Finite Group Databasebeta

← C2×#10591165 #11866976

Subgroups — C2×#10591165 #11866976

Order 1152.

1405 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64139C211yesmaximal, characteristic, complemented
2C2×C3×#930C211yesmaximal, characteristic, complemented
3C22×C3×#208C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic, complemented
5#10591165C218yesmaximal, direct product factor
6C2×#63573C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8C2×#63563C211yesmaximal, characteristic, complemented
9C2×#5135—31nomaximal
10C2×#5039—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#638—21no—
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C3×#67—21no—
15C22×C3×D12C2211yescharacteristic
16#64139—22no—
17#64139C2214yescomplemented
18C2×#3752—21no—
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C3×#930—22no—
21C3×#930C2214yescomplemented
22C2×C3×(C2×D3)⋊C4—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×#208—24no—
25C2×C3×#208C2214yescomplemented
26C22×C3×C3⋊C8C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C2×#3714—24no—
29C2×#3714C2214yescomplemented
30#63573C2214yescomplemented
31#63564C2214yescomplemented
32#63563C2214yescomplemented
33C22×C3×M16—31no—
34C2×C3×#121—31no—
35C22×#213—31no—
36C2×#930—31no—
37C2×#930—31no—
38C2×#930—61no—
39C2×#930D311yescharacteristic, complemented
40C22×#208D311yescharacteristic, complemented
41C22×D24—31no—
42C2×#832—31no—
43#5135—38no—
44C2×#821—31no—
45C2×#821—31no—
46C2×#817—31no—
47#5039—38no—
48C2×#809—31no—
49C2×#808—31no—
50C24×C32D411yescharacteristic
51C23×C3⋊D3—21no—
52C23×C3×D3—21no—
53C22×C32×C4—22no—
54C22×C32×C4—22no—
55C22×C32×C4D411yescharacteristic
56C22×C32×C4D412yes—
57C22×C32×C4C2312yes—
58C22×C32×C4C2311yescharacteristic
59C2×#638—24no—
60C2×#638—44no—
61C22×C3⋊Dic3—21no—
62C2×C4⋊(C3⋊D3)—22no—
63C2×C4⋊(C3⋊D3)—22no—
64C2×C4⋊(C3⋊D3)—21no—
65C2×C4⋊(C3⋊D3)C2312yes—
66C2×C3×#67—24no—
67C2×C3×#67—44no—
68C22×C3×Dic3—21no—
69C2×C3×D12—22no—
70C2×C3×D12—22no—
71C2×C3×D12—21no—
72C2×C3×D12C2312yes—
73#3752—24no—
74C4⋊(C3⋊Dic3)—21no—
75C4⋊(C3⋊Dic3)C2312yes—
76C3×(C2×D3)⋊C4—24no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3C2312yes—
79C3×#208—28no—
80C2×C3×C3⋊C8—22no—
81C2×C3×C3⋊C8D414yescomplemented
82C2×C3×C3⋊C8C2312yes—
83C2×C3×C3⋊C8C2312yes—
84#3714—28no—
85C2×#469—91noSylow
86C22×C3×D4—31no—
87C22×C3×D4—61no—
88C23×C3×C4—21no—
89C23×C3×C4C2×D311yescharacteristic
90C23×C3×C4C2×D311yescharacteristic
91C22×#67—21no—
92C22×#67—62no—
93C22×#67—61no—
94C22×#67—61no—
95C22×D12—31no—
96C22×D12—31no—
97C22×D12—61no—
98C22×D12C2×D311yescharacteristic
99C2×C3×M16—34no—
100C2×C3×M16—64no—
101C22×C3×C8—31no—
