Finite Group Databasebeta

← C2×C19×#2203 #18039522

Subgroups — C2×C19×#2203 #18039522

Order 4864.

1092 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 222 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
1C2×C19×#563C211yesmaximal, characteristic, complemented
2C2×C19×#456C212yesmaximal, complemented
3C2×C19×#454C211yesmaximal, characteristic
4C19×#2203C218yesmaximal, direct product factor
5C2×C19×#356C212yesmaximal, complemented
6C2×C19×#355C211yesmaximal, characteristic, complemented
7C2×C19×2−1+4C2211yescharacteristic
8C2×C19×#137—22no—
9C2×C19×AGL(1,ℤ/8)—21no—
10C19×#563—24no—
11C19×#563—22no—
12C19×#563C2214yescomplemented
13C2×C19×C4⋊Q8C2212yes—
14C2×C19×#126—22no—
15C2×C19×#125—21no—
16C2×C19×#124C2211yescharacteristic
17C2×C19×#123—21no—
18C2×C19×C22⋊Q8—22no—
19C19×#456—24no—
20C19×#456C2218yescomplemented
21C19×#454—22no—
22C19×#454C2214yes—
23C2×C19×#104—21no—
24C2×C19×#104—22no—
25C2×C19×#101C2211yescharacteristic
26C2×C19×#101C2212yes—
27C19×#356C2218yescomplemented
28C19×#355C2214yescomplemented
29C19×2−1+4—21no—
30C19×2−1+4—22no—
31C19×2−1+4—42no—
32C19×2−1+4C2312yes—
33C2×#41×C19—21no—
34C2×#41×C19—22no—
35C2×#41×C19—41no—
36C22×Q8×C19—41no—
37C22×Q8×C19D412yes—
38C22×Q8×C19C2311yescharacteristic
39C22×D4×C19D411yescharacteristic
40C23×C4×C19—21no—
41C19×#137—28no—
42C19×#137—44no—
43C19×AGL(1,ℤ/8)—24no—
44C19×AGL(1,ℤ/8)—42no—
45C2×Q16×C19—42no—
46C2×SD16×C19—42no—
47C2×SD16×C19—41no—
48C2×D8×C19—41no—
49C2×M16×C19—21no—
50C2×M16×C19—22no—
51C19×C4⋊Q8—22no—
52C19×C4⋊Q8—22no—
53C19×C4⋊Q8D414yes—
54C19×C4⋊Q8C2314yes—
55C19×#126—28no—
56C19×#126—28no—
57C19×#125—24no—
58C19×#125—24no—
59C19×#124—22no—
60C19×#124D412yes—
61C19×#124C2312yes—
62C19×#123—24no—
63C19×#123—24no—
64C19×C22⋊Q8—28no—
65C19×C22⋊Q8—28no—
66C2×C4⋊C4×C19—21no—
67C2×C4⋊C4×C19—22no—
68C2×C4⋊C4×C19—21no—
69C2×C4⋊C4×C19—22no—
70C2×C4⋊C4×C19—22no—
71C2×C22⋊C4×C19—22no—
72C2×C22⋊C4×C19—21no—
73C2×C22⋊C4×C19—22no—
74C2×C42×C19D411yescharacteristic
75C2×C42×C19D412yes—
76C19×#104—24no—
77C19×#104—28no—
78C19×#101—21no—
79C19×#101—22no—
80C19×#101C2314yes—
81C19×#101C2312yes—
82C24×C19—21no—
83#41×C19—22no—
84#41×C19—24no—
85#41×C19—22no—
86#41×C19—24no—
87#41×C19—41no—
88#41×C19—42no—
89#41×C19—42no—
90#41×C19—42no—
91#41×C19—44no—
92#41×C19—42no—
93#41×C19—41no—
94C2×Q8×C19—22no—
95C2×Q8×C19—21no—
96C2×Q8×C19—22no—
97C2×Q8×C19—41no—
98C2×Q8×C19—41no—
99C2×Q8×C19—42no—
100C2×Q8×C19—42no—
101C2×Q8×C19—42no—
102C2×Q8×C19—42no—
103C2×Q8×C19—44no—
104C2×Q8×C19C2×D414yes—
105C2×Q8×C19C2×D412yes—
106C2×Q8×C19C2×D411yescharacteristic
107C2×Q8×C19C2411yescharacteristic
108C2×D4×C19—21no—
109C2×D4×C19—22no—
110C2×D4×C19—21no—
111C2×D4×C19—41no—
112C2×D4×C19—41no—
113C2×D4×C19—41no—
114C2×D4×C19C2×D412yes—
115C22×C4×C19—21no—
116C22×C4×C19—22no—
117C22×C4×C19—22no—
118C22×C4×C19—24no—
119C22×C4×C19—41no—
120C22×C4×C19—42no—
121C22×C4×C19—81no—
122C22×C4×C19—81no—
123C22×C4×C19C2×D412yes—
124C22×C4×C19C2×D411yescharacteristic
125Q16×C19—48no—
126SD16×C19—48no—
127SD16×C19—44no—
128D8×C19—44no—
129M16×C19—22no—
130M16×C19—24no—
131M16×C19—41no—
132M16×C19—42no—
133C2×C8×C19—41no—
134C2×C8×C19—42no—
135C4⋊C4×C19—24no—
136C4⋊C4×C19—28no—
137C4⋊C4×C19—24no—
138C4⋊C4×C19—24no—
139C4⋊C4×C19—24no—
