Finite Group Databasebeta

← #18077479

Subgroups — #18077479

Order 4864.

578 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 119 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#14566809C211yesmaximal, characteristic
2#14564609C212yesmaximal, complemented
3C2×#11926284C211yesmaximal, characteristic
4#14561517C212yesmaximal, complemented
5C2×C19×#497C211yesmaximal, characteristic
6C2×#10597260C2212yes—
7#11926451—21no—
8#11926437—22no—
9#11926424—21no—
10#11926419—22no—
11#11926410C2212yes—
12#11926306—22no—
13#11926306—22no—
14#11926284—22no—
15C22×Q16×C19—21no—
16C22×SD16×C19—21no—
17C2×C19×C4⋊Q8C2211yescharacteristic
18C2×C19×#124C2211yescharacteristic
19C19×#497—22no—
20C19×#497C414yescomplemented
21C2×C19×#97C2211yescharacteristic
22C22×Q8×C19—21no—
23C22×Q8×C19D411yescharacteristic
24C22×D4×C19D411yescharacteristic
25C23×Dic19—21no—
26C2×Q16×C19—24no—
27C2×Q16×C19—42no—
28C2×Q16×C19—42no—
29C2×SD16×C19—24no—
30C2×SD16×C19—42no—
31C2×SD16×C19—42no—
32C22×C8×C19—21no—
33C19×C4⋊Q8—21no—
34C19×C4⋊Q8—22no—
35C19×C4⋊Q8C2×C412yescomplemented
36C19×#124—22no—
37C19×#124C2×C412yes—
38C19×#124D412yes—
39C2×C4⋊C4×C19—22no—
40C2×C22⋊C4×C19—22no—
41C2×C42×C19C2311yescharacteristic
42C2×C22⋊Dic19—22no—
43C2×C22⋊Dic19—21no—
44C2×C4⋊Dic19—21no—
45C2×C4⋊Dic19D412yes—
46C2×C4⋊Dic19D412yes—
47C2×C4×Dic19—21no—
48C22×C19⋊C8—22no—
49C19×#97—21no—
50C19×#97C2×C412yescomplemented
51C19⋊#95—22no—
52C19⋊#95—22no—
53C19⋊#95—22no—
54#10597260—22no—
55#10597260—22no—
56C24×C19—21no—
57C2×Q8×C19—21no—
58C2×Q8×C19—22no—
59C2×Q8×C19—41no—
60C2×Q8×C19—41no—
61C2×Q8×C19—41no—
62C2×Q8×C19—41no—
63C2×Q8×C19—41no—
64C2×Q8×C19—41no—
65C2×Q8×C19—41no—
66C2×Q8×C19C22⋊C412yes—
67C2×D4×C19—21no—
68C2×D4×C19—41no—
69C2×D4×C19—41no—
70C2×D4×C19C22⋊C412yes—
71C22×C4×C19—21no—
72C22×C4×C19—41no—
73C22×C4×C19C2×D412yes—
74C22×C4×C19C2×D411yescharacteristic
75C22×Dic19—22no—
76C22×Dic19—22no—
77C22×Dic19—81no—
78C22×Dic19—82no—
79Q16×C19—48no—
80SD16×C19—48no—
81C2×C8×C19—22no—
82C2×C8×C19—22no—
83C2×C8×C19—22no—
84C4⋊C4×C19—24no—
85C4⋊C4×C19—42no—
86C22⋊C4×C19—24no—
87C22⋊C4×C19—24no—
88C42×C19C22×C411yescharacteristic
89C42×C19C2×D411yescharacteristic
90C42×C19#4112yes—
91C22⋊Dic19—81no—
92C22⋊Dic19—82no—
93C4⋊Dic19—42no—
94C4⋊Dic19—42no—
95C4⋊Dic19—81no—
96C4×Dic19—81no—
97C2×C19⋊C8—24no—
98C2×C19⋊C8—42no—
99C2×C19⋊C8—42no—
100#9003—191nomaximal, Sylow
101C23×C19—22no—
102C23×C19—41no—
103C23×C19—41no—
104C23×C19—42no—
105C23×C19—42no—
106C23×C19#12011yescharacteristic
107Q8×C19—42no—
108Q8×C19—42no—
109Q8×C19—42no—
110Q8×C19—81no—
111Q8×C19—81no—
112Q8×C19—81no—
113D4×C19—42no—
114D4×C19—81no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—22no—
118C2×C4×C19—22no—
119C2×C4×C19—22no—
120C2×C4×C19—41no—
121C2×C4×C19—41no—
122C2×C4×C19—42no—
123C2×C4×C19—81no—
124C2×C4×C19—81no—
125C2×C4×C19C2×C22⋊C411yescharacteristic
126C2×C4×C19C4×D412yes—
127C2×C4×C19#12112yes—
128C2×C4×C19#12311yescharacteristic
129C2×Dic19—42no—
130C2×Dic19—42no—
131C2×Dic19—42no—
132C2×Dic19—42no—
133C2×Dic19—42no—
134C2×Dic19—42no—
135C2×Dic19—84no—
136C8×C19—24no—
137C19⋊C8—44no—
138C2×#497D1911yescharacteristic
139#2379—191no—
140#1993—192no—
141C2×#329—191no—
142#1295—192no—
143C22×C19—44no—
144C22×C19—42no—
145C22×C19—81no—
146C22×C19—81no—
147C22×C19—82no—
148C22×C19#38611yescharacteristic
149C22×C19#45311yescharacteristic
150C22×C19#45311yescharacteristic
151C22×C19#45512yes—
152C22×C19#45612yes—
153C4×C19—22no—
154C4×C19—22no—
155C4×C19—21no—
156C4×C19—21no—
157C4×C19—42no—
158C4×C19—82no—
159Dic19—82no—
160Dic19—82no—
161C22×Q16—21no—
162C22×SD16—21no—
