Finite Group Databasebeta

← #49132870

Subgroups — #49132870

Order 36224.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583637C212yesmaximal, complemented
2#31827108C212yesmaximal, complemented
3#31826708C212yesmaximal, complemented
4#31826677C212yesmaximal, complemented
5#31826626C212yesmaximal, complemented
6#31826597C212yesmaximal, complemented
7C4×D2264C211yesmaximal, characteristic, complemented
8#31826544C211yesmaximal, characteristic, complemented
9#495×C283C211yesmaximal, characteristic, complemented
10C2×#17985393C2212yes—
11C2×D4×D283C2212yescomplemented
12#22583637—28no—
13C2×#17985379C2212yescomplemented
14C2×D2264C2211yescharacteristic
15C2×#17985377C2212yes—
16C2×#17985375C2212yescomplemented
17#22583592—22no—
18#22583586C2212yescomplemented
19#22583583—22no—
20#22583581C2212yes—
21#22583580—22no—
22C4×D1132C2211yescharacteristic
23C4×D1132C2212yescomplemented
24C22⋊C4×D283—22no—
25#22583544C2211yescharacteristic, complemented
26C4⋊(C283⋊C8)C2211yescharacteristic, complemented
27#22583534C2212yescomplemented
28#22583532C2212yescomplemented
29#22583531C2212yescomplemented
30(C2×D283)⋊C8C2212yescomplemented
31C2×Q16×C283C2211yescharacteristic, complemented
32C2×SD16×C283C2212yescomplemented
33C2×D8×C283C2211yescharacteristic
34#124×C283C2212yescomplemented
35C4×C8×C283C2211yescharacteristic, complemented
36C23×D283—22no—
37#17985393—24no—
38#17985393—42no—
39C2×D1132—22no—
40C2×D1132D411yescharacteristic
41C2×D1132C2312yes—
42C2×C22⋊D283—22no—
43C2×C22⋊D283—22no—
44D4×D283—24no—
45D4×D283—42no—
46C2×C4×D283—22no—
47C2×C4×D283—22no—
48C2×C4×D283C2312yes—
49#17985379—24no—
50D2264D414yescomplemented
51#17985377—24no—
52#17985375—24no—
53C2×C283⋊C8C2312yes—
54C4⋊Dic283D411yescharacteristic
55C4⋊Dic283C2312yes—
56Dic283⋊C4—22no—
57C22⋊Dic283—22no—
58(C2×D283)⋊C4—22no—
59(C2×D283)⋊C4—22no—
60(C2×D283)⋊C4D412yes—
61C2×Q8×C283C2312yes—
62C2×D4×C283C2312yes—
63Q16×C283—41no—
64SD16×C283—24no—
65D8×C283—41no—
66C2×C8×C283C2311yescharacteristic
67C2×C8×C283C2311yescharacteristic
68C22⋊C4×C283—22no—
69C22⋊C4×C283—22no—
70C42×C283C2311yescharacteristic
71C22×D283—22no—
72C22×D283—44no—
73C22×D283—44no—
74C22×D283—82no—
75C22×D283C2×D412yes—
76D1132—22no—
77D1132—41no—
78D1132—44no—
79D1132C2×D414yes—
80C22⋊D283—44no—
81C22⋊D283—82no—
82C2×Dic283—22no—
83C2×Dic283C2×D412yes—
84C4×D283—22no—
85C4×D283—22no—
86C4×D283—44no—
87C4×D283—82no—
88C283⋊C8—22no—
89C23×C283—22no—
90Q8×C283—22no—
91Q8×C283—22no—
92D4×C283—22no—
93D4×C283—22no—
94C2×C4×C283—22no—
95C2×C4×C283C2×D411yescharacteristic
96C2×C4×C283C2×D411yescharacteristic
97C2×C4×C283C2411yescharacteristic
98C8×C283—21no—
99C8×C283C2×D412yes—
100C22×C283—42no—
101C22×C283—42no—
102C22×C283—42no—
103C22×C283C22×D411yescharacteristic
104C2×D283—22no—
105C2×D283—24no—
106C2×D283—22no—
107C2×D283—22no—
108C2×D283—42no—
109C2×D283—42no—
110C2×D283—88no—
111C4×C283—21no—
112C4×C283—21no—
113C4×C283—42no—
114C4×C283C22×D411yescharacteristic
115C4×C283H(5,𝔽2)11yescharacteristic
116Dic283—22no—
117Dic283—42no—
118C2×C283—82no—
119C2×C283D4211yescharacteristic
120C2×C283#57511yescharacteristic
121C2×C283#57611yescharacteristic
122D283—42no—
123D283—44no—
124C283#327311yescharacteristic, complemented, Sylow
125#3273—2831nomaximal, Sylow
126C2×AGL(1,ℤ/8)—2832no—
127#546—2832no—
128#495D28311yescharacteristic, complemented
129#468—2832no—
130#463—2832no—
