Finite Group Databasebeta

← C2×#10595266 #11910183

Subgroups — C2×#10595266 #11910183

Order 1152.

3019 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64146C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic, complemented
3C2×C3×#935C211yesmaximal, characteristic, complemented
4C2×#63981C212yesmaximal, complemented
5C2×#63978C212yesmaximal, complemented
6C2×#63971C212yesmaximal, complemented
7C2×#63969C212yesmaximal, complemented
8#10595266C2116yesmaximal, direct product factor
9C2×#63886C212yesmaximal, complemented
10C2×#63868C212yesmaximal, complemented
11C2×#5720—31nomaximal
12C2×#5666—31nomaximal
13C24×C3⋊D3C2211yescharacteristic
14C22×C32×D4C2211yescharacteristic
15C22×#638C2212yes—
16C22×C3×#67C2212yes—
17C22×C3×#67C2212yescomplemented
18C23×C3×Dic3C2211yescharacteristic, complemented
19C22×C3×D12C2211yescharacteristic, complemented
20C22×#626C2212yes—
21C22×#626C2212yes—
22C22×D3×Dic3C2212yescomplemented
23C2×#3757C2211yescharacteristic
24#64146C2218yescomplemented
25C2×#3752C2212yes—
26C2×C3×#217C2212yes—
27C2×C3×#217C2211yescharacteristic, complemented
28C3×#940C2218yescomplemented
29C3×#935C2218yescomplemented
30C2×C3×Dic3⋊C4C2212yescomplemented
31C2×C3×C4×Dic3C2211yescharacteristic, complemented
32#63981C22116yescomplemented
33#63978C22116yescomplemented
34#63971C22116yescomplemented
35#63969C22116yescomplemented
36C2×#3724C2212yescomplemented
37C2×Dic3⋊Dic3C2212yescomplemented
38C2×#3722C2212yes—
39C2×#3722C2212yes—
40C2×(C2×D3)⋊Dic3C2212yescomplemented
41#63886C22116yescomplemented
42#63868C22116yescomplemented
43C2×C3×#127—31no—
44C2×C3×#123—31no—
45C2×#940D311yescharacteristic, complemented
46C2×#939—32no—
47C2×#939—32no—
48C2×#939—32no—
49C2×#937—31no—
50C2×#937—31no—
51C2×#937—32no—
52C2×#937—61no—
53C2×#935—32no—
54C2×#935D311yescharacteristic, complemented
55C2×#930—32no—
56#5720—316no—
57#5666—316no—
58C2×#898—32no—
59C2×#895—32no—
60C2×#884—32no—
61C2×#883—32no—
62C2×#882—32no—
63C2×#876—32no—
64C24×C32C2311yescharacteristic
65C24×C32C2311yescharacteristic
66C23×C3⋊D3—44no—
67C23×C3⋊D3—42no—
68C23×C3⋊D3C2312yes—
69C23×C3⋊D3C2314yes—
70C23×C3×D3C2312yes—
71C2×C32×D4—42no—
72C2×C32×D4C2314yes—
73C22×C32×C4C2311yescharacteristic
74C2×#638—44no—
75C2×#638C2318yes—
76C22×C3⋊Dic3C2312yes—
77C2×C3×#67—44no—
78C2×C3×#67—44no—
79C2×C3×#67C2318yes—
80C2×C3×#67C2318yescomplemented
81C22×C3×Dic3—42no—
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2314yescomplemented
86C2×C3×D12—42no—
87C2×C3×D12C2314yescomplemented
88C2×#626—44no—
89C2×#626—44no—
