Finite Group Databasebeta

← #18077865

Subgroups — #18077865

Order 4864.

426 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 107 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#14573960C211yesmaximal, characteristic
2#14562230C211yesmaximal, characteristic, complemented
3#14562051C212yesmaximal
4#14561471C212yesmaximal, complemented
5C19×#2986C211yesmaximal, characteristic, complemented
6#11927094C2211yescharacteristic
7#11926901—22no—
8#11926896C412yes—
9#11926892C412yes—
10#11926538—22no—
11C4×#64520C2212yes—
12C2×C4×C19⋊C8C2211yescharacteristic
13#11926286—22no—
14#11926271—22no—
15#11926271—22no—
16C19×#533C2211yescharacteristic
17C19×#446—22no—
18C8×Q8×C19—22no—
19C19×#433—22no—
20C19×#431C2212yes—
21C2×#64541—21no—
22C19×C4⋊Q8C2×C412yes—
23C19×#125D412yes—
24C19×C22⋊Q8—22no—
25C4×Q8×C19—22no—
26C19×#117D412yes—
27C2×C42×C19C2311yescharacteristic
28#10597376—22no—
29C2×#64520—22no—
30C22×C19⋊C8—21no—
31#10597321—21no—
32#10597320C2×C411yescharacteristic
33C4×D76—22no—
34#10597315C2×C411yescharacteristic
35C19×C4⋊C8—24no—
36C19×C4⋊C8D412yes—
37C19×C4⋊C8D412yes—
38C19×C22⋊C8—22no—
39C19×#97—22no—
40C4×C8×C19—22no—
41C4×C8×C19—22no—
42#10597267—24no—
43#10597266—24no—
44#10597260—22no—
45C4×C19⋊C8—21no—
46C4×C19⋊C8—22no—
47C4×C19⋊C8C2×C412yes—
48C2×Q8×C19—22no—
49C22×C4×C19C2×D411yescharacteristic
50C22×C4×C19#4112yes—
51C2×C22⋊D19—41no—
52#64541—44no—
53C2×D76—21no—
54C2×D76—22no—
55C2×C4×D19—41no—
56C2×Dic38—21no—
57C2×C8×C19—22no—
58C2×C8×C19—22no—
59C4⋊C4×C19—22no—
60C4⋊C4×C19—24no—
61C4⋊C4×C19C22⋊C414yes—
62C22⋊C4×C19—22no—
63C42×C19—22no—
64C42×C19C22×C411yescharacteristic
65C42×C19C2×D411yescharacteristic
66C42×C19C2×D412yes—
67(C2×D19)⋊C4—42no—
68C4⋊Dic19—22no—
69#64520—24no—
70#64520—42no—
71C2×C19⋊C8—22no—
72C2×C19⋊C8—42no—
73C2×C19⋊C8—42no—
74#9070—191nomaximal, Sylow
75C23×C19#12311yescharacteristic
76C22×D19—41no—
77Q8×C19—42no—
78Q8×C19—42no—
79C2×C4×C19—22no—
80C2×C4×C19—22no—
81C2×C4×C19—22no—
82C2×C4×C19—24no—
83C2×C4×C19C2×C22⋊C411yescharacteristic
84C2×C4×C19C4×D412yes—
85C2×C4×C19#12011yescharacteristic
86C2×C4×C19#12112yes—
87C22⋊D19—82no—
88C2×Dic19—41no—
89D76—42no—
90D76—42no—
91D76—42no—
92C4×D19—82no—
93Dic38—42no—
94C8×C19—42no—
95C8×C19—42no—
96C19⋊C8—42no—
97C19⋊C8—44no—
98#3131—191no—
99#2986D1911yescharacteristic, complemented
100#1526—191no—
101#1484—192no—
102#1278—192no—
103C22×C19—22no—
104C22×C19—21no—
105C22×C19#38611yescharacteristic
106C2×D19—82no—
107C2×D19—81no—
108C4×C19—22no—
109C4×C19—21no—
110C4×C19—44no—
111C4×C19#44312yes—
112C4×C19#44412yes—
113C4×C19#45412yes—
114Dic19—81no—
115#533C2×D1911yescharacteristic
