Finite Group Databasebeta

← C19×#33503 #18039462

Subgroups — C19×#33503 #18039462

Order 4864.

526 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#41×C19C211yesmaximal, characteristic
2C19×#2183C212yesmaximal, complemented
3C19×#2169C212yesmaximal, complemented
4C19×#2168C214yesmaximal, complemented
5C19×#2163C212yesmaximal, complemented
6C19×#2162C211yesmaximal, characteristic, complemented
7C19×#2150C212yesmaximal, complemented
8C2×C19×C4⋊C16C211yesmaximal, characteristic, complemented
9C4×#41×C19C411yescharacteristic
10C2×C19×M32C2214yes—
11C22×C16×C19C2212yes—
12C8×Q8×C19C411yescharacteristic
13C8×Q8×C19C2211yescharacteristic
14C8×D4×C19C412yes—
15C8×D4×C19C411yescharacteristic
16C8×D4×C19C2212yes—
17C8×D4×C19C2211yescharacteristic
18C19×#431C412yes—
19C19×#431C411yescharacteristic
20C2×C4×C8×C19C2211yescharacteristic
21C2×C4×C8×C19C2212yes—
22C19×C4⋊C16C2212yes—
23C19×C4⋊C16C2212yes—
24C19×C4⋊C16C2211yescharacteristic
25C19×C4⋊C16C2214yes—
26C19×C4⋊C16C2211yescharacteristic
27C19×C22⋊C16C2212yes—
28C19×C22⋊C16C2214yes—
29C19×#346C2214yes—
30C4×C16×C19C2212yes—
31C2×#41×C19C811yescharacteristic
32C22×C8×C19C2×C411yescharacteristic
33C22×C8×C19C2×C412yes—
34C22×C8×C19C2311yescharacteristic
35C22×C8×C19C2312yes—
36C4×Q8×C19C811yescharacteristic
37C4×Q8×C19C2×C411yescharacteristic
38C4×D4×C19C812yes—
39C4×D4×C19C811yescharacteristic
40C4×D4×C19C2×C412yes—
41C4×D4×C19C2×C411yescharacteristic
42C19×#117C812yes—
43C19×#117C811yescharacteristic
44C2×C42×C19C2×C412yes—
45C2×C42×C19C2×C411yescharacteristic
46C19×M32—44no—
47C2×C16×C19—42no—
48C2×C16×C19C2312yes—
49C2×C16×C19C2312yes—
50C2×C16×C19C2314yes—
51C19×C4⋊C8C2×C412yes—
52C19×C4⋊C8C2×C411yescharacteristic
53C19×C4⋊C8C2×C412yes—
54C19×C4⋊C8C2×C411yescharacteristic
55C19×C22⋊C8C2×C412yes—
56C19×C22⋊C8C2×C412yes—
57C19×C22⋊C8C2×C412yes—
58C4×C8×C19C2×C411yescharacteristic
59C4×C8×C19C2×C412yes—
60C4×C8×C19C2×C411yescharacteristic
61C4×C8×C19C2×C412yes—
62C4×C8×C19C2311yescharacteristic
63C4×C8×C19C2312yes—
64C4×C8×C19C2311yescharacteristic
65#41×C19—24no—
66C2×Q8×C19C2×C811yescharacteristic
67C2×D4×C19C2×C812yes—
68C2×D4×C19C2×C811yescharacteristic
69C22×C4×C19C2×C812yes—
70C22×C4×C19C2×C812yes—
71C22×C4×C19C2×C811yescharacteristic
72C22×C4×C19C2×C811yescharacteristic
73C22×C4×C19C22×C412yes—
74C22×C4×C19C22×C411yescharacteristic
75C2×C8×C19—21no—
76C2×C8×C19—22no—
77C2×C8×C19—21no—
78C2×C8×C19—22no—
79C2×C8×C19—41no—
80C2×C8×C19—42no—
81C2×C8×C19C22×C411yescharacteristic
82C2×C8×C19C22×C411yescharacteristic
83C2×C8×C19C22×C412yes—
84C2×C8×C19C22×C411yescharacteristic
85C2×C8×C19C22×C412yes—
86C2×C8×C19C2411yescharacteristic
87C4⋊C4×C19C2×C812yes—
88C4⋊C4×C19C2×C811yescharacteristic
89C4⋊C4×C19C2×C812yes—
90C4⋊C4×C19C2×C811yescharacteristic
91C22⋊C4×C19C2×C812yes—
92C22⋊C4×C19C2×C812yes—
93C22⋊C4×C19C2×C812yes—
94C42×C19C2×C812yes—
95C42×C19C2×C811yescharacteristic
96C42×C19C2×C812yes—
97C42×C19C2×C811yescharacteristic
98C42×C19C22×C411yescharacteristic
99C42×C19C22×C412yes—
100C42×C19C22×C411yescharacteristic
101C16×C19—24no—
102C16×C19—22no—
103C16×C19—22no—
104#33503C1911yesmaximal, characteristic, direct product factor, Sylow
