Finite Group Databasebeta

← C2×#10595261 #11910182

Subgroups — C2×#10595261 #11910182

Order 1152.

2937 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64149C211yesmaximal, characteristic, complemented
2C2×C3×#937C211yesmaximal, characteristic, complemented
3C2×C3×#935C211yesmaximal, characteristic, complemented
4C2×#63978C212yesmaximal, complemented
5C2×#63977C212yesmaximal, complemented
6C2×#63975C212yesmaximal, complemented
7C2×#63958C212yesmaximal, complemented
8#10595261C2116yesmaximal, direct product factor
9C2×#63910C212yesmaximal, complemented
10C2×#63862C212yesmaximal, complemented
11C2×#5666—31nomaximal
12C2×#5595—31nomaximal
13C24×C3×D3C2211yescharacteristic
14C22×C32×D4C2211yescharacteristic
15C22×#638C2212yes—
16C22×#638C2212yescomplemented
17C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
18C22×C3×#67C2212yes—
19C23×C3×Dic3C2211yescharacteristic, complemented
20C22×#626C2212yes—
21C22×#626C2212yes—
22C22×#624C2212yescomplemented
23#64149C2218yescomplemented
24C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
25C2×C3×#217C2212yes—
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic, complemented
28C3×#937C2218yescomplemented
29C3×#935C2218yescomplemented
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×Dic3⋊C4C2212yescomplemented
32#63978C22116yescomplemented
33#63977C22116yescomplemented
34#63975C22116yescomplemented
35C2×Dic3⋊Dic3C2212yescomplemented
36C2×Dic3⋊Dic3C2212yescomplemented
37C2×#3722C2212yescomplemented
38C2×(C2×D3)⋊Dic3C2212yes—
39C2×(C2×D3)⋊Dic3C2212yes—
40#63958C22116yescomplemented
41#63910C22116yescomplemented
42#63862C22116yescomplemented
43C2×C3×#123—31no—
44C2×C3×#120—31no—
45C2×#953—32no—
46C2×#940—31no—
47C2×#940—31no—
48C2×#940—61no—
49C2×#939—32no—
50C2×#938—32no—
51C2×#937D311yescharacteristic, complemented
52C2×#935D311yescharacteristic, complemented
53C2×#930—32no—
54#5666—316no—
55#5595—316no—
56C2×#898—32no—
57C2×#895—32no—
58C2×#884—32no—
59C2×#884—32no—
60C2×#883—32no—
61C2×#883—32no—
62C2×#882—32no—
63C2×#879—32no—
64C24×C32C2311yescharacteristic
65C24×C32C2311yescharacteristic
66C23×C3⋊D3C2312yes—
67C23×C3×D3—42no—
68C23×C3×D3—44no—
69C23×C3×D3C2312yes—
70C23×C3×D3C2314yes—
71C2×C32×D4—42no—
72C2×C32×D4C2314yes—
73C22×C32×C4C2311yescharacteristic
74C2×#638—44no—
75C2×#638—44no—
76C2×#638C2318yes—
77C2×#638C2318yescomplemented
78C22×C3⋊Dic3C2312yes—
79C2×C4⋊(C3⋊D3)—42no—
80C2×C4⋊(C3⋊D3)C2314yescomplemented
81C2×C3×#67—44no—
82C2×C3×#67C2318yes—
83C22×C3×Dic3—42no—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2314yescomplemented
88C2×#626—44no—
89C2×#626—44no—
90C2×#626C2318yes—
91C2×#626C2318yes—
92C2×#624—44no—
93C2×#624C2318yescomplemented
94C4×C3⋊Dic3C2314yescomplemented
95C3×#217C2318yes—
96C3×#217C2314yes—
97C3×#217C2314yescomplemented
98C3×(C2×D3)⋊C4C2318yes—
99C3×Dic3⋊C4C2318yescomplemented
