Finite Group Databasebeta

← #14569024

Subgroups — #14569024

Order 2432.

468 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 169 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×C4×Dic38C211yesmaximal, characteristic
2#11926474C212yesmaximal
3#11926464C212yesmaximal
4#11926440C212yesmaximal
5#11926440C212yesmaximal
6#11926439C214yesmaximal
7C4×C4⋊Dic19C211yesmaximal, characteristic
8C2×C19×#125C211yesmaximal, characteristic
9C22×Dic38C2211yescharacteristic
10C19×#125—24no—
11C2×C4⋊C4×C19C2212yes—
12C2×C4⋊C4×C19C2211yescharacteristic
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×C4⋊C4×C19C2212yes—
15C2×C42×C19C2211yescharacteristic
16C2×C4⋊Dic19C2211yescharacteristic
17C2×C4⋊Dic19C2212yes—
18C2×Dic19⋊C4C2212yes—
19C2×Dic19⋊C4C2214yes—
20C2×Dic19⋊C4C2214yes—
21C2×C4×Dic19C2212yes—
22C2×C4×Dic19C2212yes—
23C4×Dic38—24no—
24C19⋊#95C2212yes—
25C19⋊#95C2214yes—
26C19⋊#95C2214yes—
27C22×C4×C19C2312yes—
28C22×C4×C19C2312yes—
29C22×C4×C19C2311yescharacteristic
30C22×C4×C19C2311yescharacteristic
31C22×C4×C19C2311yescharacteristic
32C22×Dic19C2312yes—
33C22×Dic19C2314yes—
34C22×Dic19C2312yes—
35C2×Dic38—22no—
36C2×Dic38—24no—
37C4⋊C4×C19—24no—
38C4⋊C4×C19—24no—
39C4⋊C4×C19—22no—
40C4⋊C4×C19—22no—
41C42×C19D414yes—
42C4⋊Dic19—22no—
43C4⋊Dic19Q818yescomplemented
44Dic19⋊C4—24no—
45Dic19⋊C4—28no—
46Dic19⋊C4—44no—
47C4×Dic19—24no—
48C4×Dic19—42no—
49C23×C19C2411yescharacteristic
50C2×C4×C19—22no—
51C2×C4×C19—21no—
52C2×C4×C19—21no—
53C2×C4×C19—22no—
54C2×C4×C19—22no—
55C2×C4×C19—24no—
56C2×C4×C19—22no—
57C2×C4×C19—22no—
58C2×C4×C19C2×D412yes—
59C2×C4×C19C2×D412yes—
60C2×C4×C19C2×D412yes—
61C2×C4×C19C2×Q814yes—
62C2×Dic19—22no—
63C2×Dic19—24no—
64C2×Dic19—22no—
65C2×Dic19—24no—
66C2×Dic19—22no—
67C2×Dic19—22no—
68C2×Dic19—22no—
69C2×Dic19C2×Q818yes—
70C2×Dic19#4114yes—
71Dic38—28no—
72#2584—191nomaximal, Sylow
73C22×C19C22×D411yescharacteristic
74C22×C19C22×Q812yes—
75C22×C19C2×#4112yes—
76C22×C19H(5,𝔽2)11yescharacteristic
77C22×C192−1+411yescharacteristic
78C4×C19—22no—
79C4×C19—22no—
80C4×C19—42no—
81C4×C19—42no—
82C4×C19C4⋊Q814yes—
83Dic19—24no—
84Dic19—28no—
85Dic19—42no—
86C2×#125D1911yescharacteristic
87C2×C4×Q8—191no—
88#398—192no—
89#395—192no—
90#389—194no—
91#389—192no—
92#389—192no—
93C4×C4⋊C4—191no—
94C2×C19#52511yescharacteristic
95C2×C19C2×C4⋊Q811yescharacteristic
96C2×C19#53711yescharacteristic
97C2×C19#55412yes—
98C2×C19#55712yes—
99C22×Q8—191no—
100#125—24no—
101C4×Q8—384no—
102C2×C4⋊C4—192no—
103C2×C4⋊C4—192no—
104C2×C4⋊C4—191no—
105C2×C4⋊C4—194no—
106C2×C4⋊C4—194no—
107C2×C4⋊C4C2×D1912yes—
108C2×C4⋊C4C2×D1911yescharacteristic
109C2×C4⋊C4C2×D1911yescharacteristic
110C2×C4⋊C4C2×D1912yes—
111C2×C42—192no—
112C2×C42—192no—
113C2×C42C2×D1911yescharacteristic
114#95—192no—
115#95—194no—
116#95—194no—
117C19#258411yescharacteristic, complemented, Sylow
118C2×Q8—384no—
119C2×Q8—382no—
120C22×C4—194no—
121C22×C4—192no—
122C22×C4—192no—
123C22×C4C22×D1912yes—
124C22×C4C22×D1912yes—
125C22×C4C22×D1911yescharacteristic
126C22×C4C22×D1911yescharacteristic
127C22×C4C22×D1911yescharacteristic
128C4⋊C4—24no—
129C4⋊C4—24no—
130C4⋊C4—22no—
131C4⋊C4—22no—
132C4⋊C4—198no—
133C4⋊C4—388no—
134C4⋊C4—384no—
135C4⋊C4—382no—
136C4⋊C4—764no—
137C42—384no—
138C42—762no—
139C42C22⋊D1914yes—
140C23C23×D1911yescharacteristic
141Q8—388no—
142C2×C4—22no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—24no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—198no—
151C2×C4—194no—
152C2×C4—384no—
153C2×C4—382no—
154C2×C4—384no—
155C2×C4—382no—
156C2×C4—382no—
157C2×C4—382no—
158C2×C4—382no—
159C2×C4Q8×D1914yes—
160C2×C4C2×C22⋊D1912yes—
161C2×C4C2×C22⋊D1912yes—
162C2×C4C2×C22⋊D1912yes—
163C22C2×Q8×D1912yes—
164C22#41×D1912yes—
165C22#1059743511yescharacteristic
166C22#1059743611yescharacteristic
167C22C22×C22⋊D1911yescharacteristic
168C4—22no—
169C4—22no—
170C4—42no—
171C4—42no—
172C4—384no—
173C4—388no—
174C4—762no—
175C4#1059739014yes—
176C2#1192705111yescharacteristic
177C2C2×#1059739011yescharacteristic
178C2#1192712211yescharacteristic
179C2#1192725012yes—
180C2#1192727112yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC2×C19×#125C2
hypercenterC2×#125D19
hypocenterC19#2584
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
43. C4⋊Dic19Q8semidirect
117. C19#2584semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic382
#119264742
#119264642
#119264402
#119264392
C4×C4⋊Dic192
C2×C19×#1252
#258419