Finite Group Databasebeta

← #18071230

Subgroups — #18071230

Order 4864.

420 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572002C211yesmaximal, characteristic
2#14563752C211yesmaximal, characteristic, complemented
3#14561457C212yesmaximal, complemented
4#14561455C212yesmaximal
5C19×#1831C211yesmaximal, characteristic, complemented
6C2×#10597322—21no—
7C2×C4⋊(C19⋊C8)—21no—
8#11926446C411yescharacteristic
9#11926446C411yescharacteristic
10#11926446C2211yescharacteristic
11#11926442C411yescharacteristic
12#11926442C411yescharacteristic
13#11926442C2211yescharacteristic
14#11926435—21no—
15#11926435—21no—
16#11926435—21no—
17#11926299—21no—
18#11926299C2212yes—
19C2×C19×C4⋊C8—21no—
20C43×C19C2211yescharacteristic
21C19×#336—21no—
22C19×#336C2212yes—
23C22×D76C2×C411yescharacteristic
24C22×C8×C19—22no—
25C2×C42×C19C2×C411yescharacteristic
26C2×C42×C19C2×C411yescharacteristic
27C2×C42×C19D411yescharacteristic
28C2×C42×C19D411yescharacteristic
29C2×C42×C19D411yescharacteristic
30C2×C42×C19D411yescharacteristic
31C2×C42×C19C2311yescharacteristic
32C2×(C2×D19)⋊C4—21no—
33C2×(C2×D19)⋊C4—21no—
34C2×(C2×D19)⋊C4—21no—
35C2×(C2×D19)⋊C4—21no—
36C2×(C2×D19)⋊C4—21no—
37C2×(C2×D19)⋊C4—21no—
38C2×C4⋊Dic19C2×C411yescharacteristic
39C2×C4⋊Dic19C2×C411yescharacteristic
40C2×C4⋊Dic19C2×C411yescharacteristic
41C2×Dic19⋊C4—21no—
42C2×Dic19⋊C4—21no—
43C2×Dic19⋊C4—21no—
44C22×C19⋊C8—22no—
45#10597322—42no—
46#10597322—42no—
47C19×C4⋊C8—42no—
48C19⋊#95—21no—
49C19⋊#95—21no—
50C19⋊#95—21no—
51C4⋊(C19⋊C8)—42no—
52C23×D19—21no—
53C22×C4×C19C22⋊C411yescharacteristic
54C22×C4×C19C22⋊C411yescharacteristic
55C22×C4×C19C22⋊C411yescharacteristic
56C22×C4×C19C22⋊C411yescharacteristic
57C22×C4×C19C22×C411yescharacteristic
58C22×C4×C19C2×D411yescharacteristic
59C22×C4×C19C2×D411yescharacteristic
60C22×Dic19—21no—
61C22×Dic19—21no—
62C22×Dic19—21no—
63C2×D76—22no—
64C2×D76—41no—
65C2×D76—41no—
66C2×C8×C19—42no—
67C2×C8×C19—42no—
68C2×C8×C19—42no—
69C42×C19—22no—
70C42×C19—21no—
71C42×C19—21no—
72C42×C19—41no—
73C42×C19—41no—
74C42×C19—41no—
75C42×C19—41no—
76C42×C19D812yes—
77C42×C19SD1612yes—
78(C2×D19)⋊C4—42no—
79(C2×D19)⋊C4—42no—
80(C2×D19)⋊C4—42no—
81(C2×D19)⋊C4—42no—
82(C2×D19)⋊C4—41no—
83(C2×D19)⋊C4—41no—
84(C2×D19)⋊C4—41no—
85(C2×D19)⋊C4—41no—
86C4⋊Dic19—22no—
87C4⋊Dic19—41no—
88C4⋊Dic19—41no—
89Dic19⋊C4—42no—
90Dic19⋊C4—42no—
91Dic19⋊C4—41no—
92Dic19⋊C4—41no—
93C2×C19⋊C8—42no—
94C2×C19⋊C8—42no—
95C2×C19⋊C8—42no—
96#7732—191nomaximal, Sylow
97C23×C19C2×C22⋊C411yescharacteristic
98C22×D19—41no—
99C22×D19—41no—
100C22×D19—41no—
101C22×D19—41no—
102C22×D19—41no—
103C22×D19—41no—
104C22×D19—41no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19#10212yes—
122C2×C4×C19#10212yes—
123C2×C4×C19#13112yes—
124C2×C4×C19C2×D811yescharacteristic
125C2×C4×C19C2×SD1611yescharacteristic
126C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C19#13711yescharacteristic
128C2×Dic19—41no—
129C2×Dic19—41no—
130C2×Dic19—41no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—41no—
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137D76—82no—
138C8×C19—82no—
139C19⋊C8—82no—
140#2860—191no—
141#1831—191no—
142#1831D1911yescharacteristic, complemented
143#1271—192no—
144#1270—192no—
145C22×C19#40811yescharacteristic
146C22×C19#41011yescharacteristic
147C22×C19#41311yescharacteristic
148C22×C19C2×#10211yescharacteristic
149C22×C19#41711yescharacteristic
150C22×C19#42111yescharacteristic
151C22×C19#42111yescharacteristic
152C2×D19—81no—
153C2×D19—81no—
154C2×D19—81no—
155C2×D19—81no—
156C2×D19—81no—
157C2×D19—81no—
158C2×D19—81no—
159C4×C19—22no—
160C4×C19—22no—
161C4×C19—22no—
162C4×C19—21no—
163C4×C19—21no—
164C4×C19—21no—
165C4×C19—21no—
166C4×C19—41no—
167C4×C19—41no—
168Dic19—81no—
169Dic19—81no—
170Dic19—81no—
171C2×#126—381no—
172C2×C4⋊C8—21no—
173C2×C4⋊C8—381no—
174#390—191no—
175#390—191no—
176#390—191no—
177#389—191no—
