Finite Group Databasebeta

← C19×#62840 #18068799

Subgroups — C19×#62840 #18068799

Order 4864.

6608 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19×#3567C218yesmaximal, complemented
2C19×#3556C211yesmaximal, characteristic, complemented
3C19×#3548C213yesmaximal, complemented
4C19×#3539C2112yesmaximal, complemented
5C19×#3517C2112yesmaximal, complemented
6C19×#3515C2112yesmaximal, complemented
7C19×#3512C2112yesmaximal, complemented
8C19×#3444C213yesmaximal, complemented
9C19×#564C2214yescomplemented
10C19×#562C22112yescomplemented
11C19×#560C22116yes—
12C19×#557C22112yescomplemented
13C19×#554C22112yescomplemented
14C19×#553C22148yes—
15C19×#553C22124yes—
16C19×#553C22148yescomplemented
17C19×#552C22124yes—
18C19×#552C22148yescomplemented
19C19×#550C22124yes—
20C19×#550C22112yescomplemented
21C19×#547C22124yes—
22C19×#547C22112yescomplemented
23C19×#541C22112yes—
24C19×#541C22112yescomplemented
25C19×#540C22112yes—
26C19×#540C22148yes—
27C19×#540C22112yescomplemented
28C19×#539C22148yes—
29C19×#537C22124yes—
30C19×#533C2216yes—
31C19×#533C2213yes—
32C19×#532C2216yes—
33C19×#532C2213yes—
34C19×#532C22112yescomplemented
35C19×#529C22112yes—
36C19×#529C22112yes—
37C19×#529C22112yes—
38C19×#529C22124yescomplemented
39C2×C19×#125C22112yescomplemented
40C19×#525C2216yes—
41C19×#525C22112yes—
42C19×#520C22124yescomplemented
43C4×#41×C19C2216yes—
44C4×#41×C19C22112yes—
45C22×C42×C19C2211yescharacteristic
46C2×#41×C19C2316yes—
47C2×#41×C19C23112yes—
48C2×#41×C19C23124yes—
49C23×C4×C19C2313yes—
50C19×C4⋊Q8C2316yes—
51C19×C4⋊Q8C2313yes—
52C19×C4⋊Q8C23112yes—
53C19×#127C2313yes—
54C19×#127C23112yes—
55C19×#127C23116yes—
56C19×#126C23124yes—
57C19×#126C23148yes—
58C19×#126C23116yes—
59C19×#126C23116yes—
60C19×#125C23112yes—
61C19×#125C23148yes—
62C19×#125C23112yes—
63C19×#125C23112yes—
64C19×#125C2316yes—
65C19×#125C23148yes—
66C19×#124C23112yes—
67C19×#124C2316yes—
68C19×#123C23124yes—
69C19×#123C23112yes—
70C19×#123C23148yes—
71C19×#123C23148yes—
72C19×#123C23148yes—
73C19×C22⋊Q8C23112yes—
74C19×C22⋊Q8C23112yes—
75C19×C22⋊Q8C23112yes—
76C19×C22⋊Q8C23124yes—
77C19×C22⋊Q8C23148yes—
78C19×#121C23112yes—
79C19×#121C23112yes—
80C19×#121C23112yes—
81C19×#121C23124yes—
82C19×#121C23148yes—
83C19×#121C23148yes—
84C19×#121C23148yes—
85C19×#121C23148yes—
86C19×#120C23112yes—
87C4×Q8×C19C23112yes—
88C4×Q8×C19C23112yes—
89C4×Q8×C19C23112yes—
90C4×Q8×C19C23124yes—
91C4×D4×C19C23112yes—
92C4×D4×C19C23124yes—
93C4×D4×C19C23124yes—
94C4×D4×C19C23124yes—
95C4×D4×C19C23112yes—
96C4×D4×C19C23112yes—
97C4×D4×C19C23148yes—
98C4×D4×C19C23124yes—
99C4×D4×C19C23148yes—
100C19×#117C23112yes—
101C19×#117C2316yes—
102C19×#117C23112yes—
103C19×#117C23124yes—
104C19×#117C23148yes—
105C2×C4⋊C4×C19C23124yes—
106C2×C4⋊C4×C19C23148yes—
107C2×C42×C19C2313yes—
108C2×C42×C19C2316yes—
109C2×C42×C19C2312yes—
110C2×C42×C19C2311yescharacteristic
111C2×C42×C19C23112yes—
112C24×C19C2411yescharacteristic
113#41×C19—412no—
114#41×C19—424no—
115#41×C19—448no—
116C2×Q8×C19C24112yes—
117C2×Q8×C19C2416yes—
118C2×D4×C19C24112yes—
