Finite Group Databasebeta

← C4×#64361 #11900161

Subgroups — C4×#64361 #11900161

Order 1152.

4980 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64361C211yesmaximal, characteristic
2C2×C32×C4×D4C211yesmaximal, characteristic, complemented
3#10596269C211yesmaximal, characteristic, complemented
4C2×C4×#638C214yesmaximal, complemented
5#10596017C214yesmaximal, complemented
6#10596016C214yesmaximal, complemented
7C4×D4×C3⋊D3C214yesmaximal, complemented
8C4×#3830C214yesmaximal, complemented
9#10595975C212yesmaximal, complemented
10#10595957C214yesmaximal, complemented
11C4×#3828C212yesmaximal, complemented
12C4×#1004—34nomaximal
13C22×C32×D4C2211yescharacteristic
14C23×C32×C4C2212yescomplemented
15C22×#638C2214yes—
16#64361C4116yesdirect product factor
17C2×#3830C2214yes—
18C2×D4×C3⋊D3C2214yes—
19C2×#3828C2212yes—
20C22×C4×C3⋊D3C2214yescomplemented
21C32×C4×D4C2214yescomplemented
22C32×C4×D4C2214yescomplemented
23C2×C32×C4⋊C4C2211yescharacteristic, complemented
24C2×C32×C22⋊C4C2212yescomplemented
25C2×C32×C42C2211yescharacteristic, complemented
26C2×#3757C2214yescomplemented
27D4×C3⋊Dic3C2214yescomplemented
28D4×C3⋊Dic3C2214yescomplemented
29C4×#638C2214yescomplemented
30C4×#638C2214yescomplemented
31C4×#638C2218yescomplemented
32C4×#638C2218yescomplemented
33C4×#638C2218yescomplemented
34C2×#3752C2214yescomplemented
35#64135C2212yescomplemented
36C2×#3750C2214yescomplemented
37C2×C4×C3⋊Dic3C2214yescomplemented
38#64102C2214yescomplemented
39#64101C2214yescomplemented
40C4⋊C4×C3⋊D3C2214yescomplemented
41#64096C2214yescomplemented
42#64090C2218yescomplemented
43#64090C2218yescomplemented
44C22⋊C4×C3⋊D3C2218yescomplemented
45#64086C2218yescomplemented
46C4×C4⋊(C3⋊D3)C2212yescomplemented
47C4×C4⋊(C3⋊D3)C2212yescomplemented
48#64081C2214yescomplemented
49C42×C3⋊D3C2214yescomplemented
50C4×#634C2212yescomplemented
51C4×#634C2212yescomplemented
52C2×#1004—34no—
53C2×C3×C4×D4D314yescomplemented
54#5798—34no—
55C2×C4×#67—316no—
56#5546—316no—
57#5545—316no—
58C4×D3×D4—316no—
59C4×#237—316no—
60#5504—38no—
61#5486—316no—
62C4×#235—38no—
63C24×C32C2312yes—
64C23×C3⋊D3C2314yes—
65C2×C32×D4C2×C418yescomplemented
66C2×C32×D4C2314yes—
67C22×C32×C4—44no—
68C22×C32×C4C2314yes—
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2314yes—
71C22×C32×C4C2312yes—
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C2×#638C2×C4132yescomplemented
75C2×#638C2318yes—
76C2×#638C2314yes—
77C22×C3⋊Dic3C2314yes—
78C22×C3⋊Dic3C2314yes—
79C22×C3⋊Dic3C2314yes—
80#3830C2×C4132yescomplemented
81D4×C3⋊D3C2×C4132yescomplemented
82#3828C2×C4116yescomplemented
83C2×C4⋊(C3⋊D3)C2312yes—
84C2×C4×C3⋊D3—48no—
85C2×C4×C3⋊D3C2314yes—
86C2×C4×C3⋊D3C2314yes—
87C2×C4×C3⋊D3C2318yes—