100Dic3⋊Dic3C2318yescomplemented
101Dic3⋊Dic3C2318yescomplemented
102#3722C2318yescomplemented
103(C2×D3)⋊Dic3C2318yes—
104(C2×D3)⋊Dic3C2318yes—
105C2×#560—91noSylow
106C25×C3—31no—
107C24×D3C2×D311yescharacteristic
108C22×C3×D4—21no—
109C22×C3×D4—32no—
110C22×C3×D4C2×D311yescharacteristic
111C22×C3×D4C2×D311yescharacteristic
112C23×C3×C4—31no—
113C22×#67—32no—
114C22×#67—32no—
115C22×#67—32no—
116C22×#67—32no—
117C22×#67—32no—
118C22×#67—32no—
119C22×#67—62no—
120C22×#67—62no—
121C22×#67C2×D312yes—
122C23×Dic3C2×D311yescharacteristic, complemented
123C22×D12—32no—
124C22×D12—32no—
125C22×D12—31no—
126C22×D12—31no—
127C22×D12—61no—
128C22×C4×D3—32no—
129C22×C4×D3—32no—
130C3×#123—38no—
131C3×#120—38no—
132C2×C3×C4⋊C4—32no—
133C2×C3×C22⋊C4—32no—
134C2×C3×C22⋊C4—31no—
135C2×C3×C22⋊C4—31no—
136C2×C3×C22⋊C4—32no—
137#953—316no—
138C2×#217—32no—
139C2×#217—32no—
140C2×#217C2×D311yescharacteristic
141C2×#217C2×D312yes—
142C2×#217C2×D311yescharacteristic, complemented
143#940—38no—
144#940—38no—
145#940—68no—
146#939—316no—
147#938—316no—
148#937C2×D318yescomplemented
149#935C2×D318yescomplemented
150#930—316no—
151C2×(C2×D3)⋊C4—32no—
152C2×(C2×D3)⋊C4—32no—
153C2×(C2×D3)⋊C4—32no—
154C2×(C2×D3)⋊C4—32no—
155C2×(C2×D3)⋊C4C2×D312yes—
156C2×C4⋊Dic3—32no—
157C2×C4⋊Dic3—32no—
158C2×Dic3⋊C4—32no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4C2×D312yescomplemented
161C2×C4×Dic3—31no—
162C2×C4×Dic3—31no—
163C2×C4×Dic3—61no—
164#898—316no—
165#895—316no—
166#884—316no—
167#884—316no—
168#883—316no—
169#883—316no—
170#882—316no—
171#879—316no—
172C23×C32—24no—
173C23×C32—22no—
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⋊D3C2414yes—
183C22×C3×D3—24no—
184C22×C3×D3—24no—
185C22×C3×D3—24no—
186C22×C3×D3—44no—
187C22×C3×D3—48no—
188C22×C3×D3—416no—
189C22×C3×D3C2414yes—
190C32×D4—44no—
191C2×C32×C4—22no—
192C2×C32×C4C2412yes—
193#638—48no—
194#638—48no—
195C2×C3⋊Dic3—24no—
196C2×C3⋊Dic3C2414yes—
197C4⋊(C3⋊D3)—44no—
198C3×#67—48no—
199C2×C3×Dic3—24no—
200C2×C3×Dic3—24no—
201C2×C3×Dic3—24no—
202C2×C3×Dic3—44no—
203C2×C3×Dic3C2414yes—
204C2×C3×Dic3C2414yes—
205C2×C3×Dic3C2414yes—
206#626—48no—
207#626—48no—
208#624—48no—
209#560—916no—
210C2×#127—91no—
211C2×#126—92no—
212C2×#123—31no—
213C2×#123—92no—
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—34no—
223C24×C3—122no—
224C24×C3—124no—
225C24×C3C22×D311yescharacteristic
226C24×C3C22×D311yescharacteristic
227C24×C3C22×D311yescharacteristic
228C24×C3C22×D311yescharacteristic
229C23×D3—32no—
230C23×D3—32no—
231C23×D3—42no—
232C23×D3—44no—
233C23×D3—62no—
234C23×D3C22×D312yes—
235C23×D3C22×D314yes—
236C2×C3×D4—24no—
237C2×C3×D4—38no—
238C2×C3×D4—42no—
239C2×C3×D4—42no—
240C2×C3×D4—44no—
241C2×C3×D4—124no—
242C2×C3×D4C22×D314yes—
243C2×C3×D4C22×D314yes—
244C22×C3×C4—21no—
245C22×C3×C4—32no—
246C22×C3×C4—32no—
247C22×C3×C4—32no—
248C22×C3×C4—34no—
