Finite Group Databasebeta

← #18083156

Subgroups — #18083156

Order 4864.

544 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 83 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#14574386C211yesmaximal, characteristic
2#14573575C212yesmaximal, complemented
3#14561994C212yesmaximal, complemented
4#14561512C211yesmaximal, characteristic, complemented
5C19×#1818C211yesmaximal, characteristic, complemented
6C2×#10597376C2212yes—
7#11926868—24no—
8#11926862—22no—
9#11926858—22no—
10#11926857—22no—
11#11926780—22no—
12#11926680—22no—
13#11926587—22no—
14#11926548—22no—
15#11926508C2212yes—
16#11926267—24no—
17C2×C19×#117C2211yescharacteristic
18C2×C19×C22⋊C8C2211yescharacteristic
19C2×C19×C22⋊C8C2211yescharacteristic
20C19×#336—22no—
21C23×C4×C19C2311yescharacteristic
22C22×C22⋊D19—22no—
23C22×D76D412yes—
24C22×C8×C19—21no—
25C22×C8×C19D412yes—
26C19×#117—22no—
27C19×#117—22no—
28C2×C4⋊C4×C19D411yescharacteristic
29C2×C4⋊C4×C19D411yescharacteristic
30C2×C22⋊C4×C19—21no—
31C2×C42×C19—21no—
32#10597376—22no—
33#10597376—22no—
34#10597376—22no—
35#10597376—22no—
36C2×(C2×D19)⋊C4—22no—
37C2×C4⋊Dic19D412yes—
38C2×#64520—22no—
39C2×D152—22no—
40C19×C22⋊C8—22no—
41C19×C22⋊C8—22no—
42C22⋊(C19⋊C8)—22no—
43C22⋊(C19⋊C8)D414yes—
44#10597278—24no—
45#10597275—22no—
46#10597266—24no—
47#10597266—24no—
48#10597265—24no—
49#10597264—24no—
50C24×C19#4111yescharacteristic
51C23×D19—22no—
52C22×C4×C19—21no—
53C22×C4×C19—21no—
54C22×C4×C19—42no—
55C22×C4×C19C2×D411yescharacteristic
56C22×C4×C19C2×D412yes—
57C22×C4×C19C2×D412yes—
58C22×C4×C19C2×D411yescharacteristic
59C2×C22⋊D19—42no—
60C2×C22⋊D19—42no—
61C2×C22⋊D19—84no—
62C22×Dic19—22no—
63C2×D76—22no—
64C2×D76—22no—
65C2×D76—44no—
66C2×C8×C19—22no—
67C2×C8×C19—42no—
68C2×C8×C19—42no—
69C2×C8×C19—41no—
70C4⋊C4×C19—22no—
71C4⋊C4×C19—22no—
72C22⋊C4×C19—42no—
73C42×C19—41no—
74C42×C19—41no—
75(C2×D19)⋊C4—42no—
76(C2×D19)⋊C4—42no—
77C4⋊Dic19—22no—
78C4⋊Dic19—22no—
79#64520—44no—
80C2×C19⋊C8—24no—
81D152—82no—
82#9977—191nomaximal, Sylow
83C23×C19—22no—
84C23×C19—41no—
85C23×C19—41no—
86C23×C19#12111yescharacteristic
87C23×C19#12112yes—
88C22×D19—42no—
89C22×D19—44no—
90C22×D19—82no—
91C22×D19—82no—
92C2×C4×C19—24no—
93C2×C4×C19—22no—
94C2×C4×C19—41no—
95C2×C4×C19—42no—
96C2×C4×C19—42no—
97C2×C4×C19—41no—
98C2×C4×C19—41no—
99C2×C4×C19—42no—
100C2×C4×C19#12011yescharacteristic
101C2×C4×C19#12012yes—
102C2×C4×C19#12711yescharacteristic
103C22⋊D19—84no—
104C22⋊D19—84no—
105C2×Dic19—42no—
106C2×Dic19—82no—
107D76—44no—
108D76—44no—
109C8×C19—42no—
110C8×C19—81no—
111C19⋊C8—44no—
112#3186—191no—
113#3094—192no—
114#1818D1911yescharacteristic, complemented
115#1471—192no—
116#1293—191no—
117C22×C19—21no—
118C22×C19—21no—
119C22×C19—22no—
120C22×C19—22no—
121C22×C19—22no—
122C22×C19—82no—
123C22×C19#39211yescharacteristic
124C22×C19#47212yes—
125C2×D19—82no—
126C2×D19—82no—
127C2×D19—82no—
128C2×D19—164no—
129C4×C19—22no—
130C4×C19—21no—
131C4×C19—81no—
132C4×C19—81no—
133C4×C19#45812yes—
134Dic19—82no—
135C2×#121—192no—
136C2×#117C2×D1911yescharacteristic
