Finite Group Databasebeta

← #18071636

Subgroups — #18071636

Order 4864.

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

normal subgroups only

This group has 478 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#14565107C212yesmaximal, complemented
3#14561457C212yesmaximal, complemented
4#14561456C211yesmaximal, characteristic
5C19×#2093C211yesmaximal, characteristic
6C2×#10597324—22no—
7C2×#10597264—22no—
8#11926467—22no—
9#11926464—21no—
10#11926442C2212yes—
11#11926424—21no—
12#11926306—22no—
13#11926299C2212yes—
14C2×C19×#107—21no—
15C2×C19×#102—21no—
16C19×#390C2211yescharacteristic
17C19×#384C2211yescharacteristic
18C19×#336C2211yescharacteristic
19C22×D4×C19D411yescharacteristic
20C23×Dic19—21no—
21C22×Dic38—21no—
22C22×C8×C19—21no—
23C2×C4⋊C4×C19—22no—
24C2×C4⋊C4×C19—21no—
25C2×C4⋊C4×C19D411yescharacteristic
26C2×C22⋊C4×C19—22no—
27C2×C42×C19C2311yescharacteristic
28C2×C22⋊Dic19—22no—
29C2×C22⋊Dic19—21no—
30C2×C4⋊Dic19D412yes—
31C2×C4⋊Dic19D412yes—
32C2×Dic19⋊C4—22no—
33C2×Dic19⋊C4—22no—
34C22×C19⋊C8—22no—
35#10597324—44no—
36#10597324—44no—
37C19×#107—42no—
38C19×#102—42no—
39C19⋊#95—21no—
40C19⋊#95—22no—
41#10597264—44no—
42C24×C19—21no—
43C2×D4×C19—21no—
44C2×D4×C19—41no—
45C2×D4×C19—41no—
46C2×D4×C19Q1612yes—
47C22×C4×C19—21no—
48C22×C4×C19—41no—
49C22×C4×C19C2×D412yes—
50C22×C4×C19C2×D411yescharacteristic
51C22×Dic19—22no—
52C22×Dic19—22no—
53C22×Dic19—44no—
54C22×Dic19—81no—
55C2×Dic38—44no—
56C2×Dic38—81no—
57C2×C8×C19—22no—
58C2×C8×C19—41no—
59C2×C8×C19—41no—
60C4⋊C4×C19—41no—
61C4⋊C4×C19—41no—
62C4⋊C4×C19—41no—
63C4⋊C4×C19—42no—
64C4⋊C4×C19—42no—
65C22⋊C4×C19—42no—
66C22⋊C4×C19—42no—
67C42×C19—41no—
68C22⋊Dic19—44no—
69C22⋊Dic19—81no—
70C4⋊Dic19—22no—
71C4⋊Dic19—42no—
72C4⋊Dic19D814yes—
73Dic19⋊C4—44no—
74Dic19⋊C4—42no—
75Dic19⋊C4—42no—
76C2×C19⋊C8—24no—
77C2×C19⋊C8—42no—
78C2×C19⋊C8—42no—
79#7797—191nomaximal, Sylow
80C23×C19—22no—
81C23×C19—42no—
82C23×C19—41no—
83C23×C19—42no—
84C23×C19—41no—
85C23×C19#12011yescharacteristic
86D4×C19—42no—
87D4×C19—81no—
88C2×C4×C19—21no—
89C2×C4×C19—22no—
90C2×C4×C19—22no—
91C2×C4×C19—21no—
92C2×C4×C19—42no—
93C2×C4×C19—41no—
94C2×C4×C19—82no—
95C2×C4×C19—81no—
96C2×C4×C19C2×D812yes—
97C2×C4×C19C2×Q1611yescharacteristic
98C2×C4×C19AGL(1,ℤ/8)12yes—
99C2×C4×C19#13711yescharacteristic
100C2×Dic19—24no—
101C2×Dic19—42no—
102C2×Dic19—42no—
103C2×Dic19—42no—
104C2×Dic19—42no—
105C2×Dic19—42no—
106C2×Dic19—84no—
107Dic38—84no—
108C8×C19—42no—
109C19⋊C8—44no—
110#2683—191no—
111#2093D1911yescharacteristic
112#2083—192no—
113#1271—192no—
114#1270—191no—
115C22×C19—42no—
116C22×C19—44no—
117C22×C19—82no—
118C22×C19—81no—
119C22×C19—81no—
120C22×C19#44712yes—
121C22×C19#45111yescharacteristic
122C22×C19#45311yescharacteristic
123C22×C19#45612yes—
124C22×C19#45811yescharacteristic
125C4×C19—22no—
126C4×C19—22no—
127C4×C19—21no—
128C4×C19—21no—
129C4×C19—81no—
130C4×C19—161no—
131Dic19—44no—
132Dic19—82no—
133C2×C22⋊Q8—382no—
