Finite Group Databasebeta

← C2×#10594731 #11918808

Subgroups — C2×#10594731 #11918808

Order 1152.

3157 conjugacy classes of subgroups.

The subgroup lattice has 517 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64313C212yesmaximal, complemented
2C2×#64121C211yesmaximal, characteristic, complemented
3C2×C3×D3×D8C212yesmaximal, complemented
4C2×#63932C214yesmaximal, complemented
5C2×#63927C212yesmaximal, complemented
6#10594731C2116yesmaximal, direct product factor
7C2×#63807C212yesmaximal, complemented
8C2×#63803C211yesmaximal, characteristic, complemented
9C2×#63797C211yesmaximal, characteristic, complemented
10C2×#5757—32nomaximal
11C2×#3830C2212yescomplemented
12C2×C3×D3×D4C2214yescomplemented
13C2×D3×#67—24no—
14C22×#625—22no—
15C2×#3805—22no—
16#64313—28no—
17#64313C22116yescomplemented
18C2×#3802C2212yescomplemented
19C2×#3798C2211yescharacteristic
20C2×#3795C2214yescomplemented
21C2×C32×D8C2211yescharacteristic, complemented
22C2×#3754C2212yescomplemented
23#64121C2218yescomplemented
24C2×#3746C2211yescharacteristic, complemented
25C2×C8×C3⋊D3C2211yescharacteristic, complemented
26C2×C3×#213C2214yescomplemented
27C3×D3×D8C22116yescomplemented
28C2×C3×D24C2212yescomplemented
29C2×C3×D3×C8C2212yescomplemented
30#63932C22132yescomplemented
31#63927C22116yescomplemented
32C2×#3716C2214yescomplemented
33C2×#3713C2212yescomplemented
34C2×#3712C2211yescharacteristic, complemented
35C2×#3711C2212yescomplemented
36#63807C22116yescomplemented
37#63803C2218yescomplemented
38#63797C2218yescomplemented
39C2×#1004—34no—
40C22×C3×D8—32no—
41C2×#932—34no—
42#5757—332no—
43C2×#912—32no—
44C2×#912—32no—
45C2×#912—61no—
46C2×#911—34no—
47C2×#911—34no—
48C2×D3×D8—32no—
49C2×D3×D8D312yescomplemented
50C2×#904—32no—
51C2×#901—32no—
52C23×C3×D3—24no—
53C22×D32—22no—
54C2×C32×D4C2312yes—
55C2×#638—22no—
56C22×C3⋊Dic3—22no—
57#3830—24no—
58#3830C2318yescomplemented
59C2×C4×C3⋊D3C2311yescharacteristic
60C2×#634C2312yes—
61C2×C3×#67—24no—
62C3×D3×D4—28no—
63C3×D3×D4C23116yescomplemented
64C2×C3×D12C2314yes—
65C2×C3×C4×D3C2312yes—
66D3×#67—232no—
67C2×#627D411yescharacteristic
68C2×#626D412yes—
69C2×#625—24no—
70C2×#625—22no—
71C2×#625—216no—
72C2×#625D411yescharacteristic
73#3805—216no—
74C2×D3×Dic3—24no—
75#3802—24no—
76#3802C2318yescomplemented
77#3798D414yes—
78#3798C2314yes—
79#3795—28no—
80#3795C23116yescomplemented
81C32×D8C2314yescomplemented
82C2×C32×C8C2311yescharacteristic
83#3754C2318yescomplemented
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85#3746C2314yescomplemented
86C8×C3⋊D3C2314yescomplemented
87C3×#213C23116yescomplemented
88C2×C3×C3⋊C8C2312yes—
89C3×D24C2318yescomplemented
90C3×D3×C8C2318yescomplemented
91#3716C23116yescomplemented
92#3713C2318yescomplemented
93#3712C2314yescomplemented
94#3711C2318yescomplemented
95C2×#576—91noSylow
96C22×C3×D4—34no—
97C22×#67—64no—
98C22×#67—64no—
99#1004—332no—
100#1004—616no—
101C2×#237—34no—
102C2×#237—34no—
103C2×#237—62no—
104C2×#237—64no—
105C2×D3×D4—34no—
106C2×D3×D4—64no—
107C2×D3×D4C2×D314yescomplemented
108C2×#235—32no—
109C2×#235—34no—
