Finite Group Databasebeta

← #49130742

Subgroups — #49130742

Order 36224.

584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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
2C2×#22583607C211yesmaximal, characteristic, complemented
3C4×#17985392C211yesmaximal, characteristic, complemented
4#31826666C214yesmaximal, complemented
5#31826661C214yesmaximal, complemented
6#31826471C212yesmaximal, complemented
7#423×C283C211yesmaximal, characteristic, complemented
8C2×#17985392C2211yescharacteristic
9C22×D1132—22no—
10C22×D1132C2212yes—
11#22583638—28no—
12C2×#17985381C2214yescomplemented
13C2×D2264C2214yescomplemented
14#22583607—21no—
15#22583607—21no—
16#22583607C2214yes—
17C4×Dic566C2212yescomplemented
18C4×D1132C2212yescomplemented
19C4×C22⋊D283—22no—
20#22583569C2211yescharacteristic
21#22583567—21no—
22C42×D283—21no—
23#22583532C2218yescomplemented
24C2×M16×C283C2212yes—
25C2×C42×C283C2211yescharacteristic
26C4⋊C8×C283C2214yescomplemented
27C23×D283—22no—
28#17985392—22no—
29#17985392D414yescomplemented
30C2×Dic566C2311yescharacteristic
31C2×D1132—24no—
32C2×D1132—22no—
33C2×D1132—24no—
34C2×D1132—24no—
35C2×D1132—24no—
36C2×D1132—48no—
37C2×D1132C2314yes—
38C2×D1132C2311yescharacteristic
39C2×C22⋊D283—21no—
40C2×C4×D283—21no—
41C2×C4×D283—22no—
42#17985381—28no—
43D2264—28no—
44C4⋊Dic283C2312yes—
45Dic283⋊C4—22no—
46C22⋊Dic283—21no—
47(C2×D283)⋊C4—22no—
48C4×Dic283—21no—
49C4×Dic283—22no—
50C22×C4×C283D412yes—
51C22×C4×C283C2311yescharacteristic
52M16×C283—24no—
53C2×C8×C283C2314yes—
54C42×C283D411yescharacteristic
55C42×C283D411yescharacteristic
56C42×C283C2312yes—
57C22×D283—21no—
58C22×D283—24no—
59C22×D283—48no—
60C22×D283—44no—
61Dic566—21no—
62Dic566C2×D412yescomplemented
63D1132—24no—
64D1132—21no—
65D1132—24no—
66D1132—48no—
67D1132—44no—
68D1132—48no—
69D1132C2×D412yescomplemented
70C22⋊D283—24no—
71C2×Dic283—21no—
72C2×Dic283—22no—
73C4×D283—24no—
74C4×D283—44no—
75C23×C283C2×D411yescharacteristic
76C2×C4×C283—24no—
77C2×C4×C283C2×D412yes—
78C2×C4×C283C2×D412yes—
79C2×C4×C283C2×D411yescharacteristic
80C2×C4×C283C2×D412yes—
81C2×C4×C283#4112yes—
82C2×C4×C283C2411yescharacteristic
83C8×C283—24no—
84C22×C283—22no—
85C22×C283#12112yes—
86C22×C283C22×D411yescharacteristic
87C2×D283—22no—
88C2×D283—42no—
89C2×D283—44no—
90C2×D283—48no—
91C2×D283—88no—
92C4×C283—22no—
93C4×C283#12112yes—
94C4×C283AGL(1,ℤ/8)14yescomplemented
95C4×C283C22×D411yescharacteristic
96C4×C283C2×#4111yescharacteristic
97Dic283—22no—
98Dic283—42no—
99C2×C283—22no—
100C2×C283C2×#12111yescharacteristic
101C2×C283C2×AGL(1,ℤ/8)12yes—
102D283—42no—
103D283—84no—
104C283#303811yescharacteristic, complemented, Sylow
105#3038—2831nomaximal, Sylow
106C2×AGL(1,ℤ/8)—2832no—
107C2×#127—2831no—
108C4×#41—2831no—
109#460—2834no—
110#459—2834no—
111#423D28311yescharacteristic, complemented
