Finite Group Databasebeta

← #18075032

Subgroups — #18075032

Order 4864.

1168 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 139 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
1#14563563C211yesmaximal, characteristic, complemented
2#14563553C211yesmaximal, characteristic, complemented
3#14562164C214yesmaximal, complemented
4C2×C19×#535C211yesmaximal, characteristic
5C2×#10597293—21no—
6C2×#10597290—21no—
7C2×#10597291—21no—
8C2×#10597291—21no—
9#11926508C2212yescomplemented
10#11926407C2212yescomplemented
11#11926278—28no—
12C22×#41×C19C2211yescharacteristic
13C23×D4×C19C411yescharacteristic, complemented
14C19×#535—28no—
15C2×C19×#127—21no—
16C2×C19×#124—21no—
17C2×C19×#121C412yescomplemented
18C2×C19×#121C2212yes—
19C2×C19×#120—21no—
20C2×C19×#120—21no—
21C2×C19×#117C411yescharacteristic, complemented
22C25×C19—21no—
23C2×#41×C19—24no—
24C2×#41×C19—42no—
25C2×#41×C19—42no—
26C22×Q8×C19D411yescharacteristic
27C22×D4×C19—22no—
28C22×D4×C19—22no—
29C22×D4×C19—24no—
30C22×D4×C19—21no—
31C22×D4×C19—42no—
32C22×D4×C19—42no—
33C22×D4×C19C2×C412yes—
34C22×D4×C19D411yescharacteristic
35C22×D4×C19D411yescharacteristic
36C22×D4×C19D411yescharacteristic
37C23×C4×C19C2×C411yescharacteristic
38C23×C4×C19C2×C411yescharacteristic
39C23×C4×C19C2311yescharacteristic
40C19×#127—28no—
41C19×#124—28no—
42C19×#121—24no—
43C19×#121—24no—
44C19×#121—24no—
45C19×#121D418yes—
46C19×#120—28no—
47C19×#120—28no—
48C19×#117—24no—
49C2×C4⋊C4×C19C2×C412yes—
50C2×C22⋊C4×C19—21no—
51C2×C22⋊C4×C19—22no—
52C2×C22⋊C4×C19—22no—
53C2×C42×C19—21no—
54C2×C22⋊Dic19—22no—
55C2×#64520—22no—
56#10597293—42no—
57#10597291—42no—
58#10597291—42no—
59#10597290—42no—
60C19⋊#95—24no—
61C22⋊(C19⋊C8)—24no—
62C24×C19—24no—
63C24×C19—22no—
64C24×C19—42no—
65C24×C19—42no—
66C24×C19—84no—
67C24×C19C22⋊C411yescharacteristic
68C24×C19C22⋊C411yescharacteristic
69C24×C19C2×D411yescharacteristic
70#41×C19—416no—
71C2×Q8×C19—22no—
72C2×Q8×C19—22no—
73C2×Q8×C19—41no—
74C2×D4×C19—24no—
75C2×D4×C19—22no—
76C2×D4×C19—22no—
77C2×D4×C19—22no—
78C2×D4×C19—22no—
79C2×D4×C19—28no—
80C2×D4×C19—28no—
81C2×D4×C19—22no—
82C2×D4×C19—22no—
83C2×D4×C19—22no—
84C2×D4×C19—41no—
85C2×D4×C19—41no—
86C2×D4×C19—41no—
87C2×D4×C19—42no—
88C2×D4×C19—42no—
89C2×D4×C19—416no—
90C2×D4×C19—42no—
91C2×D4×C19—42no—
92C2×D4×C19—84no—
93C2×D4×C19—84no—
94C2×D4×C19C22⋊C414yes—
95C22×C4×C19—22no—
96C22×C4×C19—22no—
97C22×C4×C19—22no—
98C22×C4×C19—22no—
99C22×C4×C19—22no—
100C22×C4×C19—41no—
101C22×C4×C19—41no—
102C22×C4×C19—41no—
103C22×C4×C19—41no—
104C22×C4×C19C22⋊C411yescharacteristic
105C22×C4×C19C22⋊C411yescharacteristic
106C22×C4×C19C22×C411yescharacteristic
107C22×C4×C19C2×D411yescharacteristic
108C22×C4×C19C2×D414yes—
109C22×Dic19—42no—
110C4⋊C4×C19—22no—
111C4⋊C4×C19C22⋊C414yes—
112C22⋊C4×C19—24no—
113C22⋊C4×C19—28no—
114C22⋊C4×C19—28no—
115C42×C19—24no—
116C22⋊Dic19—42no—
117C22⋊Dic19—42no—
118#64520—42no—
119#64520—42no—
120C2×C19⋊C8—42no—
