Finite Group Databasebeta

← #14571669

Subgroups — #14571669

Order 2432.

444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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×#10597342C211yesmaximal, characteristic
2C2×#10597392C211yesmaximal, characteristic
3#11926485C212yesmaximal, complemented
4#11926484C211yesmaximal, characteristic, complemented
5#11926483C211yesmaximal, characteristic, complemented
6#11926473C212yesmaximal
7#11926470C212yesmaximal
8#11926464C212yesmaximal, complemented
9#11926463C211yesmaximal, characteristic, complemented
10#11926406C211yesmaximal, characteristic
11C19×#395C211yesmaximal, characteristic, complemented
12C22×Q8×C19C2211yescharacteristic
13C22×C4×D19C2211yescharacteristic
14C22×Dic38C2211yescharacteristic
15C2×C4⋊C4×C19C2211yescharacteristic
16C2×C4⋊C4×C19C2212yes—
17#10597392—24no—
18C2×(C2×D19)⋊C4C2211yescharacteristic
19C2×(C2×D19)⋊C4C2211yescharacteristic
20C2×(C2×D19)⋊C4C2212yes—
21C2×(C2×D19)⋊C4C2212yes—
22C2×C4⋊Dic19C2211yescharacteristic
23C2×Dic19⋊C4C2211yescharacteristic
24C2×Dic19⋊C4C2211yescharacteristic
25C2×Dic19⋊C4C2212yes—
26C2×Dic19⋊C4C2212yes—
27#10597342—24no—
28C19×#95C2211yescharacteristic
29C19×#95C2212yes—
30C19⋊#95C2211yescharacteristic
31C19⋊#95C2212yes—
32C19⋊#95C2212yes—
33C19⋊#95C2212yes—
34C19⋊#95C2212yes—
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C23×D19C2311yescharacteristic
38C2×Q8×C19—22no—
39C2×Q8×C19—42no—
40C22×C4×C19C2311yescharacteristic
41C22×C4×C19C2312yes—
42C22×C4×C19C2312yes—
43C22×C4×C19C2311yescharacteristic
44C22×C4×C19C2311yescharacteristic
45C22×Dic19C2311yescharacteristic
46C22×Dic19C2312yes—
47C22×Dic19C2311yescharacteristic
48C22×Dic19C2312yes—
49C22×Dic19C2311yescharacteristic
50C2×C4×D19—42no—
51C2×C4×D19D414yes—
52C2×Dic38—22no—
53C2×Dic38—42no—
54C4⋊C4×C19—22no—
55C4⋊C4×C19—42no—
56(C2×D19)⋊C4—24no—
57(C2×D19)⋊C4—22no—
58(C2×D19)⋊C4—22no—
59(C2×D19)⋊C4—42no—
60C4⋊Dic19—22no—
61Dic19⋊C4—22no—
62Dic19⋊C4—24no—
63Dic19⋊C4—22no—
64Dic19⋊C4—42no—
65C23×C19C2411yescharacteristic
66C22×D19—22no—
67C22×D19—21no—
68C22×D19—22no—
69C22×D19—21no—
70C22×D19C2×D412yes—
71Q8×C19—44no—
72C2×C4×C19—22no—
73C2×C4×C19—21no—
74C2×C4×C19—22no—
75C2×C4×C19—21no—
76C2×C4×C19—22no—
77C2×C4×C19—22no—
78C2×C4×C19—22no—
79C2×C4×C19—22no—
80C2×C4×C19—21no—
81C2×C4×C19—22no—
82C2×C4×C19—21no—
83C2×C4×C19—22no—
84C2×C4×C19C2×D412yes—
85C2×Dic19—22no—
86C2×Dic19—21no—
87C2×Dic19—22no—
88C2×Dic19—21no—
89C2×Dic19—22no—
90C2×Dic19—22no—
91C2×Dic19—21no—
92C2×Dic19—24no—
93C2×Dic19—22no—
94C2×Dic19—22no—
95C2×Dic19—21no—
96C2×Dic19C2×D412yes—
97C4×D19—44no—
98Dic38—44no—
99#2817—191nomaximal, Sylow
100C22×C19C22×D411yescharacteristic
101C22×C19H(5,𝔽2)12yes—
102C22×C192−1+411yescharacteristic
103C22×C192−1+412yes—
104C22×C192−1+411yescharacteristic
105C2×D19—22no—
106C2×D19—22no—
107C2×D19—22no—
108C2×D19—42no—
109C2×D19—42no—
110C4×C19—22no—
111C4×C19—41no—
112C4×C19—42no—
113C4×C19—41no—
114C4×C19—42no—
115Dic19—22no—
116Dic19—41no—
