Finite Group Databasebeta

← C2×#10594659 #11901351

Subgroups — C2×#10594659 #11901351

Order 1152.

2833 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64106C211yesmaximal, characteristic, complemented
2C2×C3×#894C212yesmaximal, complemented
3C2×#63922C212yesmaximal, complemented
4C2×#63921C211yesmaximal, characteristic, complemented
5C2×#63913C212yesmaximal, complemented
6C2×#63912C211yesmaximal, characteristic, complemented
7C2×#63908C212yesmaximal, complemented
8C2×#63904C212yesmaximal, complemented
9C2×#63861C212yesmaximal, complemented
10#10594659C2116yesmaximal, direct product factor
11C2×#5657—32nomaximal
12C23×D32C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×#634C2211yescharacteristic, complemented
15C22×C3×D12C2212yes—
16C22×C3×C4×D3C2212yescomplemented
17C22×#626C2212yes—
18C22×#625C2212yes—
19C22×#625C2211yescharacteristic, complemented
20C22×#624C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic, complemented
22C2×#3752C2212yes—
23C2×C4⋊(C3⋊Dic3)C2212yescomplemented
24#64106C2218yescomplemented
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×(C2×D3)⋊C4C2212yescomplemented
28C2×C3×Dic3⋊C4C2212yescomplemented
29C3×#894C22116yescomplemented
30C2×#3724C2211yescharacteristic, complemented
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yescomplemented
34C2×Dic32C2212yescomplemented
35#63922C22116yescomplemented
36#63921C2218yescomplemented
37#63913C22116yescomplemented
38#63912C2218yescomplemented
39#63908C22116yescomplemented
40#63904C22116yescomplemented
41#63861C22116yescomplemented
42C2×C3×#123—32no—
43C2×#938—32no—
44C2×#937—32no—
45C2×#930—32no—
46C2×C4×#67—32no—
47#5657—332no—
48C2×#898—32no—
49C2×#897—32no—
50C2×#897—61no—
51C2×#894D312yescomplemented
52C2×#893—32no—
53C2×#885—32no—
54C2×#885—32no—
55C2×#884—32no—
56C2×#882—32no—
57C2×D3×C22⋊C4—32no—
58C2×#879—32no—
59C23×C3⋊D3C2311yescharacteristic
60C23×C3×D3C2312yes—
61C23×C3×D3C2312yes—
62C22×D32—24no—
63C22×D32—42no—
64C22×D32—42no—
65C22×D32C2314yes—
66C22×C32×C4C2312yes—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2311yescharacteristic
70C2×C4×C3⋊D3—42no—
71C2×C4×C3⋊D3C2314yes—
72C2×#634—42no—
73C2×#634C2314yescomplemented
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C2×C3×D12—44no—
77C2×C3×D12C2318yes—
78C2×C3×C4×D3—44no—
79C2×C3×C4×D3C2318yescomplemented
80C2×#626—28no—
81C2×#626C2318yes—
82C2×#625—44no—
83C2×#625—42no—
84C2×#625C2318yes—
85C2×#625C2314yescomplemented
86C2×#624—42no—
87C2×#624C2314yes—
88C32×C4⋊C4C2314yescomplemented
89#3752C2318yes—
90C4⋊(C3⋊Dic3)C2318yescomplemented
91C3×(C2×D3)⋊C4C2318yes—
92C3×(C2×D3)⋊C4C2318yes—
93C3×(C2×D3)⋊C4C2318yescomplemented