137#482—384no—
138#481—382no—
139#480—382no—
140#480—382no—
141#466—382no—
142#447—382no—
143#428—382no—
144#418—382no—
145#407—192no—
146C2×C22⋊C8C2×D1911yescharacteristic
147C2×C22⋊C8C2×D1911yescharacteristic
148#336—22no—
149#323—384no—
150C2×C19—22no—
151C2×C19—42no—
152C2×C19#201711yescharacteristic
153C2×C19#201811yescharacteristic
154C2×C19#202211yescharacteristic
155D19—162no—
156C22×D4—192no—
157C22×D4—382no—
158C23×C4C22×D1911yescharacteristic
159C2×D8—382no—
160C2×M16—382no—
161C22×C8—21no—
162C22×C8C22⋊D1912yes—
163#121—382no—
164#121—382no—
165#121—382no—
166#121—382no—
167#117—22no—
168#117—22no—
169C2×C4⋊C4—192no—
170C2×C4⋊C4D7611yescharacteristic
171C2×C4⋊C4D7611yescharacteristic
172C2×C22⋊C4—21no—
173C2×C22⋊C4—382no—
174C2×C42—21no—
175#107—384no—
176#107—382no—
177#106—384no—
178#102—384no—
179#102—384no—
180#102—384no—
181C22⋊C8—22no—
182C22⋊C8—22no—
183C22⋊C8—194no—
184C22⋊C8—382no—
185C19#997711yescharacteristic, complemented, Sylow
186C24—382no—
187C24#6454111yescharacteristic
188C2×D4—382no—
189C2×D4—382no—
190C2×D4—764no—
191C2×D4—762no—
192C2×D4—762no—
193C2×D4—1524no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—42no—
197C22×C4—382no—
198C22×C4C2×D7611yescharacteristic
199C22×C4D4×D1912yes—
200C22×C4D4×D1912yes—
201C22×C4C2×C22⋊D1911yescharacteristic
202D8—1522no—
203M16—764no—
204C2×C8—22no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—41no—
208C2×C8—384no—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—382no—
212C4⋊C4—382no—
213C22⋊C4—42no—
214C22⋊C4—762no—
215C22⋊C4—762no—
216C42—41no—
217C42—41no—
218C23—22no—
219C23—41no—
220C23—41no—
221C23—764no—
222C23—762no—
223C23—1522no—
224C23—1522no—
225C23#1059733012yes—
226C23#1059737611yescharacteristic
227D4—764no—
228D4—764no—
229D4—1524no—
230D4—1524no—
231C2×C4—22no—
232C2×C4—24no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—762no—
240C2×C4—1522no—
241C2×C4#1059732812yes—
242C2×C4#1059738311yescharacteristic
243C2×C4#1059738611yescharacteristic
244C8—42no—
245C8—81no—
246C8—764no—
247C22—21no—
248C22—21no—
249C22—22no—
250C22—22no—
251C22—22no—
252C22—82no—
253C22—3044no—
254C22—1522no—
255C22—1522no—
256C22—1522no—
257C22#1192645311yescharacteristic
258C22#1192681412yes—
259C4—21no—
260C4—22no—
261C4—81no—
262C4—81no—
263C4—1522no—
264C4#1192673312yes—
265C2—22no—
266C2—42no—
267C2—3042no—
268C2#1456473911yescharacteristic
269C2#1456474411yescharacteristic
270C2#1456476611yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1818C2
socleC22×C19#392
prime radical#14574386C2
hypercenter#1818D19
hypocenterC19#9977
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1818

Complements

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

NH ≅ G/Ntype
2. #14573575C2semidirect
3. #14561994C2semidirect
4. #14561512C2semidirect
5. C19×#1818C2semidirect
114. #1818D19semidirect
185. C19#9977semidirect

Maximal subgroups

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

subgroupindex
#145743862
#145735752
#145619942
#145615122
C19×#18182
#997719