Finite Group Databasebeta

← C2×#10595436 #11902958

Subgroups — C2×#10595436 #11902958

Order 1152.

2821 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64156C211yesmaximal, characteristic, complemented
2C2×C3×#946C212yesmaximal, complemented
3#10595436C2116yesmaximal, direct product factor
4C2×#63923C211yesmaximal, characteristic
5C2×D3×(C2×D3)⋊C4C212yesmaximal, complemented
6C2×#63904C212yesmaximal, complemented
7C2×#63897C211yesmaximal, characteristic, complemented
8C2×#63890C212yesmaximal, complemented
9C2×#63878C212yesmaximal, complemented
10C2×#63848C212yesmaximal, complemented
11C2×#5637—32nomaximal
12C23×D32C2211yescharacteristic
13C22×C32×Q8C2211yescharacteristic, complemented
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C3×C4×D3C2212yes—
16C22×#626C2212yes—
17C22×#624C2211yescharacteristic, complemented
18C22×D3×Dic3C2212yes—
19#64156C2218yescomplemented
20C2×#3752C2212yes—
21C2×#3752C2212yescomplemented
22C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
23C3×#946C22116yescomplemented
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×C4⋊Dic3C2212yescomplemented
27C2×C3×Dic3⋊C4C2212yescomplemented
28C2×C3×Dic3⋊C4C2212yescomplemented
29C2×Dic3⋊Dic3C2212yescomplemented
30C2×#3722C2211yescharacteristic
31C2×#3722C2212yes—
32C2×#3722C2211yescharacteristic, complemented
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×Dic32C2212yescomplemented
35#63923C2218yes—
36D3×(C2×D3)⋊C4C22116yescomplemented
37#63904C22116yescomplemented
38#63897C2218yescomplemented
39#63890C22116yescomplemented
40#63878C22116yescomplemented
41#63848C22116yescomplemented
42C2×C3×C22⋊Q8—32no—
43C2×#947—32no—
44C2×#947—61no—
45C2×#946D312yescomplemented
46C2×C4×#67—32no—
47C22×(C2×D3)⋊C4—32no—
48#5637—332no—
49C2×#898—32no—
50C2×#898—32no—
51C2×#894—32no—
52C2×#894—32no—
53C2×#893—32no—
54C2×#892—32no—
55C2×#886—32no—
56C2×#882—32no—
57C2×D3×C22⋊C4—32no—
58C2×#877—32no—
59C23×C3⋊D3C2311yescharacteristic
60C23×C3⋊D3C2311yescharacteristic
61C23×C3×D3C2312yes—
62C22×D32—28no—
63C22×D32—42no—
64C22×D32C2314yes—
65C2×C32×Q8—42no—
66C2×C32×Q8C2314yescomplemented
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2312yes—
69C22×C3⋊Dic3C2312yes—
70C2×C4⋊(C3⋊D3)—42no—
71C2×C4⋊(C3⋊D3)C2314yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C2×C3×C4×D3—44no—
76C2×C3×C4×D3C2318yes—
77C2×#626—28no—
78C2×#626C2318yes—
79C2×#624—42no—
80C2×#624C2314yescomplemented
81C2×D3×Dic3—28no—
82C2×D3×Dic3C2318yes—
83#3752C2318yes—
84#3752C2318yescomplemented
85C4×C3⋊Dic3C2314yescomplemented
86C3×(C2×D3)⋊C4C2318yes—
