Finite Group Databasebeta

← #18083500

Subgroups — #18083500

Order 4864.

468 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 83 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#14574980C211yesmaximal, characteristic
2#14573765C212yesmaximal
3#14562249C212yesmaximal
4#14561505C211yesmaximal, characteristic
5C19×#1985C211yesmaximal, characteristic
6#11927101C2212yes—
7#11926874—22no—
8#11926840—22no—
9#11926829—22no—
10#11926785—22no—
11#11926755—22no—
12#11926754—22no—
13#11926700—22no—
14#11926649—24no—
15#11926601C2212yes—
16#11926285—24no—
17C2×C4×Q8×C19C2211yescharacteristic
18C2×C19×C4⋊C8C2211yescharacteristic
19C2×C19×#97C2211yescharacteristic
20C19×#336—22no—
21C22×Q8×C19D411yescharacteristic
22C22×C8×C19—21no—
23C22×C8×C19D412yes—
24C4×Q8×C19—22no—
25C4×Q8×C19—22no—
26C2×C4⋊C4×C19—21no—
27C2×C4⋊C4×C19D411yescharacteristic
28C2×C42×C19—21no—
29C2×C42×C19C2311yescharacteristic
30C2×#64528—24no—
31#10597372—22no—
32#10597370—22no—
33#10597370—22no—
34C2×Dic76—22no—
35#10597316—22no—
36#10597315D412yes—
37#10597315D412yes—
38C4×Dic38—22no—
39C4×Dic38—22no—
40C19×C4⋊C8—22no—
41C19×#97—22no—
42#10597292—24no—
43C22⋊(C19⋊C8)—22no—
44#10597275—22no—
45#10597273—24no—
46#10597267—24no—
47#10597265—24no—
48C4⋊(C19⋊C8)—22no—
49#10597260D414yes—
50C2×Q8×C19—22no—
51C2×Q8×C19—42no—
52C22×C4×C19—21no—
53C22×C4×C19—21no—
54C22×C4×C19C2×D411yescharacteristic
55C22×C4×C19C2×D411yescharacteristic
56C22×C4×C19#4111yescharacteristic
57C2×Dic38—22no—
58C2×Dic38—22no—
59C2×C8×C19—22no—
60C2×C8×C19—22no—
61C2×C8×C19—41no—
62C2×C8×C19—41no—
63C2×C8×C19—42no—
64C4⋊C4×C19—22no—
65C4⋊C4×C19—42no—
66C42×C19—41no—
67C42×C19—41no—
68C42×C19C2×D412yes—
69C42×C19C2×D412yes—
70C22⋊Dic19—42no—
71#64528—48no—
72C4⋊Dic19—22no—
73C4⋊Dic19—22no—
74C4⋊Dic19—22no—
75C4⋊Dic19—22no—
76Dic19⋊C4—42no—
77Dic19⋊C4—42no—
78C4×Dic19—42no—
79C2×C19⋊C8—24no—
80Dic76—82no—
81#10031—191nomaximal, Sylow
82C23×C19#12111yescharacteristic
83Q8×C19—24no—
84Q8×C19—42no—
85C2×C4×C19—22no—
86C2×C4×C19—21no—
87C2×C4×C19—21no—
88C2×C4×C19—22no—
89C2×C4×C19—41no—
90C2×C4×C19—41no—
91C2×C4×C19—41no—
92C2×C4×C19—41no—
93C2×C4×C19—42no—
94C2×C4×C19#12011yescharacteristic
95C2×C4×C19#12012yes—
96C2×C4×C19#12112yes—
97C2×C4×C19#12711yescharacteristic
98C2×Dic19—42no—
99C2×Dic19—42no—
100Dic38—44no—
101Dic38—42no—
102Dic38—42no—
103C8×C19—42no—
104C8×C19—42no—
105C19⋊C8—44no—
106#3249—191no—
107#3113—192no—
108#1985D1911yescharacteristic
109#1531—192no—
110#1290—191no—
111C22×C19—21no—
112C22×C19—21no—
113C22×C19#39211yescharacteristic
114C22×C19#47312yes—
115C4×C19—21no—
116C4×C19—22no—
117C4×C19—22no—
118C4×C19—42no—
119C4×C19—81no—
120C4×C19#45511yescharacteristic
