Finite Group Databasebeta

← #14570665

Subgroups — #14570665

Order 2432.

456 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 157 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
2#11926477C212yesmaximal
3#11926464C212yesmaximal
4#11926463C212yesmaximal
5#11926451C211yesmaximal, characteristic
6#11926439C212yesmaximal
7#11926428C212yesmaximal
8#11926425C212yesmaximal
9C2×C19×C4⋊Q8C211yesmaximal, characteristic
10C22×Q8×C19C2211yescharacteristic
11C22×Q8×C19C2211yescharacteristic
12C22×Dic38C2211yescharacteristic
13C19×C4⋊Q8—24no—
14C2×C4⋊C4×C19C2212yes—
15C2×C4⋊C4×C19C2212yes—
16C2×C42×C19C2211yescharacteristic
17#10597390—24no—
18C2×C4⋊Dic19C2211yescharacteristic
19C2×Dic19⋊C4C2212yes—
20C2×Dic19⋊C4C2212yes—
21C2×Dic19⋊C4C2212yes—
22C2×Dic19⋊C4C2212yes—
23C2×Dic19⋊C4C2212yes—
24C2×C4×Dic19C2211yescharacteristic
25C2×C4×Dic19C2211yescharacteristic
26C19⋊#95C2212yes—
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C19⋊#95C2212yes—
32C19⋊#95C2212yes—
33C2×Q8×C19—22no—
34C2×Q8×C19—41no—
35C2×Q8×C19—41no—
36C2×Q8×C19—41no—
37C2×Q8×C19—41no—
38C2×Q8×C19D414yes—
39C22×C4×C19C2312yes—
40C22×C4×C19C2311yescharacteristic
41C22×C4×C19C2311yescharacteristic
42C22×C4×C19C2311yescharacteristic
43C22×C4×C19C2312yes—
44C22×Dic19C2312yes—
45C22×Dic19C2312yes—
46C22×Dic19C2312yes—
47C22×Dic19C2312yes—
48C2×Dic38—22no—
49C2×Dic38—41no—
50C2×Dic38—41no—
51C4⋊C4×C19—24no—
52C4⋊C4×C19—24no—
53C42×C19—22no—
54C4⋊Dic19—41no—
55Dic19⋊C4—24no—
56Dic19⋊C4—24no—
57Dic19⋊C4—42no—
58Dic19⋊C4—42no—
59Dic19⋊C4Q818yescomplemented
60C4×Dic19—22no—
61C4×Dic19—41no—
62C23×C19C2411yescharacteristic
63Q8×C19—44no—
64Q8×C19—44no—
65C2×C4×C19—22no—
66C2×C4×C19—21no—
67C2×C4×C19—21no—
68C2×C4×C19—21no—
69C2×C4×C19—21no—
70C2×C4×C19—21no—
71C2×C4×C19—21no—
72C2×C4×C19—22no—
73C2×C4×C19—22no—
74C2×C4×C19—22no—
75C2×C4×C19—22no—
76C2×C4×C19C2×D412yes—
77C2×C4×C19C2×D412yes—
78C2×C4×C19C2×D412yes—
79C2×C4×C19C2×Q814yes—
80C2×Dic19—22no—
81C2×Dic19—22no—
82C2×Dic19—22no—
83C2×Dic19—22no—
84C2×Dic19—22no—
85C2×Dic19—22no—
86C2×Dic19—22no—
87C2×Dic19—22no—
88C2×Dic19—24no—
89C2×Dic19C2×Q814yes—
90C2×Dic19C2×Q814yes—
91Dic38—44no—
92#2734—191nomaximal, Sylow
93C22×C19C22×D411yescharacteristic
94C22×C19C22×Q812yes—
95C22×C19H(5,𝔽2)11yescharacteristic
96C22×C19H(5,𝔽2)11yescharacteristic
97C22×C192−1+412yes—
98C4×C19—22no—
99C4×C19—22no—
100C4×C19—22no—
101C4×C19—24no—
102C4×C19—42no—
103Dic19—24no—
104Dic19—24no—
105Dic19—42no—
106Dic19—42no—
107C2×C4⋊Q8—191no—
108C2×C4⋊Q8D1911yescharacteristic
