Finite Group Databasebeta

← #18071329

Subgroups — #18071329

Order 4864.

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

normal subgroups only

This group has 492 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#14570565C211yesmaximal, characteristic
2#14564960C212yesmaximal, complemented
3#14561459C212yesmaximal, complemented
4#14561456C211yesmaximal, characteristic
5C19×#2013C211yesmaximal, characteristic
6C2×#10597381—21no—
7C2×#10597264—22no—
8#11926474—21no—
9#11926469—22no—
10#11926442C2212yes—
11#11926419—22no—
12#11926306—22no—
13#11926299C2212yes—
14C22×SD16×C19—21no—
15C2×C19×C4⋊Q8C2211yescharacteristic
16C2×C19×#103—21no—
17C19×#390C2211yescharacteristic
18C19×#336C2211yescharacteristic
19C22×Q8×C19—21no—
20C22×D4×C19D411yescharacteristic
21C23×Dic19—21no—
22C2×SD16×C19—42no—
23C2×SD16×C19—42no—
24C2×SD16×C19—42no—
25C22×C8×C19—21no—
26C19×C4⋊Q8—42no—
27C2×C4⋊C4×C19—22no—
28C2×C4⋊C4×C19D411yescharacteristic
29C2×C22⋊C4×C19—22no—
30C2×C42×C19C2311yescharacteristic
31C2×C22⋊Dic19—22no—
32C2×C22⋊Dic19—21no—
33#10597381—42no—
34#10597381—42no—
35C2×C4⋊Dic19—21no—
36C2×C4⋊Dic19D412yes—
37C2×C4⋊Dic19D412yes—
38C2×Dic19⋊C4—22no—
39C22×C19⋊C8—22no—
40C19×#103—42no—
41C19⋊#95—22no—
42C19⋊#95—21no—
43C19⋊#95—22no—
44#10597264—44no—
45C24×C19—21no—
46C2×Q8×C19—22no—
47C2×Q8×C19—41no—
48C2×Q8×C19—41no—
49C2×Q8×C19—41no—
50C2×Q8×C19—41no—
51C2×Q8×C19—41no—
52C2×D4×C19—21no—
53C2×D4×C19—41no—
54C2×D4×C19—41no—
55C2×D4×C19D812yes—
56C22×C4×C19—21no—
57C22×C4×C19—41no—
58C22×C4×C19C2×D412yes—
59C22×C4×C19C2×D411yescharacteristic
60C22×Dic19—22no—
61C22×Dic19—22no—
62C22×Dic19—42no—
63C22×Dic19—81no—
64C22×Dic19—81no—
65SD16×C19—48no—
66C2×C8×C19—22no—
67C2×C8×C19—41no—
68C2×C8×C19—41no—
69C4⋊C4×C19—24no—
70C4⋊C4×C19—41no—
71C4⋊C4×C19—42no—
72C22⋊C4×C19—42no—
73C22⋊C4×C19—42no—
74C42×C19—41no—
75C22⋊Dic19—42no—
76C22⋊Dic19—44no—
77C4⋊Dic19—22no—
78C4⋊Dic19—22no—
79C4⋊Dic19—42no—
80C4⋊Dic19—81no—
81Dic19⋊C4—42no—
82Dic19⋊C4—42no—
83C2×C19⋊C8—24no—
84C2×C19⋊C8—42no—
85C2×C19⋊C8—42no—
86#7751—191nomaximal, Sylow
87C23×C19—22no—
88C23×C19—42no—
89C23×C19—41no—
90C23×C19—42no—
91C23×C19—41no—
92C23×C19#12011yescharacteristic
93Q8×C19—42no—
94Q8×C19—42no—
95Q8×C19—81no—
96Q8×C19—81no—
97D4×C19—42no—
98D4×C19—81no—
99C2×C4×C19—21no—
100C2×C4×C19—22no—
101C2×C4×C19—22no—
102C2×C4×C19—21no—
103C2×C4×C19—42no—
104C2×C4×C19—41no—
105C2×C4×C19—42no—
106C2×C4×C19—81no—
107C2×C4×C19—81no—
108C2×C4×C19C2×D811yescharacteristic
109C2×C4×C19#13512yes—
110C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
111C2×C4×C19#13712yes—
112C2×Dic19—42no—
113C2×Dic19—42no—
114C2×Dic19—42no—
115C2×Dic19—42no—
116C2×Dic19—42no—
117C2×Dic19—42no—
118C2×Dic19—84no—
119C8×C19—42no—
120C19⋊C8—44no—
121#2724—191no—
122#2057—192no—
123#2013D1911yescharacteristic
124#1271—192no—
125#1270—191no—
126C22×C19—42no—
127C22×C19—44no—
128C22×C19—82no—
129C22×C19—81no—
130C22×C19—81no—
131C22×C19#44711yescharacteristic
132C22×C19#45212yes—
133C22×C19#45311yescharacteristic
134C22×C19#45612yes—
135C22×C19B(4,𝔽2)11yescharacteristic
136C4×C19—21no—
137C4×C19—21no—
138C4×C19—22no—
139C4×C19—22no—
140C4×C19—82no—
141C4×C19—81no—
