Finite Group Databasebeta

← C2×#10590823 #11863734

Subgroups — C2×#10590823 #11863734

Order 1152.

1725 conjugacy classes of subgroups.

The subgroup lattice has 625 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C211yesmaximal, characteristic, complemented
2C22×C3×#204C211yesmaximal, characteristic, complemented
3C2×#63908C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic, complemented
5C2×#63648C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
7C2×#63566C211yesmaximal, characteristic, complemented
8#10590823C218yesmaximal, direct product factor
9C2×#5172—31nomaximal
10C2×#4734—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#626—21no—
16C22×#625—21no—
17C22×#624—21no—
18C2×#3799—24no—
19C2×#3799—22no—
20C2×#3799—24no—
21C2×#3799C2214yescomplemented
22C22×C32×C8C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×C3×#204—24no—
26C2×C3×#204C2214yescomplemented
27C2×(C2×D3)⋊Dic3—21no—
28#63908—22no—
29#63908C2214yescomplemented
30C2×#3714—24no—
31C2×#3714C2214yescomplemented
32#63648C2214yescomplemented
33C3×(C2×D3)⋊C8C2214yescomplemented
34#63566C2214yescomplemented
35C22×#239—31no—
36C22×#235—31no—
37C22×C3×SD16—31no—
38C2×#938—31no—
39C22×#213—31no—
40C2×#930—31no—
41C22×D24—31no—
42C22×#204D311yescharacteristic, complemented
43C2×C3×C22⋊C8—31no—
44C2×#835—31no—
45#5172—38no—
46C2×#821—31no—
47C2×#821—31no—
48C2×#821—61no—
49C2×(C2×D3)⋊C8D311yescharacteristic, complemented
50C2×#816—31no—
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)—21no—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)D414yescomplemented
60C2×C4⋊(C3⋊D3)C2312yes—
61C22×C3×Dic3—21no—
62C22×C3×Dic3D411yescharacteristic
63C2×C3×D12—22no—
64C2×C3×D12—22no—
65C2×C3×D12—21no—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3D412yes—
70C2×C3×C4×D3C2312yes—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6D414yescomplemented
74C2×C3×Dic6C2312yes—
75C2×#626—28no—
76C2×#626—24no—
77C2×#625—24no—
78C2×#625—44no—
79C2×#624—28no—
80C2×#624—24no—
81#3799—216no—
82#3799—28no—
83#3799—28no—
84C2×C32×C8—22no—
85C2×C32×C8C2312yes—
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)C2312yes—
88C2×C3×C3⋊C8—22no—
89C2×C3×C3⋊C8C2312yes—
90C3×#204—28no—
91(C2×D3)⋊Dic3—24no—
92#3714—28no—
93C2×#449—91noSylow
94C22×C3×Q8—31no—
95C22×C3×D4—31no—
96C23×C3×C4—31no—
97C22×#67—61no—
98C22×#67—61no—
99C22×#67—61no—
100C2×#239—34no—
101C2×#239—64no—
102C2×#239—64no—
103C2×#239—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×D3—61no—
115C22×C4×D3C2×D311yescharacteristic
116C22×Dic6C2×D311yescharacteristic
117C2×C3×SD16—34no—
118C2×C3×SD16—64no—
119C22×C3×C8—21no—
120C22×C3×C8—31no—
