Finite Group Databasebeta

← #18071229

Subgroups — #18071229

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#14563752C211yesmaximal, characteristic, complemented
2#14563752C211yesmaximal, characteristic, complemented
3#14561458C212yesmaximal, complemented
4#14561456C212yesmaximal
5C19×#2860C211yesmaximal, characteristic
6C2×C4⋊(C19⋊C8)—21no—
7C2×C4⋊(C19⋊C8)—21no—
8#11926299—21no—
9#11926299—21no—
10#11926299C2212yes—
11#11926299C2212yes—
12C2×C19×#126—21no—
13C19×#390C411yescharacteristic
14C19×#390C411yescharacteristic
15C19×#390C2211yescharacteristic
16C19×#389C411yescharacteristic
17C19×#389C411yescharacteristic
18C19×#389C2211yescharacteristic
19C19×#388—21no—
20C19×#388—21no—
21C19×#388—21no—
22C43×C19C2211yescharacteristic
23C22×D4×C19C2×C411yescharacteristic
24C19×#126—42no—
25C19×#126—42no—
26C2×C4⋊C4×C19—21no—
27C2×C4⋊C4×C19—21no—
28C2×C4⋊C4×C19—21no—
29C2×C4⋊C4×C19C2×C411yescharacteristic
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C4⋊C4×C19C2×C411yescharacteristic
32C2×C22⋊C4×C19—21no—
33C2×C22⋊C4×C19—21no—
34C2×C22⋊C4×C19—21no—
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—21no—
37C2×C22⋊C4×C19—21no—
38C2×C42×C19C2×C411yescharacteristic
39C2×C42×C19C2×C411yescharacteristic
40C2×C42×C19D411yescharacteristic
41C2×C42×C19D411yescharacteristic
42C2×C42×C19D411yescharacteristic
43C2×C42×C19D411yescharacteristic
44C2×C42×C19C2311yescharacteristic
45C22×C19⋊C8—22no—
46C22×C19⋊C8—22no—
47C19×#95—21no—
48C19×#95—21no—
49C19×#95—21no—
50C4⋊(C19⋊C8)—42no—
51C4⋊(C19⋊C8)—42no—
52C24×C19—21no—
53C2×D4×C19—22no—
54C2×D4×C19—41no—
55C2×D4×C19—41no—
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—21no—
59C22×C4×C19C22⋊C411yescharacteristic
60C22×C4×C19C22⋊C411yescharacteristic
61C22×C4×C19C22⋊C411yescharacteristic
62C22×C4×C19C22⋊C411yescharacteristic
63C22×C4×C19C22×C411yescharacteristic
64C22×C4×C19C2×D411yescharacteristic
65C22×C4×C19C2×D411yescharacteristic
66C4⋊C4×C19—22no—
67C4⋊C4×C19—41no—
68C4⋊C4×C19—41no—
69C4⋊C4×C19—42no—
70C4⋊C4×C19—42no—
71C4⋊C4×C19—41no—
72C4⋊C4×C19—41no—
73C22⋊C4×C19—42no—
74C22⋊C4×C19—42no—
75C22⋊C4×C19—42no—
76C22⋊C4×C19—42no—
77C22⋊C4×C19—41no—
78C22⋊C4×C19—41no—
79C22⋊C4×C19—41no—
80C22⋊C4×C19—41no—
81C42×C19—22no—
82C42×C19—21no—
83C42×C19—21no—
84C42×C19—41no—
85C42×C19—41no—
86C42×C19—41no—
87C42×C19—41no—
88C42×C19D812yes—
89C42×C19SD1612yes—
90C2×C19⋊C8—42no—
91C2×C19⋊C8—42no—
92C2×C19⋊C8—42no—
93C2×C19⋊C8—42no—
94C2×C19⋊C8—42no—
95C2×C19⋊C8—42no—
96#7732—191nomaximal, Sylow
97C23×C19—41no—
98C23×C19—41no—
99C23×C19—41no—
100C23×C19—41no—
101C23×C19—41no—
102C23×C19—41no—
103C23×C19—41no—
104C23×C19C2×C22⋊C411yescharacteristic
105D4×C19—82no—
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—21no—
122C2×C4×C19—41no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19#10212yes—
132C2×C4×C19#10212yes—
133C2×C4×C19#13112yes—
134C2×C4×C19C2×D811yescharacteristic
135C2×C4×C19C2×SD1611yescharacteristic
136C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C19#13711yescharacteristic
138C19⋊C8—82no—
139C19⋊C8—82no—
140#2860D1911yescharacteristic
141#1831—191no—
142#1831—191no—
143#1271—192no—
144#1270—192no—
145C22×C19—81no—
146C22×C19—81no—
147C22×C19—81no—
148C22×C19—81no—
149C22×C19—81no—
150C22×C19—81no—
151C22×C19—81no—
152C22×C19#40811yescharacteristic
153C22×C19#41011yescharacteristic
154C22×C19#41311yescharacteristic
155C22×C19C2×#10211yescharacteristic
156C22×C19#41711yescharacteristic
157C22×C19#42111yescharacteristic
158C22×C19#42111yescharacteristic
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—
168C4×C19—81no—
169C4×C19—81no—
170C4×C19—81no—
171C2×#126—21no—
172C2×C4⋊C8—381no—
