Finite Group Databasebeta

← #14569758

Subgroups — #14569758

Order 2432.

448 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 153 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
2C2×#10597335C211yesmaximal, characteristic
3#11926476C211yesmaximal, characteristic
4#11926475C211yesmaximal, characteristic
5#11926474C211yesmaximal, characteristic
6#11926465C212yesmaximal
7#11926464C212yesmaximal
8#11926413C212yesmaximal
9#11926408C212yesmaximal
10#11926389C211yesmaximal, characteristic
11C19×#398C211yesmaximal, characteristic
12C22×Dic38C2212yes—
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×C4⋊C4×C19C2211yescharacteristic
15C2×C4⋊C4×C19C2212yes—
16C2×C4⋊Dic19C2211yescharacteristic
17C2×C4⋊Dic19C2211yescharacteristic
18C2×C4⋊Dic19C2212yes—
19C2×Dic19⋊C4C2211yescharacteristic
20C2×Dic19⋊C4C2211yescharacteristic
21C2×Dic19⋊C4C2211yescharacteristic
22C2×Dic19⋊C4C2211yescharacteristic
23C2×Dic19⋊C4C2212yes—
24C2×Dic19⋊C4C2212yes—
25C2×Dic19⋊C4C2212yes—
26C2×C4×Dic19C2211yescharacteristic
27C2×C4×Dic19C2212yes—
28#10597335—24no—
29#10597334—24no—
30C19×#95C2211yescharacteristic
31C19×#95C2212yes—
32C19⋊#95C2212yes—
33C19⋊#95C2211yescharacteristic
34C19⋊#95C2212yes—
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C22×C4×C19C2311yescharacteristic
38C22×C4×C19C2312yes—
39C22×C4×C19C2311yescharacteristic
40C22×C4×C19C2311yescharacteristic
41C22×C4×C19C2312yes—
42C22×Dic19C2312yes—
43C22×Dic19C2311yescharacteristic
44C22×Dic19C2311yescharacteristic
45C22×Dic19C2311yescharacteristic
46C22×Dic19C2312yes—
47C22×Dic19C2311yescharacteristic
48C2×Dic38—24no—
49C2×Dic38—42no—
50C2×Dic38—42no—
51C4⋊C4×C19—22no—
52C4⋊C4×C19—22no—
53C4⋊C4×C19—42no—
54C4⋊Dic19—22no—
55C4⋊Dic19—22no—
56C4⋊Dic19—42no—
57Dic19⋊C4—22no—
58Dic19⋊C4—24no—
59Dic19⋊C4—22no—
60Dic19⋊C4—22no—
61Dic19⋊C4—22no—
62Dic19⋊C4—42no—
63Dic19⋊C4—42no—
64C4×Dic19D414yes—
65C4×Dic19Q818yescomplemented
66C23×C19C2411yescharacteristic
67C2×C4×C19—22no—
68C2×C4×C19—22no—
69C2×C4×C19—22no—
70C2×C4×C19—21no—
71C2×C4×C19—21no—
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×C19C2×D412yes—
79C2×C4×C19C2×Q814yes—
80C2×Dic19—22no—
81C2×Dic19—21no—
82C2×Dic19—21no—
83C2×Dic19—22no—
84C2×Dic19—21no—
85C2×Dic19—21no—
86C2×Dic19—22no—
87C2×Dic19—21no—
88C2×Dic19—22no—
89C2×Dic19—21no—
90C2×Dic19—22no—
91C2×Dic19—22no—
92C2×Dic19C2×D412yes—
93C2×Dic19C2×D412yes—
94C2×Dic19C2×Q814yes—
95C2×Dic19C2×Q814yes—
96Dic38—48no—
97#2660—191nomaximal, Sylow
98C22×C19C22×D411yescharacteristic
99C22×C19C22×Q812yes—
100C22×C19H(5,𝔽2)11yescharacteristic
101C22×C19H(5,𝔽2)11yescharacteristic
102C22×C192−1+412yes—
103C4×C19—22no—
104C4×C19—24no—
105C4×C19—42no—
106C4×C19—41no—
107C4×C19—41no—
108Dic19—22no—
109Dic19—24no—
