Finite Group Databasebeta

← C19×#13684 #18019643

Subgroups — C19×#13684 #18019643

Order 4864.

378 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 58 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×#3293C211yesmaximal, characteristic
2C19×#2205C212yesmaximal, complemented
3C19×#1633C211yesmaximal, characteristic, complemented
4C19×#1411C211yesmaximal, characteristic, complemented
5C19×#1405C212yesmaximal, complemented
6C19×#578—22no—
7Q82×C19C2211yescharacteristic
8C19×#494C2211yescharacteristic
9C19×#477—21no—
10C19×#473—22no—
11C19×#456—22no—
12C19×#456—21no—
13C19×#456C2212yes—
14C19×#443—21no—
15C19×#356—22no—
16C19×#356C2212yes—
17C19×#333C2211yescharacteristic
18C19×Q8⋊C8—21no—
19C19×2−1+4—21no—
20C19×2−1+4D412yes—
21C19×#137—22no—
22C19×#137—22no—
23C19×#137—42no—
24C19×#137—42no—
25C19×#137—42no—
26C19×#135—21no—
27C19×#135—42no—
28C2×Q16×C19—22no—
29C2×Q16×C19—42no—
30C19×#131—22no—
31C19×C4⋊Q8—22no—
32C19×C4⋊Q8—41no—
33C19×C4⋊Q8D411yescharacteristic
34C19×C4⋊Q8C2311yescharacteristic
35C4×Q8×C19—21no—
36C4×Q8×C19—41no—
37C19×#108—21no—
38C19×#107—41no—
39C19×C4⋊C8—21no—
40C19×#104—22no—
41C19×#104—42no—
42C19×#103—41no—
43C19×#101—21no—
44C19×#101—22no—
45C19×#101D412yes—
46C4×C8×C19D411yescharacteristic
47#41×C19—22no—
48#41×C19—42no—
49#41×C19—42no—
50#41×C19—42no—
51#41×C19—81no—
52C2×Q8×C19—21no—
53C2×Q8×C19—22no—
54C2×Q8×C19—21no—
55C2×Q8×C19—42no—
56C2×Q8×C19—42no—
57C2×Q8×C19C2×D412yes—
58Q16×C19—21no—
59Q16×C19—42no—
60Q16×C19—42no—
61Q16×C19—42no—
62Q16×C19—42no—
63Q16×C19—82no—
64SD16×C19—22no—
65SD16×C19—42no—
66SD16×C19—42no—
67SD16×C19—82no—
68D8×C19—21no—
69M16×C19—22no—
70M16×C19—42no—
71M16×C19—42no—
72C2×C8×C19—21no—
73C2×C8×C19—42no—
74C2×C8×C19—41no—
75C4⋊C4×C19—21no—
76C4⋊C4×C19—41no—
77C4⋊C4×C19—41no—
78C4⋊C4×C19—42no—
79C4⋊C4×C19—41no—
80C42×C19—22no—
81C42×C19—41no—
82C42×C19C2×D411yescharacteristic
83#13684C1911yesmaximal, characteristic, direct product factor, Sylow
84Q8×C19—22no—
85Q8×C19—22no—
86Q8×C19—42no—
87Q8×C19—41no—
88Q8×C19—42no—
89Q8×C19—42no—
90Q8×C19—81no—
91Q8×C19—82no—
92D4×C19—22no—
93D4×C19—42no—
94D4×C19—42no—
95D4×C19—81no—
96C2×C4×C19—21no—
97C2×C4×C19—22no—
98C2×C4×C19—42no—
99C2×C4×C19—41no—
100C2×C4×C19—41no—
101C2×C4×C19—41no—
102C2×C4×C19—82no—
103C2×C4×C19—82no—
104C2×C4×C19#12011yescharacteristic
105C8×C19—21no—
106C8×C19—21no—
107C8×C19—42no—
108C8×C19—81no—
109C8×C19—82no—
110#3293C2×C1911yescharacteristic
111#2205C2×C1912yescomplemented
112#1633C2×C1911yescharacteristic, complemented
113#1411C2×C1911yescharacteristic, complemented
114#1405C2×C1912yescomplemented
115C22×C19—42no—
116C22×C19B(4,𝔽2)11yescharacteristic
117C4×C19—21no—
