteristic
552C2×C3C2×#94911yescharacteristic
553D3—42no—
554D3—244no—
555D3—242no—
556D3—242no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—62no—
561C22—62no—
562C22—62no—
563C22—84no—
564C22—124no—
565C22—362no—
566C22—362no—
567C22—362no—
568C22—724no—
569C22#6392512yes—
570C22#6393412yes—
571C22#6397112yes—
572C22C2×D3×#6711yescharacteristic
573C4—62no—
574C4—122no—
575C4—122no—
576C4#6397112yes—
577C4C2×#380411yescharacteristic
578C4C2×#381111yescharacteristic
579C3—21no—
580C3C2×#478211yescharacteristic, complemented
581C3C2×#503911yescharacteristic, complemented
582C2—82no—
583C2—122no—
584C2—722no—
585C2#1059145314yesdirect product factor
586C2C2×#6392511yescharacteristic
587C2C2×#6393411yescharacteristic
588C2C2×#6397111yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#469
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. C22×#3753C2semidirect
2. C2×C3×#938C2semidirect
3. C2×#63909C2semidirect
4. C22×#3711C2semidirect
5. C2×C3×#832C2semidirect
6. #10591453C2direct (N × H)
7. C2×#63574C2semidirect
8. C2×#63564C2semidirect
17. C2×#3753C22semidirect
21. C3×#938C22semidirect
27. #63909C22semidirect
29. C2×#3711C22semidirect
30. C3×#832C22semidirect
31. #63574C22semidirect
32. #63564C22semidirect
34. C2×#938D3semidirect
43. C2×#832D3semidirect
74. C2×C3⋊(C3⋊C8)D4semidirect
106. #938C2×D3semidirect
130. #832C2×D3semidirect
169. C3⋊(C3⋊C8)C2×D4semidirect
400. C2×C32#469semidirect
500. C32C2×#469semidirect
545. C2×C3#4782semidirect
546. C2×C3#5039semidirect
580. C3C2×#4782semidirect
581. C3C2×#5039semidirect
585. C2#10591453direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37532
C2×C3×#9382
C2×#639092
C22×#37112
C2×C3×#8322
#105914532
C2×#635742
C2×#635642
C2×#50393
C2×#47823