Finite Group Databasebeta

← #18077484

Subgroups — #18077484

Order 4864.

458 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 119 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#14566821C211yesmaximal, characteristic
2#14564609C212yesmaximal
3C2×#11926286C211yesmaximal, characteristic
4#14561517C212yesmaximal
5C2×C19×#491C211yesmaximal, characteristic
6C2×#10597260C2212yes—
7#11926443—22no—
8#11926430—22no—
9#11926430—22no—
10#11926410C2212yes—
11#11926306—22no—
12#11926306—22no—
13#11926286—22no—
14C2×C19×C4⋊Q8C2211yescharacteristic
15C2×C19×#125C2211yescharacteristic
16C19×#491—22no—
17C19×#491C414yescomplemented
18C2×C19×#103—22no—
19C2×C19×#97C2211yescharacteristic
20C22×Q8×C19—21no—
21C22×C8×C19—21no—
22C19×C4⋊Q8—21no—
23C19×C4⋊Q8—22no—
24C19×C4⋊Q8C2×C412yes—
25C19×#125—22no—
26C19×#125C2×C412yes—
27C19×#125D412yes—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19—22no—
30C2×C4⋊C4×C19D412yes—
31C2×C42×C19C2311yescharacteristic
32C2×C4⋊Dic19—22no—
33C2×C4⋊Dic19D412yes—
34C2×C4⋊Dic19D412yes—
35C2×C4×Dic19—22no—
36C22×C19⋊C8—22no—
37C19×#103—28no—
38C19×#97—21no—
39C19×#97C2×C412yes—
40C19⋊#95—22no—
41C19⋊#95—22no—
42C19⋊#95—22no—
43C19⋊#95—22no—
44#10597260—22no—
45#10597260—22no—
46C2×Q8×C19—22no—
47C2×Q8×C19—42no—
48C2×Q8×C19—42no—
49C2×Q8×C19—41no—
50C22×C4×C19—22no—
51C22×C4×C19—41no—
52C22×C4×C19C2×D412yes—
53C22×C4×C19C2×D411yescharacteristic
54C22×Dic19—22no—
55C22×Dic19—22no—
56C2×C8×C19—22no—
57C2×C8×C19—41no—
58C2×C8×C19—41no—
59C4⋊C4×C19—24no—
60C4⋊C4×C19—24no—
61C4⋊C4×C19—22no—
62C4⋊C4×C19—24no—
63C4⋊C4×C19—42no—
64C4⋊C4×C19C22⋊C414yes—
65C42×C19C22×C411yescharacteristic
66C42×C19C2×D411yescharacteristic
67C42×C19#4112yes—
68C4⋊Dic19—42no—
69C4⋊Dic19—42no—
70C4⋊Dic19—82no—
71C4×Dic19—82no—
72C2×C19⋊C8—24no—
73C2×C19⋊C8—42no—
74C2×C19⋊C8—42no—
75#9004—191nomaximal, Sylow
76C23×C19#12011yescharacteristic
77Q8×C19—44no—
78Q8×C19—82no—
79C2×C4×C19—21no—
80C2×C4×C19—21no—
81C2×C4×C19—22no—
82C2×C4×C19—22no—
83C2×C4×C19—24no—
84C2×C4×C19—42no—
85C2×C4×C19—42no—
86C2×C4×C19—42no—
87C2×C4×C19—81no—
88C2×C4×C19—81no—
89C2×C4×C19C2×C22⋊C411yescharacteristic
90C2×C4×C19C4×D412yes—
91C2×C4×C19#12112yes—
92C2×C4×C19#12311yescharacteristic
93C2×Dic19—42no—
94C2×Dic19—42no—
95C2×Dic19—42no—
96C2×Dic19—42no—
97C2×Dic19—42no—
98C2×Dic19—42no—
99C8×C19—42no—
100C19⋊C8—44no—
101C2×#491D1911yescharacteristic
102#2382—191no—
103#1993—192no—
104C2×#330—191no—
105#1295—192no—
106C22×C19#38611yescharacteristic
107C22×C19#45411yescharacteristic
108C22×C19#45411yescharacteristic
109C22×C19#45512yes—
110C22×C19#45612yes—
111C4×C19—22no—
112C4×C19—22no—
113C4×C19—21no—
114C4×C19—21no—
115C4×C19—44no—
116C4×C19—82no—
117Dic19—82no—
118Dic19—82no—
119C2×C4⋊Q8C2×D1911yescharacteristic
