Finite Group Databasebeta

← #18071845

Subgroups — #18071845

Order 4864.

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

normal subgroups only

This group has 494 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#14570661C211yesmaximal, characteristic
2#14565173C211yesmaximal, characteristic, complemented
3#14565167C212yesmaximal, complemented
4#14561455C212yesmaximal, complemented
5C19×#1272C211yesmaximal, characteristic, complemented
6C2×#10597393—21no—
7C2×#10597264—21no—
8C2×#10597274—22no—
9C2×#10597292—21no—
10C2×#10597278—22no—
11#11926461—21no—
12#11926454—22no—
13#11926446C2212yes—
14#11926436—22no—
15#11926414C2211yescharacteristic
16#11926299C2211yescharacteristic
17C19×#391C2211yescharacteristic
18C19×#336C2212yes—
19C22×Q8×C19D411yescharacteristic
20C22×D76—21no—
21C22×D76—21no—
22C22×D76D412yes—
23C22×C8×C19—22no—
24C2×C4⋊C4×C19D411yescharacteristic
25C2×C42×C19C2311yescharacteristic
26#10597393—42no—
27#10597393—42no—
28C2×(C2×D19)⋊C4—22no—
29C2×(C2×D19)⋊C4—22no—
30C2×(C2×D19)⋊C4—22no—
31C2×(C2×D19)⋊C4—22no—
32C2×C4⋊Dic19—22no—
33C2×C4⋊Dic19—21no—
34C2×C4⋊Dic19D412yes—
35C2×C4×Dic19—21no—
36C22×C19⋊C8—21no—
37C19×#95—22no—
38#10597292—42no—
39C19⋊#95—21no—
40#10597278—44no—
41#10597274—44no—
42#10597264—42no—
43C23×D19—22no—
44C2×Q8×C19—21no—
45C2×Q8×C19—41no—
46C2×Q8×C19—41no—
47C2×Q8×C19SD1612yes—
48C22×C4×C19—21no—
49C22×C4×C19—21no—
50C22×C4×C19C2×D411yescharacteristic
51C22×C4×C19C2×D412yes—
52C22×Dic19—22no—
53C22×Dic19—41no—
54C2×D76—22no—
55C2×D76—22no—
56C2×D76—42no—
57C2×D76—42no—
58C2×D76—42no—
59C2×D76—81no—
60C2×D76—81no—
61C2×D76—82no—
62C2×D76—81no—
63C2×C8×C19—24no—
64C2×C8×C19—42no—
65C2×C8×C19—42no—
66C4⋊C4×C19—41no—
67C42×C19—41no—
68(C2×D19)⋊C4—44no—
69(C2×D19)⋊C4—42no—
70(C2×D19)⋊C4—42no—
71(C2×D19)⋊C4—42no—
72(C2×D19)⋊C4—42no—
73(C2×D19)⋊C4—82no—
74C4⋊Dic19—42no—
75C4⋊Dic19—41no—
76C4⋊Dic19—42no—
77C4⋊Dic19—42no—
78C4⋊Dic19—41no—
79C4×Dic19—42no—
80C2×C19⋊C8—22no—
81C2×C19⋊C8—41no—
82C2×C19⋊C8—41no—
83#7830—191nomaximal, Sylow
84C23×C19#12011yescharacteristic
85C22×D19—42no—
86C22×D19—42no—
87C22×D19—42no—
88C22×D19—42no—
89C22×D19—42no—
90C22×D19—42no—
91C22×D19—42no—
92Q8×C19—42no—
93Q8×C19—81no—
94C2×C4×C19—21no—
95C2×C4×C19—22no—
96C2×C4×C19—21no—
97C2×C4×C19—22no—
98C2×C4×C19—22no—
99C2×C4×C19—41no—
100C2×C4×C19—41no—
101C2×C4×C19—42no—
102C2×C4×C19—41no—
103C2×C4×C19C2×SD1611yescharacteristic
104C2×C4×C19#13512yes—
105C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
106C2×C4×C19#13712yes—
107C2×Dic19—42no—
108C2×Dic19—42no—
109C2×Dic19—42no—
110C2×Dic19—82no—
111C2×Dic19—81no—
112D76—44no—
113D76—82no—
114D76—84no—
115D76—84no—
116C8×C19—44no—
117C19⋊C8—42no—
118#2733—191no—
119#2095—191no—
120#2094—192no—
121#1272D1911yescharacteristic, complemented
122#1270—192no—
123C22×C19#45011yescharacteristic
124C22×C19#45212yes—
125C22×C19#45312yes—
126C22×C19#45311yescharacteristic
127C22×C19#45811yescharacteristic
128C2×D19—82no—
129C2×D19—82no—
130C2×D19—82no—
131C2×D19—82no—
132C2×D19—82no—
133C2×D19—82no—
134C2×D19—82no—
135C4×C19—21no—
136C4×C19—21no—
137C4×C19—22no—
138C4×C19—22no—
139C4×C19—42no—
