Finite Group Databasebeta

← C2×#10590596 #11863584

Subgroups — C2×#10590596 #11863584

Order 1152.

2093 conjugacy classes of subgroups.

The subgroup lattice has 641 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D12C211yesmaximal, characteristic
2C2×C3×#897C211yesmaximal, characteristic, complemented
3C22×#3717C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic, complemented
5C2×#63636C211yesmaximal, characteristic, complemented
6C2×C3×#809C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590596C218yesmaximal, direct product factor
9C2×#5046—31nomaximal
10C2×#4776—31nomaximal
11C23×D32—21no—
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic, complemented
16C22×#626—21no—
17C2×D3×D12—24no—
18C2×D3×D12—24no—
19C2×D3×D12—22no—
20C2×D3×D12C2214yes—
21C2×C32×C4⋊C4C2211yescharacteristic, complemented
22C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
23C2×C3×(C2×D3)⋊C4—21no—
24C2×C3×C4⋊Dic3—21no—
25C22×C3×C3⋊C8C2211yescharacteristic, complemented
26C3×#897—22no—
27C3×#897C2214yescomplemented
28C2×#3717—24no—
29C2×#3717C2214yescomplemented
30C2×#3715—24no—
31C2×#3715C2214yescomplemented
32#63636C2214yescomplemented
33C3×#809C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C22×D3×D4—31no—
36C23×D12—31no—
37C2×C3×C22⋊Q8—31no—
38C22×#215—31no—
39C22×#215—31no—
40C22×#214—31no—
41C22×#204—31no—
42C2×#897D311yescharacteristic, complemented
43C2×C3×#102—31no—
44C2×#830—31no—
45C2×(C2×D3)⋊C8—31no—
46#5046—38no—
47C2×#809—31no—
48C2×#809—31no—
49C2×#809—61no—
50C2×#809D311yescharacteristic, complemented
51#4776—38no—
52C23×C3⋊D3—21no—
53C23×C3×D3—21no—
54C23×C3×D3D411yescharacteristic
55C22×D32—28no—
56C22×D32—24no—
57C22×D32—44no—
58C22×D32—44no—
59C22×C32×C4—21no—
60C22×C32×C4C2311yescharacteristic
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)—22no—
63C2×C4⋊(C3⋊D3)D414yes—
64C2×C4⋊(C3⋊D3)C2312yes—
65C22×C3×Dic3—21no—
66C22×C3×Dic3D411yescharacteristic
67C2×C3×D12—21no—
68C2×C3×D12—22no—
69C2×C3×D12D414yes—
70C2×C3×D12C2312yes—
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3D412yes—
74C2×C3×C4×D3C2312yes—
75C2×C3×Dic6—22no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6—21no—
78C2×C3×Dic6C2312yescomplemented
79C2×#626—28no—
80C2×#626—24no—
81D3×D12—216no—
82D3×D12—28no—
83D3×D12—28no—
84C32×C4⋊C4—21no—
85C32×C4⋊C4C2312yescomplemented
86C2×C3⋊(C3⋊C8)—22no—
87C2×C3⋊(C3⋊C8)C2312yescomplemented
88C3×(C2×D3)⋊C4—24no—
89C3×C4⋊Dic3—24no—
90C2×C3×C3⋊C8—22no—
91C2×C3×C3⋊C8C2312yescomplemented
92#3717—28no—
93#3715—28no—
94C2×#450—91noSylow
95C24×D3—61no—
96C24×D3—61no—
97C22×C3×Q8—31no—
98C22×C3×D4—31no—
99C23×C3×C4—31no—
100C22×#67—61no—
101C2×D3×D4—34no—
102C2×D3×D4—64no—
103C2×D3×D4—64no—
104C2×D3×D4—62no—
105C22×D12—31no—
106C22×D12—31no—
107C22×D12—34no—
108C22×D12—61no—
109C22×D12—64no—
110C22×D12—62no—
111C22×D12—61no—
112C22×D12—64no—
113C22×D12C2×D311yescharacteristic
114C22×C4×D3C2×D311yescharacteristic
