Finite Group Databasebeta

← #18077571

Subgroups — #18077571

Order 4864.

572 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C2×#11926483C211yesmaximal, characteristic
2#14566238C211yesmaximal, characteristic
3#14563726C212yesmaximal
4#14561515C212yesmaximal
5C2×C19×#324C211yesmaximal, characteristic
6C22×C4⋊Dic19C2211yescharacteristic
7#11926483—22no—
8#11926483C414yescomplemented
9#11926430—24no—
10#11926407—21no—
11#11926404C2212yes—
12C4×C22⋊Dic19—21no—
13C2×C19⋊#95—21no—
14C2×C19⋊#95—21no—
15C2×C19⋊#95C2211yescharacteristic
16#11926307—24no—
17C22×C4⋊C4×C19C2211yescharacteristic
18C2×C19×C22⋊C8C2212yes—
19C19×#324—22no—
20C23×C4×C19D411yescharacteristic
21C23×C4×C19D411yescharacteristic
22C23×C4×C19C2311yescharacteristic
23C23×Dic19—21no—
24C23×Dic19—21no—
25C22×C8×C19—22no—
26C2×C4⋊C4×C19—22no—
27C2×C4⋊C4×C19—22no—
28C2×C4⋊C4×C19C2×C412yes—
29C2×C4⋊C4×C19D412yes—
30C2×C22⋊Dic19—22no—
31C2×C4⋊Dic19—22no—
32C2×C4⋊Dic19—22no—
33C2×C4⋊Dic19—21no—
34C2×C4⋊Dic19C2×C412yes—
35C2×C4⋊Dic19D414yes—
36C2×C4×Dic19—22no—
37C19×C22⋊C8—22no—
38C19×C22⋊C8—22no—
39C19⋊#95—22no—
40C19⋊#95—24no—
41C19⋊#95—24no—
42C19⋊#95—24no—
43C19⋊#95—21no—
44C19⋊#95—22no—
45C19⋊#95C2×C412yes—
46C24×C19C2×D411yescharacteristic
47C22×C4×C19—21no—
48C22×C4×C19—21no—
49C22×C4×C19—21no—
50C22×C4×C19—22no—
51C22×C4×C19—22no—
52C22×C4×C19—21no—
53C22×C4×C19—42no—
54C22×C4×C19—42no—
55C22×C4×C19C22⋊C412yes—
56C22×C4×C19C22⋊C412yes—
57C22×C4×C19C22×C411yescharacteristic
58C22×C4×C19C2×D412yes—
59C22×C4×C19C2×D411yescharacteristic
60C22×C4×C19#4112yes—
61C22×Dic19—22no—
62C22×Dic19—22no—
63C22×Dic19—24no—
64C22×Dic19—42no—
65C22×Dic19—42no—
66C22×Dic19—44no—
67C22×Dic19—41no—
68C22×Dic19—41no—
69C22×Dic19—42no—
70C2×C8×C19—44no—
71C2×C8×C19—42no—
72C4⋊C4×C19—24no—
73C4⋊C4×C19—24no—
74C22⋊Dic19—42no—
75C22⋊Dic19—42no—
76C4⋊Dic19—24no—
77C4⋊Dic19—42no—
78C4⋊Dic19—44no—
79C4×Dic19—82no—
80#9022—191nomaximal, Sylow
81C23×C19—22no—
82C23×C19—22no—
83C23×C19C2×C22⋊C411yescharacteristic
84C23×C19#12011yescharacteristic
85C23×C19#12311yescharacteristic
86C23×C19#13512yes—
87C23×C19#13712yes—
88C2×C4×C19—24no—
89C2×C4×C19—22no—
90C2×C4×C19—22no—
91C2×C4×C19—22no—
92C2×C4×C19—22no—
93C2×C4×C19—41no—
94C2×C4×C19—41no—
95C2×C4×C19—42no—
96C2×C4×C19—42no—
97C2×C4×C19—42no—
98C2×C4×C19—42no—
99C2×C4×C19—42no—
100C2×C4×C19—81no—
101C2×C4×C19C4×D412yes—
102C2×C4×C19#12112yes—
103C2×Dic19—42no—
104C2×Dic19—42no—
105C2×Dic19—44no—
106C2×Dic19—42no—
107C2×Dic19—42no—
108C2×Dic19—44no—
109C2×Dic19—44no—
110C2×Dic19—44no—
111C2×Dic19—84no—
112C2×Dic19—82no—
113C2×Dic19—82no—
114C8×C19—82no—
115C2×#400—191no—
116#2313—191no—
117#1824—192no—
118C2×#324D1911yescharacteristic
119#1294—192no—
120C22×C19—24no—
121C22×C19—24no—
122C22×C19—21no—
123C22×C19—21no—
124C22×C19—21no—
125C22×C19—21no—
126C22×C19#38611yescharacteristic
127C22×C19#41611yescharacteristic
128C22×C19#41911yescharacteristic
129C22×C19#45212yes—
130C22×C19#45412yes—
131C22×C19#45812yes—
132C22×C19#48512yes—
133C4×C19—22no—
134C4×C19—22no—
135C4×C19—42no—
136C4×C19—42no—
137Dic19—82no—
138Dic19—84no—
