Finite Group Databasebeta

← #18078595

Subgroups — #18078595

Order 4864.

516 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 111 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#14569448C211yesmaximal, characteristic
2#14566238C211yesmaximal, characteristic
3#14562208C212yesmaximal
4#14561503C212yesmaximal
5C2×C19×#324C211yesmaximal, characteristic
6C2×#10597370C2211yescharacteristic
7#11926483C412yescomplemented
8#11926477—22no—
9#11926464C412yescomplemented
10#11926430—24no—
11#11926417—21no—
12#11926407—21no—
13#11926407—21no—
14#11926404C2211yescharacteristic
15#11926404C2212yes—
16C4×C22⋊Dic19—21no—
17#11926282—24no—
18C22×C4⋊C4×C19C2211yescharacteristic
19C2×C19×C22⋊C8C2212yes—
20C19×#324—22no—
21C23×C4×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C22×Dic38C2×C411yescharacteristic
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—21no—
31C2×C22⋊Dic19—22no—
32C2×C22⋊Dic19—21no—
33C2×C4⋊Dic19—22no—
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19C2×C411yescharacteristic
36#10597370—22no—
37#10597370—22no—
38C2×Dic19⋊C4—21no—
39C2×Dic19⋊C4—22no—
40C2×C4×Dic19—22no—
41C19×C22⋊C8—22no—
42C19×C22⋊C8—22no—
43C19⋊#95—22no—
44C19⋊#95—24no—
45C19⋊#95—22no—
46C19⋊#95—22no—
47C19⋊#95—22no—
48C19⋊#95C2×C412yes—
49C19⋊#95D414yes—
50C24×C19C2×D411yescharacteristic
51C22×C4×C19—21no—
52C22×C4×C19—21no—
53C22×C4×C19—21no—
54C22×C4×C19—22no—
55C22×C4×C19—22no—
56C22×C4×C19—21no—
57C22×C4×C19—81no—
58C22×C4×C19—81no—
59C22×C4×C19C22⋊C412yes—
60C22×C4×C19C22⋊C412yes—
61C22×C4×C19C22×C411yescharacteristic
62C22×C4×C19C2×D412yes—
63C22×C4×C19C2×D411yescharacteristic
64C22×C4×C19#4112yes—
65C22×Dic19—21no—
66C22×Dic19—21no—
67C22×Dic19—22no—
68C22×Dic19—24no—
69C2×Dic38—22no—
70C2×Dic38—81no—
71C2×C8×C19—42no—
72C2×C8×C19—82no—
73C4⋊C4×C19—24no—
74C4⋊C4×C19—24no—
75C22⋊Dic19—41no—
76C22⋊Dic19—41no—
77C22⋊Dic19—42no—
78C22⋊Dic19—42no—
79C22⋊Dic19—42no—
80C4⋊Dic19—22no—
81C4⋊Dic19—82no—
82C4⋊Dic19—81no—
83Dic19⋊C4—42no—
84Dic19⋊C4—82no—
85C4×Dic19—82no—
86#9202—191nomaximal, Sylow
87C23×C19—41no—
88C23×C19—41no—
89C23×C19C2×C22⋊C411yescharacteristic
90C23×C19#12011yescharacteristic
91C23×C19#12311yescharacteristic
92C23×C19#13512yes—
93C23×C19#13712yes—
94C2×C4×C19—22no—
95C2×C4×C19—22no—
96C2×C4×C19—22no—
97C2×C4×C19—22no—
98C2×C4×C19—42no—
99C2×C4×C19—41no—
100C2×C4×C19—42no—
101C2×C4×C19—41no—
102C2×C4×C19—42no—
103C2×C4×C19—42no—
104C2×C4×C19—42no—
105C2×C4×C19—42no—
106C2×C4×C19—81no—
107C2×C4×C19C4×D412yes—
108C2×C4×C19#12112yes—
109C2×Dic19—44no—
110C2×Dic19—42no—
111C2×Dic19—42no—
112C2×Dic19—42no—
113C2×Dic19—44no—
114C2×Dic19—42no—
115C2×Dic19—41no—
116C2×Dic19—41no—
117C2×Dic19—42no—
118C2×Dic19—44no—
119Dic38—82no—
120C8×C19—82no—
121#2627—191no—
122#2313—191no—
123#1520—192no—
124C2×#324D1911yescharacteristic
125#1289—192no—
126C22×C19—21no—
127C22×C19—21no—
128C22×C19—21no—
129C22×C19—21no—
130C22×C19—21no—
131C22×C19—21no—
132C22×C19—42no—
133C22×C19—42no—
134C22×C19#38611yescharacteristic
135C22×C19#41611yescharacteristic
136C22×C19#41911yescharacteristic
137C22×C19#45212yes—
138C22×C19#48512yes—
139C4×C19—22no—
140C4×C19—22no—
