Finite Group Databasebeta

← #18085612

Subgroups — #18085612

Order 4864.

400 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 91 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#14571907C211yesmaximal, characteristic
2#14564609C212yesmaximal
3#14561517C212yesmaximal
4#14561516C211yesmaximal, characteristic
5C19×#1960C211yesmaximal, characteristic
6C2×#10597260C2212yes—
7#11926486—22no—
8#11926483—21no—
9#11926465—22no—
10#11926464—21no—
11#11926410C2212yes—
12#11926306—22no—
13#11926306—22no—
14C2×C19×C4⋊Q8C2211yescharacteristic
15C2×C19×#103—21no—
16C2×C19×#103—21no—
17C2×C19×#97C2211yescharacteristic
18C19×#382C2211yescharacteristic
19C22×Q8×C19—21no—
20C22×Dic38—21no—
21C22×C8×C19—21no—
22C19×C4⋊Q8—22no—
23C19×C4⋊Q8—21no—
24C19×C4⋊Q8Q812yescomplemented
25C2×C4⋊C4×C19—22no—
26C2×C4⋊C4×C19D411yescharacteristic
27C2×C4⋊C4×C19D411yescharacteristic
28C2×C42×C19C2311yescharacteristic
29C2×C4⋊Dic19—21no—
30C2×C4⋊Dic19D412yes—
31C2×C4⋊Dic19D412yes—
32C2×Dic19⋊C4—22no—
33C22×C19⋊C8—22no—
34C19×#103—42no—
35C19×#103—42no—
36C19×#97—22no—
37C19×#95—22no—
38C19⋊#95—21no—
39C19⋊#95—22no—
40C19⋊#95—21no—
41C19⋊#95—22no—
42C19⋊#95—22no—
43#10597260—22no—
44#10597260—22no—
45C2×Q8×C19—22no—
46C2×Q8×C19—41no—
47C2×Q8×C19—41no—
48C2×Q8×C19—41no—
49C2×Q8×C19—41no—
50C2×Q8×C19—41no—
51C22×C4×C19—21no—
52C22×C4×C19—21no—
53C22×C4×C19—41no—
54C22×C4×C19C2×D412yes—
55C22×C4×C19C2×D411yescharacteristic
56C22×Dic19—22no—
57C22×Dic19—22no—
58C2×Dic38—81no—
59C2×Dic38—82no—
60C2×C8×C19—22no—
61C2×C8×C19—41no—
62C2×C8×C19—41no—
63C4⋊C4×C19—24no—
64C4⋊C4×C19—41no—
65C4⋊C4×C19—41no—
66C4⋊C4×C19—42no—
67C42×C19C2×Q811yescharacteristic
68C42×C19#4111yescharacteristic
69C42×C19#4112yes—
70C4⋊Dic19—42no—
71C4⋊Dic19—42no—
72C4⋊Dic19—81no—
73Dic19⋊C4—82no—
74C2×C19⋊C8—24no—
75C2×C19⋊C8—42no—
76C2×C19⋊C8—42no—
77#10359—191nomaximal, Sylow
78C23×C19#12011yescharacteristic
79Q8×C19—42no—
80Q8×C19—42no—
81Q8×C19—81no—
82Q8×C19—81no—
83C2×C4×C19—21no—
84C2×C4×C19—21no—
85C2×C4×C19—22no—
86C2×C4×C19—22no—
87C2×C4×C19—42no—
88C2×C4×C19—41no—
89C2×C4×C19—41no—
90C2×C4×C19—42no—
91C2×C4×C19—42no—
92C2×C4×C19—81no—
93C2×C4×C19—81no—
94C2×C4×C19C22⋊Q812yes—
95C2×C4×C19C22⋊Q811yescharacteristic
96C2×C4×C19#12411yescharacteristic
97C2×C4×C19#12412yes—
98C2×Dic19—42no—
99C2×Dic19—42no—
100C2×Dic19—42no—
101C2×Dic19—42no—
102C2×Dic19—42no—
103C2×Dic19—42no—
104Dic38—84no—
105C8×C19—42no—
106C19⋊C8—44no—
107#2844—191no—
108#1993—192no—
109#1960D1911yescharacteristic
110#1295—192no—
111#1295—191no—
112C22×C19#39311yescharacteristic
113C22×C19#45311yescharacteristic
114C22×C19#45411yescharacteristic
115C22×C19#45512yes—
116C22×C19#45612yes—
117C4×C19—21no—
118C4×C19—21no—
119C4×C19—22no—
120C4×C19—22no—
121C4×C19—81no—
122C4×C19—81no—
