Finite Group Databasebeta

← #14568108

Subgroups — #14568108

Order 2432.

544 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 161 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×#10597342C211yesmaximal, characteristic
2C2×C4⋊C4×D19C211yesmaximal, characteristic
3#11926476C211yesmaximal, characteristic, complemented
4#11926475C211yesmaximal, characteristic, complemented
5#11926474C211yesmaximal, characteristic, complemented
6#11926448C212yesmaximal, complemented
7#11926418C212yesmaximal
8#11926415C212yesmaximal
9#11926413C212yesmaximal, complemented
10#11926391C211yesmaximal, characteristic
11C19×#398C211yesmaximal, characteristic, complemented
12C22×C4×D19C2211yescharacteristic
13C22×C4×D19C2212yes—
14C22×Dic38C2211yescharacteristic
15C2×C4⋊C4×C19C2211yescharacteristic
16C2×C4⋊C4×C19C2211yescharacteristic
17C2×C4⋊C4×C19C2212yes—
18C2×(C2×D19)⋊C4C2211yescharacteristic
19C2×(C2×D19)⋊C4C2211yescharacteristic
20C2×(C2×D19)⋊C4C2212yes—
21C2×C4⋊Dic19C2211yescharacteristic
22C2×C4⋊Dic19C2212yes—
23C2×Dic19⋊C4C2211yescharacteristic
24C2×Dic19⋊C4C2211yescharacteristic
25C2×Dic19⋊C4C2212yes—
26C2×Dic19⋊C4C2212yes—
27C2×Dic19⋊C4C2212yes—
28C2×C4×Dic19C2212yes—
29#10597342—24no—
30C4⋊C4×D19—24no—
31C19×#95C2211yescharacteristic
32C19×#95C2212yes—
33C19⋊#95C2211yescharacteristic
34C19⋊#95C2212yes—
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C23×D19C2311yescharacteristic
38C22×C4×C19C2311yescharacteristic
39C22×C4×C19C2312yes—
40C22×C4×C19C2311yescharacteristic
41C22×C4×C19C2311yescharacteristic
42C22×C4×C19C2312yes—
43C22×Dic19C2311yescharacteristic
44C22×Dic19C2312yes—
45C22×Dic19C2311yescharacteristic
46C22×Dic19C2312yes—
47C22×Dic19C2311yescharacteristic
48C2×C4×D19—24no—
49C2×C4×D19—24no—
50C2×C4×D19—42no—
51C2×C4×D19—42no—
52C2×C4×D19D414yes—
53C2×Dic38—22no—
54C2×Dic38—24no—
55C4⋊C4×C19—22no—
56C4⋊C4×C19—22no—
57C4⋊C4×C19—42no—
58(C2×D19)⋊C4—22no—
59(C2×D19)⋊C4—22no—
60(C2×D19)⋊C4Q818yescomplemented
61C4⋊Dic19—22no—
62C4⋊Dic19—42no—
63Dic19⋊C4—22no—
64Dic19⋊C4—24no—
65Dic19⋊C4—22no—
66Dic19⋊C4—42no—
67Dic19⋊C4—42no—
68C4×Dic19—24no—
69C23×C19C2411yescharacteristic
70C22×D19—22no—
71C22×D19—21no—
72C22×D19—21no—
73C22×D19C2×D412yes—
74C22×D19C2×Q814yes—
75C2×C4×C19—22no—
76C2×C4×C19—22no—
77C2×C4×C19—22no—
78C2×C4×C19—21no—
79C2×C4×C19—22no—
80C2×C4×C19—21no—
81C2×C4×C19—22no—
82C2×C4×C19—21no—
83C2×C4×C19—22no—
84C2×C4×C19—21no—
85C2×C4×C19—22no—
86C2×C4×C19C2×D412yes—
87C2×C4×C19C2×Q814yes—
88C2×Dic19—22no—
89C2×Dic19—22no—
90C2×Dic19—21no—
91C2×Dic19—22no—
92C2×Dic19—21no—
93C2×Dic19—22no—
94C2×Dic19—21no—
95C2×Dic19—22no—
96C2×Dic19—21no—
97C2×Dic19—22no—
98C2×Dic19C2×D412yes—
99C2×Dic19C2×Q814yes—
100C2×Dic19#4114yes—
101C4×D19—28no—
102C4×D19—48no—
103Dic38—44no—
104#2502—191nomaximal, Sylow
105C22×C19C22×D411yescharacteristic
106C22×C19C22×Q812yes—
107C22×C19C2×#4112yes—
108C22×C19H(5,𝔽2)11yescharacteristic
109C22×C19H(5,𝔽2)11yescharacteristic
110C2×D19—22no—
111C2×D19—22no—
112C2×D19—24no—
113C2×D19—24no—
114C2×D19C4⋊Q814yes—
115C4×C19—22no—
116C4×C19—24no—
117C4×C19—41no—
118C4×C19—42no—
119C4×C19—41no—
120Dic19—24no—
121Dic19—41no—
122Dic19—42no—