87C3×(C2×D3)⋊C4C2318yes—
88C3×C4⋊Dic3C2318yescomplemented
89C3×Dic3⋊C4C2318yescomplemented
90C3×Dic3⋊C4C2318yescomplemented
91Dic3⋊Dic3C2318yescomplemented
92#3722C2314yes—
93#3722C2318yes—
94#3722C2314yescomplemented
95(C2×D3)⋊Dic3C2318yes—
96Dic32C2318yescomplemented
97C2×#551—91noSylow
98C24×D3—32no—
99C22×C3×Q8—21no—
100C22×C3×Q8C2×D312yescomplemented
101C23×C3×C4—32no—
102C22×#67—32no—
103C23×Dic3—32no—
104C22×D12—32no—
105C22×D12—32no—
106C22×D12—61no—
107C22×C4×D3—32no—
108C22×C4×D3—32no—
109C22×C4×D3C2×D312yes—
110C3×C22⋊Q8—316no—
111C2×C3×C4⋊C4—32no—
112C2×C3×C4⋊C4—32no—
113C2×C3×C4⋊C4—32no—
114C2×C3×C22⋊C4—32no—
115C2×C3×C22⋊C4—32no—
116C2×#217—32no—
117#947—316no—
118#947—68no—
119#946C2×D3116yescomplemented
120C4×#67—316no—
121C2×(C2×D3)⋊C4—32no—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—316no—
131C2×(C2×D3)⋊C4—62no—
132C2×(C2×D3)⋊C4—62no—
133C2×(C2×D3)⋊C4C2×D312yes—
134C2×(C2×D3)⋊C4C2×D312yes—
135C2×C4⋊Dic3—32no—
136C2×C4⋊Dic3C2×D312yescomplemented
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4C2×D312yescomplemented
139C2×Dic3⋊C4C2×D312yescomplemented
140C2×C4×Dic3—32no—
141C2×C4×Dic3—32no—
142C2×C4×Dic3—32no—
143C2×C4×Dic3—61no—
144#898—316no—
145#898—316no—
146#894—316no—
147#894—316no—
148#893—316no—
149#892—316no—
150#886—316no—
151#882—316no—
152D3×C22⋊C4—316no—
153#877—316no—
154C23×C32C2411yescharacteristic
155C22×C3⋊D3—24no—
156C22×C3⋊D3—24no—
157C22×C3⋊D3—22no—
158C22×C3⋊D3—22no—
159C22×C3⋊D3C2412yes—
160C22×C3⋊D3C2412yes—
161C22×C3×D3—24no—
162C22×C3×D3—24no—
163C22×C3×D3#4118yes—
164C22×C3×D3C2414yes—
165C2×D32—216no—
166C2×D32—44no—
167C2×D32—416no—
168C32×Q8—44no—
169C2×C32×C4—22no—
170C2×C32×C4—24no—
171C2×C32×C4C2412yes—
172C2×C32×C4C2414yes—
173C2×C3⋊Dic3—24no—
174C2×C3⋊Dic3C2414yes—
175C4⋊(C3⋊D3)—44no—
176C2×C3×Dic3—24no—
177C2×C3×Dic3—24no—
178C2×C3×Dic3—24no—
179C2×C3×Dic3C2414yes—
180C2×C3×Dic3C2414yes—
181C2×C3×Dic3C2414yes—
182C3×C4×D3—48no—
183#626—216no—
184#624—44no—
185D3×Dic3—216no—
186#551—916no—
187C2×#126—92no—
188C2×#124—91no—
189C2×#123—92no—
190C2×#123—91no—
191C2×C22⋊Q8—32no—
192C2×#120—91no—
193C2×C4×D4—92no—
194C2×#117—92no—
195C22×C22⋊C4—92no—
196C24×C3—32no—
197C23×D3—32no—
198C23×D3—32no—
199C23×D3—38no—
200C23×D3—61no—
201C23×D3—61no—
202C23×D3—68no—
203C23×D3—68no—
204C23×D3—124no—
205C23×D3C22×D312yes—
206C2×C3×Q8—24no—
207C2×C3×Q8—44no—
208C2×C3×Q8—44no—
209C2×C3×Q8C22×D318yescomplemented
210C22×C3×C4—21no—
211C22×C3×C4—22no—
212C22×C3×C4—32no—
213C22×C3×C4—32no—
214C22×C3×C4—32no—
215C22×C3×C4—38no—
216C22×C3×C4—124no—
