Finite Group Databasebeta

← C19×#21232 #18027191

Subgroups — C19×#21232 #18027191

Order 4864.

1470 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Q16×C19C211yesmaximal, characteristic
2C2×C19×#427C211yesmaximal, characteristic
3C2×C19×#419C212yesmaximal
4C2×C19×#405C211yesmaximal, characteristic
5C19×#2310C212yesmaximal
6C19×#1971C214yesmaximal, complemented
7C19×#1969C214yesmaximal, complemented
8C23×Q8×C19C2212yes—
9C22×Q16×C19—24no—
10C22×Q16×C19—24no—
11C22×Q16×C19C418yescomplemented
12C22×Q16×C19C2212yes—
13C22×Q16×C19C2212yes—
14C22×M16×C19C2211yescharacteristic
15C23×C8×C19C2211yescharacteristic
16C2×C19×#117C2212yes—
17C2×C19×#117C2211yescharacteristic
18C19×#427—24no—
19C2×C19×#107C2212yes—
20C2×C19×#106C2212yes—
21C19×#419—28no—
22C2×C19×#103C2218yes—
23C19×#405—24no—
24C2×C19×#97C2212yes—
25C2×C4×C8×C19C2212yes—
26C19×#391—24no—
27C19×#391C2218yes—
28C19×#381—24no—
29C22×Q8×C19—22no—
30C22×Q8×C19—24no—
31C22×Q8×C19—24no—
32C22×Q8×C19—24no—
33C22×Q8×C19—24no—
34C22×Q8×C19—24no—
35C22×Q8×C19C2×C418yes—
36C22×Q8×C19C2314yes—
37C23×C4×C19—22no—
38C23×C4×C19C2311yescharacteristic
39C2×Q16×C19—232no—
40C2×Q16×C19—24no—
41C2×Q16×C19—24no—
42C2×Q16×C19—24no—
43C2×Q16×C19—24no—
44C2×Q16×C19C2×C418yes—
45C2×Q16×C19C2×C418yes—
46C2×M16×C19—22no—
47C2×M16×C19—22no—
48C2×M16×C19D414yes—
49C22×C8×C19C2×C414yes—
50C22×C8×C19D414yes—
51C22×C8×C19D414yes—
52C22×C8×C19C2312yes—
53C22×C8×C19C2311yescharacteristic
54C22×C8×C19C2311yescharacteristic
55C19×#117—22no—
56C19×#117—22no—
57C19×#117—24no—
58C19×#117—24no—
59C2×C4⋊C4×C19D412yes—
60C2×C4⋊C4×C19C2314yes—
61C2×C22⋊C4×C19—22no—
62C2×C22⋊C4×C19D412yes—
63C2×C42×C19—22no—
64C2×C42×C19C2312yes—
65C19×#107—24no—
66C19×#106—24no—
67C19×#103—216no—
68C19×#97—24no—
69C4×C8×C19—24no—
70C19×#95—216no—
71C24×C19C2×D411yescharacteristic
72C2×Q8×C19—28no—
73C2×Q8×C19—24no—
74C2×Q8×C19—216no—
75C2×Q8×C19—216no—
76C2×Q8×C19—24no—
77C2×Q8×C19—24no—
78C2×Q8×C19—24no—
79C2×Q8×C19—24no—
80C2×Q8×C19—44no—
81C2×Q8×C19—48no—
82C2×Q8×C19—48no—
83C2×Q8×C19—44no—
84C2×Q8×C19C22×C418yes—
85C22×C4×C19—28no—
86C22×C4×C19—24no—
87C22×C4×C19—24no—
88C22×C4×C19—44no—
89C22×C4×C19—44no—
90C22×C4×C19C22×C412yes—
91C22×C4×C19C2×D414yes—
92C22×C4×C19C2×D412yes—
93C22×C4×C19C2×D412yes—
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2×D412yes—
96C22×C4×C19#4112yes—
97C22×C4×C19#4112yes—
98C22×C4×C19C2411yescharacteristic
99Q16×C19—216no—
100Q16×C19—216no—
101M16×C19—28no—
102C2×C8×C19—22no—
103C2×C8×C19—22no—
104C2×C8×C19C22⋊C4116yes—
105C2×C8×C19C22×C412yes—
106C2×C8×C19C22×C412yes—
107C2×C8×C19C2×D414yes—
108C2×C8×C19C2×D412yes—
109C2×C8×C19C2×D412yes—
110C2×C8×C19C2×D412yes—
111C2×C8×C19C2×D412yes—
112C4⋊C4×C19—24no—
113C4⋊C4×C19—24no—
114C4⋊C4×C19—24no—
115C22⋊C4×C19—24no—
116C22⋊C4×C19—44no—
117C42×C19—22no—
118C42×C19—22no—
119C42×C19—44no—
120#21232C1911yesmaximal, characteristic, direct product factor, Sylow
