Finite Group Databasebeta

← C2×#5770 #87185

Subgroups — C2×#5770 #87185

Order 384.

1460 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1010C211yesmaximal, characteristic, complemented
2C2×#1009C211yesmaximal, characteristic, complemented
3C2×C3×#135C211yesmaximal, characteristic, complemented
4C2×#951C211yesmaximal, characteristic, complemented
5C2×#949C211yesmaximal, characteristic, complemented
6#5770C2116yesmaximal, direct product factor
7C2×#918C212yesmaximal, complemented
8C2×#916C212yesmaximal, complemented
9C2×D3×SD16C212yesmaximal, complemented
10C2×#911C212yesmaximal, complemented
11C22×#204C211yesmaximal, characteristic, complemented
12C2×#901C211yesmaximal, characteristic, complemented
13C2×#577—31nomaximal, Sylow
14C2×C3×#41C2211yescharacteristic
15C2×C3×#41C2211yescharacteristic, complemented
16#1010—24no—
17#1010C2218yescomplemented
18#1009—24no—
19#1009C2218yescomplemented
20C2×#239C2212yes—
21C2×D3×Q8C2212yescomplemented
22C2×#237—22no—
23C2×#237C2212yescomplemented
24C2×D3×D4—22no—
25C2×D3×D4C2212yes—
26C2×#235—21no—
27C2×#235—21no—
28C2×#235C2211yescharacteristic
29C22×D12—21no—
30C22×D12C2211yescharacteristic
31C22×Dic6—21no—
32C22×Dic6C2211yescharacteristic, complemented
33C3×#135C2218yescomplemented
34C2×C3×Q16C2211yescharacteristic, complemented
35C2×C3×SD16C2211yescharacteristic, complemented
36C2×C3×SD16C2211yescharacteristic, complemented
37C2×C3×D8C2211yescharacteristic, complemented
38C22×C3×C8C2211yescharacteristic, complemented
39#951C2218yescomplemented
40#949C2218yescomplemented
41C2×#216C2212yescomplemented
42C2×#215C2212yescomplemented
43C2×#214C2212yescomplemented
44C2×#213C2212yescomplemented
45C2×#208C2211yescharacteristic, complemented
46#918C22116yescomplemented
47#916C22116yescomplemented
48D3×SD16C22116yescomplemented
49#911C22116yescomplemented
50C2×#204C2212yescomplemented
51C2×#204C2212yescomplemented
52C2×#204C2218yescomplemented
53#901C2218yescomplemented
54C2×ΓL(1,𝔽25)C2212yescomplemented
55C2×D3×C8C2212yescomplemented
56C2×2−1+4—31no—
57C2×H(5,𝔽2)—31no—
58#577—316no—
59C2×#137—31no—
60C2×#137—32no—
61C2×AGL(1,ℤ/8)—31no—
62C2×AGL(1,ℤ/8)—32no—
63C2×#135—32no—
64C2×#135D311yescharacteristic, complemented
65C22×SD16—32no—
66C22×SD16—31no—
67C2×#131—31no—
68C23×D3—21no—
69C23×D3—22no—
70C3×#41—22no—
71C3×#41—22no—
72C3×#41C2314yes—
73C3×#41C2314yescomplemented
74C2×C3×Q8C2311yescharacteristic
75C2×C3×Q8C2311yescharacteristic
76C2×C3×D4—21no—
77C2×C3×D4—21no—
78C2×C3×D4C2311yescharacteristic
79C2×C3×D4C2311yescharacteristic
80C22×C3×C4—21no—
81C22×C3×C4—21no—
82C22×C3×C4C2311yescharacteristic
83C2×#67—22no—
84C2×#67—22no—
85C2×#67D412yes—
86C22×Dic3—21no—
87C22×Dic3—22no—
88#239—24no—
89#239C2318yes—
90D3×Q8—24no—
