Finite Group Databasebeta

← #18074667

Subgroups — #18074667

Order 4864.

1330 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 1330 conjugacy classes of subgroups — too many to draw. Only its 147 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#14563556C211yesmaximal, characteristic, complemented
2#14562139C214yesmaximal, complemented
3#14561876C211yesmaximal, characteristic, complemented
4C19×#3484C211yesmaximal, characteristic
5C22×C22⋊Dic19—22no—
6C2×#10597290—22no—
7#11926508C2212yescomplemented
8C2×C19⋊#95C2212yescomplemented
9#11926281—24no—
10#11926278—24no—
11C2×C19×H(5,𝔽2)C411yescharacteristic, complemented
12C23×D4×C19C2211yescharacteristic
13C19×#546—24no—
14D42×C19—24no—
15C19×#535C412yescomplemented
16C19×#534—22no—
17C19×#525C2212yes—
18C2×C19×#120—22no—
19C19×#518C411yescharacteristic, complemented
20C25×C19D412yes—
21C19×H(5,𝔽2)—44no—
22C2×#41×C19—22no—
23C2×#41×C19C2×C412yes—
24C22×D4×C19—22no—
25C22×D4×C19—24no—
26C22×D4×C19—22no—
27C22×D4×C19—24no—
28C22×D4×C19—44no—
29C22×D4×C19C2×C411yescharacteristic
30C22×D4×C19C2×C411yescharacteristic
31C22×D4×C19D412yes—
32C23×C4×C19C2311yescharacteristic
33C23×Dic19—22no—
34C19×#127—22no—
35C19×#124—22no—
36C19×#123—24no—
37C19×#123—22no—
38C19×C22⋊Q8D414yes—
39C19×#121—28no—
40C19×#121—24no—
41C19×#121D414yes—
42C19×#120—28no—
43C19×#120—24no—
44C19×#120—24no—
45C19×#120—22no—
46C4×D4×C19—24no—
47C4×D4×C19—24no—
48C19×#117C2×C412yes—
49C2×C22⋊C4×C19—24no—
50C2×C22⋊C4×C19—22no—
51C2×C22⋊Dic19—48no—
52C2×C22⋊Dic19—44no—
53C2×#64520—22no—
54#10597290—44no—
55C19⋊#95—24no—
56C22⋊(C19⋊C8)—24no—
57C24×C19—22no—
58C24×C19—24no—
59C24×C19—24no—
60C24×C19—42no—
61C24×C19—44no—
62C24×C19—44no—
63C24×C19C22⋊C412yes—
64C24×C19C22⋊C412yes—
65C24×C19C2×D411yescharacteristic
66#41×C19—44no—
67#41×C19—48no—
68C2×Q8×C19C22⋊C412yescomplemented
69C2×D4×C19—24no—
70C2×D4×C19—24no—
71C2×D4×C19—24no—
72C2×D4×C19—22no—
73C2×D4×C19—24no—
74C2×D4×C19—28no—
75C2×D4×C19—22no—
76C2×D4×C19—22no—
77C2×D4×C19—24no—
78C2×D4×C19—42no—
79C2×D4×C19—42no—
80C2×D4×C19—416no—
81C2×D4×C19—48no—
82C2×D4×C19—44no—
83C2×D4×C19—44no—
84C2×D4×C19—84no—
85C2×D4×C19—84no—
86C2×D4×C19C22⋊C412yescomplemented
87C22×C4×C19—22no—
88C22×C4×C19—24no—
89C22×C4×C19—22no—
90C22×C4×C19—42no—
91C22×C4×C19C22×C411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D414yes—
94C22×Dic19—24no—
95C22×Dic19—44no—
96C22×Dic19—44no—
97C22×Dic19—42no—
98C22×Dic19—42no—
99C4⋊C4×C19—24no—
100C4⋊C4×C19C22⋊C414yescomplemented
101C22⋊C4×C19—24no—
102C22⋊C4×C19—28no—
103C22⋊C4×C19—22no—
104C22⋊C4×C19—24no—
105C22⋊C4×C19—24no—
106C42×C19—22no—
107C22⋊Dic19—416no—
108#64520—44no—
109C2×C19⋊C8—42no—
110#8453—191nomaximal, Sylow
111C23×C19—22no—
112C23×C19—22no—
113C23×C19—22no—
114C23×C19—22no—
115C23×C19—22no—
116C23×C19—22no—
117C23×C19—22no—
118C23×C19—22no—
119C23×C19—22no—
120C23×C19—48no—
121C23×C19—44no—
122C23×C19—44no—
