Finite Group Databasebeta

← #18080413

Subgroups — #18080413

Order 4864.

522 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 115 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#14568540C211yesmaximal, characteristic
2#14563631C211yesmaximal, characteristic, complemented
3#14562061C212yesmaximal
4#14561494C212yesmaximal, complemented
5C19×#2983C211yesmaximal, characteristic, complemented
6C2×#10597392—21no—
7C2×C4×D76C2211yescharacteristic
8#11926568C2212yes—
9C2×#10597293—21no—
10#11926474C412yes—
11#11926461C412yes—
12#11926435—22no—
13#11926410C2211yescharacteristic
14#11926401—21no—
15#11926313—21no—
16#11926273—24no—
17C2×C4×Q8×C19C2211yescharacteristic
18C19×#446—24no—
19C19×#432—22no—
20C19×#431C2212yes—
21C22×Q8×C19D411yescharacteristic
22C22×D76C2×C411yescharacteristic
23C22×C4×D19—21no—
24C4×Q8×C19—22no—
25C4×Q8×C19—22no—
26C2×C4⋊C4×C19C2×C412yes—
27C2×C4⋊C4×C19D411yescharacteristic
28C2×C42×C19D412yes—
29C2×C42×C19C2311yescharacteristic
30#10597392—44no—
31C2×(C2×D19)⋊C4—22no—
32C2×(C2×D19)⋊C4—22no—
33C2×(C2×D19)⋊C4—21no—
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19C2×C411yescharacteristic
36C2×Dic19⋊C4—22no—
37C2×#64520—22no—
38C4×D76—22no—
39C4×D76—22no—
40C19×C4⋊C8—24no—
41C19×C4⋊C8—22no—
42C19×C22⋊C8—22no—
43C19×#97—24no—
44C4×C8×C19D414yes—
45#10597293—42no—
46C19⋊#95—22no—
47C19⋊#95—21no—
48C19⋊#95C2×C412yes—
49C4⋊(C19⋊C8)—22no—
50C4⋊(C19⋊C8)—22no—
51C23×D19—21no—
52C2×Q8×C19—22no—
53C2×Q8×C19—22no—
54C2×Q8×C19—21no—
55C2×Q8×C19—21no—
56C22×C4×C19C22⋊C412yes—
57C22×C4×C19C22⋊C412yes—
58C22×C4×C19C22×C411yescharacteristic
59C22×C4×C19C2×D411yescharacteristic
60C22×C4×C19C2×D411yescharacteristic
61C22×Dic19—21no—
62C22×Dic19—22no—
63C2×D76—22no—
64C2×D76—42no—
65C2×C4×D19—42no—
66C2×C4×D19—42no—
67C2×C4×D19—41no—
68C2×C4×D19—41no—
69C2×C8×C19—24no—
70C4⋊C4×C19—24no—
71C4⋊C4×C19—22no—
72C42×C19—22no—
73C42×C19—22no—
74C42×C19C2×D412yes—
75C42×C19#4112yes—
76(C2×D19)⋊C4—44no—
77(C2×D19)⋊C4—44no—
78(C2×D19)⋊C4—41no—
79(C2×D19)⋊C4—41no—
80C4⋊Dic19—22no—
81C4⋊Dic19—42no—
82Dic19⋊C4—44no—
83#64520—42no—
84#64520—42no—
85C2×C19⋊C8—42no—
86#9490—191nomaximal, Sylow
87C23×C19C2×C22⋊C411yescharacteristic
88C22×D19—22no—
89C22×D19—41no—
90C22×D19—41no—
91C22×D19—41no—
92C22×D19—41no—
93C22×D19—41no—
94C22×D19—41no—
95Q8×C19—42no—
96Q8×C19—42no—
97C2×C4×C19—22no—
98C2×C4×C19—22no—
99C2×C4×C19—22no—
100C2×C4×C19—22no—
101C2×C4×C19—41no—
102C2×C4×C19—41no—
103C2×C4×C19—42no—
104C2×C4×C19C4×D412yes—
105C2×C4×C19#12011yescharacteristic
106C2×C4×C19#12112yes—
107C2×C4×C19#12311yescharacteristic
108C2×C4×C19AGL(1,ℤ/8)12yes—
109C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
110C2×C4×C19#13711yescharacteristic
111C2×Dic19—42no—
112C2×Dic19—42no—
113C2×Dic19—41no—
114C2×Dic19—41no—
115C2×Dic19—41no—
116C2×Dic19—42no—
117D76—24no—
118D76—42no—
119C4×D19—82no—
120C4×D19—82no—
121C8×C19—44no—
122C19⋊C8—82no—
123#2983D1911yescharacteristic, complemented
124#2536—191no—
125#1801—191no—
126#1486—192no—
127#1286—192no—
128C22×C19—21no—
129C22×C19—21no—
130C22×C19#38611yescharacteristic
131C22×C19#41711yescharacteristic
132C22×C19#41811yescharacteristic
133C2×D19—42no—
134C2×D19—42no—
135C2×D19—42no—
136C2×D19—81no—
137C2×D19—81no—
138C2×D19—81no—
139C2×D19—81no—
140C4×C19—22no—
141C4×C19—21no—
142C4×C19—21no—
143C4×C19—42no—
144C4×C19—42no—
