Finite Group Databasebeta

← C2×#10590968 #11863736

Subgroups — C2×#10590968 #11863736

Order 1152.

1773 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×#3795C211yesmaximal, characteristic, complemented
2C22×#3744C211yesmaximal, characteristic, complemented
3C2×#63909C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic, complemented
5C2×C3×#821C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
7C2×#63567C211yesmaximal, characteristic, complemented
8#10590968C218yesmaximal, direct product factor
9C2×#4781—31nomaximal
10C2×#4734—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3C2211yescharacteristic
15C22×#626—21no—
16C22×#625—21no—
17C22×D3×Dic3—21no—
18C2×#3795—24no—
19C2×#3795—24no—
20C2×#3795—22no—
21C2×#3795C2214yescomplemented
22C22×C32×C8C2211yescharacteristic
23C2×#3744—24no—
24C2×#3744C2214yescomplemented
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C2×#3722—21no—
28#63909—22no—
29#63909C2214yescomplemented
30C2×#3714—24no—
31C2×#3714C2214yescomplemented
32C3×#821C2214yescomplemented
33C3×(C2×D3)⋊C8C2214yescomplemented
34#63567C2214yescomplemented
35C22×#237—31no—
36C22×#235—31no—
37C22×#213—31no—
38C2×#930—31no—
39C22×D24—31no—
40C22×#204—31no—
41C22×#204—31no—
42C22×#204—61no—
43C2×#895—31no—
44C2×C3×#102—31no—
45C2×C3×C22⋊C8—31no—
46C2×#821D311yescharacteristic, complemented
47C2×(C2×D3)⋊C8D311yescharacteristic, complemented
48C2×#816—31no—
49C2×#810—31no—
50#4781—38no—
51#4734—38no—
52C23×C3⋊D3—21no—
53C23×C3×D3—21no—
54C23×C3×D3D411yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—21no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)C2312yes—
61C2×#634—21no—
62C2×#634—22no—
63C2×#634D414yescomplemented
64C2×#634C2312yes—
65C22×C3×Dic3—21no—
66C22×C3×Dic3D411yescharacteristic
67C2×C3×D12—21no—
68C2×C3×D12—22no—
69C2×C3×D12D414yescomplemented
70C2×C3×D12C2312yes—
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3D412yes—
74C2×C3×C4×D3C2312yes—
75C2×#626—24no—
76C2×#626—44no—
77C2×#625—28no—
78C2×#625—24no—
79C2×D3×Dic3—28no—
80C2×D3×Dic3—24no—
81#3795—216no—
82#3795—28no—
83#3795—28no—
84C2×C32×C8—22no—
85C2×C32×C8C2312yes—
86#3744—28no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2312yes—
89C2×C3×C3⋊C8—22no—
90C2×C3×C3⋊C8C2312yes—
91#3722—24no—
92#3714—28no—
93C2×#449—91noSylow
94C22×C3×D4—31no—
95C23×C3×C4—31no—
96C22×#67—61no—
97C22×#67—61no—
98C22×#67—61no—
99C23×Dic3—61no—
100C2×#237—34no—
101C2×#237—64no—
102C2×#237—64no—
103C2×#237—62no—
104C2×#235—34no—
105C2×#235—64no—
106C2×#235—62no—
107C2×#235—64no—
108C22×D12—31no—
109C22×D12—31no—
110C22×D12—61no—
111C22×D12—61no—
112C22×D12C2×D311yescharacteristic
113C22×C4×D3—61no—
114C22×C4×D3C2×D311yescharacteristic
