Finite Group Databasebeta

← C19×#8188 #18014147

Subgroups — C19×#8188 #18014147

Order 4864.

412 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 182 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×#2922C211yesmaximal, characteristic
2C19×#1476C212yesmaximal
3C19×#1452C211yesmaximal, characteristic, complemented
4C2×C19×#322C211yesmaximal, characteristic, complemented
5C19×#1278C212yesmaximal, complemented
6C4×#41×C19C2211yescharacteristic
7C19×#433—22no—
8C19×#431—22no—
9C19×#431C2212yes—
10C19×#424C412yes—
11C19×#408C412yes—
12C4×M16×C19C2211yescharacteristic
13C2×C4×C8×C19C2212yes—
14C2×C4×C8×C19C2211yescharacteristic
15C19×Q8⋊C8C414yes—
16C19×D4⋊C8C414yes—
17C19×#322—22no—
18C19×#322—22no—
19C2×#41×C19C2×C411yescharacteristic
20C2×M16×C19C2×C412yes—
21C22×C8×C19—22no—
22C22×C8×C19C2×C412yes—
23C4×Q8×C19C2×C412yes—
24C4×D4×C19—22no—
25C4×D4×C19C2×C412yes—
26C19×#117—21no—
27C19×#117C2×C411yescharacteristic
28C2×C42×C19—21no—
29C2×C42×C19C2311yescharacteristic
30C19×C4⋊C8—24no—
31C19×C4⋊C8C2×C414yes—
32C19×C22⋊C8—22no—
33C19×C22⋊C8—24no—
34C19×#97—21no—
35C4×C8×C19—22no—
36C4×C8×C19—21no—
37C4×C8×C19—22no—
38C4×C8×C19C2×C414yes—
39C4×C8×C19D412yes—
40C4×C8×C19D412yes—
41#41×C19—24no—
42C2×Q8×C19C4211yescharacteristic
43C2×D4×C19—21no—
44C2×D4×C19C4211yescharacteristic
45C22×C4×C19—21no—
46C22×C4×C19—22no—
47C22×C4×C19C22×C411yescharacteristic
48C22×C4×C19#4112yes—
49M16×C19—24no—
50C2×C8×C19—24no—
51C2×C8×C19—22no—
52C2×C8×C19—24no—
53C2×C8×C19—24no—
54C2×C8×C19—44no—
55C2×C8×C19C22⋊C414yes—
56C4⋊C4×C19—22no—
57C4⋊C4×C19C4212yes—
58C22⋊C4×C19—21no—
59C22⋊C4×C19—22no—
60C42×C19—21no—
61C42×C19—22no—
62C42×C19C22×C412yes—
63C42×C19C2×D411yescharacteristic
64C42×C19C2×D411yescharacteristic
65#8188C1911yesmaximal, characteristic, direct product factor, Sylow
66C23×C19—21no—
67C23×C19#11711yescharacteristic
68Q8×C19—22no—
69D4×C19—22no—
70D4×C19—42no—
71C2×C4×C19—24no—
72C2×C4×C19—22no—
73C2×C4×C19—21no—
74C2×C4×C19—42no—
75C2×C4×C19—44no—
76C2×C4×C19C2×C4211yescharacteristic
77C2×C4×C19C2×C22⋊C411yescharacteristic
78C2×C4×C19C4×D412yes—
79C2×C4×C19C4×D412yes—
80C2×C4×C19#13114yes—
81C8×C19—24no—
82C8×C19—44no—
83C8×C19—42no—
84C8×C19—44no—
85#2922C2×C1911yescharacteristic
86#1476C2×C1912yes—
87#1452C2×C1911yescharacteristic, complemented
88C2×#322C2×C1911yescharacteristic, complemented
89#1278C2×C1912yescomplemented
90C22×C19—22no—
91C22×C19—41no—
92C22×C19—42no—
93C22×C19C4×C22⋊C411yescharacteristic
94C22×C19#43312yes—
95C4×C19—22no—
96C4×C19—41no—
97C4×C19—42no—
98C4×C19#40512yes—
99C4×C19#40812yes—
100C4×C19#44414yes—
101C4×#41C22×C1911yescharacteristic
