Finite Group Databasebeta

← C19×#12282 #18018241

Subgroups — C19×#12282 #18018241

Order 4864.

344 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 82 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×#3189C211yesmaximal, characteristic
2C19×#2236C212yesmaximal, complemented
3C19×#2076C211yesmaximal, characteristic
4C19×#1348C212yesmaximal, complemented
5C19×#1314C211yesmaximal, characteristic
6C2×C19×C22⋊Q8—21no—
7C19×#484—22no—
8C19×#467—21no—
9C19×#467C2212yes—
10C19×#451—22no—
11C2×C19×#107C2211yescharacteristic
12C2×C19×C22⋊C8C2211yescharacteristic
13C19×#380—21no—
14C19×#366—22no—
15C19×#358—22no—
16C19×C22⋊C16C2212yes—
17C19×#340—21no—
18C19×#340C2211yescharacteristic
19C22×Q8×C19—21no—
20C23×C4×C19D411yescharacteristic
21C2×Q16×C19—21no—
22C2×Q16×C19D412yes—
23C22×C8×C19D411yescharacteristic
24C22×C8×C19C2311yescharacteristic
25C19×C22⋊Q8—22no—
26C19×C22⋊Q8—22no—
27C19×C22⋊Q8—41no—
28C19×C22⋊Q8—41no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—41no—
33C2×C22⋊C4×C19—41no—
34C2×C22⋊C4×C19—41no—
35C2×C16×C19—22no—
36C19×#107—21no—
37C19×#107—22no—
38C19×#107D412yes—
39C19×#103—22no—
40C19×#103—22no—
41C19×C22⋊C8—22no—
42C19×#95—41no—
43C24×C19D811yescharacteristic
44C2×Q8×C19—22no—
45C2×Q8×C19—41no—
46C2×Q8×C19—81no—
47C2×Q8×C19—81no—
48C22×C4×C19—21no—
49C22×C4×C19—21no—
50C22×C4×C19—41no—
51C22×C4×C19—41no—
52C22×C4×C19—41no—
53C22×C4×C19—41no—
54C22×C4×C19—41no—
55C22×C4×C19—41no—
56C22×C4×C19D811yescharacteristic
57C22×C4×C19C2×D411yescharacteristic
58Q16×C19—42no—
59Q16×C19—81no—
60C2×C8×C19—21no—
61C2×C8×C19—41no—
62C2×C8×C19—41no—
63C2×C8×C19C2×D412yes—
64C4⋊C4×C19—22no—
65C4⋊C4×C19—41no—
66C4⋊C4×C19—42no—
67C4⋊C4×C19—41no—
68C4⋊C4×C19—41no—
69C4⋊C4×C19—42no—
70C4⋊C4×C19—41no—
71C4⋊C4×C19—41no—
72C22⋊C4×C19—42no—
73C22⋊C4×C19—42no—
74C22⋊C4×C19—82no—
75C16×C19—42no—
76#12282C1911yesmaximal, characteristic, direct product factor, Sylow
77C23×C19—21no—
78C23×C19—21no—
79C23×C19—41no—
80C23×C19—41no—
81C23×C19Q3212yes—
82C23×C19C2×D811yescharacteristic
83Q8×C19—42no—
84Q8×C19—42no—
85Q8×C19—82no—
86C2×C4×C19—21no—
87C2×C4×C19—21no—
88C2×C4×C19—21no—
89C2×C4×C19—41no—
90C2×C4×C19—41no—
91C2×C4×C19—41no—
92C2×C4×C19—42no—
93C2×C4×C19—42no—
94C2×C4×C19—81no—
95C2×C4×C19—82no—
96C2×C4×C19—82no—
97C2×C4×C19—81no—
98C2×C4×C19—81no—
99C2×C4×C19—81no—
100C2×C4×C19—81no—
101C2×C4×C19—81no—
102C2×C4×C19—81no—
103C2×C4×C19#12011yescharacteristic
104C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
105C8×C19—22no—
106C8×C19—41no—
107#3189C2×C1911yescharacteristic
108#2236C2×C1912yescomplemented
109#2076C2×C1911yescharacteristic
110#1348C2×C1912yescomplemented
111#1314C2×C1911yescharacteristic
112C22×C19—21no—
113C22×C19—21no—
114C22×C19—22no—
115C22×C19—42no—
116C22×C19—41no—
117C22×C19—41no—
118C22×C19—81no—
119C22×C19#44711yescharacteristic
120C22×C19C2×Q3211yescharacteristic
121C22×C19#51011yescharacteristic
122C4×C19—21no—
123C4×C19—41no—