94C3×Dic3⋊C4C2318yescomplemented
95#3724C2314yescomplemented
96(C2×D3)⋊Dic3C2318yes—
97(C2×D3)⋊Dic3C2318yes—
98(C2×D3)⋊Dic3C2318yescomplemented
99Dic32C2318yescomplemented
100C2×#538—91noSylow
101C24×D3—32no—
102C22×C3×D4—32no—
103C23×C3×C4—32no—
104C22×#67—32no—
105C22×#67—32no—
106C22×#67—32no—
107C22×#67—32no—
108C22×D12—32no—
109C22×D12C2×D312yes—
110C22×C4×D3—32no—
111C22×C4×D3—32no—
112C22×C4×D3—61no—
113C22×C4×D3C2×D312yescomplemented
114C22×Dic6—32no—
115C22×Dic6—61no—
116C3×#123—316no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4—32no—
119C2×C3×C4⋊C4C2×D312yescomplemented
120C2×C3×C22⋊C4—32no—
121C2×C3×C22⋊C4—32no—
122C2×C3×C22⋊C4—32no—
123C2×#217—32no—
124C2×#217—32no—
125C2×#217—32no—
126#938—316no—
127#937—316no—
128#930—316no—
129C4×#67—316no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4—62no—
136C2×(C2×D3)⋊C4C2×D312yes—
137C2×(C2×D3)⋊C4C2×D312yes—
138C2×(C2×D3)⋊C4C2×D312yescomplemented
139C2×C4⋊Dic3—32no—
140C2×C4⋊Dic3—32no—
141C2×C4⋊Dic3—62no—
142C2×Dic3⋊C4—32no—
143C2×Dic3⋊C4C2×D312yescomplemented
144C2×C4×Dic3—32no—
145C2×C4×Dic3—32no—
146#898—316no—
147#897—316no—
148#897—68no—
149#894C2×D3116yescomplemented
150#893—316no—
151#885—316no—
152#885—316no—
153#884—316no—
154#882—316no—
155D3×C22⋊C4—316no—
156#879—316no—
157C23×C32C2411yescharacteristic
158C22×C3⋊D3—22no—
159C22×C3⋊D3—22no—
160C22×C3⋊D3#4114yes—
161C22×C3⋊D3C2412yes—
162C22×C3×D3—24no—
163C22×C3×D3—24no—
164C22×C3×D3—24no—
165C22×C3×D3—24no—
166C22×C3×D3—24no—
167C22×C3×D3—24no—
168C22×C3×D3C2414yes—
169C22×C3×D3C2414yes—
170C2×D32—28no—
171C2×D32—44no—
172C2×D32—44no—
173C2×D32—416no—
174C2×C32×C4—22no—
175C2×C32×C4—24no—
176C2×C32×C4C2414yes—
177C2×C32×C4C2412yes—
178C2×C3⋊Dic3—24no—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3C2414yes—
181C2×C3⋊Dic3C2412yes—
182C4×C3⋊D3—44no—
183#634—44no—
184C2×C3×Dic3—24no—
185C2×C3×Dic3—24no—
186C2×C3×Dic3C2414yes—
187C2×C3×Dic3C2414yes—
188C3×D12—48no—
189C3×C4×D3—48no—
190#626—216no—
191#625—48no—
192#625—44no—
193#624—44no—
194#538—916no—
195C2×#126—92no—
196C2×#124—92no—
197C2×#123—32no—
198C2×C22⋊Q8—91no—
199C2×#121—91no—
200C2×#121—92no—
201C2×#120—92no—
202C2×C4×D4—92no—
203C22×C22⋊C4—91no—
204C24×C3—32no—
205C24×C3—32no—
206C23×D3—32no—
207C23×D3—38no—
208C23×D3—61no—
209C23×D3—68no—
210C23×D3—124no—
211C23×D3—124no—
212C23×D3C22×D312yes—
213C23×D3C22×D312yes—
214C2×C3×D4—38no—
215C2×C3×D4—124no—
216C22×C3×C4—21no—
217C22×C3×C4—22no—
218C22×C3×C4—32no—
219C22×C3×C4—32no—
220C22×C3×C4—38no—
221C22×C3×C4—124no—
222C22×C3×C4C22×D312yes—
223C22×C3×C4C22×D312yes—
224C22×C3×C4C22×D312yes—
225C2×#67—38no—
226C2×#67—38no—
227C2×#67—38no—
228C2×#67—38no—
229C2×#67—68no—
