Finite Group Databasebeta

← #18071840

Subgroups — #18071840

Order 4864.

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

normal subgroups only

This group has 394 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#14565199C212yesmaximal
3#14565173C211yesmaximal, characteristic
4#14561457C212yesmaximal
5C19×#1272C211yesmaximal, characteristic
6C2×#10597390—21no—
7C2×#10597264—21no—
8C2×#10597292—21no—
9#11926474—21no—
10#11926465—22no—
11#11926442C2212yes—
12#11926429—22no—
13#11926414C2211yescharacteristic
14#11926307—22no—
15#11926307—22no—
16#11926299C2211yescharacteristic
17C19×#391C2211yescharacteristic
18C19×#336C2212yes—
19C22×Q8×C19D411yescharacteristic
20C22×Dic38—21no—
21C22×C8×C19—22no—
22C2×C4⋊C4×C19D411yescharacteristic
23C2×C42×C19C2311yescharacteristic
24#10597390—42no—
25#10597390—42no—
26C2×C4⋊Dic19—21no—
27C2×C4⋊Dic19—22no—
28C2×C4⋊Dic19—21no—
29C2×C4⋊Dic19D412yes—
30C2×C4⋊Dic19D412yes—
31C2×Dic19⋊C4—22no—
32C2×Dic19⋊C4—22no—
33C2×C4×Dic19—21no—
34C22×C19⋊C8—21no—
35C19×#95—22no—
36#10597292—42no—
37C19⋊#95—21no—
38C19⋊#95—22no—
39C19⋊#95—22no—
40#10597264—42no—
41C2×Q8×C19—21no—
42C2×Q8×C19—41no—
43C2×Q8×C19—41no—
44C2×Q8×C19SD1612yes—
45C22×C4×C19—21no—
46C22×C4×C19—21no—
47C22×C4×C19C2×D411yescharacteristic
48C22×C4×C19C2×D412yes—
49C22×Dic19—22no—
50C22×Dic19—22no—
51C22×Dic19—41no—
52C2×Dic38—42no—
53C2×Dic38—81no—
54C2×Dic38—81no—
55C2×C8×C19—42no—
56C2×C8×C19—42no—
57C2×C8×C19—42no—
58C4⋊C4×C19—41no—
59C42×C19—41no—
60C4⋊Dic19—22no—
61C4⋊Dic19—42no—
62C4⋊Dic19—41no—
63C4⋊Dic19—41no—
64C4⋊Dic19—44no—
65C4⋊Dic19—81no—
66C4⋊Dic19Q1614yes—
67Dic19⋊C4—44no—
68Dic19⋊C4—42no—
69Dic19⋊C4—42no—
70C4×Dic19—42no—
71C2×C19⋊C8—22no—
72C2×C19⋊C8—41no—
73C2×C19⋊C8—41no—
74#7829—191nomaximal, Sylow
75C23×C19#12011yescharacteristic
76Q8×C19—42no—
77Q8×C19—81no—
78C2×C4×C19—21no—
79C2×C4×C19—22no—
80C2×C4×C19—21no—
81C2×C4×C19—22no—
82C2×C4×C19—22no—
83C2×C4×C19—41no—
84C2×C4×C19—41no—
85C2×C4×C19—41no—
86C2×C4×C19—42no—
87C2×C4×C19C2×SD1611yescharacteristic
88C2×C4×C19C2×Q1612yes—
89C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
90C2×C4×C19#13712yes—
91C2×Dic19—24no—
92C2×Dic19—42no—
93C2×Dic19—42no—
94C2×Dic19—42no—
95C2×Dic19—42no—
96C2×Dic19—42no—
97C2×Dic19—81no—
98C2×Dic19—82no—
99Dic38—84no—
100C8×C19—82no—
101C19⋊C8—42no—
102#2734—191no—
103#2100—192no—
104#2095—191no—
105#1272D1911yescharacteristic
106#1271—192no—
107C22×C19#45011yescharacteristic
108C22×C19#45112yes—
109C22×C19#45311yescharacteristic
110C22×C19#45412yes—
111C22×C19#45811yescharacteristic
112C4×C19—21no—
113C4×C19—21no—
114C4×C19—22no—
115C4×C19—22no—
116C4×C19—42no—
117C4×C19—81no—