217C22×C3×C4C22×D312yes—
218C22×C3×C4C22×D312yes—
219C22×C3×C4C22×D312yes—
220C2×#67—38no—
221C2×#67—68no—
222C22×Dic3—32no—
223C22×Dic3—32no—
224C22×Dic3—38no—
225C22×Dic3—62no—
226C22×Dic3—68no—
227C22×Dic3C22×D312yes—
228C22×Dic3C22×D312yes—
229C22×Dic3C22×D312yes—
230C2×D12—38no—
231C2×D12—38no—
232C2×D12—64no—
233C2×D12—68no—
234C2×D12—124no—
235C2×D12—124no—
236C2×C4×D3—38no—
237C2×C4×D3—38no—
238C2×C4×D3—44no—
239C2×C4×D3—68no—
240C2×C4×D3—124no—
241C2×C4×D3C22×D318yes—
242C3×C4⋊C4—38no—
243C3×C4⋊C4—38no—
244C3×C4⋊C4—38no—
245C3×C22⋊C4—38no—
246C3×C22⋊C4—38no—
247#217—38no—
248(C2×D3)⋊C4—38no—
249(C2×D3)⋊C4—38no—
250(C2×D3)⋊C4—38no—
251(C2×D3)⋊C4—38no—
252(C2×D3)⋊C4—38no—
253(C2×D3)⋊C4—38no—
254(C2×D3)⋊C4—38no—
255(C2×D3)⋊C4—38no—
256(C2×D3)⋊C4—38no—
257(C2×D3)⋊C4—68no—
258(C2×D3)⋊C4—68no—
259(C2×D3)⋊C4C22×D318yes—
260(C2×D3)⋊C4C22×D318yes—
261C4⋊Dic3—38no—
262C4⋊Dic3C22×D318yescomplemented
263Dic3⋊C4—38no—
264Dic3⋊C4C22×D318yescomplemented
265Dic3⋊C4C22×D318yescomplemented
266C4×Dic3—38no—
267C4×Dic3—38no—
268C4×Dic3—38no—
269C4×Dic3—64no—
270C22×C32C2×#4114yes—
271C22×C32H(5,𝔽2)12yes—
272C22×C32C2511yescharacteristic
273C2×C3⋊D3—24no—
274C2×C3⋊D3—24no—
275C2×C3⋊D3—22no—
276C2×C3⋊D3—22no—
277C2×C3⋊D3—44no—
278C2×C3⋊D3—44no—
279C2×C3×D3—216no—
280C2×C3×D3—24no—
281C2×C3×D3—24no—
282C2×C3×D3C2×#4118yes—
283D32—416no—
284C32×C4—22no—
285C32×C4—24no—
286C3⋊Dic3—24no—
287C3×Dic3—24no—
288C3×Dic3—24no—
289C3×Dic3—24no—
290C25—91no—
291C22×Q8D3211yescharacteristic, complemented
292C22×D4—92no—
293C22×D4—91no—
294C23×C4—32no—
295C23×C4—91no—
296C23×C4—92no—
297#126—916no—
298#124—98no—
299#123—916no—
300#123—98no—
301C22⋊Q8—316no—
302#120—98no—
303C4×D4—916no—
304#117—916no—
305C2×C4⋊C4—32no—
306C2×C4⋊C4—32no—
307C2×C4⋊C4—32no—
308C2×C4⋊C4—92no—
309C2×C22⋊C4—32no—
310C2×C22⋊C4—32no—
311C2×C22⋊C4—916no—
312C2×C22⋊C4—92no—
313C2×C22⋊C4—91no—
314C2×C22⋊C4—91no—
315C2×C22⋊C4—92no—
316C2×C22⋊C4—92no—
317C2×C22⋊C4—92no—
318C2×C42—92no—
319C2×C42—91no—
320C23×C3—21no—
321C23×C3—38no—
322C23×C3—34no—
323C23×C3—64no—
324C23×C3—64no—
325C23×C3C23×D312yes—
326C22×D3—24no—
327C22×D3—24no—
328C22×D3—34no—
329C22×D3—34no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—616no—
333C22×D3—64no—
334C22×D3—64no—
335C22×D3—64no—
336C22×D3—64no—
337C22×D3—64no—
338C22×D3—64no—
339C22×D3—616no—
340C22×D3—122no—
341C22×D3—122no—
342C22×D3—124no—
343C22×D3—124no—
344C22×D3—128no—
345C22×D3—1232no—
346C22×D3#23918yes—
347C22×D3C23×D314yes—
348C3×Q8—48no—
349C3×Q8—48no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4—22no—
