Finite Group Databasebeta

← #14573115

Subgroups — #14573115

Order 2432.

584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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
2C2×#10597320C211yesmaximal, characteristic, complemented
3#11926744C214yesmaximal, complemented
4#11926739C214yesmaximal, complemented
5#11926568C211yesmaximal, characteristic, complemented
6#11926548C212yesmaximal, complemented
7C4×#41×C19C211yesmaximal, characteristic, complemented
8C2×#41×C19C2211yescharacteristic
9C22×D76—22no—
10C22×D76C2212yes—
11C4×Q8×C19C2212yescomplemented
12C4×D4×C19—22no—
13C4×D4×C19C2212yescomplemented
14C19×#117—21no—
15C19×#117C2211yescharacteristic
16C2×C42×C19—21no—
17C2×C42×C19C2211yescharacteristic
18#10597395—28no—
19C2×#64527C2214yescomplemented
20C2×#64525C2214yescomplemented
21C2×#64520C2212yes—
22#10597320—21no—
23#10597320—21no—
24#10597320C2214yes—
25#10597266C2218yescomplemented
26C4⋊(C19⋊C8)C2214yescomplemented
27C23×D19—22no—
28#41×C19—22no—
29#41×C19D414yescomplemented
30C2×Q8×C19C2311yescharacteristic
31C2×D4×C19—21no—
32C2×D4×C19C2311yescharacteristic
33C22×C4×C19—21no—
34C22×C4×C19—22no—
35C22×C4×C19D412yes—
36C22×C4×C19C2311yescharacteristic
37C2×D76—24no—
38C2×D76—24no—
39C2×D76—24no—
40C2×D76—24no—
41C2×D76—22no—
42C2×D76—48no—
43C2×D76C2314yes—
44C4⋊C4×C19—22no—
45C4⋊C4×C19C2312yes—
46C22⋊C4×C19—21no—
47C22⋊C4×C19—22no—
48C42×C19—21no—
49C42×C19—22no—
50C42×C19D411yescharacteristic
51C42×C19D411yescharacteristic
52C42×C19C2312yes—
53#64527—28no—
54#64525—28no—
55#64520—24no—
56C2×C19⋊C8C2314yes—
57C23×C19—21no—
58C23×C19C2×D411yescharacteristic
59C22×D19—24no—
60C22×D19—48no—
61C22×D19—44no—
62Q8×C19—21no—
63Q8×C19C2×D412yescomplemented
64D4×C19—24no—
65D4×C19—21no—
66D4×C19C2×D412yescomplemented
67C2×C4×C19—21no—
68C2×C4×C19—24no—
69C2×C4×C19—24no—
70C2×C4×C19—22no—
71C2×C4×C19—44no—
72C2×C4×C19C2×D412yes—
73C2×C4×C19C2×D412yes—
74C2×C4×C19C2×D411yescharacteristic
75C2×C4×C19C2×D412yes—
76C2×C4×C19#4112yes—
77C2×C4×C19C2411yescharacteristic
78D76—24no—
79D76—24no—
80D76—48no—
81D76—44no—
82D76—48no—
83C19⋊C8—24no—
84#3038—191nomaximal, Sylow
85C22×C19—22no—
86C22×C19—22no—
87C22×C19—42no—
88C22×C19#12112yes—
89C22×C19C22×D411yescharacteristic
90C2×D19—44no—
91C2×D19—48no—
92C2×D19—88no—
93C4×C19—22no—
94C4×C19—22no—
95C4×C19—42no—
96C4×C19#12112yes—
97C4×C19AGL(1,ℤ/8)14yescomplemented
98C4×C19C22×D411yescharacteristic
99C4×C19C2×#4111yescharacteristic
100C2×AGL(1,ℤ/8)—192no—
101C2×#127—191no—
102C4×#41D1911yescharacteristic, complemented
103#460—194no—
104#459—194no—
105#423—191no—
106#418—192no—
107C2×C19—22no—
108C2×C19—42no—
109C2×C19C2×#12111yescharacteristic
110C2×C19C2×AGL(1,ℤ/8)12yes—
111D19—84no—
112C2×#41C2×D1911yescharacteristic
113C22×D4—192no—
114C22×D4—382no—
115AGL(1,ℤ/8)—388no—
116C2×SD16—194no—
117C2×D8—194no—
118C2×M16—192no—
