Finite Group Databasebeta

← #18071849

Subgroups — #18071849

Order 4864.

350 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 87 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#14565198C212yesmaximal
2#14565173C211yesmaximal, characteristic
3#14561461C211yesmaximal, characteristic
4#14561458C212yesmaximal
5C19×#2809C211yesmaximal, characteristic
6C2×#10597264—21no—
7C2×#10597292—21no—
8#11926414C2211yescharacteristic
9#11926306—22no—
10#11926306—22no—
11#11926299C2211yescharacteristic
12#11926299C2212yes—
13C19×#400—21no—
14C19×#398—22no—
15C19×#391—21no—
16C19×#391C2211yescharacteristic
17C19×#389C2212yes—
18C19×#387—22no—
19C22×Q8×C19D411yescharacteristic
20C2×C4⋊C4×C19—22no—
21C2×C4⋊C4×C19—21no—
22C2×C4⋊C4×C19—21no—
23C2×C4⋊C4×C19D412yes—
24C2×C4⋊C4×C19D412yes—
25C2×C4⋊C4×C19D411yescharacteristic
26C2×C42×C19—21no—
27C2×C42×C19C2311yescharacteristic
28C2×C4⋊Dic19—21no—
29C2×C4⋊Dic19—22no—
30C22×C19⋊C8—21no—
31C22×C19⋊C8—22no—
32C19×#95—21no—
33C19×#95—22no—
34C19×#95—22no—
35C19×#95—22no—
36C19×#95—22no—
37#10597292—42no—
38#10597264—42no—
39C2×Q8×C19—21no—
40C2×Q8×C19—41no—
41C2×Q8×C19—41no—
42C2×Q8×C19Q1612yes—
43C22×C4×C19—21no—
44C22×C4×C19—22no—
45C22×C4×C19—22no—
46C22×C4×C19—21no—
47C22×C4×C19C2×D411yescharacteristic
48C22×C4×C19C2×D412yes—
49C22×Dic19—41no—
50C4⋊C4×C19—22no—
51C4⋊C4×C19—22no—
52C4⋊C4×C19—42no—
53C4⋊C4×C19—41no—
54C4⋊C4×C19—42no—
55C4⋊C4×C19—42no—
56C4⋊C4×C19—81no—
57C4⋊C4×C19—81no—
58C42×C19—41no—
59C42×C19—81no—
60C4⋊Dic19—41no—
61C4⋊Dic19—41no—
62C4⋊Dic19—44no—
63C2×C19⋊C8—22no—
64C2×C19⋊C8—41no—
65C2×C19⋊C8—41no—
66C2×C19⋊C8—42no—
67C2×C19⋊C8—42no—
68C2×C19⋊C8—42no—
69#7831—191nomaximal, Sylow
70C23×C19#12011yescharacteristic
71Q8×C19—42no—
72Q8×C19—81no—
73C2×C4×C19—21no—
74C2×C4×C19—22no—
75C2×C4×C19—22no—
76C2×C4×C19—21no—
77C2×C4×C19—22no—
78C2×C4×C19—41no—
79C2×C4×C19—41no—
80C2×C4×C19—42no—
81C2×C4×C19—42no—
82C2×C4×C19—42no—
83C2×C4×C19—41no—
84C2×C4×C19—42no—
85C2×C4×C19—42no—
86C2×C4×C19—42no—
87C2×C4×C19—42no—
88C2×C4×C19C2×Q1611yescharacteristic
89C2×C4×C19#13512yes—
90C2×C4×C19#13711yescharacteristic
91C2×C4×C19#13712yes—
92C2×Dic19—81no—
93C2×Dic19—82no—
94C19⋊C8—42no—
95C19⋊C8—82no—
96#2809D1911yescharacteristic
97#2100—192no—
98#2095—191no—
99#1272—191no—
100#1271—192no—
101C22×C19#45111yescharacteristic
102C22×C19#45212yes—
103C22×C19#45311yescharacteristic
104C22×C19#45412yes—
105C22×C19#45811yescharacteristic
106C4×C19—21no—
107C4×C19—21no—
108C4×C19—22no—
109C4×C19—22no—
110C4×C19—42no—
111C4×C19—82no—
112C4×C19—82no—
113C4×C19—81no—
114Dic19—161no—
115C2×#107—381no—
116C2×#103—381no—
117#400—21no—
118#398—22no—
119#391—21no—
120#391C2×D1911yescharacteristic
121#389C2×D1912yes—
122#387—22no—
123#384—191no—
124#340—382no—
125#340—382no—
126#336—191no—
127#336—192no—
128C2×C19#161411yescharacteristic
129C2×C19#161512yes—
130C2×C19#163411yescharacteristic
131C2×C19#163612yes—
132C2×C19#165711yescharacteristic
133C22×Q8C22⋊D1911yescharacteristic
134C22×C8—381no—
135C22×C8—382no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—382no—
140C2×C4⋊C4—381no—
141C2×C4⋊C4C22⋊D1912yes—
142C2×C4⋊C4C22⋊D1912yes—
143C2×C4⋊C4C22⋊D1911yescharacteristic
144C2×C42—21no—
145C2×C42C22×D1911yescharacteristic
146#107—762no—
147#103—762no—
148#95—21no—
149#95—22no—
150#95—22no—
151#95—22no—
152#95—22no—
153C19#783111yescharacteristic, complemented, Sylow
154C2×Q8—21no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8#6452812yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—761no—
163C22×C4C2×C22⋊D1911yescharacteristic
164C22×C4C2×C22⋊D1912yes—
165C2×C8—382no—
166C2×C8—761no—
167C2×C8—761no—
168C2×C8—762no—
169C2×C8—762no—
170C2×C8—762no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—41no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C4⋊C4—81no—
178C4⋊C4—81no—
179C4⋊C4—761no—
180C4⋊C4—761no—
181C4⋊C4—764no—
182C42—41no—
183C42—81no—
184C23#1059739911yescharacteristic
185Q8—42no—
186Q8—81no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—41no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—1521no—
203C2×C4—1522no—
204C2×C4#1059738811yescharacteristic
205C2×C4C2×#6452811yescharacteristic
206C2×C4#1059739612yes—
207C2×C4#1059739712yes—
208C8—762no—
209C8—1522no—
210C22#1192670011yescharacteristic
211C22#1192670612yes—
212C22#1192671211yescharacteristic
213C22#1192671712yes—
214C22#1192673411yescharacteristic
215C4—21no—
216C4—21no—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—82no—
221C4—81no—
222C4—82no—
223C4—3041no—
224C2#1456266011yescharacteristic
225C2#1456266612yes—
226C2#1456278011yescharacteristic
227C2#1456279312yes—
228C2#1456293311yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2809C2
socle, prime radicalC23×C19#120
hypercenter#2809D19
hypocenterC19#7831
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2809

Complements

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

NH ≅ G/Ntype
153. C19#7831semidirect

Maximal subgroups

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

subgroupindex
#145651982
#145651732
#145614612
#145614582
C19×#28092
#783119