Finite Group Databasebeta

← #14568996

Subgroups — #14568996

Order 2432.

468 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 151 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×Q8×Dic19C211yesmaximal, characteristic
2C2×#10597333C211yesmaximal, characteristic
3#11926484C211yesmaximal, characteristic
4#11926483C211yesmaximal, characteristic
5#11926463C211yesmaximal, characteristic
6#11926448C212yesmaximal
7#11926439C212yesmaximal
8#11926431C212yesmaximal
9#11926430C212yesmaximal
10#11926408C211yesmaximal, characteristic
11C19×#395C211yesmaximal, characteristic
12C22×Q8×C19C2211yescharacteristic
13C22×Dic38C2211yescharacteristic
14C2×C4⋊C4×C19C2212yes—
15C2×C4⋊C4×C19C2211yescharacteristic
16Q8×Dic19—24no—
17C2×C4⋊Dic19C2212yes—
18C2×C4⋊Dic19C2211yescharacteristic
19C2×Dic19⋊C4C2212yes—
20C2×Dic19⋊C4C2212yes—
21C2×Dic19⋊C4C2211yescharacteristic
22C2×Dic19⋊C4C2211yescharacteristic
23C2×C4×Dic19C2211yescharacteristic
24C2×C4×Dic19C2211yescharacteristic
25C2×C4×Dic19C2212yes—
26C2×C4×Dic19C2211yescharacteristic
27#10597333—24no—
28C19×#95C2211yescharacteristic
29C19×#95C2212yes—
30C19⋊#95C2212yes—
31C19⋊#95C2211yescharacteristic
32C19⋊#95C2212yes—
33C19⋊#95C2212yes—
34C19⋊#95C2212yes—
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C2×Q8×C19—22no—
38C2×Q8×C19—24no—
39C22×C4×C19C2311yescharacteristic
40C22×C4×C19C2312yes—
41C22×C4×C19C2311yescharacteristic
42C22×C4×C19C2311yescharacteristic
43C22×C4×C19C2312yes—
44C22×Dic19C2312yes—
45C22×Dic19C2312yes—
46C22×Dic19C2311yescharacteristic
47C22×Dic19C2311yescharacteristic
48C22×Dic19C2311yescharacteristic
49C22×Dic19C2311yescharacteristic
50C2×Dic38—22no—
51C2×Dic38—22no—
52C2×Dic38Q814yescomplemented
53C4⋊C4×C19—22no—
54C4⋊C4×C19—24no—
55C4⋊Dic19—22no—
56C4⋊Dic19—24no—
57Dic19⋊C4—22no—
58Dic19⋊C4—24no—
59Dic19⋊C4—22no—
60Dic19⋊C4—24no—
61C4×Dic19—24no—
62C4×Dic19—22no—
63C4×Dic19—22no—
64C4×Dic19D414yes—
65C23×C19C2411yescharacteristic
66Q8×C19—28no—
67C2×C4×C19—22no—
68C2×C4×C19—21no—
69C2×C4×C19—21no—
70C2×C4×C19—22no—
71C2×C4×C19—22no—
72C2×C4×C19—21no—
73C2×C4×C19—22no—
74C2×C4×C19—22no—
75C2×C4×C19—22no—
76C2×C4×C19—22no—
77C2×C4×C19C2×D412yes—
78C2×C4×C19C2×Q812yes—
79C2×C4×C19#4114yes—
80C2×Dic19—21no—
81C2×Dic19—21no—
82C2×Dic19—22no—
83C2×Dic19—21no—
84C2×Dic19—22no—
85C2×Dic19—22no—
86C2×Dic19—22no—
87C2×Dic19—22no—
88C2×Dic19—24no—
89C2×Dic19—22no—
90C2×Dic19C2×D412yes—
91C2×Dic19C2×D412yes—
92C2×Dic19C2×Q812yes—
93C2×Dic19C2×Q812yes—
94C2×Dic19#4112yes—
95Dic38—28no—
96#2581—191nomaximal, Sylow
97C22×C19C22×D411yescharacteristic
98C22×C19C22×Q811yescharacteristic
99C22×C19C2×#4112yes—
100C22×C19C2×#4111yescharacteristic
101C22×C192−1+412yes—
102C4×C19—22no—
103C4×C19—22no—
104C4×C19—24no—