119C2×D4×C19C24112yes—
120C2×D4×C19C24124yes—
121C2×D4×C19C2416yes—
122C2×D4×C19C24148yes—
123C22×C4×C19—46no—
124C22×C4×C19C2416yes—
125C22×C4×C19C2413yes—
126C22×C4×C19C24112yes—
127C22×C4×C19C2413yes—
128C22×C4×C19C2416yes—
129C22×C4×C19C24124yes—
130C22×C4×C19C24148yes—
131C4⋊C4×C19C24124yes—
132C4⋊C4×C19C24112yes—
133C4⋊C4×C19C24124yes—
134C4⋊C4×C19C24112yes—
135C4⋊C4×C19C24148yes—
136C4⋊C4×C19C24148yes—
137C4⋊C4×C19C24124yes—
138C4⋊C4×C19C24112yes—
139C22⋊C4×C19C24124yes—
140C22⋊C4×C19C24124yes—
141C22⋊C4×C19C24112yes—
142C22⋊C4×C19C24124yes—
143C22⋊C4×C19C24148yes—
144C22⋊C4×C19C24124yes—
145C42×C19C2413yes—
146C42×C19C2413yes—
147C42×C19C2416yes—
148C42×C19C2413yes—
149C42×C19C2411yescharacteristic
150C42×C19C24124yes—
151C42×C19C24112yes—
152C42×C19C24116yes—
153#62840C1911yesmaximal, characteristic, direct product factor, Sylow
154C23×C19—43no—
155C23×C19C2511yescharacteristic
156C23×C19C2512yes—
157C23×C19C25112yes—
158Q8×C19—224no—
159Q8×C19—46no—
160D4×C19—224no—
161D4×C19—412no—
162D4×C19—46no—
163D4×C19—424no—
164D4×C19—448no—
165C2×C4×C19—212no—
166C2×C4×C19—26no—
167C2×C4×C19—224no—
168C2×C4×C19—43no—
169C2×C4×C19—46no—
170C2×C4×C19—424no—
171C2×C4×C19—448no—
172C2×C4×C19C2516yes—
173C2×C4×C19C2513yes—
174C2×C4×C19C25124yes—
175C2×C4×C19C25112yes—
176C2×C4×C19C2513yes—
177#3567C2×C1918yescomplemented
178#3556C2×C1911yescharacteristic, complemented
179#3548C2×C1913yescomplemented
180#3539C2×C19112yescomplemented
181#3517C2×C19112yescomplemented
182#3515C2×C19112yescomplemented
183#3512C2×C19112yescomplemented
184#3444C2×C1913yescomplemented
185C22×C19—26no—
186C22×C19—23no—
187C22×C19—212no—
188C22×C19—224no—
189C22×C19—44no—
190C22×C19C2611yescharacteristic
191C4×C19—26no—
192C4×C19—212no—
193C4×C19—23no—
194C4×C19—224no—
195C4×C19#58516yes—
196#564C22×C1914yescomplemented
197#562C22×C19112yescomplemented
198#560C22×C19116yes—
199#557C22×C19112yescomplemented
200#554C22×C19112yescomplemented
201#553C22×C19148yes—
202#553C22×C19124yes—
203#553C22×C19148yescomplemented
204#552C22×C19124yes—
205#552C22×C19148yescomplemented
206#550C22×C19124yes—
207#550C22×C19112yescomplemented
208#547C22×C19124yes—
209#547C22×C19112yescomplemented
210#541C22×C19112yes—
211#541C22×C19112yescomplemented
212#540C22×C19112yes—
213#540C22×C19148yes—
214#540C22×C19112yescomplemented
215#539C22×C19148yes—
216#537C22×C19124yes—
217#533C22×C1916yes—
218#533C22×C1913yes—
219#532C22×C1916yes—
220#532C22×C1913yes—
221#532C22×C19112yescomplemented
222#529C22×C19112yes—
223#529C22×C19112yes—
224#529C22×C19112yes—
225#529C22×C19124yescomplemented
226C2×#125C22×C19112yescomplemented
227#525C22×C1916yes—
228#525C22×C19112yes—
229#520C22×C19124yescomplemented
230C4×#41C22×C1916yes—
231C4×#41C22×C19112yes—
232C22×C42C22×C1911yescharacteristic
233C2×C19—412no—
234C2×C19—42no—
235C2×C19—41no—
236C2×C19C2×#58513yes—
237C2×#41C23×C1916yes—
238C2×#41C23×C19112yes—
239C2×#41C23×C19124yes—
240C23×C4C23×C1913yes—
241C4⋊Q8C23×C1916yes—
242C4⋊Q8C23×C1913yes—
243C4⋊Q8C23×C19112yes—
244#127C23×C1913yes—
245#127C23×C19112yes—