121#8516—191nomaximal, Sylow
122C23×C19—21no—
123C23×C19—21no—
124C23×C19—21no—
125C23×C19—21no—
126C23×C19—24no—
127C23×C19—21no—
128C23×C19—21no—
129C23×C19—21no—
130C23×C19—42no—
131C23×C19—42no—
132C23×C19—48no—
133C23×C19—44no—
134C23×C19—44no—
135C23×C19—42no—
136C23×C19—42no—
137C23×C19—42no—
138C23×C19—88no—
139C23×C19—88no—
140C23×C19—88no—
141C23×C19#9912yes—
142C23×C19C2×C22⋊C411yescharacteristic
143C23×C19#12012yes—
144Q8×C19—44no—
145D4×C19—44no—
146D4×C19—44no—
147D4×C19—44no—
148D4×C19—44no—
149D4×C19—48no—
150D4×C19—44no—
151D4×C19—88no—
152D4×C19—88no—
153C2×C4×C19—28no—
154C2×C4×C19—21no—
155C2×C4×C19—21no—
156C2×C4×C19—21no—
157C2×C4×C19—21no—
158C2×C4×C19—21no—
159C2×C4×C19—21no—
160C2×C4×C19—24no—
161C2×C4×C19—21no—
162C2×C4×C19—21no—
163C2×C4×C19—21no—
164C2×C4×C19—44no—
165C2×C4×C19—44no—
166C2×C4×C19—44no—
167C2×C4×C19#9912yes—
168C2×C4×C19C2×C22⋊C412yes—
169C2×C4×C19#12012yes—
170C2×Dic19—82no—
171C2×Dic19—84no—
172C19⋊C8—82no—
173C2×#535D1911yescharacteristic
174#1785—191no—
175#1782—191no—
176#1510—194no—
177C22×C19—22no—
178C22×C19—24no—
179C22×C19—22no—
180C22×C19—22no—
181C22×C19—42no—
182C22×C19—42no—
183C22×C19—42no—
184C22×C19—42no—
185C22×C19—44no—
186C22×C19—44no—
187C22×C19—41no—
188C22×C19—44no—
189C22×C19—81no—
190C22×C19—81no—
191C22×C19—81no—
192C22×C19—81no—
193C22×C19—84no—
194C22×C19—84no—
195C22×C19—816no—
196C22×C19#37911yescharacteristic
197C22×C19C2×#9911yescharacteristic
198C22×C19C2×#9911yescharacteristic
199C4×C19—22no—
200C4×C19—22no—
201C4×C19—22no—
202C4×C19—44no—
203C4×C19—41no—
204Dic19—162no—
205C22×#41C2×D1911yescharacteristic
206C23×D4Dic1911yescharacteristic, complemented
207#535—28no—
208C2×#127—21no—
209C2×#124—21no—
210C2×#121Dic1912yescomplemented
211C2×#121C2×D1912yes—
212C2×#120—21no—
213C2×#120—21no—
214C2×#117Dic1911yescharacteristic, complemented
215C2×#101—381no—
216C2×#100—381no—
217C2×#99—381no—
218C2×#99—381no—
219#407—192no—
220#381—192no—
221#327—388no—
222C2×C19—21no—
223C2×C19—21no—
224C2×C19—42no—
225C2×C19—42no—
226C2×C19—81no—
227C2×C19—84no—
228C2×C19#178111yescharacteristic
229C2×C19#179512yes—
230C25—21no—
231C2×#41—24no—
232C2×#41—42no—
233C2×#41—42no—
234C22×Q8C22⋊D1911yescharacteristic
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—24no—
238C22×D4—21no—
239C22×D4—42no—
240C22×D4—42no—
241C22×D4C2×Dic1912yes—
242C22×D4C22⋊D1911yescharacteristic
243C22×D4C22⋊D1911yescharacteristic
244C22×D4C22⋊D1911yescharacteristic
245C23×C4C2×Dic1911yescharacteristic
246C23×C4C2×Dic1911yescharacteristic
247C23×C4C22×D1911yescharacteristic
248C2×M16—382no—
249#127—28no—
250#124—28no—
251#121—24no—
252#121—24no—
253#121—24no—
254#121C22⋊D1918yes—
255#120—28no—
256#120—28no—
257#117—24no—
258C2×C4⋊C4C2×Dic1912yes—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—22no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—382no—
263C2×C42—21no—
264#101—762no—
265#100—762no—
266#99—762no—
267#99—762no—
268C22⋊C8—384no—
