Finite Group Databasebeta

← #14574122

Subgroups — #14574122

Order 2432.

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

normal subgroups only

This group has 596 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×#10597395C212yesmaximal, complemented
2C22×D152C211yesmaximal, characteristic, complemented
3#11927108C212yesmaximal, complemented
4#11926930C214yesmaximal, complemented
5#11926929C212yesmaximal, complemented
6#11926919C212yesmaximal, complemented
7#11926499C211yesmaximal, characteristic, complemented
8C2×C19×#135C211yesmaximal, characteristic, complemented
9C2×#41×C19C2212yes—
10C22×D76C2212yes—
11C19×#135—24no—
12C2×Q16×C19C2211yescharacteristic, complemented
13C2×SD16×C19C2212yescomplemented
14C2×D8×C19C2211yescharacteristic, complemented
15C22×C8×C19C2211yescharacteristic
16#10597395—28no—
17#10597393C2214yescomplemented
18C2×#64527C2214yescomplemented
19#10597386C2214yescomplemented
20#10597383—24no—
21C2×#64525C2214yescomplemented
22#10597376—24no—
23#10597372C2211yescharacteristic
24C2×#64520C2211yescharacteristic
25C2×D152—24no—
26C2×D152C2212yes—
27C2×D152C2212yes—
28#10597272C2212yescomplemented
29C8×Dic19C2212yescomplemented
30C23×D19—22no—
31#41×C19—24no—
32#41×C19—24no—
33C2×Q8×C19C2312yes—
34C2×D4×C19—22no—
35C2×D4×C19C2312yes—
36C22×C4×C19—22no—
37C22×C4×C19C2311yescharacteristic
38C2×C22⋊D19—28no—
39C2×D76—24no—
40C2×D76—24no—
41C2×D76—22no—
42C2×D76C2314yes—
43Q16×C19—22no—
44SD16×C19—24no—
45D8×C19—22no—
46C2×C8×C19D414yescomplemented
47C2×C8×C19C2311yescharacteristic
48C2×C8×C19C2311yescharacteristic
49C22⋊Dic19D412yes—
50#64527—28no—
51#64525—28no—
52(C2×D19)⋊C4—28no—
53C4⋊Dic19D412yes—
54C4×Dic19C2312yes—
55#64520D414yescomplemented
56C2×C19⋊C8C2312yes—
57D152—24no—
58D152—24no—
59C23×C19—22no—
60C23×C19C2×D411yescharacteristic
61C22×D19—24no—
62C22×D19—44no—
63C22×D19—84no—
64Q8×C19—22no—
65Q8×C19—22no—
66D4×C19—22no—
67D4×C19—22no—
68D4×C19—44no—
69C2×C4×C19—22no—
70C2×C4×C19—44no—
71C2×C4×C19C2×D411yescharacteristic
72C2×C4×C19C2×D412yes—
73C2×C4×C19C2×D412yes—
74C2×C4×C19C2411yescharacteristic
75C22⋊D19—88no—
76C2×Dic19C2×D414yes—
77D76—24no—
78D76—24no—
79D76—44no—
80C8×C19C2×D412yes—
81C8×C19C2×D412yes—
82C19⋊C8C2×D414yes—
83#3155—191nomaximal, Sylow
84C22×C19—22no—
85C22×C19—42no—
86C22×C19—44no—
87C22×C19#12712yes—
88C22×C19C22×D411yescharacteristic
89C2×D19—44no—
90C2×D19—48no—
91C2×D19—88no—
92C4×C19—42no—
93C4×C19#12712yes—
94C4×C19C22×D411yescharacteristic
95C4×C19C22×D411yescharacteristic
96Dic19—24no—
97C2×AGL(1,ℤ/8)—192no—
98C2×#135D1911yescharacteristic, complemented
99C22×D8—191no—
100#535—192no—
101#496—194no—
102#495—192no—
103#493—192no—
104#405—191no—
105C2×C19—22no—
106C2×C19—82no—
107C2×C19C2×#12711yescharacteristic
108C2×C19#57612yes—
