Finite Group Databasebeta

← C2×#10591592 #11863622

Subgroups — C2×#10591592 #11863622

Order 1152.

2009 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic, complemented
3C2×#63916C211yesmaximal, characteristic
4C22×#3716C211yesmaximal, characteristic, complemented
5C2×C3×#835C211yesmaximal, characteristic, complemented
6#10591592C218yesmaximal, direct product factor
7C2×#63567C211yesmaximal, characteristic, complemented
8C2×#63557C211yesmaximal, characteristic, complemented
9C2×#5170—31nomaximal
10C2×#4806—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C2×Q8×C3⋊D3—24no—
13C2×Q8×C3⋊D3—22no—
14C2×Q8×C3⋊D3—24no—
15C2×Q8×C3⋊D3C2214yescomplemented
16C22×C4×C3⋊D3—21no—
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×#634—21no—
19C22×#634C2211yescharacteristic
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#63916C2214yes—
30C2×#3716—24no—
31C2×#3716C2214yescomplemented
32C3×#835C2214yescomplemented
33#63567C2214yescomplemented
34#63557C2214yescomplemented
35C22×D3×Q8—31no—
36C22×D3×Q8—31no—
37C22×D3×Q8—61no—
38C22×C3×SD16—31no—
39C22×#215D311yescharacteristic, complemented
40C2×#938—31no—
41C22×#214—31no—
42C22×#204—31no—
43C2×#895—31no—
44C2×C3×#103—31no—
45C2×#835D311yescharacteristic, complemented
46#5170—38no—
47C2×(C2×D3)⋊C8—31no—
48C2×(C2×D3)⋊C8—31no—
49C2×#816—31no—
50C2×#810—31no—
51#4806—38no—
52C23×C3⋊D3D411yescharacteristic
53C23×C3×D3—21no—
54C2×C32×Q8—22no—
55C2×C32×Q8—21no—
56C2×C32×Q8D414yescomplemented
57C2×C32×Q8C2312yes—
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3—21no—
61C22×C3⋊Dic3D411yescharacteristic
62Q8×C3⋊D3—216no—
63Q8×C3⋊D3—28no—
64Q8×C3⋊D3—28no—
65C2×C4×C3⋊D3—28no—
66C2×C4×C3⋊D3—24no—
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3D412yes—
70C2×C4×C3⋊D3C2312yes—
71C2×#634—28no—
72C2×#634—21no—
73C2×#634—22no—
74C2×#634—24no—
75C2×#634D414yescomplemented
76C2×#634C2312yes—
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#3716—28no—
93C2×#448—91noSylow
94C22×C3×Q8—21no—
95C22×C3×Q8C2×D311yescharacteristic
96C22×C3×Q8C2×D311yescharacteristic
97C22×C3×D4—31no—
98C22×#67—61no—
99C2×D3×Q8—34no—
100C2×D3×Q8—34no—
101C2×D3×Q8—64no—
102C2×D3×Q8—64no—
103C2×D3×Q8—64no—
104C2×D3×Q8—62no—
105C2×D3×Q8—62no—
106C2×D3×Q8—64no—
107C2×D3×Q8—68no—
108C2×D3×Q8—68no—
109C2×D3×Q8—64no—
110C2×D3×Q8—64no—
111C22×D12—61no—
112C22×D12C2×D311yescharacteristic
113C22×C4×D3—31no—
114C22×C4×D3—31no—
115C22×C4×D3—61no—
116C22×C4×D3—61no—
117C22×C4×D3—61no—
118C22×C4×D3—62no—
119C22×Dic6—31no—
120C22×Dic6—31no—
121C22×Dic6—61no—
122C22×Dic6—61no—
123C22×Dic6—61no—
124C22×Dic6—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×#214—34no—
