Finite Group Databasebeta

← #18069902

Subgroups — #18069902

Order 4864.

342 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 43 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#14563593C211yesmaximal, characteristic
2#14561569C211yesmaximal, characteristic, complemented
3C19×#1272C211yesmaximal, characteristic, complemented
4C2×#10597433C411yescharacteristic
5C2×#10597262—21no—
6#11926543—21no—
7C2×#10597293C411yescharacteristic
8#11926270—21no—
9C19×#391C2211yescharacteristic
10C19×#336—21no—
11C22×Q8×C19C2×C411yescharacteristic
12#10597433—21no—
13#10597433—42no—
14#10597433—41no—
15#10597433C812yescomplemented
16C2×#64545—41no—
17C2×Q8×D19—41no—
18C2×#64541—21no—
19C2×#64541—41no—
20C22×C8×C19—41no—
21C2×C4⋊C4×C19D411yescharacteristic
22C2×C42×C19D411yescharacteristic
23C2×#64520—21no—
24C19×#95—41no—
25#10597293—41no—
26C22⋊(C19⋊C8)—41no—
27#10597267—41no—
28#10597266—41no—
29#10597262—42no—
30C2×Q8×C19—21no—
31C2×Q8×C19—41no—
32C2×Q8×C19—41no—
33C2×Q8×C19C2×C811yescharacteristic
34C2×Q8×C19M1611yescharacteristic
35C22×C4×C19—21no—
36C22×C4×C19—21no—
37C22×C4×C19—21no—
38C22×C4×C19C22⋊C411yescharacteristic
39C2×C22⋊D19—41no—
40#64545—42no—
41#64545—42no—
42#64545—44no—
43Q8×D19—42no—
44Q8×D19—42no—
45Q8×D19—44no—
46#64541—22no—
47#64541—22no—
48#64541—41no—
49#64541—42no—
50#64541—42no—
51#64541—41no—
52#64541—42no—
53#64541—42no—
54C2×D76—21no—
55C2×D76—41no—
56C2×C4×D19—41no—
57C2×C4×D19—42no—
58C2×Dic38—21no—
59C2×Dic38—41no—
60C2×C8×C19—42no—
61C2×C8×C19—81no—
62C2×C8×C19—81no—
63C4⋊C4×C19—41no—
64C42×C19—41no—
65#64520—41no—
66#64520—41no—
67C2×C19⋊C8—41no—
68C2×C19⋊C8—81no—
69#7345—191nomaximal, Sylow
70C23×C19#9911yescharacteristic
71C22×D19—41no—
72Q8×C19—41no—
73Q8×C19—41no—
74Q8×C19—42no—
75C2×C4×C19—21no—
76C2×C4×C19—21no—
77C2×C4×C19—21no—
78C2×C4×C19—21no—
79C2×C4×C19—21no—
80C2×C4×C19—21no—
81C2×C4×C19—41no—
82C2×C4×C19—41no—
83C2×C4×C19—41no—
84C2×C4×C19—41no—
85C2×C4×C19—41no—
86C2×C4×C19—81no—
87C2×C4×C19C22⋊C811yescharacteristic
88C2×C4×C19#10011yescharacteristic
89C22⋊D19—42no—
90C22⋊D19—42no—
91C2×Dic19—41no—
92D76—22no—
93D76—41no—
94D76—42no—
95D76—42no—
96C4×D19—42no—
97C4×D19—42no—
98C4×D19—44no—
99C4×D19—44no—
100Dic38—22no—
101Dic38—41no—
102Dic38—42no—
103Dic38—42no—
104C8×C19—82no—
105C19⋊C8—81no—
106C19⋊C8—161no—
107#1793—191no—
108#1319—191no—
109#1272D1911yescharacteristic, complemented
110C22×C19—21no—
111C22×C19—21no—
112C22×C19#32311yescharacteristic
113C22×C19AΣL(1,𝔽16)11yescharacteristic
114C22×C19AΣL(1,𝔽16)11yescharacteristic
115C2×D19—42no—
116C2×D19—81no—
117C2×D19—81no—
118C4×C19—21no—
119C4×C19—21no—
120C4×C19—41no—
121C4×C19—41no—
122C4×C19—41no—
123C4×C19—41no—
124C4×C19—81no—
125Dic19—42no—
