Finite Group Databasebeta

← C2×#10595087 #11902945

Subgroups — C2×#10595087 #11902945

Order 1152.

2827 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×#64138C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C212yesmaximal, complemented
3C2×#63983C211yesmaximal, characteristic
4C2×#63969C212yesmaximal, complemented
5C2×#63953C211yesmaximal, characteristic, complemented
6#10595087C2116yesmaximal, direct product factor
7C2×D3×(C2×D3)⋊C4C212yesmaximal, complemented
8C2×#63877C212yesmaximal, complemented
9C2×#63868C212yesmaximal, complemented
10C2×#63851C212yesmaximal, complemented
11C2×#5556—32nomaximal
12C23×D32C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic, complemented
14C22×#638C2211yescharacteristic
15C22×C3×#67C2212yes—
16C22×C3×C4×D3C2212yes—
17C22×#627C2211yescharacteristic, complemented
18C22×D3×Dic3C2212yes—
19C2×#3757C2211yescharacteristic, complemented
20#64138C2218yescomplemented
21C2×#3752C2212yes—
22C2×#3750C2212yescomplemented
23C2×C3×#217C2212yescomplemented
24C3×C4×#67C22116yescomplemented
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×Dic3⋊C4C2212yescomplemented
27C2×C3×C4×Dic3C2212yescomplemented
28#63983C2218yes—
29#63969C22116yescomplemented
30C2×#3724C2212yescomplemented
31C2×Dic3⋊Dic3C2212yescomplemented
32C2×#3722C2211yescharacteristic
33C2×#3722C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×Dic32C2211yescharacteristic, complemented
37#63953C2218yescomplemented
38D3×(C2×D3)⋊C4C22116yescomplemented
39#63877C22116yescomplemented
40#63868C22116yescomplemented
41#63851C22116yescomplemented
42C2×C3×C4×D4—32no—
43C2×#937—32no—
44C2×#935—32no—
45C2×#929—32no—
46C2×#929—61no—
47C2×C4×#67D312yescomplemented
48C22×(C2×D3)⋊C4—32no—
49C2×#924—32no—
50#5556—332no—
51C2×#898—32no—
52C2×#896—32no—
53C2×#885—32no—
54C2×#883—32no—
55C2×D3×C22⋊C4—32no—
56C2×#877—32no—
57C2×#876—32no—
58C2×#872—32no—
59C24×C32C2311yescharacteristic
60C23×C3⋊D3C2311yescharacteristic
61C23×C3×D3C2312yes—
62C22×D32—28no—
63C22×D32—42no—
64C22×D32C2314yes—
65C22×C32×C4—42no—
66C22×C32×C4C2312yes—
67C22×C32×C4C2314yescomplemented
68C2×#638—42no—
69C2×#638C2314yes—
70C22×C3⋊Dic3C2312yes—
71C22×C3⋊Dic3C2311yescharacteristic
72C2×C3×#67—28no—
73C2×C3×#67C2318yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C2×C3×C4×D3—44no—
78C2×C3×C4×D3C2318yes—
79C2×#627—42no—
80C2×#627C2314yescomplemented
81C2×D3×Dic3—28no—
82C2×D3×Dic3C2318yes—
83#3757C2314yescomplemented
84#3752C2318yes—
85#3750C2318yescomplemented
86C3×#217C2318yescomplemented
87C3×(C2×D3)⋊C4C2318yes—
88C3×Dic3⋊C4C2318yescomplemented
89C3×C4×Dic3C2318yescomplemented
90#3724C2318yescomplemented
91Dic3⋊Dic3C2318yescomplemented
92#3722C2314yes—
93#3722C2318yes—
94(C2×D3)⋊Dic3C2318yes—
95(C2×D3)⋊Dic3C2318yes—
96Dic32C2314yescomplemented
97C2×#551—91noSylow
98C24×D3—32no—
99C22×C3×D4—32no—
100C23×C3×C4—21no—
101C23×C3×C4—32no—
102C23×C3×C4C2×D312yescomplemented
103C22×#67—32no—
104C22×#67—61no—
105C22×#67C2×D312yes—
106C23×Dic3—32no—
107C22×C4×D3—32no—
108C22×C4×D3C2×D312yes—
109C22×Dic6—32no—
110C3×C4×D4—316no—
111C2×C3×C4⋊C4—32no—
112C2×C3×C22⋊C4—32no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C42—32no—