246#127C23×C19116yes—
247#126C23×C19124yes—
248#126C23×C19148yes—
249#126C23×C19116yes—
250#126C23×C19116yes—
251#125C23×C19112yes—
252#125C23×C19148yes—
253#125C23×C19112yes—
254#125C23×C19112yes—
255#125C23×C1916yes—
256#125C23×C19148yes—
257#124C23×C19112yes—
258#124C23×C1916yes—
259#123C23×C19124yes—
260#123C23×C19112yes—
261#123C23×C19148yes—
262#123C23×C19148yes—
263#123C23×C19148yes—
264C22⋊Q8C23×C19112yes—
265C22⋊Q8C23×C19112yes—
266C22⋊Q8C23×C19112yes—
267C22⋊Q8C23×C19124yes—
268C22⋊Q8C23×C19148yes—
269#121C23×C19112yes—
270#121C23×C19112yes—
271#121C23×C19112yes—
272#121C23×C19124yes—
273#121C23×C19148yes—
274#121C23×C19148yes—
275#121C23×C19148yes—
276#121C23×C19148yes—
277#120C23×C19112yes—
278C4×Q8C23×C19112yes—
279C4×Q8C23×C19112yes—
280C4×Q8C23×C19112yes—
281C4×Q8C23×C19124yes—
282C4×D4C23×C19112yes—
283C4×D4C23×C19124yes—
284C4×D4C23×C19124yes—
285C4×D4C23×C19124yes—
286C4×D4C23×C19112yes—
287C4×D4C23×C19112yes—
288C4×D4C23×C19148yes—
289C4×D4C23×C19124yes—
290C4×D4C23×C19148yes—
291#117C23×C19112yes—
292#117C23×C1916yes—
293#117C23×C19112yes—
294#117C23×C19124yes—
295#117C23×C19148yes—
296C2×C4⋊C4C23×C19124yes—
297C2×C4⋊C4C23×C19148yes—
298C2×C42C23×C19112yes—
299C2×C42C23×C1913yes—
300C2×C42C23×C1916yes—
301C2×C42C23×C1912yes—
302C2×C42C23×C1911yescharacteristic
303C19#6284011yescharacteristic, direct product factor, Sylow
304C24C24×C1911yescharacteristic
305#41—412no—
306#41—424no—
307#41—448no—
308C2×Q8C24×C19112yes—
309C2×Q8C24×C1916yes—
310C2×D4C24×C19112yes—
311C2×D4C24×C19112yes—
312C2×D4C24×C19124yes—
313C2×D4C24×C1916yes—
314C2×D4C24×C19148yes—
315C22×C4—46no—
316C22×C4C24×C1916yes—
317C22×C4C24×C1913yes—
318C22×C4C24×C19112yes—
319C22×C4C24×C1913yes—
320C22×C4C24×C1916yes—
321C22×C4C24×C19124yes—
322C22×C4C24×C19148yes—
323C4⋊C4C24×C19124yes—
324C4⋊C4C24×C19112yes—
325C4⋊C4C24×C19124yes—
326C4⋊C4C24×C19112yes—
327C4⋊C4C24×C19148yes—
328C4⋊C4C24×C19148yes—
329C4⋊C4C24×C19124yes—
330C4⋊C4C24×C19112yes—
331C22⋊C4C24×C19124yes—
332C22⋊C4C24×C19124yes—
333C22⋊C4C24×C19112yes—
334C22⋊C4C24×C19124yes—
335C22⋊C4C24×C19148yes—
336C22⋊C4C24×C19124yes—
337C42C24×C1913yes—
338C42C24×C1913yes—
339C42C24×C1916yes—
340C42C24×C1913yes—
341C42C24×C1911yescharacteristic
342C42C24×C19124yes—
343C42C24×C19112yes—
344C42C24×C19116yes—
345C23—43no—
346C23C25×C1911yescharacteristic
347C23C25×C1912yes—
348C23C25×C19112yes—
349Q8—224no—
350Q8—46no—
351D4—224no—
352D4—412no—
353D4—46no—
354D4—424no—
355D4—448no—
356C2×C4—212no—
357C2×C4—26no—
358C2×C4—224no—
359C2×C4—43no—
360C2×C4—46no—
361C2×C4—424no—
362C2×C4—448no—
363C2×C4C25×C1916yes—
364C2×C4C25×C1913yes—
365C2×C4C25×C19124yes—
366C2×C4C25×C19112yes—
367C2×C4C25×C1913yes—
368C22—26no—
369C22—23no—
370C22—212no—
371C22—224no—
372C22—44no—
373C22C26×C1911yescharacteristic
374C4—26no—
375C4—212no—
376C4—23no—
377C4—224no—
378C4C19×#58516yes—
379C2—42no—
380C2—41no—
381C2—412no—
382C2C2×C19×#58513yes—
subgroupG/H
center, socleC22×C19C26
commutator, Frattini, cosocleC22C26×C19
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C19 ◁ G