90C2×#626C2318yes—
91C2×#626C2318yes—
92C2×D3×Dic3—44no—
93C2×D3×Dic3C2318yescomplemented
94#3757C2314yes—
95#3752C2318yes—
96C3×#217C2318yes—
97C3×#217C2314yescomplemented
98C3×Dic3⋊C4C2318yescomplemented
99C3×C4×Dic3C2314yescomplemented
100#3724C2318yescomplemented
101Dic3⋊Dic3C2318yescomplemented
102#3722C2318yes—
103#3722C2318yes—
104(C2×D3)⋊Dic3C2318yescomplemented
105C2×#560—91noSylow
106C24×D3—31no—
107C24×D3—31no—
108C24×D3—61no—
109C22×C3×D4—21no—
110C22×C3×D4—32no—
111C22×C3×D4—32no—
112C22×C3×D4—31no—
113C22×C3×D4C2×D311yescharacteristic
114C22×C3×D4C2×D311yescharacteristic
115C23×C3×C4—31no—
116C22×#67—32no—
117C22×#67—32no—
118C22×#67—32no—
119C22×#67—32no—
120C22×#67—62no—
121C22×#67C2×D312yes—
122C22×#67C2×D312yescomplemented
123C23×Dic3—32no—
124C23×Dic3C2×D311yescharacteristic, complemented
125C22×D12—32no—
126C22×D12—32no—
127C22×D12C2×D311yescharacteristic, complemented
128C22×C4×D3—32no—
129C3×#127—38no—
130C3×#123—38no—
131C2×C3×C4⋊C4—32no—
132C2×C3×C22⋊C4—32no—
133C2×C3×C22⋊C4—31no—
134C2×C3×C42—31no—
135C2×#217—31no—
136C2×#217—31no—
137C2×#217—32no—
138C2×#217—61no—
139C2×#217C2×D312yes—
140C2×#217C2×D311yescharacteristic, complemented
141#940C2×D318yescomplemented
142#939—316no—
143#939—316no—
144#939—316no—
145#937—38no—
146#937—38no—
147#937—316no—
148#937—68no—
149#935—316no—
150#935C2×D318yescomplemented
151#930—316no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4—32no—
154C2×(C2×D3)⋊C4—32no—
155C2×(C2×D3)⋊C4—32no—
156C2×(C2×D3)⋊C4—32no—
157C2×(C2×D3)⋊C4—32no—
158C2×(C2×D3)⋊C4—32no—
159C2×(C2×D3)⋊C4—62no—
160C2×C4⋊Dic3—32no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4—32no—
164C2×Dic3⋊C4C2×D312yescomplemented
165C2×C4×Dic3C2×D311yescharacteristic, complemented
166#898—316no—
167#895—316no—
168#884—316no—
169#883—316no—
170#882—316no—
171#876—316no—
172C23×C32—22no—
173C23×C32—24no—
174C23×C32—22no—
175C23×C32—24no—
176C23×C32C2412yes—
177C23×C32C2412yes—
178C23×C32C2411yescharacteristic
179C22×C3⋊D3—24no—
180C22×C3⋊D3—24no—
181C22×C3⋊D3—24no—
182C22×C3⋊D3—48no—
183C22×C3⋊D3—44no—
184C22×C3⋊D3—416no—
185C22×C3⋊D3C2414yes—
186C22×C3×D3—24no—
187C22×C3×D3—24no—
188C22×C3×D3—24no—
189C22×C3×D3C2414yes—
190C32×D4—44no—
191C2×C32×C4—22no—
192C2×C32×C4C2412yes—
193#638—48no—
194C2×C3⋊Dic3—24no—
195C2×C3⋊Dic3C2414yes—
196C3×#67—48no—
197C3×#67—48no—
198C2×C3×Dic3—24no—
199C2×C3×Dic3—24no—
200C2×C3×Dic3—24no—
201C2×C3×Dic3—44no—
202C2×C3×Dic3C2414yes—
203C2×C3×Dic3C2414yes—
204C2×C3×Dic3C2414yes—
205C3×D12—44no—
206#626—48no—
