Finite Group Databasebeta

← C2×#10595259 #11910184

Subgroups — C2×#10595259 #11910184

Order 1152.

2859 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64144C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic, complemented
3C2×C3×#937C211yesmaximal, characteristic, complemented
4C2×#63980C212yesmaximal, complemented
5C2×#63976C212yesmaximal, complemented
6C2×#63970C212yesmaximal, complemented
7C2×#63969C212yesmaximal, complemented
8#10595259C2116yesmaximal, direct product factor
9C2×#63885C212yesmaximal, complemented
10C2×#63859C212yesmaximal, complemented
11C2×#5720—31nomaximal
12C2×#5595—31nomaximal
13C24×C3×D3C2211yescharacteristic
14C22×C32×D4C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic, complemented
16C22×C3×#67C2212yes—
17C22×C3×#67C2212yes—
18C22×C3×#67C2212yescomplemented
19C22×C3×D12C2211yescharacteristic, complemented
20C22×#625C2212yes—
21C22×#625C2212yes—
22C22×D3×Dic3C2212yescomplemented
23C2×#3757C2212yes—
24C2×#3757C2211yescharacteristic, complemented
25#64144C2218yescomplemented
26C2×#3750C2212yescomplemented
27C2×C3×#217C2211yescharacteristic
28C3×#940C2218yescomplemented
29C3×#937C2218yescomplemented
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×C4×Dic3C2211yescharacteristic, complemented
32#63980C22116yescomplemented
33#63976C22116yescomplemented
34#63970C22116yescomplemented
35#63969C22116yescomplemented
36C2×#3724C2212yescomplemented
37C2×Dic3⋊Dic3C2212yescomplemented
38C2×(C2×D3)⋊Dic3C2212yes—
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yescomplemented
41#63885C22116yescomplemented
42#63859C22116yescomplemented
43C2×C3×#127—31no—
44C2×C3×#120—31no—
45C2×#953—32no—
46C2×#940D311yescharacteristic, complemented
47C2×#939—32no—
48C2×#939—32no—
49C2×#939—32no—
50C2×#939—32no—
51C2×#938—32no—
52C2×#937—32no—
53C2×#937D311yescharacteristic, complemented
54C2×#935—31no—
55C2×#935—31no—
56C2×#935—32no—
57C2×#935—61no—
58#5720—316no—
59#5595—316no—
60C2×#884—32no—
61C2×#883—32no—
62C2×#879—32no—
63C2×#876—32no—
64C24×C32C2311yescharacteristic
65C24×C32C2311yescharacteristic
66C23×C3×D3—42no—
67C23×C3×D3—44no—
68C23×C3×D3C2312yes—
69C23×C3×D3C2312yes—
70C23×C3×D3C2314yes—
71C2×C32×D4—42no—
72C2×C32×D4C2314yes—
73C22×C32×C4C2311yescharacteristic
74C22×C3⋊Dic3—42no—
75C22×C3⋊Dic3C2312yes—
76C22×C3⋊Dic3C2312yes—
77C22×C3⋊Dic3C2314yescomplemented
78C2×C3×#67—44no—
79C2×C3×#67—44no—
80C2×C3×#67—44no—
81C2×C3×#67C2318yes—
82C2×C3×#67C2318yes—
83C2×C3×#67C2318yescomplemented
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2312yes—
86C2×C3×D12—42no—
87C2×C3×D12C2314yescomplemented
88C2×#625—44no—
89C2×#625—44no—
90C2×#625C2318yes—
91C2×#625C2318yes—
92C2×D3×Dic3—44no—
93C2×D3×Dic3C2318yescomplemented
94#3757C2318yes—
95#3757C2314yescomplemented
96#3750C2318yescomplemented
97C3×#217C2314yes—
98C3×(C2×D3)⋊C4C2318yes—
99C3×C4×Dic3C2314yescomplemented
100#3724C2318yescomplemented
101Dic3⋊Dic3C2318yescomplemented
