Finite Group Databasebeta

← C2×#10594014 #11902909

Subgroups — C2×#10594014 #11902909

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×#64084C211yesmaximal, characteristic, complemented
2C2×C3×#872C212yesmaximal, complemented
3C2×#63923C211yesmaximal, characteristic
4C2×D3×(C2×D3)⋊C4C212yesmaximal, complemented
5C2×#63897C211yesmaximal, characteristic, complemented
6C2×#63896C212yesmaximal, complemented
7C2×#63880C212yesmaximal, complemented
8C2×#63868C212yesmaximal, complemented
9C2×#63850C212yesmaximal, complemented
10#10594014C2116yesmaximal, direct product factor
11C2×#5527—32nomaximal
12C23×D32C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×#634C2211yescharacteristic, complemented
15C22×C3×C4×D3C2212yes—
16C22×#626C2212yes—
17C22×#624C2211yescharacteristic, complemented
18C22×D3×Dic3C2212yes—
19C2×C32×C42C2211yescharacteristic, complemented
20C2×#3752C2212yes—
21C2×#3752C2212yescomplemented
22#64084C2218yescomplemented
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×Dic3⋊C4C2212yescomplemented
26C2×C3×Dic3⋊C4C2212yescomplemented
27C2×C3×C4×Dic3C2212yescomplemented
28C3×#872C22116yescomplemented
29C2×#3724C2212yescomplemented
30C2×Dic3⋊Dic3C2212yescomplemented
31C2×#3722C2211yescharacteristic
32C2×#3722C2212yes—
33C2×#3722C2211yescharacteristic, complemented
34C2×(C2×D3)⋊Dic3C2212yes—
35#63923C2218yes—
36D3×(C2×D3)⋊C4C22116yescomplemented
37#63897C2218yescomplemented
38#63896C22116yescomplemented
39#63880C22116yescomplemented
40#63868C22116yescomplemented
41#63850C22116yescomplemented
42C2×C3×#117—32no—
43C2×#929—32no—
44C22×(C2×D3)⋊C4—32no—
45#5527—332no—
46C2×#898—32no—
47C2×#896—32no—
48C2×#894—32no—
49C2×#894—32no—
50C2×#882—32no—
51C2×#67⋊C4—32no—
52C2×D3×C22⋊C4—32no—
53C2×#878—32no—
54C2×#876—32no—
55C2×#875—32no—
56C2×#875—61no—
57C2×C4×D12—32no—
58C2×#872D312yescomplemented
59C23×C3⋊D3C2311yescharacteristic
60C23×C3⋊D3C2311yescharacteristic
61C23×C3×D3C2312yes—
62C22×D32—28no—
63C22×D32—42no—
64C22×D32C2314yes—
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C2×C4⋊(C3⋊D3)—42no—
69C2×C4⋊(C3⋊D3)C2314yes—
70C2×#634—42no—
71C2×#634C2314yescomplemented
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C2×C3×C4×D3—28no—
76C2×C3×C4×D3C2318yes—
77C2×#626—28no—
78C2×#626C2318yes—
79C2×#624—42no—
80C2×#624C2314yescomplemented
81C2×D3×Dic3—44no—
82C2×D3×Dic3C2318yes—
83C32×C42C2314yescomplemented
84#3752C2318yes—
85#3752C2318yescomplemented
86C3×(C2×D3)⋊C4C2318yes—
87C3×(C2×D3)⋊C4C2318yes—
88C3×Dic3⋊C4C2318yescomplemented
89C3×Dic3⋊C4C2318yescomplemented
90C3×C4×Dic3C2318yescomplemented
91#3724C2318yescomplemented
92Dic3⋊Dic3C2318yescomplemented
93#3722C2314yes—
94#3722C2318yes—
95#3722C2314yescomplemented
96(C2×D3)⋊Dic3C2318yes—
97C2×#551—91noSylow
98C24×D3—32no—
99C23×C3×C4—32no—
100C22×#67—32no—
101C23×Dic3—32no—
102C22×D12—32no—
103C22×D12—32no—
104C22×D12—61no—
105C22×C4×D3—32no—
106C22×C4×D3—32no—
107C22×C4×D3C2×D312yes—
108C22×Dic6—32no—
109C22×Dic6—61no—
110C3×#117—316no—
111C2×C3×C4⋊C4—32no—
112C2×C3×C4⋊C4—32no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C22⋊C4—32no—
115C2×C3×C42—21no—
116C2×C3×C42—32no—
117C2×C3×C42C2×D312yescomplemented
118C2×#217—32no—
119#929—316no—
120C2×(C2×D3)⋊C4—32no—
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—316no—
130C2×(C2×D3)⋊C4—62no—
131C2×(C2×D3)⋊C4—62no—
132C2×(C2×D3)⋊C4C2×D312yes—
133C2×(C2×D3)⋊C4C2×D312yes—
