Finite Group Databasebeta

← C2×#10595438 #11901353

Subgroups — C2×#10595438 #11901353

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×#64155C211yesmaximal, characteristic, complemented
2C2×C3×#947C212yesmaximal, complemented
3#10595438C2116yesmaximal, direct product factor
4C2×#63922C212yesmaximal, complemented
5C2×#63921C211yesmaximal, characteristic, complemented
6C2×#63912C211yesmaximal, characteristic, complemented
7C2×#63891C212yesmaximal, complemented
8C2×#63885C212yesmaximal, complemented
9C2×#63880C212yesmaximal, complemented
10C2×#63859C212yesmaximal, complemented
11C2×#5678—32nomaximal
12C23×D32C2211yescharacteristic
13C22×C32×Q8C2211yescharacteristic, complemented
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×D12C2212yes—
16C22×#626C2212yes—
17C22×#625C2212yes—
18C22×#625C2211yescharacteristic, complemented
19C22×#624C2211yescharacteristic
20C22×D3×Dic3C2212yescomplemented
21#64155C2218yescomplemented
22C2×#3752C2212yes—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
24C2×#3750C2212yescomplemented
25C3×#947C22116yescomplemented
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×(C2×D3)⋊C4C2212yescomplemented
29C2×C3×(C2×D3)⋊C4C2212yescomplemented
30C2×C3×C4×Dic3C2212yescomplemented
31C2×#3724C2211yescharacteristic, complemented
32C2×Dic3⋊Dic3C2212yescomplemented
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35#63922C22116yescomplemented
36#63921C2218yescomplemented
37#63912C2218yescomplemented
38#63891C22116yescomplemented
39#63885C22116yescomplemented
40#63880C22116yescomplemented
41#63859C22116yescomplemented
42C2×C3×#124—32no—
43C2×#947D312yescomplemented
44C2×#946—32no—
45C2×#946—61no—
46C2×#939—32no—
47C2×#937—32no—
48#5678—332no—
49C2×#886—32no—
50C2×#884—32no—
51C2×#884—32no—
52C2×#883—32no—
53C2×#882—32no—
54C2×#67⋊C4—32no—
55C2×D3×C22⋊C4—32no—
56C2×#879—32no—
57C2×#876—32no—
58C2×C4×D12—32no—
59C23×C3⋊D3C2311yescharacteristic
60C23×C3×D3C2312yes—
61C23×C3×D3C2312yes—
62C22×D32—24no—
63C22×D32—42no—
64C22×D32—42no—
65C22×D32C2314yes—
66C2×C32×Q8—42no—
67C2×C32×Q8C2314yescomplemented
68C22×C32×C4C2312yes—
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3C2312yes—
71C22×C3⋊Dic3C2311yescharacteristic
72C2×C4×C3⋊D3—42no—
73C2×C4×C3⋊D3C2314yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C2×C3×D12—44no—
77C2×C3×D12C2318yes—
78C2×#626—28no—
79C2×#626C2318yes—
80C2×#625—44no—
81C2×#625—42no—
82C2×#625C2318yes—
83C2×#625C2314yescomplemented
84C2×#624—42no—
85C2×#624C2314yes—
86C2×D3×Dic3—44no—
87C2×D3×Dic3C2318yescomplemented
88#3752C2318yes—
89C4⋊(C3⋊Dic3)C2314yescomplemented
90#3750C2318yescomplemented
91C3×(C2×D3)⋊C4C2318yes—