102C22×C3×C8—31no—
103C3×#121—34no—
104C3×#121—62no—
105C2×C3×C4⋊C4—31no—
106C2×C3×C22⋊C4—61no—
107C2×#213—34no—
108C2×#213—64no—
109#930—22no—
110#930—34no—
111#930—34no—
112#930—64no—
113#930—64no—
114#930—62no—
115#930—62no—
116#930C2×D314yescomplemented
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—62no—
119C2×(C2×D3)⋊C4—61no—
120C2×(C2×D3)⋊C4—61no—
121C2×C4⋊Dic3—31no—
122C2×C4⋊Dic3—31no—
123C2×C4⋊Dic3—61no—
124C2×C4⋊Dic3C2×D311yescharacteristic
125C2×#208—24no—
126C2×#208C2×D314yescomplemented
127C22×C3⋊C8C2×D311yescharacteristic
128C22×C3⋊C8C2×D311yescharacteristic
129C2×D24—34no—
130C2×D24—64no—
131#832—34no—
132#821—34no—
133#821—34no—
134#817—34no—
135#809—34no—
136#808—34no—
137C23×C32—22no—
138C23×C32—22no—
139C23×C32—22no—
140C23×C32C2×D412yes—
141C23×C32C2×D411yescharacteristic
142C22×C3⋊D3—22no—
143C22×C3⋊D3—42no—
144C22×C3⋊D3—42no—
145C22×C3⋊D3—42no—
146C22×C3×D3—22no—
147C22×C3×D3—42no—
148C22×C3×D3—42no—
149C22×C3×D3—42no—
150C2×C32×C4—22no—
151C2×C32×C4—24no—
152C2×C32×C4—22no—
153C2×C32×C4—22no—
154C2×C32×C4C2×D412yes—
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D412yes—
157C2×C32×C4#4112yes—
158C2×C32×C4C2411yescharacteristic
159#638—48no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—42no—
162C4⋊(C3⋊D3)—22no—
163C4⋊(C3⋊D3)—22no—
164C4⋊(C3⋊D3)—42no—
165C3×#67—48no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—42no—
168C3×D12—22no—
169C3×D12—22no—
170C3×D12—42no—
171C3×C3⋊C8—22no—
172C3×C3⋊C8C2×D414yescomplemented
173C22×D8—91no—
174C22×M16—31no—
175C2×#121—31no—
176C2×#121—91no—
177#469—98no—
178C2×#106—91no—
179C2×#102—91no—
180C2×#102—91no—
181C24×C3—21no—
182C24×C3—61no—
183C24×C3D1211yescharacteristic
184C24×C3#6711yescharacteristic
185C23×D3—21no—
186C23×D3—62no—
187C23×D3—61no—
188C23×D3—61no—
189C2×C3×D4—32no—
190C2×C3×D4—64no—
191C2×C3×D4—61no—
192C2×C3×D4—62no—
193C2×C3×D4—62no—
194C2×C3×D4—124no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—21no—
202C22×C3×C4—22no—
203C22×C3×C4—42no—
204C22×C3×C4—42no—
205C22×C3×C4—61no—
206C22×C3×C4D1211yescharacteristic
207C22×C3×C4D1212yes—
208C22×C3×C4#6711yescharacteristic
209C22×C3×C4#6712yes—
210C22×C3×C4C22×D312yes—
211C22×C3×C4C22×D312yes—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C2×#67—24no—
215C2×#67—44no—
216C2×#67—68no—
217C2×#67—64no—
218C2×#67—64no—
219C2×#67—128no—
220C2×#67—124no—
221C2×#67—124no—
222C22×Dic3—21no—
223C22×Dic3—62no—
224C22×Dic3—61no—
225C22×Dic3—61no—
226C2×D12—22no—
227C2×D12—22no—
228C2×D12—21no—
229C2×D12—32no—
230C2×D12—32no—
231C2×D12—62no—
232C2×D12—62no—
233C2×D12—62no—
234C2×D12—62no—
235C2×D12—62no—
236C2×D12—62no—
237C2×D12—61no—