141C4×C19—42no—
142C4×C19—42no—
143Dic19—82no—
144Dic19—84no—
145Dic19—81no—
146Dic19—81no—
147C2×C22⋊Q8—191no—
148C22×C4⋊C4C2×D1911yescharacteristic
149C2×C22⋊C8C2×D1912yes—
150#400—192no—
151#398—382no—
152#395—192no—
153#387—384no—
154#385—381no—
155#381—381no—
156#381—381no—
157#380—191no—
158#380—192no—
159C4×C22⋊C4—381no—
160#328—384no—
161#324—22no—
162C2×C19—21no—
163C2×C19—22no—
164C2×C19—21no—
165C2×C19—22no—
166C2×C19#187311yescharacteristic
167C2×C19#191211yescharacteristic
168C2×C19#191311yescharacteristic
169C22×Q8—191no—
170C23×C4D7611yescharacteristic
171C23×C4D7611yescharacteristic
172C23×C4C22×D1911yescharacteristic
173C22×C8—22no—
174C22⋊Q8—382no—
175C22⋊Q8—382no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—191no—
179C2×C4⋊C4—381no—
180C2×C4⋊C4—382no—
181C2×C4⋊C4—382no—
182C2×C4⋊C4—381no—
183C2×C4⋊C4C4×D1912yes—
184C2×C4⋊C4C22⋊D1912yes—
185C2×C22⋊C4—381no—
186C2×C22⋊C4—382no—
187C2×C22⋊C4—381no—
188C2×C42—382no—
189C22⋊C8—22no—
190C22⋊C8—22no—
191#95—192no—
192#95—194no—
193#95—382no—
194#95—384no—
195#95—382no—
196#95—382no—
197#95—382no—
198C19#920211yescharacteristic, complemented, Sylow
199C24C2×D7611yescharacteristic
200C2×Q8—382no—
201C2×Q8—1521no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—81no—
209C22×C4—81no—
210C22×C4—384no—
211C22×C4—382no—
212C22×C4—381no—
213C22×C4—381no—
214C22×C4(C2×D19)⋊C412yes—
215C22×C4(C2×D19)⋊C412yes—
216C22×C4C2×C4×D1911yescharacteristic
217C22×C4D4×D1912yes—
218C22×C4#6454312yes—
219C22×C4C2×C22⋊D1911yescharacteristic
220C2×C8—42no—
221C2×C8—82no—
222C4⋊C4—24no—
223C4⋊C4—24no—
224C4⋊C4—382no—
225C4⋊C4—762no—
226C4⋊C4—1522no—
227C4⋊C4—1522no—
228C4⋊C4—1521no—
229C22⋊C4—761no—
230C22⋊C4—761no—
231C22⋊C4—762no—
232C22⋊C4—762no—
233C22⋊C4—762no—
234C42—1522no—
235C23—41no—
236C23—41no—
237C23#1059732811yescharacteristic
238C23#1059733211yescharacteristic
239C23#1059735012yes—
240C23#1059735512yes—
241C23C2×(C2×D19)⋊C411yescharacteristic
242Q8—1522no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—81no—
256C2×C4—764no—
257C2×C4—762no—
258C2×C4—762no—
259C2×C4—764no—
260C2×C4—762no—
261C2×C4—762no—
262C2×C4—762no—
263C2×C4—761no—
264C2×C4—761no—
265C2×C4—764no—
266C2×C4(C22⋊D19)⋊C412yes—
267C2×C4#1059738512yes—
268C8—82no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—42no—
276C22—42no—
277C22#1192642111yescharacteristic
278C22#1192654111yescharacteristic
279C22#1192655411yescharacteristic
280C22#1192670812yes—
281C22#1192688612yes—
282C4—22no—
283C4—22no—
284C4—42no—
285C4—42no—
286C4—1522no—
287C4—1524no—
288C4—1521no—
289C4—1521no—
290C2—21no—
291C2—22no—
292C2—21no—
293C2—22no—
294C2#1456394511yescharacteristic
295C2#1456417011yescharacteristic
296C2#1456417511yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#324C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenterC2×#324D19
hypocenterC19#9202
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
7. #11926483C4semidirect
9. #11926464C4semidirect
198. C19#9202semidirect

Maximal subgroups

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

subgroupindex
#145694482
#145662382
#145622082
#145615032
C2×C19×#3242
#920219