131#452—2832no—
132#447—2832no—
133C4×D8—2831no—
134#436—2831no—
135C2×#41—2832no—
136C22×D4—2832no—
137AGL(1,ℤ/8)—5668no—
138C2×Q16C2×D28311yescharacteristic, complemented
139C2×SD16—2832no—
140C2×SD16C2×D28312yescomplemented
141C2×D8—2832no—
142C2×D8—2831no—
143C2×D8C2×D28311yescharacteristic
144C2×M16—2832no—
145#124C2×D28312yescomplemented
146#123—5662no—
147C22⋊Q8—2832no—
148#121—2832no—
149#121—5662no—
150#120—5662no—
151C4×D4—2831no—
152C4×D4—2832no—
153C2×C22⋊C4—5662no—
154#107—2831no—
155C4⋊C8—2831no—
156#103—2832no—
157#102—2832no—
158#102—2832no—
159C22⋊C8—2832no—
160C4×C8C2×D28311yescharacteristic, complemented
161C24—5662no—
162#41—5664no—
163#41—11322no—
164C2×Q8C22×D28312yes—
165C2×D4—2831no—
166C2×D4—2832no—
167C2×D4—5662no—
168C2×D4—5662no—
169C2×D4—5664no—
170C2×D4—5662no—
171C2×D4—11322no—
172C2×D4C22×D28312yes—
173C22×C4—2832no—
174C22×C4—5662no—
175C22×C4—5662no—
176Q16—41no—
177SD16—24no—
178SD16—5664no—
179D8—41no—
180D8—2834no—
181D8—5664no—
182M16—5664no—
183C2×C8—2832no—
184C2×C8C22×D28311yescharacteristic
185C2×C8C22×D28311yescharacteristic
186C4⋊C4—2831no—
187C4⋊C4—2832no—
188C4⋊C4—5662no—
189C22⋊C4—22no—
190C22⋊C4—22no—
191C22⋊C4—2832no—
192C22⋊C4—5662no—
193C22⋊C4—5662no—
194C22⋊C4—5662no—
195C42C22×D28311yescharacteristic
196C23—22no—
197C23—2832no—
198C23—5662no—
199C23—11324no—
200C23—11324no—
201C23—22642no—
202Q8—22no—
203Q8—22no—
204D4—22no—
205D4—22no—
206D4—2834no—
207D4—5662no—
208D4—11321no—
209D4—11324no—
210D4—11324no—
211D4—22642no—
212C2×C4—22no—
213C2×C4—2832no—
214C2×C4—5662no—
215C2×C4—5662no—
216C2×C4—5662no—
217C2×C4—11324no—
218C2×C4—22642no—
219C2×C4D4×D28311yescharacteristic
220C2×C4D4×D28311yescharacteristic
221C2×C4C23×D28311yescharacteristic
222C8—21no—
223C8—5662no—
224C8D4×D28312yes—
225C22—42no—
226C22—42no—
227C22—42no—
228C22—5662no—
229C22—5662no—
230C22—5662no—
231C22—5664no—
232C22—11322no—
233C22—11322no—
234C22—22648no—
235C22C2×D4×D28311yescharacteristic
236C4—21no—
237C4—21no—
238C4—42no—
239C4—5662no—
240C4—11322no—
241C4C2×D4×D28311yescharacteristic
242C4#2258365511yescharacteristic
243C2—82no—
244C2—11322no—
245C2—11324no—
246C2#3182710011yescharacteristic
247C2#3182726211yescharacteristic
248C2#3182726711yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#495×C283C2
socleC22×C283C22×D4
hypercenter#495D283
hypocenterC283#3273
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#22583637C2semidirect
2. #31827108C2semidirect
3. #31826708C2semidirect
4. #31826677C2semidirect
5. #31826626C2semidirect
6. #31826597C2semidirect
7. C4×D2264C2semidirect
8. #31826544C2semidirect
9. #495×C283C2semidirect
11. C2×D4×D283C22semidirect
13. C2×#17985379C22semidirect
16. C2×#17985375C22semidirect
18. #22583586C22semidirect
23. C4×D1132C22semidirect
25. #22583544C22semidirect
26. C4⋊(C283⋊C8)C22semidirect
27. #22583534C22semidirect
28. #22583532C22semidirect
29. #22583531C22semidirect
30. (C2×D283)⋊C8C22semidirect
31. C2×Q16×C283C22semidirect
32. C2×SD16×C283C22semidirect
34. #124×C283C22semidirect
35. C4×C8×C283C22semidirect
50. D2264D4semidirect
124. C283#3273semidirect
128. #495D283semidirect
138. C2×Q16C2×D283semidirect
140. C2×SD16C2×D283semidirect
145. #124C2×D283semidirect
160. C4×C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836372
#318271082
#318267082
#318266772
#318266262
#318265972
C4×D22642
#318265442
#495×C2832
#3273283