115C22×Dic6—31no—
116C22×Dic6—31no—
117C22×Dic6—61no—
118C22×C3×C8—21no—
119C22×C3×C8—31no—
120C22×C3×C8C2×D311yescharacteristic
121C22×C3×C8C2×D311yescharacteristic
122C2×C3×C4⋊C4—31no—
123C2×#213—34no—
124C2×#213—64no—
125#930—34no—
126#930—62no—
127C2×(C2×D3)⋊C4—61no—
128C2×(C2×D3)⋊C4—61no—
129C2×C4⋊Dic3C2×D311yescharacteristic
130C22×C3⋊C8C2×D311yescharacteristic
131C2×D24—34no—
132C2×D24—64no—
133C2×#204—34no—
134C2×#204—34no—
135C2×#204—64no—
136C2×#204—64no—
137C2×#204—64no—
138C2×#204—68no—
139#895—34no—
140#895—62no—
141C3×#102—34no—
142C3×C22⋊C8—34no—
143#821C2×D314yescomplemented
144(C2×D3)⋊C8C2×D314yescomplemented
145#816—34no—
146#810—34no—
147C23×C32C2×D411yescharacteristic
148C22×C3⋊D3—22no—
149C22×C3⋊D3—42no—
150C22×C3⋊D3—42no—
151C22×C3⋊D3—42no—
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—
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2×D412yes—
163C2×C32×C4C2411yescharacteristic
164C2×C3⋊Dic3—24no—
165C2×C3⋊Dic3—22no—
166C4⋊(C3⋊D3)—22no—
167C4⋊(C3⋊D3)—22no—
168C4⋊(C3⋊D3)—42no—
169#634—24no—
170#634—22no—
171#634C2×D414yescomplemented
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—42no—
175C2×C3×Dic3C2×D412yes—
176C3×D12—24no—
177C3×D12—22no—
178C3×D12C2×D414yescomplemented
179C3×C4×D3—24no—
180C3×C4×D3—22no—
181C3×C4×D3—22no—
182#626—48no—
183#625—216no—
184D3×Dic3—216no—
185C32×C8—22no—
186C3×C3⋊C8—22no—
187C22×#41—91no—
188C22×SD16—91no—
189C22×D8—91no—
190C2×#121—91no—
191#449—98no—
192C2×#103—91no—
193C2×#102—31no—
194C2×C22⋊C8—31no—
195C24×C3—31no—
196C24×C3—61no—
197C23×D3—21no—
198C23×D3—61no—
199C23×D3—61no—
200C23×D3—121no—
201C23×D3D1211yescharacteristic
202C2×C3×D4—34no—
203C2×C3×D4—32no—
204C2×C3×D4—61no—
205C2×C3×D4—62no—
206C22×C3×C4—21no—
207C22×C3×C4—31no—
208C22×C3×C4—32no—
209C22×C3×C4—32no—
210C22×C3×C4—62no—
211C22×C3×C4—62no—
212C22×C3×C4—61no—
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C2×#67—64no—
216C2×#67—64no—
217C2×#67—68no—
218C2×#67—68no—
219C2×#67—64no—
220C2×#67—124no—
221C22×Dic3—21no—
222C22×Dic3—68no—
223C22×Dic3—61no—
224C22×Dic3—61no—
225C22×Dic3—64no—
226C22×Dic3—121no—
227C22×Dic3D1211yescharacteristic
228#237—68no—
229#237—68no—
230#237—616no—
231#235—68no—
232#235—616no—
233#235—68no—
234C2×D12—21no—
235C2×D12—22no—
236C2×D12—32no—
237C2×D12—32no—
238C2×D12—62no—
239C2×D12—64no—
240C2×D12—62no—
241C2×D12—62no—
242C2×D12—62no—
243C2×D12—62no—
244C2×D12—64no—
245C2×D12—61no—
246C2×D12—61no—
247C2×D12—122no—
248C2×D12—121no—
249C2×D12—124no—
250C2×D12D1214yescomplemented
251C2×D12C22×D312yes—
252C2×C4×D3—22no—
253C2×C4×D3—22no—
254C2×C4×D3—64no—
255C2×C4×D3—68no—
256C2×C4×D3D1212yes—
257C2×C4×D3C22×D312yes—
258C2×Dic6—34no—
