Finite Group Databasebeta

← C19×#9304 #18015263

Subgroups — C19×#9304 #18015263

Order 4864.

436 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3078C211yesmaximal, characteristic
2C19×#2982C211yesmaximal, characteristic
3C19×#1805C211yesmaximal, characteristic
4C19×#1518C211yesmaximal, characteristic
5C19×#1481C211yesmaximal, characteristic
6C19×#1301C211yesmaximal, characteristic
7C19×#1286C211yesmaximal, characteristic
8C19×#533C2211yescharacteristic
9C2×C4×Q8×C19C2211yescharacteristic
10C19×#479—22no—
11C19×#477C412yescomplemented
12C19×#475C412yescomplemented
13C8×Q8×C19—22no—
14C8×Q8×C19—22no—
15C19×#431—22no—
16C19×#431C2211yescharacteristic
17C19×#431C2211yescharacteristic
18C19×#428—21no—
19C19×#423C2211yescharacteristic
20C2×C19×C4⋊C8C2211yescharacteristic
21C19×#419—21no—
22C2×C19×#103—21no—
23C19×#382C2211yescharacteristic
24C19×#340—21no—
25C19×#328—22no—
26C19×Q8⋊C8—22no—
27C22×Q8×C19D411yescharacteristic
28C2×M16×C19—21no—
29C22×C8×C19—21no—
30C19×C4⋊Q8C2×C411yescharacteristic
31C19×C4⋊Q8C2×C411yescharacteristic
32C19×#125—21no—
33C19×C22⋊Q8—21no—
34C19×C22⋊Q8—21no—
35C4×Q8×C19—21no—
36C4×Q8×C19—21no—
37C4×Q8×C19—21no—
38C4×Q8×C19—21no—
39C4×Q8×C19C2×C412yes—
40C4×Q8×C19D412yes—
41C19×#117—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19D411yescharacteristic
45C2×C42×C19—21no—
46C2×C42×C19C2311yescharacteristic
47C19×#107—22no—
48C19×#106—22no—
49C19×C4⋊C8—24no—
50C19×C4⋊C8—21no—
51C19×C4⋊C8—21no—
52C19×C4⋊C8—21no—
53C19×C4⋊C8—21no—
54C19×C4⋊C8—21no—
55C19×C4⋊C8C2×C412yes—
56C19×#103—22no—
57C19×#103—22no—
58C19×#103—42no—
59C19×C22⋊C8—21no—
60C19×C22⋊C8D412yes—
61C4×C8×C19—24no—
62C4×C8×C19—21no—
63C4×C8×C19D412yes—
64C19×#95—21no—
65C19×#95—21no—
66C2×Q8×C19—21no—
67C2×Q8×C19—21no—
68C2×Q8×C19—21no—
69C2×Q8×C19—21no—
70C2×Q8×C19—21no—
71C2×Q8×C19C22⋊C412yes—
72C2×Q8×C19SD1612yes—
73C2×Q8×C19Q1612yes—
74C22×C4×C19—21no—
75C22×C4×C19—21no—
76C22×C4×C19—41no—
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19#4111yescharacteristic
80M16×C19—41no—
81M16×C19—41no—
82C2×C8×C19—22no—
83C2×C8×C19—22no—
84C2×C8×C19—22no—
85C2×C8×C19—41no—
86C2×C8×C19—41no—
87C2×C8×C19—41no—
88C4⋊C4×C19—22no—
89C4⋊C4×C19—21no—
90C4⋊C4×C19—22no—
91C4⋊C4×C19—21no—
92C4⋊C4×C19—21no—
93C4⋊C4×C19—21no—
94C4⋊C4×C19—21no—
95C4⋊C4×C19—41no—
96C4⋊C4×C19—41no—
97C4⋊C4×C19—41no—
98C4⋊C4×C19—41no—
99C4⋊C4×C19C22⋊C412yes—
100C22⋊C4×C19—41no—
101C42×C19—22no—
102C42×C19—22no—
103C42×C19—41no—
104C42×C19C22×C411yescharacteristic
105C42×C19C2×D411yescharacteristic
106C42×C19C2×D411yescharacteristic
107C42×C19#4111yescharacteristic
108#9304C1911yesmaximal, characteristic, direct product factor, Sylow
109C23×C19#12111yescharacteristic
110Q8×C19—22no—
111Q8×C19—22no—
112Q8×C19—22no—
113Q8×C19—42no—
114Q8×C19—81no—
115Q8×C19#10314yes—
116C2×C4×C19—22no—
117C2×C4×C19—22no—
118C2×C4×C19—22no—
119C2×C4×C19—22no—
120C2×C4×C19—41no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—41no—
124C2×C4×C19—81no—
125C2×C4×C19—81no—
126C2×C4×C19—81no—
127C2×C4×C19—81no—
128C2×C4×C19C2×C22⋊C411yescharacteristic
129C2×C4×C19C4×D411yescharacteristic
130C2×C4×C19C4×D411yescharacteristic
131C2×C4×C19#12011yescharacteristic
132C2×C4×C19#12111yescharacteristic
133C2×C4×C19#12311yescharacteristic
134C2×C4×C19C2×SD1611yescharacteristic
135C2×C4×C19C2×Q1611yescharacteristic
136C2×C4×C19#13511yescharacteristic
137C2×C4×C19#13511yescharacteristic
138C8×C19—42no—
139C8×C19—42no—
140C8×C19—42no—
141C8×C19—81no—
142#3078C2×C1911yescharacteristic
143#2982C2×C1911yescharacteristic
144#1805C2×C1911yescharacteristic
145#1518C2×C1911yescharacteristic
146#1481C2×C1911yescharacteristic
147#1301C2×C1911yescharacteristic
148#1286C2×C1911yescharacteristic
149C22×C19—21no—
150C22×C19—21no—
151C22×C19#38611yescharacteristic
152C22×C19#46511yescharacteristic
153C22×C19#46711yescharacteristic
154C4×C19—21no—
155C4×C19—21no—
156C4×C19—24no—
157C4×C19—21no—
158C4×C19—21no—
