Finite Group Databasebeta

← C2×#10591593 #11863732

Subgroups — C2×#10591593 #11863732

Order 1152.

2069 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
1C22×#3832C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic, complemented
3C2×#63916C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic, complemented
5C2×C3×#835C211yesmaximal, characteristic, complemented
6#10591593C218yesmaximal, direct product factor
7C2×#63564C211yesmaximal, characteristic, complemented
8C2×#63557C211yesmaximal, characteristic, complemented
9C2×#5172—31nomaximal
10C2×#4810—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C2×#3832—24no—
13C2×#3832—24no—
14C2×#3832—22no—
15C2×#3832C2214yescomplemented
16C22×C4⋊(C3⋊D3)—21no—
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C22×C4×C3⋊D3—21no—
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×#626—21no—
22C2×C3×#215—24no—
23C2×C3×#215C2214yescomplemented
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C2×(C2×D3)⋊Dic3—21no—
28#63916—22no—
29#63916C2214yescomplemented
30C2×#3714—24no—
31C2×#3714C2214yescomplemented
32C3×#835C2214yescomplemented
33#63564C2214yescomplemented
34#63557C2214yescomplemented
35C22×#239—31no—
36C22×#239—31no—
37C22×#239—61no—
38C22×C3×SD16—31no—
39C22×#215D311yescharacteristic, complemented
40C2×#938—31no—
41C22×#213—31no—
42C22×D24—31no—
43C2×#895—31no—
44C2×C3×#103—31no—
45C2×#835D311yescharacteristic, complemented
46#5172—38no—
47C2×#821—31no—
48C2×(C2×D3)⋊C8—31no—
49C2×(C2×D3)⋊C8—31no—
50C2×#809—31no—
51#4810—38no—
52C23×C3⋊D3—21no—
53C23×C3⋊D3D411yescharacteristic
54C23×C3×D3—21no—
55C2×C32×Q8—22no—
56C2×C32×Q8—21no—
57C2×C32×Q8D414yescomplemented
58C2×C32×Q8C2312yes—
59C22×C32×C4—21no—
60C22×C32×C4C2311yescharacteristic
61C22×C3⋊Dic3D411yescharacteristic
62#3832—216no—
63#3832—28no—
64#3832—28no—
65C2×C4⋊(C3⋊D3)—28no—
66C2×C4⋊(C3⋊D3)—24no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—22no—
69C2×C4⋊(C3⋊D3)D414yescomplemented
70C2×C4⋊(C3⋊D3)C2312yes—
71C2×C4×C3⋊D3—28no—
72C2×C4×C3⋊D3—22no—
73C2×C4×C3⋊D3—22no—
74C2×C4×C3⋊D3—24no—
75C2×C4×C3⋊D3D412yes—
76C2×C4×C3⋊D3C2312yes—
77C22×C3×Dic3—21no—
78C2×C3×D12—22no—
79C2×C3×D12—22no—
80C2×C3×D12—21no—
81C2×C3×D12C2312yes—
82C2×#626—24no—
83C2×#626—44no—
84C3×#215—28no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3C2312yes—
87C2×C3×C3⋊C8—22no—
88C2×C3×C3⋊C8—22no—
89C2×C3×C3⋊C8C2312yes—
90C2×C3×C3⋊C8C2312yes—
91(C2×D3)⋊Dic3—24no—
92#3714—28no—
93C2×#449—91noSylow
94C22×C3×Q8—21no—
95C22×C3×Q8C2×D311yescharacteristic
96C22×C3×Q8C2×D311yescharacteristic
97C22×C3×D4—31no—
98C22×#67—61no—
99C2×#239—34no—
100C2×#239—34no—
101C2×#239—64no—
102C2×#239—62no—
103C2×#239—62no—
104C2×#239—64no—
105C2×#239—64no—
106C2×#239—64no—
107C2×#239—68no—
108C2×#239—68no—
109C2×#239—64no—
110C2×#239—64no—
111C22×D12—31no—
112C22×D12—31no—
113C22×D12—61no—
114C22×D12—61no—
