Finite Group Databasebeta

← C19×#62329 #18068288

Subgroups — C19×#62329 #18068288

Order 4864.

1764 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3550C212yesmaximal
2C19×#3342C214yesmaximal, complemented
3C19×#3328C218yesmaximal, complemented
4D4×Q16×C19C214yesmaximal, complemented
5C19×#3255C212yesmaximal, complemented
6C19×#3202C214yesmaximal, complemented
7C19×#3170C212yesmaximal, complemented
8C19×#3059C214yesmaximal, complemented
9C19×#2931C211yesmaximal, characteristic
10C22×Q16×C19C2214yes—
11C2×C19×#131C2212yes—
12C19×#563—24no—
13C19×#559—22no—
14Q82×C19—22no—
15C19×#556C2218yes—
16D4×Q8×C19C2218yes—
17C19×#542—28no—
18C19×#536C2218yes—
19C19×#533C2214yes—
20C19×#532C2211yescharacteristic
21C19×#500C2212yes—
22C19×#494C2212yes—
23C19×#487C2214yes—
24C19×#485C22116yes—
25C19×#475C2218yes—
26C19×#470C2218yes—
27C19×#470C2218yes—
28C19×#467C2214yes—
29C19×#467C2214yes—
30C19×#467C2218yes—
31C19×#462C2218yes—
32C19×#451C22116yes—
33C4×Q16×C19C2214yes—
34C4×Q16×C19C2214yes—
35C19×#436C2214yes—
36C8×D4×C19C2214yes—
37C19×#427C2214yes—
38C19×#423C2211yescharacteristic
39C19×#419C2218yes—
40C19×#408C2212yes—
41C2×C4×C8×C19C2211yescharacteristic
42C2×#41×C19C2312yes—
43C22×Q8×C19C2318yes—
44C2×Q16×C19—48no—
45C2×Q16×C19C2314yes—
46C2×Q16×C19C2314yes—
47C2×Q16×C19C2318yes—
48C19×#131—44no—
49C2×M16×C19C2312yes—
50C2×M16×C19C2314yes—
51C22×C8×C19C2311yescharacteristic
52C22×C8×C19C2314yes—
53C22×C8×C19C2311yescharacteristic
54C19×C4⋊Q8—28no—
55C19×C4⋊Q8—28no—
56C19×C4⋊Q8D411yescharacteristic
57C19×C4⋊Q8C2314yes—
58C19×C4⋊Q8C2314yes—
59C19×#127D411yescharacteristic
60C19×#126—216no—
61C19×#125—24no—
62C19×#124—28no—
63C19×#124—28no—
64C19×#124D412yes—
65C19×#123—28no—
66C19×#123—28no—
67C19×C22⋊Q8—24no—
68C19×C22⋊Q8—216no—
69C19×C22⋊Q8C23116yes—
70C19×C22⋊Q8C2318yes—
71C19×#121D414yes—
72C4×Q8×C19—28no—
73C4×Q8×C19—24no—
74C4×Q8×C19C2318yes—
75C4×D4×C19—28no—
76C4×D4×C19C2314yes—
77C19×#117—24no—
78C19×#117C2318yes—
79C2×C42×C19C2311yescharacteristic
80C19×#107C2314yes—
81C19×#107C2314yes—
82C19×#106C2318yes—
83C19×C4⋊C8C2314yes—
84C19×#103C2318yes—
85C19×#103C23116yes—
86C19×#103C2318yes—
87C19×C22⋊C8C2318yes—
88C4×C8×C19C2312yes—
89C4×C8×C19C2312yes—
90#41×C19—42no—
91#41×C19—42no—
92C2×Q8×C19—24no—
93C2×Q8×C19—28no—
94C2×Q8×C19—48no—
95C2×Q8×C19—48no—
96C2×Q8×C19C2×D412yes—
97C2×Q8×C19C2418yes—
98C2×D4×C19C2×D414yes—
99C2×D4×C19C2×D414yes—
100C2×D4×C19C2×D412yes—
101C22×C4×C19—28no—
102C22×C4×C19C2×D412yes—
103C22×C4×C19C2411yescharacteristic
104C22×C4×C19C2414yes—
105Q16×C19—28no—
106Q16×C19—48no—
107Q16×C19—44no—
108M16×C19—44no—
109M16×C19—42no—
110C2×C8×C19—22no—
111C2×C8×C19—28no—
112C2×C8×C19—41no—
113C2×C8×C19C2411yescharacteristic
114C2×C8×C19C2414yes—
115C2×C8×C19C2412yes—
116C2×C8×C19C2411yescharacteristic
117C4⋊C4×C19—24no—
118C4⋊C4×C19—24no—
119C4⋊C4×C19—24no—
120C4⋊C4×C19—216no—
121C4⋊C4×C19—28no—
122C4⋊C4×C19—28no—