139Dic19—82no—
140C22×C4⋊C4—191no—
141C22×C4⋊C4C2×D1911yescharacteristic
142C2×C22⋊C8C2×D1912yes—
143#400—194no—
144#400—382no—
145#387—384no—
146#381—381no—
147#380—192no—
148C4×C22⋊C4—381no—
149C2×#95—191no—
150C2×#95—381no—
151C2×#95—381no—
152#340—384no—
153#324—22no—
154C2×C19—21no—
155C2×C19—21no—
156C2×C19—22no—
157C2×C19#161514yes—
158C2×C19#187311yescharacteristic
159C2×C19#188811yescharacteristic
160C2×C19#189011yescharacteristic
161C23×C4—381no—
162C23×C4—381no—
163C23×C4D7611yescharacteristic
164C23×C4D7611yescharacteristic
165C23×C4C22×D1911yescharacteristic
166C22×C8—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—192no—
170C2×C4⋊C4—194no—
171C2×C4⋊C4—382no—
172C2×C4⋊C4—382no—
173C2×C4⋊C4—381no—
174C2×C4⋊C4C4×D1912yes—
175C2×C4⋊C4C22⋊D1912yes—
176C2×C22⋊C4—382no—
177C2×C42—382no—
178C22⋊C8—22no—
179C22⋊C8—22no—
180#95—192no—
181#95—382no—
182#95—384no—
183#95—384no—
184#95—384no—
185#95—382no—
186#95—381no—
187C19#902211yescharacteristic, complemented, Sylow
188C24C2×D7611yescharacteristic
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—21no—
195C22×C4—42no—
196C22×C4—42no—
197C22×C4—384no—
198C22×C4—382no—
199C22×C4—382no—
200C22×C4—762no—
201C22×C4—762no—
202C22×C4—764no—
203C22×C4—761no—
204C22×C4—761no—
205C22×C4—762no—
206C22×C4(C2×D19)⋊C412yes—
207C22×C4(C2×D19)⋊C412yes—
208C22×C4C2×C4×D1911yescharacteristic
209C22×C4D4×D1912yes—
210C22×C4#6454312yes—
211C22×C4C2×C22⋊D1911yescharacteristic
212C2×C8—44no—
213C2×C8—42no—
214C4⋊C4—24no—
215C4⋊C4—24no—
216C4⋊C4—384no—
217C4⋊C4—764no—
218C4⋊C4—762no—
219C22⋊C4—762no—
220C22⋊C4—762no—
221C42—1522no—
222C23—22no—
223C23—22no—
224C23#1059732811yescharacteristic
225C23#1059733211yescharacteristic
226C23#1059735012yes—
227C23#1059735512yes—
228C23C2×(C2×D19)⋊C411yescharacteristic
229C2×C4—24no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—81no—
242C2×C4—762no—
243C2×C4—762no—
244C2×C4—764no—
245C2×C4—762no—
246C2×C4—762no—
247C2×C4—764no—
248C2×C4—764no—
249C2×C4—764no—
250C2×C4—1524no—
251C2×C4—1522no—
252C2×C4—1522no—
253C2×C4(C22⋊D19)⋊C412yes—
254C2×C4#1059738512yes—
255C8—82no—
256C22—24no—
257C22—24no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22#1192642111yescharacteristic
263C22#1192654111yescharacteristic
264C22#1192655411yescharacteristic
265C22#1192670812yes—
266C22#1192671912yes—
267C22#1192673512yes—
268C22#1192688612yes—
269C4—22no—
270C4—22no—
271C4—42no—
272C4—42no—
273C4—1522no—
274C4—1524no—
275C4—1522no—
276C2—21no—
277C2—21no—
278C2—22no—
279C2#1456266814yes—
280C2#1456394511yescharacteristic
281C2#1456403611yescharacteristic
282C2#1456404611yescharacteristic
subgroupG/H
centerC23#10597328
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#324C2
socleC23×C19#120
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenterC2×#324D19
hypocenterC19#9022
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
8. #11926483C4semidirect
187. C19#9022semidirect

Maximal subgroups

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

subgroupindex
C2×#119264832
#145662382
#145637262
#145615152
C2×C19×#3242
#902219