110C2×C3×D8—21no—
111C2×C3×D8—34no—
112C2×C3×D8—316no—
113C2×C3×D8—32no—
114C2×C3×D8C2×D312yescomplemented
115C22×C3×C8—32no—
116C2×#214—34no—
117C2×#214—34no—
118C2×#214—62no—
119#932—332no—
120C2×#213—34no—
121C2×#213C2×D314yescomplemented
122C2×#208—32no—
123#912—316no—
124#912—316no—
125#912—68no—
126#911—332no—
127#911—332no—
128D3×D8—316no—
129D3×D8C2×D3116yescomplemented
130C2×Dic12—32no—
131C2×Dic12—61no—
132#904—316no—
133C2×D24C2×D312yescomplemented
134C2×#204—34no—
135#901—316no—
136C2×ΓL(1,𝔽25)—32no—
137C2×ΓL(1,𝔽25)—32no—
138C2×D3×C8—32no—
139C2×D3×C8—61no—
140C2×D3×C8C2×D312yescomplemented
141C23×C32—22no—
142C22×C3⋊D3C2×D411yescharacteristic
143C22×C3×D3—24no—
144C22×C3×D3—216no—
145C22×C3×D3—88no—
146C22×C3×D3C2×D412yes—
147C2×D32—28no—
148C2×D32—84no—
149C32×D4—22no—
150C32×D4C2414yes—
151C2×C32×C4C2411yescharacteristic
152#638—28no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—28no—
155C2×C3⋊Dic3C2×D411yescharacteristic
156C4×C3⋊D3C2×D412yes—
157C4×C3⋊D3C2412yes—
158#634—22no—
159#634C2414yes—
160C3×#67—216no—
161C2×C3×Dic3C2×D412yes—
162C3×D12—24no—
163C3×D12C2418yes—
164C3×C4×D3C2×D414yes—
165C3×C4×D3C2414yes—
166#627C2×D414yes—
167#626C2×D418yes—
168#625—216no—
169#625—28no—
170#625C2×D414yes—
171D3×Dic3—216no—
172C32×C8C2412yes—
173C3⋊(C3⋊C8)C2412yes—
174C3×C3⋊C8C2414yes—
175C2×H(5,𝔽2)—92no—
176#576—916no—
177C2×AGL(1,ℤ/8)—92no—
178C2×AGL(1,ℤ/8)—94no—
179C2×#135—92no—
180C2×#135—91no—
181C22×D8—32no—
182C22×D8—91no—
183C2×#131—91no—
184C24×C3—64no—
185C23×D3—24no—
186C23×D3—64no—
187C2×C3×D4—22no—
188C2×C3×D4—316no—
189C2×C3×D4—34no—
190C2×C3×D4—68no—
191C2×C3×D4—64no—
192C2×C3×D4C22×D314yes—
193C22×C3×C4—32no—
194C2×#67—24no—
195C2×#67—32no—
196C2×#67—32no—
197C2×#67—64no—
198C2×#67—632no—
199C2×#67—632no—
200C2×#67—64no—
201C2×#67—64no—
202C2×#67—64no—
203C2×#67—122no—
204C22×Dic3—64no—
205C22×Dic3—64no—
206C22×Dic3—122no—
207#237—316no—
208#237—316no—
209#237—68no—
210#237—632no—
211#237—68no—
212#237—68no—
213#237—124no—
214D3×D4—28no—
215D3×D4—316no—
216D3×D4—68no—
217D3×D4—632no—
218D3×D4C22×D3116yescomplemented
219#235—38no—
220#235—38no—
221#235—316no—
222#235—68no—
223C2×D12—32no—
224C2×D12C22×D314yes—
225C2×C4×D3—32no—
226C2×C4×D3—61no—
227C2×C4×D3—64no—
228C2×C4×D3C22×D312yes—
229C2×Dic6—32no—
230C2×Dic6—34no—
231C2×Dic6—62no—
232C3×D8—24no—
233C3×D8—316no—
234C3×D8—38no—
235C3×D8C22×D318yescomplemented
236C2×C3×C8—21no—
237C2×C3×C8—32no—
238C2×C3×C8—38no—
239C2×C3×C8C22×D312yes—
240#214—316no—
241#214—316no—
242#214—68no—
243#213—316no—
244#213C22×D3116yescomplemented
245#208—38no—
246C2×C3⋊C8—32no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8C22×D312yes—
249Dic12—38no—
250Dic12—64no—
251D24C22×D318yescomplemented
252#204—316no—
253ΓL(1,𝔽25)—38no—
254ΓL(1,𝔽25)—38no—
255D3×C8—38no—
256D3×C8—64no—
257D3×C8C22×D318yescomplemented
258C22×C32—24no—
259C22×C32—44no—
260C22×C32C22×D411yescharacteristic
261C2×C3⋊D3—22no—
262C2×C3⋊D3C22×D412yes—
263C2×C3×D3—24no—
264C2×C3×D3—28no—
265C2×C3×D3—48no—
266C2×C3×D3—816no—
267C2×C3×D3C22×D414yes—
268D32—88no—