121C22×C3×C8C2×D311yescharacteristic
122C22×C3×C8C2×D311yescharacteristic
123C2×#217—61no—
124#938—34no—
125#938—62no—
126C2×#213—34no—
127C2×#213—64no—
128#930—34no—
129#930—62no—
130C2×(C2×D3)⋊C4—61no—
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—31no—
133C2×C4⋊Dic3—61no—
134C22×C3⋊C8C2×D311yescharacteristic
135C2×D24—34no—
136C2×D24—64no—
137C2×#204—24no—
138C2×#204C2×D314yescomplemented
139C3×C22⋊C8—34no—
140#835—34no—
141#821—34no—
142#821—34no—
143#821—64no—
144(C2×D3)⋊C8C2×D314yescomplemented
145#816—34no—
146C23×C32C2×D411yescharacteristic
147C22×C3⋊D3—24no—
148C22×C3⋊D3—22no—
149C22×C3⋊D3—42no—
150C22×C3⋊D3—42no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3—42no—
156C22×C3×D3—42no—
157C22×C3×D3—42no—
158C22×C3×D3C2×D412yes—
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D412yes—
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2411yescharacteristic
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—42no—
165C4⋊(C3⋊D3)—24no—
166C4⋊(C3⋊D3)—22no—
167C4⋊(C3⋊D3)C2×D414yescomplemented
168C2×C3×Dic3—22no—
169C2×C3×Dic3—24no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3C2×D412yes—
172C3×D12—22no—
173C3×D12—22no—
174C3×D12—42no—
175C3×C4×D3—24no—
176C3×C4×D3—22no—
177C3×C4×D3—22no—
178C3×Dic6—24no—
179C3×Dic6—22no—
180C3×Dic6C2×D414yescomplemented
181#626—216no—
182#625—48no—
183#624—216no—
184C32×C8—22no—
185C3×C3⋊C8—22no—
186C22×#41—91no—
187C22×SD16—31no—
188C22×D8—91no—
189C2×#121—91no—
190#449—98no—
191C2×#103—91no—
192C2×#102—91no—
193C2×C22⋊C8—31no—
194C24×C3—31no—
195C24×C3—61no—
196C23×D3—21no—
197C23×D3—61no—
198C23×D3—61no—
199C23×D3—121no—
200C23×D3D1211yescharacteristic
201C2×C3×Q8—34no—
202C2×C3×Q8—32no—
203C2×C3×Q8—61no—
204C2×C3×Q8—62no—
205C2×C3×D4—32no—
206C2×C3×D4—61no—
207C2×C3×D4—62no—
208C2×C3×D4—62no—
209C22×C3×C4—21no—
210C22×C3×C4—31no—
211C22×C3×C4—32no—
212C22×C3×C4—32no—
213C22×C3×C4—61no—
214C22×C3×C4—62no—
215C22×C3×C4—62no—
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C2×#67—64no—
219C2×#67—68no—
220C2×#67—64no—
221C2×#67—64no—
222C2×#67—124no—
223C2×#67—124no—
224C22×Dic3—21no—
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3—121no—
228C22×Dic3D1211yescharacteristic
229#239—68no—
230#239—68no—
231#239—616no—
232#235—68no—
233#235—616no—
234#235—68no—
235C2×D12—22no—
236C2×D12—22no—
237C2×D12—21no—
238C2×D12—34no—
239C2×D12—34no—
240C2×D12—32no—
241C2×D12—32no—
242C2×D12—62no—
243C2×D12—64no—
244C2×D12—68no—
245C2×D12—64no—
246C2×D12—61no—
247C2×D12—61no—
248C2×D12—62no—
249C2×D12—62no—
250C2×D12—121no—
251C2×D12—122no—
252C2×D12C22×D312yes—
253C2×C4×D3—22no—
254C2×C4×D3—22no—