105C4×C19—41no—
106C4×C19—42no—
107Dic19—22no—
108Dic19—22no—
109Dic19—41no—
110Dic19—42no—
111Dic19—42no—
112Dic19C22⋊Q814yes—
113C2×C4×Q8—191no—
114C2×C4×Q8—191no—
115#400—191no—
116#400—191no—
117#395—191no—
118#395D1911yescharacteristic
119#391—192no—
120#389—192no—
121#387—192no—
122#387—192no—
123#382—191no—
124C2×C19C2×C22⋊Q811yescharacteristic
125C2×C19#52511yescharacteristic
126C2×C19#53611yescharacteristic
127C2×C19#55612yes—
128C2×C19#55712yes—
129C22×Q8—191no—
130C22×Q8C2×D1911yescharacteristic
131C4×Q8—384no—
132C4×Q8—384no—
133C2×C4⋊C4—192no—
134C2×C4⋊C4—191no—
135C2×C4⋊C4—191no—
136C2×C4⋊C4—191no—
137C2×C4⋊C4—192no—
138C2×C4⋊C4—192no—
139C2×C4⋊C4C2×D1911yescharacteristic
140C2×C4⋊C4C2×D1912yes—
141C2×C42—191no—
142C2×C42—191no—
143C2×C42—191no—
144C2×C42—192no—
145#95—192no—
146#95—191no—
147#95—192no—
148#95—192no—
149#95—192no—
150#95—192no—
151#95—192no—
152#95C2×D1911yescharacteristic
153#95C2×D1912yes—
154C19#258111yescharacteristic, complemented, Sylow
155C2×Q8—22no—
156C2×Q8—24no—
157C2×Q8—194no—
158C2×Q8—382no—
159C2×Q8—382no—
160C22×C4—191no—
161C22×C4—191no—
162C22×C4—191no—
163C22×C4—192no—
164C22×C4—192no—
165C22×C4—191no—
166C22×C4C22×D1912yes—
167C22×C4C22×D1911yescharacteristic
168C22×C4C22×D1911yescharacteristic
169C22×C4C22×D1912yes—
170C22×C4C22×D1911yescharacteristic
171C4⋊C4—22no—
172C4⋊C4—24no—
173C4⋊C4—384no—
174C4⋊C4—382no—
175C4⋊C4—384no—
176C4⋊C4—382no—
177C4⋊C4—382no—
178C4⋊C4—384no—
179C42—194no—
180C42—382no—
181C42—384no—
182C42—382no—
183C23C23×D1911yescharacteristic
184Q8—28no—
185Q8—388no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—192no—
197C2×C4—192no—
198C2×C4—192no—
199C2×C4—192no—
200C2×C4—192no—
201C2×C4—381no—
202C2×C4—382no—
203C2×C4—381no—
204C2×C4—381no—
205C2×C4—382no—
206C2×C4—382no—
207C2×C4—382no—
208C2×C4—384no—
209C2×C4—382no—
210C2×C4—382no—
211C2×C4D4×D1912yes—
212C2×C4#6454314yes—
213C2×C4Q8×D1912yes—
214C22C2×D4×D1911yescharacteristic
215C22C2×#6454312yes—
216C22C2×Q8×D1911yescharacteristic
217C22#1059743312yes—
218C22#41×D1911yescharacteristic
219C4—22no—
220C4—24no—
221C4—22no—
222C4—41no—
223C4—42no—
224C4—194no—
225C4—382no—
226C4—382no—
227C4—761no—
228C4—762no—
229C4—762no—
230C2C22⋊Q8×D1911yescharacteristic
231C2#1192705011yescharacteristic
232C2#1192711911yescharacteristic
233C2#1192726512yes—
234C2#1192726912yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC19×#395C2
hypercenter#395D19
hypocenterC19#2581
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
52. C2×Dic38Q8semidirect
154. C19#2581semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic192
C2×#105973332
#119264842
#119264832
#119264632
#119264482
#119264392
#119264312
#119264302
#119264082
C19×#3952
#258119