259C2×Dic6—34no—
260C2×Dic6—32no—
261C2×Dic6—32no—
262C2×Dic6—64no—
263C2×Dic6—62no—
264C2×Dic6—62no—
265C2×Dic6—61no—
266C2×Dic6—61no—
267C2×Dic6—62no—
268C2×Dic6—121no—
269C2×Dic6—122no—
270C2×C3×C8—24no—
271C2×C3×C8—22no—
272C2×C3×C8—22no—
273C2×C3×C8—22no—
274C2×C3×C8—32no—
275C2×C3×C8—62no—
276C2×C3×C8C22×D312yes—
277C2×C3×C8C22×D312yes—
278C3×C4⋊C4—32no—
279C3×C4⋊C4—61no—
280#213—68no—
281(C2×D3)⋊C4—64no—
282(C2×D3)⋊C4—64no—
283C4⋊Dic3—21no—
284C4⋊Dic3C22×D312yes—
285C2×C3⋊C8—22no—
286C2×C3⋊C8C22×D312yes—
287D24—68no—
288#204—68no—
289#204—68no—
290#204—616no—
291C22×C32#12012yes—
292C22×C32#13512yes—
293C22×C32AGL(1,ℤ/8)12yes—
294C22×C32C22×D411yescharacteristic
295C2×C3⋊D3—42no—
296C2×C3⋊D3—42no—
297C2×C3⋊D3—42no—
298C2×C3⋊D3—84no—
299C2×C3×D3—24no—
300C2×C3×D3—22no—
301C2×C3×D3—22no—
302C2×C3×D3—22no—
303C2×C3×D3—42no—
304C2×C3×D3—42no—
305C2×C3×D3—44no—
306C2×C3×D3—48no—
307C32×C4#12012yes—
308C32×C4C22×D411yescharacteristic
309C32×C4C22×D411yescharacteristic
310C3⋊Dic3—24no—
311C3×Dic3—22no—
312C3×Dic3—42no—
313C2×#41—94no—
314C2×#41—182no—
315C2×#41—184no—
316C2×#41—184no—
317C22×Q8—91no—
318C22×D4—31no—
319C22×D4—91no—
320C22×D4—181no—
321C22×D4—181no—
322C23×C4—31no—
323C23×C4—181no—
324C2×SD16—94no—
325C2×SD16—184no—
326C2×D8—94no—
327C2×D8—184no—
328C22×C8—31no—
329C22×C8D3211yescharacteristic
330#121—94no—
331#121—182no—
332C2×C4⋊C4—31no—
333C2×C22⋊C4—181no—
334#103—94no—
335#102—34no—
336C22⋊C8—34no—
337C23×C3—21no—
338C23×C3—32no—
339C23×C3—64no—
340C23×C3—62no—
341C23×C3—62no—
342C23×C3—62no—
343C23×C3—62no—
344C23×C3—122no—
345C23×C3—122no—
346C23×C3C2×D1211yescharacteristic
347C23×C3D3×D411yescharacteristic
348C22×D3—22no—
349C22×D3—24no—
350C22×D3—22no—
351C22×D3—22no—
352C22×D3—22no—
353C22×D3—42no—
354C22×D3—42no—
355C22×D3—62no—
356C22×D3—62no—
357C22×D3—122no—
358C22×D3—124no—
359C22×D3—122no—
360C22×D3—122no—
361C22×D3—122no—
362C22×D3—122no—
363C22×D3—122no—
364C22×D3—122no—
365C22×D3—242no—
366C22×D3—242no—
367C22×D3C2×D1212yes—
368C3×D4—34no—
369C3×D4—64no—
370C3×D4—62no—
371C2×C3×C4—21no—
372C2×C3×C4—22no—
373C2×C3×C4—21no—
374C2×C3×C4—22no—
375C2×C3×C4—32no—
376C2×C3×C4—62no—
377C2×C3×C4—64no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—122no—
382C2×C3×C4C2×D1211yescharacteristic
383C2×C3×C4C2×D1212yes—
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D412yes—
386C2×C3×C4D3×D412yes—
387C2×C3×C4D3×D412yes—
388C2×C3×C4C23×D311yescharacteristic
389C2×C3×C4C23×D311yescharacteristic
390#67—616no—
391#67—616no—
392#67—128no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—42no—
396C2×Dic3—616no—
397C2×Dic3—64no—
398C2×Dic3—64no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—122no—