102(C2×D3)⋊Dic3C2318yes—
103(C2×D3)⋊Dic3C2318yes—
104(C2×D3)⋊Dic3C2318yescomplemented
105C2×#560—91noSylow
106C25×C3—31no—
107C24×D3C2×D311yescharacteristic
108C22×C3×D4—21no—
109C22×C3×D4—32no—
110C22×C3×D4—32no—
111C22×C3×D4—32no—
112C22×C3×D4—31no—
113C22×C3×D4C2×D311yescharacteristic
114C22×C3×D4C2×D311yescharacteristic
115C22×#67—32no—
116C22×#67—32no—
117C22×#67—32no—
118C22×#67—32no—
119C22×#67C2×D312yes—
120C22×#67C2×D312yes—
121C22×#67C2×D312yescomplemented
122C23×Dic3—31no—
123C23×Dic3—31no—
124C23×Dic3—32no—
125C23×Dic3—61no—
126C22×D12C2×D311yescharacteristic, complemented
127C22×C4×D3—32no—
128C3×#127—38no—
129C3×#120—38no—
130C2×C3×C22⋊C4—31no—
131C2×C3×C22⋊C4—32no—
132C2×C3×C42—31no—
133#953—316no—
134C2×#217—32no—
135C2×#217—32no—
136C2×#217—31no—
137C2×#217—31no—
138C2×#217—32no—
139C2×#217—32no—
140C2×#217—32no—
141C2×#217—62no—
142C2×#217—61no—
143C2×#217C2×D311yescharacteristic
144#940C2×D318yescomplemented
145#939—316no—
146#939—316no—
147#939—316no—
148#939—316no—
149#938—316no—
150#937—316no—
151#937C2×D318yescomplemented
152#935—38no—
153#935—38no—
154#935—316no—
155#935—68no—
156C2×(C2×D3)⋊C4—32no—
157C2×(C2×D3)⋊C4—32no—
158C2×(C2×D3)⋊C4—32no—
159C2×(C2×D3)⋊C4C2×D312yes—
160C2×C4⋊Dic3—32no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4—32no—
164C2×Dic3⋊C4—32no—
165C2×Dic3⋊C4—32no—
166C2×Dic3⋊C4—62no—
167C2×C4×Dic3C2×D311yescharacteristic, complemented
168#884—316no—
169#883—316no—
170#879—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—24no—
183C22×C3×D3—24no—
184C22×C3×D3—24no—
185C22×C3×D3—44no—
186C22×C3×D3—48no—
187C22×C3×D3—416no—
188C22×C3×D3C2414yes—
189C22×C3×D3C2414yes—
190C32×D4—44no—
191C2×C32×C4—22no—
192C2×C32×C4C2412yes—
193C2×C3⋊Dic3—24no—
194C2×C3⋊Dic3—24no—
195C2×C3⋊Dic3—44no—
196C2×C3⋊Dic3C2414yes—
197C2×C3⋊Dic3C2414yes—
198C3×#67—48no—
199C3×#67—48no—
200C3×#67—48no—
201C2×C3×Dic3—24no—
202C2×C3×Dic3—24no—
203C2×C3×Dic3C2414yes—
204C2×C3×Dic3C2414yes—
205C3×D12—44no—
206#625—48no—
207#625—48no—
208D3×Dic3—48no—
209#560—916no—
210C2×#127—31no—
211C2×#126—92no—
212C2×#123—92no—
213C2×#123—91no—
214C2×#121—92no—
215C2×#121—92no—
216C2×#121—92no—
217C2×#120—31no—
218C2×#120—92no—
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—32no—
222C24×C3—32no—
223C24×C3—34no—
224C24×C3—124no—
225C24×C3—122no—
226C24×C3C22×D311yescharacteristic
227C24×C3C22×D311yescharacteristic
228C24×C3C22×D311yescharacteristic
229C24×C3C22×D311yescharacteristic
230C23×D3—44no—
231C23×D3—42no—
232C23×D3C22×D312yes—
233C23×D3C22×D312yes—
234C23×D3C22×D314yes—
235C2×C3×D4—24no—
236C2×C3×D4—38no—
237C2×C3×D4—38no—
238C2×C3×D4—38no—
239C2×C3×D4—34no—
240C2×C3×D4—42no—
241C2×C3×D4—42no—
242C2×C3×D4—44no—
243C2×C3×D4—122no—
244C2×C3×D4—124no—
245C2×C3×D4—124no—
246C2×C3×D4—124no—
247C2×C3×D4C22×D314yes—
248C2×C3×D4C22×D314yes—
249C22×C3×C4—21no—
250C22×C3×C4—32no—
251C22×C3×C4—32no—