116#532—191no—
117#488—382no—
118#487—192no—
119#486—192no—
120#446—22no—
121C8×Q8—22no—
122#433—22no—
123#431C2×D1912yes—
124#416—382no—
125C4×M16—192no—
126C2×C4×C8—191no—
127#330—382no—
128D4⋊C8—382no—
129D4⋊C8—382no—
130C2×C19—41no—
131C2×C19#187612yes—
132C2×C19#188811yescharacteristic
133D19—161no—
134C2×#41—381no—
135C2×M16—382no—
136C22×C8—381no—
137C4⋊Q8—191no—
138C4⋊Q8C4×D1912yes—
139#127—191no—
140#125D7612yes—
141#124—381no—
142C22⋊Q8—22no—
143#121—382no—
144C4×Q8—22no—
145C4×D4—382no—
146#117C22⋊D1912yes—
147C2×C42C22×D1911yescharacteristic
148C4⋊C8—24no—
149C4⋊C8C22⋊D1912yes—
150C4⋊C8C22⋊D1912yes—
151#103—384no—
152#102—384no—
153C22⋊C8—22no—
154#97—22no—
155#97—382no—
156C4×C8—22no—
157C4×C8—22no—
158C4×C8—192no—
159C4×C8—381no—
160C4×C8—382no—
161C19#907011yescharacteristic, complemented, Sylow
162#41—764no—
163C2×Q8—22no—
164C2×Q8—381no—
165C2×D4—381no—
166C2×D4—382no—
167C2×D4—761no—
168C22×C4—761no—
169C22×C4#6454112yes—
170C22×C4C2×C22⋊D1911yescharacteristic
171M16—384no—
172M16—762no—
173C2×C8—22no—
174C2×C8—22no—
175C2×C8—382no—
176C2×C8—762no—
177C2×C8—762no—
178C4⋊C4—24no—
179C4⋊C4—22no—
180C4⋊C4—382no—
181C4⋊C4(C2×D19)⋊C414yes—
182C22⋊C4—22no—
183C22⋊C4—762no—
184C42—22no—
185C42C2×C4×D1911yescharacteristic
186C42C2×D7611yescharacteristic
187C42C2×C22⋊D1912yes—
188C23—761no—
189C23#1059737511yescharacteristic
190Q8—42no—
191Q8—42no—
192Q8—762no—
193D4—762no—
194D4—762no—
195D4—762no—
196D4—1522no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—761no—
202C2×C4—1522no—
203C2×C4C2×(C2×D19)⋊C411yescharacteristic
204C2×C4C4×C22⋊D1912yes—
205C2×C4#1059737612yes—
206C2×C4#1059739911yescharacteristic
207C8—42no—
208C8—42no—
209C8—762no—
210C8—764no—
211C22—22no—
212C22—21no—
213C22—1522no—
214C22—1521no—
215C22#1192642311yescharacteristic
216C4—22no—
217C4—21no—
218C4—44no—
219C4—1521no—
220C4#1192665912yes—
221C4#1192666412yes—
222C4#1192671712yes—
223C2—41no—
224C2—3041no—
225C2#1456396212yes—
226C2#1456403811yescharacteristic
subgroupG/H
centerC2×C4#10597399
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2986C2
socleC22×C19#386
prime radical#11927094C22
cosocleC2×C42×C19C23
hypercenter#2986D19
hypocenterC19#9070
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2986

Complements

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

NH ≅ G/Ntype
2. #14562230C2semidirect
4. #14561471C2semidirect
5. C19×#2986C2semidirect
99. #2986D19semidirect
161. C19#9070semidirect

Maximal subgroups

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

subgroupindex
#145739602
#145622302
#145620512
#145614712
C19×#29862
#907019