91D3×Q8C2318yescomplemented
92#237—216no—
93#237—24no—
94#237C2318yescomplemented
95D3×D4—216no—
96D3×D4—24no—
97D3×D4C2318yes—
98#235—28no—
99#235—28no—
100#235D414yes—
101#235C2314yes—
102C2×D12—22no—
103C2×D12—21no—
104C2×D12—22no—
105C2×D12—28no—
106C2×D12D411yescharacteristic
107C2×D12C2312yes—
108C2×D12C2314yes—
109C2×C4×D3—22no—
110C2×C4×D3—22no—
111C2×C4×D3C2312yes—
112C2×Dic6—21no—
113C2×Dic6—22no—
114C2×Dic6—22no—
115C2×Dic6—28no—
116C2×Dic6D411yescharacteristic
117C2×Dic6C2312yes—
118C2×Dic6C2314yescomplemented
119C3×Q16C2314yescomplemented
120C3×SD16C2314yescomplemented
121C3×SD16C2314yescomplemented
122C3×D8C2314yescomplemented
123C2×C3×C8C2311yescharacteristic
124C2×C3×C8C2311yescharacteristic
125C2×C3×C8C2314yescomplemented
126#216C2318yescomplemented
127#215C2318yescomplemented
128#214C2318yescomplemented
129#213C2318yescomplemented
130#208C2314yescomplemented
131C2×C3⋊C8C2312yes—
132#204C2318yescomplemented
133#204C2318yescomplemented
134ΓL(1,𝔽25)C2318yescomplemented
135D3×C8C2318yescomplemented
1362−1+4—38no—
1372−1+4—64no—
138H(5,𝔽2)—38no—
139H(5,𝔽2)—64no—
140C2×#41—31no—
141C2×#41—32no—
142C2×#41—32no—
143C2×#41—61no—
144C2×#41—61no—
145C2×#41—62no—
146C2×#41C2×D311yescharacteristic
147C2×#41C2×D311yescharacteristic, complemented
148C22×Q8—32no—
149C22×Q8—31no—
150C22×Q8—61no—
151C22×D4—32no—
152C22×D4—31no—
153C22×D4—61no—
154C22×D4—62no—
155#137—38no—
156#137—316no—
157AGL(1,ℤ/8)—38no—
158AGL(1,ℤ/8)—316no—
159#135—316no—
160#135C2×D318yescomplemented
161C2×Q16—32no—
162C2×Q16C2×D311yescharacteristic, complemented
163C2×SD16—32no—
164C2×SD16—32no—
165C2×SD16—316no—
166C2×SD16—32no—
167C2×SD16—32no—
168C2×SD16—38no—
169C2×SD16C2×D311yescharacteristic, complemented
170C2×SD16C2×D311yescharacteristic, complemented
171C2×D8—32no—
172C2×D8C2×D311yescharacteristic, complemented
173#131—38no—
174C2×M16—31no—
175C2×M16—32no—
176C22×C8—32no—
177C22×C8C2×D311yescharacteristic, complemented
178C23×C3—21no—
179C23×C3—21no—
180C23×C3C2×D411yescharacteristic
181C22×D3—22no—
182C22×D3—24no—
183C22×D3—28no—
184C22×D3—84no—
185C22×D3—82no—
186C22×D3C2×D412yes—
187C3×Q8—21no—
188C3×Q8—21no—
189C3×Q8C2412yes—
190C3×Q8C2412yes—
191C3×D4—24no—
192C3×D4—24no—
193C3×D4—21no—
194C3×D4—21no—
195C3×D4C2412yes—
196C3×D4C2412yes—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—24no—
200C2×C3×C4—24no—
201C2×C3×C4C2×D411yescharacteristic
202C2×C3×C4C2×D412yes—
203C2×C3×C4C2411yescharacteristic
204C2×C3×C4C2412yes—
205#67—28no—
206#67—28no—
207#67C2×D418yes—
208C2×Dic3—22no—
209C2×Dic3—24no—
210C2×Dic3—28no—
211C2×Dic3C2×D412yes—
212D12—28no—
213D12—24no—
214D12—22no—
215D12C2×D414yes—
216D12C2414yes—
217C4×D3—28no—
218C4×D3—28no—
219C4×D3C2×D414yes—
220C4×D3C2414yes—