88C2×C4×C3⋊D3C2314yes—
89C2×#634C2312yes—
90C32×C4⋊C4C2314yes—
91C32×C22⋊C4C2318yes—
92C32×C42C2312yes—
93C32×C42C2312yes—
94#3757C2318yes—
95#3757C2314yes—
96#3752C2314yes—
97#3752C2314yes—
98#3752C2318yes—
99C4⋊(C3⋊Dic3)C2312yes—
100C4⋊(C3⋊Dic3)C2312yes—
101#3750C2314yes—
102#3750C2314yes—
103#3750C2318yes—
104C4×C3⋊Dic3C2314yes—
105C4×C3⋊Dic3C2314yes—
106C4×C3⋊Dic3C2314yes—
107C4×C3⋊Dic3C2318yes—
108C4×H(5,𝔽2)—91noSylow
109C22×C3×D4C2×D314yes—
110C23×C3×C4C2×D318yescomplemented
111C22×#67—316no—
112#1004—364no—
113C2×#237—316no—
114C2×D3×D4—316no—
115C2×#235—38no—
116C22×C4×D3—316no—
117C3×C4×D4C2×D3116yescomplemented
118C3×C4×D4C2×D3116yescomplemented
119C2×C3×C4⋊C4C2×D314yescomplemented
120C2×C3×C22⋊C4C2×D318yescomplemented
121C2×C3×C42C2×D314yescomplemented
122C2×#217—316no—
123D4×Dic3—316no—
124D4×Dic3—316no—
125C4×#67—316no—
126C4×#67—316no—
127C4×#67—332no—
128C4×#67—332no—
129C4×#67—332no—
130C2×(C2×D3)⋊C4—316no—
131#926—38no—
132C2×Dic3⋊C4—316no—
133C2×C4×Dic3—316no—
134#893—316no—
135#892—316no—
136D3×C4⋊C4—316no—
137#887—316no—
138#67⋊C4—332no—
139#67⋊C4—332no—
140D3×C22⋊C4—332no—
141#877—332no—
142C4×D12—38no—
143C4×D12—38no—
144#872—316no—
145C42×D3—316no—
146C4×Dic6—38no—
147C4×Dic6—38no—
148C23×C32—42no—
149C23×C32—42no—
150C23×C32C22×C418yescomplemented
151C23×C32C2414yes—
152C23×C32C2411yescharacteristic
153C22×C3⋊D3—44no—
154C22×C3⋊D3—44no—
155C22×C3⋊D3C22×C4116yescomplemented
156C22×C3⋊D3C2414yes—
157C32×D4C22×C4116yescomplemented
158C2×C32×C4—28no—
159C2×C32×C4—22no—
160C2×C32×C4—42no—
161C2×C32×C4—44no—
162C2×C32×C4—41no—
163C2×C32×C4C22×C414yescomplemented
164C2×C32×C4C2412yes—
165C2×C32×C4C2414yes—
166C2×C32×C4C2411yescharacteristic
167C2×C32×C4C2412yes—
168C2×C32×C4C2411yescharacteristic
169#638C22×C4116yescomplemented
170#638C22×C4132yescomplemented
171C2×C3⋊Dic3—44no—
172C2×C3⋊Dic3—44no—
173C2×C3⋊Dic3C22×C4116yescomplemented
174C2×C3⋊Dic3C2414yes—
175C2×C3⋊Dic3C2414yes—
176C2×C3⋊Dic3C2414yes—
177C4⋊(C3⋊D3)C22×C418yescomplemented
178C4×C3⋊D3—28no—
179C4×C3⋊D3—48no—
180C4×C3⋊D3—44no—
181C4×C3⋊D3C22×C4116yescomplemented
182#634C22×C418yescomplemented
183C2×H(5,𝔽2)—91no—
184#520—94no—
185#520—92no—
186#518—91no—
187#518—94no—
188#518—94no—
189C4×#41—94no—
190C4×#41—92no—
191C2×C4×D4—94no—
192C2×C4×D4—94no—
193C2×C4×D4C3⋊D311yescharacteristic, complemented
194C24×C3C22×D318yes—
195C23×D3—316no—
196C2×C3×D4C4×D3132yescomplemented
197C2×C3×D4C22×D3116yes—
198C22×C3×C4—416no—
199C22×C3×C4C22×D3116yes—
200C22×C3×C4C22×D314yes—
201C22×C3×C4C22×D3116yes—
202C22×C3×C4C22×D314yes—
203C22×C3×C4C22×D318yes—
204C22×C3×C4C22×D314yes—
205C2×#67—3128no—
206C2×#67—332no—
207C2×#67—316no—
208C22×Dic3—316no—
209C22×Dic3—316no—
