Finite Group Databasebeta

← C2×#10591717 #11808310

Subgroups — C2×#10591717 #11808310

Order 1152.

1977 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3757C211yesmaximal, characteristic
2C22×C3×#217C211yesmaximal, characteristic
3C22×C3×#217C211yesmaximal, characteristic
4C22×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
5#10591717C218yesmaximal, direct product factor
6C2×#63579C211yesmaximal, characteristic, complemented
7C2×#63579C211yesmaximal, characteristic, complemented
8C2×#63579C211yesmaximal, characteristic, complemented
9C2×#4953—31nomaximal
10C2×#4952—31nomaximal
11C25×C32C2211yescharacteristic
12C23×C3⋊Dic3C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C2×#3757—24no—
19C2×#3757C2214yes—
20C2×C3×#217—24no—
21C2×C3×#217—24no—
22C2×C3×#217C2214yes—
23C2×C3×#217C2214yes—
24C2×Dic3⋊Dic3—24no—
25C2×Dic3⋊Dic3C2214yescomplemented
26#63579C2214yescomplemented
27#63579C2214yescomplemented
28#63579C2214yescomplemented
29C22×C3×C22⋊C4—31no—
30C22×C3×C22⋊C4—31no—
31C22×#217—31no—
32C22×#217—31no—
33C22×#217—61no—
34C22×#217D311yescharacteristic
35C22×#217D311yescharacteristic
36C22×C4⋊Dic3—31no—
37C22×Dic3⋊C4—31no—
38C2×C3⋊#95—31no—
39C2×C3⋊#95—31no—
40C2×C3⋊#95—31no—
41C2×C3⋊#95—31no—
42C2×C3⋊#95—31no—
43C2×C3⋊#95—31no—
44#4953—38no—
45#4952—38no—
46C24×C32—22no—
47C24×C32—22no—
48C24×C32—22no—
49C24×C32—22no—
50C24×C32—22no—
51C24×C32—22no—
52C24×C32D414yes—
53C24×C32C2312yes—
54C24×C32C2311yescharacteristic
55C22×C3⋊Dic3—22no—
56C22×C3⋊Dic3—22no—
57C22×C3⋊Dic3—22no—
58C22×C3⋊Dic3—22no—
59C22×C3⋊Dic3—22no—
60C22×C3⋊Dic3—22no—
61C22×C3⋊Dic3C2312yes—
62C22×C3⋊Dic3C2312yes—
63C22×C3×Dic3—22no—
64C22×C3×Dic3—22no—
65C22×C3×Dic3—22no—
66C22×C3×Dic3—22no—
67C22×C3×Dic3—22no—
68C22×C3×Dic3—22no—
69C22×C3×Dic3—22no—
70C22×C3×Dic3—22no—
71C22×C3×Dic3—22no—
72C22×C3×Dic3—22no—
73C22×C3×Dic3—22no—
74C22×C3×Dic3D414yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79#3757—28no—
80C3×#217—28no—
81C3×#217—28no—
82Dic3⋊Dic3—28no—
83C2×#397—91noSylow
84C25×C3—21no—
85C25×C3C2×D311yescharacteristic
86C25×C3C2×D311yescharacteristic
87C23×C3×C4—31no—
88C23×C3×C4—31no—
89C23×C3×C4—31no—
90C23×C3×C4—31no—
91C23×Dic3—31no—
92C23×Dic3—31no—
93C23×Dic3—31no—
94C23×Dic3—31no—
95C23×Dic3—61no—
96C23×Dic3—61no—
97C23×Dic3C2×D311yescharacteristic
98C23×Dic3C2×D311yescharacteristic
99C23×Dic3C2×D311yescharacteristic
100C23×Dic3C2×D311yescharacteristic
101C2×C3×C22⋊C4—34no—
102C2×C3×C22⋊C4—34no—
103C2×C3×C22⋊C4—64no—
104C2×C3×C22⋊C4—64no—
105C2×#217—24no—
106C2×#217—24no—
107C2×#217—34no—
108C2×#217—34no—
109C2×#217—64no—
110C2×#217—68no—
111C2×#217—64no—
112C2×#217—64no—
113C2×#217C2×D314yes—
114C2×#217C2×D314yes—