115C22×D12—61no—
116C22×D12—62no—
117C22×D12—61no—
118C22×D12C2×D311yescharacteristic
119C22×C4×D3—31no—
120C22×C4×D3—31no—
121C22×C4×D3—61no—
122C22×C4×D3—61no—
123C22×C4×D3—61no—
124C22×C4×D3—62no—
125C2×C3×SD16—34no—
126C2×C3×SD16—64no—
127C22×C3×C8—31no—
128C22×C3×C8—31no—
129C2×C3×C4⋊C4—31no—
130C2×#217—61no—
131C2×#215—24no—
132C2×#215C2×D314yescomplemented
133#938—34no—
134#938—62no—
135C2×#213—34no—
136C2×#213—64no—
137C2×(C2×D3)⋊C4—61no—
138C2×C4⋊Dic3C2×D311yescharacteristic
139C22×C3⋊C8C2×D311yescharacteristic
140C22×C3⋊C8C2×D311yescharacteristic
141C2×D24—34no—
142C2×D24—64no—
143#895—34no—
144#895—62no—
145C3×#103—34no—
146#835C2×D314yescomplemented
147#821—34no—
148(C2×D3)⋊C8—34no—
149(C2×D3)⋊C8—34no—
150#809—34no—
151C23×C32C2×D411yescharacteristic
152C22×C3⋊D3—24no—
153C22×C3⋊D3—22no—
154C22×C3⋊D3—22no—
155C22×C3⋊D3—22no—
156C22×C3⋊D3—22no—
157C22×C3⋊D3—42no—
158C22×C3⋊D3—42no—
159C22×C3⋊D3C2×D412yes—
160C22×C3×D3—22no—
161C22×C3×D3—42no—
162C22×C3×D3—42no—
163C22×C3×D3—42no—
164C32×Q8—24no—
165C32×Q8—22no—
166C32×Q8C2×D414yescomplemented
167C2×C32×C4—24no—
168C2×C32×C4—22no—
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D412yes—
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3C2×D412yes—
175C4⋊(C3⋊D3)—216no—
176C4⋊(C3⋊D3)—24no—
177C4⋊(C3⋊D3)—22no—
178C4⋊(C3⋊D3)C2×D414yescomplemented
179C4×C3⋊D3—216no—
180C4×C3⋊D3—24no—
181C4×C3⋊D3—22no—
182C4×C3⋊D3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—42no—
185C3×D12—22no—
186C3×D12—22no—
187C3×D12—42no—
188#626—48no—
189C3×C3⋊C8—22no—
190C3×C3⋊C8—22no—
191C22×#41—91no—
192C22×SD16—31no—
193C22×D8—91no—
194C2×#121—91no—
195#449—98no—
196C2×#103—31no—
197C2×#102—91no—
198C2×C22⋊C8—91no—
199C24×C3—61no—
200C23×D3—21no—
201C23×D3—31no—
202C23×D3—31no—
203C23×D3—61no—
204C23×D3—62no—
205C23×D3—61no—
206C23×D3—61no—
207C2×C3×Q8—22no—
208C2×C3×Q8—24no—
209C2×C3×Q8—22no—
210C2×C3×Q8—22no—
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
213C2×C3×Q8—24no—
214C2×C3×Q8—22no—
215C2×C3×Q8D1214yescomplemented
216C2×C3×Q8#6714yescomplemented
217C2×C3×Q8C22×D312yes—
218C2×C3×Q8C22×D312yes—
219C2×C3×D4—32no—
220C2×C3×D4—62no—
221C2×C3×D4—62no—
222C2×C3×D4—61no—
223C22×C3×C4—22no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—61no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C2×#67—64no—
231C2×#67—124no—
232C22×Dic3—21no—
233C22×Dic3—31no—
234C22×Dic3—31no—
235C22×Dic3—61no—
236#239—68no—
237#239—68no—
238#239—616no—
239#239—632no—
240#239—616no—
241#239—616no—
242#239—616no—
243#239—68no—
244#239—68no—
245C2×D12—22no—
246C2×D12—22no—
247C2×D12—21no—
248C2×D12—34no—
249C2×D12—34no—
250C2×D12—32no—
251C2×D12—32no—
252C2×D12—64no—
253C2×D12—62no—
254C2×D12—64no—
255C2×D12—64no—
256C2×D12—68no—
257C2×D12—616no—
258C2×D12—68no—
259C2×D12—68no—
260C2×D12—64no—
261C2×D12—62no—
262C2×D12—62no—
263C2×D12—61no—
264C2×D12—61no—
