Finite Group Databasebeta

← C19×#7488 #18013447

Subgroups — C19×#7488 #18013447

Order 4864.

270 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C19×#2132C211yesmaximal, characteristic
2C19×#1884C211yesmaximal, characteristic
3C19×#1543C211yesmaximal, characteristic
4C19×#568C411yescharacteristic
5C19×#532C2211yescharacteristic
6C19×#431—21no—
7C19×#421—21no—
8C19×#413—21no—
9C19×#410C411yescharacteristic
10C19×#356—21no—
11C19×#355C412yescomplemented
12C19×#339—21no—
13C19×#333—21no—
14C19×#331C412yescomplemented
15C2×#41×C19C2×C411yescharacteristic
16C2×#41×C19D411yescharacteristic
17C19×#131—42no—
18C2×M16×C19—21no—
19C2×M16×C19—41no—
20C2×M16×C19—41no—
21C19×C4⋊Q8D411yescharacteristic
22C19×#127C2×C411yescharacteristic
23C19×#124C2×C411yescharacteristic
24C19×#124Q811yescharacteristic
25C19×#121—41no—
26C4×D4×C19—41no—
27C19×#117—21no—
28C2×C42×C19D411yescharacteristic
29C19×C4⋊C8—22no—
30C19×#104—42no—
31C19×#101—22no—
32C19×#100—41no—
33C19×#99—41no—
34C19×C22⋊C8—41no—
35C4×C8×C19—41no—
36#41×C19—41no—
37#41×C19—41no—
38#41×C19—41no—
39#41×C19—41no—
40C2×Q8×C19C22⋊C411yescharacteristic
41C2×Q8×C19C4⋊C411yescharacteristic
42C2×D4×C19—21no—
43C2×D4×C19—21no—
44C2×D4×C19—41no—
45C2×D4×C19C4211yescharacteristic
46C2×D4×C19C4⋊C411yescharacteristic
47C22×C4×C19—21no—
48C22×C4×C19—21no—
49C22×C4×C19—21no—
50C22×C4×C19C22⋊C411yescharacteristic
51M16×C19—22no—
52M16×C19—42no—
53M16×C19—41no—
54M16×C19—42no—
55M16×C19—81no—
56C2×C8×C19—41no—
57C2×C8×C19—42no—
58C2×C8×C19—42no—
59C2×C8×C19—81no—
60C4⋊C4×C19—41no—
61C4⋊C4×C19—41no—
62C22⋊C4×C19—41no—
63C22⋊C4×C19—41no—
64C22⋊C4×C19—41no—
65C42×C19—21no—
66C42×C19—41no—
67C42×C19C22⋊C411yescharacteristic
68C42×C19C4⋊C411yescharacteristic
69#7488C1911yesmaximal, characteristic, direct product factor, Sylow
70C23×C19—21no—
71C23×C19—21no—
72C23×C19#9911yescharacteristic
73Q8×C19—41no—
74Q8×C19—41no—
75D4×C19—41no—
76D4×C19—41no—
77D4×C19—42no—
78D4×C19—82no—
79D4×C19—81no—
80C2×C4×C19—21no—
81C2×C4×C19—21no—
82C2×C4×C19—21no—
83C2×C4×C19—21no—
84C2×C4×C19—21no—
85C2×C4×C19—21no—
86C2×C4×C19—42no—
87C2×C4×C19—41no—
88C2×C4×C19—41no—
89C2×C4×C19—41no—
90C2×C4×C19—41no—
91C2×C4×C19—81no—
92C2×C4×C19#9511yescharacteristic
93C2×C4×C19#9911yescharacteristic
94C8×C19—42no—
95C8×C19—82no—
96C8×C19—82no—
97#2132C2×C1911yescharacteristic
98#1884C2×C1911yescharacteristic
99#1543C2×C1911yescharacteristic
100C22×C19—21no—
101C22×C19—41no—
102C22×C19—41no—
103C22×C19—41no—
104C22×C19—81no—
105C22×C19—81no—
106C22×C19#34211yescharacteristic
107C4×C19—22no—
108C4×C19—21no—
109C4×C19—41no—
110C4×C19—41no—
111C4×C19—41no—
112C4×C19—161no—
113C4×C19AΣL(1,𝔽16)11yescharacteristic
114C4×C19#35211yescharacteristic
115#568C4×C1911yescharacteristic
