Finite Group Databasebeta

← #14571648

Subgroups — #14571648

Order 2432.

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

normal subgroups only

This group has 478 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×#10597370C211yesmaximal, characteristic, complemented
2#11926477C212yesmaximal, complemented
3#11926474C211yesmaximal, characteristic, complemented
4#11926472C212yesmaximal, complemented
5#11926469C211yesmaximal, characteristic, complemented
6#11926467C212yesmaximal, complemented
7#11926464C211yesmaximal, characteristic, complemented
8#11926458C212yesmaximal
9#11926456C211yesmaximal, characteristic, complemented
10#11926404C211yesmaximal, characteristic, complemented
11C2×C19×#123C211yesmaximal, characteristic
12C22×D4×C19C2211yescharacteristic
13C23×C4×C19C2211yescharacteristic
14C22×Dic38C2211yescharacteristic
15C19×#123—24no—
16C2×C4⋊C4×C19C2211yescharacteristic
17C2×C4⋊C4×C19C2211yescharacteristic
18C2×C22⋊C4×C19C2211yescharacteristic
19C2×C22⋊C4×C19C2211yescharacteristic
20C2×C22⋊C4×C19C2211yescharacteristic
21C2×C22⋊Dic19C2212yes—
22C2×C22⋊Dic19C2212yes—
23C2×C22⋊Dic19C2212yes—
24C2×C22⋊Dic19C2212yes—
25C2×C4⋊Dic19C2211yescharacteristic
26C2×C4⋊Dic19C2212yes—
27#10597370—24no—
28C2×Dic19⋊C4C2212yes—
29C2×Dic19⋊C4C2212yes—
30C2×Dic19⋊C4C2212yes—
31C19⋊#95C2211yescharacteristic
32C19⋊#95C2211yescharacteristic
33C19⋊#95C2212yes—
34C19⋊#95C2212yes—
35C19⋊#95C2212yes—
36C19⋊#95C2212yes—
37C24×C19C2311yescharacteristic
38C24×C19C2311yescharacteristic
39C2×D4×C19—22no—
40C2×D4×C19—42no—
41C22×C4×C19—42no—
42C22×C4×C19D414yes—
43C22×C4×C19C2311yescharacteristic
44C22×C4×C19C2311yescharacteristic
45C22×C4×C19C2311yescharacteristic
46C22×C4×C19C2311yescharacteristic
47C22×C4×C19C2311yescharacteristic
48C22×Dic19C2312yes—
49C22×Dic19C2312yes—
50C22×Dic19C2312yes—
51C22×Dic19C2312yes—
52C2×Dic38—22no—
53C2×Dic38—42no—
54C4⋊C4×C19—22no—
55C4⋊C4×C19—22no—
56C22⋊C4×C19—22no—
57C22⋊C4×C19—22no—
58C22⋊C4×C19—22no—
59C22⋊Dic19—24no—
60C22⋊Dic19—42no—
61C22⋊Dic19—42no—
62C22⋊Dic19—42no—
63C4⋊Dic19—22no—
64C4⋊Dic19—42no—
65Dic19⋊C4—24no—
66Dic19⋊C4—42no—
67Dic19⋊C4—42no—
68C23×C19—21no—
69C23×C19—22no—
70C23×C19—22no—
71C23×C19—21no—
72C23×C19—21no—
73C23×C19—21no—
74C23×C19—22no—
75C23×C19—22no—
76C23×C19—21no—
77C23×C19C2×D412yes—
78C23×C19C2411yescharacteristic
79D4×C19—44no—
80C2×C4×C19—22no—
81C2×C4×C19—22no—
82C2×C4×C19—21no—
83C2×C4×C19—21no—
84C2×C4×C19—21no—
85C2×C4×C19—21no—
86C2×C4×C19—22no—
87C2×C4×C19—22no—
88C2×C4×C19—21no—
89C2×C4×C19—44no—
90C2×C4×C19C2×D412yes—
91C2×C4×C19C2×D412yes—
92C2×Dic19—22no—
93C2×Dic19—22no—
94C2×Dic19—22no—
95C2×Dic19—22no—
96C2×Dic19—22no—
97C2×Dic19—22no—
98C2×Dic19—22no—
99C2×Dic19—22no—
100C2×Dic19—22no—
101C2×Dic19—22no—
102C2×Dic19—22no—
103C2×Dic19—22no—
104Dic38—44no—
105#2814—191nomaximal, Sylow
106C22×C19—22no—
107C22×C19—22no—
108C22×C19—22no—
109C22×C19—42no—
110C22×C19—42no—
111C22×C19—41no—
112C22×C19—41no—
113C22×C19—41no—
114C22×C19—42no—
115C22×C19—42no—
116C22×C19C22×D411yescharacteristic
117C22×C19H(5,𝔽2)12yes—
118C22×C19H(5,𝔽2)11yescharacteristic
119C22×C192−1+412yes—
120C22×C192−1+411yescharacteristic
121C4×C19—22no—
122C4×C19—22no—
123C4×C19—41no—
124C4×C19—41no—
125C4×C19—41no—
126Dic19—42no—
127Dic19—42no—
128Dic19—42no—
129Dic19—42no—
130C2×#123D1911yescharacteristic
