Finite Group Databasebeta

← C2×#10594570 #11903844

Subgroups — C2×#10594570 #11903844

Order 1152.

2629 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic, complemented
2C2×C3×#894C212yesmaximal, complemented
3C2×#63915C211yesmaximal, characteristic, complemented
4C2×#63915C211yesmaximal, characteristic, complemented
5C2×#63914C211yesmaximal, characteristic
6C2×#63913C212yesmaximal, complemented
7C2×#63902C211yesmaximal, characteristic, complemented
8C2×C4×#625C211yesmaximal, characteristic, complemented
9C2×#63884C212yesmaximal, complemented
10C2×#63879C212yesmaximal, complemented
11C2×#63838C211yesmaximal, characteristic, complemented
12#10594570C2116yesmaximal, direct product factor
13C2×#5664—32nomaximal
14C22×#634C2211yescharacteristic
15C22×C3×D12C2212yes—
16C22×C3×C4×D3C2212yes—
17C22×#627C2211yescharacteristic
18C22×#625C2212yes—
19C22×#625C2211yescharacteristic
20C22×#625C2211yescharacteristic
21C22×D3×Dic3C2212yes—
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C4×C3⋊Dic3C2211yescharacteristic
28#64096C2218yescomplemented
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×Dic3⋊C4C2212yes—
33C3×#894C22116yescomplemented
34C2×#3724C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×(C2×D3)⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×Dic32C2212yes—
39#63915C2218yescomplemented
40#63915C2218yescomplemented
41#63914C2218yes—
42#63913C22116yescomplemented
43#63902C2218yescomplemented
44C4×#625C2218yescomplemented
45#63884C22116yescomplemented
46#63879C22116yescomplemented
47#63838C2218yescomplemented
48C2×C3×#123—32no—
49C2×#940—32no—
50C2×#935—32no—
51C2×C4×#67—32no—
52C2×C4×#67—32no—
53#5664—332no—
54C2×#894—32no—
55C2×#894D312yescomplemented
56C2×#887—32no—
57C2×#887—32no—
58C2×#887—61no—
59C2×#885—32no—
60C2×#885—32no—
61C2×#885—32no—
62C2×#885—32no—
63C2×#67⋊C4—32no—
64C2×#67⋊C4—32no—
65C23×C3×D3C2312yes—
66C23×C3×D3C2312yes—
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3⋊Dic3C2311yescharacteristic
74C2×#634—24no—
75C2×#634C2314yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C2×C3×D12—44no—
79C2×C3×D12C2318yes—
80C2×C3×C4×D3—44no—
81C2×C3×C4×D3C2318yes—
82C2×#627—24no—
83C2×#627C2314yes—
84C2×#625—24no—
85C2×#625—24no—
86C2×#625—28no—
87C2×#625C2318yes—
88C2×#625C2314yes—
89C2×#625C2314yes—
90C2×D3×Dic3—44no—
91C2×D3×Dic3C2318yes—
92C32×C4⋊C4C2314yes—
93#3750C2314yes—
94#3750C2314yes—
95C4×C3⋊Dic3C2314yes—
96C4×C3⋊Dic3C2314yes—
97C4×C3⋊Dic3C2314yes—
98C3×(C2×D3)⋊C4C2318yes—
99C3×(C2×D3)⋊C4C2318yes—
100C3×(C2×D3)⋊C4C2318yes—
101C3×Dic3⋊C4C2318yes—
102#3724C2314yes—
103(C2×D3)⋊Dic3C2318yes—
104(C2×D3)⋊Dic3C2318yes—
105(C2×D3)⋊Dic3C2318yes—
106Dic32C2318yes—
107C2×#559—91noSylow
108C22×C3×D4—32no—
109C23×C3×C4—32no—
110C22×#67—32no—
111C22×#67—32no—
112C22×#67—32no—
113C22×#67—32no—
114C23×Dic3—32no—
115C22×D12C2×D312yes—
116C22×C4×D3—32no—
117C22×C4×D3C2×D312yes—
118C22×Dic6—32no—
119C22×Dic6—32no—
120C22×Dic6—61no—
121C3×#123—316no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—32no—
124C2×C3×C4⋊C4C2×D312yes—
125C2×C3×C22⋊C4—32no—
126C2×C3×C22⋊C4—32no—