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C2×#67—38no—
255C2×#67—38no—
256C2×#67—38no—
257C2×#67—38no—
258C2×#67—44no—
259C2×#67—44no—
260C2×#67—44no—
261C2×#67—124no—
262C2×#67—124no—
263C2×#67—124no—
264C2×#67—124no—
265C2×#67C22×D318yes—
266C2×#67C22×D318yes—
267C2×#67C22×D318yescomplemented
268C22×Dic3—32no—
269C22×Dic3—32no—
270C22×Dic3—32no—
271C22×Dic3—32no—
272C22×Dic3—34no—
273C22×Dic3—34no—
274C22×Dic3—38no—
275C22×Dic3—62no—
276C22×Dic3—62no—
277C22×Dic3—64no—
278C22×Dic3—124no—
279C22×Dic3—122no—
280C22×Dic3—122no—
281C22×Dic3—124no—
282C22×Dic3C22×D312yes—
283C22×Dic3C22×D312yes—
284C2×D12—42no—
285C2×D12C22×D314yescomplemented
286C2×C4×D3—38no—
287C2×C4×D3—124no—
288C3×C22⋊C4—34no—
289C3×C22⋊C4—38no—
290C3×C42—34no—
291#217—38no—
292#217—38no—
293#217—34no—
294#217—34no—
295#217—38no—
296#217—38no—
297#217—38no—
298#217—68no—
299#217—64no—
300#217C22×D314yes—
301(C2×D3)⋊C4—38no—
302(C2×D3)⋊C4—38no—
303(C2×D3)⋊C4—38no—
304(C2×D3)⋊C4C22×D318yes—
305C4⋊Dic3—38no—
306Dic3⋊C4—38no—
307Dic3⋊C4—38no—
308Dic3⋊C4—38no—
309Dic3⋊C4—38no—
310Dic3⋊C4—38no—
311Dic3⋊C4—68no—
312C4×Dic3C22×D314yescomplemented
313C22×C32—22no—
314C22×C32—24no—
315C22×C32—24no—
316C22×C32—22no—
317C22×C32—44no—
318C22×C32—44no—
319C22×C32H(5,𝔽2)14yes—
320C22×C32H(5,𝔽2)12yes—
321C22×C32C2511yescharacteristic
322C2×C3×D3—24no—
323C2×C3×D3—24no—
324C2×C3×D3—24no—
325C2×C3×D3—24no—
326C2×C3×D3—24no—
327C2×C3×D3—24no—
328C2×C3×D3—416no—
329C2×C3×D3—48no—
330C2×C3×D3—48no—
331C32×C4—22no—
332C3⋊Dic3—24no—
333C3⋊Dic3—24no—
334C3×Dic3—24no—
335C3×Dic3—24no—
336C25—31no—
337C22×D4—32no—
338C22×D4—32no—
339C22×D4—32no—
340C22×D4—31no—
341C22×D4—92no—
342C22×D4—92no—
343C22×D4D3211yescharacteristic
344C23×C4—92no—
345C23×C4—91no—
346#127—38no—
347#126—916no—
348#123—916no—
349#123—98no—
350#121—916no—
351#121—916no—
352#121—916no—
353#120—38no—
354#120—916no—
355C2×C4⋊C4—92no—
356C2×C4⋊C4—92no—
357C2×C4⋊C4—92no—
358C2×C22⋊C4—31no—
359C2×C22⋊C4—32no—
360C2×C22⋊C4—92no—
361C2×C22⋊C4—92no—
362C2×C22⋊C4—92no—
363C2×C22⋊C4—92no—
364C2×C22⋊C4—91no—
365C2×C42—31no—
366C23×C3—24no—
367C23×C3—22no—
368C23×C3—22no—
369C23×C3—24no—
370C23×C3—24no—
371C23×C3—24no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—24no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—21no—
378C23×C3—34no—
379C23×C3—34no—
380C23×C3—44no—
381C23×C3—42no—
382C23×C3—44no—
383C23×C3—64no—
384C23×C3—64no—
385C23×C3—64no—
386C23×C3—64no—
387C23×C3—64no—
388C23×C3—64no—
389C23×C3—128no—
390C23×C3—124no—
391C23×C3—1216no—
392C23×C3C23×D312yes—
393C23×C3C23×D312yes—
394C23×C3C23×D312yes—
395C23×C3C23×D312yes—
396C23×C3C23×D311yescharacteristic
397C23×C3C23×D311yescharacteristic
398C22×D3—24no—
399C22×D3—24no—
400C22×D3—24no—
401C22×D3—24no—
402C22×D3—24no—
403C22×D3—24no—
404C22×D3—48no—
405C22×D3—44no—
406C22×D3—416no—
407C22×D3C23×D314yes—
408C22×D3C23×D314yes—
409C3×D4—44no—
410C3×D4—44no—
411C3×D4—48no—