117Dic19—41no—
118Dic19—42no—
119Dic19—42no—
120C2×C22⋊Q8—191no—
121C2×C22⋊Q8—191no—
122#400—191no—
123#400—191no—
124#400—192no—
125#397—192no—
126#397—192no—
127#395—191no—
128#395—192no—
129#395D1911yescharacteristic, complemented
130#381—191no—
131C2×C19#53411yescharacteristic
132C2×C19#53611yescharacteristic
133C2×C19#53611yescharacteristic
134C2×C19#56312yes—
135C2×C19#56312yes—
136D19—42no—
137C22×Q8—191no—
138C22×Q8C2×D1911yescharacteristic
139C23×C4—191no—
140C22⋊Q8—384no—
141C22⋊Q8—384no—
142C2×C4⋊C4—192no—
143C2×C4⋊C4—191no—
144C2×C4⋊C4—191no—
145C2×C4⋊C4—191no—
146C2×C4⋊C4—192no—
147C2×C4⋊C4C2×D1911yescharacteristic
148C2×C4⋊C4C2×D1912yes—
149C2×C22⋊C4—191no—
150C2×C22⋊C4—192no—
151C2×C22⋊C4—191no—
152C2×C22⋊C4—192no—
153#95—192no—
154#95—191no—
155#95—192no—
156#95—192no—
157#95—192no—
158#95—192no—
159#95—192no—
160#95C2×D1911yescharacteristic
161#95C2×D1912yes—
162C19#281711yescharacteristic, complemented, Sylow
163C24—191no—
164C2×Q8—22no—
165C2×Q8—42no—
166C2×Q8—382no—
167C2×Q8—762no—
168C22×C4—191no—
169C22×C4—194no—
170C22×C4—192no—
171C22×C4—192no—
172C22×C4—191no—
173C22×C4—191no—
174C22×C4—762no—
175C22×C4C22×D1912yes—
176C22×C4C22×D1911yescharacteristic
177C22×C4C22×D1911yescharacteristic
178C22×C4C22×D1912yes—
179C22×C4C22×D1911yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—42no—
182C4⋊C4—382no—
183C4⋊C4—384no—
184C4⋊C4—382no—
185C4⋊C4—382no—
186C4⋊C4—762no—
187C22⋊C4—382no—
188C22⋊C4—382no—
189C22⋊C4—384no—
190C22⋊C4—762no—
191C23—192no—
192C23—382no—
193C23—381no—
194C23—382no—
195C23—381no—
196C23C23×D1911yescharacteristic
197Q8—44no—
198Q8—764no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—192no—
212C2×C4—382no—
213C2×C4—381no—
214C2×C4—382no—
215C2×C4—381no—
216C2×C4—382no—
217C2×C4—382no—
218C2×C4—381no—
219C2×C4—384no—
220C2×C4—382no—
221C2×C4—382no—
222C2×C4—381no—
223C2×C4—764no—
224C2×C4D4×D1912yes—
225C22—382no—
226C22—382no—
227C22—382no—
228C22—762no—
229C22—762no—
230C22C2×D4×D1911yescharacteristic
231C22#1059743012yes—
232C22#1059743311yescharacteristic
233C22#1059743312yes—
234C22#1059743611yescharacteristic
235C4—22no—
236C4—42no—
237C4—41no—
238C4—41no—
239C4—42no—
240C4—382no—
241C4—761no—
242C4—761no—
243C4—762no—
244C4—762no—
245C2—762no—
246C2#1192710411yescharacteristic
247C2#1192711711yescharacteristic
248C2#1192711911yescharacteristic
249C2#1192729312yes—
250C2#1192729512yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#395C2
prime radicalC23×D19C23
hypercenter#395D19
hypocenterC19#2817
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
3. #11926485C2semidirect
4. #11926484C2semidirect
5. #11926483C2semidirect
8. #11926464C2semidirect
9. #11926463C2semidirect
11. C19×#395C2semidirect
129. #395D19semidirect
162. C19#2817semidirect

Maximal subgroups

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

subgroupindex
C2×#105973422
C2×#105973922
#119264852
#119264842
#119264832
#119264732
#119264702
#119264642
#119264632
#119264062
C19×#3952
#281719