221Dic6—24no—
222Dic6—22no—
223Dic6—28no—
224Dic6C2×D414yes—
225Dic6C2414yes—
226C3×C8C2412yes—
227C3×C8C2412yes—
228C3⋊C8C2414yes—
229C24—62no—
230C24—61no—
231#41—22no—
232#41—22no—
233#41—34no—
234#41—34no—
235#41—38no—
236#41—38no—
237#41—68no—
238#41—68no—
239#41—64no—
240#41—64no—
241#41—616no—
242#41C22×D314yes—
243#41C22×D314yescomplemented
244C2×Q8—31no—
245C2×Q8—38no—
246C2×Q8—32no—
247C2×Q8—34no—
248C2×Q8—62no—
249C2×Q8—68no—
250C2×Q8—64no—
251C2×Q8—61no—
252C2×Q8—62no—
253C2×Q8C22×D311yescharacteristic
254C2×Q8C22×D311yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—32no—
258C2×D4—38no—
259C2×D4—31no—
260C2×D4—32no—
261C2×D4—34no—
262C2×D4—68no—
263C2×D4—62no—
264C2×D4—64no—
265C2×D4—62no—
266C2×D4—616no—
267C2×D4—62no—
268C2×D4—61no—
269C2×D4—62no—
270C2×D4C22×D311yescharacteristic
271C2×D4C22×D311yescharacteristic
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—32no—
275C22×C4—62no—
276C22×C4—62no—
277C22×C4—62no—
278C22×C4—61no—
279C22×C4C22×D311yescharacteristic
280Q16—38no—
281Q16C22×D314yescomplemented
282SD16—38no—
283SD16—38no—
284SD16—38no—
285SD16—38no—
286SD16C22×D314yescomplemented
287SD16C22×D314yescomplemented
288D8—38no—
289D8C22×D314yescomplemented
290M16—34no—
291M16—38no—
292C2×C8—32no—
293C2×C8—38no—
294C2×C8C22×D311yescharacteristic
295C2×C8C22×D311yescharacteristic
296C2×C8C22×D314yescomplemented
297C22×C3—22no—
298C22×C3—22no—
299C22×C3—22no—
300C22×C3—42no—
301C22×C3—42no—
302C22×C3C22×D412yes—
303C22×C3C22×D411yescharacteristic
304C2×D3—24no—
305C2×D3—24no—
306C2×D3—44no—
307C2×D3—88no—
308C2×D3—84no—
309C2×D3C22×D414yes—
310C3×C4—22no—
311C3×C4—22no—
312C3×C4C22×D412yes—
313C3×C4C22×D411yescharacteristic
314C3×C4C2511yescharacteristic
315Dic3—24no—
316Dic3C22×D414yes—
317C23—21no—
318C23—21no—
319C23—32no—
320C23—68no—
321C23—62no—
322C23—64no—
323C23—242no—
324C23—244no—
325C23D3×D411yescharacteristic
326Q8—21no—
327Q8—21no—
328Q8—34no—
329Q8—34no—
330Q8—68no—
331Q8—64no—
332Q8—62no—
333Q8C23×D312yes—
334Q8C23×D312yes—
335D4—24no—
336D4—24no—
337D4—21no—
338D4—21no—
339D4—38no—
340D4—34no—
341D4—34no—
342D4—68no—
343D4—68no—
344D4—68no—
345D4—64no—
346D4—62no—
347D4C23×D312yes—
348D4C23×D312yes—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—24no—
352C2×C4—24no—
353C2×C4—32no—
354C2×C4—34no—
355C2×C4—34no—
356C2×C4—68no—
357C2×C4—68no—
358C2×C4—68no—
359C2×C4—64no—
360C2×C4—62no—
361C2×C4D3×D412yes—
362C2×C4D3×D411yescharacteristic
363C2×C4C23×D312yes—
364C2×C4C23×D311yescharacteristic
365C8—34no—
366C8C23×D312yes—
367C8C23×D312yes—
368C2×C3—22no—
369C2×C3—42no—
370C2×C3—42no—
371C2×C3#57712yescomplemented
372C2×C3C23×D411yescharacteristic
373D3—24no—
374D3—44no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—34no—