207#626—48no—
208D3×Dic3—48no—
209#560—916no—
210C2×#127—31no—
211C2×#126—92no—
212C2×#123—31no—
213C2×#123—92no—
214C2×#121—92no—
215C2×#121—92no—
216C2×#121—92no—
217C2×#120—92no—
218C2×#120—91no—
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—32no—
222C24×C3C22×D311yescharacteristic
223C24×C3C22×D311yescharacteristic
224C24×C3C22×D311yescharacteristic
225C24×C3C22×D311yescharacteristic
226C23×D3—32no—
227C23×D3—32no—
228C23×D3—34no—
229C23×D3—34no—
230C23×D3—62no—
231C23×D3—64no—
232C23×D3—122no—
233C23×D3—124no—
234C23×D3—122no—
235C23×D3—124no—
236C23×D3—128no—
237C23×D3—124no—
238C23×D3C22×D312yes—
239C2×C3×D4—24no—
240C2×C3×D4—38no—
241C2×C3×D4—38no—
242C2×C3×D4—34no—
243C2×C3×D4—42no—
244C2×C3×D4—42no—
245C2×C3×D4—44no—
246C2×C3×D4—122no—
247C2×C3×D4—124no—
248C2×C3×D4—124no—
249C2×C3×D4C22×D314yes—
250C2×C3×D4C22×D314yes—
251C22×C3×C4—21no—
252C22×C3×C4—32no—
253C22×C3×C4—32no—
254C22×C3×C4—32no—
255C22×C3×C4—34no—
256C22×C3×C4—122no—
257C22×C3×C4C22×D311yescharacteristic
258C22×C3×C4C22×D311yescharacteristic
259C2×#67—38no—
260C2×#67—38no—
261C2×#67—38no—
262C2×#67—38no—
263C2×#67—44no—
264C2×#67—44no—
265C2×#67—68no—
266C2×#67—124no—
267C2×#67—124no—
268C2×#67—124no—
269C2×#67—124no—
270C2×#67—128no—
271C2×#67C22×D318yes—
272C2×#67C22×D318yescomplemented
273C22×Dic3—32no—
274C22×Dic3—32no—
275C22×Dic3—38no—
276C22×Dic3—42no—
277C22×Dic3—62no—
278C22×Dic3—124no—
279C22×Dic3C22×D312yes—
280C22×Dic3C22×D312yes—
281C22×Dic3C22×D312yes—
282C22×Dic3C22×D314yescomplemented
283C2×D12—38no—
284C2×D12—38no—
285C2×D12—42no—
286C2×D12—124no—
287C2×D12—124no—
288C2×D12C22×D314yescomplemented
289C2×C4×D3—38no—
290C2×C4×D3—124no—
291C3×C4⋊C4—38no—
292C3×C22⋊C4—38no—
293C3×C22⋊C4—34no—
294C3×C42—34no—
295#217—34no—
296#217—34no—
297#217—38no—
298#217—64no—
299#217C22×D318yes—
300#217C22×D314yescomplemented
301(C2×D3)⋊C4—38no—
302(C2×D3)⋊C4—38no—
303(C2×D3)⋊C4—38no—
304(C2×D3)⋊C4—38no—
305(C2×D3)⋊C4—38no—
306(C2×D3)⋊C4—38no—
307(C2×D3)⋊C4—38no—
308(C2×D3)⋊C4—68no—
309C4⋊Dic3—38no—
310Dic3⋊C4—38no—
311Dic3⋊C4—38no—
312Dic3⋊C4—38no—
313Dic3⋊C4C22×D318yescomplemented
314C4×Dic3C22×D314yescomplemented
315C22×C32—22no—
316C22×C32—22no—
317C22×C32—24no—
318C22×C32—24no—
319C22×C32—44no—
320C22×C32—44no—
321C22×C32H(5,𝔽2)12yes—
322C22×C32H(5,𝔽2)14yes—
323C22×C32C2511yescharacteristic
324C2×C3⋊D3—24no—
325C2×C3⋊D3—24no—
326C2×C3⋊D3—24no—
327C2×C3⋊D3—416no—
328C2×C3⋊D3—48no—
329C2×C3×D3—24no—
330C2×C3×D3—24no—
331C2×C3×D3—24no—
332C2×C3×D3—48no—
333C32×C4—22no—
334C3⋊Dic3—24no—
