Finite Group Databasebeta

← C19×#12193 #18018152

Subgroups — C19×#12193 #18018152

Order 4864.

442 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#2764C211yesmaximal, characteristic, complemented
2C19×#2022C211yesmaximal, characteristic
3C19×#1607C211yesmaximal, characteristic
4C19×#1601C211yesmaximal, characteristic
5C19×#1351C211yesmaximal, characteristic, complemented
6C19×#1344C211yesmaximal, characteristic, complemented
7C19×#1317C211yesmaximal, characteristic, complemented
8C19×#534C2211yescharacteristic
9C2×C19×#123—21no—
10C19×#480—21no—
11C19×#448—21no—
12C2×C19×#99—21no—
13C19×#400—21no—
14C19×#398—21no—
15C19×#397C2211yescharacteristic
16C19×#393C2211yescharacteristic
17C19×#391—21no—
18C19×#388—21no—
19C19×#385—21no—
20C19×#383—21no—
21C19×#381C2211yescharacteristic
22C19×#342C2211yescharacteristic
23C19×#327—21no—
24C19×#327—21no—
25C19×#323C2211yescharacteristic
26C19×#323C2211yescharacteristic
27C22×Q8×C19D411yescharacteristic
28C22×D4×C19—21no—
29C23×C4×C19D411yescharacteristic
30C2×SD16×C19—41no—
31C19×#123—42no—
32C19×#123—41no—
33C19×#123—42no—
34C19×#121—21no—
35C19×#121—21no—
36C19×#120—41no—
37C2×C4⋊C4×C19—21no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19—21no—
40C2×C4⋊C4×C19—41no—
41C2×C4⋊C4×C19D411yescharacteristic
42C2×C22⋊C4×C19—21no—
43C2×C22⋊C4×C19—21no—
44C2×C22⋊C4×C19—21no—
45C2×C22⋊C4×C19—41no—
46C2×C22⋊C4×C19D411yescharacteristic
47C2×C22⋊C4×C19C2311yescharacteristic
48C2×C42×C19—21no—
49C19×#107—41no—
50C19×#103—41no—
51C19×#102—41no—
52C19×#99—42no—
53C19×C22⋊C8—21no—
54C19×C22⋊C8—21no—
55C19×#95—21no—
56C19×#95—21no—
57C19×#95—21no—
58C19×#95—21no—
59C19×#95—21no—
60C19×#95—21no—
61C19×#95—21no—
62C19×#95—21no—
63C19×#95D411yescharacteristic
64C19×#95D411yescharacteristic
65C24×C19—21no—
66C24×C19C2×D411yescharacteristic
67C2×Q8×C19—42no—
68C2×Q8×C19—41no—
69C2×D4×C19—21no—
70C2×D4×C19—21no—
71C2×D4×C19—41no—
72C2×D4×C19—41no—
73C2×D4×C19—41no—
74C2×D4×C19—41no—
75C2×D4×C19—41no—
76C2×D4×C19—41no—
77C22×C4×C19—21no—
78C22×C4×C19—21no—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—21no—
84C22×C4×C19—21no—
85C22×C4×C19—21no—
86C22×C4×C19—41no—
87C22×C4×C19—41no—
88C22×C4×C19—41no—
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91SD16×C19—82no—
92C2×C8×C19—41no—
93C2×C8×C19—41no—
94C4⋊C4×C19—21no—
95C4⋊C4×C19—21no—
96C4⋊C4×C19—41no—
97C4⋊C4×C19—44no—
98C4⋊C4×C19—81no—
99C4⋊C4×C19—81no—
100C4⋊C4×C19—81no—
101C22⋊C4×C19—22no—
102C22⋊C4×C19—41no—
103C22⋊C4×C19—42no—
104C22⋊C4×C19—41no—
105C22⋊C4×C19—41no—
106C22⋊C4×C19—44no—
107C22⋊C4×C19—41no—
108C22⋊C4×C19—41no—
109C22⋊C4×C19—41no—
110C22⋊C4×C19—41no—
111C42×C19—42no—
112#12193C1911yesmaximal, characteristic, direct product factor, Sylow
113C23×C19—21no—
114C23×C19—21no—
115C23×C19—41no—
116C23×C19—41no—
117C23×C19—41no—
118C23×C19—41no—
119C23×C19—41no—
120C23×C19—81no—
121C23×C19—81no—
122C23×C19#12011yescharacteristic
123C23×C19#13511yescharacteristic
124C23×C19AGL(1,ℤ/8)11yescharacteristic
125Q8×C19—42no—
126Q8×C19—81no—
127D4×C19—81no—
128D4×C19—81no—
129D4×C19—81no—
130D4×C19—81no—
131D4×C19—81no—
132D4×C19—81no—
133C2×C4×C19—22no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19—42no—
143C2×C4×C19—42no—
144C2×C4×C19—41no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—81no—
161C2×C4×C19—81no—
162C2×C4×C19—81no—
163C8×C19—81no—
164C8×C19—81no—
165#2764C2×C1911yescharacteristic, complemented
166#2022C2×C1911yescharacteristic
167#1607C2×C1911yescharacteristic
168#1601C2×C1911yescharacteristic
169#1351C2×C1911yescharacteristic, complemented
170#1344C2×C1911yescharacteristic, complemented
171#1317C2×C1911yescharacteristic, complemented
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—41no—
177C22×C19—41no—
178C22×C19—41no—
