Finite Group Databasebeta

← #18069627

Subgroups — #18069627

Order 4864.

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

normal subgroups only

This group has 372 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#14563627C211yesmaximal, characteristic
2#14563623C211yesmaximal, characteristic
3C19×#1869C211yesmaximal, characteristic
4#11926568—21no—
5C2×#10597290—21no—
6C2×#10597291—21no—
7#11926404—21no—
8#11926313C412yescomplemented
9#11926311C412yes—
10C23×C8×C19C411yescharacteristic, complemented
11C2×C4×D4×C19C2211yescharacteristic
12C2×C19×C22⋊C8—21no—
13C2×C19×C22⋊C8C411yescharacteristic, complemented
14C19×#336—21no—
15C22×D4×C19D411yescharacteristic
16C23×C4×C19C2×C411yescharacteristic
17C23×C4×C19D411yescharacteristic
18C22×C8×C19—21no—
19C22×C8×C19—21no—
20C22×C8×C19—42no—
21C22×C8×C19—41no—
22C4×D4×C19—41no—
23C4×D4×C19—41no—
24C2×C4⋊C4×C19C2×C411yescharacteristic
25C2×C22⋊C4×C19C2×C411yescharacteristic
26C2×C22⋊C4×C19Q811yescharacteristic
27C2×C42×C19D411yescharacteristic
28C2×C22⋊Dic19—22no—
29C2×C4⋊Dic19—41no—
30C2×#64520—22no—
31C19×C22⋊C8—42no—
32C19×C22⋊C8—41no—
33#10597291—41no—
34#10597291—41no—
35#10597290—41no—
36#10597290—41no—
37C19⋊#95—41no—
38C4⋊(C19⋊C8)—41no—
39C4⋊(C19⋊C8)—41no—
40C24×C19C22⋊C411yescharacteristic
41C24×C19C4⋊C411yescharacteristic
42C2×D4×C19—41no—
43C2×D4×C19—41no—
44C2×D4×C19D811yescharacteristic
45C2×D4×C19SD1611yescharacteristic
46C2×D4×C19SD1611yescharacteristic
47C2×D4×C19Q1611yescharacteristic
48C22×C4×C19—21no—
49C22×C4×C19—21no—
50C22×C4×C19—21no—
51C22×C4×C19—21no—
52C22×C4×C19—41no—
53C22×C4×C19—41no—
54C22×C4×C19—41no—
55C22×C4×C19—41no—
56C22×C4×C19C4211yescharacteristic
57C22×C4×C19C22⋊C411yescharacteristic
58C22×C4×C19C22⋊C411yescharacteristic
59C22×C4×C19C4⋊C411yescharacteristic
60C22×C4×C19C4⋊C411yescharacteristic
61C22×Dic19—42no—
62C2×C8×C19—22no—
63C2×C8×C19—41no—
64C2×C8×C19—42no—
65C2×C8×C19—41no—
66C2×C8×C19—42no—
67C2×C8×C19—41no—
68C2×C8×C19—41no—
69C2×C8×C19—41no—
70C4⋊C4×C19—41no—
71C22⋊C4×C19—41no—
72C22⋊C4×C19—41no—
73C42×C19—21no—
74C42×C19—21no—
75C22⋊Dic19—42no—
76C22⋊Dic19—42no—
77C4⋊Dic19—81no—
78C4⋊Dic19—81no—
79#64520—42no—
80#64520—42no—
81C2×C19⋊C8—42no—
82#7236—191nomaximal, Sylow
83C23×C19—21no—
84C23×C19—21no—
85C23×C19—21no—
86C23×C19—21no—
87C23×C19—41no—
88C23×C19—41no—
89C23×C19—41no—
90C23×C19—41no—
91C23×C19#9511yescharacteristic
92C23×C19#10211yescharacteristic
93C23×C19#10311yescharacteristic
94C23×C19#10611yescharacteristic
95C23×C19#10711yescharacteristic
96D4×C19—41no—
97D4×C19—41no—
98D4×C19—41no—
99D4×C19—41no—
100C2×C4×C19—21no—
101C2×C4×C19—21no—
102C2×C4×C19—21no—
103C2×C4×C19—21no—
104C2×C4×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—42no—
108C2×C4×C19—41no—
109C2×C4×C19—41no—
110C2×C4×C19—41no—
111C2×C4×C19—41no—
112C2×C4×C19—41no—
113C2×C4×C19—41no—
114C2×C4×C19—41no—
115C2×C4×C19—81no—
116C2×C4×C19#9911yescharacteristic
117C2×C4×C19#9911yescharacteristic
118C2×C4×C19#10211yescharacteristic
119C2×C4×C19#10311yescharacteristic
120C2×Dic19—82no—
121C2×Dic19—82no—
122C2×Dic19—82no—
123C8×C19—42no—
124C8×C19—81no—
125C19⋊C8—82no—
126#1869D1911yescharacteristic
127#1800—191no—
128#1799—191no—
129C22×C19—21no—
130C22×C19—21no—
131C22×C19—21no—
132C22×C19—21no—
133C22×C19—21no—
134C22×C19—21no—
135C22×C19—41no—
136C22×C19—41no—
137C22×C19—41no—
138C22×C19—41no—
139C22×C19—42no—
140C22×C19—41no—
141C22×C19—41no—
142C22×C19—41no—
143C22×C19—41no—
144C22×C19—81no—
145C22×C19H(3,ℤ/4)11yescharacteristic
146C22×C19#34011yescharacteristic
147C22×C19#34211yescharacteristic
148C4×C19—21no—
149C4×C19—21no—
150C4×C19—21no—
151C4×C19—41no—
152C4×C19—41no—
153C4×C19—41no—