145C4×C19#46812yes—
146C4×C19#46912yes—
147Dic19—82no—
148Dic19—81no—
149C2×C22⋊Q8—381no—
150C2×C4×Q8C2×D1911yescharacteristic
151C2×C4×D4—191no—
152#446—24no—
153#432—22no—
154#431C2×D1912yes—
155#423—192no—
156C2×#101—381no—
157#398—192no—
158#394—192no—
159#388—382no—
160#382—191no—
161#380—381no—
162#343—381no—
163D4⋊C8—384no—
164C2×C19—21no—
165C2×C19—21no—
166C2×C19#189111yescharacteristic
167C2×C19#189511yescharacteristic
168C2×C19#191211yescharacteristic
169D19—82no—
170C22×Q8D7611yescharacteristic
171C22×D4—191no—
172C23×C4—381no—
173C2×M16—382no—
174C22⋊Q8—764no—
175C4×Q8—22no—
176C4×Q8—22no—
177C4×D4—382no—
178C4×D4—382no—
179C2×C4⋊C4—191no—
180C2×C4⋊C4—382no—
181C2×C4⋊C4—381no—
182C2×C4⋊C4C4×D1912yes—
183C2×C4⋊C4D7611yescharacteristic
184C2×C22⋊C4—382no—
185C2×C22⋊C4—382no—
186C2×C22⋊C4—381no—
187C2×C42C22⋊D1912yes—
188C2×C42C22×D1911yescharacteristic
189C4⋊C8—24no—
190C4⋊C8—22no—
191C4⋊C8—382no—
192C4⋊C8—382no—
193#101—762no—
194C22⋊C8—22no—
195#97—24no—
196C4×C8C22⋊D1914yes—
197#95—192no—
198#95—382no—
199#95—381no—
200C19#949011yescharacteristic, complemented, Sylow
201C24—381no—
202C2×Q8—22no—
203C2×Q8—21no—
204C2×Q8—22no—
205C2×Q8—21no—
206C2×D4—382no—
207C2×D4—762no—
208C22×C4—382no—
209C22×C4—381no—
210C22×C4—762no—
211C22×C4—762no—
212C22×C4—761no—
213C22×C4—761no—
214C22×C4(C2×D19)⋊C412yes—
215C22×C4(C2×D19)⋊C412yes—
216C22×C4C2×C4×D1911yescharacteristic
217C22×C4C2×D7611yescharacteristic
218C22×C4C2×C22⋊D1911yescharacteristic
219M16—762no—
220M16—762no—
221C2×C8—24no—
222C2×C8—762no—
223C4⋊C4—22no—
224C4⋊C4—24no—
225C4⋊C4—382no—
226C4⋊C4—764no—
227C4⋊C4—762no—
228C22⋊C4—764no—
229C22⋊C4—764no—
230C22⋊C4—761no—
231C22⋊C4—761no—
232C42—22no—
233C42—22no—
234C42#6454112yes—
235C42C2×C22⋊D1912yes—
236C23—382no—
237C23—761no—
238C23—761no—
239C23—761no—
240C23—761no—
241C23—761no—
242C23—761no—
243C23C2×(C2×D19)⋊C411yescharacteristic
244Q8—42no—
245Q8—42no—
246D4—384no—
247D4—762no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—762no—
256C2×C4—762no—
257C2×C4—761no—
258C2×C4—762no—
259C2×C4—761no—
260C2×C4—761no—
261C2×C4—1522no—
262C2×C4—1522no—
263C2×C4#1059735412yes—
264C2×C4#1059735411yescharacteristic
265C2×C4#1059735511yescharacteristic
266C2×C4C4×C22⋊D1912yes—
267C2×C4#1059737511yescharacteristic
268C2×C4#1059737612yes—
269C2×C4#1059739911yescharacteristic
270C8—44no—
271C8—1522no—
272C22—21no—
273C22—21no—
274C22—762no—
275C22—762no—
276C22—762no—
277C22—1521no—
278C22—1521no—
279C22—1521no—
280C22—1521no—
281C22#1192642311yescharacteristic
282C22#1192654611yescharacteristic
283C22#1192655011yescharacteristic
284C4—21no—
285C4—21no—
286C4—22no—
287C4—42no—
288C4—42no—
289C4—1522no—
290C4—1521no—
291C4#1192679012yes—
292C4#1192679712yes—
293C2—21no—
294C2—21no—
295C2—1522no—
296C2#1456405311yescharacteristic
297C2#1456407311yescharacteristic
298C2#1456417211yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2983C2
socleC22×C19#386
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenter#2983D19
hypocenterC19#9490
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
2. #14563631C2semidirect
4. #14561494C2semidirect
5. C19×#2983C2semidirect
123. #2983D19semidirect
200. C19#9490semidirect

Maximal subgroups

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

subgroupindex
#145685402
#145636312
#145620612
#145614942
C19×#29832
#949019