Finite Group Databasebeta

← C19×#7396 #18013355

Subgroups — C19×#7396 #18013355

Order 4864.

296 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 42 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×#2010C211yesmaximal, characteristic
2C19×#1320C211yesmaximal, characteristic, complemented
3C19×#1297C211yesmaximal, characteristic, complemented
4C19×#575C411yescharacteristic, complemented
5C19×#525—21no—
6C19×#421—21no—
7C19×#407C2211yescharacteristic
8C4×C22⋊C4×C19—21no—
9C19×#349—21no—
10C19×H(3,ℤ/4)C411yescharacteristic, complemented
11C2×#41×C19—21no—
12C23×C4×C19D411yescharacteristic
13C19×#137—41no—
14C19×AGL(1,ℤ/8)—41no—
15C19×#135—41no—
16C2×M16×C19C2×C411yescharacteristic
17C2×M16×C19D411yescharacteristic
18C19×#123—41no—
19C19×C22⋊Q8—41no—
20C19×#121—41no—
21C19×#120—41no—
22C4×D4×C19—42no—
23C19×#117—21no—
24C2×C22⋊C4×C19—41no—
25C2×C42×C19—41no—
26C19×M32—41no—
27C19×#104—42no—
28C19×C22⋊C8—41no—
29C19×#95—22no—
30C24×C19D811yescharacteristic
31#41×C19—41no—
32#41×C19—41no—
33#41×C19—41no—
34#41×C19—41no—
35C2×Q8×C19—21no—
36C2×D4×C19—21no—
37C2×D4×C19—42no—
38C2×D4×C19—41no—
39C22×C4×C19—21no—
40C22×C4×C19—21no—
41C22×C4×C19—41no—
42C22×C4×C19—41no—
43C22×C4×C19—41no—
44C22×C4×C19—42no—
45C22×C4×C19C22⋊C411yescharacteristic
46C22×C4×C19SD1611yescharacteristic
47Q16×C19—41no—
48SD16×C19—42no—
49D8×C19—41no—
50M16×C19—41no—
51M16×C19—41no—
52C2×C8×C19—21no—
53C2×C8×C19—21no—
54C4⋊C4×C19—41no—
55C4⋊C4×C19—42no—
56C22⋊C4×C19—44no—
57C22⋊C4×C19—42no—
58C22⋊C4×C19—42no—
59C22⋊C4×C19—41no—
60C42×C19—22no—
61C42×C19—81no—
62C42×C19—81no—
63C16×C19—81no—
64#7396C1911yesmaximal, characteristic, direct product factor, Sylow
65C23×C19—21no—
66C23×C19—41no—
67C23×C19—42no—
68C23×C19—41no—
69C23×C19#10211yescharacteristic
70Q8×C19—41no—
71Q8×C19—41no—
72D4×C19—41no—
73D4×C19—41no—
74D4×C19—81no—
75D4×C19—84no—
76D4×C19—81no—
77C2×C4×C19—21no—
78C2×C4×C19—21no—
79C2×C4×C19—21no—
80C2×C4×C19—41no—
81C2×C4×C19—41no—
82C2×C4×C19—41no—
83C2×C4×C19—42no—
84C2×C4×C19—41no—
85C2×C4×C19—44no—
86C2×C4×C19—81no—
87C2×C4×C19—81no—
88C2×C4×C19—82no—
89C2×C4×C19—82no—
90C2×C4×C19—81no—
91C2×C4×C19#9911yescharacteristic
92C2×C4×C19#10411yescharacteristic
93C8×C19—41no—
94C8×C19—41no—
95#2010C2×C1911yescharacteristic
96#1320C2×C1911yescharacteristic, complemented
97#1297C2×C1911yescharacteristic, complemented
98C22×C19—22no—
99C22×C19—21no—
100C22×C19—41no—
101C22×C19—41no—
102C22×C19—42no—
103C22×C19—41no—
104C22×C19—81no—
105C22×C19—82no—
106C22×C19—81no—
107C22×C19#32711yescharacteristic
108C4×C19—21no—
109C4×C19—41no—
110C4×C19—84no—
111C4×C19—82no—
112C4×C19—81no—
113C4×C19AΣL(1,𝔽16)11yescharacteristic
114C4×C19#35311yescharacteristic