105C23×C19C22×C812yes—
106C23×C19C22×C811yescharacteristic
107Q8×C19—22no—
108D4×C19—24no—
109D4×C19—22no—
110C2×C4×C19—21no—
111C2×C4×C19—22no—
112C2×C4×C19—21no—
113C2×C4×C19—22no—
114C2×C4×C19—24no—
115C2×C4×C19—41no—
116C2×C4×C19—42no—
117C2×C4×C19M3214yescomplemented
118C2×C4×C19C22×C811yescharacteristic
119C2×C4×C19C22×C812yes—
120C2×C4×C19C22×C811yescharacteristic
121C2×C4×C19C22×C812yes—
122C2×C4×C19C22×C811yescharacteristic
123C2×C4×C19C22×C812yes—
124C2×C4×C19C22×C811yescharacteristic
125C2×C4×C19C22×C811yescharacteristic
126C2×C4×C19C23×C411yescharacteristic
127C8×C19—21no—
128C8×C19—22no—
129C8×C19—21no—
130C8×C19—21no—
131C8×C19—22no—
132C8×C19H(5,𝔽2)11yescharacteristic
133C8×C192−1+411yescharacteristic
134C8×#41C2×C1911yescharacteristic
135#2183C2×C1912yescomplemented
136#2169C2×C1912yescomplemented
137#2168C2×C1914yescomplemented
138#2163C2×C1912yescomplemented
139#2162C2×C1911yescharacteristic, complemented
140#2150C2×C1912yescomplemented
141C2×C4⋊C16C2×C1911yescharacteristic, complemented
142C22×C19—21no—
143C22×C19—21no—
144C22×C19—22no—
145C22×C19—22no—
146C22×C19—22no—
147C22×C19C2×M3212yes—
148C22×C19C23×C811yescharacteristic
149C4×C19—22no—
150C4×C19—21no—
151C4×C19—21no—
152C4×C19—22no—
153C4×C19—21no—
154C4×C19—22no—
155C4×C19C2×M3212yes—
156C4×C19C2×M3212yes—
157C4×C19#52011yescharacteristic
158C4×C19#56811yescharacteristic
159C4×#41C4×C1911yescharacteristic
160C2×M32C22×C1914yes—
161C22×C16C22×C1912yes—
162C8×Q8C4×C1911yescharacteristic
163C8×Q8C22×C1911yescharacteristic
164C8×D4C4×C1911yescharacteristic
165C8×D4C4×C1912yes—
166C8×D4C22×C1912yes—
167C8×D4C22×C1911yescharacteristic
168#431C4×C1912yes—
169#431C4×C1911yescharacteristic
170C2×C4×C8C22×C1911yescharacteristic
171C2×C4×C8C22×C1912yes—
172C4⋊C16C22×C1912yes—
173C4⋊C16C22×C1912yes—
174C4⋊C16C22×C1911yescharacteristic
175C4⋊C16C22×C1914yes—
176C4⋊C16C22×C1911yescharacteristic
177C22⋊C16C22×C1912yes—
178C22⋊C16C22×C1914yes—
179#346C22×C1914yes—
180C4×C16C22×C1912yes—
181C2×C19—22no—
182C2×C19—42no—
183C2×C19#298811yescharacteristic
184C2×C19C22×M3211yescharacteristic
185C2×C19#340711yescharacteristic
186C2×#41C8×C1911yescharacteristic
187C22×C8C2×C4×C1911yescharacteristic
188C22×C8C2×C4×C1912yes—
189C22×C8C23×C1911yescharacteristic
190C22×C8C23×C1912yes—
191C4×Q8C8×C1911yescharacteristic
192C4×Q8C2×C4×C1911yescharacteristic
193C4×D4C8×C1912yes—
194C4×D4C8×C1911yescharacteristic
195C4×D4C2×C4×C1912yes—
196C4×D4C2×C4×C1911yescharacteristic
197#117C8×C1912yes—
198#117C8×C1911yescharacteristic
199C2×C42C2×C4×C1912yes—
200C2×C42C2×C4×C1911yescharacteristic
201M32—44no—
202C2×C16—42no—
203C2×C16C23×C1912yes—
204C2×C16C23×C1912yes—
205C2×C16C23×C1914yes—
206C4⋊C8C2×C4×C1912yes—
207C4⋊C8C2×C4×C1911yescharacteristic
208C4⋊C8C2×C4×C1912yes—
209C4⋊C8C2×C4×C1911yescharacteristic
210C22⋊C8C2×C4×C1912yes—
211C22⋊C8C2×C4×C1912yes—
212C22⋊C8C2×C4×C1912yes—
213C4×C8C2×C4×C1911yescharacteristic
214C4×C8C2×C4×C1912yes—
215C4×C8C2×C4×C1911yescharacteristic
216C4×C8C2×C4×C1912yes—
217C4×C8C23×C1911yescharacteristic
218C4×C8C23×C1912yes—
219C4×C8C23×C1911yescharacteristic