159C4×C19—42no—
160C4×C19—81no—
161C4×C19—81no—
162C4×C19—161no—
163C4×C19C2×#10311yescharacteristic
164C4×C19#41611yescharacteristic
165C4×C19#46511yescharacteristic
166C4×C19#46711yescharacteristic
167#533C22×C1911yescharacteristic
168C2×C4×Q8C22×C1911yescharacteristic
169#479—22no—
170#477C4×C1912yescomplemented
171#475C4×C1912yescomplemented
172C8×Q8—22no—
173C8×Q8—22no—
174#431—22no—
175#431C22×C1911yescharacteristic
176#431C22×C1911yescharacteristic
177#428—21no—
178#423C22×C1911yescharacteristic
179C2×C4⋊C8C22×C1911yescharacteristic
180#419—21no—
181C2×#103—21no—
182#382C22×C1911yescharacteristic
183#340—21no—
184#328—22no—
185Q8⋊C8—22no—
186C2×C19—21no—
187C2×C19—21no—
188C2×C19#188111yescharacteristic
189C2×C19#189211yescharacteristic
190C2×C19#190511yescharacteristic
191C22×Q8D4×C1911yescharacteristic
192C2×M16—21no—
193C22×C8—21no—
194C4⋊Q8C2×C4×C1911yescharacteristic
195C4⋊Q8C2×C4×C1911yescharacteristic
196#125—21no—
197C22⋊Q8—21no—
198C22⋊Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201C4×Q8—21no—
202C4×Q8—21no—
203C4×Q8C2×C4×C1912yes—
204C4×Q8D4×C1912yes—
205#117—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4D4×C1911yescharacteristic
209C2×C42—21no—
210C2×C42C23×C1911yescharacteristic
211#107—22no—
212#106—22no—
213C4⋊C8—24no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8C2×C4×C1912yes—
220#103—22no—
221#103—22no—
222#103—42no—
223C22⋊C8—21no—
224C22⋊C8D4×C1912yes—
225C4×C8—24no—
226C4×C8—21no—
227C4×C8D4×C1912yes—
228#95—21no—
229#95—21no—
230C19#930411yescharacteristic, direct product factor, Sylow
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—21no—
234C2×Q8—21no—
235C2×Q8—21no—
236C2×Q8C22⋊C4×C1912yes—
237C2×Q8SD16×C1912yes—
238C2×Q8Q16×C1912yes—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—41no—
242C22×C4C2×D4×C1911yescharacteristic
243C22×C4C2×D4×C1911yescharacteristic
244C22×C4#41×C1911yescharacteristic
245M16—41no—
246M16—41no—
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C4⋊C4—22no—
254C4⋊C4—21no—
255C4⋊C4—22no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4C22⋊C4×C1912yes—
265C22⋊C4—41no—
266C42—22no—
267C42—22no—
268C42—41no—
269C42C22×C4×C1911yescharacteristic
270C42C2×D4×C1911yescharacteristic
271C42C2×D4×C1911yescharacteristic
272C42#41×C1911yescharacteristic
273C23C19×#12111yescharacteristic
274Q8—22no—
275Q8—22no—
276Q8—22no—
277Q8—42no—
278Q8—81no—
279Q8C19×#10314yes—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4C2×C22⋊C4×C1911yescharacteristic
293C2×C4C4×D4×C1911yescharacteristic
294C2×C4C4×D4×C1911yescharacteristic
295C2×C4C19×#12011yescharacteristic
296C2×C4C19×#12111yescharacteristic
297C2×C4C19×#12311yescharacteristic
298C2×C4C2×SD16×C1911yescharacteristic
299C2×C4C2×Q16×C1911yescharacteristic
300C2×C4C19×#13511yescharacteristic
301C2×C4C19×#13511yescharacteristic
302C8—42no—
303C8—42no—
304C8—42no—
305C8—81no—
306C22—21no—
307C22—21no—
308C22C19×#38611yescharacteristic
309C22C19×#46511yescharacteristic
310C22C19×#46711yescharacteristic
311C4—24no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—42no—
317C4—81no—
318C4—81no—
319C4—161no—
320C4C2×C19×#10311yescharacteristic
321C4C19×#41611yescharacteristic
322C4C19×#46511yescharacteristic
323C4C19×#46711yescharacteristic
324C2—21no—
325C2—21no—
326C2C19×#188111yescharacteristic
327C2C19×#189211yescharacteristic
328C2C19×#190511yescharacteristic
subgroupG/H
center, socleC22×C19#386
commutatorC42C22×C4×C19
Frattini, cosocleC2×C42C23×C19
prime radicalC23×C19#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G

Complements

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

NH ≅ G/Ntype
11. C19×#477C4semidirect
12. C19×#475C4semidirect
108. #9304C19direct (N × H)
170. #477C4×C19semidirect
171. #475C4×C19semidirect
230. C19#9304direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#30782
C19×#29822
C19×#18052
C19×#15182
C19×#14812
C19×#13012
C19×#12862
#930419