Finite Group Databasebeta

← #18071350

Subgroups — #18071350

Order 4864.

536 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 95 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#14564968C212yesmaximal, complemented
2#14564717C211yesmaximal, characteristic
3#14561458C212yesmaximal, complemented
4#14561456C211yesmaximal, characteristic
5C19×#2683C211yesmaximal, characteristic
6C22×#64526—21no—
7C2×#10597315C2211yescharacteristic
8C2×#10597265—22no—
9C2×#10597267—21no—
10#11926306—22no—
11#11926299C2212yes—
12#11926299C2211yescharacteristic
13C2×C19×C22⋊Q8—22no—
14C19×#396—22no—
15C19×#395—21no—
16C19×#390C2211yescharacteristic
17C19×#389C2212yes—
18C19×#386—21no—
19C22×Q8×C19—21no—
20C22×D4×C19D411yescharacteristic
21C23×C4×C19—21no—
22C22×Dic38—21no—
23C19×C22⋊Q8—44no—
24C19×C22⋊Q8—44no—
25C2×C4⋊C4×C19—22no—
26C2×C4⋊C4×C19—22no—
27C2×C4⋊C4×C19D412yes—
28C2×C4⋊C4×C19D411yescharacteristic
29C2×C4⋊C4×C19D412yes—
30C2×C22⋊C4×C19—22no—
31C2×C22⋊C4×C19—22no—
32C2×C22⋊C4×C19—21no—
33C2×C42×C19C2311yescharacteristic
34C2×#64526—42no—
35C2×#64526—42no—
36C2×#64526—42no—
37C2×C4⋊Dic19—22no—
38C22×C19⋊C8—21no—
39C22×C19⋊C8—22no—
40#10597315—42no—
41C19×#95—21no—
42C19×#95—22no—
43#10597267—42no—
44#10597265—44no—
45C24×C19—21no—
46C2×Q8×C19—44no—
47C2×Q8×C19—81no—
48C2×D4×C19—21no—
49C2×D4×C19—41no—
50C2×D4×C19—41no—
51C2×D4×C19SD1612yes—
52C22×C4×C19—22no—
53C22×C4×C19—21no—
54C22×C4×C19—22no—
55C22×C4×C19—44no—
56C22×C4×C19—81no—
57C22×C4×C19C2×D412yes—
58C22×C4×C19C2×D411yescharacteristic
59C22×Dic19—41no—
60C2×Dic38—22no—
61C2×Dic38—41no—
62C2×Dic38—41no—
63C2×Dic38—41no—
64C2×Dic38—41no—
65C2×Dic38—41no—
66C4⋊C4×C19—22no—
67C4⋊C4×C19—42no—
68C4⋊C4×C19—41no—
69C4⋊C4×C19—44no—
70C4⋊C4×C19—42no—
71C4⋊C4×C19—42no—
72C4⋊C4×C19SD1614yescomplemented
73C22⋊C4×C19—44no—
74C22⋊C4×C19—42no—
75C22⋊C4×C19—42no—
76C22⋊C4×C19—81no—
77C42×C19—41no—
78#64526—48no—
79C4⋊Dic19—24no—
80C4⋊Dic19—42no—
81C2×C19⋊C8—22no—
82C2×C19⋊C8—24no—
83C2×C19⋊C8—41no—
84C2×C19⋊C8—42no—
85C2×C19⋊C8—41no—
86C2×C19⋊C8—42no—
87#7754—191nomaximal, Sylow
88C23×C19—22no—
89C23×C19—42no—
90C23×C19—41no—
91C23×C19—42no—
92C23×C19—41no—
93C23×C19#12011yescharacteristic
94Q8×C19—84no—
95D4×C19—42no—
96D4×C19—81no—
97C2×C4×C19—21no—
98C2×C4×C19—22no—
99C2×C4×C19—22no—
100C2×C4×C19—21no—
101C2×C4×C19—24no—
102C2×C4×C19—42no—
103C2×C4×C19—42no—
104C2×C4×C19—42no—
105C2×C4×C19—42no—
106C2×C4×C19—41no—
107C2×C4×C19—42no—
108C2×C4×C19—42no—
109C2×C4×C19—84no—
110C2×C4×C19C2×SD1612yes—
111C2×C4×C19C2×SD1611yescharacteristic
112C2×C4×C19AGL(1,ℤ/8)12yes—
113C2×C4×C19#13711yescharacteristic
114C2×Dic19—42no—
115C2×Dic19—81no—
116C2×Dic19—81no—
117Dic38—42no—
118Dic38—42no—
119Dic38—81no—
120Dic38—81no—
121C19⋊C8—44no—
122C19⋊C8—42no—
123#2683D1911yescharacteristic
124#2058—192no—
125#2013—191no—
126#1271—192no—
127#1270—191no—
128C22×C19—42no—
129C22×C19—44no—
130C22×C19—82no—
131C22×C19—81no—
132C22×C19—81no—
133C22×C19#44811yescharacteristic
134C22×C19#45012yes—
135C22×C19#45311yescharacteristic
136C22×C19#45612yes—
137C22×C19B(4,𝔽2)11yescharacteristic
138C4×C19—21no—
139C4×C19—21no—
140C4×C19—22no—
141C4×C19—22no—
142C4×C19—44no—
143C4×C19—82no—
144C4×C19—81no—
145Dic19—82no—
146C22×SD16—381no—