115C2×#217—32no—
116C2×#217—32no—
117C2×#217—32no—
118C2×#217—61no—
119C2×#217C2×D312yescomplemented
120#937—316no—
121#935—316no—
122#929—316no—
123#929—68no—
124C4×#67C2×D3116yescomplemented
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—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—316no—
133C2×(C2×D3)⋊C4—62no—
134C2×(C2×D3)⋊C4C2×D312yes—
135C2×C4⋊Dic3—32no—
136#924—316no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—32no—
139C2×Dic3⋊C4—32no—
140C2×Dic3⋊C4—32no—
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—62no—
143C2×Dic3⋊C4C2×D312yescomplemented
144C2×C4×Dic3—32no—
145C2×C4×Dic3C2×D312yescomplemented
146#898—316no—
147#896—316no—
148#885—316no—
149#883—316no—
150D3×C22⋊C4—316no—
151#877—316no—
152#876—316no—
153#872—316no—
154C23×C32—22no—
155C23×C32—24no—
156C23×C32C2412yes—
157C23×C32C2411yescharacteristic
158C22×C3⋊D3—24no—
159C22×C3⋊D3—22no—
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—
168C2×C32×C4—24no—
169C2×C32×C4—44no—
170C2×C32×C4C2414yes—
171#638—44no—
172C2×C3⋊Dic3—24no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3C2412yes—
175C2×C3⋊Dic3C2414yes—
176C3×#67—216no—
177C2×C3×Dic3—24no—
178C2×C3×Dic3—24no—
179C2×C3×Dic3—24no—
180C2×C3×Dic3C2414yes—
181C2×C3×Dic3C2414yes—
182C2×C3×Dic3C2414yes—
183C3×C4×D3—48no—
184#627—44no—
185D3×Dic3—216no—
186#551—916no—
187C2×#126—92no—
188C2×#124—91no—
189C2×#123—92no—
190C2×#123—91no—
191C2×C22⋊Q8—92no—
192C2×#120—91no—
193C2×C4×D4—32no—
194C2×#117—92no—
195C22×C22⋊C4—92no—
196C24×C3—21no—
197C24×C3—32no—
198C24×C3C22×D312yes—
199C23×D3—32no—
200C23×D3—38no—
201C23×D3—61no—
202C23×D3—68no—
203C23×D3—68no—
204C23×D3—124no—
205C23×D3C22×D312yes—
206C2×C3×D4—38no—
207C2×C3×D4—68no—
208C22×C3×C4—22no—
209C22×C3×C4—24no—
210C22×C3×C4—32no—
211C22×C3×C4—32no—
212C22×C3×C4—32no—
213C22×C3×C4—38no—
214C22×C3×C4—44no—
215C22×C3×C4—44no—
216C22×C3×C4—124no—
217C22×C3×C4C22×D312yes—
218C22×C3×C4C22×D312yes—
219C22×C3×C4C22×D318yescomplemented
220C2×#67—28no—
221C2×#67—38no—
222C2×#67—64no—
223C2×#67—124no—
224C2×#67—124no—
225C2×#67C22×D318yes—
226C22×Dic3—32no—
227C22×Dic3—32no—
228C22×Dic3—32no—
229C22×Dic3—38no—
230C22×Dic3—61no—
231C22×Dic3—62no—
232C22×Dic3—68no—
233C22×Dic3C22×D312yes—
234C22×Dic3C22×D312yes—
235C22×Dic3C22×D312yes—
236C2×C4×D3—38no—
237C2×C4×D3—44no—
238C2×C4×D3—68no—
239C2×C4×D3C22×D318yes—
240C2×Dic6—38no—
241C2×Dic6—124no—
242C3×C4⋊C4—38no—
243C3×C22⋊C4—38no—
244C3×C22⋊C4—38no—
245C3×C42—38no—
246#217—38no—
247#217—38no—
248#217—38no—
249#217—64no—
250#217C22×D318yescomplemented
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—38no—
258(C2×D3)⋊C4—68no—
259(C2×D3)⋊C4C22×D318yes—
260C4⋊Dic3—38no—
261Dic3⋊C4—38no—
262Dic3⋊C4—38no—
263Dic3⋊C4—38no—
264Dic3⋊C4—38no—
265Dic3⋊C4—38no—
266Dic3⋊C4—68no—
267Dic3⋊C4C22×D318yescomplemented
268C4×Dic3—38no—
269C4×Dic3C22×D318yescomplemented
270C22×C32—22no—
271C22×C32—24no—
272C22×C32—44no—
273C22×C32C2×#4114yes—
274C22×C32H(5,𝔽2)12yes—
275C22×C32C2511yescharacteristic
276C2×C3⋊D3—24no—
277C2×C3⋊D3—22no—
278C2×C3⋊D3—44no—
279C2×C3×D3—216no—
280C2×C3×D3—24no—