123C4×C19—82no—
124Dic19—82no—
125Dic19—82no—
126C2×C4⋊Q8C2×D1911yescharacteristic
127C2×#103—21no—
128C2×#103—21no—
129C2×#97—192no—
130C2×#97C2×D1911yescharacteristic
131#400—382no—
132#400—381no—
133#395—382no—
134#395—381no—
135#382—192no—
136#382C2×D1911yescharacteristic
137#340—382no—
138#340—382no—
139C2×C19#165911yescharacteristic
140C2×C19#166011yescharacteristic
141C2×C19#166412yes—
142C2×C19#202711yescharacteristic
143C2×C19#202812yes—
144C22×Q8—21no—
145C22×Q8—381no—
146C22×C8—21no—
147C22×C8—382no—
148C4⋊Q8—21no—
149C4⋊Q8—22no—
150C4⋊Q8Dic3812yescomplemented
151C2×C4⋊C4—22no—
152C2×C4⋊C4—192no—
153C2×C4⋊C4—192no—
154C2×C4⋊C4—382no—
155C2×C4⋊C4—381no—
156C2×C4⋊C4C22⋊D1911yescharacteristic
157C2×C4⋊C4C22⋊D1911yescharacteristic
158C2×C42C22×D1911yescharacteristic
159#103—42no—
160#103—42no—
161#97—22no—
162#97—382no—
163#97—382no—
164#95—22no—
165#95—382no—
166#95—381no—
167#95—381no—
168#95—382no—
169#95—382no—
170C19#1035911yescharacteristic, complemented, Sylow
171C2×Q8—22no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—1521no—
178C2×Q8—1522no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4—382no—
183C22×C4—382no—
184C22×C4D4×D1912yes—
185C22×C4C2×C22⋊D1911yescharacteristic
186C2×C8—22no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—384no—
190C2×C8—762no—
191C2×C8—762no—
192C4⋊C4—24no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—42no—
196C4⋊C4—762no—
197C4⋊C4—762no—
198C4⋊C4—1522no—
199C4⋊C4—1521no—
200C42C2×Dic3811yescharacteristic
201C42#6454111yescharacteristic
202C42#6454312yes—
203C23#1059738311yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—81no—
207Q8—81no—
208Q8—1524no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—762no—
221C2×C4—762no—
222C2×C4—762no—
223C2×C4—762no—
224C2×C4—762no—
225C2×C4—762no—
226C2×C4#1059732412yes—
227C2×C4#1059733112yes—
228C2×C4#1059737011yescharacteristic
229C2×C4#1059738211yescharacteristic
230C8—42no—
231C8—764no—
232C22#1192645611yescharacteristic
233C22#1192671111yescharacteristic
234C22#1192671611yescharacteristic
235C22#1192672012yes—
236C22#1192672512yes—
237C4—21no—
238C4—21no—
239C4—22no—
240C4—22no—
241C4—81no—
242C4—81no—
243C4—82no—
244C4—1522no—
245C4—1522no—
246C2#1456293911yescharacteristic
247C2#1456294411yescharacteristic
248C2#1456296612yes—
249C2#1456479111yescharacteristic
250C2#1456479412yes—
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1960C2
socle, prime radicalC23×C19#120
hypercenter#1960D19
hypocenterC19#10359
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
24. C19×C4⋊Q8Q8semidirect
150. C4⋊Q8Dic38semidirect
170. C19#10359semidirect

Maximal subgroups

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

subgroupindex
#145719072
#145646092
#145615172
#145615162
C19×#19602
#1035919