Finite Group Databasebeta

← #14570009

Subgroups — #14570009

Order 2432.

592 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10597342C212yesmaximal, complemented
2C2×#10597392C212yesmaximal, complemented
3#11926468C212yesmaximal, complemented
4#11926466C212yesmaximal, complemented
5#11926464C211yesmaximal, characteristic, complemented
6#11926445C211yesmaximal, characteristic
7#11926441C212yesmaximal, complemented
8#11926422C212yesmaximal
9C19×#395C211yesmaximal, characteristic, complemented
10C22×Q8×C19C2211yescharacteristic
11C22×D76C2211yescharacteristic
12C22×C4×D19C2212yes—
13C22×Dic38C2211yescharacteristic
14C2×C4⋊C4×C19C2212yes—
15C2×C4⋊C4×C19C2211yescharacteristic
16#10597392—28no—
17C2×(C2×D19)⋊C4C2212yes—
18C2×(C2×D19)⋊C4C2212yes—
19C2×(C2×D19)⋊C4C2212yes—
20C2×(C2×D19)⋊C4C2212yes—
21C2×(C2×D19)⋊C4C2212yes—
22C2×C4⋊Dic19C2212yes—
23C2×Dic19⋊C4C2212yes—
24C2×Dic19⋊C4C2212yes—
25C2×Dic19⋊C4C2212yes—
26C2×Dic19⋊C4C2212yes—
27C2×C4×Dic19C2211yescharacteristic
28#10597342—28no—
29C19×#95C2212yes—
30C19×#95C2211yescharacteristic
31C19⋊#95C2212yes—
32C19⋊#95C2211yescharacteristic
33C23×D19C2312yes—
34C2×Q8×C19—24no—
35C2×Q8×C19—41no—
36C22×C4×C19C2311yescharacteristic
37C22×C4×C19C2311yescharacteristic
38C22×C4×C19C2312yes—
39C22×C4×C19C2312yes—
40C22×C4×C19C2311yescharacteristic
41C22×Dic19C2312yes—
42C22×Dic19C2312yes—
43C22×Dic19C2312yes—
44C2×D76—41no—
45C2×D76—41no—
46C2×D76Q814yescomplemented
47C2×C4×D19—24no—
48C2×C4×D19—24no—
49C2×C4×D19—42no—
50C2×Dic38—24no—
51C2×Dic38—41no—
52C4⋊C4×C19—24no—
53C4⋊C4×C19—41no—
54(C2×D19)⋊C4—24no—
55(C2×D19)⋊C4—24no—
56(C2×D19)⋊C4—24no—
57(C2×D19)⋊C4—24no—
58(C2×D19)⋊C4—42no—
59C4⋊Dic19—24no—
60Dic19⋊C4—24no—
61Dic19⋊C4—24no—
62Dic19⋊C4—42no—
63Dic19⋊C4D418yescomplemented
64C4×Dic19—41no—
65C23×C19C2411yescharacteristic
66C22×D19—22no—
67C22×D19—22no—
68C22×D19—22no—
69C22×D19—22no—
70C22×D19—22no—
71C22×D19—22no—
72C22×D19C2×Q814yes—
73Q8×C19—44no—
74C2×C4×C19—22no—
75C2×C4×C19—21no—
76C2×C4×C19—21no—
77C2×C4×C19—22no—
78C2×C4×C19—22no—
79C2×C4×C19—22no—
80C2×C4×C19—22no—
81C2×C4×C19—22no—
82C2×C4×C19—21no—
83C2×C4×C19—21no—
84C2×C4×C19—22no—
85C2×C4×C19C2×D414yes—
86C2×C4×C19C2×Q812yes—
87C2×Dic19—22no—
88C2×Dic19—22no—
89C2×Dic19—22no—
90C2×Dic19—22no—
91C2×Dic19—22no—
92C2×Dic19—22no—
93C2×Dic19—22no—
94C2×Dic19C2×D414yes—
95C2×Dic19C2×D414yes—
96D76—44no—
97C4×D19—48no—
98Dic38—44no—
99#2683—191nomaximal, Sylow
100C22×C19C22×D412yes—
101C22×C19C22×Q811yescharacteristic
102C22×C19H(5,𝔽2)11yescharacteristic
103C22×C19H(5,𝔽2)11yescharacteristic
104C22×C192−1+412yes—
105C2×D19—24no—
106C2×D19—24no—
107C2×D19—24no—
108C2×D19—42no—
109C2×D19—42no—
110C2×D19—42no—
111C2×D19—42no—
112C4×C19—22no—
113C4×C19—24no—
114C4×C19—42no—
115C4×C19—41no—
116C4×C19—41no—
117Dic19—24no—
118Dic19—24no—
119Dic19—42no—
120C2×C22⋊Q8—192no—
121C2×C22⋊Q8—192no—
122#396—192no—
123#396—192no—
124#395—191no—