281C2×C3×D3—24no—
282C2×C3×D3C2×#4118yes—
283D32—416no—
284C32×C4—24no—
285C3⋊Dic3—24no—
286C3⋊Dic3—22no—
287C3×Dic3—24no—
288C3×Dic3—24no—
289C3×Dic3—24no—
290C25—91no—
291C22×Q8—91no—
292C22×D4—32no—
293C22×D4—91no—
294C23×C4—32no—
295C23×C4—92no—
296C23×C4D3211yescharacteristic, complemented
297#126—916no—
298#124—98no—
299#123—916no—
300#123—98no—
301C22⋊Q8—916no—
302#120—98no—
303C4×D4—316no—
304#117—916no—
305C2×C4⋊C4—32no—
306C2×C4⋊C4—92no—
307C2×C4⋊C4—92no—
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—92no—
315C2×C22⋊C4—92no—
316C2×C22⋊C4—91no—
317C2×C22⋊C4—92no—
318C2×C42—32no—
319C2×C42—91no—
320C23×C3—24no—
321C23×C3—24no—
322C23×C3—24no—
323C23×C3—24no—
324C23×C3—22no—
325C23×C3—21no—
326C23×C3—38no—
327C23×C3—34no—
328C23×C3—44no—
329C23×C3—64no—
330C23×C3—64no—
331C23×C3C23×D314yes—
332C23×C3C23×D312yes—
333C22×D3—24no—
334C22×D3—24no—
335C22×D3—34no—
336C22×D3—62no—
337C22×D3—616no—
338C22×D3—64no—
339C22×D3—64no—
340C22×D3—64no—
341C22×D3—616no—
342C22×D3—122no—
343C22×D3—124no—
344C22×D3—128no—
345C22×D3—1232no—
346C22×D3#23518yes—
347C22×D3C23×D314yes—
348C3×D4—616no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—34no—
353C2×C3×C4—34no—
354C2×C3×C4—34no—
355C2×C3×C4—44no—
356C2×C3×C4—48no—
357C2×C3×C4—48no—
358C2×C3×C4—64no—
359C2×C3×C4—64no—
360C2×C3×C4—64no—
361C2×C3×C4—128no—
362C2×C3×C4C23×D314yes—
363C2×C3×C4C23×D314yes—
364#67—216no—
365#67—128no—
366#67—128no—
367C2×Dic3—24no—
368C2×Dic3—24no—
369C2×Dic3—24no—
370C2×Dic3—34no—
371C2×Dic3—34no—
372C2×Dic3—34no—
373C2×Dic3—62no—
374C2×Dic3—64no—
375C2×Dic3—616no—
376C2×Dic3—64no—
377C2×Dic3—64no—
378C2×Dic3—64no—
379C2×Dic3—124no—
380C2×Dic3—122no—
381C2×Dic3C23×D314yes—
382C2×Dic3C23×D314yes—
383C2×Dic3C23×D314yes—
384C4×D3—48no—
385C4×D3—616no—
386Dic6—128no—
387C2×C32—42no—
388C2×C32#55114yescomplemented
389C2×C32C22×#4112yes—
390C2×C32C2×H(5,𝔽2)11yescharacteristic
391C3⋊D3—42no—
392C3×D3—28no—
393C24—32no—
394C24—94no—
395C24—91no—
396C24—188no—
397C24—362no—
398C24C2×D3211yescharacteristic
399C2×Q8—94no—
400C2×Q8—362no—
401C2×D4—38no—
402C2×D4—68no—
403C2×D4—94no—
404C2×D4—362no—
405C22×C4—32no—
406C22×C4—32no—
407C22×C4—32no—
408C22×C4—38no—
409C22×C4—42no—
410C22×C4—98no—
411C22×C4—91no—
412C22×C4—92no—
413C22×C4—124no—
414C22×C4—188no—
415C22×C4C2×D3212yes—
416C22×C4C2×D3214yescomplemented
417C4⋊C4—38no—
418C4⋊C4—98no—
419C4⋊C4—98no—
420C4⋊C4—98no—
421C22⋊C4—38no—
422C22⋊C4—38no—
423C22⋊C4—98no—
424C22⋊C4—94no—
425C22⋊C4—98no—
426C22⋊C4—98no—
427C22⋊C4—94no—
428C22⋊C4—98no—
429C42—38no—
430C42—94no—
431C22×C3—24no—
432C22×C3—24no—
433C22×C3—24no—
434C22×C3—24no—
435C22×C3—24no—
436C22×C3—22no—
437C22×C3—21no—
438C22×C3—38no—
439C22×C3—44no—
440C22×C3—48no—
441C22×C3—48no—
442C22×C3—64no—
443C22×C3—64no—
444C22×C3—616no—
445C22×C3C2×#23514yes—
446C22×C3#100414yes—
447C22×C3D3×#4114yes—
448C22×C3C24×D312yes—
449C2×D3—24no—
450C2×D3—24no—
451C2×D3—216no—
452C2×D3—64no—
453C2×D3—64no—
454C2×D3—64no—
455C2×D3—122no—
456C2×D3—124no—
457C2×D3—1232no—
458C2×D3—128no—
459C2×D3—244no—
460C2×D3C2×#23518yes—
461C3×C4—24no—
462C3×C4—24no—
463C3×C4—44no—
464C3×C4—64no—
465C3×C4—64no—