124C4×C19—82no—
125C4×C19—82no—
126C4×C19—161no—
127C4×C19—161no—
128C4×C19#45511yescharacteristic
129C4×C19#45811yescharacteristic
130C2×C22⋊Q8—21no—
131#484—22no—
132#467—21no—
133#467C22×C1912yes—
134#451—22no—
135C2×#107C22×C1911yescharacteristic
136C2×C22⋊C8C22×C1911yescharacteristic
137#380—21no—
138#366—22no—
139#358—22no—
140C22⋊C16C22×C1912yes—
141#340—21no—
142#340C22×C1911yescharacteristic
143C2×C19—21no—
144C2×C19—21no—
145C2×C19—42no—
146C2×C19#160711yescharacteristic
147C2×C19#218811yescharacteristic
148C2×C19#219011yescharacteristic
149C22×Q8—21no—
150C23×C4D4×C1911yescharacteristic
151C2×Q16—21no—
152C2×Q16D4×C1912yes—
153C22×C8D4×C1911yescharacteristic
154C22×C8C23×C1911yescharacteristic
155C22⋊Q8—22no—
156C22⋊Q8—22no—
157C22⋊Q8—41no—
158C22⋊Q8—41no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—41no—
163C2×C22⋊C4—41no—
164C2×C22⋊C4—41no—
165C2×C16—22no—
166#107—21no—
167#107—22no—
168#107D4×C1912yes—
169#103—22no—
170#103—22no—
171C22⋊C8—22no—
172#95—41no—
173C19#1228211yescharacteristic, direct product factor, Sylow
174C24D8×C1911yescharacteristic
175C2×Q8—22no—
176C2×Q8—41no—
177C2×Q8—81no—
178C2×Q8—81no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4D8×C1911yescharacteristic
188C22×C4C2×D4×C1911yescharacteristic
189Q16—42no—
190Q16—81no—
191C2×C8—21no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8C2×D4×C1912yes—
195C4⋊C4—22no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C22⋊C4—42no—
204C22⋊C4—42no—
205C22⋊C4—82no—
206C16—42no—
207C23—21no—
208C23—21no—
209C23—41no—
210C23—41no—
211C23C19×Q3212yes—
212C23C2×D8×C1911yescharacteristic
213Q8—42no—
214Q8—42no—
215Q8—82no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—81no—
225C2×C4—82no—
226C2×C4—82no—
227C2×C4—81no—
228C2×C4—81no—
229C2×C4—81no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—81no—
233C2×C4C19×#12011yescharacteristic
234C2×C4C19×AGL(1,ℤ/8)11yescharacteristic
235C8—22no—
236C8—41no—
237C22—21no—
238C22—21no—
239C22—22no—
240C22—42no—
241C22—41no—
242C22—41no—
243C22—81no—
244C22C19×#44711yescharacteristic
245C22C2×C19×Q3211yescharacteristic
246C22C19×#51011yescharacteristic
247C4—21no—
248C4—41no—
249C4—82no—
250C4—82no—
251C4—161no—
252C4—161no—
253C4C19×#45511yescharacteristic
254C4C19×#45811yescharacteristic
255C2—21no—
256C2—21no—
257C2—42no—
258C2C19×#160711yescharacteristic
259C2C19×#218811yescharacteristic
260C2C19×#219011yescharacteristic
subgroupG/H
center, socleC22×C19#447
commutator, Frattini, cosocleC22×C8C23×C19
prime radicalC24×C19D8
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C19 ◁ C22×C4×C19 ◁ C2×C19×C22⋊C8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C19×#2236C2semidirect
4. C19×#1348C2semidirect
76. #12282C19direct (N × H)
108. #2236C2×C19semidirect
110. #1348C2×C19semidirect
173. C19#12282direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#31892
C19×#22362
C19×#20762
C19×#13482
C19×#13142
#1228219