115C2×C4⋊Dic3—34no—
116C2×C4⋊Dic3—64no—
117C2×Dic3⋊C4—34no—
118C2×Dic3⋊C4—64no—
119C3⋊#95—34no—
120C3⋊#95—34no—
121C3⋊#95—34no—
122C3⋊#95—34no—
123C3⋊#95—34no—
124C3⋊#95—34no—
125C23×C32—28no—
126C23×C32—22no—
127C23×C32—22no—
128C23×C32—28no—
129C23×C32—28no—
130C23×C32—22no—
131C23×C32—22no—
132C23×C32—22no—
133C23×C32—22no—
134C23×C32—44no—
135C23×C32—44no—
136C23×C32—44no—
137C23×C32—44no—
138C23×C32C2×D414yes—
139C23×C32C2×D412yes—
140C23×C32C2×D412yes—
141C23×C32#4112yes—
142C23×C32#4112yes—
143C23×C32#4112yes—
144C23×C32#4112yes—
145C23×C32#4112yes—
146C23×C32C2411yescharacteristic
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—44no—
154C2×C3⋊Dic3—44no—
155C2×C3×Dic3—28no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—44no—
168C2×C3×Dic3—44no—
169C2×C3×Dic3—44no—
170C2×C3×Dic3C2×D414yes—
171C22×C4⋊C4—91no—
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C22⋊C4—91no—
175#397—98no—
176C2×#95—91no—
177C2×#95—91no—
178C2×#95—91no—
179C24×C3—24no—
180C24×C3—24no—
181C24×C3—22no—
182C24×C3—22no—
183C24×C3—22no—
184C24×C3—22no—
185C24×C3—22no—
186C24×C3—22no—
187C24×C3—22no—
188C24×C3—22no—
189C24×C3—22no—
190C24×C3—22no—
191C24×C3—22no—
192C24×C3—22no—
193C24×C3—24no—
194C24×C3—22no—
195C24×C3—21no—
196C24×C3—42no—
197C24×C3—42no—
198C24×C3—42no—
199C24×C3—42no—
200C24×C3D1214yes—
201C24×C3#6714yes—
202C24×C3C22×D312yes—
203C24×C3C22×D312yes—
204C24×C3C22×D311yescharacteristic
205C24×C3C22×D311yescharacteristic
206C22×C3×C4—34no—
207C22×C3×C4—32no—
208C22×C3×C4—32no—
209C22×C3×C4—32no—
210C22×C3×C4—32no—
211C22×C3×C4—62no—
212C22×C3×C4—62no—
213C22×C3×C4—62no—
214C22×C3×C4—62no—
215C22×C3×C4—62no—
216C22×C3×C4—62no—
217C22×C3×C4—62no—
218C22×C3×C4—62no—
219C22×C3×C4—62no—
220C22×C3×C4—62no—
221C22×C3×C4—62no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—32no—
234C22×Dic3—32no—
235C22×Dic3—32no—
236C22×Dic3—32no—
237C22×Dic3—62no—
238C22×Dic3—62no—
239C22×Dic3—64no—
240C22×Dic3—64no—
241C22×Dic3—62no—
242C22×Dic3—62no—
243C22×Dic3—62no—
244C22×Dic3—62no—
245C22×Dic3—62no—
246C22×Dic3—62no—
247C22×Dic3—62no—
248C22×Dic3—62no—
249C22×Dic3—62no—
250C22×Dic3—62no—
251C22×Dic3—62no—
252C22×Dic3—62no—
253C22×Dic3—122no—
254C22×Dic3—122no—
255C22×Dic3—122no—
256C22×Dic3—122no—
257C22×Dic3#6714yes—
258C22×Dic3C22×D312yes—
259C22×Dic3C22×D312yes—
260C22×Dic3C22×D312yes—
261C22×Dic3C22×D312yes—
262C3×C22⋊C4—68no—
263C3×C22⋊C4—68no—
264#217—28no—
265#217—28no—
266#217—616no—
267#217—68no—
268#217—68no—
269C4⋊Dic3—68no—
270Dic3⋊C4—68no—
271C22×C32—24no—
272C22×C32—24no—
273C22×C32—24no—
274C22×C32—42no—
275C22×C32—42no—
276C22×C32—42no—
277C22×C32—42no—
278C22×C32—416no—
279C22×C32#12114yes—
280C22×C32#12314yes—
