Finite Group Databasebeta

← #14569582

Subgroups — #14569582

Order 2432.

416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10597334C211yesmaximal, characteristic
2C2×#10597335C211yesmaximal, characteristic
3#11926486C212yesmaximal
4#11926485C212yesmaximal
5#11926484C211yesmaximal, characteristic
6#11926483C211yesmaximal, characteristic
7#11926482C211yesmaximal, characteristic
8#11926448C212yesmaximal
9#11926448C212yesmaximal
10#11926389C211yesmaximal, characteristic
11C19×#400C211yesmaximal, characteristic
12C22×Dic38C2212yes—
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×C4⋊C4×C19C2211yescharacteristic
15C2×C4⋊Dic19C2211yescharacteristic
16C2×C4⋊Dic19C2211yescharacteristic
17C2×Dic19⋊C4C2211yescharacteristic
18C2×Dic19⋊C4C2211yescharacteristic
19C2×Dic19⋊C4C2211yescharacteristic
20C2×Dic19⋊C4C2211yescharacteristic
21C2×Dic19⋊C4C2212yes—
22C2×C4×Dic19C2212yes—
23C2×C4×Dic19C2211yescharacteristic
24#10597335—24no—
25#10597334—24no—
26C19×#95C2211yescharacteristic
27C19×#95C2212yes—
28C19×#95C2212yes—
29C19⋊#95C2211yescharacteristic
30C19⋊#95C2212yes—
31C19⋊#95C2212yes—
32C19⋊#95C2212yes—
33C19⋊#95C2212yes—
34C19⋊#95C2212yes—
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C22×C4×C19C2312yes—
38C22×C4×C19C2311yescharacteristic
39C22×C4×C19C2311yescharacteristic
40C22×C4×C19C2312yes—
41C22×C4×C19C2311yescharacteristic
42C22×Dic19C2312yes—
43C22×Dic19C2312yes—
44C22×Dic19C2311yescharacteristic
45C22×Dic19C2311yescharacteristic
46C22×Dic19C2311yescharacteristic
47C22×Dic19C2311yescharacteristic
48C2×Dic38—24no—
49C2×Dic38—28no—
50C4⋊C4×C19—22no—
51C4⋊C4×C19—22no—
52C4⋊Dic19—22no—
53C4⋊Dic19—22no—
54Dic19⋊C4—22no—
55Dic19⋊C4—24no—
56Dic19⋊C4—22no—
57Dic19⋊C4—22no—
58Dic19⋊C4—22no—
59C4×Dic19—24no—
60C4×Dic19D414yes—
61C23×C19C2411yescharacteristic
62C2×C4×C19—22no—
63C2×C4×C19—21no—
64C2×C4×C19—21no—
65C2×C4×C19—22no—
66C2×C4×C19—22no—
67C2×C4×C19—24no—
68C2×C4×C19—21no—
69C2×C4×C19—21no—
70C2×C4×C19—22no—
71C2×C4×C19—22no—
72C2×C4×C19—22no—
73C2×C4×C19C2×D412yes—
74C2×Dic19—21no—
75C2×Dic19—21no—
76C2×Dic19—21no—
77C2×Dic19—21no—
78C2×Dic19—22no—
79C2×Dic19—22no—
80C2×Dic19—24no—
81C2×Dic19—21no—
82C2×Dic19—22no—
83C2×Dic19—22no—
84C2×Dic19—21no—
85C2×Dic19—22no—
86C2×Dic19C2×D412yes—
87C2×Dic19C2×D412yes—
88C2×Dic19#4114yes—
89Dic38—48no—
90#2642—191nomaximal, Sylow
91C22×C19C22×D411yescharacteristic
92C22×C19C2×#4112yes—
93C22×C192−1+411yescharacteristic
94C22×C192−1+412yes—
95C22×C192−1+411yescharacteristic
96C4×C19—22no—
97C4×C19—42no—
98C4×C19—41no—
99C4×C19—41no—
100C4×C19—42no—
101Dic19—22no—
102Dic19—42no—
103Dic19—41no—
104Dic19—41no—
105Dic19—42no—
106Dic19#12414yes—
107C2×C4⋊Q8—191no—
108C2×#125—191no—
109#400—191no—
110#400—191no—
111#400—191no—
112#400—192no—
113#400—192no—
114#400D1911yescharacteristic
115#391—192no—
116#391—192no—
117#376—191no—
118C2×C19C2×#12411yescharacteristic
119C2×C19#53611yescharacteristic
120C2×C19#53611yescharacteristic
121C2×C19#54112yes—
122C2×C19#54112yes—
123C22×Q8—192no—
124C4⋊Q8—384no—
125#125—384no—
126C2×C4⋊C4—191no—
127C2×C4⋊C4—191no—
128C2×C4⋊C4—191no—
129C2×C4⋊C4—191no—
130C2×C4⋊C4—191no—
131C2×C4⋊C4—192no—
132C2×C4⋊C4—191no—
133C2×C4⋊C4C2×D1911yescharacteristic
134C2×C4⋊C4C2×D1911yescharacteristic
135C2×C42—191no—
136C2×C42—192no—
137#95—192no—
138#95—191no—
139#95—192no—
140#95—192no—
141#95—192no—
142#95—192no—
143#95—192no—
144#95—192no—
145#95C2×D1911yescharacteristic
146#95C2×D1912yes—
147#95C2×D1912yes—
148C19#264211yescharacteristic, complemented, Sylow
149C2×Q8—384no—
150C2×Q8—388no—
151C22×C4—191no—
152C22×C4—191no—
153C22×C4—192no—
154C22×C4—191no—
155C22×C4—191no—
156C22×C4—192no—
157C22×C4C22×D1912yes—
158C22×C4C22×D1911yescharacteristic
159C22×C4C22×D1911yescharacteristic
160C22×C4C22×D1912yes—
161C22×C4C22×D1911yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—382no—
165C4⋊C4—382no—
166C4⋊C4—382no—
167C4⋊C4—384no—
168C4⋊C4—382no—
169C4⋊C4—382no—
170C4⋊C4—382no—
171C42—194no—
172C42—384no—
173C23C23×D1911yescharacteristic
174Q8—768no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—192no—
187C2×C4—194no—
188C2×C4—192no—
189C2×C4—381no—
190C2×C4—381no—
191C2×C4—381no—
192C2×C4—381no—
193C2×C4—382no—
194C2×C4—381no—
195C2×C4—382no—
196C2×C4—382no—
197C2×C4—384no—
198C2×C4—382no—
199C2×C4—381no—
200C2×C4—382no—
201C2×C4D4×D1912yes—
202C22C2×D4×D1911yescharacteristic
203C22#1059743311yescharacteristic
204C22#41×D1912yes—
205C22#1059743612yes—
206C22#1059743611yescharacteristic
207C4—22no—
208C4—42no—
209C4—41no—
210C4—41no—
211C4—42no—
212C4—194no—
213C4—382no—
214C4—762no—
215C4—761no—
216C4—761no—
217C4—762no—
218C2#124×D1911yescharacteristic
219C2#1192711611yescharacteristic
220C2#1192711711yescharacteristic
221C2#1192715112yes—
222C2#1192715312yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC19×#400C2
hypercenter#400D19
hypocenterC19#2642
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
148. C19#2642semidirect

Maximal subgroups

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

subgroupindex
C2×#105973342
C2×#105973352
#119264862
#119264852
#119264842
#119264832
#119264822
#119264482
#119263892
C19×#4002
#264219