127C2×C3×C22⋊C4—32no—
128C2×#217—32no—
129C2×#217—32no—
130C2×#217—32no—
131#940—316no—
132#935—316no—
133C4×#67—316no—
134C4×#67—316no—
135C2×(C2×D3)⋊C4—32no—
136C2×(C2×D3)⋊C4—32no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4C2×D312yes—
139C2×(C2×D3)⋊C4C2×D312yes—
140C2×(C2×D3)⋊C4C2×D312yes—
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—32no—
143C2×Dic3⋊C4—32no—
144C2×Dic3⋊C4—61no—
145C2×Dic3⋊C4—61no—
146C2×Dic3⋊C4C2×D312yes—
147C2×C4×Dic3—32no—
148C2×C4×Dic3—32no—
149C2×C4×Dic3—32no—
150C2×C4×Dic3—32no—
151C2×C4×Dic3—32no—
152C2×C4×Dic3—61no—
153C2×C4×Dic3—61no—
154C2×C4×Dic3—61no—
155#894—316no—
156#894C2×D3116yescomplemented
157#887—316no—
158#887—316no—
159#887—68no—
160#885—316no—
161#885—316no—
162#885—316no—
163#885—316no—
164#67⋊C4—316no—
165#67⋊C4—316no—
166C23×C32C2411yescharacteristic
167C22×C3×D3—24no—
168C22×C3×D3—24no—
169C22×C3×D3—24no—
170C22×C3×D3—24no—
171C22×C3×D3—24no—
172C22×C3×D3—24no—
173C22×C3×D3C2414yes—
174C22×C3×D3C2414yes—
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4—22no—
178C2×C32×C4C2412yes—
179C2×C32×C4C2412yes—
180C2×C32×C4C2412yes—
181C2×C3⋊Dic3—22no—
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3#4114yes—
184C2×C3⋊Dic3#4114yes—
185C2×C3⋊Dic3C2412yes—
186C2×C3⋊Dic3C2412yes—
187C2×C3⋊Dic3C2412yes—
188C2×C3⋊Dic3C2412yes—
189#634—28no—
190C2×C3×Dic3—24no—
191C2×C3×Dic3—24no—
192C2×C3×Dic3C2414yes—
193C2×C3×Dic3C2414yes—
194C3×D12—48no—
195C3×C4×D3—48no—
196#627—28no—
197#625—28no—
198#625—28no—
199#625—216no—
200D3×Dic3—48no—
201#559—916no—
202C2×#127—91no—
203C2×#124—92no—
204C2×#124—91no—
205C2×#124—91no—
206C2×#123—32no—
207C2×#123—92no—
208C2×C4×Q8—91no—
209C2×C4×Q8—91no—
210C2×C4×D4—91no—
211C2×C4×D4—92no—
212C2×C4×D4—91no—
213C24×C3—32no—
214C24×C3—32no—
215C23×D3C22×D312yes—
216C23×D3C22×D312yes—
217C2×C3×D4—38no—
218C2×C3×D4—124no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—32no—
223C22×C3×C4—32no—
224C22×C3×C4—38no—
225C22×C3×C4—124no—
226C22×C3×C4C22×D312yes—
227C22×C3×C4C22×D312yes—
228C22×C3×C4C22×D312yes—
229C2×#67—38no—
230C2×#67—38no—
231C2×#67—38no—
232C2×#67—38no—
233C2×#67—68no—
234C2×#67—68no—
235C2×#67—68no—
236C2×#67—68no—
237C22×Dic3—32no—
238C22×Dic3—32no—
239C22×Dic3—32no—
240C22×Dic3—32no—
241C22×Dic3—38no—
242C22×Dic3—61no—
243C22×Dic3—61no—
244C22×Dic3—61no—
245C22×Dic3—61no—
246C22×Dic3—124no—
247C22×Dic3C22×D312yes—
248C22×Dic3C22×D312yes—
249C2×D12—44no—
250C2×D12C22×D318yes—
251C2×C4×D3—38no—
252C2×C4×D3—44no—
253C2×C4×D3—124no—
254C2×C4×D3C22×D318yes—
255C2×Dic6—38no—
256C2×Dic6—38no—
257C2×Dic6—64no—
258C2×Dic6—68no—
259C2×Dic6—68no—
260C2×Dic6—68no—
261C3×C4⋊C4—24no—
262C3×C4⋊C4—38no—
263C3×C4⋊C4C22×D318yes—
264C3×C22⋊C4—38no—
265C3×C22⋊C4—38no—
266C3×C22⋊C4—38no—
267#217—38no—
268#217—38no—
269#217—38no—
270(C2×D3)⋊C4—38no—
271(C2×D3)⋊C4—38no—
272(C2×D3)⋊C4—38no—
273(C2×D3)⋊C4C22×D318yes—
274(C2×D3)⋊C4C22×D318yes—
275(C2×D3)⋊C4C22×D318yes—
276Dic3⋊C4—38no—
277Dic3⋊C4—38no—
278Dic3⋊C4—38no—
279Dic3⋊C4—64no—
280Dic3⋊C4—64no—
281Dic3⋊C4C22×D318yes—
282C4×Dic3—38no—
283C4×Dic3—38no—