173C2×C4⋊C8—381no—
174#390Dic1911yescharacteristic
175#390Dic1911yescharacteristic
176#390C2×D1911yescharacteristic
177#389Dic1911yescharacteristic
178#389Dic1911yescharacteristic
179#389C2×D1911yescharacteristic
180#388—21no—
181#388—21no—
182#388—21no—
183C43C2×D1911yescharacteristic
184#336—192no—
185#336—192no—
186#336—381no—
187#336—381no—
188C2×C19—161no—
189C2×C19#147311yescharacteristic
190C2×C19#148011yescharacteristic
191C2×C19#149511yescharacteristic
192C2×C19#151211yescharacteristic
193C2×C19#151711yescharacteristic
194C2×C19#153511yescharacteristic
195C2×C19#154711yescharacteristic
196C22×D4C2×Dic1911yescharacteristic
197C22×C8—382no—
198C22×C8—382no—
199#126—42no—
200#126—42no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4C2×Dic1911yescharacteristic
205C2×C4⋊C4C2×Dic1911yescharacteristic
206C2×C4⋊C4C2×Dic1911yescharacteristic
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C42C2×Dic1911yescharacteristic
214C2×C42C2×Dic1911yescharacteristic
215C2×C42C22⋊D1911yescharacteristic
216C2×C42C22⋊D1911yescharacteristic
217C2×C42C22⋊D1911yescharacteristic
218C2×C42C22⋊D1911yescharacteristic
219C2×C42C22×D1911yescharacteristic
220C4⋊C8—762no—
221C4⋊C8—762no—
222#95—21no—
223#95—21no—
224#95—21no—
225C19#773211yescharacteristic, complemented, Sylow
226C24—21no—
227C2×D4—22no—
228C2×D4—41no—
229C2×D4—41no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4C22⋊Dic1911yescharacteristic
234C22×C4C22⋊Dic1911yescharacteristic
235C22×C4C22⋊Dic1911yescharacteristic
236C22×C4C22⋊Dic1911yescharacteristic
237C22×C4C22×Dic1911yescharacteristic
238C22×C4C2×C22⋊D1911yescharacteristic
239C22×C4C2×C22⋊D1911yescharacteristic
240C2×C8—762no—
241C2×C8—762no—
242C2×C8—762no—
243C2×C8—762no—
244C2×C8—762no—
245C2×C8—762no—
246C4⋊C4—22no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C42—22no—
262C42—21no—
263C42—21no—
264C42—41no—
265C42—41no—
266C42—41no—
267C42—41no—
268C42#6452512yes—
269C42#6452612yes—
270C23—41no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23C2×C22⋊Dic1911yescharacteristic
278D4—82no—
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—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4#1059728912yes—
305C2×C4#1059728912yes—
306C2×C4C2×#6452511yescharacteristic
307C2×C4C2×#6452611yescharacteristic
308C2×C4#1059739412yes—
309C2×C4#1059739511yescharacteristic
310C2×C4#1059739711yescharacteristic
311C8—1522no—
312C8—1522no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22#1192651111yescharacteristic
321C22#1192651811yescharacteristic
322C22#1192652811yescharacteristic
323C22C2×#1059728911yescharacteristic
324C22#1192654511yescharacteristic
325C22#1192656111yescharacteristic
326C22#1192656111yescharacteristic
327C4—22no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—22no—
333C4—22no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C2—161no—
340C2#1456200411yescharacteristic
341C2#1456203411yescharacteristic
342C2#1456210011yescharacteristic
343C2#1456217311yescharacteristic
344C2#1456219511yescharacteristic
345C2#1456226611yescharacteristic
346C2#1456231211yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2860C2
socleC23×C19C2×C22⋊C4
prime radicalC22×D4×C19C2×C4
cosocleC2×C42×C19C23
hypercenter#2860D19
hypocenterC19#7732
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C43 ◁ #2860

Complements

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

NH ≅ G/Ntype
1. #14563752C2semidirect
2. #14563752C2semidirect
3. #14561458C2semidirect
225. C19#7732semidirect

Maximal subgroups

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

subgroupindex
#145637522
#145614582
#145614562
C19×#28602
#773219