Finite Group Databasebeta

← #18071157

Subgroups — #18071157

Order 4864.

414 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14563778C211yesmaximal, characteristic, complemented
2#14563752C211yesmaximal, characteristic, complemented
3#14561461C212yesmaximal, complemented
4#14561456C212yesmaximal
5C19×#2861C211yesmaximal, characteristic
6C2×C4⋊(C19⋊C8)—21no—
7#11926299—21no—
8#11926299—21no—
9#11926299—21no—
10#11926299C2212yes—
11#11926299C2212yes—
12C2×C19×#125C411yescharacteristic
13C2×C19×#124C411yescharacteristic
14C19×#391C411yescharacteristic
15C19×#391C2211yescharacteristic
16C19×#390C411yescharacteristic
17C19×#390C2211yescharacteristic
18C19×#388—21no—
19C19×#388—21no—
20C19×#388—21no—
21C19×#388—21no—
22C43×C19C2211yescharacteristic
23C22×Q8×C19C2×C411yescharacteristic
24C22×D4×C19C2×C411yescharacteristic
25C19×#125—42no—
26C19×#124—42no—
27C2×C4⋊C4×C19—21no—
28C2×C4⋊C4×C19—21no—
29C2×C4⋊C4×C19C2×C411yescharacteristic
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C22⋊C4×C19—21no—
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×C42×C19C2×C411yescharacteristic
38C2×C42×C19C2×C411yescharacteristic
39C2×C42×C19D411yescharacteristic
40C2×C42×C19D411yescharacteristic
41C2×C42×C19D411yescharacteristic
42C2×C42×C19D411yescharacteristic
43C2×C42×C19C2311yescharacteristic
44C22×C19⋊C8—22no—
45C22×C19⋊C8—22no—
46C19×#95—21no—
47C19×#95—21no—
48C19×#95—21no—
49C19×#95—21no—
50C4⋊(C19⋊C8)—42no—
51C24×C19—21no—
52C2×Q8×C19—22no—
53C2×Q8×C19—41no—
54C2×Q8×C19—41no—
55C2×D4×C19—22no—
56C2×D4×C19—41no—
57C2×D4×C19—41no—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19C22⋊C411yescharacteristic
62C22×C4×C19C22⋊C411yescharacteristic
63C22×C4×C19C22⋊C411yescharacteristic
64C22×C4×C19C22⋊C411yescharacteristic
65C22×C4×C19C22×C411yescharacteristic
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19C2×D411yescharacteristic
68C4⋊C4×C19—41no—
69C4⋊C4×C19—41no—
70C4⋊C4×C19—42no—
71C4⋊C4×C19—42no—
72C22⋊C4×C19—42no—
73C22⋊C4×C19—42no—
74C22⋊C4×C19—42no—
75C22⋊C4×C19—42no—
76C22⋊C4×C19—42no—
77C22⋊C4×C19—41no—
78C22⋊C4×C19—41no—
79C42×C19—22no—
80C42×C19—22no—
81C42×C19—22no—
82C42×C19—21no—
83C42×C19—21no—
84C42×C19—41no—
85C42×C19—41no—
86C42×C19—41no—
87C2×C19⋊C8—42no—
88C2×C19⋊C8—42no—
89C2×C19⋊C8—42no—
90C2×C19⋊C8—42no—
91C2×C19⋊C8—42no—
92C2×C19⋊C8—42no—
93#7716—191nomaximal, Sylow
94C23×C19—41no—
95C23×C19—41no—
96C23×C19—41no—
97C23×C19—41no—
98C23×C19—41no—
99C23×C19—41no—
100C23×C19—41no—
101C23×C19C2×C22⋊C411yescharacteristic
102Q8×C19—82no—
103D4×C19—82no—
104C2×C4×C19—21no—
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—41no—
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#10012yes—
131C2×C4×C19#13112yes—
132C2×C4×C19#13512yes—
133C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C19#13711yescharacteristic
135C19⋊C8—82no—
136C19⋊C8—82no—
137#2861D1911yescharacteristic
138#1839—191no—
139#1831—191no—