136C2×#214—64no—
137C2×(C2×D3)⋊C4—61no—
138C2×C4⋊Dic3C2×D311yescharacteristic
139C22×C3⋊C8C2×D311yescharacteristic
140C22×C3⋊C8C2×D311yescharacteristic
141C2×#204—34no—
142C2×#204—64no—
143#895—34no—
144#895—62no—
145C3×#103—34no—
146#835C2×D314yescomplemented
147(C2×D3)⋊C8—34no—
148(C2×D3)⋊C8—34no—
149#816—34no—
150#810—34no—
151C23×C32C2×D411yescharacteristic
152C22×C3⋊D3—22no—
153C22×C3⋊D3—22no—
154C22×C3⋊D3SD1614yescomplemented
155C22×C3⋊D3C2×D412yes—
156C22×C3×D3—22no—
157C22×C3×D3—42no—
158C22×C3×D3—42no—
159C22×C3×D3—42no—
160C32×Q8—24no—
161C32×Q8—22no—
162C32×Q8C2×D414yescomplemented
163C2×C32×C4—24no—
164C2×C32×C4—22no—
165C2×C32×C4C2×D412yes—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—24no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3C2×D412yes—
173C4×C3⋊D3—216no—
174C4×C3⋊D3—24no—
175C4×C3⋊D3—22no—
176C4×C3⋊D3—22no—
177#634—216no—
178#634—24no—
179#634—22no—
180#634C2×D414yescomplemented
181C2×C3×Dic3—22no—
182C2×C3×Dic3—42no—
183C3×D12—22no—
184C3×D12—22no—
185C3×D12—42no—
186#626—48no—
187C3×C3⋊C8—22no—
188C3×C3⋊C8—22no—
189C23×Q8—91no—
190C22×SD16—31no—
191C22×SD16—91no—
192C2×#121—91no—
193#448—98no—
194C2×#103—31no—
195C2×#103—91no—
196C2×C22⋊C8—91no—
197C24×C3—61no—
198C23×D3—21no—
199C23×D3—31no—
200C23×D3—31no—
201C23×D3—61no—
202C2×C3×Q8—22no—
203C2×C3×Q8—24no—
204C2×C3×Q8—22no—
205C2×C3×Q8—22no—
206C2×C3×Q8—21no—
207C2×C3×Q8—21no—
208C2×C3×Q8—24no—
209C2×C3×Q8—22no—
210C2×C3×Q8D1214yescomplemented
211C2×C3×Q8#6714yescomplemented
212C2×C3×Q8C22×D312yes—
213C2×C3×Q8C22×D312yes—
214C2×C3×D4—32no—
215C2×C3×D4—62no—
216C2×C3×D4—62no—
217C2×C3×D4—61no—
218C22×C3×C4—22no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—61no—
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C2×#67—64no—
226C2×#67—124no—
227C22×Dic3—21no—
228C22×Dic3—31no—
229C22×Dic3—31no—
230C22×Dic3—61no—
231C22×Dic3—62no—
232C22×Dic3—61no—
233C22×Dic3—61no—
234D3×Q8—68no—
235D3×Q8—68no—
236D3×Q8—616no—
237D3×Q8—632no—
238D3×Q8—616no—
239D3×Q8—616no—
240D3×Q8—616no—
241D3×Q8—68no—
242D3×Q8—68no—
243C2×D12—22no—
244C2×D12—22no—
245C2×D12—21no—
246C2×D12—64no—
247C2×D12—124no—
248C2×D12C22×D312yes—
249C2×C4×D3—32no—
250C2×C4×D3—32no—
251C2×C4×D3—32no—
252C2×C4×D3—32no—
253C2×C4×D3—62no—
254C2×C4×D3—62no—
255C2×C4×D3—64no—
256C2×C4×D3—64no—
257C2×C4×D3—68no—
258C2×C4×D3—616no—
259C2×C4×D3—68no—
260C2×C4×D3—68no—
261C2×C4×D3—64no—
262C2×C4×D3—64no—
263C2×C4×D3—62no—
264C2×C4×D3—62no—
265C2×C4×D3—62no—
266C2×C4×D3—62no—
267C2×Dic6—34no—
268C2×Dic6—34no—
269C2×Dic6—32no—
270C2×Dic6—32no—
271C2×Dic6—64no—
272C2×Dic6—62no—
273C2×Dic6—64no—
274C2×Dic6—64no—
275C2×Dic6—68no—