121C4×C19#45611yescharacteristic
122Dic19—82no—
123Dic19—82no—
124#533—192no—
125C2×C4×Q8C2×D1911yescharacteristic
126#483—382no—
127#477—382no—
128#475—382no—
129#467—382no—
130#462—382no—
131#462—382no—
132#451—382no—
133#441—384no—
134#432—192no—
135C2×C4⋊C8C2×D1911yescharacteristic
136C2×#97C2×D1911yescharacteristic
137#336—22no—
138#330—384no—
139C2×C19—22no—
140C2×C19#200711yescharacteristic
141C2×C19#201011yescharacteristic
142C2×C19#202011yescharacteristic
143C22×Q8D7611yescharacteristic
144C2×Q16—382no—
145C2×Q16—384no—
146C22×C8—21no—
147C22×C8C22⋊D1912yes—
148C4⋊Q8—192no—
149C4⋊Q8—192no—
150#125—382no—
151C22⋊Q8—382no—
152C22⋊Q8—382no—
153C4×Q8—22no—
154C4×Q8—22no—
155C4×Q8—382no—
156C4×Q8—382no—
157#117—382no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4D7611yescharacteristic
160C2×C42—21no—
161C2×C42C22×D1911yescharacteristic
162#107—382no—
163#106—384no—
164C4⋊C8—22no—
165C4⋊C8—382no—
166#103—384no—
167#103—384no—
168#103—384no—
169C22⋊C8—382no—
170#97—22no—
171#97—194no—
172C19#1003111yescharacteristic, complemented, Sylow
173C2×Q8—22no—
174C2×Q8—42no—
175C2×Q8—382no—
176C2×Q8—382no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4C2×D7611yescharacteristic
180C22×C4#6454111yescharacteristic
181C22×C4C2×C22⋊D1911yescharacteristic
182Q16—768no—
183Q16—1522no—
184C2×C8—22no—
185C2×C8—22no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—42no—
189C2×C8—384no—
190C4⋊C4—22no—
191C4⋊C4—42no—
192C4⋊C4—382no—
193C4⋊C4—382no—
194C4⋊C4—382no—
195C4⋊C4—382no—
196C4⋊C4—762no—
197C4⋊C4—762no—
198C22⋊C4—762no—
199C42—41no—
200C42—41no—
201C42—762no—
202C42D4×D1912yes—
203C42D4×D1912yes—
204C23#1059737611yescharacteristic
205Q8—24no—
206Q8—42no—
207Q8—764no—
208Q8—762no—
209Q8—762no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—762no—
220C2×C4—762no—
221C2×C4#1059732812yes—
222C2×C4#1059733012yes—
223C2×C4#1059738311yescharacteristic
224C2×C4#1059738611yescharacteristic
225C8—42no—
226C8—42no—
227C8—764no—
228C22—21no—
229C22—21no—
230C22#1192645311yescharacteristic
231C22#1192681912yes—
232C4—21no—
233C4—22no—
234C4—22no—
235C4—42no—
236C4—81no—
237C4—1522no—
238C4—1522no—
239C4#1192672111yescharacteristic
240C4#1192672611yescharacteristic
241C2—22no—
242C2#1456468111yescharacteristic
243C2#1456470211yescharacteristic
244C2#1456475611yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1985C2
socleC22×C19#392
prime radicalC23×C19#121
hypercenter#1985D19
hypocenterC19#10031
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
172. C19#10031semidirect

Maximal subgroups

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

subgroupindex
#145749802
#145737652
#145622492
#145615052
C19×#19852
#1003119