Finite Group Databasebeta

← #18086674

Subgroups — #18086674

Order 4864.

386 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 77 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#14563809C211yesmaximal, characteristic, complemented
2#14562357C212yesmaximal, complemented
3#14562246C212yesmaximal, complemented
4#14561546C211yesmaximal, characteristic, complemented
5C19×#3253C211yesmaximal, characteristic
6#11926601C2212yes—
7C2×#10597279—22no—
8#11926568C2211yescharacteristic
9C2×#10597260C2211yescharacteristic
10#11926290—22no—
11#11926288—22no—
12#11926284—24no—
13C19×#532C2212yes—
14C19×#476—22no—
15C19×#469—22no—
16C19×#459—22no—
17C19×#423C2211yescharacteristic
18C2×#41×C19—22no—
19C2×D8×C19—22no—
20C2×M16×C19D412yes—
21C19×C4⋊Q8D412yes—
22C19×#127D412yes—
23C19×#124—22no—
24C19×#121—22no—
25C19×#121—22no—
26C4×D4×C19—22no—
27C4×D4×C19—22no—
28C2×C42×C19C2311yescharacteristic
29C2×#64520—21no—
30C22×C19⋊C8—21no—
31C19×#106—22no—
32C19×C4⋊C8—22no—
33C19×#102—24no—
34C22⋊(C19⋊C8)—22no—
35#10597279—44no—
36C4⋊(C19⋊C8)—22no—
37C4⋊(C19⋊C8)—22no—
38#10597260—21no—
39#10597260—22no—
40#10597260D412yes—
41#41×C19—84no—
42C2×Q8×C19—22no—
43C2×D4×C19—22no—
44C2×D4×C19—22no—
45C2×D4×C19—22no—
46C2×D4×C19—42no—
47C22×C4×C19—42no—
48C22×C4×C19C2×D411yescharacteristic
49C22×C4×C19#4112yes—
50D8×C19—82no—
51M16×C19—42no—
52C2×C8×C19—22no—
53C4⋊C4×C19—22no—
54C4⋊C4×C19—22no—
55C22⋊C4×C19—42no—
56C22⋊C4×C19—42no—
57C42×C19C2×D411yescharacteristic
58C42×C19C2×D412yes—
59C42×C19#4111yescharacteristic
60#64520—42no—
61C2×C19⋊C8—22no—
62C2×C19⋊C8—22no—
63C2×C19⋊C8—22no—
64C2×C19⋊C8—41no—
65C2×C19⋊C8—42no—
66#10524—191nomaximal, Sylow
67C23×C19—42no—
68C23×C19#12411yescharacteristic
69Q8×C19—82no—
70D4×C19—42no—
71D4×C19—42no—
72D4×C19—82no—
73D4×C19—82no—
74D4×C19—84no—
75C2×C4×C19—21no—
76C2×C4×C19—21no—
77C2×C4×C19—42no—
78C2×C4×C19—42no—
79C2×C4×C19—84no—
80C2×C4×C19#12011yescharacteristic
81C2×C4×C19#12111yescharacteristic
82C2×C4×C19#12112yes—
83C2×C4×C19#12312yes—
84C8×C19—42no—
85C19⋊C8—24no—
86C19⋊C8—82no—
87C19⋊C8—81no—
88#3253D1911yescharacteristic
89#1849—191no—
90#1557—192no—
91#1530—192no—
92#1307—191no—
93C22×C19—22no—
94C22×C19—21no—
95C22×C19—82no—
96C22×C19—82no—
97C22×C19—82no—
98C22×C19#39411yescharacteristic
99C4×C19—22no—
100C4×C19—22no—
101C4×C19—21no—
102C4×C19—82no—
103C4×C19#45311yescharacteristic
104C4×C19#45611yescharacteristic
105#532C2×D1912yes—
106#476—22no—
107#469—22no—
108#459—22no—
109#432—192no—
110C2×#108—382no—
111#423—191no—
112#423C2×D1911yescharacteristic
113C2×#97—191no—
114#332—382no—
115#331—382no—
116#329—384no—
117C2×C19—41no—
118C2×C19—162no—
119C2×C19#203911yescharacteristic
120C2×C19#204812yes—
121C2×#41—22no—
122C2×D8—22no—
123C2×M16—381no—
124C2×M16C22⋊D1912yes—
125C22×C8—381no—
126C4⋊Q8C22⋊D1912yes—
127#127C22⋊D1912yes—
128#124—22no—
129#121—22no—
130#121—22no—
131C4×D4—22no—
132C4×D4—22no—
133C2×C42C22×D1911yescharacteristic
134#108—764no—
135#106—22no—
136C4⋊C8—22no—
137C4⋊C8—382no—
138C4⋊C8—382no—
139#102—24no—
140C22⋊C8—382no—
141#97—192no—
142#97—382no—
143#97—381no—
144C19#1052411yescharacteristic, complemented, Sylow
145#41—84no—
146C2×Q8—22no—
147C2×D4—22no—
148C2×D4—22no—
149C2×D4—22no—
150C2×D4—42no—
151C22×C4—42no—
152C22×C4#6454312yes—
153C22×C4C2×C22⋊D1911yescharacteristic
154D8—82no—
155M16—42no—
156M16—762no—
157C2×C8—22no—
158C2×C8—382no—
159C2×C8—382no—
160C2×C8—382no—
161C2×C8—762no—
162C2×C8—761no—
163C4⋊C4—22no—
164C4⋊C4—22no—
165C22⋊C4—42no—
166C22⋊C4—42no—
167C42D4×D1911yescharacteristic
168C42#6454311yescharacteristic
169C42C2×C22⋊D1912yes—
170C23—42no—
171C23#1059738211yescharacteristic
172Q8—82no—
173D4—42no—
174D4—42no—
175D4—82no—
176D4—82no—
177D4—84no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—84no—
183C2×C4#1059738112yes—
184C2×C4#1059738411yescharacteristic
185C2×C4#1059738512yes—
186C2×C4#1059739911yescharacteristic
187C8—42no—
188C8—384no—
189C8—1522no—
190C8—1521no—
191C22—22no—
192C22—21no—
193C22—82no—
194C22—82no—
195C22—82no—
196C22#1192645811yescharacteristic
197C4—22no—
198C4—22no—
199C4—21no—
200C4—82no—
201C4#1192671211yescharacteristic
202C4#1192672711yescharacteristic
203C2—41no—
204C2—162no—
205C2#1456485611yescharacteristic
206C2#1456490512yes—
subgroupG/H
centerC22#11926458
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3253C2
socleC22×C19#394
hypercenter#3253D19
hypocenterC19#10524
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3253

Complements

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

NH ≅ G/Ntype
1. #14563809C2semidirect
2. #14562357C2semidirect
3. #14562246C2semidirect
4. #14561546C2semidirect
144. C19#10524semidirect

Maximal subgroups

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

subgroupindex
#145638092
#145623572
#145622462
#145615462
C19×#32532
#1052419