379C22—42no—
380C22—42no—
381C22—64no—
382C22—64no—
383C22—124no—
384C22—244no—
385C22—248no—
386C22C2×D3×D412yes—
387C22C2×D3×D411yescharacteristic
388C4—22no—
389C4—22no—
390C4—34no—
391C4—64no—
392C4C2×D3×D412yes—
393C4C2×D3×D411yescharacteristic
394C4C24×D311yescharacteristic
395C3C2×#57711yescharacteristic, complemented, Sylow
396C2—22no—
397C2—42no—
398C2—42no—
399C2—64no—
400C2—124no—
401C2#577012yesdirect product factor
402C2C22×D3×D411yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC3×C4C25
FrattiniC4C24×D3
FittingC2×C3×#135C2
socleC22×C3C22×D4
hypercenterC2×#135D3
hypocenterC3C2×#577
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#1010C2semidirect
2. C2×#1009C2semidirect
3. C2×C3×#135C2semidirect
4. C2×#951C2semidirect
5. C2×#949C2semidirect
6. #5770C2direct (N × H)
7. C2×#918C2semidirect
8. C2×#916C2semidirect
9. C2×D3×SD16C2semidirect
10. C2×#911C2semidirect
11. C22×#204C2semidirect
12. C2×#901C2semidirect
15. C2×C3×#41C22semidirect
17. #1010C22semidirect
19. #1009C22semidirect
21. C2×D3×Q8C22semidirect
23. C2×#237C22semidirect
32. C22×Dic6C22semidirect
33. C3×#135C22semidirect
34. C2×C3×Q16C22semidirect
35. C2×C3×SD16C22semidirect
36. C2×C3×SD16C22semidirect
37. C2×C3×D8C22semidirect
38. C22×C3×C8C22semidirect
39. #951C22semidirect
40. #949C22semidirect
41. C2×#216C22semidirect
42. C2×#215C22semidirect
43. C2×#214C22semidirect
44. C2×#213C22semidirect
45. C2×#208C22semidirect
46. #918C22semidirect
47. #916C22semidirect
48. D3×SD16C22semidirect
49. #911C22semidirect
50. C2×#204C22semidirect
51. C2×#204C22semidirect
52. C2×#204C22semidirect
53. #901C22semidirect
54. C2×ΓL(1,𝔽25)C22semidirect
55. C2×D3×C8C22semidirect
64. C2×#135D3semidirect
73. C3×#41C23semidirect
91. D3×Q8C23semidirect
94. #237C23semidirect
118. C2×Dic6C23semidirect
119. C3×Q16C23semidirect
120. C3×SD16C23semidirect
121. C3×SD16C23semidirect
122. C3×D8C23semidirect
125. C2×C3×C8C23semidirect
126. #216C23semidirect
127. #215C23semidirect
128. #214C23semidirect
129. #213C23semidirect
130. #208C23semidirect
132. #204C23semidirect
133. #204C23semidirect
134. ΓL(1,𝔽25)C23semidirect
135. D3×C8C23semidirect
147. C2×#41C2×D3semidirect
160. #135C2×D3semidirect
162. C2×Q16C2×D3semidirect
169. C2×SD16C2×D3semidirect
170. C2×SD16C2×D3semidirect
172. C2×D8C2×D3semidirect
177. C22×C8C2×D3semidirect
243. #41C22×D3semidirect
281. Q16C22×D3semidirect
286. SD16C22×D3semidirect
287. SD16C22×D3semidirect
289. D8C22×D3semidirect
296. C2×C8C22×D3semidirect
371. C2×C3#577semidirect
395. C3C2×#577semidirect
401. C2#5770direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#10102
C2×#10092
C2×C3×#1352
C2×#9512
C2×#9492
#57702
C2×#9182
C2×#9162
C2×D3×SD162
C2×#9112
C22×#2042
C2×#9012
C2×#5773