123C23×C19—44no—
124C23×C19—48no—
125C23×C19—44no—
126C23×C19—44no—
127C23×C19—44no—
128C23×C19—44no—
129C23×C19—84no—
130C23×C19—82no—
131C23×C19—84no—
132C23×C19—82no—
133C23×C19—84no—
134C23×C19#9914yes—
135C23×C19C2×C22⋊C411yescharacteristic
136C23×C19#12012yes—
137Q8×C19—42no—
138D4×C19—28no—
139D4×C19—48no—
140D4×C19—42no—
141D4×C19—44no—
142D4×C19—48no—
143D4×C19—44no—
144D4×C19—44no—
145D4×C19—44no—
146D4×C19—88no—
147C2×C4×C19—22no—
148C2×C4×C19—22no—
149C2×C4×C19—24no—
150C2×C4×C19—22no—
151C2×C4×C19—44no—
152C2×C4×C19—44no—
153C2×C4×C19—44no—
154C2×C4×C19—84no—
155C2×C4×C19C2×C22⋊C412yes—
156C2×C4×C19#12012yes—
157C2×Dic19—48no—
158C2×Dic19—44no—
159C2×Dic19—84no—
160C2×Dic19—82no—
161C2×Dic19—82no—
162C19⋊C8—82no—
163#3484D1911yescharacteristic
164#1783—191no—
165#1504—194no—
166#1438—191no—
167C22×C19—22no—
168C22×C19—24no—
169C22×C19—22no—
170C22×C19—22no—
171C22×C19—22no—
172C22×C19—22no—
173C22×C19—24no—
174C22×C19—44no—
175C22×C19—44no—
176C22×C19—44no—
177C22×C19—44no—
178C22×C19—44no—
179C22×C19—42no—
180C22×C19—42no—
181C22×C19—82no—
182C22×C19—88no—
183C22×C19—88no—
184C22×C19—82no—
185C22×C19—164no—
186C22×C19#37911yescharacteristic
187C22×C19C2×#9912yes—
188C22×C19#45312yes—
189C22×C19#45512yes—
190C4×C19—22no—
191C4×C19—22no—
192C4×C19—44no—
193C4×C19—42no—
194Dic19—84no—
195C2×H(5,𝔽2)Dic1911yescharacteristic, complemented
196C23×D4C2×D1911yescharacteristic
197#546—24no—
198D42—24no—
199#535Dic1912yescomplemented
200#534—22no—
201#525C2×D1912yes—
202C2×#120—22no—
203#518Dic1911yescharacteristic, complemented
204C22×C22⋊C4—382no—
205C2×#100—382no—
206#407—192no—
207C2×#95—192no—
208#328—384no—
209#327—384no—
210C2×C19—22no—
211C2×C19—22no—
212C2×C19—22no—
213C2×C19—44no—
214C2×C19—82no—
215C2×C19—82no—
216C2×C19#178111yescharacteristic
217C2×C19#179212yes—
218C25C22⋊D1912yes—
219H(5,𝔽2)—44no—
220C2×#41—22no—
221C2×#41C2×Dic1912yes—
222C22×D4—22no—
223C22×D4—24no—
224C22×D4—22no—
225C22×D4—24no—
226C22×D4—44no—
227C22×D4C2×Dic1911yescharacteristic
228C22×D4C2×Dic1911yescharacteristic
229C22×D4C22⋊D1912yes—
230C23×C4—382no—
231C23×C4C22×D1911yescharacteristic
232C2×M16—382no—
233#127—22no—
234#124—22no—
235#123—24no—
236#123—22no—
237C22⋊Q8C22⋊D1914yes—
238#121—28no—
239#121—24no—
240#121C22⋊D1914yes—
241#120—28no—
242#120—24no—
243#120—24no—
244#120—22no—
245C4×D4—24no—
246C4×D4—24no—
247#117C2×Dic1912yes—
248C2×C22⋊C4—24no—
249C2×C22⋊C4—22no—
250C2×C22⋊C4—768no—
251C2×C22⋊C4—764no—
252#100—764no—
253C22⋊C8—384no—
254#95—384no—
255C19#845311yescharacteristic, complemented, Sylow
256C24—22no—
257C24—24no—
258C24—24no—
259C24—42no—
260C24—44no—
261C24—44no—
262C24C22⋊Dic1912yes—
263C24C22⋊Dic1912yes—
264C24C2×C22⋊D1911yescharacteristic
265#41—44no—
266#41—48no—
267C2×Q8C22⋊Dic1912yescomplemented
268C2×D4—24no—
269C2×D4—24no—
270C2×D4—22no—
271C2×D4—24no—
272C2×D4—24no—
273C2×D4—28no—
274C2×D4—22no—
275C2×D4—22no—