265C2×D12—62no—
266C2×D12—64no—
267C2×D12—124no—
268C2×D12C22×D312yes—
269C2×C4×D3—32no—
270C2×C4×D3—32no—
271C2×C4×D3—32no—
272C2×C4×D3—32no—
273C2×C4×D3—62no—
274C2×C4×D3—62no—
275C2×C4×D3—64no—
276C2×C4×D3—64no—
277C2×C4×D3—68no—
278C2×C4×D3—616no—
279C2×C4×D3—68no—
280C2×C4×D3—68no—
281C2×C4×D3—64no—
282C2×C4×D3—64no—
283C2×C4×D3—62no—
284C2×C4×D3—62no—
285C2×C4×D3—62no—
286C2×C4×D3—62no—
287C3×SD16—68no—
288C2×C3×C8—32no—
289C2×C3×C8—32no—
290C2×C3×C8—62no—
291C2×C3×C8—62no—
292C3×C4⋊C4—32no—
293C3×C4⋊C4—61no—
294#217—64no—
295#215—28no—
296#213—68no—
297(C2×D3)⋊C4—64no—
298C4⋊Dic3—21no—
299C4⋊Dic3C22×D312yes—
300C2×C3⋊C8—22no—
301C2×C3⋊C8—22no—
302C2×C3⋊C8C22×D312yes—
303C2×C3⋊C8C22×D312yes—
304D24—68no—
305C22×C32#12012yes—
306C22×C32#13512yes—
307C22×C32AGL(1,ℤ/8)12yes—
308C22×C32C22×D411yescharacteristic
309C2×C3⋊D3—22no—
310C2×C3⋊D3—24no—
311C2×C3⋊D3—22no—
312C2×C3⋊D3—22no—
313C2×C3⋊D3—42no—
314C2×C3⋊D3—42no—
315C2×C3⋊D3—44no—
316C2×C3⋊D3—48no—
317C2×C3×D3—42no—
318C2×C3×D3—42no—
319C2×C3×D3—42no—
320C2×C3×D3—84no—
321C32×C4—24no—
322C32×C4#12012yes—
323C32×C4C22×D411yescharacteristic
324C32×C4C22×D411yescharacteristic
325C3⋊Dic3—22no—
326C3×Dic3—42no—
327C2×#41—94no—
328C2×#41—182no—
329C2×#41—184no—
330C2×#41—184no—
331C22×Q8D3211yescharacteristic
332C22×D4—31no—
333C22×D4—91no—
334C22×D4—181no—
335C22×D4—181no—
336C23×C4—91no—
337C23×C4—181no—
338C2×SD16—34no—
339C2×SD16—64no—
340C2×D8—94no—
341C2×D8—184no—
342C22×C8—31no—
343C22×C8—31no—
344#121—94no—
345#121—182no—
346C2×C4⋊C4—31no—
347C2×C22⋊C4—181no—
348#103—34no—
349#102—94no—
350C22⋊C8—94no—
351C23×C3—21no—
352C23×C3—62no—
353C23×C3—122no—
354C23×C3—122no—
355C23×C3—122no—
356C23×C3D3×D411yescharacteristic
357C23×C3D3×D411yescharacteristic
358C22×D3—22no—
359C22×D3—32no—
360C22×D3—32no—
361C22×D3—42no—
362C22×D3—42no—
363C22×D3—42no—
364C22×D3—62no—
365C22×D3—64no—
366C22×D3—68no—
367C22×D3—64no—
368C22×D3—64no—
369C22×D3—62no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—62no—
373C22×D3—62no—
374C22×D3—64no—
375C22×D3—62no—
376C22×D3—62no—
377C22×D3—62no—
378C22×D3—122no—
379C22×D3—122no—
380C22×D3—124no—
381C22×D3—124no—
382C22×D3—122no—
383C22×D3—122no—
384C22×D3—122no—
385C22×D3—122no—
386C3×Q8—24no—
387C3×Q8—28no—
388C3×Q8—24no—
389C3×Q8—24no—
390C3×Q8—22no—
391C3×Q8—22no—
392C3×Q8—24no—
393C3×Q8C2×D1214yescomplemented
394C3×Q8C2×#6714yescomplemented
395C3×D4—62no—
396C3×D4—62no—
397C3×D4—122no—
398C2×C3×C4—24no—
399C2×C3×C4—28no—
400C2×C3×C4—24no—
401C2×C3×C4—24no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—21no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—21no—
408C2×C3×C4—62no—
409C2×C3×C4—122no—
410C2×C3×C4C2×D1212yes—
411C2×C3×C4D3×D411yescharacteristic
412C2×C3×C4D3×D412yes—
413C2×C3×C4D3×D411yescharacteristic
414C2×C3×C4D3×D412yes—
415C2×C3×C4C2×#6712yes—
416C2×C3×C4C23×D311yescharacteristic