276C2×Dic6—616no—
277C2×Dic6—68no—
278C2×Dic6—68no—
279C2×Dic6—64no—
280C2×Dic6—62no—
281C2×Dic6—62no—
282C2×Dic6—61no—
283C2×Dic6—61no—
284C2×Dic6—62no—
285C3×SD16—68no—
286C2×C3×C8—32no—
287C2×C3×C8—32no—
288C2×C3×C8—62no—
289C2×C3×C8—62no—
290C3×C4⋊C4—32no—
291C3×C4⋊C4—61no—
292#217—64no—
293#215—28no—
294#214—68no—
295(C2×D3)⋊C4—64no—
296C4⋊Dic3—21no—
297C4⋊Dic3C22×D312yes—
298C2×C3⋊C8—22no—
299C2×C3⋊C8—22no—
300C2×C3⋊C8C22×D312yes—
301C2×C3⋊C8C22×D312yes—
302#204—68no—
303C22×C32#12012yes—
304C22×C32C2×SD1612yes—
305C22×C32#13712yes—
306C22×C32C22×D411yescharacteristic
307C2×C3⋊D3—22no—
308C2×C3⋊D3—22no—
309C2×C3⋊D3—28no—
310C2×C3⋊D3C2×SD1614yescomplemented
311C2×C3×D3—42no—
312C2×C3×D3—42no—
313C2×C3×D3—42no—
314C2×C3×D3—84no—
315C32×C4—24no—
316C32×C4#12012yes—
317C32×C4C22×D411yescharacteristic
318C32×C4C22×D411yescharacteristic
319C3⋊Dic3—22no—
320C3⋊Dic3—24no—
321C3×Dic3—42no—
322C22×Q8—94no—
323C22×Q8—91no—
324C22×Q8—181no—
325C22×Q8—182no—
326C22×Q8—184no—
327C22×Q8—184no—
328C22×Q8D3211yescharacteristic
329C22×D4—31no—
330C22×D4—181no—
331C23×C4—91no—
332C23×C4—181no—
333C2×SD16—34no—
334C2×SD16—64no—
335C2×SD16—94no—
336C2×SD16—184no—
337C22×C8—31no—
338C22×C8—31no—
339#121—94no—
340#121—182no—
341C2×C4⋊C4—31no—
342C2×C22⋊C4—181no—
343#103—34no—
344#103—94no—
345C22⋊C8—94no—
346C23×C3—21no—
347C23×C3—62no—
348C23×C3—122no—
349C23×C3—122no—
350C23×C3—122no—
351C23×C3D3×D411yescharacteristic
352C23×C3D3×D411yescharacteristic
353C22×D3—22no—
354C22×D3—34no—
355C22×D3—34no—
356C22×D3—32no—
357C22×D3—32no—
358C22×D3—42no—
359C22×D3—42no—
360C22×D3—42no—
361C22×D3—64no—
362C22×D3—62no—
363C22×D3—64no—
364C22×D3—64no—
365C22×D3—62no—
366C22×D3—62no—
367C22×D3—62no—
368C22×D3—62no—
369C3×Q8—24no—
370C3×Q8—28no—
371C3×Q8—24no—
372C3×Q8—24no—
373C3×Q8—22no—
374C3×Q8—22no—
375C3×Q8—24no—
376C3×Q8C2×D1214yescomplemented
377C3×Q8C2×#6714yescomplemented
378C3×D4—62no—
379C3×D4—62no—
380C3×D4—122no—
381C2×C3×C4—24no—
382C2×C3×C4—28no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—21no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—21no—
391C2×C3×C4—62no—
392C2×C3×C4—122no—
393C2×C3×C4C2×D1212yes—
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4D3×D412yes—
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D412yes—
398C2×C3×C4C2×#6712yes—
399C2×C3×C4C23×D311yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401#67—128no—
402C2×Dic3—22no—
403C2×Dic3—32no—
404C2×Dic3—32no—
405C2×Dic3—42no—
406C2×Dic3—62no—
407C2×Dic3—64no—
408C2×Dic3—64no—
409C2×Dic3—68no—
410C2×Dic3—64no—
411C2×Dic3—62no—
412C2×Dic3—64no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416D12—22no—