255C2×C4×D3—64no—
256C2×C4×D3—68no—
257C2×C4×D3—68no—
258C2×C4×D3—64no—
259C2×C4×D3D1212yes—
260C2×C4×D3C22×D312yes—
261C2×Dic6—21no—
262C2×Dic6—22no—
263C2×Dic6#6714yescomplemented
264C2×Dic6C22×D312yes—
265C3×SD16—68no—
266C2×C3×C8—22no—
267C2×C3×C8—22no—
268C2×C3×C8—22no—
269C2×C3×C8—32no—
270C2×C3×C8—42no—
271C2×C3×C8—62no—
272C2×C3×C8C22×D312yes—
273C2×C3×C8C22×D312yes—
274#217—64no—
275#213—68no—
276(C2×D3)⋊C4—64no—
277C4⋊Dic3—32no—
278C4⋊Dic3—32no—
279C4⋊Dic3—62no—
280C4⋊Dic3—61no—
281C4⋊Dic3—61no—
282C4⋊Dic3—121no—
283C2×C3⋊C8—22no—
284C2×C3⋊C8C22×D312yes—
285D24—68no—
286#204—28no—
287C22×C32#12012yes—
288C22×C32#13512yes—
289C22×C32AGL(1,ℤ/8)12yes—
290C22×C32C22×D411yescharacteristic
291C2×C3⋊D3—24no—
292C2×C3⋊D3—42no—
293C2×C3⋊D3—42no—
294C2×C3⋊D3—48no—
295C2×C3×D3—22no—
296C2×C3×D3—22no—
297C2×C3×D3—22no—
298C2×C3×D3—44no—
299C2×C3×D3—42no—
300C2×C3×D3—42no—
301C2×C3×D3—42no—
302C2×C3×D3—84no—
303C32×C4#12012yes—
304C32×C4C22×D411yescharacteristic
305C32×C4C22×D411yescharacteristic
306C3⋊Dic3—42no—
307C3×Dic3—22no—
308C3×Dic3—24no—
309C2×#41—94no—
310C2×#41—182no—
311C2×#41—184no—
312C2×#41—184no—
313C22×Q8—31no—
314C22×D4—31no—
315C22×D4—91no—
316C22×D4—181no—
317C22×D4—181no—
318C23×C4—31no—
319C23×C4—181no—
320C2×SD16—34no—
321C2×SD16—64no—
322C2×D8—94no—
323C2×D8—184no—
324C22×C8—31no—
325C22×C8D3211yescharacteristic
326#121—94no—
327#121—182no—
328C2×C4⋊C4—91no—
329C2×C22⋊C4—181no—
330#103—94no—
331#102—94no—
332C22⋊C8—34no—
333C23×C3—21no—
334C23×C3—32no—
335C23×C3—62no—
336C23×C3—62no—
337C23×C3—62no—
338C23×C3—62no—
339C23×C3—122no—
340C23×C3—122no—
341C23×C3—122no—
342C23×C3C2×D1211yescharacteristic
343C23×C3D3×D411yescharacteristic
344C22×D3—22no—
345C22×D3—22no—
346C22×D3—22no—
347C22×D3—22no—
348C22×D3—42no—
349C22×D3—42no—
350C22×D3—42no—
351C22×D3—64no—
352C22×D3—64no—
353C22×D3—62no—
354C22×D3—62no—
355C22×D3—122no—
356C22×D3—124no—
357C22×D3—122no—
358C22×D3—122no—
359C22×D3—122no—
360C22×D3—122no—
361C22×D3—242no—
362C22×D3—242no—
363C22×D3C2×D1212yes—
364C3×Q8—34no—
365C3×Q8—64no—
366C3×Q8—62no—
367C3×D4—62no—
368C3×D4—62no—
369C3×D4—122no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—32no—
375C2×C3×C4—64no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—64no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4C2×D1211yescharacteristic
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4D3×D412yes—
384C2×C3×C4D3×D412yes—
385C2×C3×C4D3×D412yes—
386C2×C3×C4C2×#6712yes—
387C2×C3×C4C23×D311yescharacteristic
388C2×C3×C4C23×D311yescharacteristic
389#67—616no—
390#67—128no—
391#67—128no—
392C2×Dic3—22no—
393C2×Dic3—24no—