163C2×C4⋊Q8C2×D1911yescharacteristic
164C2×#124C2×D1911yescharacteristic
165#497—22no—
166#497Dic1914yescomplemented
167C2×#97—192no—
168C2×#97C2×D1911yescharacteristic
169#391—381no—
170#388—382no—
171#386—381no—
172#385—382no—
173#382—192no—
174#340—382no—
175#340—382no—
176#329—382no—
177C2×C19—82no—
178C2×C19#165911yescharacteristic
179C2×C19#166011yescharacteristic
180C2×C19#166112yes—
181C2×C19#188212yes—
182C2×C19#188711yescharacteristic
183C22×Q8—21no—
184C22×Q8C22⋊D1911yescharacteristic
185C22×D4C22⋊D1911yescharacteristic
186C23×C4—381no—
187C2×Q16—24no—
188C2×Q16—42no—
189C2×Q16—42no—
190C2×SD16—24no—
191C2×SD16—42no—
192C2×SD16—42no—
193C22×C8—21no—
194C22×C8—382no—
195C4⋊Q8—22no—
196C4⋊Q8—21no—
197C4⋊Q8C2×Dic1912yescomplemented
198#124—22no—
199#124C2×Dic1912yes—
200#124C22⋊D1912yes—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—192no—
203C2×C4⋊C4—192no—
204C2×C4⋊C4—381no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4—382no—
207C2×C22⋊C4—381no—
208C2×C42—381no—
209C2×C42C22×D1911yescharacteristic
210#97—21no—
211#97—382no—
212#97—382no—
213#97C2×Dic1912yescomplemented
214#95—382no—
215#95—382no—
216#95—382no—
217C19#900311yescharacteristic, complemented, Sylow
218C24—21no—
219C2×Q8—21no—
220C2×Q8—22no—
221C2×Q8—41no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8C22⋊Dic1912yes—
229C2×D4—21no—
230C2×D4—41no—
231C2×D4—41no—
232C2×D4C22⋊Dic1912yes—
233C22×C4—21no—
234C22×C4—41no—
235C22×C4—382no—
236C22×C4—382no—
237C22×C4—1521no—
238C22×C4—1522no—
239C22×C4D4×D1912yes—
240C22×C4C2×C22⋊D1911yescharacteristic
241Q16—48no—
242SD16—48no—
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—22no—
246C2×C8—384no—
247C2×C8—762no—
248C2×C8—762no—
249C4⋊C4—24no—
250C4⋊C4—42no—
251C4⋊C4—762no—
252C4⋊C4—762no—
253C4⋊C4—1521no—
254C22⋊C4—24no—
255C22⋊C4—24no—
256C22⋊C4—1521no—
257C22⋊C4—1522no—
258C42—1521no—
259C42#6454312yes—
260C42C22×Dic1911yescharacteristic
261C42C2×C22⋊D1911yescharacteristic
262C23—22no—
263C23—41no—
264C23—41no—
265C23—42no—
266C23—42no—
267C23#1059738311yescharacteristic
268Q8—42no—
269Q8—42no—
270Q8—42no—
271Q8—81no—
272Q8—81no—
273Q8—81no—
274D4—42no—
275D4—81no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—762no—
287C2×C4—762no—
288C2×C4—762no—
289C2×C4—762no—
290C2×C4—762no—
291C2×C4—762no—
292C2×C4—1524no—
293C2×C4D4×Dic1912yes—
294C2×C4#1059738111yescharacteristic
295C2×C4#1059738512yes—
296C2×C4C2×C22⋊Dic1911yescharacteristic
297C8—24no—
298C8—764no—
299C22—44no—
300C22—42no—
301C22—81no—
302C22—81no—
303C22—82no—
304C22#1192642411yescharacteristic
305C22#1192671111yescharacteristic
306C22#1192671111yescharacteristic
307C22#1192672012yes—
308C22#1192672512yes—
309C4—22no—
310C4—22no—
311C4—21no—
312C4—21no—
313C4—42no—
314C4—82no—
315C4—1522no—
316C4—1522no—
317C2—82no—
318C2#1456293911yescharacteristic
319C2#1456294411yescharacteristic
320C2#1456294912yes—
321C2#1456400612yes—
322C2#1456403411yescharacteristic
subgroupG/H
centerC23#10597383
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC2×C19×#497C2
socleC23×C19#120
prime radicalC22×D4×C19D4
cosocleC2×C42×C19C23
hypercenterC2×#497D19
hypocenterC19#9003
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
2. #14564609C2semidirect
4. #14561517C2semidirect
20. C19×#497C4semidirect
35. C19×C4⋊Q8C2×C4semidirect
50. C19×#97C2×C4semidirect
166. #497Dic19semidirect
197. C4⋊Q8C2×Dic19semidirect
213. #97C2×Dic19semidirect
217. C19#9003semidirect

Maximal subgroups

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

subgroupindex
#145668092
#145646092
C2×#119262842
#145615172
C2×C19×#4972
#900319