417C2×C3×C4C23×D311yescharacteristic
418#67—128no—
419C2×Dic3—22no—
420C2×Dic3—32no—
421C2×Dic3—32no—
422C2×Dic3—42no—
423C2×Dic3—62no—
424C2×Dic3—64no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427D12—22no—
428D12—22no—
429D12—34no—
430D12—34no—
431D12—42no—
432D12—64no—
433D12—632no—
434D12—616no—
435D12—616no—
436D12—64no—
437D12—68no—
438D12—64no—
439D12—64no—
440D12—62no—
441D12—62no—
442D12—128no—
443C4×D3—632no—
444C4×D3—616no—
445C4×D3—616no—
446C4×D3—64no—
447C4×D3—64no—
448C4×D3—68no—
449C4×D3—64no—
450C4×D3—64no—
451C4×D3—62no—
452C4×D3—62no—
453C4×D3—62no—
454C4×D3—62no—
455C3×C8—62no—
456C3×C8—62no—
457C3⋊C8—22no—
458C3⋊C8—22no—
459C2×C32#44914yescomplemented
460C2×C32C2×#12011yescharacteristic
461C2×C32C2×#13511yescharacteristic
462C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
463C3⋊D3—42no—
464C3⋊D3—44no—
465C3×D3—82no—
466C24—61no—
467C24—91no—
468C24—181no—
469#41—188no—
470#41—1816no—
471#41—188no—
472C2×Q8—21no—
473C2×Q8—22no—
474C2×Q8#62614yescomplemented
475C2×Q8C2×D3212yes—
476C2×D4—32no—
477C2×D4—62no—
478C2×D4—62no—
479C2×D4—61no—
480C2×D4—92no—
481C2×D4—94no—
482C2×D4—184no—
483C2×D4—188no—
484C2×D4—184no—
485C2×D4—182no—
486C2×D4—181no—
487C2×D4—364no—
488C22×C4—21no—
489C22×C4—61no—
490C22×C4—91no—
491C22×C4—92no—
492C22×C4—92no—
493C22×C4—184no—
494C22×C4—188no—
495C22×C4—182no—
496C22×C4—182no—
497C22×C4C2×D3211yescharacteristic
498SD16—68no—
499D8—188no—
500C2×C8—32no—
501C2×C8—32no—
502C2×C8—62no—
503C2×C8—62no—
504C4⋊C4—32no—
505C4⋊C4—61no—
506C22⋊C4—184no—
507C22×C3—21no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—122no—
512C22×C3—122no—
513C22×C3—122no—
514C22×C3—244no—
515C22×C3#88212yes—
516C22×C3#91412yes—
517C22×C3#91412yes—
518C22×C3#91612yes—
519C22×C3#91912yes—
520C22×C3#93712yes—
521C22×C3C2×D3×D411yescharacteristic
522C22×C3C2×D3×D411yescharacteristic
523C2×D3—42no—
524C2×D3—42no—
525C2×D3—42no—
526C2×D3—68no—
527C2×D3—64no—
528C2×D3—64no—
529C2×D3—62no—
530C2×D3—62no—
531C2×D3—62no—
532C2×D3—62no—
533C2×D3—62no—
534C2×D3—64no—
535C2×D3—62no—
536C2×D3—84no—
537C2×D3—122no—
538C2×D3—122no—
539C2×D3—124no—
540C2×D3—128no—
541C2×D3—1216no—
542C2×D3—124no—
543C2×D3—124no—
544C2×D3—128no—
545C2×D3—122no—
546C2×D3—122no—
547C2×D3—122no—
548C2×D3—122no—
549C2×D3—124no—
550C2×D3—128no—
551C3×C4—28no—
552C3×C4—24no—
553C3×C4—24no—
554C3×C4—21no—
555C3×C4—21no—
556C3×C4—22no—
557C3×C4—122no—
558C3×C4#88212yes—
559C3×C4#93712yes—
560C3×C4C22×D1211yescharacteristic
561C3×C4C2×D3×D411yescharacteristic
562C3×C4C2×D3×D411yescharacteristic
563C3×C4C22×#6711yescharacteristic
564Dic3—42no—
565Dic3—64no—
566Dic3—62no—
567Dic3—62no—
568C32C2×#44911yescharacteristic, complemented, Sylow
569C23—62no—
570C23—92no—
571C23—122no—
572C23—122no—
573C23—122no—
574C23—182no—
575C23—182no—
576C23—182no—
577C23—184no—
578C23—182no—
579C23—362no—