276C2×D4—24no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4—416no—
280C2×D4—48no—
281C2×D4—44no—
282C2×D4—44no—
283C2×D4—84no—
284C2×D4—84no—
285C2×D4C22⋊Dic1912yescomplemented
286C22×C4—22no—
287C22×C4—24no—
288C22×C4—22no—
289C22×C4—42no—
290C22×C4—384no—
291C22×C4—764no—
292C22×C4—764no—
293C22×C4—762no—
294C22×C4—762no—
295C22×C4C22×Dic1911yescharacteristic
296C22×C4C2×C22⋊D1911yescharacteristic
297C22×C4C2×C22⋊D1914yes—
298M16—764no—
299C2×C8—762no—
300C4⋊C4—24no—
301C4⋊C4C22⋊Dic1914yescomplemented
302C22⋊C4—24no—
303C22⋊C4—28no—
304C22⋊C4—22no—
305C22⋊C4—24no—
306C22⋊C4—24no—
307C22⋊C4—7616no—
308C42—22no—
309C23—22no—
310C23—22no—
311C23—22no—
312C23—22no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—22no—
318C23—48no—
319C23—44no—
320C23—44no—
321C23—44no—
322C23—48no—
323C23—44no—
324C23—44no—
325C23—44no—
326C23—44no—
327C23—84no—
328C23—82no—
329C23—84no—
330C23—82no—
331C23—84no—
332C23#1059729114yes—
333C23C2×C22⋊Dic1911yescharacteristic
334C23#1059739912yes—
335Q8—42no—
336D4—28no—
337D4—48no—
338D4—42no—
339D4—44no—
340D4—48no—
341D4—44no—
342D4—44no—
343D4—44no—
344D4—88no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—24no—
348C2×C4—22no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—84no—
353C2×C4—768no—
354C2×C4—764no—
355C2×C4—1524no—
356C2×C4—1522no—
357C2×C4—1522no—
358C2×C4C2×C22⋊Dic1912yes—
359C2×C4#1059739912yes—
360C8—1522no—
361C22—22no—
362C22—24no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—24no—
368C22—44no—
369C22—44no—
370C22—44no—
371C22—44no—
372C22—44no—
373C22—42no—
374C22—42no—
375C22—82no—
376C22—88no—
377C22—88no—
378C22—82no—
379C22—164no—
380C22#1192640011yescharacteristic
381C22C2×#1059729112yes—
382C22#1192671212yes—
383C22#1192672212yes—
384C4—22no—
385C4—22no—
386C4—44no—
387C4—42no—
388C4—1524no—
389C2—22no—
390C2—22no—
391C2—22no—
392C2—44no—
393C2—82no—
394C2—82no—
395C2#1456355011yescharacteristic
396C2#1456358912yes—
subgroupG/H
centerC22#11926400
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#3484C2
socleC22×C19#379
cosocleC23×C4×C19C23
hypercenter#3484D19
hypocenterC19#8453
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3484

Complements

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

NH ≅ G/Ntype
1. #14563556C2semidirect
2. #14562139C2semidirect
3. #14561876C2semidirect
7. #11926508C22semidirect
8. C2×C19⋊#95C22semidirect
11. C2×C19×H(5,𝔽2)C4semidirect
15. C19×#535C4semidirect
19. C19×#518C4semidirect
68. C2×Q8×C19C22⋊C4semidirect
86. C2×D4×C19C22⋊C4semidirect
100. C4⋊C4×C19C22⋊C4semidirect
195. C2×H(5,𝔽2)Dic19semidirect
199. #535Dic19semidirect
203. #518Dic19semidirect
255. C19#8453semidirect
267. C2×Q8C22⋊Dic19semidirect
285. C2×D4C22⋊Dic19semidirect
301. C4⋊C4C22⋊Dic19semidirect

Maximal subgroups

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

subgroupindex
#145635562
#145621392
#145618762
C19×#34842
#845319