249C22×C3×C4—122no—
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C2×#67—38no—
253C2×#67—38no—
254C2×#67—38no—
255C2×#67—38no—
256C2×#67—38no—
257C2×#67—38no—
258C2×#67—44no—
259C2×#67—68no—
260C2×#67—68no—
261C2×#67—124no—
262C2×#67—124no—
263C2×#67—124no—
264C2×#67—124no—
265C2×#67—124no—
266C2×#67—124no—
267C2×#67—128no—
268C2×#67—128no—
269C2×#67C22×D318yes—
270C22×Dic3—32no—
271C22×Dic3—32no—
272C22×Dic3—42no—
273C22×Dic3—62no—
274C22×Dic3C22×D312yes—
275C22×Dic3C22×D312yes—
276C22×Dic3C22×D312yes—
277C22×Dic3C22×D314yescomplemented
278C2×D12—38no—
279C2×D12—38no—
280C2×D12—34no—
281C2×D12—34no—
282C2×D12—64no—
283C2×D12—122no—
284C2×D12—122no—
285C2×D12—124no—
286C2×D12—124no—
287C2×D12—124no—
288C2×C4×D3—38no—
289C2×C4×D3—38no—
290C2×C4×D3—124no—
291C2×C4×D3—124no—
292C3×C4⋊C4—38no—
293C3×C22⋊C4—38no—
294C3×C22⋊C4—34no—
295C3×C22⋊C4—34no—
296C3×C22⋊C4—38no—
297#217—38no—
298#217—38no—
299#217C22×D314yes—
300#217C22×D318yes—
301#217C22×D314yescomplemented
302(C2×D3)⋊C4—38no—
303(C2×D3)⋊C4—38no—
304(C2×D3)⋊C4—38no—
305(C2×D3)⋊C4—38no—
306(C2×D3)⋊C4C22×D318yes—
307C4⋊Dic3—38no—
308C4⋊Dic3—38no—
309Dic3⋊C4—38no—
310Dic3⋊C4—38no—
311Dic3⋊C4C22×D318yescomplemented
312C4×Dic3—34no—
313C4×Dic3—34no—
314C4×Dic3—64no—
315C22×C32—22no—
316C22×C32—24no—
317C22×C32—24no—
318C22×C32—22no—
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—48no—
328C2×C3×D3—24no—
329C2×C3×D3—24no—
330C2×C3×D3—24no—
331C2×C3×D3—416no—
332C2×C3×D3—48no—
333C32×C4—22no—
334C3⋊Dic3—24no—
335C3×Dic3—24no—
336C3×Dic3—24no—
337C3×Dic3—24no—
338C25—31no—
339C22×D4—32no—
340C22×D4—92no—
341C22×D4—92no—
342C22×D4—92no—
343C22×D4—92no—
344C22×D4—91no—
345C22×D4D3211yescharacteristic
346C23×C4—31no—
347C23×C4—92no—
348#127—98no—
349#126—916no—
350#123—38no—
351#123—916no—
352#121—916no—
353#121—916no—
354#121—916no—
355#120—38no—
356#120—916no—
357C2×C4⋊C4—32no—
358C2×C4⋊C4—92no—
359C2×C4⋊C4—92no—
360C2×C22⋊C4—31no—
361C2×C22⋊C4—32no—
362C2×C22⋊C4—31no—
363C2×C22⋊C4—32no—
364C2×C22⋊C4—92no—
365C2×C22⋊C4—92no—
366C2×C22⋊C4—92no—
367C2×C42—91no—
368C23×C3—22no—
369C23×C3—24no—
370C23×C3—24no—
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—24no—
375C23×C3—24no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—21no—
379C23×C3—34no—
380C23×C3—44no—
381C23×C3—44no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—64no—
385C23×C3—64no—
386C23×C3—64no—
387C23×C3—124no—
388C23×C3—128no—
389C23×C3—1216no—
390C23×C3C23×D312yes—
391C23×C3C23×D312yes—
392C23×C3C23×D312yes—
393C23×C3C23×D312yes—
394C23×C3C23×D311yescharacteristic
395C23×C3C23×D311yescharacteristic
396C22×D3—24no—
397C22×D3—24no—
398C22×D3—24no—
399C22×D3—34no—
400C22×D3—34no—
401C22×D3—44no—
402C22×D3—48no—
403C22×D3—416no—
404C22×D3—64no—
405C22×D3—64no—
406C22×D3—64no—
407C22×D3—64no—
408C22×D3—64no—
409C22×D3—64no—
410C22×D3—64no—
411C22×D3—124no—
