Finite Group Databasebeta

← #14568625

Subgroups — #14568625

Order 2432.

540 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 177 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×#10597315C211yesmaximal, characteristic
2C2×#10597390C211yesmaximal, characteristic
3C2×#10597390C211yesmaximal, characteristic
4C2×#10597333C211yesmaximal, characteristic
5#11926478C214yesmaximal
6#11926449C211yesmaximal, characteristic
7#11926441C214yesmaximal
8C4×Dic19⋊C4C211yesmaximal, characteristic
9C19×#391C211yesmaximal, characteristic
10C22×Q8×C19C2211yescharacteristic
11C22×Dic38C2211yescharacteristic
12C22×Dic38C2211yescharacteristic
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×C42×C19C2211yescharacteristic
15#10597390—24no—
16#10597390—24no—
17C2×C4⋊Dic19C2214yes—
18C2×Dic19⋊C4C2212yes—
19C2×Dic19⋊C4C2214yes—
20C2×Dic19⋊C4C2212yes—
21C2×Dic19⋊C4C2212yes—
22C2×Dic19⋊C4C2212yes—
23C2×C4×Dic19C2211yescharacteristic
24C2×C4×Dic19C2212yes—
25C2×C4×Dic19C2211yescharacteristic
26#10597333—24no—
27#10597315—24no—
28C19×#95C2214yes—
29C19⋊#95C2212yes—
30C19⋊#95C2214yes—
31C2×Q8×C19—22no—
32C2×Q8×C19—22no—
33C2×Q8×C19—22no—
34C22×C4×C19C2312yes—
35C22×C4×C19C2312yes—
36C22×C4×C19C2312yes—
37C22×C4×C19C2311yescharacteristic
38C22×Dic19C2312yes—
39C22×Dic19C2312yes—
40C22×Dic19C2311yescharacteristic
41C22×Dic19C2312yes—
42C22×Dic19C2311yescharacteristic
43C2×Dic38—22no—
44C2×Dic38—22no—
45C2×Dic38—22no—
46C2×Dic38—22no—
47C2×Dic38—22no—
48C2×Dic38D414yes—
49C4⋊C4×C19—22no—
50C42×C19—22no—
51C4⋊Dic19—28no—
52Dic19⋊C4—28no—
53Dic19⋊C4—24no—
54Dic19⋊C4—24no—
55Dic19⋊C4—24no—
56Dic19⋊C4Q818yescomplemented
57C4×Dic19—22no—
58C4×Dic19—24no—
59C4×Dic19D414yes—
60C23×C19C2411yescharacteristic
61Q8×C19—44no—
62C2×C4×C19—22no—
63C2×C4×C19—22no—
64C2×C4×C19—22no—
65C2×C4×C19—22no—
66C2×C4×C19—22no—
67C2×C4×C19—22no—
68C2×C4×C19—24no—
69C2×C4×C19C2×D412yes—
70C2×C4×C19C2×D412yes—
71C2×C4×C19C2×Q814yes—
72C2×C4×C19#4112yes—
73C2×Dic19—22no—
74C2×Dic19—22no—
75C2×Dic19—22no—
76C2×Dic19—22no—
77C2×Dic19—22no—
78C2×Dic19—22no—
79C2×Dic19—22no—
80C2×Dic19—22no—
81C2×Dic19C2×D412yes—
82C2×Dic19C2×D414yes—
83C2×Dic19C2×D412yes—
84C2×Dic19C2×Q814yes—
85C2×Dic19C2×Q814yes—
86Dic38—28no—
87Dic38—44no—
88#2546—191nomaximal, Sylow
89C22×C19C22×D411yescharacteristic
90C22×C19C22×D411yescharacteristic
91C22×C19C22×Q812yes—
92C22×C19C2×#4111yescharacteristic
93C22×C192−1+412yes—
94C4×C19—24no—
95C4×C19—42no—
96C4×C19—42no—
97C4×C19#12114yes—
98Dic19—24no—
99Dic19—22no—
100Dic19—24no—
101Dic19—42no—
102Dic19C4⋊Q814yescomplemented