123C4⋊C4×C19C2×D414yes—
124C4⋊C4×C19C2418yes—
125C22⋊C4×C19—28no—
126C22⋊C4×C19—28no—
127C22⋊C4×C19—216no—
128C22⋊C4×C19C2×D418yes—
129C42×C19—28no—
130C42×C19—28no—
131C42×C19C2×D411yescharacteristic
132C42×C19C2×D411yescharacteristic
133C42×C19C2412yes—
134#62329C1911yesmaximal, characteristic, direct product factor, Sylow
135C23×C19C22×D411yescharacteristic
136C23×C19C22×D414yes—
137Q8×C19—28no—
138Q8×C19—28no—
139Q8×C19—42no—
140Q8×C19—48no—
141Q8×C19—88no—
142D4×C19—28no—
143D4×C19—42no—
144D4×C19—44no—
145C2×C4×C19—24no—
146C2×C4×C19—21no—
147C2×C4×C19—24no—
148C2×C4×C19—21no—
149C2×C4×C19—24no—
150C2×C4×C19—28no—
151C2×C4×C19—28no—
152C2×C4×C19—88no—
153C2×C4×C19C22×D414yes—
154C2×C4×C19C22×D411yescharacteristic
155C2×C4×C19C22×D412yes—
156C2×C4×C19C22×D412yes—
157C2×C4×C19C2511yescharacteristic
158C8×C19—21no—
159C8×C19—24no—
160C8×C19—22no—
161C8×C19H(5,𝔽2)12yes—
162#3550C2×C1912yes—
163#3342C2×C1914yescomplemented
164#3328C2×C1918yescomplemented
165D4×Q16C2×C1914yescomplemented
166#3255C2×C1912yescomplemented
167#3202C2×C1914yescomplemented
168#3170C2×C1912yescomplemented
169#3059C2×C1914yescomplemented
170#2931C2×C1911yescharacteristic
171C22×C19—24no—
172C22×C19—21no—
173C22×C19—22no—
174C22×C19—28no—
175C22×C19C23×D411yescharacteristic
176C4×C19—21no—
177C4×C19—24no—
178C4×C19—22no—
179C4×C19—48no—
180C4×C19—48no—
181C4×C19#57814yes—
182C4×C19C2×H(5,𝔽2)11yescharacteristic
183C4×C19#58511yescharacteristic
184C22×Q16C22×C1914yes—
185C2×#131C22×C1912yes—
186#563—24no—
187#559—22no—
188Q82—22no—
189#556C22×C1918yes—
190D4×Q8C22×C1918yes—
191#542—28no—
192#536C22×C1918yes—
193#533C22×C1914yes—
194#532C22×C1911yescharacteristic
195#500C22×C1912yes—
196#494C22×C1912yes—
197#487C22×C1914yes—
198#485C22×C19116yes—
199#475C22×C1918yes—
200#470C22×C1918yes—
201#470C22×C1918yes—
202#467C22×C1918yes—
203#467C22×C1914yes—
204#467C22×C1914yes—
205#462C22×C1918yes—
206#451C22×C19116yes—
207C4×Q16C22×C1914yes—
208C4×Q16C22×C1914yes—
209#436C22×C1914yes—
210C8×D4C22×C1914yes—
211#427C22×C1914yes—
212#423C22×C1911yescharacteristic
213#419C22×C1918yes—
214#408C22×C1912yes—
215C2×C4×C8C22×C1911yescharacteristic
216C2×C19—44no—
217C2×C19—41no—
218C2×C19#349611yescharacteristic
219C2×C19C2×#57812yes—
220C2×#41C23×C1912yes—
221C22×Q8C23×C1918yes—
222C2×Q16—48no—
223C2×Q16C23×C1914yes—
224C2×Q16C23×C1918yes—
225C2×Q16C23×C1914yes—
226#131—44no—
227C2×M16C23×C1912yes—
228C2×M16C23×C1914yes—
229C22×C8C23×C1911yescharacteristic
230C22×C8C23×C1914yes—
231C22×C8C23×C1911yescharacteristic
232C4⋊Q8—28no—
233C4⋊Q8—28no—
234C4⋊Q8D4×C1911yescharacteristic
235C4⋊Q8C23×C1914yes—
236C4⋊Q8C23×C1914yes—
237#127D4×C1911yescharacteristic
238#126—216no—
239#125—24no—
240#124—28no—
241#124—28no—
242#124D4×C1912yes—
243#123—28no—
244#123—28no—
245C22⋊Q8—24no—
246C22⋊Q8—216no—
247C22⋊Q8C23×C1918yes—
248C22⋊Q8C23×C19116yes—
249#121D4×C1914yes—
250C4×Q8—28no—
251C4×Q8—24no—