355C2×C3×C4—24no—
356C2×C3×C4—34no—
357C2×C3×C4—34no—
358C2×C3×C4—34no—
359C2×C3×C4—44no—
360C2×C3×C4—64no—
361C2×C3×C4—64no—
362C2×C3×C4—64no—
363C2×C3×C4—128no—
364C2×C3×C4C23×D314yes—
365C2×C3×C4C23×D314yes—
366C2×C3×C4C23×D314yes—
367#67—616no—
368C2×Dic3—24no—
369C2×Dic3—24no—
370C2×Dic3—24no—
371C2×Dic3—34no—
372C2×Dic3—34no—
373C2×Dic3—64no—
374C2×Dic3—616no—
375C2×Dic3—64no—
376C2×Dic3—64no—
377C2×Dic3—124no—
378C2×Dic3C23×D314yes—
379C2×Dic3C23×D314yes—
380C2×Dic3C23×D314yes—
381D12—616no—
382D12—128no—
383D12—128no—
384C4×D3—48no—
385C4×D3—616no—
386C4×D3—128no—
387C2×C32#55114yescomplemented
388C2×C32C22×#4112yes—
389C2×C32C2×H(5,𝔽2)11yescharacteristic
390C3⋊D3—42no—
391C3⋊D3—42no—
392C3×D3—28no—
393C24—32no—
394C24—94no—
395C24—91no—
396C24—91no—
397C24—188no—
398C24—362no—
399C2×Q8—42no—
400C2×Q8C2×D3214yescomplemented
401C2×D4—98no—
402C2×D4—94no—
403C2×D4—188no—
404C2×D4—362no—
405C22×C4—32no—
406C22×C4—32no—
407C22×C4—32no—
408C22×C4—38no—
409C22×C4—94no—
410C22×C4—98no—
411C22×C4—92no—
412C22×C4—124no—
413C22×C4—188no—
414C22×C4—362no—
415C22×C4C2×D3211yescharacteristic
416C22×C4C2×D3212yes—
417C4⋊C4—38no—
418C4⋊C4—38no—
419C4⋊C4—38no—
420C4⋊C4—98no—
421C22⋊C4—38no—
422C22⋊C4—38no—
423C22⋊C4—98no—
424C22⋊C4—94no—
425C22⋊C4—94no—
426C22⋊C4—98no—
427C22⋊C4—98no—
428C22⋊C4—98no—
429C42—98no—
430C42—94no—
431C22×C3—24no—
432C22×C3—22no—
433C22×C3—21no—
434C22×C3—38no—
435C22×C3—616no—
436C22×C3—64no—
437C22×C3—64no—
438C22×C3#100414yes—
439C22×C3C2×#23914yes—
440C22×C3D3×#4114yes—
441C22×C3C24×D312yes—
442C2×D3—216no—
443C2×D3—24no—
444C2×D3—24no—
445C2×D3—64no—
446C2×D3—64no—
447C2×D3—64no—
448C2×D3—64no—
449C2×D3—64no—
450C2×D3—64no—
451C2×D3—122no—
452C2×D3—122no—
453C2×D3—124no—
454C2×D3—124no—
455C2×D3—1232no—
456C2×D3—128no—
457C2×D3—128no—
458C2×D3—244no—
459C2×D3—244no—
460C2×D3C2×#23918yes—
461C3×C4—24no—
462C3×C4—24no—
463C3×C4—24no—
464C3×C4—24no—
465C3×C4—44no—
466C3×C4—64no—
467C3×C4—64no—
468C3×C4—64no—
469Dic3—24no—
470Dic3—24no—
471Dic3—24no—
472Dic3—64no—
473Dic3—64no—
474Dic3—124no—
475C32C2×#55111yescharacteristic, complemented, Sylow
476C23—38no—
477C23—34no—
478C23—64no—
479C23—64no—
480C23—92no—
481C23—92no—
482C23—1816no—
483C23—184no—
484C23—184no—
485C23—182no—
486C23—182no—
487C23—364no—
488C23—3616no—
489C23C22×D3211yescharacteristic
490Q8—44no—
491D4—1816no—
492D4—364no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—34no—
496C2×C4—34no—
497C2×C4—34no—
498C2×C4—64no—
499C2×C4—64no—
500C2×C4—64no—
501C2×C4—94no—
502C2×C4—128no—
503C2×C4—1816no—
