Finite Group Databasebeta

← #18078290

Subgroups — #18078290

Order 4864.

1088 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 151 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×C4×C22⋊Dic19C211yesmaximal, characteristic, complemented
2#14563545C211yesmaximal, characteristic, complemented
3C2×#11926278C212yesmaximal, complemented
4#14561513C212yesmaximal, complemented
5C19×#2847C211yesmaximal, characteristic
6C22×C22⋊Dic19—21no—
7C22×C4×Dic19—21no—
8C2×C22⋊(C19⋊C8)—22no—
9C2×C22⋊(C19⋊C8)C2212yes—
10C4×C22⋊Dic19—24no—
11C2×C19⋊#95C2212yes—
12#11926278—24no—
13C24×C4×C19C2211yescharacteristic
14C2×C19×#121C412yescomplemented
15C2×C19×#121C2211yescharacteristic
16C2×C19×#120—21no—
17C19×#386—22no—
18C19×#386—21no—
19C19×#380C412yescomplemented
20C19×#380C2211yescharacteristic
21C25×C19D411yescharacteristic
22C22×D4×C19—22no—
23C22×D4×C19—21no—
24C22×D4×C19C2×C411yescharacteristic
25C23×C4×C19—22no—
26C23×C4×C19—22no—
27C23×C4×C19—44no—
28C23×C4×C19C2×C412yes—
29C23×C4×C19D411yescharacteristic
30C23×C4×C19D412yes—
31C23×C4×C19C2311yescharacteristic
32C23×Dic19—22no—
33C19×#121—22no—
34C19×#121—22no—
35C19×#121—44no—
36C19×#120—44no—
37C2×C4⋊C4×C19C2×C411yescharacteristic
38C2×C4⋊C4×C19C2×C412yes—
39C2×C22⋊C4×C19—22no—
40C2×C22⋊C4×C19—21no—
41C2×C22⋊C4×C19—22no—
42C2×C22⋊C4×C19—21no—
43C2×C22⋊Dic19—24no—
44C2×C22⋊Dic19—28no—
45C2×C4×Dic19—24no—
46C2×C4×Dic19—44no—
47C22×C19⋊C8—22no—
48C19×#95—22no—
49C19×#95—21no—
50C19⋊#95—22no—
51C19⋊#95D414yescomplemented
52C22⋊(C19⋊C8)—22no—
53C22⋊(C19⋊C8)—22no—
54C22⋊(C19⋊C8)—44no—
55C24×C19—24no—
56C24×C19—21no—
57C24×C19—21no—
58C24×C19—22no—
59C24×C19—22no—
60C24×C19—21no—
61C24×C19—42no—
62C24×C19C22⋊C412yes—
63C24×C19C2×D411yescharacteristic
64C2×D4×C19—22no—
65C2×D4×C19—42no—
66C2×D4×C19—44no—
67C2×D4×C19—44no—
68C2×D4×C19—44no—
69C2×D4×C19—41no—
70C2×D4×C19—41no—
71C2×D4×C19—42no—
72C2×D4×C19—42no—
73C22×C4×C19—21no—
74C22×C4×C19—21no—
75C22×C4×C19—24no—
76C22×C4×C19—24no—
77C22×C4×C19—24no—
78C22×C4×C19—24no—
79C22×C4×C19—24no—
80C22×C4×C19—21no—
81C22×C4×C19—22no—
82C22×C4×C19—42no—
83C22×C4×C19—42no—
84C22×C4×C19—42no—
85C22×C4×C19—48no—
86C22×C4×C19—48no—
87C22×C4×C19C22⋊C412yes—
88C22×C4×C19C22×C411yescharacteristic
89C22×C4×C19C2×D412yes—
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19#4112yes—
92C22×Dic19—28no—
93C22×Dic19—24no—
94C22×Dic19—44no—
95C22×Dic19—42no—
96C22×Dic19—42no—
97C4⋊C4×C19—22no—
98C4⋊C4×C19—42no—
99C22⋊C4×C19—44no—
100C22⋊C4×C19—42no—
101C22⋊C4×C19—44no—
102C22⋊C4×C19—42no—
103C22⋊Dic19—216no—
104C4×Dic19—48no—
105C2×C19⋊C8—44no—
106C2×C19⋊C8—42no—
107#9150—191nomaximal, Sylow
108C23×C19—22no—
109C23×C19—22no—
110C23×C19—24no—
111C23×C19—24no—
112C23×C19—22no—
113C23×C19—22no—
114C23×C19—22no—
115C23×C19—22no—
116C23×C19—22no—
117C23×C19—22no—
118C23×C19—48no—
119C23×C19—48no—
120C23×C19—42no—
121C23×C19—42no—
122C23×C19—42no—