252C4×Q8C23×C1918yes—
253C4×D4—28no—
254C4×D4C23×C1914yes—
255#117—24no—
256#117C23×C1918yes—
257C2×C42C23×C1911yescharacteristic
258#107C23×C1914yes—
259#107C23×C1914yes—
260#106C23×C1918yes—
261C4⋊C8C23×C1914yes—
262#103C23×C1918yes—
263#103C23×C19116yes—
264#103C23×C1918yes—
265C22⋊C8C23×C1918yes—
266C4×C8C23×C1912yes—
267C4×C8C23×C1912yes—
268C19#6232911yescharacteristic, direct product factor, Sylow
269#41—42no—
270#41—42no—
271C2×Q8—24no—
272C2×Q8—28no—
273C2×Q8—48no—
274C2×Q8—48no—
275C2×Q8C2×D4×C1912yes—
276C2×Q8C24×C1918yes—
277C2×D4C2×D4×C1914yes—
278C2×D4C2×D4×C1914yes—
279C2×D4C2×D4×C1912yes—
280C22×C4—28no—
281C22×C4C2×D4×C1912yes—
282C22×C4C24×C1914yes—
283C22×C4C24×C1911yescharacteristic
284Q16—28no—
285Q16—48no—
286Q16—44no—
287M16—44no—
288M16—42no—
289C2×C8—22no—
290C2×C8—28no—
291C2×C8—41no—
292C2×C8C24×C1912yes—
293C2×C8C24×C1911yescharacteristic
294C2×C8C24×C1914yes—
295C2×C8C24×C1911yescharacteristic
296C4⋊C4—24no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—216no—
300C4⋊C4—28no—
301C4⋊C4—28no—
302C4⋊C4C2×D4×C1914yes—
303C4⋊C4C24×C1918yes—
304C22⋊C4—28no—
305C22⋊C4—28no—
306C22⋊C4—216no—
307C22⋊C4C2×D4×C1918yes—
308C42—28no—
309C42—28no—
310C42C2×D4×C1911yescharacteristic
311C42C2×D4×C1911yescharacteristic
312C42C24×C1912yes—
313C23C22×D4×C1911yescharacteristic
314C23C22×D4×C1914yes—
315Q8—28no—
316Q8—28no—
317Q8—42no—
318Q8—48no—
319Q8—88no—
320D4—28no—
321D4—42no—
322D4—44no—
323C2×C4—24no—
324C2×C4—21no—
325C2×C4—24no—
326C2×C4—21no—
327C2×C4—24no—
328C2×C4—28no—
329C2×C4—28no—
330C2×C4—88no—
331C2×C4C22×D4×C1914yes—
332C2×C4C22×D4×C1911yescharacteristic
333C2×C4C22×D4×C1912yes—
334C2×C4C22×D4×C1912yes—
335C2×C4C25×C1911yescharacteristic
336C8—21no—
337C8—24no—
338C8—22no—
339C8C19×H(5,𝔽2)12yes—
340C22—24no—
341C22—21no—
342C22—22no—
343C22—28no—
344C22C23×D4×C1911yescharacteristic
345C4—21no—
346C4—24no—
347C4—22no—
348C4—48no—
349C4—48no—
350C4C19×#57814yes—
351C4C2×C19×H(5,𝔽2)11yescharacteristic
352C4C19×#58511yescharacteristic
353C2—44no—
354C2—41no—
355C2C19×#349611yescharacteristic
356C2C2×C19×#57812yes—
subgroupG/H
center, socleC22×C19C23×D4
commutator, Frattini, cosocleC2×C4C25×C19
prime radicalC19×#532C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C19 ◁ C19×#532 ◁ G

Complements

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

NH ≅ G/Ntype
2. C19×#3342C2semidirect
3. C19×#3328C2semidirect
4. D4×Q16×C19C2semidirect
5. C19×#3255C2semidirect
6. C19×#3202C2semidirect
7. C19×#3170C2semidirect
8. C19×#3059C2semidirect
134. #62329C19direct (N × H)
163. #3342C2×C19semidirect
164. #3328C2×C19semidirect
165. D4×Q16C2×C19semidirect
166. #3255C2×C19semidirect
167. #3202C2×C19semidirect
168. #3170C2×C19semidirect
169. #3059C2×C19semidirect
268. C19#62329direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#35502
C19×#33422
C19×#33282
D4×Q16×C192
C19×#32552
C19×#32022
C19×#31702
C19×#30592
C19×#29312
#6232919