230C2×#67—124no—
231C2×#67—124no—
232C2×#67—124no—
233C22×Dic3—32no—
234C22×Dic3—32no—
235C22×Dic3—32no—
236C22×Dic3—61no—
237C22×Dic3—62no—
238C22×Dic3C22×D312yes—
239C22×Dic3C22×D312yes—
240C2×D12—38no—
241C2×D12—44no—
242C2×D12—68no—
243C2×D12C22×D318yes—
244C2×C4×D3—38no—
245C2×C4×D3—38no—
246C2×C4×D3—44no—
247C2×C4×D3—64no—
248C2×C4×D3—124no—
249C2×C4×D3—124no—
250C2×C4×D3—124no—
251C2×C4×D3C22×D318yescomplemented
252C2×Dic6—38no—
253C2×Dic6—64no—
254C2×Dic6—124no—
255C2×Dic6—124no—
256C3×C4⋊C4—24no—
257C3×C4⋊C4—38no—
258C3×C4⋊C4C22×D318yescomplemented
259C3×C22⋊C4—38no—
260C3×C22⋊C4—38no—
261C3×C22⋊C4—38no—
262#217—38no—
263#217—38no—
264#217—38no—
265(C2×D3)⋊C4—38no—
266(C2×D3)⋊C4—38no—
267(C2×D3)⋊C4—38no—
268(C2×D3)⋊C4—38no—
269(C2×D3)⋊C4—38no—
270(C2×D3)⋊C4—68no—
271(C2×D3)⋊C4C22×D318yes—
272(C2×D3)⋊C4C22×D318yes—
273(C2×D3)⋊C4C22×D318yescomplemented
274C4⋊Dic3—38no—
275C4⋊Dic3—38no—
276C4⋊Dic3—68no—
277Dic3⋊C4—38no—
278Dic3⋊C4C22×D318yescomplemented
279C4×Dic3—38no—
280C4×Dic3—38no—
281C22×C32C2×#4112yes—
282C22×C32H(5,𝔽2)12yes—
283C22×C32H(5,𝔽2)12yes—
284C22×C32C2511yescharacteristic
285C2×C3⋊D3—28no—
286C2×C3⋊D3—22no—
287C2×C3⋊D3—22no—
288C2×C3⋊D3C2×#4114yes—
289C2×C3×D3—24no—
290C2×C3×D3—24no—
291C2×C3×D3—24no—
292C2×C3×D3—24no—
293C2×C3×D3—24no—
294C2×C3×D3—24no—
295C2×C3×D3—48no—
296C2×C3×D3—48no—
297D32—416no—
298C32×C4—22no—
299C32×C4—24no—
300C3⋊Dic3—24no—
301C3⋊Dic3—22no—
302C3×Dic3—24no—
303C3×Dic3—24no—
304C25—91no—
305C22×Q8—91no—
306C22×D4—32no—
307C22×D4—92no—
308C22×D4—92no—
309C22×D4—91no—
310C23×C4—32no—
311C23×C4—91no—
312C23×C4—91no—
313#126—916no—
314#124—916no—
315#123—316no—
316C22⋊Q8—98no—
317#121—98no—
318#121—916no—
319#120—916no—
320C4×D4—916no—
321C2×C4⋊C4—32no—
322C2×C4⋊C4—91no—
323C2×C4⋊C4—92no—
324C2×C4⋊C4D3211yescharacteristic, complemented
325C2×C22⋊C4—32no—
326C2×C22⋊C4—32no—
327C2×C22⋊C4—32no—
328C2×C22⋊C4—98no—
329C2×C22⋊C4—92no—
330C2×C22⋊C4—92no—
331C2×C22⋊C4—92no—
332C2×C22⋊C4—92no—
333C2×C42—92no—
334C23×C3—21no—
335C23×C3—34no—
336C23×C3—34no—
337C23×C3—64no—
338C23×C3—64no—
339C23×C3—64no—
340C23×C3—64no—
341C23×C3—64no—
342C23×C3—64no—
343C23×C3C23×D312yes—
344C22×D3—24no—
345C22×D3—24no—
346C22×D3—24no—
347C22×D3—24no—
348C22×D3—24no—
349C22×D3—24no—
350C22×D3—38no—
351C22×D3—34no—
352C22×D3—64no—
353C22×D3—62no—
354C22×D3—616no—
355C22×D3—64no—
356C22×D3—64no—
357C22×D3—122no—
358C22×D3—122no—
359C22×D3—128no—
360C22×D3—128no—
361C22×D3—1232no—
362C22×D3C23×D314yes—
363C22×D3C23×D314yes—
364C3×D4—128no—
365C2×C3×C4—24no—
366C2×C3×C4—24no—
367C2×C3×C4—24no—
368C2×C3×C4—24no—
369C2×C3×C4—22no—
370C2×C3×C4—24no—
371C2×C3×C4—34no—
372C2×C3×C4—34no—
373C2×C3×C4—44no—