412C22×D3—124no—
413C22×D3—124no—
414C22×D3C23×D314yes—
415C3×D4—44no—
416C3×D4—44no—
417C3×D4—48no—
418C3×D4—128no—
419C2×C3×C4—24no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—34no—
424C2×C3×C4—34no—
425C2×C3×C4—34no—
426C2×C3×C4—64no—
427C2×C3×C4—64no—
428C2×C3×C4—64no—
429C2×C3×C4—124no—
430C2×C3×C4C23×D312yes—
431C2×C3×C4C23×D312yes—
432#67—48no—
433#67—128no—
434#67—128no—
435#67—128no—
436#67—128no—
437#67—128no—
438#67—128no—
439#67—1216no—
440#67—1216no—
441C2×Dic3—24no—
442C2×Dic3—24no—
443C2×Dic3—24no—
444C2×Dic3—34no—
445C2×Dic3—34no—
446C2×Dic3—44no—
447C2×Dic3—64no—
448C2×Dic3—68no—
449C2×Dic3—64no—
450C2×Dic3—64no—
451C2×Dic3C23×D314yes—
452C2×Dic3C23×D314yes—
453C2×Dic3C23×D314yes—
454D12—124no—
455D12—124no—
456D12—128no—
457D12—128no—
458D12—128no—
459C4×D3—128no—
460C4×D3—128no—
461C2×C32—42no—
462C2×C32—42no—
463C2×C32#56014yescomplemented
464C2×C32C2×H(5,𝔽2)11yescharacteristic
465C2×C32C2×H(5,𝔽2)12yes—
466C3⋊D3—44no—
467C3×D3—44no—
468C24—32no—
469C24—34no—
470C24—92no—
471C24—124no—
472C24—122no—
473C24C2×D3211yescharacteristic
474C24C2×D3211yescharacteristic
475C2×D4—38no—
476C2×D4—42no—
477C2×D4—98no—
478C2×D4—98no—
479C2×D4—98no—
480C2×D4—98no—
481C2×D4—94no—
482C2×D4—124no—
483C2×D4—362no—
484C2×D4—364no—
485C2×D4—364no—
486C2×D4—364no—
487C2×D4—364no—
488C2×D4C2×D3214yes—
489C22×C4—32no—
490C22×C4—32no—
491C22×C4—32no—
492C22×C4—34no—
493C22×C4—98no—
494C22×C4—92no—
495C22×C4—122no—
496C22×C4—364no—
497C22×C4C2×D3211yescharacteristic
498C4⋊C4—38no—
499C4⋊C4—98no—
500C4⋊C4—98no—
501C22⋊C4—34no—
502C22⋊C4—38no—
503C22⋊C4—34no—
504C22⋊C4—38no—
505C22⋊C4—98no—
506C22⋊C4—98no—
507C22⋊C4—98no—
508C42—94no—
509C22×C3—22no—
510C22×C3—24no—
511C22×C3—24no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—24no—
516C22×C3—24no—
517C22×C3—24no—
518C22×C3—22no—
519C22×C3—21no—
520C22×C3—44no—
521C22×C3—44no—
522C22×C3—42no—
523C22×C3—42no—
524C22×C3—44no—
525C22×C3—44no—
526C22×C3—44no—
527C22×C3—44no—
528C22×C3—64no—
529C22×C3—64no—
530C22×C3—64no—
531C22×C3—84no—
532C22×C3—84no—
533C22×C3—1216no—
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—416no—
545C2×D3—48no—
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—124no—
555C2×D3—128no—
556C2×D3—128no—
557C2×D3—248no—
558C3×C4—24no—
559C3×C4—22no—
560C3×C4—22no—
561C3×C4—64no—
562C3×C4—64no—
563C3×C4—64no—
564Dic3—24no—
565Dic3—24no—
566Dic3—24no—
567Dic3—68no—
568Dic3—64no—
569Dic3—64no—
570C32C2×#56011yescharacteristic, complemented, Sylow
571C23—24no—
572C23—24no—
573C23—22no—
574C23—22no—
575C23—34no—
576C23—64no—
577C23—64no—
578C23—64no—
579C23—94no—
580C23—128no—
581C23—124no—
582C23—1216no—
583C23—184no—
584C23—184no—
585C23—184no—
586C23C22×D3212yes—
587C23C22×D3212yes—
588C23C22×D3211yescharacteristic
589D4—44no—
590D4—128no—
591D4—364no—
592D4—368no—
593D4—368no—
594D4—368no—
595D4—368no—