269C32×C4C22×D411yescharacteristic
270C32×C4C2511yescharacteristic
271C3⋊Dic3—24no—
272C3⋊Dic3C22×D412yes—
273C3×Dic3C22×D414yes—
274H(5,𝔽2)—916no—
275H(5,𝔽2)—188no—
276C2×#41—91no—
277C2×#41—94no—
278C2×#41—92no—
279C2×#41—182no—
280C22×D4—34no—
281C22×D4—92no—
282C22×D4—184no—
283C22×D4—182no—
284AGL(1,ℤ/8)—916no—
285AGL(1,ℤ/8)—932no—
286#135—916no—
287#135—98no—
288C2×Q16—91no—
289C2×SD16—94no—
290C2×SD16—92no—
291C2×D8—34no—
292C2×D8—316no—
293C2×D8—32no—
294C2×D8—98no—
295C2×D8—92no—
296C2×D8D3211yescharacteristic, complemented
297#131—98no—
298C2×M16—91no—
299C2×M16—92no—
300C22×C8—32no—
301C22×C8—91no—
302C23×C3—24no—
303C23×C3—32no—
304C23×C3—42no—
305C23×C3—616no—
306C23×C3—64no—
307C23×C3—248no—
308C22×D3—24no—
309C22×D3—216no—
310C22×D3—32no—
311C22×D3—61no—
312C22×D3—616no—
313C22×D3—88no—
314C22×D3—248no—
315C22×D3D3×D412yes—
316C3×D4—24no—
317C3×D4—24no—
318C3×D4—38no—
319C3×D4—42no—
320C3×D4—616no—
321C3×D4—64no—
322C3×D4C23×D318yes—
323C2×C3×C4—21no—
324C2×C3×C4—32no—
325C2×C3×C4—34no—
326C2×C3×C4—34no—
327C2×C3×C4C23×D312yes—
328#67—216no—
329#67—38no—
330#67—38no—
331#67—616no—
332#67—616no—
333#67—616no—
334#67—616no—
335#67—128no—
336C2×Dic3—32no—
337C2×Dic3—61no—
338C2×Dic3—616no—
339C2×Dic3—64no—
340C2×Dic3—616no—
341C2×Dic3—128no—
342C2×Dic3—122no—
343C2×Dic3D3×D412yes—
344D12—24no—
345D12—38no—
346D12C23×D318yes—
347C4×D3—34no—
348C4×D3—34no—
349C4×D3—62no—
350C4×D3—62no—
351C4×D3—616no—
352C4×D3D3×D414yes—
353C4×D3C23×D314yes—
354Dic6—38no—
355Dic6—38no—
356Dic6—64no—
357Dic6—64no—
358Dic6—122no—
359C3×C8—22no—
360C3×C8—34no—
361C3×C8C23×D314yes—
362C3⋊C8—34no—
363C3⋊C8—62no—
364C3⋊C8C23×D314yes—
365C2×C32—44no—
366C2×C32#57612yescomplemented
367C2×C32C23×D411yescharacteristic
368C3⋊D3—22no—
369C3×D3—24no—
370C3×D3—48no—
371C24—64no—
372C24—182no—
373#41—94no—
374#41—94no—
375#41—916no—
376#41—98no—
377#41—188no—
378#41—184no—
379#41—1816no—
380C2×Q8—91no—
381C2×Q8—92no—
382C2×D4—316no—
383C2×D4—34no—
384C2×D4—68no—
385C2×D4—64no—
386C2×D4—92no—
387C2×D4—98no—
388C2×D4—91no—
389C2×D4—184no—
390C2×D4—182no—
391C2×D4—1832no—
392C2×D4—1816no—
393C2×D4—182no—
394C2×D4—184no—
395C2×D4C2×D3212yes—
396C22×C4—32no—
397C22×C4—91no—
398C22×C4—184no—
399C22×C4—182no—
400Q16—94no—
401SD16—916no—
402SD16—98no—
403D8—316no—
404D8—38no—
405D8—98no—
406D8C2×D3214yescomplemented
407M16—94no—
408M16—98no—
409C2×C8—32no—
410C2×C8—38no—
411C2×C8—91no—
412C2×C8—94no—
413C2×C8C2×D3211yescharacteristic
414C22×C3—28no—
415C22×C3—21no—
416C22×C3—34no—
417C22×C3—44no—
418C22×C3—48no—
419C22×C3—64no—
420C22×C3—68no—
421C22×C3—84no—
422C22×C3—128no—
423C22×C3—2416no—
424C22×C3C2×D3×D412yes—
425C2×D3—24no—
426C2×D3—28no—
427C2×D3—34no—
428C2×D3—48no—
429C2×D3—62no—
430C2×D3—64no—
431C2×D3—816no—
432C2×D3—122no—
433C2×D3—2416no—
434C2×D3C2×D3×D414yes—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—34no—
438C3×C4C2×D3×D412yes—
439C3×C4C24×D312yes—
440Dic3—34no—
441Dic3—62no—
442Dic3—68no—
443Dic3—124no—
444Dic3C2×D3×D414yes—
445C32C2×#57611yescharacteristic, complemented, Sylow
446C23—22no—