179C22×C19—41no—
180C22×C19—81no—
181C22×C19—82no—
182C22×C19—81no—
183C22×C19—81no—
184C22×C19—81no—
185C22×C19—161no—
186C22×C19#44911yescharacteristic
187C22×C19#45311yescharacteristic
188C22×C19B(4,𝔽2)11yescharacteristic
189C4×C19—41no—
190C4×C19—42no—
191C4×C19—41no—
192C4×C19—81no—
193C4×C19—81no—
194C4×C19—81no—
195C4×C19—82no—
196C4×C19—81no—
197C4×C19—81no—
198C4×C19—81no—
199#534C22×C1911yescharacteristic
200C2×#123—21no—
201#480—21no—
202#448—21no—
203C2×#99—21no—
204#400—21no—
205#398—21no—
206#397C22×C1911yescharacteristic
207#393C22×C1911yescharacteristic
208#391—21no—
209#388—21no—
210#385—21no—
211#383—21no—
212#381C22×C1911yescharacteristic
213#342C22×C1911yescharacteristic
214#327—21no—
215#327—21no—
216#323C22×C1911yescharacteristic
217#323C22×C1911yescharacteristic
218C2×C19—21no—
219C2×C19—21no—
220C2×C19—41no—
221C2×C19—41no—
222C2×C19—161no—
223C2×C19#160011yescharacteristic
224C2×C19#219711yescharacteristic
225C2×C19#220111yescharacteristic
226C22×Q8D4×C1911yescharacteristic
227C22×D4—21no—
228C23×C4D4×C1911yescharacteristic
229C2×SD16—41no—
230#123—42no—
231#123—41no—
232#123—42no—
233#121—21no—
234#121—21no—
235#120—41no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—41no—
240C2×C4⋊C4D4×C1911yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—41no—
245C2×C22⋊C4D4×C1911yescharacteristic
246C2×C22⋊C4C23×C1911yescharacteristic
247C2×C42—21no—
248#107—41no—
249#103—41no—
250#102—41no—
251#99—42no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95D4×C1911yescharacteristic
263#95D4×C1911yescharacteristic
264C19#1219311yescharacteristic, direct product factor, Sylow
265C24—21no—
266C24C2×D4×C1911yescharacteristic
267C2×Q8—42no—
268C2×Q8—41no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4C2×D4×C1911yescharacteristic
290C22×C4C2×D4×C1911yescharacteristic
291SD16—82no—
292C2×C8—41no—
293C2×C8—41no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—44no—
298C4⋊C4—81no—
299C4⋊C4—81no—
300C4⋊C4—81no—
301C22⋊C4—22no—
302C22⋊C4—41no—
303C22⋊C4—42no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—44no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C42—42no—
312C23—21no—
313C23—21no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—81no—
320C23—81no—
321C23C19×#12011yescharacteristic
322C23C19×#13511yescharacteristic
323C23C19×AGL(1,ℤ/8)11yescharacteristic
324Q8—42no—
325Q8—81no—
326D4—81no—
327D4—81no—
328D4—81no—
329D4—81no—
330D4—81no—
331D4—81no—
332C2×C4—22no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C8—81no—
363C8—81no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—81no—
373C22—82no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—161no—
378C22C19×#44911yescharacteristic
379C22C19×#45311yescharacteristic
380C22C19×B(4,𝔽2)11yescharacteristic
381C4—41no—
382C4—42no—
383C4—41no—
384C4—81no—
385C4—81no—
386C4—81no—
387C4—82no—
388C4—81no—
389C4—81no—
390C4—81no—
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—161no—
396C2C19×#160011yescharacteristic
397C2C19×#219711yescharacteristic
398C2C19×#220111yescharacteristic
subgroupG/H
center, socleC22×C19B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C19
prime radicalC19×#534C22
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C19 ◁ C23×C19 ◁ C2×C22⋊C4×C19 ◁ G

Complements

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

NH ≅ G/Ntype
1. C19×#2764C2semidirect
5. C19×#1351C2semidirect
6. C19×#1344C2semidirect
7. C19×#1317C2semidirect
112. #12193C19direct (N × H)
165. #2764C2×C19semidirect
169. #1351C2×C19semidirect
170. #1344C2×C19semidirect
171. #1317C2×C19semidirect
264. C19#12193direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#27642
C19×#20222
C19×#16072
C19×#16012
C19×#13512
C19×#13442
C19×#13172
#1219319