102#433—22no—
103#431—22no—
104#431C22×C1912yes—
105#424C4×C1912yes—
106#408C4×C1912yes—
107C4×M16C22×C1911yescharacteristic
108C2×C4×C8C22×C1912yes—
109C2×C4×C8C22×C1911yescharacteristic
110Q8⋊C8C4×C1914yes—
111D4⋊C8C4×C1914yes—
112#322—22no—
113#322—22no—
114C2×C19—22no—
115C2×C19—81no—
116C2×C19#175011yescharacteristic
117C2×C19#176512yes—
118C2×#41C2×C4×C1911yescharacteristic
119C2×M16C2×C4×C1912yes—
120C22×C8—22no—
121C22×C8C2×C4×C1912yes—
122C4×Q8C2×C4×C1912yes—
123C4×D4—22no—
124C4×D4C2×C4×C1912yes—
125#117—21no—
126#117C2×C4×C1911yescharacteristic
127C2×C42—21no—
128C2×C42C23×C1911yescharacteristic
129C4⋊C8—24no—
130C4⋊C8C2×C4×C1914yes—
131C22⋊C8—22no—
132C22⋊C8—24no—
133#97—21no—
134C4×C8—22no—
135C4×C8—22no—
136C4×C8—21no—
137C4×C8C2×C4×C1914yes—
138C4×C8D4×C1912yes—
139C4×C8D4×C1912yes—
140C19#818811yescharacteristic, direct product factor, Sylow
141#41—24no—
142C2×Q8C42×C1911yescharacteristic
143C2×D4—21no—
144C2×D4C42×C1911yescharacteristic
145C22×C4—21no—
146C22×C4—22no—
147C22×C4C22×C4×C1911yescharacteristic
148C22×C4#41×C1912yes—
149M16—24no—
150C2×C8—24no—
151C2×C8—22no—
152C2×C8—24no—
153C2×C8—24no—
154C2×C8—44no—
155C2×C8C22⋊C4×C1914yes—
156C4⋊C4—22no—
157C4⋊C4C42×C1912yes—
158C22⋊C4—21no—
159C22⋊C4—22no—
160C42—21no—
161C42—22no—
162C42C22×C4×C1912yes—
163C42C2×D4×C1911yescharacteristic
164C42C2×D4×C1911yescharacteristic
165C23—21no—
166C23C19×#11711yescharacteristic
167Q8—22no—
168D4—22no—
169D4—42no—
170C2×C4—24no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—42no—
174C2×C4—44no—
175C2×C4C2×C42×C1911yescharacteristic
176C2×C4C2×C22⋊C4×C1911yescharacteristic
177C2×C4C4×D4×C1912yes—
178C2×C4C4×D4×C1912yes—
179C2×C4C19×#13114yes—
180C8—24no—
181C8—44no—
182C8—42no—
183C8—44no—
184C22—22no—
185C22—41no—
186C22—42no—
187C22C4×C22⋊C4×C1911yescharacteristic
188C22C19×#43312yes—
189C4—22no—
190C4—41no—
191C4—42no—
192C4C19×#40512yes—
193C4C19×#40812yes—
194C4C19×#44414yes—
195C2—22no—
196C2—81no—
197C2C19×#175011yescharacteristic
198C2C19×#176512yes—
subgroupG/H
centerC42×C19C2×D4
commutatorC2×C4C2×C42×C19
Frattini, cosocleC2×C42C23×C19
socleC22×C19C4×C22⋊C4
prime radicalC2×#41×C19C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C42×C19 ◁ C2×C4×C8×C19 ◁ G

Complements

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

NH ≅ G/Ntype
3. C19×#1452C2semidirect
4. C2×C19×#322C2semidirect
5. C19×#1278C2semidirect
65. #8188C19direct (N × H)
87. #1452C2×C19semidirect
88. C2×#322C2×C19semidirect
89. #1278C2×C19semidirect
140. C19#8188direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#29222
C19×#14762
C19×#14522
C2×C19×#3222
C19×#12782
#818819