126C2×2−1+4—191no—
127C2×#104—381no—
128#417—381no—
129C2×#101—191no—
130#391C2×D1911yescharacteristic
131#336—21no—
132#324—381no—
133C2×C19—21no—
134C2×C19—21no—
135C2×C19#131611yescharacteristic
136C2×C19#140411yescharacteristic
137C2×C19#140511yescharacteristic
138D19—82no—
1392−1+4—192no—
1402−1+4—381no—
1412−1+4—761no—
1422−1+4—762no—
143C2×#41—381no—
144C2×#41—761no—
145C2×#41—761no—
146C22×Q8—761no—
147C22×Q8C4×D1911yescharacteristic
148C2×M16—381no—
149C22×C8—41no—
150C2×C4⋊C4D7611yescharacteristic
151C2×C42C22⋊D1911yescharacteristic
152#104—762no—
153#103—761no—
154#102—761no—
155#101—761no—
156C22⋊C8—761no—
157#95—41no—
158C19#734511yescharacteristic, complemented, Sylow
159#41—382no—
160#41—382no—
161#41—761no—
162#41—762no—
163#41—762no—
164#41—762no—
165#41—762no—
166#41—762no—
167#41—762no—
168#41—764no—
169#41—761no—
170C2×Q8—21no—
171C2×Q8—41no—
172C2×Q8—41no—
173C2×Q8—381no—
174C2×Q8—761no—
175C2×Q8—762no—
176C2×Q8—762no—
177C2×Q8—764no—
178C2×Q8C8×D1911yescharacteristic
179C2×Q8#6451511yescharacteristic
180C2×D4—381no—
181C2×D4—761no—
182C2×D4—761no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—761no—
187C22×C4—762no—
188C22×C4(C2×D19)⋊C411yescharacteristic
189M16—761no—
190M16—761no—
191C2×C8—42no—
192C2×C8—81no—
193C2×C8—81no—
194C2×C8—761no—
195C2×C8—1521no—
196C4⋊C4—41no—
197C42—41no—
198C23—761no—
199C23#1059726311yescharacteristic
200Q8—41no—
201Q8—41no—
202Q8—42no—
203Q8—382no—
204Q8—761no—
205Q8—762no—
206Q8—762no—
207D4—382no—
208D4—761no—
209D4—762no—
210D4—762no—
211D4—762no—
212D4—762no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—81no—
225C2×C4—762no—
226C2×C4—762no—
227C2×C4—764no—
228C2×C4—764no—
229C2×C4—761no—
230C2×C4(C2×D19)⋊C811yescharacteristic
231C2×C4#1059728011yescharacteristic
232C8—82no—
233C8—3041no—
234C8—1521no—
235C22—21no—
236C22—21no—
237C22—762no—
238C22—1521no—
239C22—1521no—
240C22#1192626711yescharacteristic
241C22#1192633011yescharacteristic
242C22#1192633211yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—81no—
250C4—762no—
251C2—21no—
252C2—21no—
253C2—1522no—
254C2#1456156211yescharacteristic
255C2#1456178711yescharacteristic
256C2#1456179011yescharacteristic
subgroupG/H
centerC22#11926332
commutatorC2×Q8×C19C2×C8
Frattini#391C2×D19
FittingC19×#1272C2
socleC22×C19AΣL(1,𝔽16)
prime radicalC2×#10597433C4
cosocleC19×#391C22
hypercenter#1272D19
hypocenterC19#7345
LCSG ▷ C2×Q8×C19 ▷ C2×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #14561569C2semidirect
3. C19×#1272C2semidirect
15. #10597433C8semidirect
109. #1272D19semidirect
158. C19#7345semidirect

Maximal subgroups

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

subgroupindex
#145635932
#145615692
C19×#12722
#734519