Finite Group Databasebeta

← #49132873

Subgroups — #49132873

Order 36224.

520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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×#22583638C212yesmaximal, complemented
2#31827111C212yesmaximal, complemented
3#31826849C211yesmaximal, characteristic, complemented
4#31826711C212yesmaximal, complemented
5#31826681C212yesmaximal, complemented
6#31826629C212yesmaximal, complemented
7#31826601C212yesmaximal, complemented
8C4×D2264C211yesmaximal, characteristic, complemented
9#436×C283C211yesmaximal, characteristic, complemented
10C2×#17985392C2212yes—
11C22×D1132C2212yescomplemented
12#22583638—28no—
13C2×Dic1132C2211yescharacteristic, complemented
14C2×#17985381C2212yescomplemented
15C2×#17985381C2212yescomplemented
16C2×D2264C2212yes—
17C2×D2264C2211yescharacteristic
18C2×D2264C2211yescharacteristic
19#22583598C2212yescomplemented
20#22583595—22no—
21#22583589C2212yescomplemented
22#22583584C2212yes—
23#22583583—22no—
24#22583578—22no—
25C4×D1132C2212yescomplemented
26C22⋊C4×D283—22no—
27#22583544C2211yescharacteristic, complemented
28#22583535C2212yescomplemented
29#22583532C2212yescomplemented
30#22583532C2212yescomplemented
31C2×M16×C283C2212yescomplemented
32C4×D4×C283C2211yescharacteristic
33C4⋊C8×C283C2211yescharacteristic, complemented
34C22⋊C8×C283C2212yescomplemented
35C4×C8×C283C2211yescharacteristic, complemented
36C23×D283—22no—
37#17985392—24no—
38#17985392—42no—
39C2×Dic566C2312yes—
40C2×D1132—24no—
41C2×D1132—22no—
42C2×D1132—42no—
43C2×D1132C2312yes—
44C2×D1132C2312yes—
45C2×C22⋊D283—22no—
46C2×C22⋊D283—22no—
47C2×C4×D283—22no—
48C2×C4×D283—22no—
49Dic1132—41no—
50#17985381—24no—
51#17985381—24no—
52D2264—24no—
53D2264—41no—
54D2264D414yescomplemented
55C4⋊Dic283C2312yes—
56Dic283⋊C4—22no—
57C22⋊Dic283—22no—
58(C2×D283)⋊C4—22no—
59(C2×D283)⋊C4—22no—
60(C2×D283)⋊C4—22no—
61(C2×D283)⋊C4—22no—
62C2×D4×C283D411yescharacteristic
63C22×C4×C283C2312yes—
64M16×C283—24no—
65C2×C8×C283C2312yes—
66C2×C8×C283C2311yescharacteristic
67C2×C8×C283C2311yescharacteristic
68C4⋊C4×C283D411yescharacteristic
69C22⋊C4×C283D412yes—
70C42×C283C2311yescharacteristic
71C22×D283—22no—
72C22×D283—22no—
73C22×D283—44no—
74C22×D283—44no—
75C22×D283—82no—
76Dic566—22no—
77Dic566—22no—
78D1132—22no—
79D1132—22no—
80D1132—22no—
81D1132—44no—
82D1132C2×D414yes—
83C22⋊D283—44no—
84C22⋊D283—82no—
85C2×Dic283—22no—
86C2×Dic283—22no—
87C4×D283—44no—
88C4×D283—82no—
89C23×C283C2×D412yes—
90D4×C283—41no—
91C2×C4×C283—22no—
92C2×C4×C283—22no—
93C2×C4×C283C2×D411yescharacteristic
94C2×C4×C283C2×D411yescharacteristic
95C2×C4×C283C2×D412yes—
96C2×C4×C283C2411yescharacteristic
97C8×C283—22no—
98C8×C283—21no—
99C8×C283C2×D412yes—
100C22×C283—22no—
101C22×C283—22no—
102C22×C283—22no—
103C22×C283C22×D411yescharacteristic
104C2×D283—24no—
105C2×D283—42no—
106C2×D283—42no—
107C2×D283—42no—
108C2×D283—42no—
109C2×D283—42no—
110C2×D283—88no—
111C4×C283—22no—
112C4×C283—21no—
113C4×C283—21no—
114C4×C283C22×D411yescharacteristic
115C4×C283H(5,𝔽2)11yescharacteristic
116Dic283—42no—
117Dic283—42no—
118C2×C283—42no—
119C2×C283D4211yescharacteristic
120C2×C283#57511yescharacteristic
121C2×C283#57611yescharacteristic
122D283—44no—
123D283—82no—
124C283#327311yescharacteristic, complemented, Sylow
125#3273—2831nomaximal, Sylow
126C2×AGL(1,ℤ/8)—2832no—
127#546—2832no—
128#495—2831no—
129#468—2832no—
130#463—2832no—
131#452—2832no—
132#447—2832no—
