Finite Group Databasebeta

← #14568587

Subgroups — #14568587

Order 2432.

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

normal subgroups only

This group has 676 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×#10597334C211yesmaximal, characteristic, complemented
2C2×#10597342C214yesmaximal, complemented
3C2×#10597339C211yesmaximal, characteristic
4#11926479C214yesmaximal, complemented
5#11926446C211yesmaximal, characteristic
6#11926445C211yesmaximal, characteristic
7#11926413C211yesmaximal, characteristic, complemented
8C4×Dic19⋊C4C211yesmaximal, characteristic, complemented
9C19×#384C211yesmaximal, characteristic, complemented
10C22×D76C2211yescharacteristic
11C22×C4×D19C2212yes—
12C22×Dic38C2212yes—
13C2×C4⋊C4×C19C2214yes—
14C2×C4⋊C4×C19C2211yescharacteristic
15C2×C4⋊C4×C19C2211yescharacteristic
16C2×C42×C19C2211yescharacteristic
17C2×(C2×D19)⋊C4C2214yes—
18C2×(C2×D19)⋊C4C2214yes—
19C2×(C2×D19)⋊C4C2212yes—
20C2×C4⋊Dic19C2211yescharacteristic
21C2×Dic19⋊C4C2214yes—
22C2×Dic19⋊C4C2212yes—
23C2×Dic19⋊C4C2212yes—
24C2×C4×Dic19C2211yescharacteristic
25C2×C4×Dic19C2211yescharacteristic
26#10597342—216no—
27#10597339—24no—
28#10597334—24no—
29C19⋊#95C2212yes—
30C23×D19C2312yes—
31C22×C4×C19C2312yes—
32C22×C4×C19C2312yes—
33C22×C4×C19C2312yes—
34C22×C4×C19C2311yescharacteristic
35C22×Dic19C2312yes—
36C22×Dic19C2311yescharacteristic
37C22×Dic19C2312yes—
38C22×Dic19C2311yescharacteristic
39C2×D76—22no—
40C2×D76—22no—
41C2×D76Q814yescomplemented
42C2×C4×D19—24no—
43C2×C4×D19—28no—
44C2×Dic38—24no—
45C2×Dic38—28no—
46C4⋊C4×C19—22no—
47C4⋊C4×C19—22no—
48C4⋊C4×C19—28no—
49C42×C19—22no—
50(C2×D19)⋊C4—28no—
51(C2×D19)⋊C4—24no—
52(C2×D19)⋊C4—28no—
53C4⋊Dic19—22no—
54Dic19⋊C4—24no—
55Dic19⋊C4—28no—
56Dic19⋊C4D418yescomplemented
57C4×Dic19—22no—
58C4×Dic19D414yes—
59C23×C19C2411yescharacteristic
60C22×D19—24no—
61C22×D19—22no—
62C22×D19—22no—
63C22×D19—24no—
64C22×D19C2×Q814yes—
65C2×C4×C19—22no—
66C2×C4×C19—22no—
67C2×C4×C19—22no—
68C2×C4×C19—24no—
69C2×C4×C19—24no—
70C2×C4×C19—22no—
71C2×C4×C19C2×D414yes—
72C2×C4×C19C2×D412yes—
73C2×C4×C19C2×Q812yes—
74C2×C4×C19#4112yes—
75C2×Dic19—22no—
76C2×Dic19—22no—
77C2×Dic19—22no—
78C2×Dic19—22no—
79C2×Dic19—24no—
80C2×Dic19C2×D412yes—
81C2×Dic19C2×D414yes—
82C2×Dic19C2×D412yes—
83C2×Dic19C2×D414yes—
84D76—28no—
85C4×D19—48no—
86Dic38—48no—
87#2542—191nomaximal, Sylow
88C22×C19C22×D411yescharacteristic
89C22×C19C22×D412yes—
90C22×C19C22×Q811yescharacteristic
91C22×C19C2×#4111yescharacteristic
92C22×C192−1+412yes—
93C2×D19—24no—
94C2×D19—28no—
95C2×D19—42no—
96C2×D19—42no—
97C2×D19—44no—
98C4×C19—24no—
99C4×C19—42no—
100C4×C19—42no—
101C4×C19C22⋊Q814yescomplemented
102Dic19—22no—
103Dic19—24no—
104Dic19—42no—
105Dic19#12714yes—
106C2×C4⋊Q8—191no—
107C2×C22⋊Q8—194no—
108C2×C4×D4—191no—
109#399—194no—
110#390—191no—
111#390—191no—
112#384—191no—