110Dic19—42no—
111Dic19—41no—
112Dic19—41no—
113Dic19C4⋊Q814yes—
114C2×C4⋊Q8—191no—
115C2×#125—191no—
116#398—191no—
117#398—191no—
118#398—191no—
119#398D1911yescharacteristic
120#395—192no—
121#395—192no—
122#384—192no—
123#382—192no—
124#376—191no—
125C2×C19C2×C4⋊Q811yescharacteristic
126C2×C19#53511yescharacteristic
127C2×C19#53611yescharacteristic
128C2×C19#54412yes—
129C2×C19#54412yes—
130C22×Q8—192no—
131C4⋊Q8—384no—
132#125—384no—
133C2×C4⋊C4—191no—
134C2×C4⋊C4—191no—
135C2×C4⋊C4—191no—
136C2×C4⋊C4—191no—
137C2×C4⋊C4—191no—
138C2×C4⋊C4—192no—
139C2×C4⋊C4—191no—
140C2×C4⋊C4—192no—
141C2×C4⋊C4—192no—
142C2×C4⋊C4—192no—
143C2×C4⋊C4C2×D1911yescharacteristic
144C2×C4⋊C4C2×D1911yescharacteristic
145C2×C4⋊C4C2×D1912yes—
146C2×C42—191no—
147C2×C42—192no—
148#95—192no—
149#95—191no—
150#95—192no—
151#95—192no—
152#95—192no—
153#95C2×D1911yescharacteristic
154#95C2×D1912yes—
155C19#266011yescharacteristic, complemented, Sylow
156C2×Q8—384no—
157C2×Q8—762no—
158C2×Q8—762no—
159C22×C4—191no—
160C22×C4—192no—
161C22×C4—191no—
162C22×C4—191no—
163C22×C4—192no—
164C22×C4—191no—
165C22×C4C22×D1911yescharacteristic
166C22×C4C22×D1912yes—
167C22×C4C22×D1911yescharacteristic
168C22×C4C22×D1911yescharacteristic
169C22×C4C22×D1912yes—
170C4⋊C4—22no—
171C4⋊C4—22no—
172C4⋊C4—42no—
173C4⋊C4—382no—
174C4⋊C4—382no—
175C4⋊C4—382no—
176C4⋊C4—384no—
177C4⋊C4—382no—
178C4⋊C4—382no—
179C4⋊C4—382no—
180C4⋊C4—762no—
181C4⋊C4—762no—
182C4⋊C4—762no—
183C42—194no—
184C42—198no—
185C23C23×D1911yescharacteristic
186Q8—768no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—192no—
199C2×C4—194no—
200C2×C4—192no—
201C2×C4—194no—
202C2×C4—381no—
203C2×C4—382no—
204C2×C4—381no—
205C2×C4—382no—
206C2×C4—381no—
207C2×C4—381no—
208C2×C4—382no—
209C2×C4—381no—
210C2×C4—382no—
211C2×C4—381no—
212C2×C4—382no—
213C2×C4—382no—
214C2×C4D4×D1912yes—
215C2×C4Q8×D1914yes—
216C22C2×D4×D1911yescharacteristic
217C22#1059743011yescharacteristic
218C22C2×Q8×D1912yes—
219C22#1059743511yescharacteristic
220C22#1059743612yes—
221C4—22no—
222C4—24no—
223C4—42no—
224C4—41no—
225C4—41no—
226C4—194no—
227C4—382no—
228C4—384no—
229C4—762no—
230C4—761no—
231C4—761no—
232C2C4⋊Q8×D1911yescharacteristic
233C2#1192711011yescharacteristic
234C2#1192711611yescharacteristic
235C2#1192717312yes—
236C2#1192717412yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC19×#398C2
hypercenter#398D19
hypocenterC19#2660
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
65. C4×Dic19Q8semidirect
155. C19#2660semidirect

Maximal subgroups

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

subgroupindex
C2×#105973342
C2×#105973352
#119264762
#119264752
#119264742
#119264652
#119264642
#119264132
#119264082
#119263892
C19×#3982
#266019