103C2×C4⋊Q8—191no—
104C2×C4⋊Q8—191no—
105C2×C4⋊Q8—191no—
106C2×C4×Q8—191no—
107#398—194no—
108#391—191no—
109#391D1911yescharacteristic
110#389—194no—
111C4×C4⋊C4—191no—
112C2×C19C2×#12111yescharacteristic
113C2×C19C2×C4⋊Q811yescharacteristic
114C2×C19#53611yescharacteristic
115C2×C19D4×Q812yes—
116C2×C19#55712yes—
117C22×Q8—191no—
118C22×Q8—191no—
119C22×Q8C2×D1911yescharacteristic
120C4⋊Q8—384no—
121C4⋊Q8—384no—
122C4⋊Q8—384no—
123C4×Q8—384no—
124C2×C4⋊C4—192no—
125C2×C4⋊C4—192no—
126C2×C4⋊C4—192no—
127C2×C4⋊C4—194no—
128C2×C4⋊C4—194no—
129C2×C4⋊C4—192no—
130C2×C4⋊C4C2×D1911yescharacteristic
131C2×C42—191no—
132C2×C42—192no—
133C2×C42—191no—
134C2×C42C2×D1911yescharacteristic
135#95—192no—
136#95—194no—
137#95C2×D1914yes—
138C19#254611yescharacteristic, complemented, Sylow
139C2×Q8—22no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8—194no—
143C2×Q8—382no—
144C2×Q8—382no—
145C2×Q8—382no—
146C2×Q8—382no—
147C2×Q8—382no—
148C22×C4—191no—
149C22×C4—192no—
150C22×C4—191no—
151C22×C4—192no—
152C22×C4—192no—
153C22×C4C22×D1912yes—
154C22×C4C22×D1912yes—
155C22×C4C22×D1912yes—
156C22×C4C22×D1911yescharacteristic
157C4⋊C4—22no—
158C4⋊C4—198no—
159C4⋊C4—384no—
160C4⋊C4—384no—
161C4⋊C4—384no—
162C4⋊C4—388no—
163C4⋊C4—388no—
164C42—22no—
165C42—194no—
166C42—384no—
167C42—382no—
168C23C23×D1911yescharacteristic
169Q8—44no—
170Q8—388no—
171Q8—764no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—24no—
179C2×C4—192no—
180C2×C4—194no—
181C2×C4—192no—
182C2×C4—194no—
183C2×C4—194no—
184C2×C4—382no—
185C2×C4—382no—
186C2×C4—382no—
187C2×C4—382no—
188C2×C4—382no—
189C2×C4—382no—
190C2×C4—382no—
191C2×C4—382no—
192C2×C4#6454112yes—
193C2×C4D4×D1912yes—
194C2×C4D4×D1912yes—
195C2×C4Q8×D1914yes—
196C22C2×#6454111yescharacteristic
197C22C2×D4×D1911yescharacteristic
198C22C2×D4×D1911yescharacteristic
199C22C2×Q8×D1912yes—
200C22#1059743612yes—
201C4—24no—
202C4—42no—
203C4—42no—
204C4—194no—
205C4—382no—
206C4—384no—
207C4—384no—
208C4—762no—
209C4#1059733014yes—
210C2C2×#1059733011yescharacteristic
211C2C4⋊Q8×D1911yescharacteristic
212C2#1192711411yescharacteristic
213C2#1192720712yes—
214C2#1192727212yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC19×#391C2
hypercenter#391D19
hypocenterC19#2546
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
56. Dic19⋊C4Q8semidirect
102. Dic19C4⋊Q8semidirect
138. C19#2546semidirect

Maximal subgroups

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

subgroupindex
C2×#105973152
C2×#105973902
C2×#105973332
#119264782
#119264492
#119264412
C4×Dic19⋊C42
C19×#3912
#254619