Finite Group Databasebeta

← C19×#10224 #18016183

Subgroups — C19×#10224 #18016183

Order 4864.

462 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3230C211yesmaximal, characteristic
2C19×#3209C211yesmaximal, characteristic
3C19×#3162C211yesmaximal, characteristic
4C19×#1993C211yesmaximal, characteristic
5C19×#1518C211yesmaximal, characteristic
6C19×#1518C211yesmaximal, characteristic
7C19×#1281C211yesmaximal, characteristic
8C19×#533C2211yescharacteristic
9C19×#533C2211yescharacteristic
10C2×C19×C4⋊Q8C2211yescharacteristic
11C19×#501—21no—
12C19×#501—21no—
13C19×#501—21no—
14C19×#501—21no—
15C19×#500—21no—
16C19×#494—21no—
17C19×#487—21no—
18C19×#487—21no—
19C19×#484—22no—
20C19×#477—22no—
21C19×#462—22no—
22C19×#451—22no—
23C19×#431C2211yescharacteristic
24C19×#431C2211yescharacteristic
25C19×#427—22no—
26C2×C19×#97C2211yescharacteristic
27C19×#382C2211yescharacteristic
28C19×#340—22no—
29C19×#328—22no—
30C19×#328—22no—
31C22×Q8×C19—21no—
32C2×Q16×C19—24no—
33C22×C8×C19D412yes—
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8—21no—
36C19×C4⋊Q8—21no—
37C19×C4⋊Q8D412yes—
38C19×C4⋊Q8D411yescharacteristic
39C19×C4⋊Q8D411yescharacteristic
40C19×C4⋊Q8D411yescharacteristic
41C19×C4⋊Q8D411yescharacteristic
42C19×#125—21no—
43C19×#125—21no—
44C19×C22⋊Q8—21no—
45C19×C22⋊Q8—21no—
46C19×C22⋊Q8—21no—
47C19×C22⋊Q8—21no—
48C4×Q8×C19—21no—
49C4×Q8×C19—21no—
50C4×Q8×C19—21no—
51C4×Q8×C19—21no—
52C19×#117—21no—
53C19×#117—21no—
54C2×C4⋊C4×C19—21no—
55C2×C4⋊C4×C19—21no—
56C2×C4⋊C4×C19—21no—
57C2×C42×C19C2311yescharacteristic
58C19×#107—22no—
59C19×#107—22no—
60C19×#107—24no—
61C19×#106—22no—
62C19×#106—22no—
63C19×C4⋊C8—21no—
64C19×C4⋊C8—21no—
65C19×#103—24no—
66C19×#103—24no—
67C19×C22⋊C8D412yes—
68C19×C22⋊C8D412yes—
69C19×#97—21no—
70C19×#97—21no—
71C4×C8×C19—21no—
72C4×C8×C19—21no—
73C19×#95—21no—
74C19×#95—21no—
75C2×Q8×C19—21no—
76C2×Q8×C19—21no—
77C2×Q8×C19—22no—
78C2×Q8×C19—21no—
79C2×Q8×C19—21no—
80C2×Q8×C19—41no—
81C2×Q8×C19—82no—
82C22×C4×C19—41no—
83C22×C4×C19—41no—
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87Q16×C19—84no—
88C2×C8×C19—22no—
89C2×C8×C19—22no—
90C2×C8×C19—22no—
91C2×C8×C19—22no—
92C2×C8×C19Q1614yescomplemented
93C4⋊C4×C19—22no—
94C4⋊C4×C19—21no—
95C4⋊C4×C19—21no—
96C4⋊C4×C19—21no—
97C4⋊C4×C19—21no—
98C4⋊C4×C19—21no—
99C4⋊C4×C19—21no—
100C4⋊C4×C19—22no—
101C4⋊C4×C19—21no—
102C4⋊C4×C19—21no—
103C4⋊C4×C19—41no—
104C4⋊C4×C19—41no—
105C4⋊C4×C19—41no—
106C4⋊C4×C19—41no—
107C4⋊C4×C19—41no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19—42no—
110C22⋊C4×C19—41no—
111C22⋊C4×C19—41no—
112C42×C19—41no—
113C42×C19—41no—
114C42×C19C2×D411yescharacteristic
115C42×C19C2×D411yescharacteristic
116C42×C19C2×D411yescharacteristic
117C42×C19#4111yescharacteristic
118#10224C1911yesmaximal, characteristic, direct product factor, Sylow
119C23×C19#12711yescharacteristic
120Q8×C19—42no—
121Q8×C19—44no—
122Q8×C19—42no—
123Q8×C19—81no—
124Q8×C19—81no—
125Q8×C19—82no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—42no—
133C2×C4×C19—82no—
134C2×C4×C19—81no—
135C2×C4×C19—81no—
136C2×C4×C19—81no—
137C2×C4×C19#12011yescharacteristic
138C2×C4×C19#12011yescharacteristic
139C2×C4×C19#12011yescharacteristic
140C2×C4×C19#12111yescharacteristic
141C2×C4×C19#12111yescharacteristic
142C2×C4×C19#12111yescharacteristic
143C2×C4×C19C2×Q1612yes—
144C2×C4×C19#13712yes—
145C8×C19—24no—
146C8×C19—42no—
147C8×C19—42no—
148#3230C2×C1911yescharacteristic
149#3209C2×C1911yescharacteristic
150#3162C2×C1911yescharacteristic
151#1993C2×C1911yescharacteristic
152#1518C2×C1911yescharacteristic
153#1518C2×C1911yescharacteristic
154#1281C2×C1911yescharacteristic
155C22×C19—21no—
156C22×C19—21no—
157C22×C19#39211yescharacteristic
158C22×C19#49411yescharacteristic
159C22×C19#49711yescharacteristic