417D12—22no—
418D12—42no—
419D12—128no—
420C4×D3—632no—
421C4×D3—616no—
422C4×D3—616no—
423C4×D3—64no—
424C4×D3—64no—
425C4×D3—68no—
426C4×D3—64no—
427C4×D3—64no—
428C4×D3—62no—
429C4×D3—62no—
430C4×D3—62no—
431C4×D3—62no—
432Dic6—34no—
433Dic6—34no—
434Dic6—64no—
435Dic6—632no—
436Dic6—616no—
437Dic6—616no—
438Dic6—64no—
439Dic6—68no—
440Dic6—64no—
441Dic6—64no—
442Dic6—62no—
443Dic6—62no—
444C3×C8—62no—
445C3×C8—62no—
446C3⋊C8—22no—
447C3⋊C8—22no—
448C2×C32#44814yescomplemented
449C2×C32C2×#12011yescharacteristic
450C2×C32C22×SD1611yescharacteristic
451C2×C32C2×#13711yescharacteristic
452C3⋊D3—24no—
453C3×D3—82no—
454C24—61no—
455C24—91no—
456C2×Q8—21no—
457C2×Q8—22no—
458C2×Q8—92no—
459C2×Q8—94no—
460C2×Q8—184no—
461C2×Q8—188no—
462C2×Q8—188no—
463C2×Q8—1816no—
464C2×Q8—188no—
465C2×Q8—182no—
466C2×Q8—181no—
467C2×Q8#62614yescomplemented
468C2×Q8C2×D3212yes—
469C2×D4—32no—
470C2×D4—62no—
471C2×D4—62no—
472C2×D4—61no—
473C2×D4—184no—
474C2×D4—364no—
475C22×C4—21no—
476C22×C4—61no—
477C22×C4—91no—
478C22×C4—92no—
479C22×C4—92no—
480C22×C4—184no—
481C22×C4—188no—
482C22×C4—181no—
483C22×C4—182no—
484C22×C4—182no—
485C22×C4C2×D3211yescharacteristic
486SD16—68no—
487SD16—188no—
488C2×C8—32no—
489C2×C8—32no—
490C2×C8—62no—
491C2×C8—62no—
492C4⋊C4—32no—
493C4⋊C4—61no—
494C22⋊C4—184no—
495C22×C3—21no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—122no—
500C22×C3—122no—
501C22×C3—122no—
502C22×C3—244no—
503C22×C3#88212yes—
504C22×C3D3×SD1612yes—
505C22×C3D3×SD1612yes—
506C22×C3#91512yes—
507C22×C3#91812yes—
508C22×C3#93712yes—
509C22×C3C2×D3×D411yescharacteristic
510C22×C3C2×D3×D411yescharacteristic
511C2×D3—34no—
512C2×D3—34no—
513C2×D3—42no—
514C2×D3—42no—
515C2×D3—42no—
516C2×D3—64no—
517C2×D3—64no—
518C2×D3—64no—
519C2×D3—616no—
520C2×D3—68no—
521C2×D3—62no—
522C2×D3—62no—
523C2×D3—62no—
524C2×D3—62no—
525C2×D3—68no—
526C2×D3—84no—
527C3×C4—28no—
528C3×C4—24no—
529C3×C4—24no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—22no—
533C3×C4—122no—
534C3×C4#88212yes—
535C3×C4#93712yes—
536C3×C4C22×D1211yescharacteristic
537C3×C4C2×D3×D411yescharacteristic
538C3×C4C2×D3×D411yescharacteristic
539C3×C4C22×#6711yescharacteristic
540Dic3—42no—
541Dic3—64no—
542Dic3—68no—
543Dic3—64no—
544Dic3—62no—
545Dic3—64no—
546Dic3—62no—
547C32C2×#44811yescharacteristic, complemented, Sylow
548C23—62no—
549C23—92no—
550C23—94no—
551C23—122no—
552C23—122no—
553C23—122no—
554C23—182no—
555C23—182no—
556C23#381111yescharacteristic
557Q8—22no—
558Q8—24no—
559Q8—94no—
560Q8—1816no—
561Q8—182no—
562Q8—184no—
563Q8C2×#62614yescomplemented
564D4—62no—
565D4—62no—
