Finite Group Databasebeta

← #18080393

Subgroups — #18080393

Order 4864.

542 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 131 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#14568540C211yesmaximal, characteristic
2#14563631C211yesmaximal, characteristic, complemented
3#14562061C212yesmaximal
4#14561494C212yesmaximal, complemented
5C19×#2982C211yesmaximal, characteristic, complemented
6C2×#10597392—21no—
7C2×C4×D76C2211yescharacteristic
8#11926568C2212yes—
9C2×#10597293—21no—
10#11926474C412yes—
11#11926461C412yes—
12#11926435—22no—
13#11926410C2211yescharacteristic
14#11926401—21no—
15#11926313—21no—
16#11926273—24no—
17C2×C4×Q8×C19C2211yescharacteristic
18C8×Q8×C19—24no—
19C19×#431—22no—
20C19×#431C2212yes—
21C22×Q8×C19D411yescharacteristic
22C22×D76C2×C411yescharacteristic
23C22×C4×D19—21no—
24C4×Q8×C19—22no—
25C4×Q8×C19—22no—
26C2×C4⋊C4×C19C2×C412yes—
27C2×C4⋊C4×C19D411yescharacteristic
28C2×C42×C19D412yes—
29C2×C42×C19C2311yescharacteristic
30#10597392—42no—
31#10597392—42no—
32C2×(C2×D19)⋊C4—22no—
33C2×(C2×D19)⋊C4—22no—
34C2×(C2×D19)⋊C4—21no—
35C2×C4⋊Dic19—21no—
36C2×C4⋊Dic19C2×C411yescharacteristic
37C2×Dic19⋊C4—22no—
38C2×#64520—22no—
39C4×D76—22no—
40C4×D76—22no—
41C19×C4⋊C8—24no—
42C19×C4⋊C8—22no—
43C19×C22⋊C8—22no—
44C4×C8×C19—24no—
45C4×C8×C19D414yes—
46#10597293—42no—
47C19⋊#95—22no—
48C19⋊#95—21no—
49C19⋊#95C2×C412yes—
50C4⋊(C19⋊C8)—22no—
51C4⋊(C19⋊C8)—22no—
52C23×D19—21no—
53C2×Q8×C19—22no—
54C2×Q8×C19—22no—
55C2×Q8×C19D812yes—
56C2×Q8×C19SD1612yes—
57C22×C4×C19C22⋊C412yes—
58C22×C4×C19C22⋊C412yes—
59C22×C4×C19C22×C411yescharacteristic
60C22×C4×C19C2×D411yescharacteristic
61C22×C4×C19C2×D411yescharacteristic
62C22×Dic19—21no—
63C22×Dic19—22no—
64C2×D76—22no—
65C2×D76—42no—
66C2×C4×D19—42no—
67C2×C4×D19—41no—
68C2×C4×D19—41no—
69C2×C4×D19—42no—
70C2×C8×C19—24no—
71C4⋊C4×C19—24no—
72C4⋊C4×C19—22no—
73C42×C19—22no—
74C42×C19—22no—
75C42×C19C2×D412yes—
76C42×C19#4112yes—
77(C2×D19)⋊C4—44no—
78(C2×D19)⋊C4—44no—
79(C2×D19)⋊C4—41no—
80(C2×D19)⋊C4—41no—
81C4⋊Dic19—22no—
82C4⋊Dic19—41no—
83C4⋊Dic19—41no—
84Dic19⋊C4—44no—
85#64520—42no—
86#64520—42no—
87C2×C19⋊C8—42no—
88#9486—191nomaximal, Sylow
89C23×C19C2×C22⋊C411yescharacteristic
90C22×D19—22no—
91C22×D19—41no—
92C22×D19—41no—
93C22×D19—41no—
94C22×D19—41no—
95C22×D19—41no—
96C22×D19—41no—
97Q8×C19—24no—
98Q8×C19—24no—
99C2×C4×C19—22no—
100C2×C4×C19—22no—
101C2×C4×C19—22no—
102C2×C4×C19—41no—
103C2×C4×C19—41no—
104C2×C4×C19—42no—
105C2×C4×C19#10214yes—
106C2×C4×C19C4×D412yes—
107C2×C4×C19#12011yescharacteristic
108C2×C4×C19#12112yes—
109C2×C4×C19#12311yescharacteristic
110C2×C4×C19C2×D811yescharacteristic
111C2×C4×C19C2×SD1611yescharacteristic
112C2×C4×C19#13512yes—
113C2×Dic19—42no—
114C2×Dic19—42no—
115C2×Dic19—41no—
116C2×Dic19—41no—
117C2×Dic19—42no—
118C2×Dic19—41no—
119D76—24no—
120D76—42no—
121C4×D19—82no—
122C4×D19—82no—
123C8×C19—44no—
124C19⋊C8—82no—
125#2982D1911yescharacteristic, complemented
126#2536—191no—
127#1801—191no—
128#1486—192no—
129#1286—192no—
130C22×C19—21no—
131C22×C19—21no—
132C22×C19#38611yescharacteristic
133C22×C19C2×#10211yescharacteristic
134C22×C19#41611yescharacteristic
135C2×D19—42no—
136C2×D19—42no—
137C2×D19—42no—
138C2×D19—81no—
139C2×D19—81no—
140C2×D19—81no—
141C2×D19—81no—
142C4×C19—22no—
143C4×C19—24no—
144C4×C19—21no—
145C4×C19—21no—
146C4×C19—42no—
147C4×C19#46512yes—
148C4×C19#46612yes—
