Finite Group Databasebeta

← #18071883

Subgroups — #18071883

Order 4864.

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

normal subgroups only

This group has 414 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#14571628C211yesmaximal, characteristic
2#14565173C211yesmaximal, characteristic
3#14565172C212yesmaximal
4#14561460C212yesmaximal
5C19×#1272C211yesmaximal, characteristic
6C2×#10597275—22no—
7C2×#10597264—21no—
8C2×#10597273—22no—
9C2×#10597292—21no—
10#11926465—22no—
11#11926464—21no—
12#11926451—21no—
13#11926450C2212yes—
14#11926448—22no—
15#11926414C2211yescharacteristic
16#11926299C2211yescharacteristic
17C19×#391C2211yescharacteristic
18C19×#336C2212yes—
19C22×Q8×C19D411yescharacteristic
20C22×Dic38—21no—
21C22×Dic38D412yes—
22C22×C8×C19—22no—
23C2×C4⋊C4×C19D411yescharacteristic
24C2×C42×C19C2311yescharacteristic
25C2×C4⋊Dic19—21no—
26C2×C4⋊Dic19—22no—
27C2×C4⋊Dic19—21no—
28C2×C4⋊Dic19D412yes—
29C2×Dic19⋊C4—22no—
30C2×C4×Dic19—21no—
31C22×C19⋊C8—21no—
32C19×#95—22no—
33#10597292—42no—
34C19⋊#95—21no—
35C19⋊#95—22no—
36C19⋊#95—22no—
37C19⋊#95—22no—
38#10597275—44no—
39#10597273—44no—
40#10597264—42no—
41C2×Q8×C19—21no—
42C2×Q8×C19—41no—
43C2×Q8×C19—41no—
44C2×Q8×C19Q1612yes—
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—22no—
53C2×Dic38—42no—
54C2×Dic38—42no—
55C2×Dic38—82no—
56C2×Dic38—81no—
57C2×Dic38Q1614yes—
58C2×C8×C19—24no—
59C2×C8×C19—42no—
60C2×C8×C19—42no—
61C4⋊C4×C19—41no—
62C42×C19—41no—
63C4⋊Dic19—42no—
64C4⋊Dic19—41no—
65C4⋊Dic19—42no—
66C4⋊Dic19—42no—
67C4⋊Dic19—41no—
68C4⋊Dic19—81no—
69Dic19⋊C4—82no—
70C4×Dic19—81no—
71C2×C19⋊C8—22no—
72C2×C19⋊C8—41no—
73C2×C19⋊C8—41no—
74#7837—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—42no—
86C2×C4×C19—41no—
87C2×C4×C19C2×Q1611yescharacteristic
88C2×C4×C19C2×Q1612yes—
89C2×C4×C19#13711yescharacteristic
90C2×C4×C19#13712yes—
91C2×Dic19—24no—
92C2×Dic19—42no—
93C2×Dic19—42no—
94C2×Dic19—42no—
95C2×Dic19—42no—
96C2×Dic19—42no—
97C2×Dic19—82no—
98C2×Dic19—81no—
99Dic38—44no—
100Dic38—82no—
101Dic38—84no—
102C8×C19—44no—
103C19⋊C8—42no—
104#2811—191no—
105#2095—191no—
106#2095—192no—
107#1272—192no—
108#1272D1911yescharacteristic
109C22×C19#45112yes—
110C22×C19#45111yescharacteristic
111C22×C19#45312yes—
112C22×C19#45311yescharacteristic
113C22×C19#45811yescharacteristic
114C4×C19—21no—
115C4×C19—22no—
116C4×C19—22no—
117C4×C19—21no—
118C4×C19—42no—
119C4×C19—81no—
120Dic19—44no—
121Dic19—82no—
122Dic19—161no—
123C2×#107—382no—
124C2×#107—381no—
125C2×#103—382no—
126C2×#103—381no—
127#395—382no—
128#395—381no—
129#391—192no—
130#391—382no—
131#391—381no—
132#391C2×D1911yescharacteristic
133#384—191no—
134#336—191no—
135#336C2×D1912yes—
136C2×C19#161412yes—
137C2×C19#161411yescharacteristic
138C2×C19#163311yescharacteristic
139C2×C19#163312yes—
140C2×C19#165511yescharacteristic
141C22×Q8—192no—
142C22×Q8—381no—
143C22×Q8D7611yescharacteristic
144C22×C8—22no—
145C22×C8—381no—
146C2×C4⋊C4—192no—
147C2×C4⋊C4—381no—
148C2×C4⋊C4—382no—
149C2×C4⋊C4—382no—
150C2×C4⋊C4—381no—
151C2×C4⋊C4D7611yescharacteristic
152C2×C42—381no—
153C2×C42C22×D1911yescharacteristic
154#107—762no—
155#107—764no—
156#103—764no—
157#103—762no—
158#95—22no—
159#95—382no—
160#95—381no—
161#95—382no—
162#95—382no—
163C19#783711yescharacteristic, complemented, Sylow
164C2×Q8—21no—
165C2×Q8—41no—
166C2×Q8—41no—
167C2×Q8—194no—
168C2×Q8—382no—
169C2×Q8—762no—
170C2×Q8—762no—
171C2×Q8—1522no—
172C2×Q8—1521no—
173C2×Q8Dic7612yes—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—382no—
177C22×C4—382no—
178C22×C4—761no—
179C22×C4C2×D7611yescharacteristic
180C22×C4D4×D1912yes—
181C2×C8—24no—
182C2×C8—42no—
183C2×C8—42no—
184C2×C8—382no—
185C2×C8—761no—
186C2×C8—761no—
187C4⋊C4—41no—
188C4⋊C4—762no—
189C4⋊C4—762no—
190C4⋊C4—761no—
191C4⋊C4—762no—
192C4⋊C4—761no—
193C4⋊C4—1522no—
194C4⋊C4—1521no—
195C42—41no—
196C42—1521no—
197C23#1059732811yescharacteristic
198Q8—42no—
199Q8—81no—
200Q8—764no—
201Q8—1522no—
202Q8—1524no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—384no—
213C2×C4—762no—
214C2×C4—762no—
215C2×C4—762no—
216C2×C4—762no—
217C2×C4—762no—
218C2×C4—1522no—
219C2×C4—1521no—
220C2×C4C2×Dic7611yescharacteristic
221C2×C4#1059735511yescharacteristic
222C2×C4#1059736112yes—
223C2×C4Q16×D1912yes—
224C8—44no—
225C8—762no—
226C22#1192670112yes—
227C22#1192670211yescharacteristic
228C22#1192671312yes—
229C22#1192671411yescharacteristic
230C22#1192673511yescharacteristic
231C4—22no—
232C4—22no—
233C4—21no—
234C4—21no—
235C4—42no—
236C4—81no—
237C4—3041no—
238C4—764no—
239C4—1522no—
240C2#1456266112yes—
241C2#1456266211yescharacteristic
242C2#1456277611yescharacteristic
243C2#1456277712yes—
244C2#1456292511yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1272C2
socle, prime radicalC23×C19#120
hypercenter#1272D19
hypocenterC19#7837
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
163. C19#7837semidirect

Maximal subgroups

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

subgroupindex
#145716282
#145651732
#145651722
#145614602
C19×#12722
#783719