142Dic19—82no—
143Dic19—82no—
144C22×SD16—21no—
145C2×C4⋊Q8C2×D1911yescharacteristic
146C2×#123—381no—
147C2×#107—382no—
148C2×#103—21no—
149#398—381no—
150#397—382no—
151#390C2×D1911yescharacteristic
152#389—192no—
153#385—382no—
154#340—382no—
155#336—192no—
156#336C2×D1911yescharacteristic
157C2×C19—82no—
158C2×C19#159511yescharacteristic
159C2×C19#160312yes—
160C2×C19#163011yescharacteristic
161C2×C19#164712yes—
162C2×C19#166011yescharacteristic
163C22×Q8—21no—
164C22×D4C22⋊D1911yescharacteristic
165C23×C4—381no—
166C2×SD16—42no—
167C2×SD16—42no—
168C2×SD16—42no—
169C22×C8—21no—
170C22×C8—382no—
171C4⋊Q8—42no—
172#123—762no—
173#123—762no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—192no—
176C2×C4⋊C4—192no—
177C2×C4⋊C4—382no—
178C2×C4⋊C4—381no—
179C2×C4⋊C4C22⋊D1911yescharacteristic
180C2×C22⋊C4—22no—
181C2×C22⋊C4—382no—
182C2×C22⋊C4—381no—
183C2×C42C22×D1911yescharacteristic
184#107—764no—
185#103—42no—
186#95—382no—
187#95—381no—
188#95—382no—
189C19#775111yescharacteristic, complemented, Sylow
190C24—21no—
191C2×Q8—22no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8—41no—
195C2×Q8—41no—
196C2×Q8—41no—
197C2×D4—21no—
198C2×D4—41no—
199C2×D4—41no—
200C2×D4#6452512yes—
201C22×C4—21no—
202C22×C4—41no—
203C22×C4—382no—
204C22×C4—382no—
205C22×C4—762no—
206C22×C4—1521no—
207C22×C4—1521no—
208C22×C4D4×D1912yes—
209C22×C4C2×C22⋊D1911yescharacteristic
210SD16—48no—
211C2×C8—22no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—384no—
215C2×C8—762no—
216C2×C8—762no—
217C4⋊C4—24no—
218C4⋊C4—41no—
219C4⋊C4—42no—
220C4⋊C4—382no—
221C4⋊C4—382no—
222C4⋊C4—762no—
223C4⋊C4—762no—
224C4⋊C4—762no—
225C4⋊C4—1521no—
226C22⋊C4—42no—
227C22⋊C4—42no—
228C22⋊C4—762no—
229C22⋊C4—764no—
230C42—41no—
231C23—22no—
232C23—42no—
233C23—41no—
234C23—42no—
235C23—41no—
236C23#1059738311yescharacteristic
237Q8—42no—
238Q8—42no—
239Q8—81no—
240Q8—81no—
241D4—42no—
242D4—81no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—762no—
253C2×C4—762no—
254C2×C4—762no—
255C2×C4—762no—
256C2×C4—762no—
257C2×C4—762no—
258C2×C4—1524no—
259C2×C4#1059736112yes—
260C2×C4#1059736212yes—
261C2×C4C2×#6452511yescharacteristic
262C2×C4#1059739511yescharacteristic
263C8—42no—
264C8—764no—
265C22—44no—
266C22—42no—
267C22—82no—
268C22—81no—
269C22—81no—
270C22#1192667711yescharacteristic
271C22#1192670312yes—
272C22#1192671111yescharacteristic
273C22#1192672512yes—
274C22#1192673011yescharacteristic
275C4—22no—
276C4—22no—
277C4—21no—
278C4—21no—
279C4—81no—
280C4—82no—
281C4—1522no—
282C4—1522no—
283C2—82no—
284C2#1456255211yescharacteristic
285C2#1456259512yes—
286C2#1456275411yescharacteristic
287C2#1456286812yes—
288C2#1456294411yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2013C2
socleC23×C19#120
prime radicalC22×D4×C19D4
hypercenter#2013D19
hypocenterC19#7751
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2013

Complements

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

NH ≅ G/Ntype
2. #14564960C2semidirect
3. #14561459C2semidirect
189. C19#7751semidirect

Maximal subgroups

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

subgroupindex
#145705652
#145649602
#145614592
#145614562
C19×#20132
#775119