Finite Group Databasebeta

← #18071355

Subgroups — #18071355

Order 4864.

480 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 87 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#14564776C212yesmaximal, complemented
2#14564717C211yesmaximal, characteristic
3#14561461C212yesmaximal, complemented
4#14561456C211yesmaximal, characteristic
5C19×#2804C211yesmaximal, characteristic
6C22×#64526—21no—
7C2×#10597315C2211yescharacteristic
8C2×#10597292—22no—
9C2×#10597267—21no—
10#11926306—22no—
11#11926299C2211yescharacteristic
12#11926299C2212yes—
13C19×#400—21no—
14C19×#393—22no—
15C19×#391C2212yes—
16C19×#390C2211yescharacteristic
17C19×#386—21no—
18C19×#385—22no—
19C22×Q8×C19D412yes—
20C22×D4×C19D411yescharacteristic
21C23×C4×C19—21no—
22C22×Dic38—21no—
23C2×C4⋊C4×C19—21no—
24C2×C4⋊C4×C19D411yescharacteristic
25C2×C4⋊C4×C19D412yes—
26C2×C22⋊C4×C19—22no—
27C2×C22⋊C4×C19—22no—
28C2×C22⋊C4×C19—21no—
29C2×C42×C19C2311yescharacteristic
30C2×#64526—42no—
31C2×#64526—42no—
32C2×#64526—42no—
33C2×C4⋊Dic19—22no—
34C22×C19⋊C8—21no—
35C22×C19⋊C8—22no—
36#10597315—42no—
37C19×#95—22no—
38C19×#95—21no—
39C19×#95—22no—
40C19×#95—22no—
41#10597292—44no—
42#10597267—42no—
43C24×C19—21no—
44C2×Q8×C19—22no—
45C2×Q8×C19—22no—
46C2×Q8×C19—42no—
47C2×Q8×C19—42no—
48C2×D4×C19—21no—
49C2×D4×C19—41no—
50C2×D4×C19—41no—
51C2×D4×C19SD1612yes—
52C22×C4×C19—21no—
53C22×C4×C19—22no—
54C22×C4×C19—22no—
55C22×C4×C19—81no—
56C22×C4×C19—82no—
57C22×C4×C19C2×D411yescharacteristic
58C22×C4×C19C2×D412yes—
59C22×Dic19—41no—
60C2×Dic38—22no—
61C2×Dic38—41no—
62C2×Dic38—41no—
63C2×Dic38—41no—
64C2×Dic38—41no—
65C2×Dic38—41no—
66C4⋊C4×C19—42no—
67C4⋊C4×C19—41no—
68C4⋊C4×C19—81no—
69C22⋊C4×C19—42no—
70C22⋊C4×C19—42no—
71C22⋊C4×C19—82no—
72C22⋊C4×C19—81no—
73C42×C19—41no—
74#64526—48no—
75C4⋊Dic19—24no—
76C4⋊Dic19—42no—
77C2×C19⋊C8—22no—
78C2×C19⋊C8—41no—
79C2×C19⋊C8—41no—
80C2×C19⋊C8—42no—
81C2×C19⋊C8—42no—
82C2×C19⋊C8—42no—
83#7755—191nomaximal, Sylow
84C23×C19—22no—
85C23×C19—42no—
86C23×C19—41no—
87C23×C19—42no—
88C23×C19—41no—
89C23×C19#12011yescharacteristic
90Q8×C19—44no—
91Q8×C19—82no—
92D4×C19—42no—
93D4×C19—81no—
94C2×C4×C19—21no—
95C2×C4×C19—22no—
96C2×C4×C19—22no—
97C2×C4×C19—21no—
98C2×C4×C19—42no—
99C2×C4×C19—42no—
100C2×C4×C19—41no—
101C2×C4×C19—42no—
102C2×C4×C19—42no—
103C2×C4×C19—42no—
104C2×C4×C19—42no—
105C2×C4×C19—42no—
106C2×C4×C19—84no—
107C2×C4×C19C2×SD1611yescharacteristic
108C2×C4×C19#13512yes—
109C2×C4×C19#13711yescharacteristic
110C2×C4×C19#13712yes—
111C2×Dic19—42no—
112C2×Dic19—81no—
113C2×Dic19—81no—
114Dic38—42no—
115Dic38—42no—
116Dic38—81no—
117Dic38—81no—
118C19⋊C8—42no—
119C19⋊C8—82no—
120#2804D1911yescharacteristic
121#2024—192no—
122#2013—191no—
123#1272—192no—
124#1270—191no—
125C22×C19—42no—
126C22×C19—44no—
127C22×C19—82no—
128C22×C19—81no—
129C22×C19—81no—
130C22×C19#44811yescharacteristic
131C22×C19#45212yes—
132C22×C19#45311yescharacteristic
133C22×C19#45512yes—
134C22×C19B(4,𝔽2)11yescharacteristic
135C4×C19—21no—
136C4×C19—21no—
137C4×C19—22no—
138C4×C19—22no—
139C4×C19—82no—
140C4×C19—81no—
141C4×C19—82no—