125#395D1911yescharacteristic, complemented
126#390—191no—
127#389—192no—
128#386—192no—
129C2×C19#53712yes—
130C2×C19#54311yescharacteristic
131C2×C19D4211yescharacteristic
132C2×C19D4×Q812yes—
133C2×C19#56311yescharacteristic
134D19—44no—
135C22×Q8—191no—
136C22×Q8C2×D1911yescharacteristic
137C22×D4—191no—
138C23×C4—192no—
139C22⋊Q8—388no—
140C22⋊Q8—388no—
141C2×C4⋊C4—192no—
142C2×C4⋊C4—192no—
143C2×C4⋊C4—192no—
144C2×C4⋊C4—192no—
145C2×C4⋊C4—192no—
146C2×C4⋊C4C2×D1912yes—
147C2×C4⋊C4C2×D1911yescharacteristic
148C2×C22⋊C4—192no—
149C2×C22⋊C4—192no—
150C2×C22⋊C4—192no—
151C2×C22⋊C4—192no—
152C2×C22⋊C4—192no—
153C2×C42—191no—
154#95—192no—
155#95—191no—
156#95C2×D1912yes—
157#95C2×D1911yescharacteristic
158C19#268311yescharacteristic, complemented, Sylow
159C24—192no—
160C2×Q8—24no—
161C2×Q8—41no—
162C2×Q8—384no—
163C2×Q8—761no—
164C2×D4—194no—
165C2×D4—761no—
166C2×D4—761no—
167C22×C4—192no—
168C22×C4—192no—
169C22×C4—192no—
170C22×C4—384no—
171C22×C4—384no—
172C22×C4—762no—
173C22×C4C22×D1911yescharacteristic
174C22×C4C22×D1912yes—
175C22×C4C22×D1911yescharacteristic
176C22×C4C22×D1912yes—
177C22×C4C22×D1911yescharacteristic
178C4⋊C4—24no—
179C4⋊C4—41no—
180C4⋊C4—198no—
181C4⋊C4—384no—
182C4⋊C4—384no—
183C4⋊C4—384no—
184C4⋊C4—762no—
185C22⋊C4—384no—
186C22⋊C4—384no—
187C22⋊C4—384no—
188C22⋊C4—384no—
189C22⋊C4—762no—
190C42—761no—
191C23—194no—
192C23—382no—
193C23—382no—
194C23—382no—
195C23—382no—
196C23—382no—
197C23—382no—
198C23C23×D1911yescharacteristic
199Q8—44no—
200Q8—764no—
201D4—764no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—194no—
214C2×C4—194no—
215C2×C4—382no—
216C2×C4—382no—
217C2×C4—382no—
218C2×C4—382no—
219C2×C4—382no—
220C2×C4—382no—
221C2×C4—382no—
222C2×C4—768no—
223C2×C4D4×D1914yes—
224C2×C4Q8×D1912yes—
225C22—384no—
226C22—384no—
227C22—384no—
228C22—762no—
229C22—762no—
230C22—762no—
231C22—762no—
232C22C2×D4×D1912yes—
233C22#1059743011yescharacteristic
234C22C2×Q8×D1911yescharacteristic
235C22#1059743312yes—
236C22#1059743511yescharacteristic
237C4—22no—
238C4—24no—
239C4—42no—
240C4—41no—
241C4—41no—
242C4—384no—
243C4—384no—
244C4—762no—
245C2—764no—
246C2#1192712412yes—
247C2#1192716911yescharacteristic
248C2#1192717611yescharacteristic
249C2#1192720912yes—
250C2#1192729311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#395C2
prime radicalC22×D76C22
hypercenter#395D19
hypocenterC19#2683
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#10597342C2semidirect
2. C2×#10597392C2semidirect
3. #11926468C2semidirect
4. #11926466C2semidirect
5. #11926464C2semidirect
7. #11926441C2semidirect
9. C19×#395C2semidirect
46. C2×D76Q8semidirect
63. Dic19⋊C4D4semidirect
125. #395D19semidirect
158. C19#2683semidirect

Maximal subgroups

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

subgroupindex
C2×#105973422
C2×#105973922
#119264682
#119264662
#119264642
#119264452
#119264412
#119264222
C19×#3952
#268319