238C2×D12—61no—
239C2×D12—122no—
240C2×D12—122no—
241C2×D12C22×D312yes—
242C3×M16—68no—
243C2×C3×C8—34no—
244C2×C3×C8—32no—
245C2×C3×C8—32no—
246C2×C3×C8—62no—
247C3×C4⋊C4—32no—
248C3×C4⋊C4—61no—
249C3×C22⋊C4—64no—
250#213—68no—
251(C2×D3)⋊C4—24no—
252(C2×D3)⋊C4—68no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—64no—
255C4⋊Dic3—21no—
256C4⋊Dic3—32no—
257C4⋊Dic3—32no—
258C4⋊Dic3—62no—
259C4⋊Dic3—62no—
260C4⋊Dic3—61no—
261C4⋊Dic3—61no—
262C4⋊Dic3C22×D312yes—
263#208—28no—
264C2×C3⋊C8—22no—
265C2×C3⋊C8#6714yescomplemented
266C2×C3⋊C8C22×D312yes—
267C2×C3⋊C8C22×D312yes—
268D24—68no—
269C22×C32—22no—
270C22×C32—22no—
271C22×C32—22no—
272C22×C32—44no—
273C22×C32#12112yes—
274C22×C32AGL(1,ℤ/8)12yes—
275C22×C32AGL(1,ℤ/8)12yes—
276C22×C32C22×D411yescharacteristic
277C2×C3⋊D3—42no—
278C2×C3⋊D3—42no—
279C2×C3⋊D3—42no—
280C2×C3⋊D3—84no—
281C2×C3×D3—42no—
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—84no—
285C32×C4—22no—
286C32×C4#12112yes—
287C32×C4C22×D411yescharacteristic
288C32×C4C2×#4111yescharacteristic
289C3⋊Dic3—42no—
290C3×Dic3—42no—
291C22×D4—31no—
292C22×D4—61no—
293C22×D4—91no—
294C22×D4—181no—
295C23×C4D3211yescharacteristic
296C2×D8—94no—
297C2×D8—184no—
298C2×M16—34no—
299C2×M16—64no—
300C22×C8—31no—
301C22×C8—31no—
302#121—34no—
303#121—62no—
304#121—94no—
305#121—182no—
306C2×C4⋊C4—31no—
307C2×C4⋊C4—91no—
308C2×C22⋊C4—61no—
309C2×C22⋊C4—181no—
310#106—94no—
311#102—94no—
312#102—94no—
313C23×C3—24no—
314C23×C3—22no—
315C23×C3—22no—
316C23×C3—22no—
317C23×C3—22no—
318C23×C3—22no—
319C23×C3—22no—
320C23×C3—22no—
321C23×C3—21no—
322C23×C3—42no—
323C23×C3—42no—
324C23×C3—62no—
325C23×C3—122no—
326C23×C3—122no—
327C23×C3—122no—
328C23×C3C2×D1212yes—
329C23×C3C2×D1211yescharacteristic
330C23×C3C2×#6712yes—
331C23×C3C2×#6711yescharacteristic
332C22×D3—22no—
333C22×D3—42no—
334C22×D3—42no—
335C22×D3—42no—
336C22×D3—64no—
337C22×D3—62no—
338C22×D3—62no—
339C22×D3—124no—
340C22×D3—124no—
341C22×D3—124no—
342C22×D3—122no—
343C22×D3—122no—
344C22×D3—122no—
345C22×D3—122no—
346C22×D3—122no—
347C22×D3—122no—
348C3×D4—62no—
349C3×D4—62no—
350C3×D4—128no—
351C3×D4—122no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—24no—
355C2×C3×C4—24no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—21no—
361C2×C3×C4—22no—
362C2×C3×C4—21no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—42no—
366C2×C3×C4—42no—
367C2×C3×C4—44no—
368C2×C3×C4—42no—
369C2×C3×C4—62no—
370C2×C3×C4—122no—
371C2×C3×C4C2×D1212yes—
372C2×C3×C4C2×D1211yescharacteristic
373C2×C3×C4#23512yes—
374C2×C3×C4D3×D412yes—
375C2×C3×C4#23712yes—
376C2×C3×C4C2×#6712yes—
377C2×C3×C4C2×#6711yescharacteristic
378C2×C3×C4C2×#6712yes—