142Dic19—82no—
143C22×SD16—381no—
144C2×C4⋊Q8—191no—
145C2×#103—382no—
146C2×#103—381no—
147#400—21no—
148#393—22no—
149#391C2×D1912yes—
150#390C2×D1911yescharacteristic
151#386—21no—
152#385—22no—
153#340—382no—
154#336—191no—
155#336—192no—
156C2×C19—82no—
157C2×C19#159611yescharacteristic
158C2×C19#160612yes—
159C2×C19#163011yescharacteristic
160C2×C19#164312yes—
161C2×C19#165911yescharacteristic
162C22×Q8—381no—
163C22×Q8C22⋊D1912yes—
164C22×D4C22⋊D1911yescharacteristic
165C23×C4—21no—
166C2×SD16—762no—
167C2×SD16—762no—
168C2×SD16—762no—
169C22×C8—381no—
170C22×C8—382no—
171C4⋊Q8—762no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—382no—
174C2×C4⋊C4C22⋊D1912yes—
175C2×C4⋊C4C22⋊D1911yescharacteristic
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—21no—
179C2×C42C22×D1911yescharacteristic
180#103—762no—
181#103—764no—
182#95—22no—
183#95—21no—
184#95—22no—
185#95—22no—
186C19#775511yescharacteristic, complemented, Sylow
187C24—21no—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8—42no—
191C2×Q8—42no—
192C2×Q8—382no—
193C2×Q8—761no—
194C2×Q8—761no—
195C2×Q8—761no—
196C2×Q8—761no—
197C2×Q8—761no—
198C2×D4—21no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4#6452712yes—
202C22×C4—22no—
203C22×C4—21no—
204C22×C4—22no—
205C22×C4—81no—
206C22×C4—82no—
207C22×C4—761no—
208C22×C4C2×C22⋊D1911yescharacteristic
209C22×C4C2×C22⋊D1912yes—
210SD16—768no—
211C2×C8—382no—
212C2×C8—761no—
213C2×C8—761no—
214C2×C8—762no—
215C2×C8—762no—
216C2×C8—762no—
217C4⋊C4—41no—
218C4⋊C4—42no—
219C4⋊C4—81no—
220C4⋊C4—384no—
221C4⋊C4—762no—
222C22⋊C4—42no—
223C22⋊C4—42no—
224C22⋊C4—82no—
225C22⋊C4—81no—
226C42—41no—
227C23—22no—
228C23—42no—
229C23—41no—
230C23—42no—
231C23—41no—
232C23#1059739911yescharacteristic
233Q8—44no—
234Q8—82no—
235Q8—762no—
236Q8—762no—
237Q8—1521no—
238Q8—1521no—
239D4—42no—
240D4—81no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—84no—
254C2×C4—762no—
255C2×C4—1521no—
256C2×C4—1521no—
257C2×C4C2×#6452711yescharacteristic
258C2×C4#1059738811yescharacteristic
259C2×C4#1059739612yes—
260C2×C4#1059739712yes—
261C8—762no—
262C8—1522no—
263C22—44no—
264C22—42no—
265C22—82no—
266C22—81no—
267C22—81no—
268C22#1192668311yescharacteristic
269C22#1192670612yes—
270C22#1192671211yescharacteristic
271C22#1192672212yes—
272C22#1192673111yescharacteristic
273C4—22no—
274C4—22no—
275C4—21no—
276C4—21no—
277C4—82no—
278C4—82no—
279C4—81no—
280C4—1522no—
281C2—82no—
282C2#1456255811yescharacteristic
283C2#1456261512yes—
284C2#1456275611yescharacteristic
285C2#1456284212yes—
286C2#1456294111yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2804C2
socleC23×C19#120
prime radicalC22×D4×C19D4
hypercenter#2804D19
hypocenterC19#7755
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2804

Complements

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

NH ≅ G/Ntype
1. #14564776C2semidirect
3. #14561461C2semidirect
186. C19#7755semidirect

Maximal subgroups

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

subgroupindex
#145647762
#145647172
#145614612
#145614562
C19×#28042
#775519