220C19#3350311yescharacteristic, direct product factor, Sylow
221#41—24no—
222C2×Q8C2×C8×C1911yescharacteristic
223C2×D4C2×C8×C1912yes—
224C2×D4C2×C8×C1911yescharacteristic
225C22×C4C2×C8×C1912yes—
226C22×C4C2×C8×C1912yes—
227C22×C4C2×C8×C1911yescharacteristic
228C22×C4C2×C8×C1911yescharacteristic
229C22×C4C22×C4×C1912yes—
230C22×C4C22×C4×C1911yescharacteristic
231C2×C8—21no—
232C2×C8—22no—
233C2×C8—21no—
234C2×C8—22no—
235C2×C8—41no—
236C2×C8—42no—
237C2×C8C22×C4×C1911yescharacteristic
238C2×C8C22×C4×C1911yescharacteristic
239C2×C8C22×C4×C1912yes—
240C2×C8C22×C4×C1911yescharacteristic
241C2×C8C22×C4×C1912yes—
242C2×C8C24×C1911yescharacteristic
243C4⋊C4C2×C8×C1912yes—
244C4⋊C4C2×C8×C1911yescharacteristic
245C4⋊C4C2×C8×C1912yes—
246C4⋊C4C2×C8×C1911yescharacteristic
247C22⋊C4C2×C8×C1912yes—
248C22⋊C4C2×C8×C1912yes—
249C22⋊C4C2×C8×C1912yes—
250C42C2×C8×C1912yes—
251C42C2×C8×C1911yescharacteristic
252C42C2×C8×C1912yes—
253C42C2×C8×C1911yescharacteristic
254C42C22×C4×C1911yescharacteristic
255C42C22×C4×C1912yes—
256C42C22×C4×C1911yescharacteristic
257C16—24no—
258C16—22no—
259C16—22no—
260C23C22×C8×C1912yes—
261C23C22×C8×C1911yescharacteristic
262Q8—22no—
263D4—24no—
264D4—22no—
265C2×C4—24no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4C19×M3214yescomplemented
273C2×C4C22×C8×C1911yescharacteristic
274C2×C4C22×C8×C1912yes—
275C2×C4C22×C8×C1911yescharacteristic
276C2×C4C22×C8×C1912yes—
277C2×C4C22×C8×C1911yescharacteristic
278C2×C4C22×C8×C1912yes—
279C2×C4C22×C8×C1911yescharacteristic
280C2×C4C22×C8×C1911yescharacteristic
281C2×C4C23×C4×C1911yescharacteristic
282C8—21no—
283C8—22no—
284C8—21no—
285C8—21no—
286C8—22no—
287C8C19×H(5,𝔽2)11yescharacteristic
288C8C19×2−1+411yescharacteristic
289C22—21no—
290C22—21no—
291C22—22no—
292C22—22no—
293C22—22no—
294C22C2×C19×M3212yes—
295C22C23×C8×C1911yescharacteristic
296C4—21no—
297C4—22no—
298C4—22no—
299C4—21no—
300C4—21no—
301C4—22no—
302C4C2×C19×M3212yes—
303C4C2×C19×M3212yes—
304C4C19×#52011yescharacteristic
305C4C19×#56811yescharacteristic
306C2—22no—
307C2—42no—
308C2C19×#298811yescharacteristic
309C2C22×C19×M3211yescharacteristic
310C2C19×#340711yescharacteristic
subgroupG/H
centerC2×C8×C19C24
commutatorC22C23×C8×C19
Frattini, cosocleC2×C8C24×C19
socleC22×C19C23×C8
prime radicalC2×#41×C19C8
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C8×C19 ◁ G

Complements

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

NH ≅ G/Ntype
2. C19×#2183C2semidirect
3. C19×#2169C2semidirect
4. C19×#2168C2semidirect
5. C19×#2163C2semidirect
6. C19×#2162C2semidirect
7. C19×#2150C2semidirect
8. C2×C19×C4⋊C16C2semidirect
104. #33503C19direct (N × H)
117. C2×C4×C19M32semidirect
135. #2183C2×C19semidirect
136. #2169C2×C19semidirect
137. #2168C2×C19semidirect
138. #2163C2×C19semidirect
139. #2162C2×C19semidirect
140. #2150C2×C19semidirect
141. C2×C4⋊C16C2×C19semidirect
220. C19#33503direct (N × H)
272. C2×C4C19×M32semidirect

Maximal subgroups

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

subgroupindex
C8×#41×C192
C19×#21832
C19×#21692
C19×#21682
C19×#21632
C19×#21622
C19×#21502
C2×C19×C4⋊C162
#3350319