178#389—191no—
179#389—191no—
180#388—381no—
181#388—381no—
182#388—381no—
183C43C2×D1911yescharacteristic
184#336—21no—
185#336—192no—
186#336—381no—
187#336C2×D1912yes—
188C2×C19#147311yescharacteristic
189C2×C19#148011yescharacteristic
190C2×C19#149511yescharacteristic
191C2×C19#151211yescharacteristic
192C2×C19#151711yescharacteristic
193C2×C19#153511yescharacteristic
194C2×C19#154711yescharacteristic
195D19—161no—
196C22×D4—191no—
197C22×C8—22no—
198C22×C8—382no—
199#126—762no—
200#126—762no—
201C2×C4⋊C4—191no—
202C2×C4⋊C4—191no—
203C2×C4⋊C4—191no—
204C2×C4⋊C4—381no—
205C2×C4⋊C4—381no—
206C2×C4⋊C4—381no—
207C2×C22⋊C4—381no—
208C2×C22⋊C4—381no—
209C2×C22⋊C4—381no—
210C2×C22⋊C4—381no—
211C2×C22⋊C4—381no—
212C2×C22⋊C4—381no—
213C2×C42C4×D1911yescharacteristic
214C2×C42C4×D1911yescharacteristic
215C2×C42D7611yescharacteristic
216C2×C42D7611yescharacteristic
217C2×C42C22⋊D1911yescharacteristic
218C2×C42C22⋊D1911yescharacteristic
219C2×C42C22×D1911yescharacteristic
220C4⋊C8—42no—
221C4⋊C8—762no—
222#95—381no—
223#95—381no—
224#95—381no—
225C19#773211yescharacteristic, complemented, Sylow
226C24—381no—
227C2×D4—382no—
228C2×D4—761no—
229C2×D4—761no—
230C22×C4—381no—
231C22×C4—381no—
232C22×C4—381no—
233C22×C4(C2×D19)⋊C411yescharacteristic
234C22×C4(C2×D19)⋊C411yescharacteristic
235C22×C4(C2×D19)⋊C411yescharacteristic
236C22×C4(C2×D19)⋊C411yescharacteristic
237C22×C4C2×C4×D1911yescharacteristic
238C22×C4C2×D7611yescharacteristic
239C22×C4C2×C22⋊D1911yescharacteristic
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—762no—
244C2×C8—762no—
245C2×C8—762no—
246C4⋊C4—382no—
247C4⋊C4—761no—
248C4⋊C4—761no—
249C4⋊C4—762no—
250C4⋊C4—762no—
251C4⋊C4—761no—
252C4⋊C4—761no—
253C22⋊C4—762no—
254C22⋊C4—762no—
255C22⋊C4—761no—
256C22⋊C4—761no—
257C22⋊C4—762no—
258C22⋊C4—762no—
259C22⋊C4—761no—
260C22⋊C4—761no—
261C42—21no—
262C42—21no—
263C42—22no—
264C42—41no—
265C42—41no—
266C42—41no—
267C42—41no—
268C42#6451612yes—
269C42D15212yes—
270C23—761no—
271C23—761no—
272C23—761no—
273C23—761no—
274C23—761no—
275C23—761no—
276C23—761no—
277C23C2×(C2×D19)⋊C411yescharacteristic
278D4—1522no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—761no—
296C2×C4—761no—
297C2×C4—761no—
298C2×C4—761no—
299C2×C4—761no—
300C2×C4—761no—
301C2×C4—761no—
302C2×C4—761no—
303C2×C4—761no—
304C2×C4#1059727812yes—
305C2×C4#1059727812yes—
306C2×C4C2×#6451611yescharacteristic
307C2×C4C2×D15211yescharacteristic
308C2×C4#1059735312yes—
309C2×C4#1059737811yescharacteristic
310C2×C4#1059738811yescharacteristic
311C8—82no—
312C8—1522no—
313C22—1521no—
314C22—1521no—
315C22—1521no—
316C22—1521no—
317C22—1521no—
318C22—1521no—
319C22—1521no—
320C22#1192651211yescharacteristic
321C22#1192651711yescharacteristic
322C22#1192652611yescharacteristic
323C22C2×#1059727811yescharacteristic
324C22#1192654311yescharacteristic
325C22#1192656011yescharacteristic
326C22#1192656211yescharacteristic
327C4—22no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—22no—
333C4—22no—
334C4—41no—
335C4—41no—
336C4—1521no—
337C4—1521no—
338C4—1521no—
339C2—3041no—
340C2#1456200511yescharacteristic
341C2#1456203511yescharacteristic
342C2#1456209811yescharacteristic
343C2#1456217111yescharacteristic
344C2#1456219611yescharacteristic
345C2#1456226711yescharacteristic
346C2#1456231011yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1831C2
socleC23×C19C2×C22⋊C4
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenter#1831D19
hypocenterC19#7732
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C43 ◁ #1831

Complements

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

NH ≅ G/Ntype
2. #14563752C2semidirect
3. #14561457C2semidirect
5. C19×#1831C2semidirect
142. #1831D19semidirect
225. C19#7732semidirect

Maximal subgroups

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

subgroupindex
#145720022
#145637522
#145614572
#145614552
C19×#18312
#773219