210C22×Dic3—316no—
211#237—3128no—
212D3×D4—3128no—
213#235—364no—
214C2×D12—38no—
215C2×C4×D3—316no—
216C2×C4×D3—316no—
217C2×C4×D3—316no—
218C2×C4×D3—332no—
219C2×C4×D3—1232no—
220C2×Dic6—38no—
221C3×C4⋊C4C22×D3116yes—
222C3×C22⋊C4C22×D3132yes—
223C3×C42C22×D318yes—
224C3×C42C22×D318yes—
225#217—332no—
226#217—316no—
227(C2×D3)⋊C4—316no—
228(C2×D3)⋊C4—316no—
229(C2×D3)⋊C4—332no—
230C4⋊Dic3—38no—
231C4⋊Dic3—38no—
232Dic3⋊C4—316no—
233Dic3⋊C4—316no—
234Dic3⋊C4—332no—
235C4×Dic3—316no—
236C4×Dic3—316no—
237C4×Dic3—316no—
238C4×Dic3—332no—
239C22×C32—24no—
240C22×C32—21no—
241C22×C32—24no—
242C22×C32—21no—
243C22×C32—48no—
244C22×C32C23×C418yes—
245C22×C32C23×C412yes—
246C22×C32C2511yescharacteristic
247C2×C3⋊D3—24no—
248C2×C3⋊D3—24no—
249C2×C3⋊D3—416no—
250C2×C3⋊D3C23×C418yes—
251C32×C4—24no—
252C32×C4—21no—
253C32×C4—22no—
254C32×C4C23×C414yes—
255C32×C4H(5,𝔽2)12yescomplemented
256C3⋊Dic3—24no—
257C3⋊Dic3—24no—
258C3⋊Dic3C23×C418yes—
259H(5,𝔽2)—916no—
260C2×#41—94no—
261C2×#41—92no—
262C22×D4—94no—
263C22×D4—94no—
264C22×D4C2×C3⋊D311yescharacteristic
265C23×C4—94no—
266C23×C4C2×C3⋊D312yescomplemented
267C4×Q8—94no—
268C4×Q8—92no—
269C4×Q8—92no—
270C4×D4—94no—
271C4×D4—94no—
272C4×D4—98no—
273C4×D4—94no—
274C4×D4—98no—
275C4×D4—98no—
276C4×D4—94no—
277C4×D4—94no—
278C4×D4—98no—
279C4×D4—98no—
280C4×D4—92no—
281C4×D4—92no—
282C4×D4C2×C3⋊D314yescomplemented
283C4×D4C2×C3⋊D314yescomplemented
284#117—92no—
285#117—94no—
286#117—98no—
287#117—94no—
288C2×C4⋊C4—94no—
289C2×C4⋊C4—94no—
290C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
291C2×C22⋊C4—94no—
292C2×C22⋊C4—94no—
293C2×C22⋊C4—98no—
294C2×C22⋊C4C2×C3⋊D312yescomplemented
295C2×C42—94no—
296C2×C42—94no—
297C2×C42C2×C3⋊D311yescharacteristic, complemented
298C23×C3—48no—
299C23×C3—48no—
300C23×C3C2×C4×D3132yescomplemented
301C23×C3C23×D314yes—
302C23×C3C23×D3116yes—
303C22×D3—316no—
304C22×D3—364no—
305C22×D3—1216no—
306C22×D3—1216no—
307C3×D4C2×C4×D3164yescomplemented
308C2×C3×C4—232no—
309C2×C3×C4—28no—
310C2×C3×C4—48no—
311C2×C3×C4—416no—
312C2×C3×C4—44no—
313C2×C3×C4C2×C4×D3116yescomplemented
314C2×C3×C4C23×D318yes—
315C2×C3×C4C23×D3116yes—
316C2×C3×C4C23×D314yes—
317C2×C3×C4C23×D318yes—
318C2×C3×C4C23×D314yes—
319#67—364no—
320#67—3128no—
321C2×Dic3—364no—
322C2×Dic3—316no—
323C2×Dic3—316no—
324C2×Dic3—316no—
325C2×Dic3—1216no—
326C2×Dic3—1216no—
327D12—332no—
328C4×D3—364no—
329C4×D3—632no—
330C4×D3—1216no—
331C4×D3—1232no—
332Dic6—332no—
333C2×C32—28no—
334C2×C32—22no—
335C2×C32C24×C411yescharacteristic
336C2×C32C2×H(5,𝔽2)11yescharacteristic
337C2×C32#58511yescharacteristic
338C3⋊D3—28no—
339C24—94no—
340C24C22×C3⋊D312yes—
341#41—932no—
342#41—916no—
343C2×Q8—92no—