394C2×Dic3—22no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—122no—
398C2×Dic3—122no—
399C2×Dic3—122no—
400C2×Dic3—242no—
401C2×Dic3C2×D1212yes—
402D12—22no—
403D12—22no—
404D12—34no—
405D12—34no—
406D12—42no—
407D12—64no—
408D12—616no—
409D12—64no—
410D12—64no—
411D12—62no—
412D12—62no—
413D12—122no—
414D12—124no—
415C4×D3—24no—
416C4×D3—22no—
417C4×D3—22no—
418C4×D3—616no—
419C4×D3—616no—
420Dic6—24no—
421Dic6—22no—
422Dic6C2×#6714yescomplemented
423C3×C8—22no—
424C3×C8—22no—
425C3×C8—42no—
426C3×C8—62no—
427C3⋊C8—22no—
428C2×C32#44914yescomplemented
429C2×C32C2×#12011yescharacteristic
430C2×C32C2×#13511yescharacteristic
431C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
432C3⋊D3—44no—
433C3×D3—42no—
434C3×D3—82no—
435C24—31no—
436C24—61no—
437C24—181no—
438#41—188no—
439#41—188no—
440#41—1816no—
441C2×Q8—32no—
442C2×Q8—34no—
443C2×Q8—61no—
444C2×Q8—62no—
445C2×D4—32no—
446C2×D4—61no—
447C2×D4—62no—
448C2×D4—62no—
449C2×D4—92no—
450C2×D4—94no—
451C2×D4—184no—
452C2×D4—188no—
453C2×D4—184no—
454C2×D4—181no—
455C2×D4—182no—
456C2×D4—364no—
457C22×C4—31no—
458C22×C4—32no—
459C22×C4—32no—
460C22×C4—61no—
461C22×C4—62no—
462C22×C4—62no—
463C22×C4—184no—
464C22×C4—188no—
465C22×C4—181no—
466C22×C4C2×D3211yescharacteristic
467SD16—68no—
468D8—188no—
469C2×C8—22no—
470C2×C8—32no—
471C2×C8—62no—
472C2×C8C2×D3212yes—
473C4⋊C4—92no—
474C4⋊C4—181no—
475C22⋊C4—184no—
476C22×C3—21no—
477C22×C3—22no—
478C22×C3—22no—
479C22×C3—22no—
480C22×C3—62no—
481C22×C3—62no—
482C22×C3—62no—
483C22×C3—124no—
484C22×C3—122no—
485C22×C3—122no—
486C22×C3—122no—
487C22×C3—244no—
488C22×C3#88212yes—
489C22×C3#90412yes—
490C22×C3#90812yes—
491C22×C3#91412yes—
492C22×C3#91612yes—
493C22×C3#93712yes—
494C22×C3C22×D1211yescharacteristic
495C22×C3C2×D3×D411yescharacteristic
496C2×D3—22no—
497C2×D3—22no—
498C2×D3—22no—
499C2×D3—44no—
500C2×D3—42no—
501C2×D3—42no—
502C2×D3—42no—
503C2×D3—64no—
504C2×D3—64no—
505C2×D3—84no—
506C2×D3—124no—
507C2×D3—128no—
508C2×D3—122no—
509C2×D3—122no—
510C2×D3—128no—
511C2×D3—122no—
512C2×D3—122no—
513C2×D3—248no—
514C2×D3—242no—
515C2×D3—242no—
516C3×C4—21no—
517C3×C4—21no—
518C3×C4—22no—
519C3×C4—64no—
520C3×C4—62no—
521C3×C4#88212yes—
522C3×C4#93712yes—
523C3×C4C2×D3×D411yescharacteristic
524C3×C4C2×D3×D411yescharacteristic
525C3×C4C2×D3×D411yescharacteristic
526C3×C4C22×#6711yescharacteristic
527Dic3—22no—
528Dic3—24no—
529Dic3—122no—
530Dic3—122no—
531Dic3—242no—
532C32C2×#44911yescharacteristic, complemented, Sylow
533C23—32no—
534C23—62no—
535C23—62no—
536C23—62no—
537C23—62no—
538C23—122no—
539C23—122no—
540C23—122no—
541C23—182no—
542C23—184no—
543C23—362no—
544C23—362no—