118C4×C19—21no—
119C4×C19—21no—
120C4×C19—42no—
121C4×C19—42no—
122C4×C19—42no—
123C4×C19—81no—
124C4×C19—81no—
125#578—22no—
126Q82C22×C1911yescharacteristic
127#494C22×C1911yescharacteristic
128#477—21no—
129#473—22no—
130#456—21no—
131#456—22no—
132#456C22×C1912yes—
133#443—21no—
134#356—22no—
135#356C22×C1912yes—
136#333C22×C1911yescharacteristic
137Q8⋊C8—21no—
138C2×C19—21no—
139C2×C19—82no—
140C2×C19#219611yescharacteristic
1412−1+4—21no—
1422−1+4D4×C1912yes—
143#137—22no—
144#137—22no—
145#137—42no—
146#137—42no—
147#137—42no—
148#135—21no—
149#135—42no—
150C2×Q16—22no—
151C2×Q16—42no—
152#131—22no—
153C4⋊Q8—22no—
154C4⋊Q8—41no—
155C4⋊Q8D4×C1911yescharacteristic
156C4⋊Q8C23×C1911yescharacteristic
157C4×Q8—21no—
158C4×Q8—41no—
159#108—21no—
160#107—41no—
161C4⋊C8—21no—
162#104—22no—
163#104—42no—
164#103—41no—
165#101—21no—
166#101—22no—
167#101D4×C1912yes—
168C4×C8D4×C1911yescharacteristic
169C19#1368411yescharacteristic, direct product factor, Sylow
170#41—22no—
171#41—42no—
172#41—42no—
173#41—42no—
174#41—81no—
175C2×Q8—21no—
176C2×Q8—22no—
177C2×Q8—21no—
178C2×Q8—42no—
179C2×Q8—42no—
180C2×Q8C2×D4×C1912yes—
181Q16—21no—
182Q16—42no—
183Q16—42no—
184Q16—42no—
185Q16—42no—
186Q16—82no—
187SD16—22no—
188SD16—42no—
189SD16—42no—
190SD16—82no—
191D8—21no—
192M16—22no—
193M16—42no—
194M16—42no—
195C2×C8—21no—
196C2×C8—42no—
197C2×C8—41no—
198C4⋊C4—21no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—42no—
202C4⋊C4—41no—
203C42—22no—
204C42—41no—
205C42C2×D4×C1911yescharacteristic
206Q8—22no—
207Q8—22no—
208Q8—42no—
209Q8—41no—
210Q8—42no—
211Q8—42no—
212Q8—81no—
213Q8—82no—
214D4—22no—
215D4—42no—
216D4—42no—
217D4—81no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—82no—
225C2×C4—82no—
226C2×C4C19×#12011yescharacteristic
227C8—21no—
228C8—21no—
229C8—42no—
230C8—81no—
231C8—82no—
232C22—42no—
233C22C19×B(4,𝔽2)11yescharacteristic
234C4—21no—
235C4—21no—
236C4—21no—
237C4—42no—
238C4—42no—
239C4—42no—
240C4—81no—
241C4—81no—
242C2—21no—
243C2—82no—
244C2C19×#219611yescharacteristic
subgroupG/H
center, socleC2×C19#2196
commutator, Frattini, cosocleC4⋊Q8C23×C19
prime radicalC19×#3293C2
LCSG ▷ C4⋊Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C19 ◁ C22×C19 ◁ C2×C4×C19 ◁ C19×C4⋊Q8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C19×#2205C2semidirect
3. C19×#1633C2semidirect
4. C19×#1411C2semidirect
5. C19×#1405C2semidirect
83. #13684C19direct (N × H)
111. #2205C2×C19semidirect
112. #1633C2×C19semidirect
113. #1411C2×C19semidirect
114. #1405C2×C19semidirect
169. C19#13684direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#32932
C19×#22052
C19×#16332
C19×#14112
C19×#14052
#1368419