Finite Group Databasebeta

← #18083832

Subgroups — #18083832

Order 4864.

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

normal subgroups only

This group has 552 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
1C2×#11926909C212yesmaximal
2#14571703C211yesmaximal, characteristic, complemented
3#14564458C211yesmaximal, characteristic
4C2×#11926285C212yesmaximal, complemented
5C19×#1295C211yesmaximal, characteristic, complemented
6C2×#10597320C2211yescharacteristic
7C2×#10597316C2212yes—
8#11926909—24no—
9#11926909—24no—
10C2×#10597278—22no—
11C2×#10597278—22no—
12C2×#10597266—22no—
13C2×#10597260C2211yescharacteristic
14#11926484—22no—
15#11926476—22no—
16#11926474—22no—
17#11926285—24no—
18C2×C19×#97C2212yes—
19C19×#382C2211yescharacteristic
20C22×D76—21no—
21C22×D76—22no—
22C22×C8×C19—22no—
23C2×C4⋊C4×C19D412yes—
24C2×C42×C19C2311yescharacteristic
25C2×C4⋊Dic19—22no—
26C2×C4⋊Dic19D412yes—
27C2×C4⋊Dic19D412yes—
28C2×Dic19⋊C4—22no—
29C2×Dic19⋊C4—22no—
30C22×C19⋊C8—21no—
31#10597320—22no—
32#10597320—21no—
33#10597320D412yes—
34#10597316—22no—
35#10597316—22no—
36#10597316—22no—
37#10597316—22no—
38C19×#97—22no—
39C19×#97D414yes—
40C19×#95—22no—
41C19⋊#95—24no—
42C19⋊#95—22no—
43#10597278—28no—
44#10597278—28no—
45#10597266—44no—
46#10597260—22no—
47C23×D19—41no—
48C22×C4×C19—22no—
49C22×C4×C19C2×D411yescharacteristic
50C22×C4×C19C2×D412yes—
51C22×Dic19—22no—
52C22×Dic19—22no—
53C2×D76—24no—
54C2×D76—22no—
55C2×D76—42no—
56C2×D76—48no—
57C2×D76—42no—
58C2×D76—42no—
59C2×D76—41no—
60C2×C8×C19—24no—
61C2×C8×C19—44no—
62C4⋊C4×C19—42no—
63C42×C19C2×D412yes—
64C42×C19C2×D411yescharacteristic
65C42×C19#4111yescharacteristic
66C4⋊Dic19—22no—
67C4⋊Dic19—22no—
68C4⋊Dic19—22no—
69C4⋊Dic19—22no—
70C4⋊Dic19—82no—
71Dic19⋊C4—42no—
72Dic19⋊C4—42no—
73Dic19⋊C4—42no—
74Dic19⋊C4—42no—
75C2×C19⋊C8—22no—
76C2×C19⋊C8—41no—
77C2×C19⋊C8—41no—
78#10080—191nomaximal, Sylow
79C23×C19#12011yescharacteristic
80C22×D19—42no—
81C22×D19—81no—
82C22×D19—84no—
83C22×D19—81no—
84C2×C4×C19—21no—
85C2×C4×C19—21no—
86C2×C4×C19—24no—
87C2×C4×C19—42no—
88C2×C4×C19—44no—
89C2×C4×C19#12012yes—
90C2×C4×C19#12111yescharacteristic
91C2×C4×C19#12112yes—
92C2×C4×C19#12711yescharacteristic
93C2×Dic19—42no—
94C2×Dic19—42no—
95C2×Dic19—42no—
96C2×Dic19—44no—
97C2×Dic19—42no—
98D76—48no—
99D76—44no—
100D76—84no—
101D76—82no—
102C8×C19—44no—
103C19⋊C8—42no—
104C2×#490—192no—
105#2822—191no—
106#1961—191no—
107C2×#330—192no—
108#1295D1911yescharacteristic, complemented
109C22×C19#39211yescharacteristic
110C22×C19#45311yescharacteristic
111C22×C19#45414yes—
112C22×C19#45411yescharacteristic
113C2×D19—84no—
114C2×D19—82no—
115C2×D19—162no—
116C2×D19—162no—
117C4×C19—22no—
118C4×C19—22no—
119C4×C19—21no—
120C4×C19—21no—
121C4×C19—82no—