92C3×(C2×D3)⋊C4C2318yes—
93C3×(C2×D3)⋊C4C2318yescomplemented
94C3×(C2×D3)⋊C4C2318yescomplemented
95C3×C4×Dic3C2318yescomplemented
96#3724C2314yescomplemented
97Dic3⋊Dic3C2318yescomplemented
98(C2×D3)⋊Dic3C2318yes—
99(C2×D3)⋊Dic3C2318yes—
100C2×#538—91noSylow
101C24×D3—32no—
102C22×C3×Q8—21no—
103C22×C3×Q8C2×D312yescomplemented
104C22×C3×D4—32no—
105C22×#67—32no—
106C22×#67—32no—
107C22×#67—32no—
108C22×#67—32no—
109C23×Dic3—32no—
110C22×D12—32no—
111C22×D12C2×D312yes—
112C22×C4×D3—32no—
113C22×C4×D3—32no—
114C22×C4×D3—32no—
115C22×C4×D3—61no—
116C3×#124—316no—
117C2×C3×C22⋊C4—32no—
118C2×C3×C22⋊C4—32no—
119C2×C3×C22⋊C4—32no—
120C2×C3×C22⋊C4—32no—
121C2×C3×C42—32no—
122C2×#217—32no—
123C2×#217—32no—
124#947C2×D3116yescomplemented
125#946—316no—
126#946—68no—
127#939—316no—
128#937—316no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—62no—
134C2×(C2×D3)⋊C4C2×D312yes—
135C2×(C2×D3)⋊C4C2×D312yes—
136C2×(C2×D3)⋊C4C2×D312yescomplemented
137C2×(C2×D3)⋊C4C2×D312yescomplemented
138C2×C4⋊Dic3—32no—
139C2×C4⋊Dic3—32no—
140C2×C4⋊Dic3—61no—
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—32no—
143C2×Dic3⋊C4—32no—
144C2×Dic3⋊C4—32no—
145C2×Dic3⋊C4—62no—
146C2×C4×Dic3C2×D312yescomplemented
147#886—316no—
148#884—316no—
149#884—316no—
150#883—316no—
151#882—316no—
152#67⋊C4—316no—
153D3×C22⋊C4—316no—
154#879—316no—
155#876—316no—
156C4×D12—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—
174C32×Q8—44no—
175C2×C32×C4—22no—
176C2×C32×C4—24no—
177C2×C32×C4C2414yes—
178C2×C32×C4C2412yes—
179C2×C3⋊Dic3—24no—
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3C2412yes—
182C2×C3⋊Dic3C2414yes—
183C4×C3⋊D3—44no—
184C2×C3×Dic3—24no—
185C2×C3×Dic3—24no—
186C2×C3×Dic3C2414yes—
187C2×C3×Dic3C2414yes—
188C3×D12—48no—
189#626—216no—
190#625—48no—
191#625—44no—
192#624—44no—
193D3×Dic3—48no—
194#538—916no—
195C2×#126—92no—
196C2×#124—32no—
197C2×#123—92no—
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×Q8—24no—
215C2×C3×Q8—44no—
216C2×C3×Q8—44no—
217C2×C3×Q8C22×D318yescomplemented
218C2×C3×D4—38no—
219C2×C3×D4—124no—
220C22×C3×C4—21no—
221C22×C3×C4—22no—
222C22×C3×C4—32no—
223C22×C3×C4—32no—
224C22×C3×C4C22×D312yes—
225C22×C3×C4C22×D312yes—
226C22×C3×C4C22×D312yes—
227C2×#67—38no—
228C2×#67—38no—
229C2×#67—38no—
230C2×#67—38no—
231C2×#67—68no—
232C2×#67—124no—
233C2×#67—124no—
234C2×#67—124no—
235C22×Dic3—32no—
236C22×Dic3—32no—
237C22×Dic3—32no—
238C22×Dic3—38no—
239C22×Dic3—61no—
240C22×Dic3—62no—
241C22×Dic3—124no—
242C22×Dic3C22×D312yes—
243C22×Dic3C22×D312yes—
244C2×D12—38no—
245C2×D12—44no—
246C2×D12—68no—
247C2×D12C22×D318yes—
248C2×C4×D3—38no—
249C2×C4×D3—38no—
250C2×C4×D3—38no—
251C2×C4×D3—64no—