335C3×Dic3—24no—
336C3×Dic3—24no—
337C3×Dic3—24no—
338C25—91no—
339C22×D4—32no—
340C22×D4—32no—
341C22×D4—31no—
342C22×D4—92no—
343C22×D4—92no—
344C22×D4—92no—
345C22×D4D3211yescharacteristic
346C23×C4—31no—
347C23×C4—92no—
348#127—38no—
349#126—916no—
350#123—38no—
351#123—916no—
352#121—916no—
353#121—916no—
354#121—916no—
355#120—916no—
356#120—98no—
357C2×C4⋊C4—32no—
358C2×C4⋊C4—92no—
359C2×C4⋊C4—92no—
360C2×C22⋊C4—32no—
361C2×C22⋊C4—31no—
362C2×C22⋊C4—92no—
363C2×C22⋊C4—92no—
364C2×C22⋊C4—92no—
365C2×C22⋊C4—91no—
366C2×C22⋊C4—92no—
367C2×C42—31no—
368C23×C3—24no—
369C23×C3—22no—
370C23×C3—24no—
371C23×C3—24no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—24no—
376C23×C3—24no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—21no—
380C23×C3—34no—
381C23×C3—44no—
382C23×C3—44no—
383C23×C3—42no—
384C23×C3—64no—
385C23×C3—64no—
386C23×C3—64no—
387C23×C3C23×D312yes—
388C23×C3C23×D312yes—
389C23×C3C23×D312yes—
390C23×C3C23×D312yes—
391C23×C3C23×D311yescharacteristic
392C23×C3C23×D311yescharacteristic
393C22×D3—24no—
394C22×D3—24no—
395C22×D3—24no—
396C22×D3—34no—
397C22×D3—34no—
398C22×D3—64no—
399C22×D3—68no—
400C22×D3—64no—
401C22×D3—64no—
402C22×D3—64no—
403C22×D3—64no—
404C22×D3—64no—
405C22×D3—64no—
406C22×D3—124no—
407C22×D3—124no—
408C22×D3—124no—
409C22×D3—128no—
410C22×D3—124no—
411C22×D3—128no—
412C22×D3—1216no—
413C22×D3—128no—
414C22×D3—1232no—
415C22×D3—1216no—
416C22×D3—1216no—
417C22×D3C23×D314yes—
418C3×D4—44no—
419C3×D4—44no—
420C3×D4—48no—
421C3×D4—124no—
422C3×D4—128no—
423C3×D4—128no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—34no—
428C2×C3×C4—34no—
429C2×C3×C4—34no—
430C2×C3×C4—42no—
431C2×C3×C4—64no—
432C2×C3×C4—64no—
433C2×C3×C4—64no—
434C2×C3×C4—124no—
435C2×C3×C4C23×D312yes—
436C2×C3×C4C23×D312yes—
437#67—48no—
438#67—48no—
439#67—128no—
440#67—128no—
441#67—128no—
442#67—128no—
443#67—1216no—
444C2×Dic3—24no—
445C2×Dic3—24no—
446C2×Dic3—24no—
447C2×Dic3—34no—
448C2×Dic3—34no—
449C2×Dic3—44no—
450C2×Dic3—64no—
451C2×Dic3—64no—
452C2×Dic3—64no—
453C2×Dic3—124no—
454C2×Dic3—128no—
455C2×Dic3C23×D314yes—
456C2×Dic3C23×D314yes—
457C2×Dic3C23×D314yes—
458D12—44no—
459D12—128no—
460D12—128no—
461C4×D3—128no—
462C2×C32—42no—
463C2×C32—42no—
464C2×C32#56014yescomplemented
465C2×C32C2×H(5,𝔽2)11yescharacteristic
466C2×C32C2×H(5,𝔽2)12yes—
467C3⋊D3—44no—
468C3×D3—44no—
469C24—32no—
470C24—92no—
471C24—94no—
472C24—364no—
473C24—362no—
474C24C2×D3211yescharacteristic
475C24C2×D3211yescharacteristic
476C2×D4—38no—
477C2×D4—38no—
478C2×D4—34no—