134C2×#107—21no—
135C2×#107—382no—
136C2×#102—21no—
137#396—382no—
138#395—381no—
139#390C2×D1911yescharacteristic
140#389—192no—
141#386—381no—
142#384C2×D1911yescharacteristic
143#340—382no—
144#336—192no—
145#336C2×D1911yescharacteristic
146C2×C19—82no—
147C2×C19#161012yes—
148C2×C19#161411yescharacteristic
149C2×C19#161911yescharacteristic
150C2×C19#164912yes—
151C2×C19#166011yescharacteristic
152C22×Q8—381no—
153C22×D4C22⋊D1911yescharacteristic
154C23×C4—381no—
155C22×C8—21no—
156C22×C8—382no—
157C22⋊Q8—764no—
158C22⋊Q8—764no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—192no—
162C2×C4⋊C4—192no—
163C2×C4⋊C4—382no—
164C2×C4⋊C4—382no—
165C2×C4⋊C4C22⋊D1911yescharacteristic
166C2×C22⋊C4—22no—
167C2×C22⋊C4—382no—
168C2×C22⋊C4—381no—
169C2×C42C22×D1911yescharacteristic
170#107—42no—
171#107—764no—
172#102—42no—
173#95—381no—
174#95—382no—
175C19#779711yescharacteristic, complemented, Sylow
176C24—21no—
177C2×Q8—764no—
178C2×Q8—1521no—
179C2×D4—21no—
180C2×D4—41no—
181C2×D4—41no—
182C2×D4#6452812yes—
183C22×C4—21no—
184C22×C4—41no—
185C22×C4—382no—
186C22×C4—382no—
187C22×C4—764no—
188C22×C4—1521no—
189C22×C4D4×D1912yes—
190C22×C4C2×C22⋊D1911yescharacteristic
191C2×C8—22no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—384no—
195C2×C8—762no—
196C2×C8—762no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—194no—
203C4⋊C4—382no—
204C4⋊C4—762no—
205C4⋊C4—764no—
206C4⋊C4—762no—
207C4⋊C4—762no—
208C22⋊C4—42no—
209C22⋊C4—42no—
210C22⋊C4—764no—
211C22⋊C4—1521no—
212C42—41no—
213C23—22no—
214C23—42no—
215C23—41no—
216C23—42no—
217C23—41no—
218C23#1059738311yescharacteristic
219Q8—1524no—
220D4—42no—
221D4—81no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—82no—
229C2×C4—81no—
230C2×C4—384no—
231C2×C4—762no—
232C2×C4—762no—
233C2×C4—762no—
234C2×C4—762no—
235C2×C4—762no—
236C2×C4—1524no—
237C2×C4D8×D1912yes—
238C2×C4#1059735712yes—
239C2×C4C2×#6452811yescharacteristic
240C2×C4#1059739711yescharacteristic
241C8—42no—
242C8—764no—
243C22—44no—
244C22—42no—
245C22—82no—
246C22—81no—
247C22—81no—
248C22#1192667612yes—
249C22#1192669911yescharacteristic
250C22#1192671111yescharacteristic
251C22#1192672512yes—
252C22#1192673311yescharacteristic
253C4—22no—
254C4—22no—
255C4—21no—
256C4—21no—
257C4—81no—
258C4—161no—
259C4—764no—
260C4—1522no—
261C2—82no—
262C2#1456263612yes—
263C2#1456265911yescharacteristic
264C2#1456268711yescharacteristic
265C2#1456288312yes—
266C2#1456294411yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2093C2
socleC23×C19#120
prime radicalC22×D4×C19D4
hypercenter#2093D19
hypocenterC19#7797
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2093

Complements

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

NH ≅ G/Ntype
2. #14565107C2semidirect
3. #14561457C2semidirect
175. C19#7797semidirect

Maximal subgroups

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

subgroupindex
#145700072
#145651072
#145614572
#145614562
C19×#20932
#779719