Finite Group Databasebeta

← C19×#3093 #14560950

Subgroups — C19×#3093 #14560950

Order 2432.

414 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 184 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
1C19×#525C211yesmaximal, characteristic
2C2×C19×#117C211yesmaximal, characteristic, complemented
3C19×#485C214yesmaximal, complemented
4C19×#482C214yesmaximal, complemented
5C19×#428C212yesmaximal, complemented
6C19×#417C212yesmaximal, complemented
7C19×#407C211yesmaximal, characteristic, complemented
8C2×#41×C19C2211yescharacteristic
9C23×C4×C19C2211yescharacteristic
10C2×M16×C19C2212yes—
11C19×#123—21no—
12C19×C22⋊Q8C2212yes—
13C19×#121C2212yes—
14C19×#120—21no—
15C4×D4×C19—22no—
16C19×#117—22no—
17C19×#117C2211yescharacteristic
18C19×#117C2214yes—
19C2×C4⋊C4×C19C2212yes—
20C2×C22⋊C4×C19—21no—
21C2×C42×C19—21no—
22C19×#107C2214yescomplemented
23C19×#106C2214yescomplemented
24C19×#103C2214yescomplemented
25C19×#102C2214yescomplemented
26C19×C22⋊C8C2214yes—
27C24×C19D411yescharacteristic
28#41×C19—24no—
29C2×Q8×C19C2311yescharacteristic
30C2×D4×C19—22no—
31C2×D4×C19—21no—
32C2×D4×C19C2311yescharacteristic
33C22×C4×C19—24no—
34C22×C4×C19—22no—
35C22×C4×C19—21no—
36C22×C4×C19D411yescharacteristic
37C22×C4×C19D412yes—
38C22×C4×C19C2312yes—
39C22×C4×C19C2311yescharacteristic
40M16×C19—24no—
41C2×C8×C19C2314yes—
42C4⋊C4×C19—22no—
43C4⋊C4×C19—22no—
44C4⋊C4×C19C2314yes—
45C4⋊C4×C19C2312yes—
46C22⋊C4×C19—24no—
47C22⋊C4×C19—21no—
48C22⋊C4×C19—22no—
49C22⋊C4×C19—22no—
50C42×C19—24no—
51C42×C19—21no—
52C23×C19—22no—
53C23×C19—21no—
54C23×C19—42no—
55C23×C19C2×D412yes—
56C23×C19C2×D411yescharacteristic
57Q8×C19—22no—
58D4×C19—22no—
59D4×C19—44no—
60D4×C19—42no—
61C2×C4×C19—22no—
62C2×C4×C19—24no—
63C2×C4×C19—24no—
64C2×C4×C19—24no—
65C2×C4×C19—22no—
66C2×C4×C19—21no—
67C2×C4×C19—44no—
68C2×C4×C19—42no—
69C2×C4×C19C2×D412yes—
70C2×C4×C19C2×D411yescharacteristic
71C2×C4×C19#4114yes—
72C2×C4×C19C2411yescharacteristic
73C8×C19—24no—
74#3093C1911yesmaximal, characteristic, direct product factor, Sylow
75C22×C19—22no—
76C22×C19—22no—
77C22×C19—22no—
78C22×C19—22no—
79C22×C19—44no—
80C22×C19—41no—
81C22×C19—42no—
82C22×C19#12312yes—
83C22×C19C22×D411yescharacteristic
84C4×C19—22no—
85C4×C19—41no—
86C4×C19—44no—
87C4×C19—42no—
88C4×C19#12312yes—
89C4×C19C2×#4112yes—
90#525C2×C1911yescharacteristic
91C2×#117C2×C1911yescharacteristic, complemented
92#485C2×C1914yescomplemented
93#482C2×C1914yescomplemented
94#428C2×C1912yescomplemented
95#417C2×C1912yescomplemented
96#407C2×C1911yescharacteristic, complemented
97C2×C19—22no—
98C2×C19—42no—
99C2×C19—81no—
100C2×C19C2×#12311yescharacteristic
101C2×C19#57512yes—
102C2×#41C22×C1911yescharacteristic
103C23×C4C22×C1911yescharacteristic
104C2×M16C22×C1912yes—
105#123—21no—
106C22⋊Q8C22×C1912yes—
107#121C22×C1912yes—
108#120—21no—
109C4×D4—22no—
110#117—22no—
111#117C22×C1914yes—
112#117C22×C1911yescharacteristic
113C2×C4⋊C4C22×C1912yes—
114C2×C22⋊C4—21no—
115C2×C42—21no—
116#107C22×C1914yescomplemented
117#106C22×C1914yescomplemented
118#103C22×C1914yescomplemented
119#102C22×C1914yescomplemented
120C22⋊C8C22×C1914yes—
121C19#309311yescharacteristic, direct product factor, Sylow
122C24D4×C1911yescharacteristic
123#41—24no—
124C2×Q8C23×C1911yescharacteristic
125C2×D4—22no—
126C2×D4—21no—
127C2×D4C23×C1911yescharacteristic
128C22×C4—24no—
129C22×C4—22no—
130C22×C4—21no—
131C22×C4D4×C1911yescharacteristic
132C22×C4D4×C1912yes—
133C22×C4C23×C1912yes—
134C22×C4C23×C1911yescharacteristic
135M16—24no—
136C2×C8C23×C1914yes—
137C4⋊C4—22no—
138C4⋊C4—22no—
139C4⋊C4C23×C1914yes—
140C4⋊C4C23×C1912yes—
141C22⋊C4—24no—
142C22⋊C4—21no—
143C22⋊C4—22no—
144C22⋊C4—22no—
145C42—24no—
146C42—21no—
147C23—22no—
148C23—21no—
149C23—42no—
150C23C2×D4×C1912yes—
151C23C2×D4×C1911yescharacteristic
152Q8—22no—
153D4—22no—
154D4—44no—
155D4—42no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—44no—
163C2×C4—42no—
164C2×C4C2×D4×C1912yes—
165C2×C4C2×D4×C1911yescharacteristic
166C2×C4#41×C1914yes—
167C2×C4C24×C1911yescharacteristic
168C8—24no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—41no—
175C22—42no—
176C22C19×#12312yes—
177C22C22×D4×C1911yescharacteristic
178C4—22no—
179C4—41no—
180C4—44no—
181C4—42no—
182C4C19×#12312yes—
183C4C2×#41×C1912yes—
184C2—22no—
185C2—42no—
186C2—81no—
187C2C2×C19×#12311yescharacteristic
188C2C19×#57512yes—
subgroupG/H
center, socleC22×C19C22×D4
commutator, Frattini, cosocleC2×C4C24×C19
prime radicalC19×#525C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C19×#117C2semidirect
3. C19×#485C2semidirect
4. C19×#482C2semidirect
5. C19×#428C2semidirect
6. C19×#417C2semidirect
7. C19×#407C2semidirect
22. C19×#107C22semidirect
23. C19×#106C22semidirect
24. C19×#103C22semidirect
25. C19×#102C22semidirect
74. #3093C19direct (N × H)
91. C2×#117C2×C19semidirect
92. #485C2×C19semidirect
93. #482C2×C19semidirect
94. #428C2×C19semidirect
95. #417C2×C19semidirect
96. #407C2×C19semidirect
116. #107C22×C19semidirect
117. #106C22×C19semidirect
118. #103C22×C19semidirect
119. #102C22×C19semidirect
121. C19#3093direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#5252
C2×C19×#1172
C19×#4852
C19×#4822
C19×#4282
C19×#4172
C19×#4072
#309319