119#127—194no—
120#127—381no—
121#127—381no—
122C4×Q8C2×D1912yescomplemented
123C4×D4—22no—
124C4×D4C2×D1912yescomplemented
125#117—21no—
126#117C2×D1911yescharacteristic
127C2×C42—21no—
128C2×C42C2×D1911yescharacteristic
129C4⋊C8—194no—
130#102—198no—
131C19#303811yescharacteristic, complemented, Sylow
132C24—382no—
133#41—22no—
134#41D7614yescomplemented
135C2×Q8C22×D1911yescharacteristic
136C2×D4—21no—
137C2×D4—194no—
138C2×D4—384no—
139C2×D4—384no—
140C2×D4—384no—
141C2×D4—384no—
142C2×D4—382no—
143C2×D4—768no—
144C2×D4C22×D1911yescharacteristic
145C22×C4—21no—
146C22×C4—22no—
147C22×C4C22⋊D1912yes—
148C22×C4C22×D1911yescharacteristic
149SD16—388no—
150D8—388no—
151M16—384no—
152C2×C8—194no—
153C4⋊C4—22no—
154C4⋊C4C22×D1912yes—
155C22⋊C4—21no—
156C22⋊C4—22no—
157C42—21no—
158C42—22no—
159C42C22⋊D1911yescharacteristic
160C42C22⋊D1911yescharacteristic
161C42C22×D1912yes—
162C23—21no—
163C23—384no—
164C23—768no—
165C23—764no—
166C23C2×C22⋊D1911yescharacteristic
167Q8—21no—
168Q8C2×D7612yescomplemented
169D4—24no—
170D4—21no—
171D4—384no—
172D4—384no—
173D4—768no—
174D4—764no—
175D4—768no—
176D4C2×D7612yescomplemented
177C2×C4—21no—
178C2×C4—24no—
179C2×C4—24no—
180C2×C4—22no—
181C2×C4—44no—
182C2×C4C2×D7612yes—
183C2×C4#6454112yes—
184C2×C4C2×C22⋊D1912yes—
185C2×C4C2×C22⋊D1911yescharacteristic
186C2×C4C2×C22⋊D1912yes—
187C2×C4C23×D1911yescharacteristic
188C8—384no—
189C22—22no—
190C22—22no—
191C22—42no—
192C22—768no—
193C22—764no—
194C22—1528no—
195C22#1059737612yes—
196C22C22×C22⋊D1911yescharacteristic
197C4—22no—
198C4—22no—
199C4—42no—
200C4#1059737612yes—
201C4#1059739514yescomplemented
202C4C22×D7611yescharacteristic
203C4C2×#6454111yescharacteristic
204C2—22no—
205C2—42no—
206C2—1524no—
207C2C2×#1059737611yescharacteristic
208C2C2×#1059739512yes—
subgroupG/H
centerC22C22×C22⋊D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC4×#41×C19C2
socleC22×C19C22×D4
hypercenterC4×#41D19
hypocenterC19#3038
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#10597395C2semidirect
2. C2×#10597320C2semidirect
3. #11926744C2semidirect
4. #11926739C2semidirect
5. #11926568C2semidirect
6. #11926548C2semidirect
7. C4×#41×C19C2semidirect
11. C4×Q8×C19C22semidirect
13. C4×D4×C19C22semidirect
19. C2×#64527C22semidirect
20. C2×#64525C22semidirect
25. #10597266C22semidirect
26. C4⋊(C19⋊C8)C22semidirect
29. #41×C19D4semidirect
63. Q8×C19C2×D4semidirect
66. D4×C19C2×D4semidirect
97. C4×C19AGL(1,ℤ/8)semidirect
102. C4×#41D19semidirect
122. C4×Q8C2×D19semidirect
124. C4×D4C2×D19semidirect
131. C19#3038semidirect
134. #41D76semidirect
168. Q8C2×D76semidirect
176. D4C2×D76semidirect
201. C4#10597395semidirect

Maximal subgroups

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

subgroupindex
C2×#105973952
C2×#105973202
#119267442
#119267392
#119265682
#119265482
C4×#41×C192
#303819