115#575C4×C1911yescharacteristic, complemented
116#525—21no—
117#421—21no—
118#407C22×C1911yescharacteristic
119C4×C22⋊C4—21no—
120#349—21no—
121H(3,ℤ/4)C4×C1911yescharacteristic, complemented
122C2×C19—21no—
123C2×C19—42no—
124C2×C19—41no—
125C2×C19—161no—
126C2×C19#134311yescharacteristic
127C2×#41—21no—
128C23×C4D4×C1911yescharacteristic
129#137—41no—
130AGL(1,ℤ/8)—41no—
131#135—41no—
132C2×M16C2×C4×C1911yescharacteristic
133C2×M16D4×C1911yescharacteristic
134#123—41no—
135C22⋊Q8—41no—
136#121—41no—
137#120—41no—
138C4×D4—42no—
139#117—21no—
140C2×C22⋊C4—41no—
141C2×C42—41no—
142M32—41no—
143#104—42no—
144C22⋊C8—41no—
145#95—22no—
146C19#739611yescharacteristic, direct product factor, Sylow
147C24D8×C1911yescharacteristic
148#41—41no—
149#41—41no—
150#41—41no—
151#41—41no—
152C2×Q8—21no—
153C2×D4—21no—
154C2×D4—42no—
155C2×D4—41no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—42no—
162C22×C4C22⋊C4×C1911yescharacteristic
163C22×C4SD16×C1911yescharacteristic
164Q16—41no—
165SD16—42no—
166D8—41no—
167M16—41no—
168M16—41no—
169C2×C8—21no—
170C2×C8—21no—
171C4⋊C4—41no—
172C4⋊C4—42no—
173C22⋊C4—44no—
174C22⋊C4—42no—
175C22⋊C4—42no—
176C22⋊C4—41no—
177C42—22no—
178C42—81no—
179C42—81no—
180C16—81no—
181C23—21no—
182C23—41no—
183C23—42no—
184C23—41no—
185C23C19×#10211yescharacteristic
186Q8—41no—
187Q8—41no—
188D4—41no—
189D4—41no—
190D4—81no—
191D4—84no—
192D4—81no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—41no—
201C2×C4—44no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—82no—
205C2×C4—82no—
206C2×C4—81no—
207C2×C4C19×#9911yescharacteristic
208C2×C4C19×#10411yescharacteristic
209C8—41no—
210C8—41no—
211C22—22no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—42no—
216C22—41no—
217C22—81no—
218C22—82no—
219C22—81no—
220C22C19×#32711yescharacteristic
221C4—21no—
222C4—41no—
223C4—84no—
224C4—82no—
225C4—81no—
226C4C19×AΣL(1,𝔽16)11yescharacteristic
227C4C19×#35311yescharacteristic
228C2—21no—
229C2—41no—
230C2—42no—
231C2—161no—
232C2C19×#134311yescharacteristic
subgroupG/H
centerC4×C19#353
commutatorC2×M16C2×C4×C19
Frattini, cosocle#407C22×C19
socleC2×C19#1343
prime radicalC19×#2010C2
LCSG ▷ C2×M16 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C19 ◁ C2×C4×C19 ◁ C22×C4×C19 ◁ C19×#407 ◁ G

Complements

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

NH ≅ G/Ntype
2. C19×#1320C2semidirect
3. C19×#1297C2semidirect
4. C19×#575C4semidirect
10. C19×H(3,ℤ/4)C4semidirect
64. #7396C19direct (N × H)
96. #1320C2×C19semidirect
97. #1297C2×C19semidirect
115. #575C4×C19semidirect
121. H(3,ℤ/4)C4×C19semidirect
146. C19#7396direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#20102
C19×#13202
C19×#12972
#739619