112#418—2832no—
113C2×#41—2831no—
114C22×D4—2832no—
115C22×D4—5662no—
116AGL(1,ℤ/8)—5668no—
117C2×SD16—2834no—
118C2×D8—2834no—
119C2×M16C2×D28312yes—
120#127—2834no—
121#127—5661no—
122#127—5661no—
123C4×Q8—2832no—
124C4×D4—2832no—
125C4×D4—5662no—
126#117—2831no—
127#117—5661no—
128C2×C42—5661no—
129C2×C42C2×D28311yescharacteristic
130C4⋊C8C2×D28314yescomplemented
131#102—2838no—
132C24—5662no—
133#41—2834no—
134#41—5662no—
135C2×Q8—2831no—
136C2×D4—2831no—
137C2×D4—2834no—
138C2×D4—5661no—
139C2×D4—5664no—
140C2×D4—5664no—
141C2×D4—5664no—
142C2×D4—5662no—
143C2×D4—5664no—
144C2×D4—11328no—
145C22×C4—5661no—
146C22×C4—5662no—
147C22×C4D113212yes—
148C22×C4C22×D28311yescharacteristic
149SD16—5668no—
150D8—5668no—
151M16—24no—
152C2×C8C22×D28314yes—
153C4⋊C4—2832no—
154C4⋊C4—5662no—
155C22⋊C4—5661no—
156C22⋊C4—5662no—
157C42—5661no—
158C42—5662no—
159C42D113211yescharacteristic
160C42D113211yescharacteristic
161C42C22×D28312yes—
162C23—5661no—
163C23—5664no—
164C23—11328no—
165C23—11324no—
166C23C2×D113211yescharacteristic
167Q8—2832no—
168Q8—5661no—
169D4—2832no—
170D4—5664no—
171D4—5664no—
172D4—5661no—
173D4—5664no—
174D4—11328no—
175D4—11324no—
176D4—11328no—
177C2×C4—24no—
178C2×C4—5661no—
179C2×C4—5664no—
180C2×C4—5662no—
181C2×C4—11324no—
182C2×C4D4×D28312yes—
183C2×C4C2×D113212yes—
184C2×C4C2×D113211yescharacteristic
185C2×C4C2×D113212yes—
186C2×C4#1798539312yes—
187C2×C4C23×D28311yescharacteristic
188C8—24no—
189C22—22no—
190C22—5662no—
191C22—11322no—
192C22—11324no—
193C22—11328no—
194C22—22648no—
195C22#2258358512yes—
196C22C22×D113211yescharacteristic
197C4—22no—
198C4—5662no—
199C4—11322no—
200C4#2258358512yes—
201C4#2258363814yescomplemented
202C4C2×D4×D28311yescharacteristic
203C4C2×#1798539311yescharacteristic
204C2—22no—
205C2—11322no—
206C2—22644no—
207C2C2×#2258358511yescharacteristic
208C2C2×#2258363812yes—
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#423×C283C2
socleC22×C283C22×D4
hypercenter#423D283
hypocenterC283#3038
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
1. C2×#22583638C2semidirect
2. C2×#22583607C2semidirect
3. C4×#17985392C2semidirect
4. #31826666C2semidirect
5. #31826661C2semidirect
6. #31826471C2semidirect
7. #423×C283C2semidirect
12. C2×#17985381C22semidirect
13. C2×D2264C22semidirect
17. C4×Dic566C22semidirect
18. C4×D1132C22semidirect
23. #22583532C22semidirect
26. C4⋊C8×C283C22semidirect
29. #17985392D4semidirect
62. Dic566C2×D4semidirect
69. D1132C2×D4semidirect
94. C4×C283AGL(1,ℤ/8)semidirect
104. C283#3038semidirect
111. #423D283semidirect
130. C4⋊C8C2×D283semidirect
201. C4#22583638semidirect

Maximal subgroups

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

subgroupindex
C2×#225836382
C2×#225836072
C4×#179853922
#318266662
#318266612
#318264712
#423×C2832
#3038283