140C4×C19—81no—
141Dic19—82no—
142Dic19—161no—
143C2×#124—381no—
144C2×#107—381no—
145C2×#106—382no—
146C2×#103—381no—
147C2×#102—382no—
148#394—381no—
149#392—382no—
150#391C2×D1911yescharacteristic
151#390—192no—
152#388—382no—
153#384—191no—
154#336—191no—
155#336C2×D1912yes—
156C2×C19#161311yescharacteristic
157C2×C19#161812yes—
158C2×C19#163112yes—
159C2×C19#163411yescharacteristic
160C2×C19#165511yescharacteristic
161D19—162no—
162C22×Q8D7611yescharacteristic
163C22×D4—192no—
164C22×D4—381no—
165C22×D4—381no—
166C22×C8—22no—
167C22×C8—381no—
168#124—762no—
169#124—762no—
170C2×C4⋊C4—192no—
171C2×C4⋊C4—381no—
172C2×C4⋊C4—382no—
173C2×C4⋊C4D7611yescharacteristic
174C2×C22⋊C4—382no—
175C2×C22⋊C4—382no—
176C2×C22⋊C4—382no—
177C2×C22⋊C4—382no—
178C2×C42—381no—
179C2×C42C22×D1911yescharacteristic
180#107—762no—
181#106—764no—
182#103—762no—
183#102—764no—
184#95—22no—
185#95—381no—
186C19#783011yescharacteristic, complemented, Sylow
187C24—382no—
188C2×Q8—21no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8#6451612yes—
192C2×D4—382no—
193C2×D4—382no—
194C2×D4—762no—
195C2×D4—762no—
196C2×D4—762no—
197C2×D4—1521no—
198C2×D4—1521no—
199C2×D4—1522no—
200C2×D4—1521no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—382no—
204C22×C4—761no—
205C22×C4C2×D7611yescharacteristic
206C22×C4D4×D1912yes—
207C2×C8—24no—
208C2×C8—42no—
209C2×C8—42no—
210C2×C8—382no—
211C2×C8—761no—
212C2×C8—761no—
213C4⋊C4—41no—
214C4⋊C4—762no—
215C4⋊C4—762no—
216C4⋊C4—761no—
217C4⋊C4—762no—
218C4⋊C4—761no—
219C22⋊C4—764no—
220C22⋊C4—762no—
221C22⋊C4—762no—
222C22⋊C4—762no—
223C22⋊C4—762no—
224C22⋊C4—1522no—
225C42—41no—
226C42—762no—
227C23—762no—
228C23—762no—
229C23—762no—
230C23—762no—
231C23—762no—
232C23—762no—
233C23—762no—
234C23#1059732811yescharacteristic
235Q8—42no—
236Q8—81no—
237D4—764no—
238D4—1522no—
239D4—1524no—
240D4—1524no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—762no—
251C2×C4—762no—
252C2×C4—762no—
253C2×C4—1522no—
254C2×C4—1521no—
255C2×C4C2×#6451611yescharacteristic
256C2×C4#1059735411yescharacteristic
257C2×C4#1059736212yes—
258C2×C4#1059736412yes—
259C8—44no—
260C8—762no—
261C22—1522no—
262C22—1522no—
263C22—1522no—
264C22—1522no—
265C22—1522no—
266C22—1522no—
267C22—1522no—
268C22#1192669711yescharacteristic
269C22#1192670912yes—
270C22#1192671312yes—
271C22#1192671411yescharacteristic
272C22#1192673511yescharacteristic
273C4—21no—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—42no—
278C4—81no—
279C4—3041no—
280C4—1522no—
281C2—3042no—
282C2#1456265711yescharacteristic
283C2#1456268612yes—
284C2#1456276412yes—
285C2#1456278111yescharacteristic
286C2#1456292511yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1272C2
socleC23×C19#120
prime radical#14570661C2
hypercenter#1272D19
hypocenterC19#7830
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #14565173C2semidirect
3. #14565167C2semidirect
4. #14561455C2semidirect
5. C19×#1272C2semidirect
121. #1272D19semidirect
186. C19#7830semidirect

Maximal subgroups

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

subgroupindex
#145706612
#145651732
#145651672
#145614552
C19×#12722
#783019