281C22×C32#12314yes—
282C22×C32#12314yes—
283C22×C32#12414yes—
284C22×C32#12614yes—
285C22×C32#12614yes—
286C22×C32C22×D411yescharacteristic
287C22×C32C22×D411yescharacteristic
288C22×C32C2×#4111yescharacteristic
289C22×C32C2×#4111yescharacteristic
290C22×C32C2×#4111yescharacteristic
291C22×C32C2×#4111yescharacteristic
292C22×C32C2×#4111yescharacteristic
293C3⋊Dic3—42no—
294C3⋊Dic3—42no—
295C3×Dic3—24no—
296C3×Dic3—42no—
297C3×Dic3—42no—
298C3×Dic3—42no—
299C25D3211yescharacteristic
300C23×C4—31no—
301C23×C4—31no—
302C23×C4—31no—
303C23×C4—31no—
304C23×C4—91no—
305C23×C4—91no—
306C2×C4⋊C4—94no—
307C2×C4⋊C4—184no—
308C2×C22⋊C4—34no—
309C2×C22⋊C4—34no—
310C2×C22⋊C4—64no—
311C2×C22⋊C4—64no—
312C2×C22⋊C4—94no—
313C2×C22⋊C4—184no—
314#95—94no—
315#95—94no—
316#95—94no—
317C23×C3—24no—
318C23×C3—24no—
319C23×C3—216no—
320C23×C3—28no—
321C23×C3—28no—
322C23×C3—28no—
323C23×C3—28no—
324C23×C3—28no—
325C23×C3—28no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—22no—
334C23×C3—22no—
335C23×C3—22no—
336C23×C3—22no—
337C23×C3—22no—
338C23×C3—21no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—24no—
346C23×C3—22no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3—48no—
352C23×C3—48no—
353C23×C3—48no—
354C23×C3—48no—
355C23×C3—48no—
356C23×C3—48no—
357C23×C3—44no—
358C23×C3—44no—
359C23×C3—44no—
360C23×C3—44no—
361C23×C3—44no—
362C23×C3—44no—
363C23×C3—44no—
364C23×C3—44no—
365C23×C3C2×D1214yes—
366C23×C3C2×D1212yes—
367C23×C3#23512yes—
368C23×C3#23512yes—
369C23×C3#23512yes—
370C23×C3D3×D412yes—
371C23×C3#23712yes—
372C23×C3#23712yes—
373C23×C3#23712yes—
374C23×C3#23712yes—
375C23×C3#23712yes—
376C23×C3#23712yes—
377C23×C3#23712yes—
378C23×C3C2×#6714yes—
379C23×C3C2×#6712yes—
380C23×C3C2×#6712yes—
381C23×C3C23×D311yescharacteristic
382C23×C3C23×D311yescharacteristic
383C2×C3×C4—34no—
384C2×C3×C4—68no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4—62no—
396C2×C3×C4—124no—
397C2×C3×C4—124no—
398C2×C3×C4—124no—
399C2×Dic3—28no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—44no—
412C2×Dic3—44no—
413C2×Dic3—44no—
414C2×Dic3—64no—
415C2×Dic3—64no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—122no—
429C2×Dic3—122no—
430C2×Dic3—122no—
431C2×Dic3—122no—
432C2×Dic3—128no—
433C2×Dic3—128no—
434C2×Dic3—124no—
435C2×Dic3—124no—
436C2×Dic3—124no—
437C2×Dic3—124no—
438C2×Dic3C2×#6714yes—
439C2×C32—44no—
440C2×C32#39718yescomplemented
441C2×C32C2×#12111yescharacteristic
442C2×C32C2×#12311yescharacteristic
443C2×C32C2×#12311yescharacteristic
444C2×C32C2×#12311yescharacteristic
445C2×C32C2×#12411yescharacteristic
446C2×C32C2×#12611yescharacteristic
447C2×C32C2×#12611yescharacteristic