Complements

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

NH ≅ G/Ntype
1. C19×#3567C2semidirect
2. C19×#3556C2semidirect
3. C19×#3548C2semidirect
4. C19×#3539C2semidirect
5. C19×#3517C2semidirect
6. C19×#3515C2semidirect
7. C19×#3512C2semidirect
8. C19×#3444C2semidirect
9. C19×#564C22semidirect
10. C19×#562C22semidirect
12. C19×#557C22semidirect
13. C19×#554C22semidirect
16. C19×#553C22semidirect
18. C19×#552C22semidirect
20. C19×#550C22semidirect
22. C19×#547C22semidirect
24. C19×#541C22semidirect
27. C19×#540C22semidirect
34. C19×#532C22semidirect
38. C19×#529C22semidirect
39. C2×C19×#125C22semidirect
42. C19×#520C22semidirect
153. #62840C19direct (N × H)
177. #3567C2×C19semidirect
178. #3556C2×C19semidirect
179. #3548C2×C19semidirect
180. #3539C2×C19semidirect
181. #3517C2×C19semidirect
182. #3515C2×C19semidirect
183. #3512C2×C19semidirect
184. #3444C2×C19semidirect
196. #564C22×C19semidirect
197. #562C22×C19semidirect
199. #557C22×C19semidirect
200. #554C22×C19semidirect
203. #553C22×C19semidirect
205. #552C22×C19semidirect
207. #550C22×C19semidirect
209. #547C22×C19semidirect
211. #541C22×C19semidirect
214. #540C22×C19semidirect
221. #532C22×C19semidirect
225. #529C22×C19semidirect
226. C2×#125C22×C19semidirect
229. #520C22×C19semidirect
303. C19#62840direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#35672
C19×#35562
C19×#35482
C19×#35392
C19×#35172
C19×#35152
C19×#35122
C19×#34442
#6284019