123Dic19—41no—
124Dic19#12314yes—
125C2×C22⋊Q8—191no—
126C22×C4⋊C4—191no—
127#398—191no—
128#398—191no—
129#398—191no—
130#398D1911yescharacteristic, complemented
131#391—192no—
132#385—192no—
133#385—192no—
134#384—192no—
135C4×C22⋊C4—191no—
136C2×C19C2×#12311yescharacteristic
137C2×C19C2×C4⋊Q811yescharacteristic
138C2×C19#53511yescharacteristic
139C2×C19#55412yes—
140C2×C19#55412yes—
141D19—24no—
142C22×Q8—191no—
143C23×C4—191no—
144C23×C4—192no—
145C22⋊Q8—384no—
146C2×C4⋊C4—192no—
147C2×C4⋊C4—191no—
148C2×C4⋊C4—191no—
149C2×C4⋊C4—191no—
150C2×C4⋊C4—192no—
151C2×C4⋊C4—192no—
152C2×C4⋊C4—192no—
153C2×C4⋊C4—384no—
154C2×C4⋊C4C2×D1911yescharacteristic
155C2×C4⋊C4C2×D1911yescharacteristic
156C2×C4⋊C4C2×D1912yes—
157C2×C22⋊C4—192no—
158C2×C22⋊C4—191no—
159C2×C22⋊C4—191no—
160C2×C42—192no—
161#95—191no—
162#95—192no—
163#95—192no—
164#95—192no—
165#95C2×D1911yescharacteristic
166#95C2×D1912yes—
167C19#250211yescharacteristic, complemented, Sylow
168C24—191no—
169C2×Q8—382no—
170C2×Q8—384no—
171C22×C4—191no—
172C22×C4—192no—
173C22×C4—194no—
174C22×C4—191no—
175C22×C4—192no—
176C22×C4—191no—
177C22×C4—384no—
178C22×C4—384no—
179C22×C4—762no—
180C22×C4—762no—
181C22×C4C22×D1911yescharacteristic
182C22×C4C22×D1912yes—
183C22×C4C22×D1911yescharacteristic
184C22×C4C22×D1911yescharacteristic
185C22×C4C22×D1912yes—
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—42no—
189C4⋊C4—384no—
190C4⋊C4—382no—
191C4⋊C4—382no—
192C4⋊C4—382no—
193C4⋊C4—762no—
194C4⋊C4—762no—
195C4⋊C4—762no—
196C22⋊C4—198no—
197C22⋊C4—382no—
198C22⋊C4—382no—
199C42—384no—
200C23—192no—
201C23—194no—
202C23—381no—
203C23—382no—
204C23—381no—
205C23C23×D1911yescharacteristic
206Q8—764no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—192no—
219C2×C4—194no—
220C2×C4—194no—
221C2×C4—388no—
222C2×C4—382no—
223C2×C4—382no—
224C2×C4—381no—
225C2×C4—381no—
226C2×C4—382no—
227C2×C4—381no—
228C2×C4—382no—
229C2×C4—382no—
230C2×C4—381no—
231C2×C4—382no—
232C2×C4—768no—
233C2×C4D4×D1912yes—
234C2×C4Q8×D1914yes—
235C22—194no—
236C22—382no—
237C22—382no—
238C22—384no—
239C22—384no—
240C22C2×D4×D1911yescharacteristic
241C22#1059743011yescharacteristic
242C22C2×Q8×D1912yes—
243C22#41×D1912yes—
244C22#1059743511yescharacteristic
245C4—22no—
246C4—24no—
247C4—41no—
248C4—42no—
249C4—41no—
250C4—194no—
251C4—384no—
252C4—761no—
253C4—762no—
254C4—761no—
255C2—384no—
256C2#123×D1911yescharacteristic
257C2C4⋊Q8×D1911yescharacteristic
258C2#1192711011yescharacteristic
259C2#1192724812yes—
260C2#1192725012yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#398C2
prime radicalC23×D19C23
hypercenter#398D19
hypocenterC19#2502
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. #11926476C2semidirect
4. #11926475C2semidirect
5. #11926474C2semidirect
6. #11926448C2semidirect
9. #11926413C2semidirect
11. C19×#398C2semidirect
60. (C2×D19)⋊C4Q8semidirect
130. #398D19semidirect
167. C19#2502semidirect

Maximal subgroups

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

subgroupindex
C2×#105973422
C2×C4⋊C4×D192
#119264762
#119264752
#119264742
#119264482
#119264182
#119264152
#119264132
#119263912
C19×#3982
#250219