379C2×C3×C4C23×D311yescharacteristic
380C2×C3×C4C23×D311yescharacteristic
381#67—48no—
382#67—1216no—
383#67—128no—
384#67—128no—
385C2×Dic3—22no—
386C2×Dic3—42no—
387C2×Dic3—64no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—124no—
391C2×Dic3—122no—
392C2×Dic3—122no—
393D12—22no—
394D12—22no—
395D12—42no—
396D12—62no—
397D12—62no—
398D12—62no—
399D12—62no—
400D12—122no—
401D12—122no—
402D12—124no—
403D12—122no—
404D12—122no—
405C3×C8—34no—
406C3×C8—62no—
407C3⋊C8—22no—
408C3⋊C8C2×#6714yescomplemented
409C2×C32—42no—
410C2×C32#46914yescomplemented
411C2×C32C2×#12111yescharacteristic
412C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
413C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
414C3⋊D3—82no—
415C3×D3—82no—
416C24—61no—
417C24—181no—
418C24#62611yescharacteristic
419C2×D4—32no—
420C2×D4—64no—
421C2×D4—62no—
422C2×D4—61no—
423C2×D4—62no—
424C2×D4—92no—
425C2×D4—124no—
426C2×D4—184no—
427C2×D4—182no—
428C2×D4—181no—
429C2×D4—182no—
430C2×D4—364no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—61no—
434C22×C4—181no—
435C22×C4#62612yes—
436C22×C4#62611yescharacteristic
437C22×C4C2×D3212yes—
438C22×C4C2×D3211yescharacteristic
439D8—188no—
440M16—68no—
441C2×C8—32no—
442C2×C8—34no—
443C2×C8—32no—
444C2×C8—62no—
445C4⋊C4—32no—
446C4⋊C4—61no—
447C4⋊C4—92no—
448C4⋊C4—181no—
449C22⋊C4—64no—
450C22⋊C4—184no—
451C22×C3—24no—
452C22×C3—22no—
453C22×C3—22no—
454C22×C3—22no—
455C22×C3—22no—
456C22×C3—22no—
457C22×C3—22no—
458C22×C3—21no—
459C22×C3—22no—
460C22×C3—22no—
461C22×C3—22no—
462C22×C3—42no—
463C22×C3—42no—
464C22×C3—48no—
465C22×C3—44no—
466C22×C3—44no—
467C22×C3—122no—
468C22×C3—122no—
469C22×C3—122no—
470C22×C3—244no—
471C22×C3#90812yes—
472C22×C3#90812yes—
473C22×C3#93012yes—
474C22×C3#93212yes—
475C22×C3#93912yes—
476C22×C3#94912yes—
477C22×C3C22×D1211yescharacteristic
478C22×C3C22×#6711yescharacteristic
479C2×D3—42no—
480C2×D3—42no—
481C2×D3—42no—
482C2×D3—84no—
483C2×D3—124no—
484C2×D3—124no—
485C2×D3—124no—
486C2×D3—122no—
487C2×D3—122no—
488C2×D3—122no—
489C2×D3—122no—
490C2×D3—122no—
491C2×D3—122no—
492C2×D3—248no—
493C2×D3—244no—
494C2×D3—244no—
495C3×C4—22no—
496C3×C4—22no—
497C3×C4—21no—
498C3×C4—21no—
499C3×C4—22no—
500C3×C4—42no—
501C3×C4—122no—
502C3×C4#93012yes—
503C3×C4#93912yes—
504C3×C4C2×#23511yescharacteristic
505C3×C4C2×D3×D411yescharacteristic
506C3×C4C2×#23711yescharacteristic
507C3×C4C22×#6711yescharacteristic
508Dic3—42no—
509Dic3—124no—
510Dic3—122no—
511Dic3—122no—
512C32C2×#46911yescharacteristic, complemented, Sylow
513C23—22no—
514C23—22no—
515C23—22no—
516C23—62no—
517C23—122no—
518C23—122no—
519C23—122no—
520C23—182no—
521C23—362no—