566D4—122no—
567D4—368no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—62no—
571C2×C4—92no—
572C2×C4—122no—
573C2×C4—1816no—
574C2×C4—182no—
575C2×C4—182no—
576C2×C4—184no—
577C2×C4—182no—
578C2×C4—182no—
579C2×C4—184no—
580C2×C4C2×#62612yes—
581C2×C4#381112yes—
582C2×C4#381111yescharacteristic
583C2×C4C22×D3211yescharacteristic
584C8—62no—
585C8—62no—
586C2×C3—21no—
587C2×C3—24no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—242no—
591C2×C3#480614yescomplemented
592C2×C3#517014yescomplemented
593C2×C3C2×#88211yescharacteristic
594C2×C3C2×D3×SD1611yescharacteristic
595C2×C3C2×D3×SD1611yescharacteristic
596C2×C3C2×#91511yescharacteristic
597C2×C3C2×#91811yescharacteristic
598C2×C3C2×#93711yescharacteristic
599D3—68no—
600D3—64no—
601D3—64no—
602D3—82no—
603C22—94no—
604C22—122no—
605C22—122no—
606C22—122no—
607C22—182no—
608C22—188no—
609C22—182no—
610C22—244no—
611C22#6394012yes—
612C22#6395112yes—
613C22#6398112yes—
614C22C2×#381111yescharacteristic
615C4—24no—
616C4—122no—
617C4—182no—
618C4—184no—
619C4#6398112yes—
620C4C22×#62611yescharacteristic
621C4C2×#381111yescharacteristic
622C3—21no—
623C3C2×#480611yescharacteristic, complemented
624C3C2×#517011yescharacteristic, complemented
625C2—184no—
626C2—242no—
627C2#1059159214yesdirect product factor
628C2C2×#6394011yescharacteristic
629C2C2×#6395111yescharacteristic
630C2C2×#6398111yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC2×#63916C2
hypercenterC22×Q8D32
hypocenterC32C2×#448
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×Q8×C3⋊D3C2semidirect
2. C22×C3×#215C2semidirect
4. C22×#3716C2semidirect
5. C2×C3×#835C2semidirect
6. #10591592C2direct (N × H)
7. C2×#63567C2semidirect
8. C2×#63557C2semidirect
15. C2×Q8×C3⋊D3C22semidirect
23. C2×C3×#215C22semidirect
31. C2×#3716C22semidirect
32. C3×#835C22semidirect
33. #63567C22semidirect
34. #63557C22semidirect
39. C22×#215D3semidirect
45. C2×#835D3semidirect
56. C2×C32×Q8D4semidirect
75. C2×#634D4semidirect
132. C2×#215C2×D3semidirect
146. #835C2×D3semidirect
154. C22×C3⋊D3SD16semidirect
162. C32×Q8C2×D4semidirect
180. #634C2×D4semidirect
210. C2×C3×Q8D12semidirect
211. C2×C3×Q8#67semidirect
310. C2×C3⋊D3C2×SD16semidirect
376. C3×Q8C2×D12semidirect
377. C3×Q8C2×#67semidirect
448. C2×C32#448semidirect
467. C2×Q8#626semidirect
547. C32C2×#448semidirect
563. Q8C2×#626semidirect
591. C2×C3#4806semidirect
592. C2×C3#5170semidirect
623. C3C2×#4806semidirect
624. C3C2×#5170semidirect
627. C2#10591592direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×C3⋊D32
C22×C3×#2152
C2×#639162
C22×#37162
C2×C3×#8352
#105915922
C2×#635672
C2×#635572
C2×#51703
C2×#48063