Finite Group Databasebeta

← #18071637

Subgroups — #18071637

Order 4864.

478 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 95 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#14565163C211yesmaximal, characteristic
2#14565106C212yesmaximal, complemented
3#14561458C212yesmaximal, complemented
4#14561456C211yesmaximal, characteristic
5C19×#2683C211yesmaximal, characteristic
6C2×#10597264—21no—
7C2×#10597264—22no—
8C2×#10597289—21no—
9#11926414C2211yescharacteristic
10#11926306—22no—
11#11926299C2211yescharacteristic
12#11926299C2212yes—
13C2×C19×C22⋊Q8—22no—
14C19×#396—22no—
15C19×#395—21no—
16C19×#390C2211yescharacteristic
17C19×#389C2212yes—
18C19×#386—21no—
19C22×Q8×C19—21no—
20C22×D4×C19D411yescharacteristic
21C23×C4×C19—21no—
22C19×C22⋊Q8—44no—
23C19×C22⋊Q8—44no—
24C2×C4⋊C4×C19—22no—
25C2×C4⋊C4×C19—22no—
26C2×C4⋊C4×C19D412yes—
27C2×C4⋊C4×C19D412yes—
28C2×C4⋊C4×C19D411yescharacteristic
29C2×C22⋊C4×C19—22no—
30C2×C22⋊C4×C19—22no—
31C2×C22⋊C4×C19—21no—
32C2×C42×C19C2311yescharacteristic
33C2×C4⋊Dic19—21no—
34C2×C4⋊Dic19—22no—
35C22×C19⋊C8—21no—
36C22×C19⋊C8—22no—
37C19×#95—21no—
38C19×#95—22no—
39#10597289—42no—
40#10597264—42no—
41#10597264—44no—
42C24×C19—21no—
43C2×Q8×C19—44no—
44C2×Q8×C19—81no—
45C2×D4×C19—21no—
46C2×D4×C19—41no—
47C2×D4×C19—41no—
48C2×D4×C19Q1612yes—
49C22×C4×C19—22no—
50C22×C4×C19—21no—
51C22×C4×C19—22no—
52C22×C4×C19—44no—
53C22×C4×C19—81no—
54C22×C4×C19C2×D412yes—
55C22×C4×C19C2×D411yescharacteristic
56C22×Dic19—41no—
57C4⋊C4×C19—22no—
58C4⋊C4×C19—42no—
59C4⋊C4×C19—41no—
60C4⋊C4×C19—44no—
61C4⋊C4×C19—42no—
62C4⋊C4×C19—42no—
63C4⋊C4×C19D814yes—
64C22⋊C4×C19—44no—
65C22⋊C4×C19—42no—
66C22⋊C4×C19—42no—
67C22⋊C4×C19—81no—
68C42×C19—41no—
69C4⋊Dic19—41no—
70C4⋊Dic19—41no—
71C4⋊Dic19—42no—
72C4⋊Dic19—42no—
73C2×C19⋊C8—22no—
74C2×C19⋊C8—24no—
75C2×C19⋊C8—42no—
76C2×C19⋊C8—41no—
77C2×C19⋊C8—42no—
78C2×C19⋊C8—41no—
79#7797—191nomaximal, Sylow
80C23×C19—22no—
81C23×C19—42no—
82C23×C19—41no—
83C23×C19—42no—
84C23×C19—41no—
85C23×C19#12011yescharacteristic
86Q8×C19—84no—
87D4×C19—42no—
88D4×C19—81no—
89C2×C4×C19—21no—
90C2×C4×C19—22no—
91C2×C4×C19—22no—
92C2×C4×C19—21no—
93C2×C4×C19—24no—
94C2×C4×C19—42no—
95C2×C4×C19—42no—
96C2×C4×C19—42no—
97C2×C4×C19—42no—
98C2×C4×C19—41no—
99C2×C4×C19—42no—
100C2×C4×C19—42no—
101C2×C4×C19—84no—
102C2×C4×C19C2×D812yes—
103C2×C4×C19C2×Q1611yescharacteristic
104C2×C4×C19AGL(1,ℤ/8)12yes—
105C2×C4×C19#13711yescharacteristic
106C2×Dic19—82no—
107C2×Dic19—81no—
108C19⋊C8—44no—
109C19⋊C8—42no—
110#2683D1911yescharacteristic
111#2093—191no—
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—44no—
130C4×C19—82no—
131C4×C19—81no—
132Dic19—161no—
133C2×C22⋊Q8—22no—
134C2×#107—382no—
135C2×#107—381no—
136C2×#102—381no—
137#396—22no—
138#395—21no—
139#390C2×D1911yescharacteristic
140#389C2×D1912yes—