133C4×D8—2831no—
134#436D28311yescharacteristic, complemented
135C2×#41—2832no—
136C22×D4—2832no—
137AGL(1,ℤ/8)—5668no—
138C2×Q16—2831no—
139C2×SD16—2832no—
140C2×SD16—2832no—
141C2×D8—2831no—
142C2×D8—2832no—
143C2×D8—2831no—
144C2×M16C2×D28312yescomplemented
145#124—2832no—
146#123—5662no—
147C22⋊Q8—2832no—
148#121—2832no—
149#121—5662no—
150#120—5662no—
151C4×D4—2832no—
152C4×D4C2×D28311yescharacteristic
153C2×C22⋊C4—5662no—
154#107—2831no—
155C4⋊C8C2×D28311yescharacteristic, complemented
156#103—2832no—
157#102—2832no—
158#102—2832no—
159C22⋊C8C2×D28312yescomplemented
160C4×C8C2×D28311yescharacteristic, complemented
161C24—5662no—
162#41—5664no—
163#41—11322no—
164C2×Q8—2832no—
165C2×D4—2832no—
166C2×D4—2832no—
167C2×D4—5664no—
168C2×D4—5662no—
169C2×D4—5662no—
170C2×D4—5662no—
171C2×D4—11322no—
172C2×D4D113211yescharacteristic
173C22×C4—5662no—
174C22×C4—5662no—
175C22×C4C22×D28312yes—
176Q16—11321no—
177SD16—5664no—
178SD16—5664no—
179D8—2834no—
180D8—5664no—
181D8—11321no—
182M16—24no—
183C2×C8C22×D28311yescharacteristic
184C2×C8C22×D28312yes—
185C2×C8C22×D28311yescharacteristic
186C4⋊C4—2832no—
187C4⋊C4—5662no—
188C4⋊C4D113211yescharacteristic
189C22⋊C4—5662no—
190C22⋊C4—5662no—
191C22⋊C4—5662no—
192C22⋊C4—5662no—
193C22⋊C4—5662no—
194C22⋊C4D113212yes—
195C42C22×D28311yescharacteristic
196C23—5662no—
197C23—5662no—
198C23—11324no—
199C23—11324no—
200C23—22642no—
201C23C2×D113212yes—
202Q8—5662no—
203Q8—5662no—
204D4—41no—
205D4—2834no—
206D4—5662no—
207D4—5662no—
208D4—5662no—
209D4—11324no—
210D4—11324no—
211D4—22642no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—5662no—
215C2×C4—5662no—
216C2×C4—11324no—
217C2×C4—22642no—
218C2×C4C2×D113211yescharacteristic
219C2×C4C2×D113211yescharacteristic
220C2×C4C2×D113212yes—
221C2×C4C23×D28311yescharacteristic
222C8—22no—
223C8—21no—
224C8D4×D28312yes—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—5664no—
229C22—11322no—
230C22—11322no—
231C22—11322no—
232C22—11322no—
233C22—11322no—
234C22—22648no—
235C22C22×D113211yescharacteristic
236C4—21no—
237C4—21no—
238C4—22no—
239C4—11322no—
240C4—11322no—
241C4C2×D4×D28311yescharacteristic
242C4#2258365611yescharacteristic
243C2—42no—
244C2—11324no—
245C2—22642no—
246C2D4×D113211yescharacteristic
247C2#3182726511yescharacteristic
248C2#3182727011yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#436×C283C2
socleC22×C283C22×D4
hypercenter#436D283
hypocenterC283#3273
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#22583638C2semidirect
2. #31827111C2semidirect
3. #31826849C2semidirect
4. #31826711C2semidirect
5. #31826681C2semidirect
6. #31826629C2semidirect
7. #31826601C2semidirect
8. C4×D2264C2semidirect
9. #436×C283C2semidirect
11. C22×D1132C22semidirect
13. C2×Dic1132C22semidirect
14. C2×#17985381C22semidirect
15. C2×#17985381C22semidirect
19. #22583598C22semidirect
21. #22583589C22semidirect
25. C4×D1132C22semidirect
27. #22583544C22semidirect
28. #22583535C22semidirect
29. #22583532C22semidirect
30. #22583532C22semidirect
31. C2×M16×C283C22semidirect
33. C4⋊C8×C283C22semidirect
34. C22⋊C8×C283C22semidirect
35. C4×C8×C283C22semidirect
54. D2264D4semidirect
124. C283#3273semidirect
134. #436D283semidirect
144. C2×M16C2×D283semidirect
155. C4⋊C8C2×D283semidirect
159. C22⋊C8C2×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×#225836382
#318271112
#318268492
#318267112
#318266812
#318266292
#318266012
C4×D22642
#436×C2832
#3273283