122Dic19—82no—
123Dic19—82no—
124C2×#127—191no—
125C2×#125—192no—
126#490—384no—
127#490—384no—
128C2×#102—382no—
129C2×#102—382no—
130C2×#102—382no—
131C2×#97—191no—
132C2×#97C2×D1912yes—
133#400—382no—
134#398—382no—
135#398—382no—
136#382C2×D1911yescharacteristic
137#330—384no—
138C2×C19#165712yes—
139C2×C19#165812yes—
140C2×C19#200312yes—
141C2×C19#200611yescharacteristic
142D19—162no—
143C22×D4—381no—
144C22×D4—382no—
145C22×C8—22no—
146C22×C8—381no—
147#127—192no—
148#127—382no—
149#127—381no—
150#125—382no—
151#125—382no—
152#125—382no—
153#125—382no—
154C2×C4⋊C4—192no—
155C2×C4⋊C4—192no—
156C2×C4⋊C4—382no—
157C2×C4⋊C4—382no—
158C2×C4⋊C4—382no—
159C2×C4⋊C4D7612yes—
160C2×C42C22×D1911yescharacteristic
161#102—388no—
162#102—388no—
163#102—764no—
164#97—22no—
165#97—382no—
166#97D7614yes—
167#95—22no—
168#95—384no—
169#95—382no—
170C19#1008011yescharacteristic, complemented, Sylow
171C24—761no—
172C2×D4—384no—
173C2×D4—382no—
174C2×D4—762no—
175C2×D4—768no—
176C2×D4—762no—
177C2×D4—761no—
178C2×D4—762no—
179C22×C4—22no—
180C22×C4—382no—
181C22×C4—382no—
182C22×C4C2×D7611yescharacteristic
183C22×C4D4×D1912yes—
184C2×C8—24no—
185C2×C8—44no—
186C2×C8—382no—
187C2×C8—761no—
188C2×C8—761no—
189C4⋊C4—42no—
190C4⋊C4—382no—
191C4⋊C4—382no—
192C4⋊C4—382no—
193C4⋊C4—382no—
194C4⋊C4—762no—
195C4⋊C4—762no—
196C4⋊C4—762no—
197C4⋊C4—762no—
198C4⋊C4—1522no—
199C42C2×D7612yes—
200C42D4×D1911yescharacteristic
201C42#6454511yescharacteristic
202C23—762no—
203C23—1521no—
204C23—1524no—
205C23—1521no—
206C23#1059732811yescharacteristic
207D4—768no—
208D4—764no—
209D4—1524no—
210D4—1522no—
211C2×C4—21no—
212C2×C4—24no—
213C2×C4—21no—
214C2×C4—42no—
215C2×C4—44no—
216C2×C4—762no—
217C2×C4—762no—
218C2×C4—762no—
219C2×C4—764no—
220C2×C4—762no—
221C2×C4#1059732011yescharacteristic
222C2×C4#1059732812yes—
223C2×C4#1059734112yes—
224C2×C4#1059734111yescharacteristic
225C8—44no—
226C8—762no—
227C22—3042no—
228C22—3042no—
229C22—1524no—
230C22—1522no—
231C22#1192645411yescharacteristic
232C22#1192671411yescharacteristic
233C22#1192671814yes—
234C22#1192671911yescharacteristic
235C4—22no—
236C4—22no—
237C4—21no—
238C4—21no—
239C4—82no—
240C4—1522no—
241C4—1522no—
242C2—3042no—
243C2#1456293412yes—
244C2#1456293812yes—
245C2#1456466012yes—
246C2#1456467911yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1295C2
socleC23×C19#120
prime radicalC2×#10597320C22
hypercenter#1295D19
hypocenterC19#10080
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
2. #14571703C2semidirect
4. C2×#11926285C2semidirect
5. C19×#1295C2semidirect
108. #1295D19semidirect
170. C19#10080semidirect

Maximal subgroups

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

subgroupindex
C2×#119269092
#145717032
#145644582
C2×#119262852
C19×#12952
#1008019