121C23×C19—24no—
122C23×C19C4×D412yes—
123C23×C19#12112yes—
124C23×C19#12712yes—
125C23×C19C22×D411yescharacteristic
126Q8×C19—28no—
127Q8×C19—28no—
128Q8×C19—44no—
129Q8×C19—44no—
130Q8×C19—416no—
131C2×C4×C19—28no—
132C2×C4×C19—24no—
133C2×C4×C19—28no—
134C2×C4×C19—44no—
135C2×C4×C19—44no—
136C2×C4×C19—416no—
137C2×C4×C19—44no—
138C2×C4×C19—48no—
139C2×C4×C19C2×C22⋊C414yes—
140C2×C4×C19C4×D414yes—
141C2×C4×C19C4×D412yes—
142C2×C4×C19#12114yes—
143C2×C4×C19#12112yes—
144C2×C4×C19#12414yes—
145C2×C4×C19#12712yes—
146C2×C4×C19C23×C411yescharacteristic
147C2×C4×C19C22×D411yescharacteristic
148C2×C4×C19C22×D411yescharacteristic
149C2×C4×C19C22×D411yescharacteristic
150C2×C4×C19C2×#4111yescharacteristic
151C2×C4×C19C2×#4111yescharacteristic
152C8×C19—24no—
153C8×C19C2×C22⋊C414yes—
154C8×C19C2×C22⋊C414yes—
155C23×Q16C2×C1911yescharacteristic
156C2×#427C2×C1911yescharacteristic
157C2×#419C2×C1912yes—
158C2×#405C2×C1911yescharacteristic
159#2310C2×C1912yes—
160#1971C2×C1914yescomplemented
161#1969C2×C1914yescomplemented
162C22×C19—24no—
163C22×C19—24no—
164C22×C19—24no—
165C22×C19#39014yes—
166C22×C19C2×C4×D411yescharacteristic
167C22×C19C2×#12111yescharacteristic
168C22×C19C2×#12711yescharacteristic
169C22×C19#57814yes—
170C4×C19—44no—
171C4×C19—48no—
172C4×C19—84no—
173C4×C19#39014yes—
174C4×C19C22×C22⋊C411yescharacteristic
175C4×C19C2×C4×D411yescharacteristic
176C4×C19C2×#12111yescharacteristic
177C4×C19C2×#12411yescharacteristic
178C23×Q8C22×C1912yes—
179C22×Q16—24no—
180C22×Q16—24no—
181C22×Q16C4×C1918yescomplemented
182C22×Q16C22×C1912yes—
183C22×Q16C22×C1912yes—
184C22×M16C22×C1911yescharacteristic
185C23×C8C22×C1911yescharacteristic
186C2×#117C22×C1912yes—
187C2×#117C22×C1911yescharacteristic
188#427—24no—
189C2×#107C22×C1912yes—
190C2×#106C22×C1912yes—
191#419—28no—
192C2×#103C22×C1918yes—
193#405—24no—
194C2×#97C22×C1912yes—
195C2×C4×C8C22×C1912yes—
196#391—24no—
197#391C22×C1918yes—
198#381—24no—
199C2×C19—24no—
200C2×C19C2×#39011yescharacteristic
201C2×C19#295012yes—
202C2×C19#305912yes—
203C2×C19#315612yes—
204C22×Q8—22no—
205C22×Q8—24no—
206C22×Q8—24no—
207C22×Q8—24no—
208C22×Q8—24no—
209C22×Q8—24no—
210C22×Q8C2×C4×C1918yes—
211C22×Q8C23×C1914yes—
212C23×C4—22no—
213C23×C4C23×C1911yescharacteristic
214C2×Q16—232no—
215C2×Q16—24no—
216C2×Q16—24no—
217C2×Q16—24no—
218C2×Q16—24no—
219C2×Q16C2×C4×C1918yes—
220C2×Q16C2×C4×C1918yes—
221C2×M16—22no—
222C2×M16—22no—
223C2×M16D4×C1914yes—
224C22×C8C2×C4×C1914yes—
225C22×C8D4×C1914yes—
226C22×C8D4×C1914yes—
227C22×C8C23×C1912yes—
228C22×C8C23×C1911yescharacteristic
229C22×C8C23×C1911yescharacteristic
230#117—22no—
231#117—22no—
232#117—24no—
233#117—24no—
234C2×C4⋊C4D4×C1912yes—
235C2×C4⋊C4C23×C1914yes—
236C2×C22⋊C4—22no—
237C2×C22⋊C4D4×C1912yes—
238C2×C42—22no—
239C2×C42C23×C1912yes—
240#107—24no—
241#106—24no—
242#103—216no—
243#97—24no—
244C4×C8—24no—
245#95—216no—
246C19#2123211yescharacteristic, direct product factor, Sylow