118Dic19—44no—
119Dic19—82no—
120Dic19—161no—
121C2×C4⋊Q8—381no—
122C2×#107—381no—
123C2×#103—381no—
124#398—381no—
125#395—382no—
126#391C2×D1911yescharacteristic
127#389—192no—
128#387—382no—
129#384—191no—
130#340—382no—
131#340—382no—
132#336—191no—
133#336C2×D1912yes—
134C2×C19#161311yescharacteristic
135C2×C19#161712yes—
136C2×C19#163311yescharacteristic
137C2×C19#163712yes—
138C2×C19#165711yescharacteristic
139C22×Q8—381no—
140C22×Q8D7611yescharacteristic
141C22×C8—22no—
142C22×C8—381no—
143C4⋊Q8—762no—
144C4⋊Q8—762no—
145C2×C4⋊C4—192no—
146C2×C4⋊C4—192no—
147C2×C4⋊C4—382no—
148C2×C4⋊C4—382no—
149C2×C4⋊C4—381no—
150C2×C4⋊C4—382no—
151C2×C4⋊C4—381no—
152C2×C4⋊C4D7611yescharacteristic
153C2×C42—381no—
154C2×C42C22×D1911yescharacteristic
155#107—762no—
156#103—762no—
157#95—22no—
158#95—381no—
159#95—382no—
160#95—382no—
161C19#782911yescharacteristic, complemented, Sylow
162C2×Q8—21no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—762no—
166C2×Q8—1521no—
167C2×Q8—1521no—
168C2×Q8#6451612yes—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—382no—
172C22×C4—382no—
173C22×C4—761no—
174C22×C4C2×D7611yescharacteristic
175C22×C4D4×D1912yes—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—42no—
179C2×C8—382no—
180C2×C8—761no—
181C2×C8—761no—
182C4⋊C4—41no—
183C4⋊C4—194no—
184C4⋊C4—382no—
185C4⋊C4—762no—
186C4⋊C4—764no—
187C4⋊C4—761no—
188C4⋊C4—761no—
189C4⋊C4—764no—
190C4⋊C4—762no—
191C4⋊C4—762no—
192C4⋊C4—1521no—
193C42—41no—
194C42—762no—
195C23#1059732811yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—1524no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—384no—
209C2×C4—762no—
210C2×C4—762no—
211C2×C4—762no—
212C2×C4—762no—
213C2×C4—762no—
214C2×C4—1521no—
215C2×C4—1522no—
216C2×C4C2×#6451611yescharacteristic
217C2×C4#1059735411yescharacteristic
218C2×C4#1059736112yes—
219C2×C4Q16×D1912yes—
220C8—82no—
221C8—762no—
222C22#1192669711yescharacteristic
223C22#1192670112yes—
224C22#1192671411yescharacteristic
225C22#1192671812yes—
226C22#1192673511yescharacteristic
227C4—21no—
228C4—21no—
229C4—22no—
230C4—22no—
231C4—42no—
232C4—81no—
233C4—3041no—
234C4—764no—
235C4—1522no—
236C2#1456265711yescharacteristic
237C2#1456267812yes—
238C2#1456277611yescharacteristic
239C2#1456280212yes—
240C2#1456293411yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1272C2
socle, prime radicalC23×C19#120
hypercenter#1272D19
hypocenterC19#7829
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
161. C19#7829semidirect

Maximal subgroups

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

subgroupindex
#145706672
#145651992
#145651732
#145614572
C19×#12722
#782919