Finite Group Databasebeta

← #18071669

Subgroups — #18071669

Order 4864.

366 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 83 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#14571623C211yesmaximal, characteristic
2#14565107C212yesmaximal
3#14561461C211yesmaximal, characteristic
4#14561457C212yesmaximal
5C19×#2096C211yesmaximal, characteristic
6C2×#10597264—22no—
7#11926483—21no—
8#11926476—22no—
9#11926451—21no—
10#11926442C2212yes—
11#11926431—22no—
12#11926306—22no—
13#11926299C2212yes—
14C2×C19×#106—21no—
15C2×C19×#103—21no—
16C19×#391C2211yescharacteristic
17C19×#384C2211yescharacteristic
18C19×#336C2211yescharacteristic
19C22×Q8×C19D411yescharacteristic
20C22×C8×C19—21no—
21C2×C4⋊C4×C19—22no—
22C2×C4⋊C4×C19—21no—
23C2×C4⋊C4×C19D411yescharacteristic
24C2×C42×C19C2311yescharacteristic
25C2×C4⋊Dic19—21no—
26C2×C4⋊Dic19—21no—
27C2×C4⋊Dic19D412yes—
28C2×C4⋊Dic19D412yes—
29C2×Dic19⋊C4—22no—
30C2×C4×Dic19—21no—
31C22×C19⋊C8—22no—
32C19×#106—42no—
33C19×#103—42no—
34C19×#95—22no—
35C19⋊#95—21no—
36C19⋊#95—22no—
37C19⋊#95—22no—
38C19⋊#95—22no—
39#10597264—44no—
40C2×Q8×C19—21no—
41C2×Q8×C19—41no—
42C2×Q8×C19—41no—
43C2×Q8×C19Q1612yes—
44C22×C4×C19—21no—
45C22×C4×C19—21no—
46C22×C4×C19—41no—
47C22×C4×C19C2×D412yes—
48C22×C4×C19C2×D411yescharacteristic
49C22×Dic19—22no—
50C22×Dic19—22no—
51C2×C8×C19—22no—
52C2×C8×C19—41no—
53C2×C8×C19—41no—
54C4⋊C4×C19—41no—
55C4⋊C4×C19—41no—
56C4⋊C4×C19—41no—
57C4⋊C4×C19—42no—
58C4⋊C4×C19—42no—
59C42×C19—41no—
60C4⋊Dic19—22no—
61C4⋊Dic19—22no—
62C4⋊Dic19—42no—
63C4⋊Dic19—81no—
64C4⋊Dic19—81no—
65Dic19⋊C4—42no—
66Dic19⋊C4—42no—
67C4×Dic19—81no—
68C2×C19⋊C8—24no—
69C2×C19⋊C8—42no—
70C2×C19⋊C8—42no—
71#7802—191nomaximal, Sylow
72C23×C19#12011yescharacteristic
73Q8×C19—42no—
74Q8×C19—81no—
75C2×C4×C19—21no—
76C2×C4×C19—22no—
77C2×C4×C19—22no—
78C2×C4×C19—21no—
79C2×C4×C19—22no—
80C2×C4×C19—41no—
81C2×C4×C19—41no—
82C2×C4×C19—41no—
83C2×C4×C19—42no—
84C2×C4×C19—82no—
85C2×C4×C19—81no—
86C2×C4×C19C2×Q1611yescharacteristic
87C2×C4×C19#13512yes—
88C2×C4×C19AGL(1,ℤ/8)12yes—
89C2×C4×C19#13711yescharacteristic
90C2×Dic19—42no—
91C2×Dic19—42no—
92C2×Dic19—42no—
93C2×Dic19—42no—
94C2×Dic19—42no—
95C2×Dic19—42no—
96C8×C19—42no—
97C19⋊C8—44no—
98#2809—191no—
99#2096D1911yescharacteristic
100#2083—192no—
101#1272—191no—
102#1271—192no—
103C22×C19#44912yes—
104C22×C19#45111yescharacteristic
105C22×C19#45311yescharacteristic
106C22×C19#45612yes—
107C22×C19#45811yescharacteristic
108C4×C19—22no—
109C4×C19—22no—
110C4×C19—21no—
111C4×C19—21no—
112C4×C19—42no—
113C4×C19—81no—
114C4×C19—161no—
115Dic19—82no—
116Dic19—82no—
117C2×#107—382no—
118C2×#106—21no—
119C2×#103—21no—
120#400—381no—
121#398—382no—
122#391—381no—
123#391C2×D1911yescharacteristic
124#389—192no—
125#387—382no—
126#384C2×D1911yescharacteristic
127#340—382no—
128#336—192no—
129#336C2×D1911yescharacteristic
130C2×C19#160912yes—
131C2×C19#161411yescharacteristic
132C2×C19#162411yescharacteristic
133C2×C19#164812yes—
134C2×C19#166011yescharacteristic
135C22×Q8C22⋊D1911yescharacteristic
136C22×C8—21no—
137C22×C8—382no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—192no—
141C2×C4⋊C4—192no—
142C2×C4⋊C4—382no—
143C2×C4⋊C4—381no—
144C2×C4⋊C4—381no—
145C2×C4⋊C4C22⋊D1911yescharacteristic
146C2×C42—381no—
147C2×C42C22×D1911yescharacteristic
148#107—764no—
149#106—42no—
150#103—42no—
151#95—22no—
152#95—381no—
153#95—382no—
154#95—382no—
155#95—382no—
156C19#780211yescharacteristic, complemented, Sylow
157C2×Q8—21no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8#6452812yes—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—41no—
164C22×C4—382no—
165C22×C4—382no—
166C22×C4D4×D1912yes—
167C22×C4C2×C22⋊D1911yescharacteristic
168C2×C8—22no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—384no—
172C2×C8—762no—
173C2×C8—762no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—42no—
178C4⋊C4—42no—
179C4⋊C4—382no—
180C4⋊C4—382no—
181C4⋊C4—762no—
182C4⋊C4—762no—
183C4⋊C4—762no—
184C4⋊C4—1521no—
185C4⋊C4—1521no—
186C42—41no—
187C42—1521no—
188C23#1059738311yescharacteristic
189Q8—42no—
190Q8—81no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—82no—
201C2×C4—81no—
202C2×C4—762no—
203C2×C4—762no—
204C2×C4—762no—
205C2×C4—762no—
206C2×C4—762no—
207C2×C4—762no—
208C2×C4#1059736012yes—
209C2×C4#1059736212yes—
210C2×C4C2×#6452811yescharacteristic
211C2×C4#1059739711yescharacteristic
212C8—42no—
213C8—764no—
214C22#1192668812yes—
215C22#1192669911yescharacteristic
216C22#1192671111yescharacteristic
217C22#1192672512yes—
218C22#1192673311yescharacteristic
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—42no—
224C4—81no—
225C4—161no—
226C4—1522no—
227C4—1522no—
228C2#1456263112yes—
229C2#1456265911yescharacteristic
230C2#1456271611yescharacteristic
231C2#1456287612yes—
232C2#1456294411yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2096C2
socle, prime radicalC23×C19#120
hypercenter#2096D19
hypocenterC19#7802
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2096

Complements

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

NH ≅ G/Ntype
156. C19#7802semidirect

Maximal subgroups

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

subgroupindex
#145716232
#145651072
#145614612
#145614572
C19×#20962
#780219