147C2×C4⋊Q8—191no—
148C2×C22⋊Q8—22no—
149C2×#106—382no—
150C2×#103—381no—
151#396—22no—
152#395—21no—
153#390C2×D1911yescharacteristic
154#389C2×D1912yes—
155#386—21no—
156#340—382no—
157#336—192no—
158#336—191no—
159C2×C19—82no—
160C2×C19#159611yescharacteristic
161C2×C19#160412yes—
162C2×C19#162911yescharacteristic
163C2×C19#165112yes—
164C2×C19#166011yescharacteristic
165C22×Q8—21no—
166C22×Q8—381no—
167C22×D4C22⋊D1911yescharacteristic
168C23×C4—21no—
169C2×SD16—762no—
170C2×SD16—762no—
171C2×SD16—762no—
172C22×C8—381no—
173C22×C8—382no—
174C4⋊Q8—762no—
175C22⋊Q8—44no—
176C22⋊Q8—44no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—382no—
180C2×C4⋊C4C22⋊D1912yes—
181C2×C4⋊C4C22⋊D1912yes—
182C2×C4⋊C4C22⋊D1911yescharacteristic
183C2×C22⋊C4—22no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—21no—
186C2×C42C22×D1911yescharacteristic
187#106—764no—
188#103—762no—
189#95—21no—
190#95—22no—
191C19#775411yescharacteristic, complemented, Sylow
192C24—21no—
193C2×Q8—44no—
194C2×Q8—81no—
195C2×Q8—382no—
196C2×Q8—761no—
197C2×Q8—761no—
198C2×Q8—761no—
199C2×Q8—761no—
200C2×Q8—761no—
201C2×D4—21no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4#6452712yes—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—44no—
209C22×C4—81no—
210C22×C4—761no—
211C22×C4C2×C22⋊D1912yes—
212C22×C4C2×C22⋊D1911yescharacteristic
213SD16—768no—
214C2×C8—382no—
215C2×C8—384no—
216C2×C8—762no—
217C2×C8—761no—
218C2×C8—762no—
219C2×C8—761no—
220C4⋊C4—22no—
221C4⋊C4—41no—
222C4⋊C4—42no—
223C4⋊C4—44no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—384no—
227C4⋊C4—762no—
228C4⋊C4#6452614yescomplemented
229C22⋊C4—44no—
230C22⋊C4—42no—
231C22⋊C4—42no—
232C22⋊C4—81no—
233C42—41no—
234C23—22no—
235C23—42no—
236C23—41no—
237C23—42no—
238C23—41no—
239C23#1059739911yescharacteristic
240Q8—84no—
241Q8—762no—
242Q8—762no—
243Q8—1521no—
244Q8—1521no—
245D4—42no—
246D4—81no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—24no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—84no—
260C2×C4—762no—
261C2×C4—1521no—
262C2×C4—1521no—
263C2×C4#1059737812yes—
264C2×C4C2×#6452612yes—
265C2×C4C2×#6452711yescharacteristic
266C2×C4#1059738811yescharacteristic
267C8—762no—
268C8—764no—
269C22—44no—
270C22—42no—
271C22—82no—
272C22—81no—
273C22—81no—
274C22#1192668311yescharacteristic
275C22#1192669512yes—
276C22#1192671211yescharacteristic
277C22#1192672712yes—
278C22#1192673111yescharacteristic
279C4—22no—
280C4—22no—
281C4—21no—
282C4—21no—
283C4—44no—
284C4—82no—
285C4—81no—
286C4—1522no—
287C2—82no—
288C2#1456255811yescharacteristic
289C2#1456260412yes—
290C2#1456275111yescharacteristic
291C2#1456289812yes—
292C2#1456294611yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2683C2
socleC23×C19#120
prime radicalC22×D4×C19D4
hypercenter#2683D19
hypocenterC19#7754
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2683

Complements

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

NH ≅ G/Ntype
1. #14564968C2semidirect
3. #14561458C2semidirect
72. C4⋊C4×C19SD16semidirect
191. C19#7754semidirect
228. C4⋊C4#64526semidirect

Maximal subgroups

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

subgroupindex
#145649682
#145647172
#145614582
#145614562
C19×#26832
#775419