412C3×D4—124no—
413C3×D4—128no—
414C3×D4—128no—
415C3×D4—128no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—34no—
420C2×C3×C4—34no—
421C2×C3×C4—42no—
422C2×C3×C4—64no—
423C2×C3×C4—64no—
424C2×C3×C4C23×D312yes—
425C2×C3×C4C23×D312yes—
426#67—48no—
427#67—48no—
428#67—48no—
429#67—128no—
430#67—128no—
431#67—128no—
432#67—128no—
433C2×Dic3—24no—
434C2×Dic3—24no—
435C2×Dic3—34no—
436C2×Dic3—34no—
437C2×Dic3—34no—
438C2×Dic3—34no—
439C2×Dic3—64no—
440C2×Dic3—64no—
441C2×Dic3—64no—
442C2×Dic3—64no—
443C2×Dic3—64no—
444C2×Dic3—64no—
445C2×Dic3—124no—
446C2×Dic3—124no—
447C2×Dic3—128no—
448C2×Dic3—124no—
449C2×Dic3—124no—
450C2×Dic3—128no—
451C2×Dic3C23×D314yes—
452C2×Dic3C23×D314yes—
453D12—44no—
454C4×D3—128no—
455C2×C32—42no—
456C2×C32—42no—
457C2×C32#56014yescomplemented
458C2×C32C2×H(5,𝔽2)12yes—
459C2×C32C2×H(5,𝔽2)11yescharacteristic
460C3×D3—44no—
461C3×D3—44no—
462C24—32no—
463C24—32no—
464C24—34no—
465C24—124no—
466C24—122no—
467C24C2×D3211yescharacteristic
468C24C2×D3211yescharacteristic
469C2×D4—38no—
470C2×D4—38no—
471C2×D4—38no—
472C2×D4—34no—
473C2×D4—42no—
474C2×D4—98no—
475C2×D4—98no—
476C2×D4—122no—
477C2×D4—124no—
478C2×D4—124no—
479C2×D4—124no—
480C2×D4—364no—
481C2×D4—364no—
482C2×D4C2×D3214yes—
483C22×C4—32no—
484C22×C4—32no—
485C22×C4—98no—
486C22×C4—92no—
487C22×C4—92no—
488C22×C4—94no—
489C22×C4—364no—
490C22×C4—362no—
491C22×C4C2×D3211yescharacteristic
492C4⋊C4—98no—
493C4⋊C4—98no—
494C4⋊C4—98no—
495C22⋊C4—34no—
496C22⋊C4—38no—
497C22⋊C4—98no—
498C22⋊C4—98no—
499C22⋊C4—98no—
500C22⋊C4—98no—
501C22⋊C4—94no—
502C42—34no—
503C22×C3—24no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—24no—
507C22×C3—24no—
508C22×C3—24no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—24no—
512C22×C3—24no—
513C22×C3—22no—
514C22×C3—21no—
515C22×C3—44no—
516C22×C3—42no—
517C22×C3—44no—
518C22×C3—48no—
519C22×C3—44no—
520C22×C3—44no—
521C22×C3—44no—
522C22×C3—44no—
523C22×C3—64no—
524C22×C3—64no—
525C22×C3—64no—
526C22×C3—64no—
527C22×C3—64no—
528C22×C3—64no—
529C22×C3—84no—
530C22×C3—1216no—
531C22×C3—128no—
532C22×C3—128no—
533C22×C3#100414yes—
534C22×C3#100414yes—
535C22×C3#100412yes—
536C22×C3#100412yes—
537C22×C3C24×D311yescharacteristic
538C22×C3C24×D311yescharacteristic
539C2×D3—24no—
540C2×D3—24no—
541C2×D3—24no—
542C2×D3—24no—
543C2×D3—24no—
544C2×D3—24no—
545C2×D3—416no—
546C2×D3—48no—
547C2×D3—48no—
548C3×C4—22no—
549C3×C4—22no—
550C3×C4—42no—
551C3×C4—64no—
552C3×C4—64no—
553Dic3—24no—
554Dic3—24no—
555Dic3—64no—
556Dic3—64no—
557Dic3—64no—
558Dic3—64no—
559Dic3—124no—
560Dic3—124no—
561C32C2×#56011yescharacteristic, complemented, Sylow
562C23—24no—
563C23—24no—
564C23—22no—
565C23—22no—
566C23—34no—
567C23—34no—
568C23—64no—
569C23—64no—
570C23—64no—
571C23—64no—
572C23—64no—
573C23—64no—
574C23—128no—
575C23—124no—
576C23—1216no—
577C23C22×D3212yes—
578C23C22×D3212yes—
579C23C22×D3211yescharacteristic
580D4—44no—
581D4—124no—
