Finite Group Databasebeta

← C19×#8667 #18014626

Subgroups — C19×#8667 #18014626

Order 4864.

454 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#41×C19C211yesmaximal, characteristic
2C19×#1806C212yesmaximal
3C4×C19×#107C211yesmaximal, characteristic, complemented
4C19×#1567C211yesmaximal, characteristic, complemented
5C19×#1303C212yesmaximal, complemented
6C4×#41×C19C2211yescharacteristic
7C8×Q8×C19C411yescharacteristic, complemented
8C8×Q8×C19C411yescharacteristic, complemented
9C8×D4×C19—21no—
10C8×D4×C19—21no—
11C8×D4×C19C411yescharacteristic, complemented
12C8×D4×C19C411yescharacteristic, complemented
13C19×#431—21no—
14C19×#431C2211yescharacteristic
15C2×C19×#107—21no—
16C19×#423C2212yes—
17C2×C19×#104—22no—
18C2×C4×C8×C19—21no—
19C2×C4×C8×C19C2211yescharacteristic
20C4×C4⋊C4×C19C2212yes—
21C19×#340—21no—
22C19×#339—22no—
23C19×#335—21no—
24C19×#335—21no—
25C2×#41×C19D411yescharacteristic
26C2×M16×C19—22no—
27C22×C8×C19—21no—
28C22×C8×C19—21no—
29C22×C8×C19D411yescharacteristic
30C22×C8×C19D411yescharacteristic
31C4×Q8×C19C2×C411yescharacteristic
32C4×Q8×C19Q811yescharacteristic
33C4×D4×C19—21no—
34C4×D4×C19—21no—
35C4×D4×C19C2×C411yescharacteristic
36C4×D4×C19Q811yescharacteristic
37C19×#117—21no—
38C19×#117D411yescharacteristic
39C2×C4⋊C4×C19—22no—
40C2×C42×C19—21no—
41C2×C42×C19—22no—
42C2×C42×C19C2311yescharacteristic
43C19×#107—24no—
44C19×C4⋊C8—21no—
45C19×C4⋊C8—21no—
46C19×C4⋊C8—22no—
47C19×C4⋊C8—22no—
48C19×C4⋊C8C2×C411yescharacteristic
49C19×C4⋊C8C2×C411yescharacteristic
50C19×#104—44no—
51C19×C22⋊C8—21no—
52C19×C22⋊C8—21no—
53C19×C22⋊C8—21no—
54C4×C8×C19—21no—
55C4×C8×C19—21no—
56C4×C8×C19—21no—
57C4×C8×C19C2×C411yescharacteristic
58C4×C8×C19C2×C411yescharacteristic
59C4×C8×C19D411yescharacteristic
60C4×C8×C19D411yescharacteristic
61C19×#95—22no—
62#41×C19—21no—
63#41×C19—21no—
64#41×C19D812yes—
65#41×C19Q1612yes—
66C2×Q8×C19C4⋊C411yescharacteristic
67C2×D4×C19—21no—
68C2×D4×C19C4⋊C411yescharacteristic
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—42no—
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19#4111yescharacteristic
76M16×C19—42no—
77M16×C19—42no—
78C2×C8×C19—22no—
79C2×C8×C19—21no—
80C2×C8×C19—21no—
81C2×C8×C19—41no—
82C2×C8×C19—42no—
83C2×C8×C19—42no—
84C2×C8×C19—42no—
85C2×C8×C19C22⋊C411yescharacteristic
86C2×C8×C19C22⋊C411yescharacteristic
87C2×C8×C19C22⋊C411yescharacteristic
88C2×C8×C19C22⋊C411yescharacteristic
89C4⋊C4×C19—21no—
90C4⋊C4×C19—21no—
91C4⋊C4×C19—24no—
92C4⋊C4×C19—42no—
93C4⋊C4×C19C4⋊C411yescharacteristic
94C4⋊C4×C19C4⋊C411yescharacteristic
95C22⋊C4×C19—21no—
96C22⋊C4×C19—21no—
97C22⋊C4×C19—21no—
98C42×C19—21no—
99C42×C19—21no—
100C42×C19—21no—
101C42×C19—42no—
102C42×C19—42no—
103C42×C19C22×C411yescharacteristic
104C42×C19C2×D411yescharacteristic
105C42×C19C2×Q811yescharacteristic
106C42×C19#4111yescharacteristic
107#8667C1911yesmaximal, characteristic, direct product factor, Sylow
108C23×C19—21no—
109C23×C19#12111yescharacteristic
110Q8×C19—21no—
111Q8×C19#10712yescomplemented
112D4×C19—22no—
113D4×C19—22no—
114D4×C19—21no—
115D4×C19#10712yescomplemented
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—22no—