545C23D3×D1211yescharacteristic
546Q8—34no—
547Q8—62no—
548Q8—64no—
549D4—62no—
550D4—62no—
551D4—94no—
552D4—122no—
553D4—1816no—
554D4—182no—
555D4—184no—
556D4—368no—
557C2×C4—32no—
558C2×C4—62no—
559C2×C4—62no—
560C2×C4—64no—
561C2×C4—62no—
562C2×C4—62no—
563C2×C4—64no—
564C2×C4—1816no—
565C2×C4—182no—
566C2×C4—362no—
567C2×C4D3×D1211yescharacteristic
568C2×C4#380212yes—
569C2×C4D3×#6712yes—
570C2×C4C22×D3211yescharacteristic
571C8—22no—
572C8—62no—
573C2×C3—24no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—122no—
578C2×C3—242no—
579C2×C3#473414yescomplemented
580C2×C3#517214yescomplemented
581C2×C3C2×#88211yescharacteristic
582C2×C3C2×#90411yescharacteristic
583C2×C3C2×#90811yescharacteristic
584C2×C3C2×#91411yescharacteristic
585C2×C3C2×#91611yescharacteristic
586C2×C3C2×#93711yescharacteristic
587D3—42no—
588D3—82no—
589D3—124no—
590D3—124no—
591D3—244no—
592C22—62no—
593C22—62no—
594C22—62no—
595C22—124no—
596C22—122no—
597C22—122no—
598C22—122no—
599C22—184no—
600C22—244no—
601C22—368no—
602C22—362no—
603C22—362no—
604C22#6379412yes—
605C22#6380612yes—
606C22#6392212yes—
607C22C2×D3×D1211yescharacteristic
608C4—62no—
609C4—64no—
610C4—362no—
611C4#6392212yes—
612C4C2×#380211yescharacteristic
613C4C2×D3×#6711yescharacteristic
614C3—21no—
615C3C2×#473411yescharacteristic, complemented
616C3C2×#517211yescharacteristic, complemented
617C2—122no—
618C2—242no—
619C2—364no—
620C2#1059082314yesdirect product factor
621C2C2×#6379411yescharacteristic
622C2C2×#6380611yescharacteristic
623C2C2×#6392211yescharacteristic
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×#3799C2semidirect
2. C22×C3×#204C2semidirect
3. C2×#63908C2semidirect
4. C22×#3714C2semidirect
5. C2×#63648C2semidirect
6. C2×C3×(C2×D3)⋊C8C2semidirect
7. C2×#63566C2semidirect
8. #10590823C2direct (N × H)
21. C2×#3799C22semidirect
26. C2×C3×#204C22semidirect
29. #63908C22semidirect
31. C2×#3714C22semidirect
32. #63648C22semidirect
33. C3×(C2×D3)⋊C8C22semidirect
34. #63566C22semidirect
42. C22×#204D3semidirect
49. C2×(C2×D3)⋊C8D3semidirect
59. C2×C4⋊(C3⋊D3)D4semidirect
73. C2×C3×Dic6D4semidirect
138. C2×#204C2×D3semidirect
144. (C2×D3)⋊C8C2×D3semidirect
167. C4⋊(C3⋊D3)C2×D4semidirect
180. C3×Dic6C2×D4semidirect
263. C2×Dic6#67semidirect
422. Dic6C2×#67semidirect
428. C2×C32#449semidirect
532. C32C2×#449semidirect
579. C2×C3#4734semidirect
580. C2×C3#5172semidirect
615. C3C2×#4734semidirect
616. C3C2×#5172semidirect
620. C2#10590823direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37992
C22×C3×#2042
C2×#639082
C22×#37142
C2×#636482
C2×C3×(C2×D3)⋊C82
C2×#635662
#105908232
C2×#51723
C2×#47343