141#386—21no—
142#384—191no—
143#340—382no—
144#336—192no—
145#336—191no—
146C2×C19—82no—
147C2×C19#161012yes—
148C2×C19#161411yescharacteristic
149C2×C19#161911yescharacteristic
150C2×C19#164912yes—
151C2×C19#166011yescharacteristic
152C22×Q8—21no—
153C22×D4C22⋊D1911yescharacteristic
154C23×C4—21no—
155C22×C8—382no—
156C22×C8—381no—
157C22⋊Q8—44no—
158C22⋊Q8—44no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—382no—
162C2×C4⋊C4—381no—
163C2×C4⋊C4C22⋊D1912yes—
164C2×C4⋊C4C22⋊D1912yes—
165C2×C4⋊C4C22⋊D1911yescharacteristic
166C2×C22⋊C4—22no—
167C2×C22⋊C4—22no—
168C2×C22⋊C4—21no—
169C2×C42C22×D1911yescharacteristic
170#107—762no—
171#107—764no—
172#102—762no—
173#95—21no—
174#95—22no—
175C19#779711yescharacteristic, complemented, Sylow
176C24—21no—
177C2×Q8—44no—
178C2×Q8—81no—
179C2×D4—21no—
180C2×D4—41no—
181C2×D4—41no—
182C2×D4#6452812yes—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—21no—
186C22×C4—44no—
187C22×C4—81no—
188C22×C4—761no—
189C22×C4C2×C22⋊D1912yes—
190C22×C4C2×C22⋊D1911yescharacteristic
191C2×C8—382no—
192C2×C8—384no—
193C2×C8—762no—
194C2×C8—761no—
195C2×C8—762no—
196C2×C8—761no—
197C4⋊C4—22no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—44no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—761no—
204C4⋊C4—761no—
205C4⋊C4—762no—
206C4⋊C4—762no—
207C4⋊C4#6452514yes—
208C22⋊C4—44no—
209C22⋊C4—42no—
210C22⋊C4—42no—
211C22⋊C4—81no—
212C42—41no—
213C23—22no—
214C23—42no—
215C23—41no—
216C23—42no—
217C23—41no—
218C23#1059739911yescharacteristic
219Q8—84no—
220D4—42no—
221D4—81no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—24no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—84no—
235C2×C4—1522no—
236C2×C4—1521no—
237C2×C4C2×#6452512yes—
238C2×C4#1059737812yes—
239C2×C4#1059738811yescharacteristic
240C2×C4C2×#6452811yescharacteristic
241C8—764no—
242C8—762no—
243C22—44no—
244C22—42no—
245C22—82no—
246C22—81no—
247C22—81no—
248C22#1192667812yes—
249C22#1192670011yescharacteristic
250C22#1192671211yescharacteristic
251C22#1192672712yes—
252C22#1192673411yescharacteristic
253C4—22no—
254C4—22no—
255C4—21no—
256C4—21no—
257C4—44no—
258C4—82no—
259C4—81no—
260C4—3041no—
261C2—82no—
262C2#1456263812yes—
263C2#1456266011yescharacteristic
264C2#1456268911yescharacteristic
265C2#1456288412yes—
266C2#1456294611yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2683C2
socleC23×C19#120
prime radicalC22×D4×C19D4
hypercenter#2683D19
hypocenterC19#7797
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2683

Complements

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

NH ≅ G/Ntype
2. #14565106C2semidirect
3. #14561458C2semidirect
175. C19#7797semidirect

Maximal subgroups

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

subgroupindex
#145651632
#145651062
#145614582
#145614562
C19×#26832
#779719