123C23×C19—42no—
124C23×C19—41no—
125C23×C19—42no—
126C23×C19—41no—
127C23×C19—41no—
128C23×C19—42no—
129C23×C19#10414yes—
130C23×C19C2×C22⋊C411yescharacteristic
131C23×C19#12011yescharacteristic
132C23×C19#12311yescharacteristic
133C23×C19#13512yes—
134C23×C19AGL(1,ℤ/8)12yes—
135D4×C19—82no—
136D4×C19—88no—
137D4×C19—82no—
138D4×C19—82no—
139C2×C4×C19—24no—
140C2×C4×C19—24no—
141C2×C4×C19—22no—
142C2×C4×C19—22no—
143C2×C4×C19—22no—
144C2×C4×C19—22no—
145C2×C4×C19—42no—
146C2×C4×C19—42no—
147C2×C4×C19—48no—
148C2×C4×C19—48no—
149C2×C4×C19—41no—
150C2×C4×C19—42no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—42no—
154C2×C4×C19—42no—
155C2×C4×C19#9914yes—
156C2×C4×C19C4×D412yes—
157C2×C4×C19#12112yes—
158C2×Dic19—28no—
159C2×Dic19—44no—
160C2×Dic19—48no—
161C2×Dic19—48no—
162C2×Dic19—44no—
163C19⋊C8—82no—
164#2847D1911yescharacteristic
165C2×C4×C22⋊C4—191no—
166#1779—191no—
167C2×#327—192no—
168#1294—192no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19—21no—
173C22×C19—24no—
174C22×C19—24no—
175C22×C19—24no—
176C22×C19—24no—
177C22×C19—24no—
178C22×C19—48no—
179C22×C19—48no—
180C22×C19—42no—
181C22×C19—42no—
182C22×C19—42no—
183C22×C19—42no—
184C22×C19—81no—
185C22×C19—81no—
186C22×C19—81no—
187C22×C19—82no—
188C22×C19—82no—
189C22×C19#38611yescharacteristic
190C22×C19C2×#9912yes—
191C22×C19#41611yescharacteristic
192C22×C19#41811yescharacteristic
193C22×C19C2×#10412yes—
194C22×C19#44912yes—
195C22×C19#48212yes—
196C4×C19—22no—
197C4×C19—24no—
198C4×C19—22no—
199C4×C19—81no—
200C4×C19—82no—
201Dic19—48no—
202C24×C4C2×D1911yescharacteristic
203C2×#121Dic1912yescomplemented
204C2×#121C2×D1911yescharacteristic
205C2×#120—21no—
206C22×C22⋊C4—381no—
207C22×C42—381no—
208C2×C22⋊C8—192no—
209C2×C22⋊C8—382no—
210#386—21no—
211#386—22no—
212#380Dic1912yescomplemented
213#380C2×D1911yescharacteristic
214C4×C22⋊C4—384no—
215C2×#95—192no—
216#327—384no—
217C2×C19—22no—
218C2×C19—22no—
219C2×C19—44no—
220C2×C19—161no—
221C2×C19#150112yes—
222C2×C19#150712yes—
223C2×C19#187511yescharacteristic
224C2×C19#189611yescharacteristic
225C2×C19#189811yescharacteristic
226C25C22⋊D1911yescharacteristic
227C22×D4—22no—
228C22×D4—21no—
229C22×D4C2×Dic1911yescharacteristic
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—44no—
233C23×C4—382no—
234C23×C4C2×Dic1912yes—
235C23×C4C22⋊D1911yescharacteristic
236C23×C4C22⋊D1912yes—
237C23×C4C22×D1911yescharacteristic
238C22×C8—382no—
239#121—22no—
240#121—22no—
241#121—44no—
242#120—44no—
243C2×C4⋊C4C2×Dic1911yescharacteristic
244C2×C4⋊C4C2×Dic1912yes—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—388no—
250C2×C22⋊C4—384no—
251C2×C42—384no—
252C2×C42—764no—
253C22⋊C8—382no—
254C22⋊C8—382no—
255C22⋊C8—764no—
256#95—22no—
257#95—21no—
258#95—194no—
259#95—382no—
260C19#915011yescharacteristic, complemented, Sylow
261C24—21no—
262C24—21no—
263C24—24no—
264C24—22no—
265C24—22no—
266C24—21no—