247C24C2×D4×C1911yescharacteristic
248C2×Q8—28no—
249C2×Q8—24no—
250C2×Q8—216no—
251C2×Q8—216no—
252C2×Q8—24no—
253C2×Q8—24no—
254C2×Q8—24no—
255C2×Q8—24no—
256C2×Q8—48no—
257C2×Q8—44no—
258C2×Q8—48no—
259C2×Q8—44no—
260C2×Q8C22×C4×C1918yes—
261C22×C4—28no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—44no—
265C22×C4—44no—
266C22×C4C22×C4×C1912yes—
267C22×C4C2×D4×C1914yes—
268C22×C4C2×D4×C1912yes—
269C22×C4C2×D4×C1912yes—
270C22×C4C2×D4×C1911yescharacteristic
271C22×C4C2×D4×C1912yes—
272C22×C4#41×C1912yes—
273C22×C4#41×C1912yes—
274C22×C4C24×C1911yescharacteristic
275Q16—216no—
276Q16—216no—
277M16—28no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8C22⋊C4×C19116yes—
281C2×C8C22×C4×C1912yes—
282C2×C8C22×C4×C1912yes—
283C2×C8C2×D4×C1914yes—
284C2×C8C2×D4×C1912yes—
285C2×C8C2×D4×C1912yes—
286C2×C8C2×D4×C1912yes—
287C2×C8C2×D4×C1912yes—
288C4⋊C4—24no—
289C4⋊C4—24no—
290C4⋊C4—24no—
291C22⋊C4—24no—
292C22⋊C4—44no—
293C42—22no—
294C42—22no—
295C42—44no—
296C23—24no—
297C23C4×D4×C1912yes—
298C23C19×#12112yes—
299C23C19×#12712yes—
300C23C22×D4×C1911yescharacteristic
301Q8—28no—
302Q8—28no—
303Q8—416no—
304Q8—44no—
305Q8—44no—
306C2×C4—28no—
307C2×C4—24no—
308C2×C4—28no—
309C2×C4—416no—
310C2×C4—44no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—48no—
314C2×C4C2×C22⋊C4×C1914yes—
315C2×C4C4×D4×C1912yes—
316C2×C4C4×D4×C1914yes—
317C2×C4C19×#12112yes—
318C2×C4C19×#12114yes—
319C2×C4C19×#12414yes—
320C2×C4C19×#12712yes—
321C2×C4C23×C4×C1911yescharacteristic
322C2×C4C22×D4×C1911yescharacteristic
323C2×C4C22×D4×C1911yescharacteristic
324C2×C4C22×D4×C1911yescharacteristic
325C2×C4C2×#41×C1911yescharacteristic
326C2×C4C2×#41×C1911yescharacteristic
327C8—24no—
328C8C2×C22⋊C4×C1914yes—
329C8C2×C22⋊C4×C1914yes—
330C22—24no—
331C22—24no—
332C22—24no—
333C22C19×#39014yes—
334C22C2×C4×D4×C1911yescharacteristic
335C22C2×C19×#12111yescharacteristic
336C22C2×C19×#12711yescharacteristic
337C22C19×#57814yes—
338C4—44no—
339C4—48no—
340C4—84no—
341C4C19×#39014yes—
342C4C22×C22⋊C4×C1911yescharacteristic
343C4C2×C4×D4×C1911yescharacteristic
344C4C2×C19×#12111yescharacteristic
345C4C2×C19×#12411yescharacteristic
346C2—24no—
347C2C2×C19×#39011yescharacteristic
348C2C19×#295012yes—
349C2C19×#305912yes—
350C2C19×#315612yes—
subgroupG/H
center, socleC23×C19C22×D4
commutatorC2×C4C23×C4×C19
Frattini, cosocleC22×C4C24×C19
prime radicalC24×C19C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C19 ◁ C2×C19×#117 ◁ G

Complements

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

NH ≅ G/Ntype
6. C19×#1971C2semidirect
7. C19×#1969C2semidirect
11. C22×Q16×C19C4semidirect
120. #21232C19direct (N × H)
160. #1971C2×C19semidirect
161. #1969C2×C19semidirect
181. C22×Q16C4×C19semidirect
246. C19#21232direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Q16×C192
C2×C19×#4272
C2×C19×#4192
C2×C19×#4052
C19×#23102
C19×#19712
C19×#19692
#2123219