Finite Group Databasebeta

← #14570601

Subgroups — #14570601

Order 2432.

512 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10597324C212yesmaximal, complemented
2#11926486C212yesmaximal, complemented
3#11926474C211yesmaximal, characteristic, complemented
4#11926472C212yesmaximal, complemented
5#11926449C211yesmaximal, characteristic, complemented
6#11926438C212yesmaximal, complemented
7#11926424C212yesmaximal
8#11926419C212yesmaximal, complemented
9C19×#394C211yesmaximal, characteristic
10C22×D4×C19C2211yescharacteristic
11C23×Dic19C2212yes—
12C22×Dic38C2211yescharacteristic
13C2×C4⋊C4×C19C2211yescharacteristic
14C2×C22⋊C4×C19C2212yes—
15C2×C22⋊C4×C19C2212yes—
16C2×C22⋊Dic19C2212yes—
17C2×C22⋊Dic19C2212yes—
18C2×C22⋊Dic19C2212yes—
19C2×C4⋊Dic19C2212yes—
20C2×C4⋊Dic19C2211yescharacteristic
21C2×Dic19⋊C4C2212yes—
22C2×Dic19⋊C4C2212yes—
23C2×C4×Dic19C2211yescharacteristic
24#10597324—28no—
25C19×#95C2211yescharacteristic
26C19⋊#95C2212yes—
27C19⋊#95C2212yes—
28C19⋊#95C2212yes—
29C19⋊#95C2212yes—
30C19⋊#95C2212yes—
31C19⋊#95C2211yescharacteristic
32C24×C19C2312yes—
33C2×D4×C19—24no—
34C2×D4×C19—41no—
35C22×C4×C19C2311yescharacteristic
36C22×C4×C19C2312yes—
37C22×C4×C19C2311yescharacteristic
38C22×C4×C19C2311yescharacteristic
39C22×Dic19—24no—
40C22×Dic19—42no—
41C22×Dic19—42no—
42C22×Dic19C2312yes—
43C22×Dic19C2312yes—
44C22×Dic19C2312yes—
45C22×Dic19C2312yes—
46C2×Dic38—41no—
47C2×Dic38—41no—
48C2×Dic38D414yescomplemented
49C4⋊C4×C19—41no—
50C22⋊C4×C19—24no—
51C22⋊C4×C19—24no—
52C22⋊Dic19—24no—
53C22⋊Dic19—24no—
54C22⋊Dic19—42no—
55C4⋊Dic19—24no—
56C4⋊Dic19—41no—
57Dic19⋊C4—24no—
58Dic19⋊C4—24no—
59C4×Dic19—41no—
60C23×C19—22no—
61C23×C19—22no—
62C23×C19—22no—
63C23×C19—22no—
64C23×C19—22no—
65C23×C19—22no—
66C23×C19#4114yes—
67C23×C19C2411yescharacteristic
68D4×C19—44no—
69C2×C4×C19—21no—
70C2×C4×C19—21no—
71C2×C4×C19—22no—
72C2×C4×C19—22no—
73C2×C4×C19—22no—
74C2×C4×C19—22no—
75C2×C4×C19—21no—
76C2×C4×C19—21no—
77C2×C4×C19—22no—
78C2×C4×C19C2×D412yes—
79C2×Dic19—22no—
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—22no—
89C2×Dic19—22no—
90C2×Dic19—48no—
91C2×Dic19C2×D414yes—
92Dic38—44no—
93#2728—191nomaximal, Sylow
94C22×C19—24no—
95C22×C19—24no—
96C22×C19—24no—
97C22×C19—42no—
98C22×C19—42no—
99C22×C19—42no—
100C22×C19—42no—
101C22×C19C22×D411yescharacteristic
102C22×C19C2×#4112yes—
103C22×C19H(5,𝔽2)11yescharacteristic
104C22×C19H(5,𝔽2)11yescharacteristic
105C22×C192−1+412yes—
106C4×C19—22no—
107C4×C19—42no—
108C4×C19—41no—
109C4×C19—41no—
110Dic19—24no—
111Dic19—42no—
112Dic19—42no—
113Dic19—42no—
114C2×C22⋊Q8—192no—
115#400—192no—
116#398—191no—
117#397—192no—
118#394D1911yescharacteristic
119#391—191no—
120#388—192no—
121#386—192no—