115C22×Dic6C2×D311yescharacteristic, complemented
116C22×C3×C8—31no—
117C3×C22⋊Q8—34no—
118C3×C22⋊Q8—62no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—61no—
121C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
122C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
123C2×C3×C22⋊C4—61no—
124C2×#215—34no—
125C2×#215—34no—
126C2×#215—64no—
127C2×#215—64no—
128C2×#214—34no—
129C2×#214—64no—
130C2×(C2×D3)⋊C4—21no—
131C2×C4⋊Dic3—21no—
132C22×C3⋊C8—31no—
133C22×C3⋊C8—31no—
134C22×C3⋊C8—61no—
135C22×C3⋊C8C2×D311yescharacteristic, complemented
136C2×#204—34no—
137C2×#204—64no—
138#897—22no—
139#897C2×D314yescomplemented
140C3×#102—34no—
141#830—34no—
142(C2×D3)⋊C8—34no—
143#809—34no—
144#809—34no—
145#809—64no—
146#809C2×D314yescomplemented
147C23×C32C2×D411yescharacteristic
148C22×C3⋊D3—24no—
149C22×C3⋊D3—22no—
150C22×C3⋊D3—42no—
151C22×C3⋊D3—42no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3—24no—
155C22×C3×D3—22no—
156C22×C3×D3—42no—
157C22×C3×D3—42no—
158C22×C3×D3SD1614yescomplemented
159C22×C3×D3C2×D412yes—
160C2×D32—216no—
161C2×D32—48no—
162C2×D32—432no—
163C2×D32—48no—
164C2×C32×C4—22no—
165C2×C32×C4—42no—
166C2×C32×C4C2×D412yes—
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C4⋊(C3⋊D3)—24no—
171C4⋊(C3⋊D3)—22no—
172C4⋊(C3⋊D3)C2×D414yes—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—42no—
176C2×C3×Dic3C2×D412yes—
177C3×D12—24no—
178C3×D12—22no—
179C3×D12C2×D414yes—
180C3×C4×D3—24no—
181C3×C4×D3—22no—
182C3×C4×D3—22no—
183C3×Dic6—22no—
184C3×Dic6—22no—
185C3×Dic6—42no—
186#626—216no—
187C3⋊(C3⋊C8)—22no—
188C3×C3⋊C8—22no—
189C23×D4—91no—
190C22×SD16—91no—
191C22×SD16—91no—
192C2×C22⋊Q8—31no—
193#450—98no—
194C2×#102—31no—
195C2×#102—91no—
196C2×C22⋊C8—91no—
197C24×C3—31no—
198C24×C3—61no—
199C23×D3—21no—
200C23×D3—64no—
201C23×D3—68no—
202C23×D3—68no—
203C23×D3—61no—
204C23×D3—61no—
205C23×D3—64no—
206C23×D3—121no—
207C23×D3—124no—
208C23×D3—124no—
209C23×D3—124no—
210C23×D3—124no—
211C23×D3#6711yescharacteristic
212C2×C3×Q8—32no—
213C2×C3×Q8—61no—
214C2×C3×Q8—62no—
215C2×C3×Q8—62no—
216C2×C3×D4—34no—
217C2×C3×D4—32no—
218C2×C3×D4—62no—
219C2×C3×D4—61no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—31no—
224C22×C3×C4—32no—
225C22×C3×C4—32no—
226C22×C3×C4—41no—
227C22×C3×C4—62no—
228C22×C3×C4—62no—
229C22×C3×C4—61no—
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C2×#67—68no—
233C2×#67—64no—
234C22×Dic3—21no—
235C22×Dic3#6711yescharacteristic
236D3×D4—68no—
237D3×D4—68no—
238D3×D4—616no—
239C2×D12—22no—
240C2×D12—21no—
241C2×D12—34no—
242C2×D12—34no—
243C2×D12—32no—
244C2×D12—32no—
245C2×D12—62no—
246C2×D12—64no—
247C2×D12—68no—
248C2×D12—616no—
249C2×D12—64no—
250C2×D12—68no—
251C2×D12—62no—
252C2×D12—61no—
253C2×D12—62no—
254C2×D12—61no—
255C2×D12—68no—
256C2×D12—122no—
257C2×D12—121no—
258C2×D12D1214yes—
259C2×D12C22×D312yes—
260C2×C4×D3—22no—
261C2×C4×D3—22no—
262C2×C4×D3#6712yes—
263C2×C4×D3C22×D312yes—