120C2×#125C2×D1911yescharacteristic
121#491—22no—
122#491Dic1914yescomplemented
123C2×#103—22no—
124C2×#97—192no—
125C2×#97C2×D1911yescharacteristic
126#389—382no—
127#387—382no—
128#387—382no—
129#382—192no—
130#340—382no—
131#340—382no—
132#330—382no—
133C2×C19#166211yescharacteristic
134C2×C19#166311yescharacteristic
135C2×C19#166412yes—
136C2×C19#188212yes—
137C2×C19#188811yescharacteristic
138C22×Q8—21no—
139C22×C8—21no—
140C22×C8—382no—
141C4⋊Q8—22no—
142C4⋊Q8—21no—
143C4⋊Q8C2×Dic1912yes—
144#125—22no—
145#125C2×Dic1912yes—
146#125C22⋊D1912yes—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—192no—
150C2×C4⋊C4—192no—
151C2×C4⋊C4—382no—
152C2×C4⋊C4C22⋊D1912yes—
153C2×C42—382no—
154C2×C42C22×D1911yescharacteristic
155#103—28no—
156#97—21no—
157#97—382no—
158#97—382no—
159#97C2×Dic1912yes—
160#95—382no—
161#95—382no—
162#95—382no—
163#95—382no—
164C19#900411yescharacteristic, complemented, Sylow
165C2×Q8—22no—
166C2×Q8—42no—
167C2×Q8—42no—
168C2×Q8—41no—
169C22×C4—22no—
170C22×C4—41no—
171C22×C4—382no—
172C22×C4—382no—
173C22×C4D4×D1912yes—
174C22×C4C2×C22⋊D1911yescharacteristic
175C2×C8—22no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—384no—
179C2×C8—762no—
180C2×C8—762no—
181C4⋊C4—24no—
182C4⋊C4—22no—
183C4⋊C4—24no—
184C4⋊C4—24no—
185C4⋊C4—42no—
186C4⋊C4—762no—
187C4⋊C4—762no—
188C4⋊C4—1522no—
189C4⋊C4C22⋊Dic1914yes—
190C42—1522no—
191C42#6454312yes—
192C42C22×Dic1911yescharacteristic
193C42C2×C22⋊D1911yescharacteristic
194C23#1059738311yescharacteristic
195Q8—44no—
196Q8—82no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—81no—
206C2×C4—81no—
207C2×C4—762no—
208C2×C4—762no—
209C2×C4—762no—
210C2×C4—762no—
211C2×C4—762no—
212C2×C4—762no—
213C2×C4D4×Dic1912yes—
214C2×C4#1059738111yescharacteristic
215C2×C4#1059738512yes—
216C2×C4C2×C22⋊Dic1911yescharacteristic
217C8—42no—
218C8—764no—
219C22#1192642411yescharacteristic
220C22#1192671611yescharacteristic
221C22#1192671611yescharacteristic
222C22#1192672012yes—
223C22#1192672512yes—
224C4—22no—
225C4—22no—
226C4—21no—
227C4—21no—
228C4—44no—
229C4—82no—
230C4—1522no—
231C4—1522no—
232C2#1456295611yescharacteristic
233C2#1456296111yescharacteristic
234C2#1456296612yes—
235C2#1456400612yes—
236C2#1456403911yescharacteristic
subgroupG/H
centerC23#10597383
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC2×C19×#491C2
socle, prime radicalC23×C19#120
cosocleC2×C42×C19C23
hypercenterC2×#491D19
hypocenterC19#9004
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
17. C19×#491C4semidirect
122. #491Dic19semidirect
164. C19#9004semidirect

Maximal subgroups

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

subgroupindex
#145668212
#145646092
C2×#119262862
#145615172
C2×C19×#4912
#900419