Finite Group Databasebeta

← #18087038

Subgroups — #18087038

Order 4864.

374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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#14563804C211yesmaximal, characteristic
2#14563768C212yesmaximal
3#14561516C212yesmaximal
4#14561516C211yesmaximal, characteristic
5C19×#2844C211yesmaximal, characteristic
6C2×#10597264—21no—
7C2×#10597265—21no—
8C2×#10597260C2212yes—
9C2×#10597260C2211yescharacteristic
10#11926414C2211yescharacteristic
11#11926306—22no—
12#11926306—22no—
13C19×#400—22no—
14C19×#400—21no—
15C19×#395—22no—
16C19×#395—21no—
17C19×#382C2212yes—
18C19×#382C2211yescharacteristic
19C22×Q8×C19—21no—
20C2×C4⋊C4×C19—21no—
21C2×C4⋊C4×C19—22no—
22C2×C4⋊C4×C19D412yes—
23C2×C4⋊C4×C19D412yes—
24C2×C4⋊C4×C19D411yescharacteristic
25C2×C4⋊C4×C19D411yescharacteristic
26C2×C42×C19C2311yescharacteristic
27C2×C4⋊Dic19—22no—
28C2×C4⋊Dic19—21no—
29C22×C19⋊C8—21no—
30C22×C19⋊C8—22no—
31C19×#95—21no—
32C19×#95—22no—
33C19×#95—21no—
34C19×#95—22no—
35C19×#95—22no—
36C19×#95—22no—
37#10597265—42no—
38#10597264—42no—
39#10597260—21no—
40#10597260—22no—
41#10597260Q812yescomplemented
42#10597260Q814yescomplemented
43C2×Q8×C19—81no—
44C2×Q8×C19—82no—
45C22×C4×C19—21no—
46C22×C4×C19—22no—
47C22×C4×C19—21no—
48C22×C4×C19—22no—
49C22×C4×C19C2×D411yescharacteristic
50C22×C4×C19C2×D412yes—
51C22×Dic19—41no—
52C4⋊C4×C19—42no—
53C4⋊C4×C19—42no—
54C4⋊C4×C19—41no—
55C4⋊C4×C19—41no—
56C4⋊C4×C19—81no—
57C4⋊C4×C19—82no—
58C42×C19C2×Q811yescharacteristic
59C42×C19C2×Q812yes—
60C42×C19#4111yescharacteristic
61C4⋊Dic19—41no—
62C4⋊Dic19—41no—
63C4⋊Dic19—44no—
64C2×C19⋊C8—22no—
65C2×C19⋊C8—22no—
66C2×C19⋊C8—22no—
67C2×C19⋊C8—24no—
68C2×C19⋊C8—42no—
69C2×C19⋊C8—42no—
70#10584—191nomaximal, Sylow
71C23×C19#12011yescharacteristic
72Q8×C19—84no—
73C2×C4×C19—21no—
74C2×C4×C19—22no—
75C2×C4×C19—22no—
76C2×C4×C19—21no—
77C2×C4×C19—41no—
78C2×C4×C19—41no—
79C2×C4×C19—42no—
80C2×C4×C19—42no—
81C2×C4×C19—42no—
82C2×C4×C19—42no—
83C2×C4×C19—42no—
84C2×C4×C19—42no—
85C2×C4×C19—42no—
86C2×C4×C19—42no—
87C2×C4×C19C22⋊Q811yescharacteristic
88C2×C4×C19C22⋊Q812yes—
89C2×C4×C19C4⋊Q811yescharacteristic
90C2×C4×C19C4⋊Q812yes—
91C2×Dic19—81no—
92C2×Dic19—82no—
93C19⋊C8—24no—
94C19⋊C8—44no—
95#2844D1911yescharacteristic
96#1847—191no—
97#1836—192no—
98#1295—192no—
99#1295—191no—
100C22×C19#39511yescharacteristic
101C22×C19#45311yescharacteristic
102C22×C19#45412yes—
103C22×C19#45512yes—
104C22×C19#45611yescharacteristic
105C4×C19—21no—
106C4×C19—21no—
107C4×C19—22no—
108C4×C19—22no—
109C4×C19—81no—
110C4×C19—81no—
111C4×C19—82no—
112C4×C19—82no—
113Dic19—161no—
114C2×#107—381no—
115C2×#106—381no—
116C2×#97—192no—
117C2×#97—191no—
118#400—22no—
119#400—21no—
120#395—22no—
121#395—21no—
122#384—191no—
123#382C2×D1912yes—
124#382C2×D1911yescharacteristic
125#340—382no—
126#340—382no—
127C2×C19#165711yescharacteristic
128C2×C19#165911yescharacteristic
129C2×C19#166412yes—
130C2×C19#206011yescharacteristic
131C2×C19#206112yes—
132C22×Q8—21no—
133C22×C8—381no—
134C22×C8—382no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—382no—
138C2×C4⋊C4—381no—
139C2×C4⋊C4C22⋊D1912yes—
140C2×C4⋊C4C22⋊D1912yes—
141C2×C4⋊C4C22⋊D1911yescharacteristic
142C2×C4⋊C4C22⋊D1911yescharacteristic
143C2×C42C22×D1911yescharacteristic
144#107—762no—
145#106—762no—
146#97—192no—
147#97—194no—
148#97—381no—
149#97—382no—
150#95—22no—
151#95—21no—
152#95—21no—
153#95—22no—
154#95—22no—
155#95—22no—
156C19#1058411yescharacteristic, complemented, Sylow
157C2×Q8—81no—
158C2×Q8—82no—
159C22×C4—21no—
160C22×C4—22no—
161C22×C4—21no—
162C22×C4—22no—
163C22×C4—761no—
164C22×C4C2×C22⋊D1911yescharacteristic
165C22×C4C2×C22⋊D1912yes—
166C2×C8—382no—
167C2×C8—382no—
168C2×C8—382no—
169C2×C8—384no—
170C2×C8—762no—
171C2×C8—762no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—81no—
177C4⋊C4—82no—
178C4⋊C4—761no—
179C4⋊C4—761no—
180C4⋊C4—764no—
181C42Q8×D1912yes—
182C42Q8×D1911yescharacteristic
183C42#6454511yescharacteristic
184C23#1059739911yescharacteristic
185Q8—84no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—1521no—
201C2×C4—1522no—
202C2×C4#1059739011yescharacteristic
203C2×C4#1059739012yes—
204C2×C4#1059739211yescharacteristic
205C2×C4#1059739212yes—
206C8—384no—
207C8—764no—
208C22#1192646311yescharacteristic
209C22#1192671211yescharacteristic
210C22#1192671712yes—
211C22#1192672212yes—
212C22#1192672711yescharacteristic
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—81no—
218C4—81no—
219C4—82no—
220C4—82no—
221C4—3041no—
222C2#1456293311yescharacteristic
223C2#1456294111yescharacteristic
224C2#1456296912yes—
225C2#1456497711yescharacteristic
226C2#1456498212yes—
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2844C2
socle, prime radicalC23×C19#120
hypercenter#2844D19
hypocenterC19#10584
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2844

Complements

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

NH ≅ G/Ntype
41. #10597260Q8semidirect
42. #10597260Q8semidirect
156. C19#10584semidirect

Maximal subgroups

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

subgroupindex
#145638042
#145637682
#145615162
C19×#28442
#1058419