447C23—32no—
448C23—616no—
449C23—64no—
450C23—91no—
451C23—188no—
452C23—248no—
453C23—724no—
454Q8—94no—
455Q8—94no—
456Q8—182no—
457D4—22no—
458D4—38no—
459D4—616no—
460D4—64no—
461D4—98no—
462D4—94no—
463D4—188no—
464D4—188no—
465D4—1816no—
466D4C22×D3214yes—
467C2×C4—32no—
468C2×C4—34no—
469C2×C4—34no—
470C2×C4—91no—
471C2×C4—92no—
472C2×C4—92no—
473C2×C4—1816no—
474C2×C4—188no—
475C2×C4—182no—
476C2×C4C22×D3211yescharacteristic
477C8—34no—
478C8—92no—
479C8C22×D3212yes—
480C2×C3—21no—
481C2×C3—22no—
482C2×C3—48no—
483C2×C3—64no—
484C2×C3—84no—
485C2×C3—128no—
486C2×C3#575714yescomplemented
487C2×C3C22×D3×D412yes—
488D3—24no—
489D3—48no—
490D3—64no—
491D3—122no—
492C22—24no—
493C22—34no—
494C22—44no—
495C22—64no—
496C22—68no—
497C22—92no—
498C22—128no—
499C22—182no—
500C22—2416no—
501C22—728no—
502C22D32×D411yescharacteristic
503C4—34no—
504C4—92no—
505C4—184no—
506C4D32×D411yescharacteristic
507C4C23×D3211yescharacteristic
508C3—21no—
509C3C2×#575712yescomplemented
510C2—44no—
511C2—64no—
512C2—128no—
513C2—182no—
514C2#1059473112yesdirect product factor
515C2C2×D32×D411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32C2×#576
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#64313C2semidirect
2. C2×#64121C2semidirect
3. C2×C3×D3×D8C2semidirect
4. C2×#63932C2semidirect
5. C2×#63927C2semidirect
6. #10594731C2direct (N × H)
7. C2×#63807C2semidirect
8. C2×#63803C2semidirect
9. C2×#63797C2semidirect
11. C2×#3830C22semidirect
12. C2×C3×D3×D4C22semidirect
17. #64313C22semidirect
18. C2×#3802C22semidirect
20. C2×#3795C22semidirect
21. C2×C32×D8C22semidirect
22. C2×#3754C22semidirect
23. #64121C22semidirect
24. C2×#3746C22semidirect
25. C2×C8×C3⋊D3C22semidirect
26. C2×C3×#213C22semidirect
27. C3×D3×D8C22semidirect
28. C2×C3×D24C22semidirect
29. C2×C3×D3×C8C22semidirect
30. #63932C22semidirect
31. #63927C22semidirect
32. C2×#3716C22semidirect
33. C2×#3713C22semidirect
34. C2×#3712C22semidirect
35. C2×#3711C22semidirect
36. #63807C22semidirect
37. #63803C22semidirect
38. #63797C22semidirect
49. C2×D3×D8D3semidirect
58. #3830C23semidirect
63. C3×D3×D4C23semidirect
76. #3802C23semidirect
80. #3795C23semidirect
81. C32×D8C23semidirect
83. #3754C23semidirect
85. #3746C23semidirect
86. C8×C3⋊D3C23semidirect
87. C3×#213C23semidirect
89. C3×D24C23semidirect
90. C3×D3×C8C23semidirect
91. #3716C23semidirect
92. #3713C23semidirect
93. #3712C23semidirect
94. #3711C23semidirect
107. C2×D3×D4C2×D3semidirect
114. C2×C3×D8C2×D3semidirect
121. C2×#213C2×D3semidirect
129. D3×D8C2×D3semidirect
133. C2×D24C2×D3semidirect
140. C2×D3×C8C2×D3semidirect
218. D3×D4C22×D3semidirect
235. C3×D8C22×D3semidirect
244. #213C22×D3semidirect
251. D24C22×D3semidirect
257. D3×C8C22×D3semidirect
296. C2×D8D32semidirect
366. C2×C32#576semidirect
406. D8C2×D32semidirect
445. C32C2×#576semidirect
486. C2×C3#5757semidirect
509. C3C2×#5757semidirect
514. C2#10594731direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643132
C2×#641212
C2×C3×D3×D82
C2×#639322
C2×#639272
#105947312
C2×#638072
C2×#638032
C2×#637972
C2×#57573