134C2×C4⋊Dic3—32no—
135C2×Dic3⋊C4—32no—
136C2×Dic3⋊C4—32no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4C2×D312yescomplemented
139C2×Dic3⋊C4C2×D312yescomplemented
140C2×C4×Dic3C2×D312yescomplemented
141#898—316no—
142#896—316no—
143#894—316no—
144#894—316no—
145#882—316no—
146#67⋊C4—316no—
147D3×C22⋊C4—316no—
148#878—316no—
149#876—316no—
150#875—316no—
151#875—68no—
152C4×D12—316no—
153#872C2×D3116yescomplemented
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—
168C2×C32×C4—22no—
169C2×C32×C4—24no—
170C2×C32×C4C2414yes—
171C2×C32×C4C2412yes—
172C2×C3⋊Dic3—24no—
173C2×C3⋊Dic3C2414yes—
174C4⋊(C3⋊D3)—44no—
175#634—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—216no—
183#626—216no—
184#624—44no—
185D3×Dic3—48no—
186#551—916no—
187C2×#126—92no—
188C2×#124—91no—
189C2×#123—91no—
190C2×#123—92no—
191C2×C22⋊Q8—92no—
192C2×#120—91no—
193C2×C4×D4—92no—
194C2×#117—32no—
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—
206C22×C3×C4—21no—
207C22×C3×C4—22no—
208C22×C3×C4—32no—
209C22×C3×C4—32no—
210C22×C3×C4—32no—
211C22×C3×C4—38no—
212C22×C3×C4—68no—
213C22×C3×C4C22×D312yes—
214C22×C3×C4C22×D312yes—
215C22×C3×C4C22×D312yes—
216C2×#67—38no—
217C2×#67—68no—
218C22×Dic3—32no—
219C22×Dic3—32no—
220C22×Dic3—38no—
221C22×Dic3—62no—
222C22×Dic3—124no—
223C22×Dic3C22×D312yes—
224C22×Dic3C22×D312yes—
225C22×Dic3C22×D312yes—
226C2×D12—38no—
227C2×D12—38no—
228C2×D12—64no—
229C2×D12—68no—
230C2×D12—124no—
231C2×D12—124no—
232C2×C4×D3—28no—
233C2×C4×D3—38no—
234C2×C4×D3—38no—
235C2×C4×D3—124no—
236C2×C4×D3—124no—
237C2×C4×D3C22×D318yes—
238C2×Dic6—38no—
239C2×Dic6—64no—
240C2×Dic6—124no—
241C2×Dic6—124no—
242C3×C4⋊C4—38no—
243C3×C4⋊C4—38no—
244C3×C22⋊C4—38no—
245C3×C22⋊C4—38no—
246C3×C42—24no—
247C3×C42—38no—
248C3×C42C22×D318yescomplemented
249#217—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—38no—
258(C2×D3)⋊C4—38no—
259(C2×D3)⋊C4—68no—
260(C2×D3)⋊C4—68no—
261(C2×D3)⋊C4C22×D318yes—
262(C2×D3)⋊C4C22×D318yes—
263C4⋊Dic3—38no—
264Dic3⋊C4—38no—
265Dic3⋊C4—38no—
266Dic3⋊C4—38no—
267Dic3⋊C4C22×D318yescomplemented
268Dic3⋊C4C22×D318yescomplemented
269C4×Dic3C22×D318yescomplemented
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×Q8—91no—
292C22×D4—92no—
293C22×D4—91no—
294C23×C4—32no—
295C23×C4—91no—
296C23×C4—92no—
297#126—916no—
298#124—98no—
299#123—98no—
300#123—916no—
301C22⋊Q8—916no—
302#120—98no—
303C4×D4—916no—
304#117—316no—
305C2×C4⋊C4—32no—
306C2×C4⋊C4—32no—
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—91no—
315C2×C22⋊C4—92no—
316C2×C22⋊C4—92no—
317C2×C22⋊C4—92no—
318C2×C42—32no—
319C2×C42D3211yescharacteristic, complemented
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#23518yes—
347C22×D3C23×D314yes—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—22no—
353C2×C3×C4—24no—
354C2×C3×C4—34no—
355C2×C3×C4—34no—
356C2×C3×C4—34no—
357C2×C3×C4—44no—
358C2×C3×C4—616no—
359C2×C3×C4—64no—
360C2×C3×C4—64no—
361C2×C3×C4—64no—
362C2×C3×C4C23×D314yes—
363C2×C3×C4C23×D314yes—
364C2×C3×C4C23×D314yes—
365#67—616no—
366C2×Dic3—24no—
367C2×Dic3—24no—
368C2×Dic3—24no—
369C2×Dic3—34no—
370C2×Dic3—34no—
371C2×Dic3—64no—
372C2×Dic3—64no—
373C2×Dic3—64no—
374C2×Dic3—124no—
375C2×Dic3—128no—
376C2×Dic3C23×D314yes—
377C2×Dic3C23×D314yes—
378C2×Dic3C23×D314yes—
379D12—616no—
380D12—128no—
381D12—128no—
382C4×D3—216no—
383C4×D3—128no—
384C4×D3—128no—
385Dic6—128no—