109D19—84no—
110C2×#41C2×D1912yes—
111C22×D4—192no—
112AGL(1,ℤ/8)—388no—
113#135—24no—
114C2×Q16C2×D1911yescharacteristic, complemented
115C2×SD16—194no—
116C2×SD16C2×D1912yescomplemented
117C2×D8—194no—
118C2×D8—192no—
119C2×D8—192no—
120C2×D8—384no—
121C2×D8C2×D1911yescharacteristic, complemented
122C2×M16—191no—
123C22×C8C2×D1911yescharacteristic
124#127—194no—
125#124—194no—
126#121—384no—
127#120—384no—
128#117—191no—
129#97—192no—
130C4×C8—192no—
131C19#315511yescharacteristic, complemented, Sylow
132C24—382no—
133#41—24no—
134#41—24no—
135C2×Q8C22×D1912yes—
136C2×D4—22no—
137C2×D4—194no—
138C2×D4—388no—
139C2×D4—384no—
140C2×D4—382no—
141C2×D4—384no—
142C2×D4C22×D1912yes—
143C22×C4—22no—
144C22×C4C22×D1911yescharacteristic
145Q16—22no—
146SD16—24no—
147SD16—388no—
148D8—22no—
149D8—388no—
150D8—384no—
151D8—384no—
152M16—194no—
153C2×C8—192no—
154C2×C8C22⋊D1914yescomplemented
155C2×C8C22×D1911yescharacteristic
156C2×C8C22×D1911yescharacteristic
157C4⋊C4—192no—
158C22⋊C4—192no—
159C22⋊C4—388no—
160C42—192no—
161C23—22no—
162C23—384no—
163C23—764no—
164C23—1524no—
165C23D4×D1911yescharacteristic
166Q8—22no—
167Q8—22no—
168D4—22no—
169D4—22no—
170D4—44no—
171D4—384no—
172D4—384no—
173D4—764no—
174D4—1528no—
175C2×C4—22no—
176C2×C4—44no—
177C2×C4—194no—
178C2×C4D4×D1911yescharacteristic
179C2×C4D4×D1912yes—
180C2×C4C2×C22⋊D1912yes—
181C2×C4C23×D1911yescharacteristic
182C8—194no—
183C8C2×C22⋊D1912yes—
184C8C2×C22⋊D1912yes—
185C22—22no—
186C22—42no—
187C22—44no—
188C22—764no—
189C22—768no—
190C22—1528no—
191C22#1059738612yes—
192C22C2×D4×D1911yescharacteristic
193C4—42no—
194C4—384no—
195C4#1059738612yes—
196C4C2×D4×D1911yescharacteristic
197C4C22×C22⋊D1911yescharacteristic
198C2—22no—
199C2—82no—
200C2—1524no—
201C2C2×#1059738611yescharacteristic
202C2#1192734612yes—
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC2×C19×#135C2
socleC22×C19C22×D4
hypercenterC2×#135D19
hypocenterC19#3155
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#10597395C2semidirect
2. C22×D152C2semidirect
3. #11927108C2semidirect
4. #11926930C2semidirect
5. #11926929C2semidirect
6. #11926919C2semidirect
7. #11926499C2semidirect
8. C2×C19×#135C2semidirect
12. C2×Q16×C19C22semidirect
13. C2×SD16×C19C22semidirect
14. C2×D8×C19C22semidirect
17. #10597393C22semidirect
18. C2×#64527C22semidirect
19. #10597386C22semidirect
21. C2×#64525C22semidirect
28. #10597272C22semidirect
29. C8×Dic19C22semidirect
46. C2×C8×C19D4semidirect
55. #64520D4semidirect
98. C2×#135D19semidirect
114. C2×Q16C2×D19semidirect
116. C2×SD16C2×D19semidirect
121. C2×D8C2×D19semidirect
131. C19#3155semidirect
154. C2×C8C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105973952
C22×D1522
#119271082
#119269302
#119269292
#119269192
#119264992
C2×C19×#1352
#315519