131C2×C22⋊Q8—191no—
132#398—191no—
133#398—192no—
134#397—191no—
135#397—192no—
136#396—192no—
137#395—191no—
138#394—192no—
139#393—191no—
140#380—191no—
141C2×C19—42no—
142C2×C19—81no—
143C2×C19#53411yescharacteristic
144C2×C19#53611yescharacteristic
145C2×C19#53711yescharacteristic
146C2×C19#56212yes—
147C2×C19#56312yes—
148C22×Q8—191no—
149C22×D4C2×D1911yescharacteristic
150C23×C4C2×D1911yescharacteristic
151#123—24no—
152C22⋊Q8—384no—
153C2×C4⋊C4—192no—
154C2×C4⋊C4—191no—
155C2×C4⋊C4—192no—
156C2×C4⋊C4—192no—
157C2×C4⋊C4—192no—
158C2×C4⋊C4C2×D1911yescharacteristic
159C2×C4⋊C4C2×D1911yescharacteristic
160C2×C22⋊C4—192no—
161C2×C22⋊C4—192no—
162C2×C22⋊C4—192no—
163C2×C22⋊C4—192no—
164C2×C22⋊C4C2×D1911yescharacteristic
165C2×C22⋊C4C2×D1911yescharacteristic
166C2×C22⋊C4C2×D1911yescharacteristic
167#95—191no—
168#95—191no—
169#95—192no—
170#95—192no—
171#95—192no—
172#95—192no—
173C19#281411yescharacteristic, complemented, Sylow
174C24C22×D1911yescharacteristic
175C24C22×D1911yescharacteristic
176C2×Q8—382no—
177C2×Q8—762no—
178C2×D4—22no—
179C2×D4—42no—
180C22×C4—42no—
181C22×C4—192no—
182C22×C4—192no—
183C22×C4—192no—
184C22×C4—192no—
185C22×C4C22⋊D1914yes—
186C22×C4C22×D1911yescharacteristic
187C22×C4C22×D1911yescharacteristic
188C22×C4C22×D1911yescharacteristic
189C22×C4C22×D1911yescharacteristic
190C22×C4C22×D1911yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—384no—
194C4⋊C4—382no—
195C4⋊C4—762no—
196C4⋊C4—762no—
197C4⋊C4—762no—
198C22⋊C4—22no—
199C22⋊C4—22no—
200C22⋊C4—22no—
201C22⋊C4—384no—
202C22⋊C4—762no—
203C22⋊C4—762no—
204C22⋊C4—762no—
205C23—22no—
206C23—21no—
207C23—22no—
208C23—21no—
209C23—22no—
210C23—21no—
211C23—21no—
212C23—22no—
213C23—21no—
214C23C2×C22⋊D1912yes—
215C23C23×D1911yescharacteristic
216Q8—764no—
217D4—44no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—44no—
228C2×C4—382no—
229C2×C4—382no—
230C2×C4—382no—
231C2×C4—382no—
232C2×C4—382no—
233C2×C4—382no—
234C2×C4—382no—
235C2×C4—382no—
236C2×C4—382no—
237C2×C4—382no—
238C2×C4—382no—
239C2×C4—382no—
240C2×C4C2×C22⋊D1912yes—
241C2×C4C2×C22⋊D1912yes—
242C22—22no—
243C22—22no—
244C22—22no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—42no—
252C22#1059743012yes—
253C22#1059743511yescharacteristic
254C22#1059743611yescharacteristic
255C22#1059743612yes—
256C22C22×C22⋊D1911yescharacteristic
257C4—22no—
258C4—22no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4—762no—
263C4—762no—
264C4—762no—
265C4—762no—
266C2—42no—
267C2—81no—
268C2#1192710311yescharacteristic
269C2#1192711511yescharacteristic
270C2#1192712211yescharacteristic
271C2#1192729112yes—
272C2#1192729712yes—
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC2×C19×#123C2
prime radicalC22×D4×C19C22
hypercenterC2×#123D19
hypocenterC19#2814
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#10597370C2semidirect
2. #11926477C2semidirect
3. #11926474C2semidirect
4. #11926472C2semidirect
5. #11926469C2semidirect
6. #11926467C2semidirect
7. #11926464C2semidirect
9. #11926456C2semidirect
10. #11926404C2semidirect
173. C19#2814semidirect

Maximal subgroups

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

subgroupindex
C2×#105973702
#119264772
#119264742
#119264722
#119264692
#119264672
#119264642
#119264582
#119264562
#119264042
C2×C19×#1232
#281419