Finite Group Databasebeta

← #18071822

Subgroups — #18071822

Order 4864.

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

normal subgroups only

This group has 462 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#14570007C211yesmaximal, characteristic
2#14565199C212yesmaximal, complemented
3#14565168C211yesmaximal, characteristic
4#14561459C212yesmaximal, complemented
5C19×#1270C211yesmaximal, characteristic
6C2×#10597324—22no—
7C2×#10597265—21no—
8C2×#10597289—21no—
9#11926467—22no—
10#11926464—21no—
11#11926442C2212yes—
12#11926424—21no—
13#11926414C2211yescharacteristic
14#11926307—22no—
15#11926307—22no—
16#11926299C2211yescharacteristic
17C19×#390C2211yescharacteristic
18C19×#336C2212yes—
19C22×D4×C19D411yescharacteristic
20C23×Dic19—21no—
21C22×Dic38—21no—
22C22×C8×C19—22no—
23C2×C4⋊C4×C19D411yescharacteristic
24C2×C22⋊C4×C19—22no—
25C2×C42×C19C2311yescharacteristic
26C2×C22⋊Dic19—22no—
27C2×C22⋊Dic19—21no—
28C2×C4⋊Dic19—21no—
29C2×C4⋊Dic19—22no—
30C2×C4⋊Dic19D412yes—
31C2×C4⋊Dic19D412yes—
32C2×Dic19⋊C4—22no—
33C2×Dic19⋊C4—22no—
34C22×C19⋊C8—21no—
35#10597324—44no—
36#10597324—44no—
37#10597289—42no—
38C19⋊#95—21no—
39C19⋊#95—22no—
40#10597265—42no—
41C24×C19—21no—
42C2×D4×C19—21no—
43C2×D4×C19—41no—
44C2×D4×C19—41no—
45C2×D4×C19Q1612yes—
46C22×C4×C19—21no—
47C22×C4×C19C2×D411yescharacteristic
48C22×C4×C19C2×D412yes—
49C22×Dic19—22no—
50C22×Dic19—22no—
51C22×Dic19—44no—
52C22×Dic19—41no—
53C22×Dic19—81no—
54C2×Dic38—44no—
55C2×Dic38—81no—
56C2×C8×C19—42no—
57C2×C8×C19—42no—
58C2×C8×C19—42no—
59C4⋊C4×C19—41no—
60C22⋊C4×C19—42no—
61C22⋊C4×C19—42no—
62C42×C19—41no—
63C22⋊Dic19—44no—
64C22⋊Dic19—81no—
65C4⋊Dic19—22no—
66C4⋊Dic19—42no—
67C4⋊Dic19—41no—
68C4⋊Dic19—41no—
69C4⋊Dic19—44no—
70C4⋊Dic19SD1614yes—
71Dic19⋊C4—44no—
72Dic19⋊C4—42no—
73Dic19⋊C4—42no—
74C2×C19⋊C8—22no—
75C2×C19⋊C8—41no—
76C2×C19⋊C8—41no—
77#7826—191nomaximal, Sylow
78C23×C19—22no—
79C23×C19—42no—
80C23×C19—41no—
81C23×C19—42no—
82C23×C19—41no—
83C23×C19#12011yescharacteristic
84D4×C19—42no—
85D4×C19—81no—
86C2×C4×C19—21no—
87C2×C4×C19—22no—
88C2×C4×C19—21no—
89C2×C4×C19—22no—
90C2×C4×C19—42no—
91C2×C4×C19—41no—
92C2×C4×C19C2×SD1612yes—
93C2×C4×C19C2×Q1611yescharacteristic
94C2×C4×C19AGL(1,ℤ/8)12yes—
95C2×C4×C19#13711yescharacteristic
96C2×Dic19—24no—
97C2×Dic19—42no—
98C2×Dic19—42no—
99C2×Dic19—42no—
100C2×Dic19—42no—
101C2×Dic19—42no—
102C2×Dic19—84no—
103C2×Dic19—81no—
104C2×Dic19—82no—
105Dic38—84no—
106C8×C19—82no—
107C19⋊C8—42no—
108#2683—191no—
109#2100—192no—
110#2094—191no—
111#1271—192no—
112#1270D1911yescharacteristic
113C22×C19—42no—
114C22×C19—44no—
115C22×C19—82no—
116C22×C19—81no—
117C22×C19—81no—
118C22×C19#45012yes—
119C22×C19#45111yescharacteristic
120C22×C19#45311yescharacteristic
121C22×C19#45412yes—
122C22×C19#45811yescharacteristic
123C4×C19—21no—
124C4×C19—21no—
125C4×C19—22no—
126C4×C19—22no—
127C4×C19—81no—