466C3×C4—64no—
467Dic3—24no—
468Dic3—24no—
469Dic3—24no—
470Dic3—64no—
471Dic3—64no—
472Dic3—64no—
473Dic3—122no—
474Dic3—124no—
475C32C2×#55111yescharacteristic, complemented, Sylow
476C23—24no—
477C23—22no—
478C23—38no—
479C23—34no—
480C23—64no—
481C23—64no—
482C23—92no—
483C23—1816no—
484C23—184no—
485C23—182no—
486C23—364no—
487C23—3616no—
488C23C22×D3212yes—
489C23C22×D3211yescharacteristic
490Q8—364no—
491D4—616no—
492D4—364no—
493C2×C4—24no—
494C2×C4—34no—
495C2×C4—34no—
496C2×C4—34no—
497C2×C4—44no—
498C2×C4—64no—
499C2×C4—64no—
500C2×C4—64no—
501C2×C4—92no—
502C2×C4—94no—
503C2×C4—128no—
504C2×C4—1816no—
505C2×C4—184no—
506C2×C4—182no—
507C2×C4C22×D3214yes—
508C2×C3—24no—
509C2×C3—22no—
510C2×C3—21no—
511C2×C3—44no—
512C2×C3—44no—
513C2×C3—68no—
514C2×C3#555618yescomplemented
515C2×C3C22×#23512yes—
516C2×C3C2×#100412yes—
517C2×C3C2×D3×#4112yes—
518D3—28no—
519D3—124no—
520D3—242no—
521C22—24no—
522C22—22no—
523C22—38no—
524C22—44no—
525C22—616no—
526C22—64no—
527C22—64no—
528C22—184no—
529C22—182no—
530C22—3616no—
531C22—364no—
532C22D3×#23514yes—
533C22#6433012yes—
534C22C23×D3211yescharacteristic
535C4—24no—
536C4—64no—
537C4—64no—
538C4—64no—
539C4—184no—
540C4—182no—
541C3—21no—
542C3C2×#555612yescomplemented
543C2—42no—
544C2—68no—
545C2—362no—
546C2#1059508714yesdirect product factor
547C2C2×D3×#23512yes—
548C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC2×#63983C2
hypercenterC23×C4D32
hypocenterC32C2×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64138C2semidirect
2. C2×C3×C4×#67C2semidirect
4. C2×#63969C2semidirect
5. C2×#63953C2semidirect
6. #10595087C2direct (N × H)
7. C2×D3×(C2×D3)⋊C4C2semidirect
8. C2×#63877C2semidirect
9. C2×#63868C2semidirect
10. C2×#63851C2semidirect
13. C23×C32×C4C22semidirect
17. C22×#627C22semidirect
19. C2×#3757C22semidirect
20. #64138C22semidirect
22. C2×#3750C22semidirect
23. C2×C3×#217C22semidirect
24. C3×C4×#67C22semidirect
26. C2×C3×Dic3⋊C4C22semidirect
27. C2×C3×C4×Dic3C22semidirect
29. #63969C22semidirect
30. C2×#3724C22semidirect
31. C2×Dic3⋊Dic3C22semidirect
36. C2×Dic32C22semidirect
37. #63953C22semidirect
38. D3×(C2×D3)⋊C4C22semidirect
39. #63877C22semidirect
40. #63868C22semidirect
41. #63851C22semidirect
47. C2×C4×#67D3semidirect
67. C22×C32×C4C23semidirect
80. C2×#627C23semidirect
83. #3757C23semidirect
85. #3750C23semidirect
86. C3×#217C23semidirect
88. C3×Dic3⋊C4C23semidirect
89. C3×C4×Dic3C23semidirect
90. #3724C23semidirect
91. Dic3⋊Dic3C23semidirect
96. Dic32C23semidirect
102. C23×C3×C4C2×D3semidirect
119. C2×#217C2×D3semidirect
124. C4×#67C2×D3semidirect
143. C2×Dic3⋊C4C2×D3semidirect
145. C2×C4×Dic3C2×D3semidirect
219. C22×C3×C4C22×D3semidirect
250. #217C22×D3semidirect
267. Dic3⋊C4C22×D3semidirect
269. C4×Dic3C22×D3semidirect
296. C23×C4D32semidirect
388. C2×C32#551semidirect
416. C22×C4C2×D32semidirect
475. C32C2×#551semidirect
514. C2×C3#5556semidirect
542. C3C2×#5556semidirect
546. C2#10595087direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641382
C2×C3×C4×#672
C2×#639832
C2×#639692
C2×#639532
#105950872
C2×D3×(C2×D3)⋊C42
C2×#638772
C2×#638682
C2×#638512
C2×#55563