264C2×Dic6—22no—
265C2×Dic6—22no—
266C2×Dic6—21no—
267C2×Dic6C22×D312yescomplemented
268C2×C3×C8—32no—
269C2×C3×C8—62no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—22no—
273C3×C4⋊C4—41no—
274C3×C4⋊C4—64no—
275C3×C4⋊C4C22×D312yescomplemented
276C3×C4⋊C4C22×D312yescomplemented
277C3×C22⋊C4—64no—
278#215—68no—
279#215—68no—
280#214—68no—
281(C2×D3)⋊C4—24no—
282C4⋊Dic3—24no—
283C2×C3⋊C8—22no—
284C2×C3⋊C8—32no—
285C2×C3⋊C8—32no—
286C2×C3⋊C8—62no—
287C2×C3⋊C8—62no—
288C2×C3⋊C8—62no—
289C2×C3⋊C8—122no—
290C2×C3⋊C8C22×D312yescomplemented
291#204—68no—
292C22×C32#12012yes—
293C22×C32C2×SD1612yes—
294C22×C32AGL(1,ℤ/8)12yes—
295C22×C32C22×D411yescharacteristic
296C2×C3⋊D3—24no—
297C2×C3⋊D3—42no—
298C2×C3⋊D3—42no—
299C2×C3⋊D3—48no—
300C2×C3×D3—22no—
301C2×C3×D3—22no—
302C2×C3×D3—28no—
303C2×C3×D3—24no—
304C2×C3×D3—42no—
305C2×C3×D3—42no—
306C2×C3×D3—48no—
307C2×C3×D3C2×SD1614yescomplemented
308D32—432no—
309C32×C4—42no—
310C32×C4#12012yes—
311C32×C4C22×D411yescharacteristic
312C32×C4C22×D411yescharacteristic
313C3×Dic3—22no—
314C3×Dic3—42no—
315C25—181no—
316C22×Q8—31no—
317C22×D4—31no—
318C22×D4—94no—
319C22×D4—91no—
320C22×D4—182no—
321C22×D4—181no—
322C22×D4—184no—
323C22×D4—184no—
324C23×C4—31no—
325C2×SD16—94no—
326C2×SD16—94no—
327C2×SD16—184no—
328C2×SD16—184no—
329C22×C8—31no—
330C22×C8—91no—
331C22⋊Q8—34no—
332C22⋊Q8—62no—
333C2×C4⋊C4—61no—
334C2×C4⋊C4D3211yescharacteristic, complemented
335C2×C22⋊C4—61no—
336#102—34no—
337#102—94no—
338C22⋊C8—94no—
339C23×C3—21no—
340C23×C3—34no—
341C23×C3—32no—
342C23×C3—62no—
343C23×C3—62no—
344C23×C3—64no—
345C23×C3—62no—
346C23×C3—122no—
347C23×C3—122no—
348C23×C3D3×D411yescharacteristic
349C23×C3C2×#6711yescharacteristic
350C22×D3—22no—
351C22×D3—22no—
352C22×D3—24no—
353C22×D3—22no—
354C22×D3—42no—
355C22×D3—42no—
356C22×D3—616no—
357C22×D3—616no—
358C22×D3—64no—
359C22×D3—64no—
360C22×D3—62no—
361C22×D3—62no—
362C22×D3—122no—
363C22×D3—124no—
364C22×D3—1232no—
365C22×D3—128no—
366C22×D3—128no—
367C22×D3—128no—
368C22×D3—1232no—
369C22×D3—122no—
370C22×D3—122no—
371C22×D3—122no—
372C22×D3—122no—
373C22×D3—128no—
374C22×D3—242no—
375C22×D3—242no—
376C22×D3#21514yescomplemented
377C22×D3C2×#6712yes—
378C3×Q8—62no—
379C3×Q8—62no—
380C3×Q8—122no—
381C3×D4—34no—
382C3×D4—64no—
383C3×D4—62no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—21no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—21no—
390C2×C3×C4—32no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—62no—
395C2×C3×C4—64no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
399C2×C3×C4—82no—
400C2×C3×C4—122no—
401C2×C3×C4C2×D1212yes—
402C2×C3×C4D3×D412yes—
403C2×C3×C4D3×D412yes—
404C2×C3×C4D3×D412yes—
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4C2×#6711yescharacteristic
407C2×C3×C4C23×D311yescharacteristic
408C2×C3×C4C23×D311yescharacteristic
409#67—616no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—42no—