128Dic19—44no—
129Dic19—82no—
130Dic19—161no—
131C2×C22⋊Q8—382no—
132C2×#106—381no—
133C2×#102—381no—
134#396—382no—
135#395—381no—
136#390C2×D1911yescharacteristic
137#389—192no—
138#386—381no—
139#384—191no—
140#340—382no—
141#340—382no—
142#336—191no—
143#336C2×D1912yes—
144C2×C19—82no—
145C2×C19#161411yescharacteristic
146C2×C19#161612yes—
147C2×C19#162911yescharacteristic
148C2×C19#163712yes—
149C2×C19#165711yescharacteristic
150C22×Q8—381no—
151C22×D4D7611yescharacteristic
152C23×C4—381no—
153C22×C8—22no—
154C22×C8—381no—
155C22⋊Q8—764no—
156C22⋊Q8—764no—
157C2×C4⋊C4—192no—
158C2×C4⋊C4—192no—
159C2×C4⋊C4—382no—
160C2×C4⋊C4—382no—
161C2×C4⋊C4—381no—
162C2×C4⋊C4—382no—
163C2×C4⋊C4D7611yescharacteristic
164C2×C22⋊C4—22no—
165C2×C22⋊C4—382no—
166C2×C22⋊C4—381no—
167C2×C42C22×D1911yescharacteristic
168#106—762no—
169#102—762no—
170#95—381no—
171#95—382no—
172C19#782611yescharacteristic, complemented, Sylow
173C24—21no—
174C2×Q8—764no—
175C2×Q8—1521no—
176C2×D4—21no—
177C2×D4—41no—
178C2×D4—41no—
179C2×D4Dic7612yes—
180C22×C4—21no—
181C22×C4—382no—
182C22×C4—382no—
183C22×C4—764no—
184C22×C4—761no—
185C22×C4—1521no—
186C22×C4C2×D7611yescharacteristic
187C22×C4D4×D1912yes—
188C2×C8—42no—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—382no—
192C2×C8—761no—
193C2×C8—761no—
194C4⋊C4—41no—
195C4⋊C4—194no—
196C4⋊C4—382no—
197C4⋊C4—762no—
198C4⋊C4—761no—
199C4⋊C4—761no—
200C4⋊C4—764no—
201C4⋊C4—764no—
202C4⋊C4—762no—
203C4⋊C4—762no—
204C22⋊C4—42no—
205C22⋊C4—42no—
206C22⋊C4—764no—
207C22⋊C4—1521no—
208C42—41no—
209C23—22no—
210C23—42no—
211C23—41no—
212C23—42no—
213C23—41no—
214C23#1059732811yescharacteristic
215Q8—1524no—
216D4—42no—
217D4—81no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—384no—
225C2×C4—762no—
226C2×C4—762no—
227C2×C4—762no—
228C2×C4—762no—
229C2×C4—762no—
230C2×C4—1521no—
231C2×C4—1522no—
232C2×C4—1524no—
233C2×C4C2×Dic7611yescharacteristic
234C2×C4#1059735511yescharacteristic
235C2×C4#1059735712yes—
236C2×C4SD16×D1912yes—
237C8—82no—
238C8—762no—
239C22—42no—
240C22—44no—
241C22—82no—
242C22—81no—
243C22—81no—
244C22#1192669612yes—
245C22#1192670211yescharacteristic
246C22#1192671411yescharacteristic
247C22#1192671812yes—
248C22#1192673511yescharacteristic
249C4—21no—
250C4—21no—
251C4—22no—
252C4—22no—
253C4—81no—
254C4—3041no—
255C4—764no—
256C4—1522no—
257C2—82no—
258C2#1456266211yescharacteristic
259C2#1456267312yes—
260C2#1456275211yescharacteristic
261C2#1456280312yes—
262C2#1456293411yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1270C2
socleC23×C19#120
prime radicalC22×D4×C19D4
hypercenter#1270D19
hypocenterC19#7826
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #14565199C2semidirect
4. #14561459C2semidirect
172. C19#7826semidirect

Maximal subgroups

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

subgroupindex
#145700072
#145651992
#145651682
#145614592
C19×#12702
#782619