160C4×C19—21no—
161C4×C19—21no—
162C4×C19—21no—
163C4×C19—21no—
164C4×C19—82no—
165C4×C19—81no—
166C4×C19—81no—
167C4×C19—81no—
168C4×C19—81no—
169C4×C19—161no—
170C4×C19#45112yes—
171C4×C19#46212yes—
172#533C22×C1911yescharacteristic
173#533C22×C1911yescharacteristic
174C2×C4⋊Q8C22×C1911yescharacteristic
175#501—21no—
176#501—21no—
177#501—21no—
178#501—21no—
179#500—21no—
180#494—21no—
181#487—21no—
182#487—21no—
183#484—22no—
184#477—22no—
185#462—22no—
186#451—22no—
187#431C22×C1911yescharacteristic
188#431C22×C1911yescharacteristic
189#427—22no—
190C2×#97C22×C1911yescharacteristic
191#382C22×C1911yescharacteristic
192#340—22no—
193#328—22no—
194#328—22no—
195C2×C19—21no—
196C2×C19—21no—
197C2×C19#200811yescharacteristic
198C2×C19#200911yescharacteristic
199C2×C19#201611yescharacteristic
200C22×Q8—21no—
201C2×Q16—24no—
202C22×C8D4×C1912yes—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8D4×C1912yes—
207C4⋊Q8D4×C1911yescharacteristic
208C4⋊Q8D4×C1911yescharacteristic
209C4⋊Q8D4×C1911yescharacteristic
210C4⋊Q8D4×C1911yescharacteristic
211#125—21no—
212#125—21no—
213C22⋊Q8—21no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C4×Q8—21no—
218C4×Q8—21no—
219C4×Q8—21no—
220C4×Q8—21no—
221#117—21no—
222#117—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C42C23×C1911yescharacteristic
227#107—22no—
228#107—22no—
229#107—24no—
230#106—22no—
231#106—22no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234#103—24no—
235#103—24no—
236C22⋊C8D4×C1912yes—
237C22⋊C8D4×C1912yes—
238#97—21no—
239#97—21no—
240C4×C8—21no—
241C4×C8—21no—
242#95—21no—
243#95—21no—
244C19#1022411yescharacteristic, direct product factor, Sylow
245C2×Q8—21no—
246C2×Q8—22no—
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—41no—
251C2×Q8—82no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4C2×D4×C1911yescharacteristic
255C22×C4C2×D4×C1911yescharacteristic
256C22×C4C2×D4×C1911yescharacteristic
257Q16—84no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8Q16×C1914yescomplemented
263C4⋊C4—21no—
264C4⋊C4—22no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—22no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C42—41no—
283C42—41no—
284C42C2×D4×C1911yescharacteristic
285C42C2×D4×C1911yescharacteristic
286C42C2×D4×C1911yescharacteristic
287C42#41×C1911yescharacteristic
288C23C19×#12711yescharacteristic
289Q8—42no—
290Q8—44no—
291Q8—42no—
292Q8—81no—
293Q8—81no—
294Q8—82no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—82no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4C19×#12011yescharacteristic
307C2×C4C19×#12011yescharacteristic
308C2×C4C19×#12011yescharacteristic
309C2×C4C19×#12111yescharacteristic
310C2×C4C19×#12111yescharacteristic
311C2×C4C19×#12111yescharacteristic
312C2×C4C2×Q16×C1912yes—
313C2×C4C19×#13712yes—
314C8—24no—
315C8—42no—
316C8—42no—
317C22—21no—
318C22—21no—
319C22C19×#39211yescharacteristic
320C22C19×#49411yescharacteristic
321C22C19×#49711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—82no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4—81no—
331C4—161no—
332C4C19×#45112yes—
333C4C19×#46212yes—
334C2—21no—
335C2—21no—
336C2C19×#200811yescharacteristic
337C2C19×#200911yescharacteristic
338C2C19×#201611yescharacteristic
subgroupG/H
center, socleC22×C19#392
commutator, Frattini, cosocleC2×C42C23×C19
prime radicalC23×C19#127
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G

Complements

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

NH ≅ G/Ntype
92. C2×C8×C19Q16semidirect
118. #10224C19direct (N × H)
244. C19#10224direct (N × H)
262. C2×C8Q16×C19semidirect

Maximal subgroups

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

subgroupindex
C19×#32302
C19×#32092
C19×#31622
C19×#19932
C19×#15182
C19×#12812
#1022419