154C4×C19AΣL(1,𝔽16)11yescharacteristic
155C4×C19#35211yescharacteristic
156Dic19—162no—
157C23×C8Dic1911yescharacteristic, complemented
158C2×C4×D4C2×D1911yescharacteristic
159#423—381no—
160C2×#100—381no—
161C2×#99—381no—
162C2×C22⋊C8—21no—
163C2×C22⋊C8Dic1911yescharacteristic, complemented
164#380—381no—
165#343—192no—
166#342—192no—
167#336—21no—
168C2×C19—21no—
169C2×C19—21no—
170C2×C19—41no—
171C2×C19—41no—
172C2×C19—41no—
173C2×C19—41no—
174C2×C19#128911yescharacteristic
175C2×C19#139011yescharacteristic
176C2×C19#139511yescharacteristic
177C22×D4D7611yescharacteristic
178C23×C4C2×Dic1911yescharacteristic
179C23×C4C22⋊D1911yescharacteristic
180C2×M16—382no—
181C22×C8—21no—
182C22×C8—21no—
183C22×C8—42no—
184C22×C8—41no—
185C4×D4—41no—
186C4×D4—41no—
187C2×C4⋊C4—761no—
188C2×C4⋊C4C4×D1911yescharacteristic
189C2×C22⋊C4—382no—
190C2×C22⋊C4Dic3811yescharacteristic
191C2×C22⋊C4C4×D1911yescharacteristic
192C2×C42C22⋊D1911yescharacteristic
193C4⋊C8—761no—
194C4⋊C8—761no—
195#100—761no—
196#100—761no—
197#99—761no—
198#99—761no—
199C22⋊C8—42no—
200C22⋊C8—41no—
201#95—761no—
202C19#723611yescharacteristic, complemented, Sylow
203C24C4⋊Dic1911yescharacteristic
204C24(C2×D19)⋊C411yescharacteristic
205C2×D4—41no—
206C2×D4—41no—
207C2×D4#6451611yescharacteristic
208C2×D4#6451611yescharacteristic
209C2×D4D15211yescharacteristic
210C2×D4Dic7611yescharacteristic
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—762no—
220C22×C4C4×Dic1911yescharacteristic
221C22×C4Dic19⋊C411yescharacteristic
222C22×C4Dic19⋊C411yescharacteristic
223C22×C4(C2×D19)⋊C411yescharacteristic
224C22×C4C22⋊Dic1911yescharacteristic
225M16—762no—
226M16—762no—
227C2×C8—22no—
228C2×C8—41no—
229C2×C8—42no—
230C2×C8—41no—
231C2×C8—42no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—762no—
236C4⋊C4—41no—
237C4⋊C4—1521no—
238C4⋊C4—1521no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—762no—
242C22⋊C4—762no—
243C42—21no—
244C42—21no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—41no—
250C23—41no—
251C23—41no—
252C23—41no—
253C23#1059727311yescharacteristic
254C23#1059727411yescharacteristic
255C23#1059727511yescharacteristic
256C23#1059727811yescharacteristic
257C23C19⋊#9511yescharacteristic
258D4—41no—
259D4—41no—
260D4—41no—
261D4—41no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—81no—
278C2×C4—1522no—
279C2×C4—1522no—
280C2×C4—1522no—
281C2×C4#1059727311yescharacteristic
282C2×C4#1059727811yescharacteristic
283C2×C4#1059729111yescharacteristic
284C2×C4#1059729111yescharacteristic
285C8—42no—
286C8—81no—
287C8—1522no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—41no—
303C22—81no—
304C22#1192630111yescharacteristic
305C22#1192630711yescharacteristic
306C22#1192631111yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—3042no—
314C4#1192633111yescharacteristic
315C4#1192633411yescharacteristic
316C2—21no—
317C2—21no—
318C2—41no—
319C2—41no—
320C2—41no—
321C2—41no—
322C2#1456150311yescharacteristic
323C2#1456175311yescharacteristic
324C2#1456176411yescharacteristic
subgroupG/H
centerC22#11926311
commutatorC22×C4×C19C42
FrattiniC2×C4×D4C2×D19
FittingC19×#1869C2
socleC22×C19#342
prime radicalC22×D4×C19D4
cosocleC2×C4×D4×C19C22
hypercenter#1869D19
hypocenterC19#7236
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1869

Complements

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

NH ≅ G/Ntype
8. #11926313C4semidirect
10. C23×C8×C19C4semidirect
13. C2×C19×C22⋊C8C4semidirect
157. C23×C8Dic19semidirect
163. C2×C22⋊C8Dic19semidirect
202. C19#7236semidirect

Maximal subgroups

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

subgroupindex
#145636272
#145636232
C19×#18692
#723619