Finite Group Databasebeta

← #14569040

Subgroups — #14569040

Order 2432.

412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 145 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
1#11926464C212yesmaximal
2#11926464C211yesmaximal, characteristic
3#11926449C211yesmaximal, characteristic
4#11926448C212yesmaximal
5#11926439C212yesmaximal
6#11926429C212yesmaximal
7#11926427C212yesmaximal
8C4⋊C4×Dic19C212yesmaximal
9C19×#398C211yesmaximal, characteristic
10C22×Dic38C2211yescharacteristic
11C22×Dic38C2211yescharacteristic
12C2×C4⋊C4×C19C2212yes—
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×C4⋊C4×C19C2211yescharacteristic
15C2×C4⋊Dic19C2212yes—
16C2×Dic19⋊C4C2212yes—
17C2×Dic19⋊C4C2212yes—
18C2×Dic19⋊C4C2212yes—
19C2×C4×Dic19C2212yes—
20C2×C4×Dic19C2211yescharacteristic
21C2×C4×Dic19C2212yes—
22C19×#95C2211yescharacteristic
23C19×#95C2212yes—
24C19⋊#95C2212yes—
25C19⋊#95C2212yes—
26C19⋊#95C2212yes—
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2211yescharacteristic
30C19⋊#95C2212yes—
31C22×C4×C19C2311yescharacteristic
32C22×C4×C19C2312yes—
33C22×C4×C19C2311yescharacteristic
34C22×C4×C19C2312yes—
35C22×C4×C19C2311yescharacteristic
36C22×Dic19C2312yes—
37C22×Dic19C2312yes—
38C22×Dic19C2312yes—
39C22×Dic19C2312yes—
40C2×Dic38—22no—
41C2×Dic38—24no—
42C2×Dic38—41no—
43C2×Dic38—41no—
44C2×Dic38—41no—
45C4⋊C4×C19—24no—
46C4⋊C4×C19—41no—
47C4⋊C4×C19—41no—
48C4⋊Dic19Q818yescomplemented
49Dic19⋊C4—24no—
50Dic19⋊C4—42no—
51Dic19⋊C4—42no—
52C4×Dic19—24no—
53C4×Dic19—41no—
54C4×Dic19—42no—
55C23×C19C2411yescharacteristic
56C2×C4×C19—22no—
57C2×C4×C19—22no—
58C2×C4×C19—21no—
59C2×C4×C19—21no—
60C2×C4×C19—22no—
61C2×C4×C19—22no—
62C2×C4×C19—22no—
63C2×C4×C19—22no—
64C2×C4×C19—22no—
65C2×C4×C19—21no—
66C2×C4×C19—21no—
67C2×C4×C19C2×Q814yes—
68C2×C4×C19#4112yes—
69C2×Dic19—22no—
70C2×Dic19—22no—
71C2×Dic19—22no—
72C2×Dic19—22no—
73C2×Dic19—22no—
74C2×Dic19—22no—
75C2×Dic19—22no—
76C2×Dic19—22no—
77C2×Dic19—22no—
78C2×Dic19C2×Q814yes—
79C2×Dic19C2×Q814yes—
80C2×Dic19#4114yes—
81Dic38—44no—
82Dic38—44no—
83#2586—191nomaximal, Sylow
84C22×C19C22×Q812yes—
85C22×C19C2×#4111yescharacteristic
86C22×C19C2×#4112yes—
87C22×C19H(5,𝔽2)11yescharacteristic
88C22×C19H(5,𝔽2)11yescharacteristic
89C4×C19—24no—
90C4×C19—22no—
91C4×C19—42no—
92C4×C19—41no—
93C4×C19—41no—
94Dic19—24no—
95Dic19—24no—
96Dic19—24no—
97Dic19—42no—
98#398D1911yescharacteristic
99#395—191no—
100#395—192no—
101#391—191no—
102#391—192no—
103#389—192no—
104#387—192no—
105#387—192no—
106C4×C4⋊C4—192no—
107C2×C19#53312yes—
108C2×C19#53811yescharacteristic
109C2×C19#55111yescharacteristic
110C2×C19#55412yes—
111C2×C19Q8211yescharacteristic
112C22×Q8—191no—
113C22×Q8—191no—
114C2×C4⋊C4—192no—
115C2×C4⋊C4—192no—
116C2×C4⋊C4—192no—
117C2×C4⋊C4—192no—
118C2×C4⋊C4C2×D1912yes—
119C2×C4⋊C4C2×D1911yescharacteristic
120C2×C4⋊C4C2×D1911yescharacteristic
121C2×C42—192no—
122C2×C42—191no—
123C2×C42—192no—
124#95—192no—
125#95—192no—
126#95—191no—
127#95—192no—
128#95—192no—
129#95—192no—
130#95—192no—
131#95C2×D1911yescharacteristic
132#95C2×D1912yes—
133C19#258611yescharacteristic, complemented, Sylow
134C2×Q8—384no—
135C2×Q8—382no—
136C2×Q8—761no—
137C2×Q8—761no—
138C2×Q8—761no—
139C22×C4—192no—
140C22×C4—192no—
141C22×C4—192no—
142C22×C4—192no—
143C22×C4C22×D1911yescharacteristic
144C22×C4C22×D1911yescharacteristic
145C22×C4C22×D1912yes—
146C22×C4C22×D1911yescharacteristic
147C22×C4C22×D1912yes—
148C4⋊C4—24no—
149C4⋊C4—41no—
150C4⋊C4—41no—
151C4⋊C4—198no—
152C4⋊C4—384no—
153C4⋊C4—762no—
154C4⋊C4—762no—
155C42—384no—
156C42—761no—
157C42—762no—
158C23C23×D1911yescharacteristic
159Q8—764no—
160Q8—764no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—194no—
173C2×C4—194no—
174C2×C4—194no—
175C2×C4—382no—
176C2×C4—382no—
177C2×C4—382no—
178C2×C4—382no—
179C2×C4—382no—
180C2×C4—382no—
181C2×C4—382no—
182C2×C4—382no—
183C2×C4—382no—
184C2×C4#6454312yes—
185C2×C4Q8×D1914yes—
186C22C2×#6454311yescharacteristic
187C22#1059743011yescharacteristic
188C22C2×Q8×D1912yes—
189C22#41×D1912yes—
190C22#1059743511yescharacteristic
191C4—24no—
192C4—22no—
193C4—42no—
194C4—41no—
195C4—41no—
196C4—384no—
197C4—384no—
198C4—384no—
199C4—762no—
200C2#1192709612yes—
201C2#1192713111yescharacteristic
202C2#1192722211yescharacteristic
203C2#1192725012yes—
204C2#1192727411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC19×#398C2
hypercenter#398D19
hypocenterC19#2586
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
48. C4⋊Dic19Q8semidirect
133. C19#2586semidirect

Maximal subgroups

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

subgroupindex
#119264642
#119264492
#119264482
#119264392
#119264292
#119264272
C4⋊C4×Dic192
C19×#3982
#258619