413C2×Dic3C2×#6712yes—
414D12—24no—
415D12—22no—
416D12—34no—
417D12—34no—
418D12—64no—
419D12—616no—
420D12—64no—
421D12—64no—
422D12—62no—
423D12—62no—
424D12—122no—
425D12—124no—
426D12C2×D1214yes—
427C4×D3—24no—
428C4×D3—22no—
429C4×D3—22no—
430Dic6—22no—
431Dic6—22no—
432Dic6—42no—
433C3×C8—62no—
434C3⋊C8—22no—
435C3⋊C8—62no—
436C3⋊C8—62no—
437C3⋊C8—122no—
438C2×C32#45014yescomplemented
439C2×C32C2×#12011yescharacteristic
440C2×C32C22×SD1611yescharacteristic
441C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
442C3⋊D3—44no—
443C3×D3—24no—
444C3×D3—44no—
445C24—31no—
446C24—61no—
447C24—184no—
448C24—188no—
449C24—181no—
450C24—364no—
451C24—364no—
452C2×Q8—32no—
453C2×Q8—61no—
454C2×Q8—62no—
455C2×Q8—62no—
456C2×D4—32no—
457C2×D4—34no—
458C2×D4—62no—
459C2×D4—61no—
460C2×D4—92no—
461C2×D4—94no—
462C2×D4—184no—
463C2×D4—188no—
464C2×D4—188no—
465C2×D4—1816no—
466C2×D4—188no—
467C2×D4—182no—
468C2×D4—181no—
469C22×C4—21no—
470C22×C4—31no—
471C22×C4—32no—
472C22×C4—32no—
473C22×C4—62no—
474C22×C4—62no—
475C22×C4—61no—
476C22×C4C2×D3211yescharacteristic
477SD16—188no—
478SD16—188no—
479C2×C8—32no—
480C2×C8—62no—
481C2×C8—92no—
482C2×C8—182no—
483C4⋊C4—21no—
484C4⋊C4—64no—
485C4⋊C4C2×D3212yescomplemented
486C22⋊C4—64no—
487C22×C3—21no—
488C22×C3—22no—
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—34no—
492C22×C3—62no—
493C22×C3—62no—
494C22×C3—68no—
495C22×C3—64no—
496C22×C3—122no—
497C22×C3—128no—
498C22×C3—122no—
499C22×C3#88212yes—
500C22×C3#91112yes—
501C22×C3D3×SD1612yes—
502C22×C3#93712yes—
503C22×C3C2×#21512yes—
504C22×C3#94912yes—
505C22×C3C2×D3×D411yescharacteristic
506C22×C3C22×#6711yescharacteristic
507C2×D3—22no—
508C2×D3—28no—
509C2×D3—22no—
510C2×D3—24no—
511C2×D3—42no—
512C2×D3—42no—
513C2×D3—48no—
514C2×D3—64no—
515C2×D3—64no—
516C2×D3—124no—
517C2×D3—1232no—
518C2×D3—1232no—
519C2×D3—122no—
520C2×D3—122no—
521C2×D3—128no—
522C2×D3—122no—
523C2×D3—128no—
524C2×D3—122no—
525C2×D3—242no—
526C2×D3—248no—
527C2×D3—242no—
528C2×D3C2×#21514yescomplemented
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—22no—
532C3×C4—42no—
533C3×C4—42no—
534C3×C4—62no—
535C3×C4—82no—
536C3×C4—122no—
537C3×C4#88212yes—
538C3×C4#93712yes—
539C3×C4C22×D1211yescharacteristic
540C3×C4C2×D3×D411yescharacteristic
541C3×C4C2×D3×D411yescharacteristic
542C3×C4C2×D3×D411yescharacteristic
543Dic3—22no—
544Dic3—42no—
545C32C2×#45011yescharacteristic, complemented, Sylow
546C23—32no—
547C23—34no—
548C23—62no—
549C23—62no—
550C23—62no—
551C23—64no—
552C23—122no—
553C23—122no—
554C23—1816no—
555C23—182no—
556C23—184no—
557C23—368no—
558C23—368no—
559C23—3632no—
560C23—362no—
561C23—362no—
562C23D3×#6711yescharacteristic
563Q8—62no—
564Q8—62no—
565Q8—122no—
566D4—34no—
567D4—62no—
568D4—64no—
569D4—94no—
570D4—1816no—
571D4—182no—
572D4—184no—
573C2×C4—22no—
574C2×C4—32no—
575C2×C4—42no—
576C2×C4—62no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—64no—
