Finite Group Databasebeta

← #18085783

Subgroups — #18085783

Order 4864.

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

normal subgroups only

This group has 406 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#14563735C212yesmaximal
2#14563710C211yesmaximal, characteristic
3#14561543C211yesmaximal, characteristic
4#14561488C212yesmaximal
5C19×#2608C211yesmaximal, characteristic
6C2×#10597372C2211yescharacteristic
7#11926508C2212yes—
8#11926407C2211yescharacteristic
9#11926310—22no—
10#11926304—22no—
11#11926304—22no—
12C19×#396—22no—
13C19×#389—22no—
14C19×#387—22no—
15C19×#381C2211yescharacteristic
16C4×C22⋊C4×C19C2212yes—
17C23×C4×C19C2311yescharacteristic
18C2×C4⋊C4×C19—22no—
19C2×C4⋊C4×C19—22no—
20C2×C4⋊C4×C19—22no—
21C2×C22⋊C4×C19—22no—
22C2×C22⋊C4×C19D412yes—
23C2×C42×C19D412yes—
24C2×C42×C19D412yes—
25C2×C22⋊Dic19—21no—
26C2×C22⋊Dic19—21no—
27#10597372—22no—
28#10597372—22no—
29C2×C4⋊Dic19Q812yes—
30C2×C4×Dic19—21no—
31C2×#64520—22no—
32C19×#95—22no—
33C19×#95—22no—
34C19×#95—22no—
35C19⋊#95—22no—
36C22⋊(C19⋊C8)—22no—
37C22⋊(C19⋊C8)—22no—
38C24×C19C2×D411yescharacteristic
39C22×C4×C19—22no—
40C22×C4×C19—22no—
41C22×C4×C19—22no—
42C22×C4×C19—42no—
43C22×C4×C19C2×D412yes—
44C22×C4×C19C2×Q811yescharacteristic
45C22×C4×C19#4112yes—
46C22×C4×C19#4111yescharacteristic
47C22×Dic19—22no—
48C22×Dic19—41no—
49C4⋊C4×C19—44no—
50C4⋊C4×C19—44no—
51C4⋊C4×C19—82no—
52C22⋊C4×C19—44no—
53C22⋊C4×C19—42no—
54C42×C19—42no—
55C42×C19—42no—
56C22⋊Dic19—41no—
57C22⋊Dic19—41no—
58C22⋊Dic19—42no—
59C4⋊Dic19—24no—
60C4×Dic19—42no—
61#64520—42no—
62#64520—42no—
63C2×C19⋊C8—42no—
64#10389—191nomaximal, Sylow
65C23×C19—22no—
66C23×C19—42no—
67C23×C19#12011yescharacteristic
68C23×C19C22⋊Q811yescharacteristic
69C23×C19#12411yescharacteristic
70C2×C4×C19—22no—
71C2×C4×C19—22no—
72C2×C4×C19—24no—
73C2×C4×C19—41no—
74C2×C4×C19—41no—
75C2×C4×C19—42no—
76C2×C4×C19—42no—
77C2×C4×C19—42no—
78C2×C4×C19—42no—
79C2×C4×C19—42no—
80C2×C4×C19—42no—
81C2×C4×C19—42no—
82C2×C4×C19—42no—
83C2×C4×C19—42no—
84C2×C4×C19C22⋊Q812yes—
85C2×C4×C19#12412yes—
86C2×Dic19—42no—
87C2×Dic19—82no—
88C2×Dic19—81no—
89C2×Dic19—82no—
90C19⋊C8—82no—
91#2608D1911yescharacteristic
92#1826—192no—
93#1820—191no—
94#1306—191no—
95#1284—192no—
96C22×C19—22no—
97C22×C19—21no—
98C22×C19—21no—
99C22×C19—22no—
100C22×C19—22no—
101C22×C19—82no—
102C22×C19#39311yescharacteristic
103C22×C19#45812yes—
104C4×C19—22no—
105C4×C19—22no—
106C4×C19—44no—
107C4×C19—82no—
108C4×C19—82no—
109Dic19—82no—
110Dic19—161no—
111C2×#117—191no—
112#407—192no—
113#396—22no—
114#389—22no—
115#387—22no—
116#381—191no—
117#381C2×D1911yescharacteristic
118C4×C22⋊C4C2×D1912yes—
119#342—382no—
120#339—382no—
121#339—382no—
122C2×C19—22no—
123C2×C19—41no—
124C2×C19—41no—
125C2×C19#203011yescharacteristic
126C2×C19#203112yes—
127C23×C4C22×D1911yescharacteristic
128C2×M16—382no—
129#117—382no—
130#117—382no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—192no—
135C2×C22⋊C4—22no—
136C2×C22⋊C4—381no—
137C2×C22⋊C4—381no—
138C2×C22⋊C4C22⋊D1912yes—
139C2×C42—381no—
140C2×C42C22⋊D1912yes—
141C2×C42C22⋊D1912yes—
142C22⋊C8—382no—
143C22⋊C8—382no—
144#95—22no—
145#95—22no—
146#95—22no—
147#95—382no—
148C19#1038911yescharacteristic, complemented, Sylow
149C24C2×C22⋊D1911yescharacteristic
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—42no—
154C22×C4—382no—
155C22×C4—761no—
156C22×C4Q8×D1911yescharacteristic
157C22×C4#6454512yes—
158C22×C4#6454511yescharacteristic
159C22×C4C2×C22⋊D1912yes—
160M16—762no—
161M16—762no—
162C2×C8—762no—
163C4⋊C4—44no—
164C4⋊C4—44no—
165C4⋊C4—82no—
166C4⋊C4—384no—
167C22⋊C4—44no—
168C22⋊C4—42no—
169C22⋊C4—761no—
170C22⋊C4—761no—
171C22⋊C4—762no—
172C42—42no—
173C42—42no—
174C42—762no—
175C23—22no—
176C23—42no—
177C23#1059739211yescharacteristic
178C23#1059739311yescharacteristic
179C23#1059739911yescharacteristic
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—762no—
195C2×C4—1521no—
196C2×C4—1522no—
197C2×C4—1522no—
198C2×C4#1059739212yes—
199C2×C4#1059739312yes—
200C8—1522no—
201C22—22no—
202C22—21no—
203C22—21no—
204C22—22no—
205C22—22no—
206C22—82no—
207C22#1192645511yescharacteristic
208C22#1192673412yes—
209C4—22no—
210C4—22no—
211C4—44no—
212C4—82no—
213C4—82no—
214C4—3041no—
215C4—1522no—
216C2—22no—
217C2—41no—
218C2—41no—
219C2#1456480111yescharacteristic
220C2#1456480412yes—
subgroupG/H
centerC22#11926455
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2608C2
socleC22×C19#393
prime radicalC24×C19C2×D4
hypercenter#2608D19
hypocenterC19#10389
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2608

Complements

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

NH ≅ G/Ntype
148. C19#10389semidirect

Maximal subgroups

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

subgroupindex
#145637352
#145637102
#145615432
#145614882
C19×#26082
#1038919