120C2×C4×C19—22no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—41no—
124C2×C4×C19—42no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—44no—
128C2×C4×C19—82no—
129C2×C4×C19—82no—
130C2×C4×C19C2×C22⋊C411yescharacteristic
131C2×C4×C19C2×C4⋊C411yescharacteristic
132C2×C4×C19#11711yescharacteristic
133C2×C4×C19#12111yescharacteristic
134C2×C4×C19C22⋊Q811yescharacteristic
135C2×C4×C19C22⋊Q811yescharacteristic
136C2×C4×C19C2×D811yescharacteristic
137C2×C4×C19C2×Q1611yescharacteristic
138C2×C4×C19#13511yescharacteristic
139C2×C4×C19#13511yescharacteristic
140C8×C19—21no—
141C8×C19—21no—
142C8×C19—21no—
143C8×C19—41no—
144C8×C19—41no—
145C8×C19—82no—
146C8×C19#10412yescomplemented
147C8×#41C2×C1911yescharacteristic
148#1806C2×C1912yes—
149C4×#107C2×C1911yescharacteristic, complemented
150#1567C2×C1911yescharacteristic, complemented
151#1303C2×C1912yescomplemented
152C22×C19—21no—
153C22×C19—21no—
154C22×C19—22no—
155C22×C19—41no—
156C22×C19—41no—
157C22×C19#38011yescharacteristic
158C22×C19#46611yescharacteristic
159C22×C19#46711yescharacteristic
160C4×C19—21no—
161C4×C19—22no—
162C4×C19—21no—
163C4×C19—21no—
164C4×C19—41no—
165C4×C19—41no—
166C4×C19—84no—
167C4×C19C2×#10411yescharacteristic
168C4×C19#42111yescharacteristic
169C4×C19C2×#10711yescharacteristic
170C4×C19#42711yescharacteristic
171C4×C19#46611yescharacteristic
172C4×C19#46711yescharacteristic
173C4×#41C22×C1911yescharacteristic
174C8×Q8C4×C1911yescharacteristic, complemented
175C8×Q8C4×C1911yescharacteristic, complemented
176C8×D4—21no—
177C8×D4—21no—
178C8×D4C4×C1911yescharacteristic, complemented
179C8×D4C4×C1911yescharacteristic, complemented
180#431—21no—
181#431C22×C1911yescharacteristic
182C2×#107—21no—
183#423C22×C1912yes—
184C2×#104—22no—
185C2×C4×C8—21no—
186C2×C4×C8C22×C1911yescharacteristic
187C4×C4⋊C4C22×C1912yes—
188#340—21no—
189#339—22no—
190#335—21no—
191#335—21no—
192C2×C19—21no—
193C2×C19—21no—
194C2×C19—42no—
195C2×C19#180611yescharacteristic
196C2×C19#180811yescharacteristic
197C2×C19#181411yescharacteristic
198C2×#41D4×C1911yescharacteristic
199C2×M16—22no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8D4×C1911yescharacteristic
203C22×C8D4×C1911yescharacteristic
204C4×Q8C2×C4×C1911yescharacteristic
205C4×Q8Q8×C1911yescharacteristic
206C4×D4—21no—
207C4×D4—21no—
208C4×D4C2×C4×C1911yescharacteristic
209C4×D4Q8×C1911yescharacteristic
210#117—21no—
211#117D4×C1911yescharacteristic
212C2×C4⋊C4—22no—
213C2×C42—21no—
214C2×C42—22no—
215C2×C42C23×C1911yescharacteristic
216#107—24no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—22no—
220C4⋊C8—22no—
221C4⋊C8C2×C4×C1911yescharacteristic
222C4⋊C8C2×C4×C1911yescharacteristic
223#104—44no—
224C22⋊C8—21no—
225C22⋊C8—21no—
226C22⋊C8—21no—
227C4×C8—21no—
228C4×C8—21no—
229C4×C8—21no—
230C4×C8C2×C4×C1911yescharacteristic
231C4×C8C2×C4×C1911yescharacteristic
232C4×C8D4×C1911yescharacteristic
233C4×C8D4×C1911yescharacteristic
234#95—22no—
235C19#866711yescharacteristic, direct product factor, Sylow
236#41—21no—
237#41—21no—
238#41D8×C1912yes—
239#41Q16×C1912yes—
240C2×Q8C4⋊C4×C1911yescharacteristic
241C2×D4—21no—