479C2×D4—42no—
480C2×D4—98no—
481C2×D4—98no—
482C2×D4—98no—
483C2×D4—122no—
484C2×D4—124no—
485C2×D4—124no—
486C2×D4—364no—
487C2×D4—364no—
488C2×D4—364no—
489C2×D4C2×D3214yes—
490C22×C4—32no—
491C22×C4—32no—
492C22×C4—32no—
493C22×C4—34no—
494C22×C4—98no—
495C22×C4—92no—
496C22×C4—122no—
497C22×C4—364no—
498C22×C4C2×D3211yescharacteristic
499C4⋊C4—38no—
500C4⋊C4—98no—
501C4⋊C4—98no—
502C22⋊C4—38no—
503C22⋊C4—34no—
504C22⋊C4—98no—
505C22⋊C4—98no—
506C22⋊C4—98no—
507C22⋊C4—94no—
508C22⋊C4—98no—
509C42—34no—
510C22×C3—24no—
511C22×C3—22no—
512C22×C3—24no—
513C22×C3—24no—
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—24no—
518C22×C3—24no—
519C22×C3—24no—
520C22×C3—22no—
521C22×C3—21no—
522C22×C3—44no—
523C22×C3—44no—
524C22×C3—42no—
525C22×C3—48no—
526C22×C3—44no—
527C22×C3—44no—
528C22×C3—44no—
529C22×C3—44no—
530C22×C3—64no—
531C22×C3—64no—
532C22×C3—64no—
533C22×C3—84no—
534C22×C3—128no—
535C22×C3#100414yes—
536C22×C3#100412yes—
537C22×C3#100412yes—
538C22×C3#100914yes—
539C22×C3C24×D311yescharacteristic
540C22×C3C24×D311yescharacteristic
541C2×D3—24no—
542C2×D3—24no—
543C2×D3—24no—
544C2×D3—48no—
545C2×D3—68no—
546C2×D3—64no—
547C2×D3—64no—
548C2×D3—64no—
549C2×D3—64no—
550C2×D3—64no—
551C2×D3—64no—
552C2×D3—124no—
553C2×D3—124no—
554C2×D3—1216no—
555C2×D3—1232no—
556C2×D3—1216no—
557C2×D3—1216no—
558C2×D3—128no—
559C2×D3—128no—
560C3×C4—22no—
561C3×C4—22no—
562C3×C4—42no—
563C3×C4—64no—
564C3×C4—64no—
565C3×C4—64no—
566Dic3—24no—
567Dic3—24no—
568Dic3—24no—
569Dic3—64no—
570Dic3—64no—
571Dic3—124no—
572C32C2×#56011yescharacteristic, complemented, Sylow
573C23—24no—
574C23—24no—
575C23—22no—
576C23—22no—
577C23—34no—
578C23—64no—
579C23—64no—
580C23—64no—
581C23—94no—
582C23—184no—
583C23—184no—
584C23—184no—
585C23—368no—
586C23—364no—
587C23—3616no—
588C23C22×D3212yes—
589C23C22×D3212yes—
590C23C22×D3211yescharacteristic
591D4—44no—
592D4—124no—
593D4—128no—
594D4—128no—
595D4—368no—
596D4—368no—
597D4—368no—
598C2×C4—22no—
599C2×C4—34no—
600C2×C4—34no—
601C2×C4—34no—
602C2×C4—64no—
603C2×C4—64no—
604C2×C4—64no—
605C2×C4—94no—
606C2×C4—124no—
607C2×C4—184no—
608C2×C4—368no—
609C2×C4C22×D3212yes—
610C2×C3—22no—
611C2×C3—21no—
612C2×C3—24no—
613C2×C3—44no—
614C2×C3—42no—
615C2×C3—42no—
616C2×C3—42no—
617C2×C3—42no—
618C2×C3—82no—
619C2×C3—124no—
620C2×C3#566614yescomplemented
621C2×C3#572014yescomplemented
622C2×C3C2×#100412yes—
623C2×C3C2×#100411yescharacteristic
624C2×C3C2×#100411yescharacteristic
625C2×C3C2×#100912yes—
626D3—44no—
627D3—128no—
628D3—124no—