252C2×C4×D3—124no—
253C2×C4×D3—124no—
254C2×C4×D3—124no—
255C2×C4×D3—124no—
256C3×C22⋊C4—38no—
257C3×C22⋊C4—38no—
258C3×C22⋊C4—38no—
259C3×C22⋊C4—38no—
260C3×C42—38no—
261#217—38no—
262#217—38no—
263(C2×D3)⋊C4—38no—
264(C2×D3)⋊C4—38no—
265(C2×D3)⋊C4—38no—
266(C2×D3)⋊C4—38no—
267(C2×D3)⋊C4—68no—
268(C2×D3)⋊C4C22×D318yes—
269(C2×D3)⋊C4C22×D318yes—
270(C2×D3)⋊C4C22×D318yescomplemented
271(C2×D3)⋊C4C22×D318yescomplemented
272C4⋊Dic3—38no—
273C4⋊Dic3—38no—
274C4⋊Dic3—64no—
275Dic3⋊C4—38no—
276Dic3⋊C4—38no—
277Dic3⋊C4—38no—
278Dic3⋊C4—38no—
279Dic3⋊C4—68no—
280C4×Dic3C22×D318yescomplemented
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×Q8D3211yescharacteristic, complemented
306C22×D4—32no—
307C22×D4—92no—
308C22×D4—92no—
309C22×D4—91no—
310C23×C4—91no—
311C23×C4—92no—
312C23×C4—91no—
313#126—916no—
314#124—316no—
315#123—916no—
316C22⋊Q8—98no—
317#121—98no—
318#121—916no—
319#120—916no—
320C4×D4—916no—
321C2×C4⋊C4—92no—
322C2×C4⋊C4—91no—
323C2×C4⋊C4—92no—
324C2×C4⋊C4—91no—
325C2×C22⋊C4—32no—
326C2×C22⋊C4—32no—
327C2×C22⋊C4—32no—
328C2×C22⋊C4—32no—
329C2×C22⋊C4—98no—
330C2×C22⋊C4—92no—
331C2×C22⋊C4—92no—
332C2×C22⋊C4—92no—
333C2×C42—32no—
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×Q8—48no—
365C3×Q8—48no—
366C3×D4—128no—
367C2×C3×C4—24no—
368C2×C3×C4—24no—
369C2×C3×C4—24no—
370C2×C3×C4—24no—
371C2×C3×C4—22no—
372C2×C3×C4—24no—
373C2×C3×C4—34no—
374C2×C3×C4—34no—
375C2×C3×C4—44no—
376C2×C3×C4—64no—
377C2×C3×C4—64no—
378C2×C3×C4C23×D314yes—
379C2×C3×C4C23×D314yes—
380C2×C3×C4C23×D314yes—
381#67—616no—
382#67—128no—
383#67—128no—
384#67—128no—
385C2×Dic3—24no—
386C2×Dic3—24no—
387C2×Dic3—34no—
388C2×Dic3—34no—
389C2×Dic3—34no—
390C2×Dic3—62no—
391C2×Dic3—64no—
392C2×Dic3—64no—
393C2×Dic3—64no—
394C2×Dic3—64no—
395C2×Dic3—122no—
396C2×Dic3—124no—
397C2×Dic3—128no—
398C2×Dic3C23×D314yes—
399C2×Dic3C23×D314yes—
400D12—48no—
401D12—616no—
402C4×D3—128no—
403C4×D3—128no—
404C4×D3—128no—
405C4×D3—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—42no—
421C2×Q8C2×D3214yescomplemented
422C2×D4—38no—
423C2×D4—98no—
424C2×D4—98no—
425C2×D4—94no—
426C2×D4—124no—
427C2×D4—188no—
428C2×D4—364no—
429C2×D4—362no—
430C22×C4—32no—
431C22×C4—32no—
432C22×C4—94no—
433C22×C4—98no—
434C22×C4—92no—
435C22×C4—91no—
436C22×C4—94no—
437C22×C4—362no—
438C22×C4—362no—
439C22×C4—364no—
440C22×C4C2×D3212yes—
441C22×C4C2×D3211yescharacteristic
442C4⋊C4—98no—
443C4⋊C4—94no—
444C4⋊C4—98no—
445C4⋊C4—94no—
446C22⋊C4—38no—
447C22⋊C4—38no—
448C22⋊C4—38no—
449C22⋊C4—38no—
450C22⋊C4—98no—
451C22⋊C4—98no—
452C22⋊C4—98no—
453C42—38no—
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—122no—
500Dic3—124no—