122#385—192no—
123C2×C19—44no—
124C2×C19#53411yescharacteristic
125C2×C19#53912yes—
126C2×C19#54812yes—
127C2×C19#55111yescharacteristic
128C2×C19#56311yescharacteristic
129C22×Q8—191no—
130C22×D4C2×D1911yescharacteristic
131C23×C4—192no—
132C22⋊Q8—388no—
133C2×C4⋊C4—192no—
134C2×C4⋊C4—192no—
135C2×C4⋊C4—192no—
136C2×C4⋊C4—191no—
137C2×C4⋊C4C2×D1911yescharacteristic
138C2×C22⋊C4—192no—
139C2×C22⋊C4—192no—
140C2×C22⋊C4—192no—
141C2×C22⋊C4C2×D1912yes—
142C2×C22⋊C4C2×D1912yes—
143C2×C42—191no—
144#95—192no—
145#95—192no—
146#95—192no—
147#95—192no—
148#95—192no—
149#95—191no—
150#95C2×D1911yescharacteristic
151C19#272811yescharacteristic, complemented, Sylow
152C24C22×D1912yes—
153C2×Q8—194no—
154C2×Q8—761no—
155C2×Q8—761no—
156C2×D4—24no—
157C2×D4—41no—
158C22×C4—192no—
159C22×C4—192no—
160C22×C4—192no—
161C22×C4—192no—
162C22×C4—384no—
163C22×C4—762no—
164C22×C4—762no—
165C22×C4C22×D1911yescharacteristic
166C22×C4C22×D1911yescharacteristic
167C22×C4C22×D1912yes—
168C22×C4C22×D1911yescharacteristic
169C4⋊C4—41no—
170C4⋊C4—384no—
171C4⋊C4—384no—
172C4⋊C4—384no—
173C4⋊C4—761no—
174C22⋊C4—24no—
175C22⋊C4—24no—
176C22⋊C4—384no—
177C22⋊C4—384no—
178C22⋊C4—762no—
179C42—761no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23—22no—
184C23—22no—
185C23—22no—
186C23#6454314yes—
187C23C23×D1911yescharacteristic
188Q8—764no—
189D4—44no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—194no—
200C2×C4—382no—
201C2×C4—382no—
202C2×C4—382no—
203C2×C4—382no—
204C2×C4—382no—
205C2×C4—382no—
206C2×C4—382no—
207C2×C4—382no—
208C2×C4—382no—
209C2×C4—382no—
210C2×C4—382no—
211C2×C4—768no—
212C2×C4D4×D1912yes—
213C22—24no—
214C22—24no—
215C22—24no—
216C22—42no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22C2×D4×D1911yescharacteristic
221C22C2×#6454312yes—
222C22#1059743011yescharacteristic
223C22#1059743511yescharacteristic
224C22#1059743612yes—
225C4—22no—
226C4—42no—
227C4—41no—
228C4—41no—
229C4—384no—
230C4—762no—
231C4—762no—
232C4—762no—
233C2—44no—
234C2#1192710211yescharacteristic
235C2#1192713812yes—
236C2#1192720012yes—
237C2#1192722511yescharacteristic
238C2#1192729411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#394C2
prime radicalC22×D4×C19C22
hypercenter#394D19
hypocenterC19#2728
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#10597324C2semidirect
2. #11926486C2semidirect
3. #11926474C2semidirect
4. #11926472C2semidirect
5. #11926449C2semidirect
6. #11926438C2semidirect
8. #11926419C2semidirect
48. C2×Dic38D4semidirect
151. C19#2728semidirect

Maximal subgroups

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

subgroupindex
C2×#105973242
#119264862
#119264742
#119264722
#119264492
#119264382
#119264242
#119264192
C19×#3942
#272819