522C23—362no—
523C23—362no—
524C23C2×#62612yes—
525C23C2×#62611yescharacteristic
526D4—62no—
527D4—62no—
528D4—128no—
529D4—122no—
530D4—182no—
531D4—182no—
532D4—368no—
533D4—362no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—62no—
539C2×C4—122no—
540C2×C4—182no—
541C2×C4—362no—
542C2×C4#380412yes—
543C2×C4C2×#62612yes—
544C2×C4C2×#62611yescharacteristic
545C2×C4D3×#6712yes—
546C2×C4C22×D3211yescharacteristic
547C8—34no—
548C8—62no—
549C2×C3—21no—
550C2×C3—24no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—44no—
554C2×C3—42no—
555C2×C3—42no—
556C2×C3—242no—
557C2×C3#503914yescomplemented
558C2×C3#513514yescomplemented
559C2×C3C2×#90811yescharacteristic
560C2×C3C2×#90811yescharacteristic
561C2×C3C2×#93011yescharacteristic
562C2×C3C2×#93211yescharacteristic
563C2×C3C2×#93911yescharacteristic
564C2×C3C2×#94911yescharacteristic
565D3—82no—
566D3—244no—
567D3—242no—
568D3—242no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—44no—
573C22—122no—
574C22—122no—
575C22—122no—
576C22—244no—
577C22—362no—
578C22—362no—
579C22—362no—
580C22—724no—
581C22#6382512yes—
582C22#6383012yes—
583C22#6397812yes—
584C22C22×#62611yescharacteristic
585C4—22no—
586C4—122no—
587C4—362no—
588C4#6397812yes—
589C4C2×#380411yescharacteristic
590C4C2×D3×#6711yescharacteristic
591C3—21no—
592C3C2×#503911yescharacteristic, complemented
593C3C2×#513511yescharacteristic, complemented
594C2—42no—
595C2—242no—
596C2—722no—
597C2#1059116514yesdirect product factor
598C2C2×#6382511yescharacteristic
599C2C2×#6383011yescharacteristic
600C2C2×#6397811yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
hypercenterC23×C4D32
hypocenterC32C2×#469
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64139C2semidirect
2. C2×C3×#930C2semidirect
3. C22×C3×#208C2semidirect
4. C22×#3714C2semidirect
5. #10591165C2direct (N × H)
6. C2×#63573C2semidirect
7. C2×#63564C2semidirect
8. C2×#63563C2semidirect
17. #64139C22semidirect
21. C3×#930C22semidirect
25. C2×C3×#208C22semidirect
29. C2×#3714C22semidirect
30. #63573C22semidirect
31. #63564C22semidirect
32. #63563C22semidirect
39. C2×#930D3semidirect
40. C22×#208D3semidirect
81. C2×C3×C3⋊C8D4semidirect
116. #930C2×D3semidirect
126. C2×#208C2×D3semidirect
172. C3×C3⋊C8C2×D4semidirect
265. C2×C3⋊C8#67semidirect
408. C3⋊C8C2×#67semidirect
410. C2×C32#469semidirect
512. C32C2×#469semidirect
557. C2×C3#5039semidirect
558. C2×C3#5135semidirect
592. C3C2×#5039semidirect
593. C3C2×#5135semidirect
597. C2#10591165direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641392
C2×C3×#9302
C22×C3×#2082
C22×#37142
#105911652
C2×#635732
C2×#635642
C2×#635632
C2×#51353
C2×#50393