269#95—384no—
270C19#851611yescharacteristic, complemented, Sylow
271C24—24no—
272C24—22no—
273C24—42no—
274C24—42no—
275C24—84no—
276C24C22⋊Dic1911yescharacteristic
277C24C22⋊Dic1911yescharacteristic
278C24C2×C22⋊D1911yescharacteristic
279#41—416no—
280C2×Q8—22no—
281C2×Q8—22no—
282C2×Q8—41no—
283C2×D4—24no—
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—28no—
289C2×D4—28no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—42no—
297C2×D4—42no—
298C2×D4—416no—
299C2×D4—42no—
300C2×D4—42no—
301C2×D4—84no—
302C2×D4—84no—
303C2×D4C22⋊Dic1914yes—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—762no—
314C22×C4C22⋊Dic1911yescharacteristic
315C22×C4C22⋊Dic1911yescharacteristic
316C22×C4C22×Dic1911yescharacteristic
317C22×C4C2×C22⋊D1911yescharacteristic
318C22×C4C2×C22⋊D1914yes—
319M16—762no—
320M16—762no—
321C2×C8—762no—
322C4⋊C4—22no—
323C4⋊C4C22⋊Dic1914yes—
324C22⋊C4—24no—
325C22⋊C4—28no—
326C22⋊C4—28no—
327C22⋊C4—762no—
328C22⋊C4—762no—
329C42—24no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—24no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—42no—
339C23—42no—
340C23—48no—
341C23—44no—
342C23—44no—
343C23—42no—
344C23—42no—
345C23—42no—
346C23—88no—
347C23—88no—
348C23—88no—
349C23#1059729112yes—
350C23C2×C22⋊Dic1911yescharacteristic
351C23#1059739912yes—
352Q8—44no—
353D4—44no—
354D4—44no—
355D4—44no—
356D4—44no—
357D4—48no—
358D4—44no—
359D4—88no—
360D4—88no—
361C2×C4—28no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—24no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—44no—
373C2×C4—44no—
374C2×C4—44no—
375C2×C4—1522no—
376C2×C4—1524no—
377C2×C4#1059729112yes—
378C2×C4C2×C22⋊Dic1912yes—
379C2×C4#1059739912yes—
380C8—1522no—
381C22—22no—
382C22—24no—
383C22—22no—
384C22—22no—
385C22—42no—
386C22—42no—
387C22—42no—
388C22—42no—
389C22—44no—
390C22—44no—
391C22—41no—
392C22—44no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22—84no—
398C22—84no—
399C22—816no—
400C22#1192640011yescharacteristic
401C22C2×#1059729111yescharacteristic
402C22C2×#1059729111yescharacteristic
403C4—22no—
404C4—22no—
405C4—22no—
406C4—44no—
407C4—41no—
408C4—3042no—
409C2—21no—
410C2—21no—
411C2—42no—
412C2—42no—
413C2—84no—
414C2—81no—
415C2#1456355011yescharacteristic
416C2#1456360512yes—
subgroupG/H
centerC22#11926400
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC2×C19×#535C2
socleC22×C19#379
cosocleC23×C4×C19C23
hypercenterC2×#535D19
hypocenterC19#8516
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. #14563563C2semidirect
2. #14563553C2semidirect
3. #14562164C2semidirect
9. #11926508C22semidirect
10. #11926407C22semidirect
13. C23×D4×C19C4semidirect
17. C2×C19×#121C4semidirect
21. C2×C19×#117C4semidirect
206. C23×D4Dic19semidirect
210. C2×#121Dic19semidirect
214. C2×#117Dic19semidirect
270. C19#8516semidirect

Maximal subgroups

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

subgroupindex
#145635632
#145635532
#145621642
C2×C19×#5352
#851619