Finite Group Databasebeta

← C19×#9297 #18015256

Subgroups — C19×#9297 #18015256

Order 4864.

454 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3209C211yesmaximal, characteristic
2C19×#2331C211yesmaximal, characteristic
3C19×#1995C211yesmaximal, characteristic
4C19×#1548C211yesmaximal, characteristic
5C19×#1518C211yesmaximal, characteristic
6C19×#1286C211yesmaximal, characteristic
7C19×#1274C211yesmaximal, characteristic
8C19×#533C2211yescharacteristic
9C2×C19×C4⋊Q8C2211yescharacteristic
10C19×#494C412yescomplemented
11C19×#487C412yescomplemented
12C19×#462—22no—
13C19×#451—22no—
14C19×#431C2211yescharacteristic
15C19×#431C2211yescharacteristic
16C19×#423C2211yescharacteristic
17C19×#391—22no—
18C19×#389—21no—
19C19×#387—22no—
20C19×#382C2211yescharacteristic
21C4×C4⋊C4×C19—21no—
22C19×#376C2211yescharacteristic
23C19×#339—21no—
24C19×#339—21no—
25C19×#333—22no—
26C19×#328—22no—
27C22×Q8×C19D412yes—
28C2×Q16×C19—24no—
29C2×M16×C19—21no—
30C19×C4⋊Q8—21no—
31C19×C4⋊Q8—21no—
32C19×C4⋊Q8C2×C411yescharacteristic
33C19×C4⋊Q8C2×C411yescharacteristic
34C19×C4⋊Q8C2×C412yes—
35C19×C4⋊Q8D412yes—
36C19×#125—21no—
37C19×C22⋊Q8—21no—
38C19×C22⋊Q8—21no—
39C4×Q8×C19—21no—
40C4×Q8×C19—21no—
41C19×#117—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19—22no—
46C2×C42×C19—22no—
47C2×C42×C19D411yescharacteristic
48C2×C42×C19D411yescharacteristic
49C2×C42×C19C2311yescharacteristic
50C19×C4⋊C8—21no—
51C19×C4⋊C8—21no—
52C19×C4⋊C8—21no—
53C19×C4⋊C8—21no—
54C19×#103—24no—
55C19×C22⋊C8—21no—
56C19×C22⋊C8—21no—
57C4×C8×C19—21no—
58C4×C8×C19C2×C412yes—
59C19×#95—22no—
60C19×#95—22no—
61C19×#95—21no—
62C19×#95—21no—
63C19×#95—21no—
64C19×#95D412yes—
65C2×Q8×C19—22no—
66C2×Q8×C19—21no—
67C2×Q8×C19—21no—
68C2×Q8×C19—82no—
69C2×Q8×C19C22⋊C414yes—
70C22×C4×C19—21no—
71C22×C4×C19—22no—
72C22×C4×C19—22no—
73C22×C4×C19—21no—
74C22×C4×C19C2×D411yescharacteristic
75C22×C4×C19C2×D411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77Q16×C19—84no—
78M16×C19—41no—
79M16×C19—41no—
80C2×C8×C19—22no—
81C2×C8×C19—41no—
82C2×C8×C19—41no—
83C4⋊C4×C19—22no—
84C4⋊C4×C19—22no—
85C4⋊C4×C19—22no—
86C4⋊C4×C19—22no—
87C4⋊C4×C19—21no—
88C4⋊C4×C19—21no—
89C4⋊C4×C19—21no—
90C4⋊C4×C19—21no—
91C4⋊C4×C19—41no—
92C4⋊C4×C19—41no—
93C4⋊C4×C19—41no—
94C4⋊C4×C19—41no—
95C4⋊C4×C19—82no—
96C22⋊C4×C19—41no—
97C42×C19—21no—
98C42×C19—21no—
99C42×C19—21no—
100C42×C19—41no—
101C42×C19—82no—
102C42×C19Q1612yescomplemented
103C42×C19C22×C411yescharacteristic
104C42×C19C2×D411yescharacteristic
105C42×C19#4111yescharacteristic
106C42×C19#4111yescharacteristic
107#9297C1911yesmaximal, characteristic, direct product factor, Sylow
108C23×C19#12011yescharacteristic
109Q8×C19—44no—
110Q8×C19—42no—
111Q8×C19—82no—
112Q8×C19—81no—
113C2×C4×C19—24no—
114C2×C4×C19—22no—
115C2×C4×C19—41no—
116C2×C4×C19—41no—
117C2×C4×C19—41no—
118C2×C4×C19—42no—
119C2×C4×C19—42no—
120C2×C4×C19—41no—
121C2×C4×C19—42no—
122C2×C4×C19—41no—
123C2×C4×C19—42no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—42no—
129C2×C4×C19C2×C22⋊C411yescharacteristic
130C2×C4×C19C4×D411yescharacteristic
131C2×C4×C19C4×D411yescharacteristic
132C2×C4×C19#12111yescharacteristic
133C2×C4×C19#12111yescharacteristic
134C2×C4×C19#12311yescharacteristic
135C2×C4×C19C2×Q1611yescharacteristic
136C2×C4×C19#13511yescharacteristic
137C2×C4×C19#13711yescharacteristic
138C2×C4×C19#13711yescharacteristic
139C8×C19—42no—
140C8×C19—81no—
141C8×C19—81no—
142#3209C2×C1911yescharacteristic
143#2331C2×C1911yescharacteristic
144#1995C2×C1911yescharacteristic
145#1548C2×C1911yescharacteristic
146#1518C2×C1911yescharacteristic
147#1286C2×C1911yescharacteristic
148#1274C2×C1911yescharacteristic
149C22×C19—21no—
150C22×C19—21no—
151C22×C19#38611yescharacteristic
152C22×C19#45111yescharacteristic
153C22×C19#45211yescharacteristic
154C4×C19—21no—
155C4×C19—21no—
156C4×C19—21no—