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—44no—
520D4—128no—
521D4—1816no—
522D4—368no—
523D4—364no—
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—184no—
533C2×C4—182no—
534C2×C4—364no—
535C2×C4—364no—
536C2×C4—368no—
537C2×C4C22×D3214yes—
538C2×C4C22×D3212yes—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—24no—
543C2×C3—124no—
544C2×C3—124no—
545C2×C3#567818yescomplemented
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#6431912yes—
567C22#6432012yes—
568C22#6433012yes—
569C22C23×D3211yescharacteristic
570C4—22no—
571C4—24no—
572C4—64no—
573C4—64no—
574C4—184no—
575C4—182no—
576C3—21no—
577C3C2×#567812yescomplemented
578C2—124no—
579C2—124no—
580C2—184no—
581C2#1059543814yesdirect product factor
582C2C2×#6431911yescharacteristic
583C2C2×#6432011yescharacteristic
584C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
hypercenterC22×Q8D32
hypocenterC32C2×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64155C2semidirect
2. C2×C3×#947C2semidirect
3. #10595438C2direct (N × H)
4. C2×#63922C2semidirect
5. C2×#63921C2semidirect
6. C2×#63912C2semidirect
7. C2×#63891C2semidirect
8. C2×#63885C2semidirect
9. C2×#63880C2semidirect
10. C2×#63859C2semidirect
13. C22×C32×Q8C22semidirect
18. C22×#625C22semidirect
20. C22×D3×Dic3C22semidirect
21. #64155C22semidirect
23. C2×C4⋊(C3⋊Dic3)C22semidirect
24. C2×#3750C22semidirect
25. C3×#947C22semidirect
28. C2×C3×(C2×D3)⋊C4C22semidirect
29. C2×C3×(C2×D3)⋊C4C22semidirect
30. C2×C3×C4×Dic3C22semidirect
31. C2×#3724C22semidirect
32. C2×Dic3⋊Dic3C22semidirect
35. #63922C22semidirect
36. #63921C22semidirect
37. #63912C22semidirect
38. #63891C22semidirect
39. #63885C22semidirect
40. #63880C22semidirect
41. #63859C22semidirect
43. C2×#947D3semidirect
67. C2×C32×Q8C23semidirect
83. C2×#625C23semidirect
87. C2×D3×Dic3C23semidirect
89. C4⋊(C3⋊Dic3)C23semidirect
90. #3750C23semidirect
93. C3×(C2×D3)⋊C4C23semidirect
94. C3×(C2×D3)⋊C4C23semidirect
95. C3×C4×Dic3C23semidirect
96. #3724C23semidirect
97. Dic3⋊Dic3C23semidirect
103. C22×C3×Q8C2×D3semidirect
124. #947C2×D3semidirect
136. C2×(C2×D3)⋊C4C2×D3semidirect
137. C2×(C2×D3)⋊C4C2×D3semidirect
146. C2×C4×Dic3C2×D3semidirect
217. C2×C3×Q8C22×D3semidirect
270. (C2×D3)⋊C4C22×D3semidirect
271. (C2×D3)⋊C4C22×D3semidirect
280. C4×Dic3C22×D3semidirect
305. C22×Q8D32semidirect
406. C2×C32#538semidirect
421. C2×Q8C2×D32semidirect
501. C32C2×#538semidirect
545. C2×C3#5678semidirect
577. C3C2×#5678semidirect
581. C2#10595438direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641552
C2×C3×#9472
#105954382
C2×#639222
C2×#639212
C2×#639122
C2×#638912
C2×#638852
C2×#638802
C2×#638592
C2×#56783