582D4—128no—
583D4—128no—
584D4—128no—
585D4—368no—
586D4—368no—
587C2×C4—22no—
588C2×C4—34no—
589C2×C4—34no—
590C2×C4—64no—
591C2×C4—64no—
592C2×C4—94no—
593C2×C4—94no—
594C2×C4—184no—
595C2×C4—184no—
596C2×C4—368no—
597C2×C4—364no—
598C2×C4C22×D3212yes—
599C2×C3—22no—
600C2×C3—21no—
601C2×C3—24no—
602C2×C3—44no—
603C2×C3—42no—
604C2×C3—42no—
605C2×C3—42no—
606C2×C3—42no—
607C2×C3—82no—
608C2×C3—124no—
609C2×C3—124no—
610C2×C3#559514yescomplemented
611C2×C3#572014yescomplemented
612C2×C3C2×#100412yes—
613C2×C3C2×#100412yes—
614C2×C3C2×#100411yescharacteristic
615C2×C3C2×#100411yescharacteristic
616D3—44no—
617D3—44no—
618C22—24no—
619C22—24no—
620C22—22no—
621C22—22no—
622C22—44no—
623C22—44no—
624C22—64no—
625C22—64no—
626C22—64no—
627C22—64no—
628C22—64no—
629C22—64no—
630C22—1216no—
631C22—128no—
632C22—128no—
633C22#6431314yes—
634C22#6433012yes—
635C22C23×D3211yescharacteristic
636C4—22no—
637C4—64no—
638C4—64no—
639C4—184no—
640C4—184no—
641C3—21no—
642C3C2×#559511yescharacteristic, complemented
643C3C2×#572011yescharacteristic, complemented
644C2—42no—
645C2—42no—
646C2—124no—
647C2—124no—
648C2#1059525914yesdirect product factor
649C2C2×#6431312yes—
650C2C2×#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×#64144C2semidirect
2. C2×C3×#940C2semidirect
3. C2×C3×#937C2semidirect
4. C2×#63980C2semidirect
5. C2×#63976C2semidirect
6. C2×#63970C2semidirect
7. C2×#63969C2semidirect
8. #10595259C2direct (N × H)
9. C2×#63885C2semidirect
10. C2×#63859C2semidirect
15. C23×C3⋊Dic3C22semidirect
18. C22×C3×#67C22semidirect
19. C22×C3×D12C22semidirect
22. C22×D3×Dic3C22semidirect
24. C2×#3757C22semidirect
25. #64144C22semidirect
26. C2×#3750C22semidirect
28. C3×#940C22semidirect
29. C3×#937C22semidirect
31. C2×C3×C4×Dic3C22semidirect
32. #63980C22semidirect
33. #63976C22semidirect
34. #63970C22semidirect
35. #63969C22semidirect
36. C2×#3724C22semidirect
37. C2×Dic3⋊Dic3C22semidirect
40. C2×(C2×D3)⋊Dic3C22semidirect
41. #63885C22semidirect
42. #63859C22semidirect
46. C2×#940D3semidirect
53. C2×#937D3semidirect
77. C22×C3⋊Dic3C23semidirect
83. C2×C3×#67C23semidirect
87. C2×C3×D12C23semidirect
93. C2×D3×Dic3C23semidirect
95. #3757C23semidirect
96. #3750C23semidirect
99. C3×C4×Dic3C23semidirect
100. #3724C23semidirect
101. Dic3⋊Dic3C23semidirect
104. (C2×D3)⋊Dic3C23semidirect
121. C22×#67C2×D3semidirect
126. C22×D12C2×D3semidirect
144. #940C2×D3semidirect
151. #937C2×D3semidirect
167. C2×C4×Dic3C2×D3semidirect
267. C2×#67C22×D3semidirect
285. C2×D12C22×D3semidirect
312. C4×Dic3C22×D3semidirect
457. C2×C32#560semidirect
561. C32C2×#560semidirect
610. C2×C3#5595semidirect
611. C2×C3#5720semidirect
642. C3C2×#5595semidirect
643. C3C2×#5720semidirect
648. C2#10595259direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641442
C2×C3×#9402
C2×C3×#9372
C2×#639802
C2×#639762
C2×#639702
C2×#639692
#105952592
C2×#638852
C2×#638592
C2×#57203
C2×#55953