116#532C22×C1911yescharacteristic
117#431—21no—
118#421—21no—
119#413—21no—
120#410C4×C1911yescharacteristic
121#356—21no—
122#355C4×C1912yescomplemented
123#339—21no—
124#333—21no—
125#331C4×C1912yescomplemented
126C2×C19—21no—
127C2×C19—41no—
128C2×C19—81no—
129C2×C19—81no—
130C2×C19#139011yescharacteristic
131C2×#41C2×C4×C1911yescharacteristic
132C2×#41D4×C1911yescharacteristic
133#131—42no—
134C2×M16—21no—
135C2×M16—41no—
136C2×M16—41no—
137C4⋊Q8D4×C1911yescharacteristic
138#127C2×C4×C1911yescharacteristic
139#124C2×C4×C1911yescharacteristic
140#124Q8×C1911yescharacteristic
141#121—41no—
142C4×D4—41no—
143#117—21no—
144C2×C42D4×C1911yescharacteristic
145C4⋊C8—22no—
146#104—42no—
147#101—22no—
148#100—41no—
149#99—41no—
150C22⋊C8—41no—
151C4×C8—41no—
152C19#748811yescharacteristic, direct product factor, Sylow
153#41—41no—
154#41—41no—
155#41—41no—
156#41—41no—
157C2×Q8C22⋊C4×C1911yescharacteristic
158C2×Q8C4⋊C4×C1911yescharacteristic
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—41no—
162C2×D4C42×C1911yescharacteristic
163C2×D4C4⋊C4×C1911yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4C22⋊C4×C1911yescharacteristic
168M16—22no—
169M16—42no—
170M16—41no—
171M16—42no—
172M16—81no—
173C2×C8—41no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—81no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C22⋊C4—41no—
180C22⋊C4—41no—
181C22⋊C4—41no—
182C42—21no—
183C42—41no—
184C42C22⋊C4×C1911yescharacteristic
185C42C4⋊C4×C1911yescharacteristic
186C23—21no—
187C23—21no—
188C23C19×#9911yescharacteristic
189Q8—41no—
190Q8—41no—
191D4—41no—
192D4—41no—
193D4—42no—
194D4—82no—
195D4—81no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—42no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—81no—
208C2×C4C19×#9511yescharacteristic
209C2×C4C19×#9911yescharacteristic
210C8—42no—
211C8—82no—
212C8—82no—
213C22—21no—
214C22—41no—
215C22—41no—
216C22—41no—
217C22—81no—
218C22—81no—
219C22C19×#34211yescharacteristic
220C4—22no—
221C4—21no—
222C4—41no—
223C4—41no—
224C4—41no—
225C4—161no—
226C4C19×AΣL(1,𝔽16)11yescharacteristic
227C4C19×#35211yescharacteristic
228C2—21no—
229C2—41no—
230C2—81no—
231C2—81no—
232C2C19×#139011yescharacteristic
subgroupG/H
centerC4×C19AΣL(1,𝔽16)
commutatorC2×D4C42×C19
Frattini, cosocle#532C22×C19
socleC2×C19#1390
prime radicalC19×#532C22
LCSG ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C19 ◁ C2×C4×C19 ◁ C22×C4×C19 ◁ C19×#532 ◁ G

Complements

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

NH ≅ G/Ntype
11. C19×#355C4semidirect
14. C19×#331C4semidirect
69. #7488C19direct (N × H)
122. #355C4×C19semidirect
125. #331C4×C19semidirect
152. C19#7488direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#21322
C19×#18842
C19×#15432
#748819