113#384D1911yescharacteristic, complemented
114C4×C4⋊C4—191no—
115C2×C19C2×C22⋊Q811yescharacteristic
116C2×C19C2×#12711yescharacteristic
117C2×C19#53611yescharacteristic
118C2×C19#54712yes—
119C2×C19D4×Q812yes—
120D19—44no—
121C22×Q8—192no—
122C22×D4—191no—
123C23×C4—192no—
124C4⋊Q8—384no—
125C22⋊Q8—3816no—
126C4×D4—384no—
127C2×C4⋊C4—192no—
128C2×C4⋊C4—194no—
129C2×C4⋊C4—191no—
130C2×C4⋊C4—192no—
131C2×C4⋊C4C2×D1911yescharacteristic
132C2×C4⋊C4C2×D1914yes—
133C2×C4⋊C4C2×D1911yescharacteristic
134C2×C22⋊C4—192no—
135C2×C22⋊C4—194no—
136C2×C22⋊C4—194no—
137C2×C42—191no—
138C2×C42—191no—
139C2×C42C2×D1911yescharacteristic
140#95—192no—
141C19#254211yescharacteristic, complemented, Sylow
142C24—192no—
143C2×Q8—388no—
144C2×Q8—384no—
145C2×D4—194no—
146C2×D4—382no—
147C2×D4—382no—
148C22×C4—191no—
149C22×C4—191no—
150C22×C4—192no—
151C22×C4—192no—
152C22×C4—384no—
153C22×C4—388no—
154C22×C4C22×D1912yes—
155C22×C4C22×D1912yes—
156C22×C4C22×D1912yes—
157C22×C4C22×D1911yescharacteristic
158C4⋊C4—22no—
159C4⋊C4—28no—
160C4⋊C4—22no—
161C4⋊C4—198no—
162C4⋊C4—388no—
163C4⋊C4—384no—
164C4⋊C4—382no—
165C22⋊C4—384no—
166C22⋊C4—388no—
167C22⋊C4—388no—
168C42—22no—
169C42—194no—
170C42—382no—
171C23—194no—
172C23—382no—
173C23—384no—
174C23—382no—
175C23—384no—
176C23C23×D1911yescharacteristic
177Q8—768no—
178D4—388no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—24no—
184C2×C4—22no—
185C2×C4—192no—
186C2×C4—194no—
187C2×C4—192no—
188C2×C4—194no—
189C2×C4—382no—
190C2×C4—382no—
191C2×C4—382no—
192C2×C4—384no—
193C2×C4—382no—
194C2×C4—768no—
195C2×C4#6454112yes—
196C2×C4D4×D1914yes—
197C2×C4D4×D1912yes—
198C2×C4Q8×D1912yes—
199C22—384no—
200C22—388no—
201C22—762no—
202C22—762no—
203C22—764no—
204C22C2×#6454111yescharacteristic
205C22C2×D4×D1911yescharacteristic
206C22C2×D4×D1912yes—
207C22C2×Q8×D1911yescharacteristic
208C22#1059743312yes—
209C4—24no—
210C4—42no—
211C4—42no—
212C4—194no—
213C4—382no—
214C4—384no—
215C4—762no—
216C4#1059734214yescomplemented
217C2—764no—
218C2C2×#1059734211yescharacteristic
219C2#127×D1911yescharacteristic
220C2#1192711911yescharacteristic
221C2#1192719512yes—
222C2#1192720912yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#384C2
prime radicalC22×D76C22
hypercenter#384D19
hypocenterC19#2542
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
1. C2×#10597334C2semidirect
2. C2×#10597342C2semidirect
4. #11926479C2semidirect
7. #11926413C2semidirect
8. C4×Dic19⋊C4C2semidirect
9. C19×#384C2semidirect
41. C2×D76Q8semidirect
56. Dic19⋊C4D4semidirect
101. C4×C19C22⋊Q8semidirect
113. #384D19semidirect
141. C19#2542semidirect
216. C4#10597342semidirect

Maximal subgroups

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

subgroupindex
C2×#105973342
C2×#105973422
C2×#105973392
#119264792
#119264462
#119264452
#119264132
C4×Dic19⋊C42
C19×#3842
#254219