580C23—362no—
581C23#381111yescharacteristic
582Q8—22no—
583Q8—24no—
584Q8C2×#62614yescomplemented
585D4—62no—
586D4—62no—
587D4—94no—
588D4—122no—
589D4—1816no—
590D4—182no—
591D4—184no—
592D4—368no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—62no—
596C2×C4—92no—
597C2×C4—122no—
598C2×C4—1816no—
599C2×C4—182no—
600C2×C4—182no—
601C2×C4—182no—
602C2×C4—184no—
603C2×C4C2×#62612yes—
604C2×C4#381112yes—
605C2×C4#381111yescharacteristic
606C2×C4C22×D3211yescharacteristic
607C8—62no—
608C8—62no—
609C2×C3—21no—
610C2×C3—24no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—242no—
614C2×C3#481014yescomplemented
615C2×C3#517214yescomplemented
616C2×C3C2×#88211yescharacteristic
617C2×C3C2×#91411yescharacteristic
618C2×C3C2×#91411yescharacteristic
619C2×C3C2×#91611yescharacteristic
620C2×C3C2×#91911yescharacteristic
621C2×C3C2×#93711yescharacteristic
622D3—82no—
623D3—124no—
624D3—128no—
625D3—122no—
626D3—124no—
627D3—122no—
628D3—124no—
629C22—122no—
630C22—122no—
631C22—122no—
632C22—182no—
633C22—184no—
634C22—182no—
635C22—182no—
636C22—244no—
637C22—362no—
638C22—364no—
639C22—368no—
640C22—362no—
641C22#6394112yes—
642C22#6395012yes—
643C22#6398112yes—
644C22C2×#381111yescharacteristic
645C4—24no—
646C4—122no—
647C4—182no—
648C4#6398112yes—
649C4C22×#62611yescharacteristic
650C4C2×#381111yescharacteristic
651C3—21no—
652C3C2×#481011yescharacteristic, complemented
653C3C2×#517211yescharacteristic, complemented
654C2—242no—
655C2—362no—
656C2—364no—
657C2#1059159314yesdirect product factor
658C2C2×#6394111yescharacteristic
659C2C2×#6395011yescharacteristic
660C2C2×#6398111yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
hypercenterC22×Q8D32
hypocenterC32C2×#449
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#3832C2semidirect
2. C22×C3×#215C2semidirect
3. C2×#63916C2semidirect
4. C22×#3714C2semidirect
5. C2×C3×#835C2semidirect
6. #10591593C2direct (N × H)
7. C2×#63564C2semidirect
8. C2×#63557C2semidirect
15. C2×#3832C22semidirect
23. C2×C3×#215C22semidirect
29. #63916C22semidirect
31. C2×#3714C22semidirect
32. C3×#835C22semidirect
33. #63564C22semidirect
34. #63557C22semidirect
39. C22×#215D3semidirect
45. C2×#835D3semidirect
57. C2×C32×Q8D4semidirect
69. C2×C4⋊(C3⋊D3)D4semidirect
132. C2×#215C2×D3semidirect
146. #835C2×D3semidirect
166. C32×Q8C2×D4semidirect
178. C4⋊(C3⋊D3)C2×D4semidirect
215. C2×C3×Q8D12semidirect
216. C2×C3×Q8#67semidirect
393. C3×Q8C2×D12semidirect
394. C3×Q8C2×#67semidirect
459. C2×C32#449semidirect
474. C2×Q8#626semidirect
568. C32C2×#449semidirect
584. Q8C2×#626semidirect
614. C2×C3#4810semidirect
615. C2×C3#5172semidirect
652. C3C2×#4810semidirect
653. C3C2×#5172semidirect
657. C2#10591593direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38322
C22×C3×#2152
C2×#639162
C22×#37142
C2×C3×#8352
#105915932
C2×#635642
C2×#635572
C2×#51723
C2×#48103