Finite Group Databasebeta

← #14569753

Subgroups — #14569753

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×#10597390C211yesmaximal, characteristic
2C2×#10597335C211yesmaximal, characteristic
3#11926478C212yesmaximal
4#11926477C212yesmaximal
5#11926465C211yesmaximal, characteristic
6#11926464C211yesmaximal, characteristic
7#11926463C211yesmaximal, characteristic
8#11926413C212yesmaximal
9#11926408C212yesmaximal
10#11926389C211yesmaximal, characteristic
11C19×#395C211yesmaximal, characteristic
12C22×Q8×C19C2211yescharacteristic
13C22×Dic38C2211yescharacteristic
14C2×C4⋊C4×C19C2211yescharacteristic
15C2×C4⋊C4×C19C2212yes—
16#10597390—24no—
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×Dic19⋊C4C2212yes—
27C2×C4×Dic19C2211yescharacteristic
28C2×C4×Dic19C2212yes—
29#10597335—24no—
30C19×#95C2211yescharacteristic
31C19×#95C2212yes—
32C19⋊#95C2211yescharacteristic
33C19⋊#95C2212yes—
34C19⋊#95C2212yes—
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C2×Q8×C19—22no—
38C2×Q8×C19—42no—
39C22×C4×C19C2311yescharacteristic
40C22×C4×C19C2312yes—
41C22×C4×C19C2311yescharacteristic
42C22×C4×C19C2311yescharacteristic
43C22×C4×C19C2312yes—
44C22×Dic19C2312yes—
45C22×Dic19C2311yescharacteristic
46C22×Dic19C2311yescharacteristic
47C22×Dic19C2311yescharacteristic
48C22×Dic19C2312yes—
49C22×Dic19C2311yescharacteristic
50C2×Dic38—22no—
51C2×Dic38—42no—
52C4⋊C4×C19—22no—
53C4⋊C4×C19—42no—
54C4⋊Dic19—22no—
55C4⋊Dic19—42no—
56Dic19⋊C4—22no—
57Dic19⋊C4—24no—
58Dic19⋊C4—24no—
59Dic19⋊C4—22no—
60Dic19⋊C4—22no—
61Dic19⋊C4—22no—
62Dic19⋊C4—42no—
63Dic19⋊C4—42no—
64C4×Dic19D414yes—
65C4×Dic19Q818yescomplemented
66C23×C19C2411yescharacteristic
67Q8×C19—44no—
68C2×C4×C19—22no—
69C2×C4×C19—22no—
70C2×C4×C19—22no—
71C2×C4×C19—21no—
72C2×C4×C19—22no—
73C2×C4×C19—21no—
74C2×C4×C19—22no—
75C2×C4×C19—22no—
76C2×C4×C19—22no—
77C2×C4×C19—21no—
78C2×C4×C19—21no—
79C2×C4×C19C2×D412yes—
80C2×C4×C19C2×Q814yes—
81C2×Dic19—22no—
82C2×Dic19—21no—
83C2×Dic19—22no—
84C2×Dic19—21no—
85C2×Dic19—21no—
86C2×Dic19—21no—
87C2×Dic19—22no—
88C2×Dic19—22no—
89C2×Dic19—22no—
90C2×Dic19—22no—
91C2×Dic19—21no—
92C2×Dic19—21no—
93C2×Dic19C2×D412yes—
94C2×Dic19C2×D412yes—
95C2×Dic19C2×Q814yes—
96C2×Dic19C2×Q814yes—
97Dic38—44no—
98#2660—191nomaximal, Sylow
99C22×C19C22×D411yescharacteristic
100C22×C19C22×Q812yes—
101C22×C19H(5,𝔽2)12yes—
102C22×C192−1+411yescharacteristic
103C22×C192−1+411yescharacteristic
104C4×C19—22no—
105C4×C19—24no—
106C4×C19—41no—
107C4×C19—42no—
108C4×C19—41no—
109Dic19—22no—
110Dic19—24no—
111Dic19—42no—
112Dic19—41no—
113Dic19—41no—
114Dic19C4⋊Q814yes—
115C2×C4⋊Q8—191no—
116C2×#125—191no—
117#398—192no—
118#398—192no—
119#395—191no—