149Dic19—82no—
150Dic19—81no—
151C2×C22⋊Q8—381no—
152C2×C4×Q8C2×D1911yescharacteristic
153C2×C4×D4—191no—
154C8×Q8—24no—
155#431—22no—
156#431C2×D1912yes—
157#423—192no—
158C2×#101—381no—
159#398—192no—
160#394—192no—
161#388—382no—
162#382—191no—
163#380—381no—
164#343—381no—
165D4⋊C8—384no—
166C2×C19—21no—
167C2×C19—21no—
168C2×C19#189111yescharacteristic
169C2×C19#189311yescharacteristic
170C2×C19#191211yescharacteristic
171D19—82no—
172C22×Q8D7611yescharacteristic
173C22×D4—191no—
174C23×C4—381no—
175C2×M16—382no—
176C22⋊Q8—762no—
177C22⋊Q8—762no—
178C4×Q8—22no—
179C4×Q8—22no—
180C4×D4—382no—
181C4×D4—382no—
182C2×C4⋊C4—191no—
183C2×C4⋊C4—382no—
184C2×C4⋊C4—381no—
185C2×C4⋊C4C4×D1912yes—
186C2×C4⋊C4D7611yescharacteristic
187C2×C22⋊C4—382no—
188C2×C22⋊C4—382no—
189C2×C22⋊C4—381no—
190C2×C42C22⋊D1912yes—
191C2×C42C22×D1911yescharacteristic
192C4⋊C8—24no—
193C4⋊C8—22no—
194C4⋊C8—382no—
195C4⋊C8—382no—
196#101—762no—
197C22⋊C8—22no—
198C4×C8—24no—
199C4×C8C22⋊D1914yes—
200#95—192no—
201#95—382no—
202#95—381no—
203C19#948611yescharacteristic, complemented, Sylow
204C24—381no—
205C2×Q8—22no—
206C2×Q8—22no—
207C2×Q8#6451612yes—
208C2×Q8D15212yes—
209C2×D4—382no—
210C2×D4—762no—
211C22×C4—382no—
212C22×C4—381no—
213C22×C4—762no—
214C22×C4—761no—
215C22×C4—761no—
216C22×C4—762no—
217C22×C4(C2×D19)⋊C412yes—
218C22×C4(C2×D19)⋊C412yes—
219C22×C4C2×C4×D1911yescharacteristic
220C22×C4C2×D7611yescharacteristic
221C22×C4C2×C22⋊D1911yescharacteristic
222M16—762no—
223M16—762no—
224C2×C8—24no—
225C2×C8—762no—
226C4⋊C4—22no—
227C4⋊C4—24no—
228C4⋊C4—382no—
229C4⋊C4—764no—
230C4⋊C4—761no—
231C4⋊C4—761no—
232C22⋊C4—764no—
233C22⋊C4—761no—
234C22⋊C4—764no—
235C22⋊C4—761no—
236C42—22no—
237C42—22no—
238C42#6454112yes—
239C42C2×C22⋊D1912yes—
240C23—382no—
241C23—761no—
242C23—761no—
243C23—761no—
244C23—761no—
245C23—761no—
246C23—761no—
247C23C2×(C2×D19)⋊C411yescharacteristic
248Q8—24no—
249Q8—24no—
250D4—384no—
251D4—762no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—762no—
259C2×C4—762no—
260C2×C4—762no—
261C2×C4—761no—
262C2×C4—761no—
263C2×C4—761no—
264C2×C4—1522no—
265C2×C4—1522no—
266C2×C4#1059727814yes—
267C2×C4C2×#6451611yescharacteristic
268C2×C4C2×D15211yescharacteristic
269C2×C4#1059735012yes—
270C2×C4C4×C22⋊D1912yes—
271C2×C4#1059737511yescharacteristic
272C2×C4#1059737612yes—
273C2×C4#1059739911yescharacteristic
274C8—44no—
275C8—1522no—
276C22—21no—
277C22—21no—
278C22—762no—
279C22—762no—
280C22—762no—
281C22—1521no—
282C22—1521no—
283C22—1521no—
284C22—1521no—
285C22#1192642311yescharacteristic
286C22C2×#1059727811yescharacteristic
287C22#1192654111yescharacteristic
288C4—21no—
289C4—21no—
290C4—22no—
291C4—24no—
292C4—42no—
293C4—1522no—
294C4—1521no—
295C4#1192677312yes—
296C4#1192678012yes—
297C2—21no—
298C2—21no—
299C2—1522no—
300C2#1456405311yescharacteristic
301C2#1456406311yescharacteristic
302C2#1456417211yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2982C2
socleC22×C19#386
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenter#2982D19
hypocenterC19#9486
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
2. #14563631C2semidirect
4. #14561494C2semidirect
5. C19×#2982C2semidirect
125. #2982D19semidirect
203. C19#9486semidirect

Maximal subgroups

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

subgroupindex
#145685402
#145636312
#145620612
#145614942
C19×#29822
#948619