580C2×C4—62no—
581C2×C4—122no—
582C2×C4D3×D1212yes—
583C2×C4#380212yes—
584C2×C4D3×#6711yescharacteristic
585C2×C4C22×D3211yescharacteristic
586C8—62no—
587C8—182no—
588C2×C3—21no—
589C2×C3—24no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—64no—
593C2×C3—124no—
594C2×C3#477614yescomplemented
595C2×C3#504614yescomplemented
596C2×C3C2×#88211yescharacteristic
597C2×C3C2×#91111yescharacteristic
598C2×C3C2×D3×SD1611yescharacteristic
599C2×C3C2×#93711yescharacteristic
600C2×C3C22×#21511yescharacteristic
601C2×C3C2×#94911yescharacteristic
602D3—24no—
603D3—44no—
604D3—124no—
605D3—124no—
606D3—244no—
607C22—34no—
608C22—62no—
609C22—68no—
610C22—62no—
611C22—64no—
612C22—122no—
613C22—128no—
614C22—122no—
615C22—184no—
616C22—3632no—
617C22—362no—
618C22—368no—
619C22—362no—
620C22#6392212yes—
621C22#6392512yes—
622C22D3×#21512yes—
623C22C2×D3×#6711yescharacteristic
624C4—42no—
625C4—62no—
626C4—122no—
627C4#6392212yes—
628C4C2×D3×D1211yescharacteristic
629C4C2×#380211yescharacteristic
630C3—21no—
631C3C2×#477611yescharacteristic, complemented
632C3C2×#504611yescharacteristic, complemented
633C2—64no—
634C2—124no—
635C2—364no—
636C2#1059059614yesdirect product factor
637C2C2×#6392211yescharacteristic
638C2C2×#6392511yescharacteristic
639C2C2×D3×#21511yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×D3×D12C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#450
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#897C2semidirect
3. C22×#3717C2semidirect
4. C22×#3715C2semidirect
5. C2×#63636C2semidirect
6. C2×C3×#809C2semidirect
7. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
8. #10590596C2direct (N × H)
15. C22×C3×Dic6C22semidirect
21. C2×C32×C4⋊C4C22semidirect
22. C22×C3⋊(C3⋊C8)C22semidirect
25. C22×C3×C3⋊C8C22semidirect
27. C3×#897C22semidirect
29. C2×#3717C22semidirect
31. C2×#3715C22semidirect
32. #63636C22semidirect
33. C3×#809C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
42. C2×#897D3semidirect
50. C2×#809D3semidirect
78. C2×C3×Dic6C23semidirect
85. C32×C4⋊C4C23semidirect
87. C2×C3⋊(C3⋊C8)C23semidirect
91. C2×C3×C3⋊C8C23semidirect
115. C22×Dic6C2×D3semidirect
121. C2×C3×C4⋊C4C2×D3semidirect
122. C2×C3×C4⋊C4C2×D3semidirect
135. C22×C3⋊C8C2×D3semidirect
139. #897C2×D3semidirect
146. #809C2×D3semidirect
158. C22×C3×D3SD16semidirect
267. C2×Dic6C22×D3semidirect
275. C3×C4⋊C4C22×D3semidirect
276. C3×C4⋊C4C22×D3semidirect
290. C2×C3⋊C8C22×D3semidirect
307. C2×C3×D3C2×SD16semidirect
334. C2×C4⋊C4D32semidirect
376. C22×D3#215semidirect
438. C2×C32#450semidirect
485. C4⋊C4C2×D32semidirect
528. C2×D3C2×#215semidirect
545. C32C2×#450semidirect
594. C2×C3#4776semidirect
595. C2×C3#5046semidirect
631. C3C2×#4776semidirect
632. C3C2×#5046semidirect
636. C2#10590596direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D122
C2×C3×#8972
C22×#37172
C22×#37152
C2×#636362
C2×C3×#8092
C2×(C2×D3)⋊(C3⋊C8)2
#105905962
C2×#50463
C2×#47763