120#395—191no—
121#395—191no—
122#395D1911yescharacteristic
123#384—192no—
124#382—192no—
125#376—191no—
126C2×C19C2×C4⋊Q811yescharacteristic
127C2×C19#53511yescharacteristic
128C2×C19#53611yescharacteristic
129C2×C19#54412yes—
130C2×C19#54412yes—
131C22×Q8—191no—
132C22×Q8C2×D1911yescharacteristic
133C4⋊Q8—384no—
134#125—384no—
135C2×C4⋊C4—191no—
136C2×C4⋊C4—191no—
137C2×C4⋊C4—191no—
138C2×C4⋊C4—191no—
139C2×C4⋊C4—191no—
140C2×C4⋊C4—192no—
141C2×C4⋊C4—192no—
142C2×C4⋊C4—192no—
143C2×C4⋊C4—192no—
144C2×C4⋊C4—192no—
145C2×C4⋊C4C2×D1911yescharacteristic
146C2×C4⋊C4C2×D1912yes—
147C2×C42—191no—
148C2×C42—192no—
149#95—191no—
150#95—192no—
151#95—192no—
152#95—192no—
153#95—192no—
154#95C2×D1911yescharacteristic
155#95C2×D1912yes—
156C19#266011yescharacteristic, complemented, Sylow
157C2×Q8—22no—
158C2×Q8—42no—
159C2×Q8—382no—
160C2×Q8—762no—
161C22×C4—191no—
162C22×C4—192no—
163C22×C4—191no—
164C22×C4—191no—
165C22×C4—192no—
166C22×C4—191no—
167C22×C4C22×D1911yescharacteristic
168C22×C4C22×D1912yes—
169C22×C4C22×D1911yescharacteristic
170C22×C4C22×D1911yescharacteristic
171C22×C4C22×D1912yes—
172C4⋊C4—22no—
173C4⋊C4—42no—
174C4⋊C4—382no—
175C4⋊C4—382no—
176C4⋊C4—382no—
177C4⋊C4—384no—
178C4⋊C4—384no—
179C4⋊C4—382no—
180C4⋊C4—382no—
181C4⋊C4—762no—
182C4⋊C4—762no—
183C4⋊C4—762no—
184C42—194no—
185C42—198no—
186C23C23×D1911yescharacteristic
187Q8—44no—
188Q8—764no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—192no—
201C2×C4—194no—
202C2×C4—192no—
203C2×C4—194no—
204C2×C4—382no—
205C2×C4—381no—
206C2×C4—382no—
207C2×C4—381no—
208C2×C4—381no—
209C2×C4—381no—
210C2×C4—382no—
211C2×C4—382no—
212C2×C4—382no—
213C2×C4—382no—
214C2×C4—381no—
215C2×C4—381no—
216C2×C4D4×D1912yes—
217C2×C4Q8×D1914yes—
218C22C2×D4×D1911yescharacteristic
219C22#1059743012yes—
220C22C2×Q8×D1912yes—
221C22#1059743311yescharacteristic
222C22#1059743611yescharacteristic
223C4—22no—
224C4—24no—
225C4—42no—
226C4—41no—
227C4—41no—
228C4—194no—
229C4—382no—
230C4—384no—
231C4—762no—
232C4—761no—
233C4—761no—
234C2C4⋊Q8×D1911yescharacteristic
235C2#1192710911yescharacteristic
236C2#1192711711yescharacteristic
237C2#1192717112yes—
238C2#1192717312yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC19×#395C2
hypercenter#395D19
hypocenterC19#2660
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #395

Complements

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

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

Maximal subgroups

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

subgroupindex
C2×#105973902
C2×#105973352
#119264782
#119264772
#119264652
#119264642
#119264632
#119264132
#119264082
#119263892
C19×#3952
#266019