157C4×C19—21no—
158C4×C19—42no—
159C4×C19—44no—
160C4×C19—82no—
161C4×C19—81no—
162C4×C19—81no—
163C4×C19—81no—
164C4×C19C4×Q1611yescharacteristic
165C4×C19#44111yescharacteristic
166C4×C19#46211yescharacteristic
167C4×C19#46411yescharacteristic
168#533C22×C1911yescharacteristic
169C2×C4⋊Q8C22×C1911yescharacteristic
170#494C4×C1912yescomplemented
171#487C4×C1912yescomplemented
172#462—22no—
173#451—22no—
174#431C22×C1911yescharacteristic
175#431C22×C1911yescharacteristic
176#423C22×C1911yescharacteristic
177#391—22no—
178#389—21no—
179#387—22no—
180#382C22×C1911yescharacteristic
181C4×C4⋊C4—21no—
182#376C22×C1911yescharacteristic
183#339—21no—
184#339—21no—
185#333—22no—
186#328—22no—
187C2×C19—21no—
188C2×C19—21no—
189C2×C19#187811yescharacteristic
190C2×C19#190511yescharacteristic
191C2×C19#191111yescharacteristic
192C22×Q8D4×C1912yes—
193C2×Q16—24no—
194C2×M16—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8C2×C4×C1911yescharacteristic
198C4⋊Q8C2×C4×C1911yescharacteristic
199C4⋊Q8C2×C4×C1912yes—
200C4⋊Q8D4×C1912yes—
201#125—21no—
202C22⋊Q8—21no—
203C22⋊Q8—21no—
204C4×Q8—21no—
205C4×Q8—21no—
206#117—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—22no—
211C2×C42—22no—
212C2×C42D4×C1911yescharacteristic
213C2×C42D4×C1911yescharacteristic
214C2×C42C23×C1911yescharacteristic
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219#103—24no—
220C22⋊C8—21no—
221C22⋊C8—21no—
222C4×C8—21no—
223C4×C8C2×C4×C1912yes—
224#95—22no—
225#95—22no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95D4×C1912yes—
230C19#929711yescharacteristic, direct product factor, Sylow
231C2×Q8—22no—
232C2×Q8—21no—
233C2×Q8—21no—
234C2×Q8—82no—
235C2×Q8C22⋊C4×C1914yes—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4C2×D4×C1911yescharacteristic
241C22×C4C2×D4×C1911yescharacteristic
242C22×C4C2×D4×C1911yescharacteristic
243Q16—84no—
244M16—41no—
245M16—41no—
246C2×C8—22no—
247C2×C8—41no—
248C2×C8—41no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—82no—
262C22⋊C4—41no—
263C42—21no—
264C42—21no—
265C42—21no—
266C42—41no—
267C42—82no—
268C42Q16×C1912yescomplemented
269C42C22×C4×C1911yescharacteristic
270C42C2×D4×C1911yescharacteristic
271C42#41×C1911yescharacteristic
272C42#41×C1911yescharacteristic
273C23C19×#12011yescharacteristic
274Q8—44no—
275Q8—42no—
276Q8—82no—
277Q8—81no—
278C2×C4—24no—
279C2×C4—22no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4C2×C22⋊C4×C1911yescharacteristic
295C2×C4C4×D4×C1911yescharacteristic
296C2×C4C4×D4×C1911yescharacteristic
297C2×C4C19×#12111yescharacteristic
298C2×C4C19×#12111yescharacteristic
299C2×C4C19×#12311yescharacteristic
300C2×C4C2×Q16×C1911yescharacteristic
301C2×C4C19×#13511yescharacteristic
302C2×C4C19×#13711yescharacteristic
303C2×C4C19×#13711yescharacteristic
304C8—42no—
305C8—81no—
306C8—81no—
307C22—21no—
308C22—21no—
309C22C19×#38611yescharacteristic
310C22C19×#45111yescharacteristic
311C22C19×#45211yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—42no—
317C4—44no—
318C4—82no—
319C4—81no—
320C4—81no—
321C4—81no—
322C4C4×Q16×C1911yescharacteristic
323C4C19×#44111yescharacteristic
324C4C19×#46211yescharacteristic
325C4C19×#46411yescharacteristic
326C2—21no—
327C2—21no—
328C2C19×#187811yescharacteristic
329C2C19×#190511yescharacteristic
330C2C19×#191111yescharacteristic
subgroupG/H
center, socleC22×C19#386
commutatorC42C22×C4×C19
Frattini, cosocleC2×C42C23×C19
prime radicalC23×C19#120
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
10. C19×#494C4semidirect
11. C19×#487C4semidirect
102. C42×C19Q16semidirect
107. #9297C19direct (N × H)
170. #494C4×C19semidirect
171. #487C4×C19semidirect
230. C19#9297direct (N × H)
268. C42Q16×C19semidirect

Maximal subgroups

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

subgroupindex
C19×#32092
C19×#23312
C19×#19952
C19×#15482
C19×#15182
C19×#12862
C19×#12742
#929719