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24#62614yes—
455C24C2×D3212yes—
456C24C2×D3211yescharacteristic
457C22×C4—32no—
458C22×C4—34no—
459C22×C4—32no—
460C22×C4—32no—
461C22×C4—32no—
462C22×C4—62no—
463C22×C4—62no—
464C22×C4—62no—
465C22×C4—62no—
466C22×C4—62no—
467C22×C4—62no—
468C22×C4—62no—
469C22×C4—62no—
470C22×C4—62no—
471C22×C4—62no—
472C22×C4—62no—
473C22×C4—92no—
474C22×C4—92no—
475C22×C4—182no—
476C22×C4—182no—
477C22×C4—182no—
478C22×C4—182no—
479C22×C4—182no—
480C22×C4—182no—
481C4⋊C4—188no—
482C22⋊C4—68no—
483C22⋊C4—68no—
484C22⋊C4—188no—
485C22×C3—28no—
486C22×C3—24no—
487C22×C3—24no—
488C22×C3—24no—
489C22×C3—24no—
490C22×C3—24no—
491C22×C3—24no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—24no—
500C22×C3—24no—
501C22×C3—24no—
502C22×C3—24no—
503C22×C3—24no—
504C22×C3—24no—
505C22×C3—24no—
506C22×C3—44no—
507C22×C3—44no—
508C22×C3—44no—
509C22×C3—44no—
510C22×C3—44no—
511C22×C3—44no—
512C22×C3—432no—
513C22×C3—416no—
514C22×C3—416no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3—42no—
518C22×C3—42no—
519C22×C3—42no—
520C22×C3—42no—
521C22×C3—42no—
522C22×C3—42no—
523C22×C3#87914yes—
524C22×C3#87914yes—
525C22×C3#87914yes—
526C22×C3#87914yes—
527C22×C3#88314yes—
528C22×C3#88514yes—
529C22×C3#88614yes—
530C22×C3#88614yes—
531C22×C3#92914yes—
532C22×C3#93014yes—
533C22×C3#93514yes—
534C22×C3#93514yes—
535C22×C3#93614yes—
536C22×C3#93914yes—
537C22×C3C22×D1211yescharacteristic
538C22×C3C2×#23511yescharacteristic
539C22×C3C2×#23511yescharacteristic
540C22×C3C2×#23511yescharacteristic
541C22×C3C2×D3×D411yescharacteristic
542C22×C3C2×#23711yescharacteristic
543C22×C3C2×#23711yescharacteristic
544C22×C3C2×#23711yescharacteristic
545C22×C3C2×#23711yescharacteristic
546C22×C3C2×#23711yescharacteristic
547C22×C3C2×#23711yescharacteristic
548C22×C3C2×#23711yescharacteristic
549C22×C3C22×#6711yescharacteristic
550C22×C3C22×#6711yescharacteristic
551C3×C4—64no—
552C3×C4—122no—
553C3×C4—122no—
554C3×C4—122no—
555Dic3—24no—
556Dic3—42no—
557Dic3—42no—
558Dic3—42no—
559Dic3—124no—
560Dic3—124no—
561Dic3—122no—
562Dic3—122no—
563Dic3—122no—
564Dic3—122no—
565C32C2×#39711yescharacteristic, complemented, Sylow
566C23—22no—
567C23—22no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—28no—
573C23—28no—
574C23—28no—
575C23—44no—
576C23—44no—
577C23—44no—
578C23—44no—
579C23#380412yes—
580C23#380412yes—
581C23#380412yes—
582C23#380512yes—
583C23#380512yes—
584C23C2×#62614yes—
585C23C2×#62612yes—
586C23D3×#6712yes—
587C23C22×D3211yescharacteristic
588C2×C4—34no—
589C2×C4—62no—
590C2×C4—62no—
591C2×C4—68no—
592C2×C4—62no—
593C2×C4—62no—
594C2×C4—62no—
595C2×C4—62no—
596C2×C4—62no—
597C2×C4—62no—
598C2×C4—62no—