596C2×C4—22no—
597C2×C4—34no—
598C2×C4—34no—
599C2×C4—34no—
600C2×C4—64no—
601C2×C4—64no—
602C2×C4—64no—
603C2×C4—94no—
604C2×C4—124no—
605C2×C4—184no—
606C2×C4—368no—
607C2×C4C22×D3212yes—
608C2×C3—22no—
609C2×C3—21no—
610C2×C3—24no—
611C2×C3—42no—
612C2×C3—42no—
613C2×C3—42no—
614C2×C3—42no—
615C2×C3—82no—
616C2×C3—82no—
617C2×C3—124no—
618C2×C3#559514yescomplemented
619C2×C3#566614yescomplemented
620C2×C3C2×#100412yes—
621C2×C3C2×#100411yescharacteristic
622C2×C3C2×#100411yescharacteristic
623C2×C3C2×#100912yes—
624D3—44no—
625D3—124no—
626D3—124no—
627D3—244no—
628C22—24no—
629C22—24no—
630C22—22no—
631C22—22no—
632C22—44no—
633C22—44no—
634C22—64no—
635C22—64no—
636C22—64no—
637C22—1216no—
638C22—128no—
639C22—184no—
640C22—184no—
641C22—184no—
642C22—368no—
643C22#6431414yes—
644C22#6433012yes—
645C22C23×D3211yescharacteristic
646C4—22no—
647C4—64no—
648C4—64no—
649C4—64no—
650C4—184no—
651C3—21no—
652C3C2×#559511yescharacteristic, complemented
653C3C2×#566611yescharacteristic, complemented
654C2—42no—
655C2—42no—
656C2—124no—
657C2—364no—
658C2#1059526114yesdirect product factor
659C2C2×#6431412yes—
660C2C2×#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×#64149C2semidirect
2. C2×C3×#937C2semidirect
3. C2×C3×#935C2semidirect
4. C2×#63978C2semidirect
5. C2×#63977C2semidirect
6. C2×#63975C2semidirect
7. C2×#63958C2semidirect
8. #10595261C2direct (N × H)
9. C2×#63910C2semidirect
10. C2×#63862C2semidirect
16. C22×#638C22semidirect
17. C22×C4⋊(C3⋊D3)C22semidirect
19. C23×C3×Dic3C22semidirect
22. C22×#624C22semidirect
23. #64149C22semidirect
24. C2×C4×C3⋊Dic3C22semidirect
27. C2×C3×#217C22semidirect
28. C3×#937C22semidirect
29. C3×#935C22semidirect
31. C2×C3×Dic3⋊C4C22semidirect
32. #63978C22semidirect
33. #63977C22semidirect
34. #63975C22semidirect
35. C2×Dic3⋊Dic3C22semidirect
36. C2×Dic3⋊Dic3C22semidirect
37. C2×#3722C22semidirect
40. #63958C22semidirect
41. #63910C22semidirect
42. #63862C22semidirect
51. C2×#937D3semidirect
52. C2×#935D3semidirect
77. C2×#638C23semidirect
80. C2×C4⋊(C3⋊D3)C23semidirect
87. C22×C3×Dic3C23semidirect
93. C2×#624C23semidirect
94. C4×C3⋊Dic3C23semidirect
97. C3×#217C23semidirect
99. C3×Dic3⋊C4C23semidirect
100. Dic3⋊Dic3C23semidirect
101. Dic3⋊Dic3C23semidirect
102. #3722C23semidirect
122. C23×Dic3C2×D3semidirect
142. C2×#217C2×D3semidirect
148. #937C2×D3semidirect
149. #935C2×D3semidirect
160. C2×Dic3⋊C4C2×D3semidirect
277. C22×Dic3C22×D3semidirect
301. #217C22×D3semidirect
311. Dic3⋊C4C22×D3semidirect
463. C2×C32#560semidirect
570. C32C2×#560semidirect
618. C2×C3#5595semidirect
619. C2×C3#5666semidirect
652. C3C2×#5595semidirect
653. C3C2×#5666semidirect
658. C2#10595261direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641492
C2×C3×#9372
C2×C3×#9352
C2×#639782
C2×#639772
C2×#639752
C2×#639582
#105952612
C2×#639102
C2×#638622
C2×#56663
C2×#55953