374C2×C3×C4—64no—
375C2×C3×C4—64no—
376C2×C3×C4—128no—
377C2×C3×C4C23×D314yes—
378C2×C3×C4C23×D314yes—
379C2×C3×C4C23×D314yes—
380#67—616no—
381#67—128no—
382#67—128no—
383#67—128no—
384C2×Dic3—24no—
385C2×Dic3—24no—
386C2×Dic3—34no—
387C2×Dic3—34no—
388C2×Dic3—34no—
389C2×Dic3—62no—
390C2×Dic3—64no—
391C2×Dic3—64no—
392C2×Dic3—64no—
393C2×Dic3—64no—
394C2×Dic3—124no—
395C2×Dic3—122no—
396C2×Dic3C23×D314yes—
397C2×Dic3C23×D314yes—
398D12—48no—
399D12—616no—
400C4×D3—48no—
401C4×D3—128no—
402C4×D3—128no—
403C4×D3—128no—
404Dic6—128no—
405Dic6—128no—
406C2×C32#53814yescomplemented
407C2×C32C22×#4111yescharacteristic
408C2×C32C2×H(5,𝔽2)11yescharacteristic
409C2×C32C2×H(5,𝔽2)11yescharacteristic
410C3⋊D3—24no—
411C3×D3—44no—
412C3×D3—44no—
413C24—32no—
414C24—32no—
415C24—94no—
416C24—91no—
417C24—184no—
418C24—362no—
419C24—362no—
420C2×Q8—94no—
421C2×Q8—362no—
422C2×D4—38no—
423C2×D4—98no—
424C2×D4—98no—
425C2×D4—94no—
426C2×D4—124no—
427C2×D4—188no—
428C2×D4—362no—
429C2×D4—364no—
430C22×C4—32no—
431C22×C4—32no—
432C22×C4—38no—
433C22×C4—94no—
434C22×C4—92no—
435C22×C4—91no—
436C22×C4—94no—
437C22×C4—124no—
438C22×C4—362no—
439C22×C4—362no—
440C22×C4C2×D3211yescharacteristic
441C22×C4C2×D3212yes—
442C4⋊C4—38no—
443C4⋊C4—94no—
444C4⋊C4—98no—
445C4⋊C4C2×D3214yescomplemented
446C22⋊C4—38no—
447C22⋊C4—38no—
448C22⋊C4—38no—
449C22⋊C4—98no—
450C22⋊C4—98no—
451C22⋊C4—98no—
452C22⋊C4—98no—
453C42—98no—
454C22×C3—22no—
455C22×C3—22no—
456C22×C3—22no—
457C22×C3—21no—
458C22×C3—64no—
459C22×C3—64no—
460C22×C3—64no—
461C22×C3—64no—
462C22×C3—64no—
463C22×C3—64no—
464C22×C3—128no—
465C22×C3—128no—
466C22×C3#100414yes—
467C22×C3D3×#4114yes—
468C22×C3#100914yes—
469C22×C3C24×D312yes—
470C2×D3—24no—
471C2×D3—24no—
472C2×D3—24no—
473C2×D3—24no—
474C2×D3—24no—
475C2×D3—24no—
476C2×D3—38no—
477C2×D3—48no—
478C2×D3—48no—
479C2×D3—64no—
480C2×D3—616no—
481C2×D3—64no—
482C2×D3—64no—
483C2×D3—122no—
484C2×D3—122no—
485C2×D3—128no—
486C2×D3—1232no—
487C3×C4—24no—
488C3×C4—24no—
489C3×C4—24no—
490C3×C4—24no—
491C3×C4—44no—
492C3×C4—64no—
493C3×C4—64no—
494Dic3—24no—
495Dic3—24no—
496Dic3—64no—
497Dic3—64no—
498Dic3—64no—
499Dic3—124no—
500Dic3—122no—
501C32C2×#53811yescharacteristic, complemented, Sylow
502C23—34no—
503C23—34no—
504C23—64no—
505C23—64no—
506C23—64no—
507C23—64no—
508C23—64no—
509C23—64no—
510C23—94no—
511C23—92no—
512C23—188no—
513C23—182no—
514C23—182no—
515C23—364no—
516C23—364no—
517C23—3616no—
518C23C22×D3211yescharacteristic
519Q8—364no—
520D4—128no—
521D4—1816no—
522D4—364no—
523D4—368no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—34no—
527C2×C4—34no—
528C2×C4—64no—
529C2×C4—64no—
530C2×C4—94no—