109#398—192no—
110#395—192no—
111#395—192no—
112#391—191no—
113#389—192no—
114#387—192no—
115#387—192no—
116C2×C19#53411yescharacteristic
117C2×C19#54412yes—
118C2×C19D4×Q812yes—
119C2×C19Q8211yescharacteristic
120C2×C19#56311yescharacteristic
121C22×Q8—191no—
122C22×Q8C2×D1911yescharacteristic
123C22×Q8C2×D1911yescharacteristic
124C4⋊Q8—24no—
125C4⋊Q8—384no—
126C2×C4⋊C4—192no—
127C2×C4⋊C4—192no—
128C2×C4⋊C4—192no—
129C2×C4⋊C4—192no—
130C2×C4⋊C4—191no—
131C2×C4⋊C4—192no—
132C2×C4⋊C4C2×D1912yes—
133C2×C4⋊C4C2×D1912yes—
134C2×C42—191no—
135C2×C42—191no—
136C2×C42C2×D1911yescharacteristic
137#95—192no—
138#95—192no—
139#95—192no—
140#95—192no—
141#95—192no—
142#95—192no—
143#95—192no—
144C19#273411yescharacteristic, complemented, Sylow
145C2×Q8—22no—
146C2×Q8—41no—
147C2×Q8—41no—
148C2×Q8—41no—
149C2×Q8—41no—
150C2×Q8—382no—
151C2×Q8—761no—
152C2×Q8—761no—
153C2×Q8C22⋊D1914yes—
154C22×C4—192no—
155C22×C4—192no—
156C22×C4—192no—
157C22×C4—192no—
158C22×C4C22×D1912yes—
159C22×C4C22×D1912yes—
160C22×C4C22×D1911yescharacteristic
161C22×C4C22×D1911yescharacteristic
162C22×C4C22×D1911yescharacteristic
163C4⋊C4—24no—
164C4⋊C4—24no—
165C4⋊C4—198no—
166C4⋊C4—384no—
167C4⋊C4—384no—
168C4⋊C4—762no—
169C4⋊C4—762no—
170C4⋊C4—761no—
171C42—22no—
172C42—382no—
173C42—761no—
174C23C23×D1911yescharacteristic
175Q8—44no—
176Q8—44no—
177Q8—764no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—194no—
190C2×C4—194no—
191C2×C4—382no—
192C2×C4—382no—
193C2×C4—382no—
194C2×C4—382no—
195C2×C4—382no—
196C2×C4—382no—
197C2×C4—382no—
198C2×C4—384no—
199C2×C4—382no—
200C2×C4Q8×D1914yes—
201C2×C4C2×C22⋊D1912yes—
202C2×C4C2×C22⋊D1912yes—
203C2×C4C2×C22⋊D1912yes—
204C22#1059743011yescharacteristic
205C22#1059743011yescharacteristic
206C22C2×Q8×D1912yes—
207C22#1059743312yes—
208C22C22×C22⋊D1911yescharacteristic
209C4—22no—
210C4—22no—
211C4—22no—
212C4—24no—
213C4—42no—
214C4—384no—
215C4—384no—
216C4—762no—
217C4—762no—
218C2#1192710311yescharacteristic
219C2#1192717112yes—
220C2Q8×C22⋊D1912yes—
221C2#1192727411yescharacteristic
222C2#1192729311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, prime radical, cosocleC23×C19C24
FittingC2×C19×C4⋊Q8C2
hypercenterC2×C4⋊Q8D19
hypocenterC19#2734
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
59. Dic19⋊C4Q8semidirect
144. C19#2734semidirect

Maximal subgroups

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

subgroupindex
C2×#105973902
#119264772
#119264642
#119264632
#119264512
#119264392
#119264282
#119264252
C2×C19×C4⋊Q82
#273419