Finite Group Databasebeta

← #18071368

Subgroups — #18071368

Order 4864.

468 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 87 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
1#14570667C211yesmaximal, characteristic
2#14564964C212yesmaximal
3#14564734C211yesmaximal, characteristic
4#14561457C212yesmaximal
5C19×#1272C211yesmaximal, characteristic
6C22×#64528—21no—
7C2×#10597315C2211yescharacteristic
8C2×#10597390—21no—
9C2×#10597275—22no—
10C2×#10597267—21no—
11#11926474—21no—
12#11926465—22no—
13#11926442C2212yes—
14#11926429—22no—
15#11926307—22no—
16#11926299C2211yescharacteristic
17C19×#391C2211yescharacteristic
18C19×#336C2212yes—
19C22×Q8×C19D411yescharacteristic
20C22×Dic38—21no—
21C22×Dic38—21no—
22C22×C8×C19—22no—
23C2×C4⋊C4×C19D411yescharacteristic
24C2×C42×C19C2311yescharacteristic
25#10597390—42no—
26#10597390—42no—
27C2×#64528—42no—
28C2×#64528—42no—
29C2×#64528—42no—
30C2×C4⋊Dic19—22no—
31C2×C4⋊Dic19—21no—
32C2×C4⋊Dic19D412yes—
33C2×C4⋊Dic19D412yes—
34C2×Dic19⋊C4—22no—
35C2×Dic19⋊C4—22no—
36C2×C4×Dic19—21no—
37C22×C19⋊C8—21no—
38#10597315—42no—
39C19×#95—22no—
40C19⋊#95—21no—
41C19⋊#95—22no—
42C19⋊#95—22no—
43#10597275—44no—
44#10597267—42no—
45C2×Q8×C19—21no—
46C2×Q8×C19—41no—
47C2×Q8×C19—41no—
48C2×Q8×C19D812yes—
49C22×C4×C19—21no—
50C22×C4×C19—21no—
51C22×C4×C19C2×D411yescharacteristic
52C22×C4×C19C2×D412yes—
53C22×Dic19—22no—
54C22×Dic19—22no—
55C22×Dic19—41no—
56C2×Dic38—22no—
57C2×Dic38—41no—
58C2×Dic38—41no—
59C2×Dic38—41no—
60C2×Dic38—41no—
61C2×Dic38—42no—
62C2×Dic38—41no—
63C2×Dic38—81no—
64C2×Dic38—81no—
65C2×C8×C19—24no—
66C2×C8×C19—42no—
67C2×C8×C19—42no—
68C4⋊C4×C19—41no—
69C42×C19—41no—
70#64528—48no—
71C4⋊Dic19—22no—
72C4⋊Dic19—24no—
73C4⋊Dic19—42no—
74C4⋊Dic19—42no—
75C4⋊Dic19—81no—
76C4⋊Dic19Q1614yescomplemented
77Dic19⋊C4—44no—
78Dic19⋊C4—42no—
79Dic19⋊C4—42no—
80C4×Dic19—42no—
81C2×C19⋊C8—22no—
82C2×C19⋊C8—41no—
83C2×C19⋊C8—41no—
84#7757—191nomaximal, Sylow
85C23×C19#12011yescharacteristic
86Q8×C19—42no—
87Q8×C19—81no—
88C2×C4×C19—21no—
89C2×C4×C19—22no—
90C2×C4×C19—21no—
91C2×C4×C19—22no—
92C2×C4×C19—22no—
93C2×C4×C19—41no—
94C2×C4×C19—41no—
95C2×C4×C19—41no—
96C2×C4×C19—42no—
97C2×C4×C19C2×D811yescharacteristic
98C2×C4×C19C2×Q1612yes—
99C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
100C2×C4×C19#13712yes—
101C2×Dic19—24no—
102C2×Dic19—42no—
103C2×Dic19—42no—
104C2×Dic19—42no—
105C2×Dic19—42no—
106C2×Dic19—42no—
107C2×Dic19—42no—
108C2×Dic19—81no—
109C2×Dic19—81no—
110Dic38—42no—
111Dic38—42no—
112Dic38—81no—
113Dic38—81no—
114Dic38—84no—
115C8×C19—44no—
116C19⋊C8—42no—
117#2734—191no—
118#2057—192no—
119#2016—191no—
120#1272D1911yescharacteristic
121#1271—192no—
122C22×C19#44711yescharacteristic
123C22×C19#45112yes—
124C22×C19#45311yescharacteristic
125C22×C19#45612yes—
126C22×C19B(4,𝔽2)11yescharacteristic
127C4×C19—21no—
128C4×C19—21no—
129C4×C19—22no—
130C4×C19—22no—
131C4×C19—42no—
