Finite Group Databasebeta

← #14566798

Subgroups — #14566798

Order 2432.

464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 173 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×#10597370C211yesmaximal, characteristic
2#11926448C212yesmaximal, complemented
3#11926439C212yesmaximal, complemented
4#11926438C212yesmaximal
5#11926432C212yesmaximal
6#11926427C212yesmaximal, complemented
7#11926425C212yesmaximal, complemented
8#11926407C211yesmaximal, characteristic
9C19×#380C211yesmaximal, characteristic
10C23×C4×C19C2211yescharacteristic
11C22×Dic38C2211yescharacteristic
12C2×C4⋊C4×C19C2212yes—
13C2×C22⋊C4×C19C2211yescharacteristic
14C2×C22⋊C4×C19C2211yescharacteristic
15C2×C22⋊Dic19C2212yes—
16C2×C22⋊Dic19C2212yes—
17C2×C4⋊Dic19C2211yescharacteristic
18#10597370C418yescomplemented
19C2×Dic19⋊C4C2212yes—
20C2×Dic19⋊C4C2212yes—
21C2×Dic19⋊C4C2212yes—
22C2×C4×Dic19C2212yes—
23C2×C4×Dic19C2212yes—
24C19×#95C2212yes—
25C19⋊#95C2211yescharacteristic
26C19⋊#95C2212yes—
27C19⋊#95C2211yescharacteristic
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C19⋊#95C2212yes—
32C24×C19C2311yescharacteristic
33C22×C4×C19—42no—
34C22×C4×C19C2×C414yes—
35C22×C4×C19C2312yes—
36C22×C4×C19C2312yes—
37C22×C4×C19C2311yescharacteristic
38C22×C4×C19C2311yescharacteristic
39C22×Dic19C2312yes—
40C22×Dic19C2312yes—
41C22×Dic19C2312yes—
42C22×Dic19C2312yes—
43C2×Dic38—42no—
44C2×Dic38C2×C414yes—
45C4⋊C4×C19—42no—
46C22⋊C4×C19—41no—
47C22⋊C4×C19—41no—
48C22⋊Dic19—42no—
49C22⋊Dic19C2×C418yes—
50C4⋊Dic19C2×C414yes—
51Dic19⋊C4—42no—
52Dic19⋊C4—42no—
53Dic19⋊C4C2×C418yes—
54C4×Dic19—42no—
55C4×Dic19—42no—
56C23×C19—22no—
57C23×C19—21no—
58C23×C19—21no—
59C23×C19—22no—
60C23×C19C22×C412yes—
61C23×C19C2411yescharacteristic
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—22no—
69C2×C4×C19—22no—
70C2×C4×C19—44no—
71C2×C4×C19C22×C412yes—
72C2×C4×C19C22×C412yes—
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×Dic19—22no—
82C2×Dic19—22no—
83C2×Dic19C22×C414yes—
84C2×Dic19C22×C414yes—
85Dic38—44no—
86#2378—191nomaximal, Sylow
87C22×C19—22no—
88C22×C19—22no—
89C22×C19—22no—
90C22×C19—42no—
91C22×C19—42no—
92C22×C19C23×C411yescharacteristic
93C22×C19H(5,𝔽2)12yes—
94C22×C19H(5,𝔽2)11yescharacteristic
95C22×C192−1+411yescharacteristic
96C22×C192−1+412yes—
97C4×C19—22no—
98C4×C19—22no—
99C4×C19—42no—
100C4×C19—42no—
101Dic19—24no—
102Dic19—24no—
103Dic19—42no—
104Dic19—42no—
105C2×C22⋊Q8—191no—
106#391—192no—
107#389—192no—
108#388—192no—
109#388—192no—
110#387—192no—
111#387—192no—
112#381—191no—
113#380D1911yescharacteristic
114C2×C19—42no—
115C2×C19#51811yescharacteristic
116C2×C19#51911yescharacteristic
117C2×C19#52011yescharacteristic
118C2×C19#56212yes—
119C2×C19#56312yes—
120C22×Q8—191no—
121C23×C4C2×D1911yescharacteristic
122C22⋊Q8—198no—
123C2×C4⋊C4—191no—
124C2×C4⋊C4—192no—
125C2×C4⋊C4—192no—
126C2×C4⋊C4—192no—
127C2×C4⋊C4C2×D1912yes—
128C2×C22⋊C4—192no—
129C2×C22⋊C4—192no—
130C2×C22⋊C4C2×D1911yescharacteristic
131C2×C22⋊C4C2×D1911yescharacteristic
132C2×C42—192no—
133C2×C42—192no—
134#95—191no—
135#95—192no—
136#95—191no—
137#95—192no—
138#95—192no—
139#95—192no—
140#95—192no—
141#95C2×D1912yes—
142C19#237811yescharacteristic, complemented, Sylow
143C24C22×D1911yescharacteristic
144C2×Q8—194no—
145C2×Q8—762no—
146C22×C4—42no—
147C22×C4—192no—
148C22×C4—192no—
149C22×C4—192no—
150C22×C4—192no—
151C22×C4C4×D1914yes—
152C22×C4C22×D1912yes—
153C22×C4C22×D1912yes—
154C22×C4C22×D1911yescharacteristic
155C22×C4C22×D1911yescharacteristic
156C4⋊C4—42no—
157C4⋊C4—198no—
158C4⋊C4—194no—
159C4⋊C4—762no—
160C4⋊C4—762no—
161C22⋊C4—41no—
162C22⋊C4—41no—
163C22⋊C4—198no—
164C22⋊C4—762no—
165C42—762no—
166C42—762no—
167C23—21no—
168C23—22no—
169C23—21no—
170C23—22no—
171C23C2×C4×D1912yes—
172C23C23×D1911yescharacteristic
173Q8—764no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—44no—
183C2×C4—194no—
184C2×C4—194no—
185C2×C4—382no—
186C2×C4—382no—
187C2×C4—382no—
188C2×C4—382no—
189C2×C4—382no—
190C2×C4—382no—
191C2×C4—382no—
192C2×C4—382no—
193C2×C4—382no—
194C2×C4—382no—
195C2×C4C2×C4×D1912yes—
196C2×C4C2×C4×D1912yes—
197C22—22no—
198C22—22no—
199C22—22no—
200C22—42no—
201C22—42no—
202C22C22×C4×D1911yescharacteristic
203C22#1059743012yes—
204C22#1059743011yescharacteristic
205C22#1059743311yescharacteristic
206C22#1059743612yes—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—42no—
211C4—384no—
212C4—384no—
213C4—762no—
214C4—762no—
215C2—42no—
216C2#1192701711yescharacteristic
217C2#1192702111yescharacteristic
218C2#1192702511yescharacteristic
219C2#1192728912yes—
220C2#1192729512yes—
subgroupG/H
center, FrattiniC23C23×D19
commutatorC22×C19C23×C4
FittingC19×#380C2
socle, cosocleC23×C19C24
prime radicalC24×C19C23
hypercenter#380D19
hypocenterC19#2378
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. #11926448C2semidirect
3. #11926439C2semidirect
6. #11926427C2semidirect
7. #11926425C2semidirect
18. #10597370C4semidirect
142. C19#2378semidirect

Maximal subgroups

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

subgroupindex
C2×#105973702
#119264482
#119264392
#119264382
#119264322
#119264272
#119264252
#119264072
C19×#3802
#237819