402C2×Dic3—124no—
403C2×Dic3C2×D1212yes—
404D12—24no—
405D12—22no—
406D12—64no—
407D12—62no—
408D12—62no—
409D12—62no—
410D12—62no—
411D12—122no—
412D12—124no—
413D12—128no—
414D12—122no—
415D12—122no—
416D12C2×D1214yescomplemented
417C4×D3—24no—
418C4×D3—22no—
419C4×D3—22no—
420C4×D3—616no—
421Dic6—34no—
422Dic6—34no—
423Dic6—64no—
424Dic6—64no—
425Dic6—64no—
426Dic6—62no—
427Dic6—62no—
428Dic6—122no—
429Dic6—124no—
430C3×C8—24no—
431C3×C8—22no—
432C3×C8—22no—
433C3×C8—62no—
434C3⋊C8—22no—
435C2×C32#44914yescomplemented
436C2×C32C2×#12011yescharacteristic
437C2×C32C2×#13511yescharacteristic
438C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
439C3⋊D3—82no—
440C3×D3—42no—
441C3×D3—44no—
442C24—31no—
443C24—61no—
444C24—181no—
445#41—188no—
446#41—188no—
447#41—1816no—
448C2×Q8—92no—
449C2×Q8—94no—
450C2×Q8—181no—
451C2×Q8—182no—
452C2×D4—32no—
453C2×D4—34no—
454C2×D4—61no—
455C2×D4—62no—
456C2×D4—92no—
457C2×D4—184no—
458C2×D4—184no—
459C2×D4—188no—
460C2×D4—182no—
461C2×D4—181no—
462C2×D4—182no—
463C2×D4—364no—
464C22×C4—31no—
465C22×C4—32no—
466C22×C4—32no—
467C22×C4—62no—
468C22×C4—62no—
469C22×C4—61no—
470C22×C4—184no—
471C22×C4—188no—
472C22×C4—181no—
473C22×C4C2×D3211yescharacteristic
474SD16—188no—
475D8—188no—
476C2×C8—22no—
477C2×C8—32no—
478C2×C8—62no—
479C2×C8C2×D3212yes—
480C4⋊C4—32no—
481C4⋊C4—61no—
482C22⋊C4—184no—
483C22×C3—21no—
484C22×C3—22no—
485C22×C3—22no—
486C22×C3—22no—
487C22×C3—64no—
488C22×C3—62no—
489C22×C3—62no—
490C22×C3—62no—
491C22×C3—122no—
492C22×C3—122no—
493C22×C3—128no—
494C22×C3—124no—
495C22×C3#88212yes—
496C22×C3#88212yes—
497C22×C3#90412yes—
498C22×C3#90812yes—
499C22×C3#91112yes—
500C22×C3#91612yes—
501C22×C3C22×D1211yescharacteristic
502C22×C3C2×D3×D411yescharacteristic
503C2×D3—22no—
504C2×D3—22no—
505C2×D3—24no—
506C2×D3—22no—
507C2×D3—42no—
508C2×D3—44no—
509C2×D3—42no—
510C2×D3—48no—
511C2×D3—124no—
512C2×D3—122no—
513C2×D3—122no—
514C2×D3—122no—
515C2×D3—122no—
516C2×D3—122no—
517C2×D3—122no—
518C2×D3—242no—
519C2×D3—242no—
520C2×D3—248no—
521C2×D3—244no—
522C2×D3—244no—
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—22no—
526C3×C4—62no—
527C3×C4—122no—
528C3×C4#88212yes—
529C3×C4#88212yes—
530C3×C4C22×D1211yescharacteristic
531C3×C4C2×D3×D411yescharacteristic
532C3×C4C2×D3×D411yescharacteristic
533C3×C4C2×D3×D411yescharacteristic
534Dic3—22no—
535Dic3—42no—
536Dic3—64no—
537Dic3—64no—
538Dic3—124no—
539C32C2×#44911yescharacteristic, complemented, Sylow
540C23—32no—
541C23—62no—
542C23—62no—
543C23—62no—
544C23—62no—
545C23—64no—
546C23—122no—
547C23—122no—
548C23—182no—
549C23—362no—
550C23—362no—
551C23—362no—
552C23D3×D1211yescharacteristic
