Finite Group Databasebeta

← #18071367

Subgroups — #18071367

Order 4864.

468 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 95 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#14564963C212yesmaximal
2#14564734C211yesmaximal, characteristic
3#14561461C211yesmaximal, characteristic
4#14561458C212yesmaximal
5C19×#2734C211yesmaximal, characteristic
6C22×#64528—21no—
7C2×#10597315C2211yescharacteristic
8C2×#10597264—22no—
9C2×#10597267—21no—
10#11926306—22no—
11#11926299C2212yes—
12#11926299C2211yescharacteristic
13C2×C19×C4⋊Q8—21no—
14C19×#398—21no—
15C19×#395—22no—
16C19×#391C2211yescharacteristic
17C19×#389C2212yes—
18C19×#387—22no—
19C22×Q8×C19—21no—
20C22×Q8×C19D411yescharacteristic
21C22×Dic38—21no—
22C19×C4⋊Q8—42no—
23C19×C4⋊Q8—42no—
24C2×C4⋊C4×C19—22no—
25C2×C4⋊C4×C19—22no—
26C2×C4⋊C4×C19—21no—
27C2×C4⋊C4×C19D412yes—
28C2×C4⋊C4×C19D411yescharacteristic
29C2×C4⋊C4×C19D412yes—
30C2×C42×C19—21no—
31C2×C42×C19C2311yescharacteristic
32C2×#64528—42no—
33C2×#64528—42no—
34C2×#64528—42no—
35C2×C4⋊Dic19—22no—
36C22×C19⋊C8—21no—
37C22×C19⋊C8—22no—
38#10597315—42no—
39C19×#95—21no—
40C19×#95—22no—
41C19×#95—22no—
42C19×#95—22no—
43#10597267—42no—
44#10597264—44no—
45C2×Q8×C19—21no—
46C2×Q8×C19—42no—
47C2×Q8×C19—41no—
48C2×Q8×C19—41no—
49C2×Q8×C19—81no—
50C2×Q8×C19—81no—
51C2×Q8×C19D812yes—
52C22×C4×C19—22no—
53C22×C4×C19—21no—
54C22×C4×C19—22no—
55C22×C4×C19—21no—
56C22×C4×C19C2×D411yescharacteristic
57C22×C4×C19C2×D412yes—
58C22×Dic19—41no—
59C2×Dic38—22no—
60C2×Dic38—41no—
61C2×Dic38—41no—
62C2×Dic38—41no—
63C2×Dic38—41no—
64C2×Dic38—41no—
65C4⋊C4×C19—22no—
66C4⋊C4×C19—42no—
67C4⋊C4×C19—41no—
68C4⋊C4×C19—44no—
69C4⋊C4×C19—42no—
70C4⋊C4×C19—42no—
71C4⋊C4×C19—81no—
72C4⋊C4×C19Q1614yescomplemented
73C42×C19—41no—
74C42×C19—42no—
75#64528—48no—
76C4⋊Dic19—24no—
77C4⋊Dic19—42no—
78C2×C19⋊C8—22no—
79C2×C19⋊C8—24no—
80C2×C19⋊C8—41no—
81C2×C19⋊C8—42no—
82C2×C19⋊C8—41no—
83C2×C19⋊C8—42no—
84#7757—191nomaximal, Sylow
85C23×C19#12011yescharacteristic
86Q8×C19—42no—
87Q8×C19—81no—
88Q8×C19—84no—
89C2×C4×C19—21no—
90C2×C4×C19—22no—
91C2×C4×C19—22no—
92C2×C4×C19—21no—
93C2×C4×C19—22no—
94C2×C4×C19—24no—
95C2×C4×C19—42no—
96C2×C4×C19—41no—
97C2×C4×C19—42no—
98C2×C4×C19—41no—
99C2×C4×C19—42no—
100C2×C4×C19—41no—
101C2×C4×C19—42no—
102C2×C4×C19—42no—
103C2×C4×C19—42no—
104C2×C4×C19C2×D811yescharacteristic
105C2×C4×C19C2×Q1612yes—
106C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
107C2×C4×C19#13712yes—
108C2×Dic19—42no—
109C2×Dic19—81no—
110C2×Dic19—81no—
111Dic38—42no—
112Dic38—42no—
113Dic38—81no—
114Dic38—81no—
115C19⋊C8—44no—
116C19⋊C8—42no—
117#2734D1911yescharacteristic
118#2057—192no—
119#2016—191no—
120#1272—191no—
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—44no—
133C4×C19—82no—
134C4×C19—81no—
135Dic19—82no—
136C22×Q16—381no—
137C2×C4⋊Q8—21no—
138C2×C4⋊Q8—191no—
139C2×#107—382no—