140C4⋊C4×C19—24no—
141C4⋊C4×C19—24no—
142C22⋊C4×C19—28no—
143C22⋊C4×C19—24no—
144C22⋊C4×C19—24no—
145C22⋊C4×C19—24no—
146C42×C19—21no—
147C42×C19—22no—
148C42×C19C2×D412yes—
149C42×C19C2×D414yes—
150C2×#2203C1911yesmaximal, characteristic, direct product factor, Sylow
151C23×C19—22no—
152C23×C19—44no—
153C23×C19—41no—
154C23×C19—41no—
155C23×C19—41no—
156C23×C19#12011yescharacteristic
157Q8×C19—22no—
158Q8×C19—24no—
159Q8×C19—41no—
160Q8×C19—42no—
161Q8×C19—41no—
162Q8×C19—44no—
163Q8×C19—41no—
164Q8×C19—42no—
165Q8×C19—82no—
166D4×C19—22no—
167D4×C19—24no—
168D4×C19—42no—
169D4×C19—41no—
170D4×C19—42no—
171D4×C19—42no—
172D4×C19—42no—
173D4×C19—81no—
174C2×C4×C19—21no—
175C2×C4×C19—22no—
176C2×C4×C19—21no—
177C2×C4×C19—22no—
178C2×C4×C19—22no—
179C2×C4×C19—24no—
180C2×C4×C19—24no—
181C2×C4×C19—42no—
182C2×C4×C19—44no—
183C2×C4×C19—42no—
184C2×C4×C19—44no—
185C2×C4×C19—42no—
186C2×C4×C19—44no—
187C2×C4×C19—42no—
188C2×C4×C19—42no—
189C2×C4×C19—41no—
190C2×C4×C19—84no—
191C2×C4×C19#12012yes—
192C2×C4×C19#12011yescharacteristic
193C2×C4×C19C22×D412yes—
194C2×C4×C19C22×D411yescharacteristic
195C8×C19—42no—
196C8×C19—44no—
197C2×#563C2×C1911yescharacteristic, complemented
198C2×#456C2×C1912yescomplemented
199C2×#454C2×C1911yescharacteristic
200#2203C2×C1918yesdirect product factor
201C2×#356C2×C1912yescomplemented
202C2×#355C2×C1911yescharacteristic, complemented
203C22×C19—22no—
204C22×C19—44no—
205C22×C19—42no—
206C22×C19—42no—
207C22×C19—82no—
208C22×C19—82no—
209C22×C19—82no—
210C22×C19B(4,𝔽2)11yescharacteristic
211C22×C19B(4,𝔽2)11yescharacteristic
212C22×C19C2×#12011yescharacteristic
213C4×C19—21no—
214C4×C19—22no—
215C4×C19—21no—
216C4×C19—22no—
217C4×C19—42no—
218C4×C19—44no—
219C4×C19—44no—
220C4×C19—42no—
221C2×2−1+4C22×C1911yescharacteristic
222C2×#137—22no—
223C2×AGL(1,ℤ/8)—21no—
224#563—24no—
225#563—22no—
226#563C22×C1914yescomplemented
227C2×C4⋊Q8C22×C1912yes—
228C2×#126—22no—
229C2×#125—21no—
230C2×#124C22×C1911yescharacteristic
231C2×#123—21no—
232C2×C22⋊Q8—22no—
233#456—24no—
234#456C22×C1918yescomplemented
235#454—22no—
236#454C22×C1914yes—
237C2×#104—21no—
238C2×#104—22no—
239C2×#101C22×C1912yes—
240C2×#101C22×C1911yescharacteristic
241#356C22×C1918yescomplemented
242#355C22×C1914yescomplemented
243C2×C19—21no—
244C2×C19—21no—
245C2×C19—82no—
246C2×C19—82no—
247C2×C19#220312yesdirect product factor
248C2×C19C2×B(4,𝔽2)11yescharacteristic
2492−1+4—21no—
2502−1+4—22no—
2512−1+4—42no—
2522−1+4C23×C1912yes—
253C2×#41—21no—
254C2×#41—22no—
255C2×#41—41no—
256C22×Q8—41no—
257C22×Q8D4×C1912yes—
258C22×Q8C23×C1911yescharacteristic
259C22×D4D4×C1911yescharacteristic
260C23×C4—21no—
261#137—28no—
262#137—44no—
263AGL(1,ℤ/8)—24no—
264AGL(1,ℤ/8)—42no—
265C2×Q16—42no—
266C2×SD16—42no—
267C2×SD16—41no—
268C2×D8—41no—
269C2×M16—21no—
270C2×M16—22no—
271C4⋊Q8—22no—
272C4⋊Q8—22no—
273C4⋊Q8D4×C1914yes—
274C4⋊Q8C23×C1914yes—
275#126—28no—
276#126—28no—
277#125—24no—
278#125—24no—
279#124—22no—
280#124D4×C1912yes—
281#124C23×C1912yes—
282#123—24no—
283#123—24no—
284C22⋊Q8—28no—
285C22⋊Q8—28no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—22no—
294C2×C42D4×C1911yescharacteristic
295C2×C42D4×C1912yes—
296#104—24no—
297#104—28no—
298#101—21no—
299#101—22no—
300#101C23×C1914yes—