553Q8—94no—
554Q8—182no—
555Q8—184no—
556D4—34no—
557D4—62no—
558D4—64no—
559D4—1816no—
560D4—182no—
561D4—182no—
562D4—368no—
563D4—362no—
564C2×C4—32no—
565C2×C4—62no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—64no—
569C2×C4—62no—
570C2×C4—122no—
571C2×C4—1816no—
572C2×C4—182no—
573C2×C4—184no—
574C2×C4D3×D1212yes—
575C2×C4D3×D1211yescharacteristic
576C2×C4#381112yes—
577C2×C4C22×D3211yescharacteristic
578C8—22no—
579C8—62no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—24no—
583C2×C3—21no—
584C2×C3—124no—
585C2×C3—122no—
586C2×C3#473414yescomplemented
587C2×C3#478114yescomplemented
588C2×C3C2×#88211yescharacteristic
589C2×C3C2×#88211yescharacteristic
590C2×C3C2×#90411yescharacteristic
591C2×C3C2×#90811yescharacteristic
592C2×C3C2×#91111yescharacteristic
593C2×C3C2×#91611yescharacteristic
594D3—42no—
595D3—44no—
596D3—244no—
597D3—242no—
598D3—242no—
599C22—62no—
600C22—62no—
601C22—62no—
602C22—64no—
603C22—122no—
604C22—122no—
605C22—124no—
606C22—128no—
607C22—362no—
608C22—362no—
609C22—362no—
610C22—724no—
611C22#6379512yes—
612C22#6380612yes—
613C22#6392312yes—
614C22C2×D3×D1211yescharacteristic
615C4—62no—
616C4—122no—
617C4—184no—
618C4#6392312yes—
619C4C2×D3×D1211yescharacteristic
620C4C2×#381111yescharacteristic
621C3—21no—
622C3C2×#473411yescharacteristic, complemented
623C3C2×#478111yescharacteristic, complemented
624C2—122no—
625C2—124no—
626C2—722no—
627C2#1059096814yesdirect product factor
628C2C2×#6379511yescharacteristic
629C2C2×#6380611yescharacteristic
630C2C2×#6392311yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
hypercenterC22×C8D32
hypocenterC32C2×#449
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×#3795C2semidirect
2. C22×#3744C2semidirect
3. C2×#63909C2semidirect
4. C22×#3714C2semidirect
5. C2×C3×#821C2semidirect
6. C2×C3×(C2×D3)⋊C8C2semidirect
7. C2×#63567C2semidirect
8. #10590968C2direct (N × H)
21. C2×#3795C22semidirect
24. C2×#3744C22semidirect
29. #63909C22semidirect
31. C2×#3714C22semidirect
32. C3×#821C22semidirect
33. C3×(C2×D3)⋊C8C22semidirect
34. #63567C22semidirect
46. C2×#821D3semidirect
47. C2×(C2×D3)⋊C8D3semidirect
63. C2×#634D4semidirect
69. C2×C3×D12D4semidirect
143. #821C2×D3semidirect
144. (C2×D3)⋊C8C2×D3semidirect
171. #634C2×D4semidirect
178. C3×D12C2×D4semidirect
250. C2×D12D12semidirect
416. D12C2×D12semidirect
435. C2×C32#449semidirect
539. C32C2×#449semidirect
586. C2×C3#4734semidirect
587. C2×C3#4781semidirect
622. C3C2×#4734semidirect
623. C3C2×#4781semidirect
627. C2#10590968direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37952
C22×#37442
C2×#639092
C22×#37142
C2×C3×#8212
C2×C3×(C2×D3)⋊C82
C2×#635672
#105909682
C2×#47813
C2×#47343