629D3—124no—
630C22—24no—
631C22—24no—
632C22—22no—
633C22—22no—
634C22—44no—
635C22—44no—
636C22—64no—
637C22—64no—
638C22—64no—
639C22—128no—
640C22—184no—
641C22—184no—
642C22—184no—
643C22—3616no—
644C22—368no—
645C22#6431414yes—
646C22#6433012yes—
647C22C23×D3211yescharacteristic
648C4—22no—
649C4—64no—
650C4—64no—
651C4—64no—
652C4—184no—
653C3—21no—
654C3C2×#566611yescharacteristic, complemented
655C3C2×#572011yescharacteristic, complemented
656C2—42no—
657C2—42no—
658C2—124no—
659C2—364no—
660C2#1059526614yesdirect product factor
661C2C2×#6431412yes—
662C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#560
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64146C2semidirect
2. C2×C3×#940C2semidirect
3. C2×C3×#935C2semidirect
4. C2×#63981C2semidirect
5. C2×#63978C2semidirect
6. C2×#63971C2semidirect
7. C2×#63969C2semidirect
8. #10595266C2direct (N × H)
9. C2×#63886C2semidirect
10. C2×#63868C2semidirect
17. C22×C3×#67C22semidirect
18. C23×C3×Dic3C22semidirect
19. C22×C3×D12C22semidirect
22. C22×D3×Dic3C22semidirect
24. #64146C22semidirect
27. C2×C3×#217C22semidirect
28. C3×#940C22semidirect
29. C3×#935C22semidirect
30. C2×C3×Dic3⋊C4C22semidirect
31. C2×C3×C4×Dic3C22semidirect
32. #63981C22semidirect
33. #63978C22semidirect
34. #63971C22semidirect
35. #63969C22semidirect
36. C2×#3724C22semidirect
37. C2×Dic3⋊Dic3C22semidirect
40. C2×(C2×D3)⋊Dic3C22semidirect
41. #63886C22semidirect
42. #63868C22semidirect
45. C2×#940D3semidirect
54. C2×#935D3semidirect
80. C2×C3×#67C23semidirect
85. C22×C3×Dic3C23semidirect
87. C2×C3×D12C23semidirect
93. C2×D3×Dic3C23semidirect
97. C3×#217C23semidirect
98. C3×Dic3⋊C4C23semidirect
99. C3×C4×Dic3C23semidirect
100. #3724C23semidirect
101. Dic3⋊Dic3C23semidirect
104. (C2×D3)⋊Dic3C23semidirect
122. C22×#67C2×D3semidirect
124. C23×Dic3C2×D3semidirect
127. C22×D12C2×D3semidirect
140. C2×#217C2×D3semidirect
141. #940C2×D3semidirect
150. #935C2×D3semidirect
164. C2×Dic3⋊C4C2×D3semidirect
165. C2×C4×Dic3C2×D3semidirect
272. C2×#67C22×D3semidirect
282. C22×Dic3C22×D3semidirect
288. C2×D12C22×D3semidirect
300. #217C22×D3semidirect
313. Dic3⋊C4C22×D3semidirect
314. C4×Dic3C22×D3semidirect
464. C2×C32#560semidirect
572. C32C2×#560semidirect
620. C2×C3#5666semidirect
621. C2×C3#5720semidirect
654. C3C2×#5666semidirect
655. C3C2×#5720semidirect
660. C2#10595266direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641462
C2×C3×#9402
C2×C3×#9352
C2×#639812
C2×#639782
C2×#639712
C2×#639692
#105952662
C2×#638862
C2×#638682
C2×#57203
C2×#56663