132C4×C19—81no—
133Dic19—44no—
134Dic19—82no—
135Dic19—82no—
136C22×Q16—381no—
137C2×C4⋊Q8—191no—
138C2×C4⋊Q8—381no—
139C2×#107—382no—
140C2×#103—381no—
141#398—381no—
142#395—382no—
143#391C2×D1911yescharacteristic
144#389—192no—
145#387—382no—
146#340—382no—
147#336—191no—
148#336C2×D1912yes—
149C2×C19#159511yescharacteristic
150C2×C19#160512yes—
151C2×C19#163311yescharacteristic
152C2×C19#164912yes—
153C2×C19#166011yescharacteristic
154C22×Q8—381no—
155C22×Q8—381no—
156C22×Q8D7611yescharacteristic
157C2×Q16—762no—
158C2×Q16—762no—
159C2×Q16—762no—
160C22×C8—22no—
161C22×C8—381no—
162C4⋊Q8—762no—
163C4⋊Q8—762no—
164C4⋊Q8—762no—
165C2×C4⋊C4—192no—
166C2×C4⋊C4—192no—
167C2×C4⋊C4—382no—
168C2×C4⋊C4—382no—
169C2×C4⋊C4—382no—
170C2×C4⋊C4—381no—
171C2×C4⋊C4D7611yescharacteristic
172C2×C42—381no—
173C2×C42C22×D1911yescharacteristic
174#107—764no—
175#103—762no—
176#95—22no—
177#95—381no—
178#95—382no—
179#95—382no—
180C19#775711yescharacteristic, complemented, Sylow
181C2×Q8—21no—
182C2×Q8—41no—
183C2×Q8—41no—
184C2×Q8—382no—
185C2×Q8—761no—
186C2×Q8—762no—
187C2×Q8—761no—
188C2×Q8—761no—
189C2×Q8—761no—
190C2×Q8—761no—
191C2×Q8—1521no—
192C2×Q8—1521no—
193C2×Q8D15212yes—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—382no—
197C22×C4—382no—
198C22×C4—761no—
199C22×C4C2×D7611yescharacteristic
200C22×C4D4×D1912yes—
201Q16—768no—
202C2×C8—24no—
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—382no—
206C2×C8—761no—
207C2×C8—761no—
208C4⋊C4—41no—
209C4⋊C4—194no—
210C4⋊C4—384no—
211C4⋊C4—382no—
212C4⋊C4—762no—
213C4⋊C4—764no—
214C4⋊C4—762no—
215C4⋊C4—762no—
216C4⋊C4—762no—
217C4⋊C4—1521no—
218C42—41no—
219C42—762no—
220C23#1059732811yescharacteristic
221Q8—42no—
222Q8—81no—
223Q8—762no—
224Q8—762no—
225Q8—1521no—
226Q8—1521no—
227Q8—1524no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—384no—
238C2×C4—762no—
239C2×C4—762no—
240C2×C4—762no—
241C2×C4—762no—
242C2×C4—762no—
243C2×C4—762no—
244C2×C4—1521no—
245C2×C4—1521no—
246C2×C4C2×D15211yescharacteristic
247C2×C4#1059735411yescharacteristic
248C2×C4#1059736112yes—
249C2×C4Q16×D1912yes—
250C8—44no—
251C8—762no—
252C22#1192668011yescharacteristic
253C22#1192670112yes—
254C22#1192671411yescharacteristic
255C22#1192672812yes—
256C22#1192673211yescharacteristic
257C4—22no—
258C4—22no—
259C4—21no—
260C4—21no—
261C4—42no—
262C4—81no—
263C4—764no—
264C4—1522no—
265C4—1522no—
266C2#1456255511yescharacteristic
267C2#1456261012yes—
268C2#1456277611yescharacteristic
269C2#1456288612yes—
270C2#1456294711yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1272C2
socle, prime radicalC23×C19#120
hypercenter#1272D19
hypocenterC19#7757
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
76. C4⋊Dic19Q16semidirect
180. C19#7757semidirect

Maximal subgroups

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

subgroupindex
#145706672
#145649642
#145647342
#145614572
C19×#12722
#775719