284C4×Dic3—38no—
285C4×Dic3—38no—
286C4×Dic3—38no—
287C4×Dic3—64no—
288C4×Dic3—64no—
289C4×Dic3—64no—
290C22×C32C2×#4112yes—
291C22×C32C2×#4112yes—
292C22×C32H(5,𝔽2)12yes—
293C22×C32C2511yescharacteristic
294C2×C3×D3—24no—
295C2×C3×D3—24no—
296C2×C3×D3—24no—
297C2×C3×D3—24no—
298C2×C3×D3—24no—
299C2×C3×D3—24no—
300C2×C3×D3—48no—
301C2×C3×D3—48no—
302C32×C4—22no—
303C32×C4—22no—
304C32×C4—22no—
305C3⋊Dic3—22no—
306C3⋊Dic3—22no—
307C3⋊Dic3C2×#4114yes—
308C3⋊Dic3C2×#4114yes—
309C3×Dic3—24no—
310C3×Dic3—24no—
311C22×Q8—91no—
312C22×Q8—91no—
313C22×D4—32no—
314C22×D4—91no—
315C22×D4—92no—
316C22×D4—91no—
317C23×C4—32no—
318C23×C4—92no—
319#127—98no—
320#124—916no—
321#124—98no—
322#124—98no—
323#123—316no—
324#123—916no—
325C4×Q8—98no—
326C4×Q8—98no—
327C4×D4—98no—
328C4×D4—916no—
329C4×D4—98no—
330C2×C4⋊C4—32no—
331C2×C4⋊C4—91no—
332C2×C4⋊C4—91no—
333C2×C4⋊C4—91no—
334C2×C4⋊C4D3211yescharacteristic
335C2×C22⋊C4—32no—
336C2×C22⋊C4—32no—
337C2×C22⋊C4—32no—
338C2×C22⋊C4—92no—
339C2×C22⋊C4—92no—
340C2×C22⋊C4—92no—
341C2×C42—92no—
342C2×C42—91no—
343C2×C42—91no—
344C2×C42—91no—
345C23×C3—21no—
346C23×C3—34no—
347C23×C3—34no—
348C23×C3—64no—
349C23×C3—64no—
350C23×C3—64no—
351C23×C3—64no—
352C23×C3—64no—
353C23×C3—64no—
354C23×C3C23×D312yes—
355C22×D3—24no—
356C22×D3—24no—
357C22×D3—24no—
358C22×D3—24no—
359C22×D3—24no—
360C22×D3—24no—
361C22×D3C23×D314yes—
362C22×D3C23×D314yes—
363C3×D4—128no—
364C2×C3×C4—24no—
365C2×C3×C4—24no—
366C2×C3×C4—24no—
367C2×C3×C4—24no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—34no—
372C2×C3×C4—34no—
373C2×C3×C4—42no—
374C2×C3×C4—42no—
375C2×C3×C4—64no—
376C2×C3×C4—64no—
377C2×C3×C4—128no—
378C2×C3×C4C23×D314yes—
379C2×C3×C4C23×D314yes—
380C2×C3×C4C23×D314yes—
381#67—616no—
382#67—616no—
383#67—616no—
384#67—616no—
385C2×Dic3—24no—
386C2×Dic3—24no—
387C2×Dic3—38no—
388C2×Dic3—38no—
389C2×Dic3—34no—
390C2×Dic3—34no—
391C2×Dic3—34no—
392C2×Dic3—34no—
393C2×Dic3—64no—
394C2×Dic3—64no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—64no—
400C2×Dic3—64no—
401C2×Dic3—64no—
402C2×Dic3—122no—
403C2×Dic3—128no—
404C2×Dic3C23×D314yes—
405C2×Dic3C23×D314yes—
406D12—48no—
407C4×D3—48no—
408C4×D3—128no—
409Dic6—616no—
410Dic6—616no—
411Dic6—616no—
412C2×C32#55914yescomplemented
413C2×C32C22×#4111yescharacteristic
414C2×C32C22×#4111yescharacteristic
415C2×C32C2×H(5,𝔽2)11yescharacteristic
416C3×D3—44no—
417C3×D3—44no—
418C24—32no—
419C24—32no—
420C2×Q8—94no—
421C2×Q8—94no—
422C2×Q8—184no—
423C2×Q8—184no—
424C2×D4—38no—
425C2×D4—94no—
426C2×D4—98no—
427C2×D4—94no—
428C2×D4—124no—
429C2×D4—188no—
430C2×D4—184no—
431C2×D4—184no—
432C22×C4—32no—
433C22×C4—32no—
434C22×C4—38no—
435C22×C4—98no—
436C22×C4—91no—
437C22×C4—91no—
438C22×C4—91no—
439C22×C4—91no—
440C22×C4—124no—
441C22×C4—364no—
442C22×C4C2×D3211yescharacteristic
443C22×C4C2×D3211yescharacteristic
444C22×C4C2×D3211yescharacteristic
445C4⋊C4—38no—
446C4⋊C4—94no—
447C4⋊C4—94no—
448C4⋊C4—94no—
449C4⋊C4C2×D3214yes—
450C22⋊C4—38no—
451C22⋊C4—38no—
452C22⋊C4—38no—
453C22⋊C4—98no—
454C22⋊C4—98no—
455C22⋊C4—98no—
456C42—98no—
457C42—94no—