242C2×D4C4⋊C4×C1911yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—42no—
247C22×C4C2×D4×C1911yescharacteristic
248C22×C4C2×D4×C1911yescharacteristic
249C22×C4#41×C1911yescharacteristic
250M16—42no—
251M16—42no—
252C2×C8—22no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—41no—
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—42no—
259C2×C8C22⋊C4×C1911yescharacteristic
260C2×C8C22⋊C4×C1911yescharacteristic
261C2×C8C22⋊C4×C1911yescharacteristic
262C2×C8C22⋊C4×C1911yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—24no—
266C4⋊C4—42no—
267C4⋊C4C4⋊C4×C1911yescharacteristic
268C4⋊C4C4⋊C4×C1911yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42—42no—
276C42—42no—
277C42C22×C4×C1911yescharacteristic
278C42C2×D4×C1911yescharacteristic
279C42C2×Q8×C1911yescharacteristic
280C42#41×C1911yescharacteristic
281C23—21no—
282C23C19×#12111yescharacteristic
283Q8—21no—
284Q8C19×#10712yescomplemented
285D4—22no—
286D4—22no—
287D4—21no—
288D4C19×#10712yescomplemented
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—44no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4C2×C22⋊C4×C1911yescharacteristic
304C2×C4C2×C4⋊C4×C1911yescharacteristic
305C2×C4C19×#11711yescharacteristic
306C2×C4C19×#12111yescharacteristic
307C2×C4C19×C22⋊Q811yescharacteristic
308C2×C4C19×C22⋊Q811yescharacteristic
309C2×C4C2×D8×C1911yescharacteristic
310C2×C4C2×Q16×C1911yescharacteristic
311C2×C4C19×#13511yescharacteristic
312C2×C4C19×#13511yescharacteristic
313C8—21no—
314C8—21no—
315C8—21no—
316C8—41no—
317C8—41no—
318C8—82no—
319C8C19×#10412yescomplemented
320C22—21no—
321C22—21no—
322C22—22no—
323C22—41no—
324C22—41no—
325C22C19×#38011yescharacteristic
326C22C19×#46611yescharacteristic
327C22C19×#46711yescharacteristic
328C4—21no—
329C4—22no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—84no—
335C4C2×C19×#10411yescharacteristic
336C4C19×#42111yescharacteristic
337C4C2×C19×#10711yescharacteristic
338C4C19×#42711yescharacteristic
339C4C19×#46611yescharacteristic
340C4C19×#46711yescharacteristic
341C2—21no—
342C2—21no—
343C2—42no—
344C2C19×#180611yescharacteristic
345C2C19×#180811yescharacteristic
346C2C19×#181411yescharacteristic
subgroupG/H
centerC2×C4×C19#121
commutatorC42C22×C4×C19
Frattini, cosocleC2×C42C23×C19
socleC22×C19#380
prime radicalC2×#41×C19D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ G

Complements

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

NH ≅ G/Ntype
3. C4×C19×#107C2semidirect
4. C19×#1567C2semidirect
5. C19×#1303C2semidirect
7. C8×Q8×C19C4semidirect
8. C8×Q8×C19C4semidirect
11. C8×D4×C19C4semidirect
12. C8×D4×C19C4semidirect
107. #8667C19direct (N × H)
111. Q8×C19#107semidirect
115. D4×C19#107semidirect
146. C8×C19#104semidirect
149. C4×#107C2×C19semidirect
150. #1567C2×C19semidirect
151. #1303C2×C19semidirect
174. C8×Q8C4×C19semidirect
175. C8×Q8C4×C19semidirect
178. C8×D4C4×C19semidirect
179. C8×D4C4×C19semidirect
235. C19#8667direct (N × H)
284. Q8C19×#107semidirect
288. D4C19×#107semidirect
319. C8C19×#104semidirect

Maximal subgroups

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

subgroupindex
C8×#41×C192
C19×#18062
C4×C19×#1072
C19×#15672
C19×#13032
#866719