386Dic6—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—94no—
400C2×Q8—362no—
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—68no—
410C22×C4—94no—
411C22×C4—98no—
412C22×C4—92no—
413C22×C4—362no—
414C22×C4—364no—
415C22×C4C2×D3212yes—
416C22×C4C2×D3211yescharacteristic
417C4⋊C4—38no—
418C4⋊C4—38no—
419C4⋊C4—98no—
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—38no—
430C42C2×D3214yescomplemented
431C22×C3—24no—
432C22×C3—22no—
433C22×C3—21no—
434C22×C3—38no—
435C22×C3—64no—
436C22×C3—64no—
437C22×C3—616no—
438C22×C3C2×#23514yes—
439C22×C3D3×#4114yes—
440C22×C3#100914yes—
441C22×C3C24×D312yes—
442C2×D3—24no—
443C2×D3—24no—
444C2×D3—216no—
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×#23518yes—
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—364no—
491D4—1816no—
492D4—364no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—34no—
496C2×C4—34no—
497C2×C4—34no—
498C2×C4—616no—
499C2×C4—64no—
500C2×C4—64no—
501C2×C4—64no—
502C2×C4—94no—
503C2×C4—184no—
504C2×C4—364no—
505C2×C4—368no—
506C2×C4C22×D3214yes—
507C2×C4C22×D3212yes—
508C2×C3—22no—
509C2×C3—21no—
510C2×C3—24no—
511C2×C3—68no—
512C2×C3#552718yescomplemented
513C2×C3C22×#23512yes—
514C2×C3C2×D3×#4112yes—
515C2×C3C2×#100912yes—
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×#23514yes—
533C22#6430812yes—
534C22C23×D3211yescharacteristic
535C4—24no—
536C4—22no—
537C4—64no—
538C4—64no—
539C4—64no—
540C4—184no—
541C3—21no—
542C3C2×#552712yescomplemented
543C2—68no—
544C2—362no—
545C2—362no—
546C2#1059401414yesdirect product factor
547C2C2×D3×#23512yes—
548C2C2×#6430811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC2×#63923C2
hypercenterC2×C42D32
hypocenterC32C2×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64084C2semidirect
2. C2×C3×#872C2semidirect
4. C2×D3×(C2×D3)⋊C4C2semidirect
5. C2×#63897C2semidirect
6. C2×#63896C2semidirect
7. C2×#63880C2semidirect
8. C2×#63868C2semidirect
9. C2×#63850C2semidirect
10. #10594014C2direct (N × H)
14. C22×#634C22semidirect
17. C22×#624C22semidirect
19. C2×C32×C42C22semidirect
21. C2×#3752C22semidirect
22. #64084C22semidirect
25. C2×C3×Dic3⋊C4C22semidirect
26. C2×C3×Dic3⋊C4C22semidirect
27. C2×C3×C4×Dic3C22semidirect
28. C3×#872C22semidirect
29. C2×#3724C22semidirect
30. C2×Dic3⋊Dic3C22semidirect
33. C2×#3722C22semidirect
36. D3×(C2×D3)⋊C4C22semidirect
37. #63897C22semidirect
38. #63896C22semidirect
39. #63880C22semidirect
40. #63868C22semidirect
41. #63850C22semidirect
58. C2×#872D3semidirect
71. C2×#634C23semidirect
80. C2×#624C23semidirect
83. C32×C42C23semidirect
85. #3752C23semidirect
88. C3×Dic3⋊C4C23semidirect
89. C3×Dic3⋊C4C23semidirect
90. C3×C4×Dic3C23semidirect
91. #3724C23semidirect
92. Dic3⋊Dic3C23semidirect
95. #3722C23semidirect
117. C2×C3×C42C2×D3semidirect
138. C2×Dic3⋊C4C2×D3semidirect
139. C2×Dic3⋊C4C2×D3semidirect
140. C2×C4×Dic3C2×D3semidirect
153. #872C2×D3semidirect
248. C3×C42C22×D3semidirect
267. Dic3⋊C4C22×D3semidirect
268. Dic3⋊C4C22×D3semidirect
269. C4×Dic3C22×D3semidirect
319. C2×C42D32semidirect
387. C2×C32#551semidirect
430. C42C2×D32semidirect
475. C32C2×#551semidirect
512. C2×C3#5527semidirect
542. C3C2×#5527semidirect
546. C2#10594014direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640842
C2×C3×#8722
C2×#639232
C2×D3×(C2×D3)⋊C42
C2×#638972
C2×#638962
C2×#638802
C2×#638682
C2×#638502
#105940142
C2×#55273