458C42—94no—
459C42—94no—
460C22×C3—22no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—21no—
464C22×C3—64no—
465C22×C3—64no—
466C22×C3—64no—
467C22×C3—64no—
468C22×C3—64no—
469C22×C3—64no—
470C22×C3—128no—
471C22×C3—128no—
472C22×C3#100414yes—
473C22×C3D3×#4114yes—
474C22×C3D3×#4114yes—
475C22×C3C24×D312yes—
476C2×D3—24no—
477C2×D3—24no—
478C2×D3—24no—
479C2×D3—24no—
480C2×D3—24no—
481C2×D3—24no—
482C2×D3—48no—
483C2×D3—48no—
484C3×C4—24no—
485C3×C4—24no—
486C3×C4—24no—
487C3×C4—24no—
488C3×C4—42no—
489C3×C4—42no—
490C3×C4—64no—
491C3×C4—64no—
492Dic3—24no—
493Dic3—24no—
494Dic3—38no—
495Dic3—38no—
496Dic3—64no—
497Dic3—64no—
498Dic3—64no—
499Dic3—64no—
500Dic3—64no—
501Dic3—122no—
502C32C2×#55911yescharacteristic, complemented, Sylow
503C23—34no—
504C23—34no—
505C23—64no—
506C23—64no—
507C23—64no—
508C23—64no—
509C23—64no—
510C23—64no—
511C23C22×D3211yescharacteristic
512Q8—188no—
513Q8—188no—
514D4—128no—
515D4—1816no—
516D4—188no—
517D4—188no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—34no—
522C2×C4—34no—
523C2×C4—64no—
524C2×C4—64no—
525C2×C4—94no—
526C2×C4—94no—
527C2×C4—92no—
528C2×C4—92no—
529C2×C4—92no—
530C2×C4—92no—
531C2×C4—128no—
532C2×C4—182no—
533C2×C4—182no—
534C2×C4—368no—
535C2×C4C22×D3212yes—
536C2×C4C22×D3212yes—
537C2×C4C22×D3212yes—
538C2×C3—24no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—124no—
543C2×C3—124no—
544C2×C3#566418yescomplemented
545C2×C3C2×#100412yes—
546C2×C3C2×D3×#4112yes—
547C2×C3C2×D3×#4112yes—
548D3—44no—
549D3—44no—
550C22—64no—
551C22—64no—
552C22—64no—
553C22—64no—
554C22—64no—
555C22—64no—
556C22—128no—
557C22—128no—
558C22#6430612yes—
559C22#6431312yes—
560C22#6431912yes—
561C22C23×D3211yescharacteristic
562C4—22no—
563C4—22no—
564C4—22no—
565C4—64no—
566C4—64no—
567C4—94no—
568C4—94no—
569C4—182no—
570C4—182no—
571C3—21no—
572C3C2×#566412yescomplemented
573C2—124no—
574C2—124no—
575C2#1059457014yesdirect product factor
576C2C2×#6430611yescharacteristic
577C2C2×#6431311yescharacteristic
578C2C2×#6431911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC2×#63914C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#559
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64096C2semidirect
2. C2×C3×#894C2semidirect
3. C2×#63915C2semidirect
4. C2×#63915C2semidirect
6. C2×#63913C2semidirect
7. C2×#63902C2semidirect
8. C2×C4×#625C2semidirect
9. C2×#63884C2semidirect
10. C2×#63879C2semidirect
11. C2×#63838C2semidirect
12. #10594570C2direct (N × H)
28. #64096C22semidirect
33. C3×#894C22semidirect
39. #63915C22semidirect
40. #63915C22semidirect
42. #63913C22semidirect
43. #63902C22semidirect
44. C4×#625C22semidirect
45. #63884C22semidirect
46. #63879C22semidirect
47. #63838C22semidirect
55. C2×#894D3semidirect
156. #894C2×D3semidirect
412. C2×C32#559semidirect
502. C32C2×#559semidirect
544. C2×C3#5664semidirect
572. C3C2×#5664semidirect
575. C2#10594570direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640962
C2×C3×#8942
C2×#639152
C2×#639142
C2×#639132
C2×#639022
C2×C4×#6252
C2×#638842
C2×#638792
C2×#638382
#105945702
C2×#56643