301#101C23×C1912yes—
302C19C2×#220311yescharacteristic, direct product factor, Sylow
303C24—21no—
304#41—22no—
305#41—24no—
306#41—22no—
307#41—24no—
308#41—41no—
309#41—42no—
310#41—42no—
311#41—42no—
312#41—44no—
313#41—42no—
314#41—41no—
315C2×Q8—22no—
316C2×Q8—21no—
317C2×Q8—22no—
318C2×Q8—41no—
319C2×Q8—41no—
320C2×Q8—42no—
321C2×Q8—42no—
322C2×Q8—42no—
323C2×Q8—42no—
324C2×Q8—44no—
325C2×Q8C2×D4×C1914yes—
326C2×Q8C2×D4×C1912yes—
327C2×Q8C2×D4×C1911yescharacteristic
328C2×Q8C24×C1911yescharacteristic
329C2×D4—21no—
330C2×D4—22no—
331C2×D4—21no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4C2×D4×C1912yes—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—24no—
340C22×C4—41no—
341C22×C4—42no—
342C22×C4—81no—
343C22×C4—81no—
344C22×C4C2×D4×C1912yes—
345C22×C4C2×D4×C1911yescharacteristic
346Q16—48no—
347SD16—48no—
348SD16—44no—
349D8—44no—
350M16—22no—
351M16—24no—
352M16—41no—
353M16—42no—
354C2×C8—41no—
355C2×C8—42no—
356C4⋊C4—24no—
357C4⋊C4—28no—
358C4⋊C4—24no—
359C4⋊C4—24no—
360C4⋊C4—24no—
361C4⋊C4—24no—
362C4⋊C4—24no—
363C22⋊C4—28no—
364C22⋊C4—24no—
365C22⋊C4—24no—
366C22⋊C4—24no—
367C42—21no—
368C42—22no—
369C42C2×D4×C1912yes—
370C42C2×D4×C1914yes—
371C23—22no—
372C23—44no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23C19×#12011yescharacteristic
377Q8—22no—
378Q8—24no—
379Q8—41no—
380Q8—42no—
381Q8—41no—
382Q8—44no—
383Q8—41no—
384Q8—42no—
385Q8—82no—
386D4—22no—
387D4—24no—
388D4—42no—
389D4—41no—
390D4—42no—
391D4—42no—
392D4—42no—
393D4—81no—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—42no—
402C2×C4—44no—
403C2×C4—42no—
404C2×C4—44no—
405C2×C4—42no—
406C2×C4—44no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—84no—
411C2×C4C19×#12012yes—
412C2×C4C19×#12011yescharacteristic
413C2×C4C22×D4×C1912yes—
414C2×C4C22×D4×C1911yescharacteristic
415C8—42no—
416C8—44no—
417C22—22no—
418C22—44no—
419C22—42no—
420C22—42no—
421C22—82no—
422C22—82no—
423C22—82no—
424C22C19×B(4,𝔽2)11yescharacteristic
425C22C19×B(4,𝔽2)11yescharacteristic
426C22C2×C19×#12011yescharacteristic
427C4—21no—
428C4—22no—
429C4—21no—
430C4—22no—
431C4—42no—
432C4—44no—
433C4—44no—
434C4—42no—
435C2—21no—
436C2—21no—
437C2—82no—
438C2—82no—
439C2C19×#220312yesdirect product factor
440C2C2×C19×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C19B(4,𝔽2)
commutator, Frattini, cosocleC2×Q8C24×C19
prime radicalC2×C19×#454C2
LCSG ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C19 ◁ C23×C19 ◁ C22×Q8×C19 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C19×#563C2semidirect
2. C2×C19×#456C2semidirect
4. C19×#2203C2direct (N × H)
5. C2×C19×#356C2semidirect
6. C2×C19×#355C2semidirect
12. C19×#563C22semidirect
20. C19×#456C22semidirect
27. C19×#356C22semidirect
28. C19×#355C22semidirect
150. C2×#2203C19direct (N × H)
197. C2×#563C2×C19semidirect
198. C2×#456C2×C19semidirect
200. #2203C2×C19direct (N × H)
201. C2×#356C2×C19semidirect
202. C2×#355C2×C19semidirect
226. #563C22×C19semidirect
234. #456C22×C19semidirect
241. #356C22×C19semidirect
242. #355C22×C19semidirect
247. C2×C19#2203direct (N × H)
302. C19C2×#2203direct (N × H)
439. C2C19×#2203direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C19×#5632
C2×C19×#4562
C2×C19×#4542
C19×#22032
C2×C19×#3562
C2×C19×#3552
C2×#220319