140C2×#103—381no—
141#398—21no—
142#395—22no—
143#391C2×D1911yescharacteristic
144#389C2×D1912yes—
145#387—22no—
146#340—382no—
147#336—192no—
148#336—191no—
149C2×C19#159511yescharacteristic
150C2×C19#160512yes—
151C2×C19#163311yescharacteristic
152C2×C19#164912yes—
153C2×C19#166011yescharacteristic
154C22×Q8—21no—
155C22×Q8—381no—
156C22×Q8C22⋊D1911yescharacteristic
157C2×Q16—762no—
158C2×Q16—762no—
159C2×Q16—762no—
160C22×C8—381no—
161C22×C8—382no—
162C4⋊Q8—42no—
163C4⋊Q8—42no—
164C4⋊Q8—762no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4—382no—
169C2×C4⋊C4C22⋊D1912yes—
170C2×C4⋊C4C22⋊D1912yes—
171C2×C4⋊C4C22⋊D1911yescharacteristic
172C2×C42—21no—
173C2×C42C22×D1911yescharacteristic
174#107—764no—
175#103—762no—
176#95—21no—
177#95—22no—
178#95—22no—
179#95—22no—
180C19#775711yescharacteristic, complemented, Sylow
181C2×Q8—21no—
182C2×Q8—42no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—81no—
186C2×Q8—81no—
187C2×Q8—382no—
188C2×Q8—761no—
189C2×Q8—761no—
190C2×Q8—761no—
191C2×Q8—761no—
192C2×Q8—761no—
193C2×Q8#6452512yes—
194C22×C4—22no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—22no—
198C22×C4—761no—
199C22×C4C2×C22⋊D1911yescharacteristic
200C22×C4C2×C22⋊D1912yes—
201Q16—768no—
202C2×C8—382no—
203C2×C8—384no—
204C2×C8—762no—
205C2×C8—761no—
206C2×C8—761no—
207C2×C8—762no—
208C4⋊C4—22no—
209C4⋊C4—41no—
210C4⋊C4—42no—
211C4⋊C4—44no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—81no—
215C4⋊C4—384no—
216C4⋊C4—762no—
217C4⋊C4#6452814yescomplemented
218C42—41no—
219C42—42no—
220C23#1059739911yescharacteristic
221Q8—42no—
222Q8—81no—
223Q8—84no—
224Q8—762no—
225Q8—762no—
226Q8—1521no—
227Q8—1521no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—24no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—762no—
244C2×C4—1521no—
245C2×C4—1521no—
246C2×C4C2×#6452511yescharacteristic
247C2×C4#1059737811yescharacteristic
248C2×C4#1059738812yes—
249C2×C4C2×#6452812yes—
250C8—762no—
251C8—764no—
252C22#1192667811yescharacteristic
253C22#1192670012yes—
254C22#1192671211yescharacteristic
255C22#1192672712yes—
256C22#1192673111yescharacteristic
257C4—22no—
258C4—22no—
259C4—21no—
260C4—21no—
261C4—44no—
262C4—42no—
263C4—81no—
264C4—82no—
265C4—1522no—
266C2#1456255311yescharacteristic
267C2#1456260912yes—
268C2#1456277511yescharacteristic
269C2#1456288412yes—
270C2#1456294611yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2734C2
socle, prime radicalC23×C19#120
hypercenter#2734D19
hypocenterC19#7757
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2734

Complements

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

NH ≅ G/Ntype
72. C4⋊C4×C19Q16semidirect
180. C19#7757semidirect
217. C4⋊C4#64528semidirect

Maximal subgroups

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

subgroupindex
#145649632
#145647342
#145614612
#145614582
C19×#27342
#775719