Finite Group Databasebeta

← C19×#10624 #18016583

Subgroups — C19×#10624 #18016583

Order 4864.

350 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 134 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×#1984C211yesmaximal, characteristic
2C19×#1834C211yesmaximal, characteristic
3C19×#1803C212yesmaximal
4C19×#1296C212yesmaximal
5C19×#1277C211yesmaximal, characteristic
6C2×C4×Q8×C19C2211yescharacteristic
7C2×C19×C4⋊C8C2211yescharacteristic
8C2×C19×C4⋊C8C2212yes—
9C2×C19×#103—22no—
10C2×C4×C8×C19C2211yescharacteristic
11C19×#384C2212yes—
12C19×#340—22no—
13C19×#340—22no—
14C19×#336—22no—
15C22×Q8×C19D411yescharacteristic
16C22×C8×C19—22no—
17C22×C8×C19—21no—
18C22×C8×C19D412yes—
19C4×Q8×C19—22no—
20C4×Q8×C19—22no—
21C2×C4⋊C4×C19—21no—
22C2×C4⋊C4×C19—22no—
23C2×C4⋊C4×C19—22no—
24C2×C4⋊C4×C19—22no—
25C2×C4⋊C4×C19D411yescharacteristic
26C2×C42×C19—21no—
27C2×C42×C19C2311yescharacteristic
28C19×C4⋊C8—22no—
29C19×C4⋊C8—22no—
30C19×C4⋊C8—22no—
31C19×#103—44no—
32C4×C8×C19—22no—
33C2×Q8×C19—21no—
34C2×Q8×C19—22no—
35C2×Q8×C19—22no—
36C2×Q8×C19Q1612yes—
37C22×C4×C19—21no—
38C22×C4×C19—21no—
39C22×C4×C19—42no—
40C22×C4×C19C2×D411yescharacteristic
41C22×C4×C19C2×D411yescharacteristic
42C22×C4×C19#4111yescharacteristic
43C2×C8×C19—22no—
44C2×C8×C19—22no—
45C2×C8×C19—22no—
46C2×C8×C19—42no—
47C2×C8×C19—41no—
48C2×C8×C19—42no—
49C2×C8×C19—42no—
50C2×C8×C19—42no—
51C4⋊C4×C19—22no—
52C4⋊C4×C19—42no—
53C4⋊C4×C19—42no—
54C4⋊C4×C19—42no—
55C4⋊C4×C19—42no—
56C4⋊C4×C19—42no—
57C4⋊C4×C19—82no—
58C42×C19—41no—
59C42×C19—41no—
60C42×C19#4112yes—
61C42×C19#4112yes—
62#10624C1911yesmaximal, characteristic, direct product factor, Sylow
63C23×C19#12111yescharacteristic
64Q8×C19—24no—
65Q8×C19—42no—
66C2×C4×C19—22no—
67C2×C4×C19—22no—
68C2×C4×C19—41no—
69C2×C4×C19—41no—
70C2×C4×C19—41no—
71C2×C4×C19—42no—
72C2×C4×C19—82no—
73C2×C4×C19—82no—
74C2×C4×C19—82no—
75C2×C4×C19#12312yes—
76C2×C4×C19#12311yescharacteristic
77C2×C4×C19#12411yescharacteristic
78C2×C4×C19#12612yes—
79C2×C4×C19C2×Q1611yescharacteristic
80C2×C4×C19#13511yescharacteristic
81C2×C4×C19#13512yes—
82C2×C4×C19AGL(1,ℤ/8)12yes—
83C2×C4×C19#13712yes—
84C8×C19—42no—
85C8×C19—82no—
86C8×C19—81no—
87#1984C2×C1911yescharacteristic
88#1834C2×C1911yescharacteristic
89#1803C2×C1912yes—
90#1296C2×C1912yes—
91#1277C2×C1911yescharacteristic
92C22×C19#39711yescharacteristic
93C22×C19#46412yes—
94C22×C19#46711yescharacteristic
95C22×C19#46911yescharacteristic
96C22×C19#47112yes—
97C4×C19—22no—
98C4×C19—42no—
99C4×C19—81no—
100C4×C19—162no—
101C4×C19#48212yes—
102C4×C19#48412yes—
103C4×C19#48512yes—
104C4×C19#48811yescharacteristic
105C4×C19#49111yescharacteristic
106C2×C4×Q8C22×C1911yescharacteristic
107C2×C4⋊C8C22×C1912yes—
108C2×C4⋊C8C22×C1911yescharacteristic
109C2×#103—22no—
110C2×C4×C8C22×C1911yescharacteristic
111#384C22×C1912yes—
112#340—22no—
113#340—22no—
114#336—22no—
115C2×C19#168412yes—
116C2×C19#170212yes—
117C2×C19#207411yescharacteristic
118C2×C19#207611yescharacteristic
119C2×C19#207911yescharacteristic
120C22×Q8D4×C1911yescharacteristic
121C22×C8—21no—
122C22×C8—22no—
123C22×C8D4×C1912yes—
124C4×Q8—22no—
125C4×Q8—22no—
126C2×C4⋊C4—21no—
127C2×C4⋊C4—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4D4×C1911yescharacteristic
131C2×C42—21no—
132C2×C42C23×C1911yescharacteristic
133C4⋊C8—22no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136#103—44no—
137C4×C8—22no—
138C19#1062411yescharacteristic, direct product factor, Sylow
139C2×Q8—21no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8Q16×C1912yes—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—42no—
146C22×C4C2×D4×C1911yescharacteristic
147C22×C4C2×D4×C1911yescharacteristic
148C22×C4#41×C1911yescharacteristic
149C2×C8—22no—
150C2×C8—22no—
151C2×C8—22no—
152C2×C8—42no—
153C2×C8—41no—
154C2×C8—42no—
155C2×C8—42no—
156C2×C8—42no—
157C4⋊C4—22no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—42no—
162C4⋊C4—42no—
163C4⋊C4—82no—
164C42—41no—
165C42—41no—
166C42#41×C1912yes—
167C42#41×C1912yes—
168C23C19×#12111yescharacteristic
169Q8—24no—
170Q8—42no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—82no—
178C2×C4—82no—
179C2×C4—82no—
180C2×C4C19×#12312yes—
181C2×C4C19×#12311yescharacteristic
182C2×C4C19×#12411yescharacteristic
183C2×C4C19×#12612yes—
184C2×C4C2×Q16×C1911yescharacteristic
185C2×C4C19×#13511yescharacteristic
186C2×C4C19×#13512yes—
187C2×C4C19×AGL(1,ℤ/8)12yes—
188C2×C4C19×#13712yes—
189C8—42no—
190C8—82no—
191C8—81no—
192C22C19×#39711yescharacteristic
193C22C19×#46412yes—
194C22C19×#46711yescharacteristic
195C22C19×#46911yescharacteristic
196C22C19×#47112yes—
197C4—22no—
198C4—42no—
199C4—81no—
200C4—162no—
201C4C19×#48212yes—
202C4C19×#48412yes—
203C4C19×#48512yes—
204C4C19×#48811yescharacteristic
205C4C19×#49111yescharacteristic
206C2C19×#168412yes—
207C2C19×#170212yes—
208C2C19×#207411yescharacteristic
209C2C19×#207611yescharacteristic
210C2C19×#207911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C19#121
commutator, Frattini, cosocleC2×C42C23×C19
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C19 ◁ C2×C42×C19 ◁ G

Complements

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

NH ≅ G/Ntype
62. #10624C19direct (N × H)
138. C19#10624direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#19842
C19×#18342
C19×#18032
C19×#12962
C19×#12772
#1062419