344C2×D4—94no—
345C2×D4—98no—
346C2×D4—932no—
347C2×D4—932no—
348C2×D4—92no—
349C2×D4C4×C3⋊D318yescomplemented
350C2×D4C22×C3⋊D314yes—
351C22×C4—44no—
352C22×C4—94no—
353C22×C4—94no—
354C22×C4—94no—
355C22×C4—94no—
356C22×C4—94no—
357C22×C4—94no—
358C22×C4—98no—
359C22×C4—368no—
360C22×C4C22×C3⋊D314yes—
361C22×C4C22×C3⋊D311yescharacteristic
362C22×C4C22×C3⋊D311yescharacteristic
363C22×C4C22×C3⋊D314yes—
364C22×C4C22×C3⋊D312yes—
365C22×C4C22×C3⋊D311yescharacteristic
366C4⋊C4—98no—
367C4⋊C4—94no—
368C4⋊C4—92no—
369C4⋊C4—94no—
370C4⋊C4—92no—
371C4⋊C4C22×C3⋊D314yes—
372C22⋊C4—94no—
373C22⋊C4—98no—
374C22⋊C4—98no—
375C22⋊C4—94no—
376C22⋊C4—94no—
377C22⋊C4C22×C3⋊D318yes—
378C42—98no—
379C42—94no—
380C42—94no—
381C42—94no—
382C42C22×C3⋊D312yes—
383C42C22×C3⋊D312yes—
384C22×C3—216no—
385C22×C3—24no—
386C22×C3—216no—
387C22×C3—24no—
388C22×C3—432no—
389C22×C3C22×C4×D3132yes—
390C22×C3C22×C4×D318yes—
391C22×C3C24×D314yes—
392C2×D3—332no—
393C2×D3—616no—
394C2×D3—616no—
395C2×D3—1264no—
396C3×C4—216no—
397C3×C4—24no—
398C3×C4—28no—
399C3×C4C22×C4×D3116yes—
400C3×C4#100418yescomplemented
401Dic3—332no—
402Dic3—616no—
403Dic3—616no—
404C32C4×H(5,𝔽2)11yescharacteristic, complemented, Sylow
405C23—42no—
406C23—42no—
407C23—94no—
408C23—916no—
409C23—364no—
410C23—364no—
411C23C2×C4×C3⋊D318yescomplemented
412C23C23×C3⋊D311yescharacteristic
413C23C23×C3⋊D314yes—
414Q8—98no—
415D4—932no—
416D4—916no—
417D4—98no—
418D4C2×C4×C3⋊D3116yescomplemented
419C2×C4—22no—
420C2×C4—28no—
421C2×C4—44no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—916no—
425C2×C4—94no—
426C2×C4—916no—
427C2×C4—94no—
428C2×C4—94no—
429C2×C4—188no—
430C2×C4—368no—
431C2×C4—364no—
432C2×C4—364no—
433C2×C4—364no—
434C2×C4C2×C4×C3⋊D314yescomplemented
435C2×C4C23×C3⋊D312yes—
436C2×C4C23×C3⋊D314yes—
437C2×C4C23×C3⋊D311yescharacteristic
438C2×C4C23×C3⋊D312yes—
439C2×C4C23×C3⋊D311yescharacteristic
440C2×C3—232no—
441C2×C3—28no—
442C2×C3C23×C4×D314yes—
443C2×C3C2×#100414yes—
444C2×C3#596414yes—
445D3—632no—
446C22—21no—
447C22—24no—
448C22—21no—
449C22—24no—
450C22—48no—
451C22—98no—
452C22—184no—
453C22—184no—
454C22—3616no—
455C22C22×C4×C3⋊D318yes—
456C22C22×C4×C3⋊D312yes—
457C22C24×C3⋊D311yescharacteristic
458C4—21no—
459C4—24no—
460C4—22no—
461C4—98no—
462C4—184no—
463C4—184no—
464C4C22×C4×C3⋊D314yes—
465C4#6436112yesdirect product factor
466C3C4×#100414yescomplemented
467C2—22no—
468C2—28no—
469C2—188no—
470C2C23×C4×C3⋊D311yescharacteristic
471C2C2×#6436111yescharacteristic
472C2#1059675611yescharacteristic
subgroupG/H
centerC2×C4C23×C3⋊D3
commutatorC2×C32C24×C4
FrattiniC22C24×C3⋊D3
FittingC2×C32×C4×D4C2
socle, cosocleC22×C32C25
prime radicalC2×#64361C2
hypercenterC2×C4×D4C3⋊D3