599C2×C4—62no—
600C2×C4—62no—
601C2×C4—124no—
602C2×C4—124no—
603C2×C4—124no—
604C2×C4—182no—
605C2×C4—182no—
606C2×C4—182no—
607C2×C4—182no—
608C2×C4—182no—
609C2×C4—182no—
610C2×C4—364no—
611C2×C4—364no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—21no—
618C2×C3—21no—
619C2×C3—28no—
620C2×C3—48no—
621C2×C3—44no—
622C2×C3—44no—
623C2×C3#495218yescomplemented
624C2×C3#495318yescomplemented
625C2×C3C2×#87911yescharacteristic
626C2×C3C2×#87911yescharacteristic
627C2×C3C2×#87911yescharacteristic
628C2×C3C2×#87911yescharacteristic
629C2×C3C2×#88311yescharacteristic
630C2×C3C2×#88511yescharacteristic
631C2×C3C2×#88611yescharacteristic
632C2×C3C2×#88611yescharacteristic
633C2×C3C2×#92911yescharacteristic
634C2×C3C2×#93011yescharacteristic
635C2×C3C2×#93511yescharacteristic
636C2×C3C2×#93511yescharacteristic
637C2×C3C2×#93611yescharacteristic
638C2×C3C2×#93911yescharacteristic
639C22—24no—
640C22—24no—
641C22—24no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—416no—
647C22#6395614yes—
648C22#6395614yes—
649C22#6395914yes—
650C22#6396214yes—
651C22#6396614yes—
652C22#6396914yes—
653C22#6397814yes—
654C22C2×#380411yescharacteristic
655C22C2×#380411yescharacteristic
656C22C2×#380411yescharacteristic
657C22C2×#380511yescharacteristic
658C22C2×#380511yescharacteristic
659C22C22×#62611yescharacteristic
660C22C2×D3×#6711yescharacteristic
661C4—64no—
662C4—122no—
663C4—122no—
664C4—122no—
665C4—362no—
666C4—362no—
667C3—21no—
668C3C2×#495211yescharacteristic, complemented
669C3C2×#495311yescharacteristic, complemented
670C2—44no—
671C2#1059171718yesdirect product factor
672C2C2×#6395611yescharacteristic
673C2C2×#6395611yescharacteristic
674C2C2×#6395911yescharacteristic
675C2C2×#6396211yescharacteristic
676C2C2×#6396611yescharacteristic
677C2C2×#6396911yescharacteristic
678C2C2×#6397811yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC23×C32C24
FrattiniC23C22×D32
Fitting, prime radicalC25×C32C22
socleC24×C32C23
hypercenterC25D32
hypocenterC32C2×#397
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C25

Complements

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

NH ≅ G/Ntype
4. C22×Dic3⋊Dic3C2semidirect
5. #10591717C2direct (N × H)
6. C2×#63579C2semidirect
7. C2×#63579C2semidirect
8. C2×#63579C2semidirect
25. C2×Dic3⋊Dic3C22semidirect
26. #63579C22semidirect
27. #63579C22semidirect
28. #63579C22semidirect
440. C2×C32#397semidirect
565. C32C2×#397semidirect
623. C2×C3#4952semidirect
624. C2×C3#4953semidirect
668. C3C2×#4952semidirect
669. C3C2×#4953semidirect
671. C2#10591717direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37572
C22×C3×#2172
C22×Dic3⋊Dic32
#105917172
C2×#635792
C2×#49533
C2×#49523