504C2×C4—184no—
505C2×C4—364no—
506C2×C4C22×D3212yes—
507C2×C4C22×D3214yes—
508C2×C3—22no—
509C2×C3—21no—
510C2×C3—24no—
511C2×C3—68no—
512C2×C3#563718yescomplemented
513C2×C3C2×#100412yes—
514C2×C3C22×#23912yes—
515C2×C3C2×D3×#4112yes—
516D3—28no—
517D3—124no—
518D3—124no—
519D3—242no—
520D3—242no—
521C22—38no—
522C22—64no—
523C22—64no—
524C22—616no—
525C22—184no—
526C22—184no—
527C22—182no—
528C22—182no—
529C22—3616no—
530C22—364no—
531C22—364no—
532C22D3×#23914yes—
533C22#6433012yes—
534C22C23×D3211yescharacteristic
535C4—24no—
536C4—22no—
537C4—64no—
538C4—64no—
539C4—64no—
540C4—184no—
541C3—21no—
542C3C2×#563712yescomplemented
543C2—68no—
544C2—362no—
545C2—362no—
546C2#1059543614yesdirect product factor
547C2C2×D3×#23912yes—
548C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
prime radicalC2×#63923C2
hypercenterC22×Q8D32
hypocenterC32C2×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64156C2semidirect
2. C2×C3×#946C2semidirect
3. #10595436C2direct (N × H)
5. C2×D3×(C2×D3)⋊C4C2semidirect
6. C2×#63904C2semidirect
7. C2×#63897C2semidirect
8. C2×#63890C2semidirect
9. C2×#63878C2semidirect
10. C2×#63848C2semidirect
13. C22×C32×Q8C22semidirect
17. C22×#624C22semidirect
19. #64156C22semidirect
21. C2×#3752C22semidirect
22. C2×C4×C3⋊Dic3C22semidirect
23. C3×#946C22semidirect
26. C2×C3×C4⋊Dic3C22semidirect
27. C2×C3×Dic3⋊C4C22semidirect
28. C2×C3×Dic3⋊C4C22semidirect
29. C2×Dic3⋊Dic3C22semidirect
32. C2×#3722C22semidirect
34. C2×Dic32C22semidirect
36. D3×(C2×D3)⋊C4C22semidirect
37. #63904C22semidirect
38. #63897C22semidirect
39. #63890C22semidirect
40. #63878C22semidirect
41. #63848C22semidirect
45. C2×#946D3semidirect
66. C2×C32×Q8C23semidirect
80. C2×#624C23semidirect
84. #3752C23semidirect
85. C4×C3⋊Dic3C23semidirect
88. C3×C4⋊Dic3C23semidirect
89. C3×Dic3⋊C4C23semidirect
90. C3×Dic3⋊C4C23semidirect
91. Dic3⋊Dic3C23semidirect
94. #3722C23semidirect
96. Dic32C23semidirect
100. C22×C3×Q8C2×D3semidirect
119. #946C2×D3semidirect
136. C2×C4⋊Dic3C2×D3semidirect
138. C2×Dic3⋊C4C2×D3semidirect
139. C2×Dic3⋊C4C2×D3semidirect
209. C2×C3×Q8C22×D3semidirect
262. C4⋊Dic3C22×D3semidirect
264. Dic3⋊C4C22×D3semidirect
265. Dic3⋊C4C22×D3semidirect
291. C22×Q8D32semidirect
387. C2×C32#551semidirect
400. C2×Q8C2×D32semidirect
475. C32C2×#551semidirect
512. C2×C3#5637semidirect
542. C3C2×#5637semidirect
546. C2#10595436direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641562
C2×C3×#9462
#105954362
C2×#639232
C2×D3×(C2×D3)⋊C42
C2×#639042
C2×#638972
C2×#638902
C2×#638782
C2×#638482
C2×#56373