531C2×C4—92no—
532C2×C4—128no—
533C2×C4—182no—
534C2×C4—184no—
535C2×C4—364no—
536C2×C4—364no—
537C2×C4C22×D3212yes—
538C2×C4C22×D3214yes—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—24no—
543C2×C3—124no—
544C2×C3—124no—
545C2×C3#565718yescomplemented
546C2×C3C2×#100412yes—
547C2×C3C2×D3×#4112yes—
548C2×C3C2×#100912yes—
549D3—44no—
550D3—44no—
551D3—68no—
552D3—124no—
553C22—64no—
554C22—64no—
555C22—64no—
556C22—64no—
557C22—64no—
558C22—64no—
559C22—94no—
560C22—128no—
561C22—128no—
562C22—182no—
563C22—182no—
564C22—188no—
565C22—3616no—
566C22#6430812yes—
567C22#6431312yes—
568C22#6431912yes—
569C22C23×D3211yescharacteristic
570C4—22no—
571C4—24no—
572C4—64no—
573C4—64no—
574C4—182no—
575C4—184no—
576C3—21no—
577C3C2×#565712yescomplemented
578C2—124no—
579C2—124no—
580C2—184no—
581C2#1059465914yesdirect product factor
582C2C2×#6430811yescharacteristic
583C2C2×#6431311yescharacteristic
584C2C2×#6431911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64106C2semidirect
2. C2×C3×#894C2semidirect
3. C2×#63922C2semidirect
4. C2×#63921C2semidirect
5. C2×#63913C2semidirect
6. C2×#63912C2semidirect
7. C2×#63908C2semidirect
8. C2×#63904C2semidirect
9. C2×#63861C2semidirect
10. #10594659C2direct (N × H)
14. C22×#634C22semidirect
16. C22×C3×C4×D3C22semidirect
19. C22×#625C22semidirect
21. C2×C32×C4⋊C4C22semidirect
23. C2×C4⋊(C3⋊Dic3)C22semidirect
24. #64106C22semidirect
27. C2×C3×(C2×D3)⋊C4C22semidirect
28. C2×C3×Dic3⋊C4C22semidirect
29. C3×#894C22semidirect
30. C2×#3724C22semidirect
33. C2×(C2×D3)⋊Dic3C22semidirect
34. C2×Dic32C22semidirect
35. #63922C22semidirect
36. #63921C22semidirect
37. #63913C22semidirect
38. #63912C22semidirect
39. #63908C22semidirect
40. #63904C22semidirect
41. #63861C22semidirect
51. C2×#894D3semidirect
73. C2×#634C23semidirect
79. C2×C3×C4×D3C23semidirect
85. C2×#625C23semidirect
88. C32×C4⋊C4C23semidirect
90. C4⋊(C3⋊Dic3)C23semidirect
93. C3×(C2×D3)⋊C4C23semidirect
94. C3×Dic3⋊C4C23semidirect
95. #3724C23semidirect
98. (C2×D3)⋊Dic3C23semidirect
99. Dic32C23semidirect
113. C22×C4×D3C2×D3semidirect
119. C2×C3×C4⋊C4C2×D3semidirect
138. C2×(C2×D3)⋊C4C2×D3semidirect
143. C2×Dic3⋊C4C2×D3semidirect
149. #894C2×D3semidirect
251. C2×C4×D3C22×D3semidirect
258. C3×C4⋊C4C22×D3semidirect
273. (C2×D3)⋊C4C22×D3semidirect
278. Dic3⋊C4C22×D3semidirect
324. C2×C4⋊C4D32semidirect
406. C2×C32#538semidirect
445. C4⋊C4C2×D32semidirect
501. C32C2×#538semidirect
545. C2×C3#5657semidirect
577. C3C2×#5657semidirect
581. C2#10594659direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641062
C2×C3×#8942
C2×#639222
C2×#639212
C2×#639132
C2×#639122
C2×#639082
C2×#639042
C2×#638612
#105946592
C2×#56573