hypocenterC32C4×H(5,𝔽2)
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C32×C4×D4C2semidirect
3. #10596269C2semidirect
4. C2×C4×#638C2semidirect
5. #10596017C2semidirect
6. #10596016C2semidirect
7. C4×D4×C3⋊D3C2semidirect
8. C4×#3830C2semidirect
9. #10595975C2semidirect
10. #10595957C2semidirect
11. C4×#3828C2semidirect
14. C23×C32×C4C22semidirect
16. #64361C4direct (N × H)
20. C22×C4×C3⋊D3C22semidirect
21. C32×C4×D4C22semidirect
22. C32×C4×D4C22semidirect
23. C2×C32×C4⋊C4C22semidirect
24. C2×C32×C22⋊C4C22semidirect
25. C2×C32×C42C22semidirect
26. C2×#3757C22semidirect
27. D4×C3⋊Dic3C22semidirect
28. D4×C3⋊Dic3C22semidirect
29. C4×#638C22semidirect
30. C4×#638C22semidirect
31. C4×#638C22semidirect
32. C4×#638C22semidirect
33. C4×#638C22semidirect
34. C2×#3752C22semidirect
35. #64135C22semidirect
36. C2×#3750C22semidirect
37. C2×C4×C3⋊Dic3C22semidirect
38. #64102C22semidirect
39. #64101C22semidirect
40. C4⋊C4×C3⋊D3C22semidirect
41. #64096C22semidirect
42. #64090C22semidirect
43. #64090C22semidirect
44. C22⋊C4×C3⋊D3C22semidirect
45. #64086C22semidirect
46. C4×C4⋊(C3⋊D3)C22semidirect
47. C4×C4⋊(C3⋊D3)C22semidirect
48. #64081C22semidirect
49. C42×C3⋊D3C22semidirect
50. C4×#634C22semidirect
51. C4×#634C22semidirect
53. C2×C3×C4×D4D3semidirect
65. C2×C32×D4C2×C4semidirect
74. C2×#638C2×C4semidirect
80. #3830C2×C4semidirect
81. D4×C3⋊D3C2×C4semidirect
82. #3828C2×C4semidirect
110. C23×C3×C4C2×D3semidirect
117. C3×C4×D4C2×D3semidirect
118. C3×C4×D4C2×D3semidirect
119. C2×C3×C4⋊C4C2×D3semidirect
120. C2×C3×C22⋊C4C2×D3semidirect
121. C2×C3×C42C2×D3semidirect
150. C23×C32C22×C4semidirect
155. C22×C3⋊D3C22×C4semidirect
157. C32×D4C22×C4semidirect
163. C2×C32×C4C22×C4semidirect
169. #638C22×C4semidirect
170. #638C22×C4semidirect
173. C2×C3⋊Dic3C22×C4semidirect
177. C4⋊(C3⋊D3)C22×C4semidirect
181. C4×C3⋊D3C22×C4semidirect
182. #634C22×C4semidirect
193. C2×C4×D4C3⋊D3semidirect
196. C2×C3×D4C4×D3semidirect
255. C32×C4H(5,𝔽2)semidirect
266. C23×C4C2×C3⋊D3semidirect
282. C4×D4C2×C3⋊D3semidirect
283. C4×D4C2×C3⋊D3semidirect
290. C2×C4⋊C4C2×C3⋊D3semidirect
294. C2×C22⋊C4C2×C3⋊D3semidirect
297. C2×C42C2×C3⋊D3semidirect
300. C23×C3C2×C4×D3semidirect
307. C3×D4C2×C4×D3semidirect
313. C2×C3×C4C2×C4×D3semidirect
349. C2×D4C4×C3⋊D3semidirect
400. C3×C4#1004semidirect
404. C32C4×H(5,𝔽2)semidirect
411. C23C2×C4×C3⋊D3semidirect
418. D4C2×C4×C3⋊D3semidirect
434. C2×C4C2×C4×C3⋊D3semidirect
465. C4#64361direct (N × H)
466. C3C4×#1004semidirect

Maximal subgroups

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

subgroupindex
C2×#643612
C2×C32×C4×D42
#105962692
C2×C4×#6382
#105960172
#105960162
C4×D4×C3⋊D32
C4×#38302
#105959752
#105959572
C4×#38282
C4×#10043