267C24—42no—
268C24C22⋊Dic1912yes—
269C24C2×C22⋊D1911yescharacteristic
270C2×D4—22no—
271C2×D4—42no—
272C2×D4—44no—
273C2×D4—44no—
274C2×D4—42no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—42no—
278C2×D4—44no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—24no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—48no—
292C22×C4—48no—
293C22×C4—388no—
294C22×C4—384no—
295C22×C4—764no—
296C22×C4—762no—
297C22×C4—762no—
298C22×C4C22⋊Dic1912yes—
299C22×C4D4×D1912yes—
300C22×C4#6454312yes—
301C22×C4C22×Dic1911yescharacteristic
302C22×C4C2×C22⋊D1911yescharacteristic
303C2×C8—764no—
304C2×C8—762no—
305C4⋊C4—22no—
306C4⋊C4—42no—
307C22⋊C4—44no—
308C22⋊C4—42no—
309C22⋊C4—42no—
310C22⋊C4—44no—
311C22⋊C4—3816no—
312C42—768no—
313C23—22no—
314C23—22no—
315C23—24no—
316C23—24no—
317C23—22no—
318C23—22no—
319C23—22no—
320C23—22no—
321C23—22no—
322C23—22no—
323C23—48no—
324C23—48no—
325C23—42no—
326C23—42no—
327C23—42no—
328C23—42no—
329C23—41no—
330C23—41no—
331C23—42no—
332C23—41no—
333C23—42no—
334C23#1059729414yes—
335C23#1059737812yes—
336C23#1059738111yescharacteristic
337C23#1059738311yescharacteristic
338C23#1059739612yes—
339C23C2×C22⋊Dic1911yescharacteristic
340D4—82no—
341D4—88no—
342D4—82no—
343D4—82no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—48no—
353C2×C4—48no—
354C2×C4—41no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—388no—
361C2×C4—764no—
362C2×C4—768no—
363C2×C4—768no—
364C2×C4—764no—
365C2×C4#1059729114yes—
366C2×C4D4×Dic1912yes—
367C2×C4#1059738512yes—
368C8—1522no—
369C22—24no—
370C22—24no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—24no—
376C22—24no—
377C22—24no—
378C22—48no—
379C22—48no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—82no—
385C22—82no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22#1192642411yescharacteristic
390C22C2×#1059729112yes—
391C22#1192654011yescharacteristic
392C22#1192654911yescharacteristic
393C22C2×#1059729412yes—
394C22#1192668712yes—
395C22#1192686512yes—
396C4—22no—
397C4—24no—
398C4—22no—
399C4—82no—
400C4—81no—
401C4—768no—
402C2—22no—
403C2—22no—
404C2—44no—
405C2—161no—
406C2#1456212612yes—
407C2#1456215112yes—
408C2#1456395811yescharacteristic
409C2#1456407911yescharacteristic
410C2#1456408911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic19
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
Fitting, prime radicalC19×#2847C2
socleC23×C19C2×C22⋊C4
cosocleC23×C4×C19C23
hypercenter#2847D19
hypocenterC19#9150
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. C2×C4×C22⋊Dic19C2semidirect
2. #14563545C2semidirect
3. C2×#11926278C2semidirect
4. #14561513C2semidirect
14. C2×C19×#121C4semidirect
19. C19×#380C4semidirect
51. C19⋊#95D4semidirect
203. C2×#121Dic19semidirect
212. #380Dic19semidirect
260. C19#9150semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊Dic192
#145635452
C2×#119262782
#145615132
C19×#28472
#915019