140#1272—192no—
141#1270—192no—
142C22×C19—81no—
143C22×C19—81no—
144C22×C19—81no—
145C22×C19—81no—
146C22×C19—81no—
147C22×C19—81no—
148C22×C19—81no—
149C22×C19#40811yescharacteristic
150C22×C19#41011yescharacteristic
151C22×C19C2×#10011yescharacteristic
152C22×C19#41611yescharacteristic
153C22×C19#41711yescharacteristic
154C22×C19#42111yescharacteristic
155C22×C19#42111yescharacteristic
156C4×C19—22no—
157C4×C19—22no—
158C4×C19—21no—
159C4×C19—21no—
160C4×C19—22no—
161C4×C19—41no—
162C4×C19—41no—
163C4×C19—41no—
164C4×C19—81no—
165C4×C19—81no—
166C4×C19—81no—
167C2×#125Dic1911yescharacteristic
168C2×#124Dic1911yescharacteristic
169C2×C4⋊C8—381no—
170#391Dic1911yescharacteristic
171#391C2×D1911yescharacteristic
172#390Dic1911yescharacteristic
173#390C2×D1911yescharacteristic
174#388—21no—
175#388—21no—
176#388—21no—
177#388—21no—
178C43C2×D1911yescharacteristic
179#336—192no—
180#336—192no—
181#336—381no—
182#336—381no—
183#336—381no—
184C2×C19—161no—
185C2×C19#146911yescharacteristic
186C2×C19#148211yescharacteristic
187C2×C19#149511yescharacteristic
188C2×C19#151211yescharacteristic
189C2×C19#152111yescharacteristic
190C2×C19#153611yescharacteristic
191C2×C19#155111yescharacteristic
192C22×Q8C2×Dic1911yescharacteristic
193C22×D4C2×Dic1911yescharacteristic
194C22×C8—382no—
195C22×C8—382no—
196#125—42no—
197#124—42no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4C2×Dic1911yescharacteristic
201C2×C4⋊C4C2×Dic1911yescharacteristic
202C2×C22⋊C4—21no—
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C42C2×Dic1911yescharacteristic
209C2×C42C2×Dic1911yescharacteristic
210C2×C42C22⋊D1911yescharacteristic
211C2×C42C22⋊D1911yescharacteristic
212C2×C42C22⋊D1911yescharacteristic
213C2×C42C22⋊D1911yescharacteristic
214C2×C42C22×D1911yescharacteristic
215C4⋊C8—762no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220C19#771611yescharacteristic, complemented, Sylow
221C24—21no—
222C2×Q8—22no—
223C2×Q8—41no—
224C2×Q8—41no—
225C2×D4—22no—
226C2×D4—41no—
227C2×D4—41no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4C22⋊Dic1911yescharacteristic
232C22×C4C22⋊Dic1911yescharacteristic
233C22×C4C22⋊Dic1911yescharacteristic
234C22×C4C22⋊Dic1911yescharacteristic
235C22×C4C22×Dic1911yescharacteristic
236C22×C4C2×C22⋊D1911yescharacteristic
237C22×C4C2×C22⋊D1911yescharacteristic
238C2×C8—762no—
239C2×C8—762no—
240C2×C8—762no—
241C2×C8—762no—
242C2×C8—762no—
243C2×C8—762no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—41no—
252C22⋊C4—42no—
253C22⋊C4—41no—
254C22⋊C4—42no—
255C42—22no—
256C42—21no—
257C42—22no—
258C42—21no—
259C42—22no—
260C42—41no—
261C42—41no—
262C42—41no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23C2×C22⋊Dic1911yescharacteristic
271Q8—82no—
272D4—82no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
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—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4#1059729012yes—
300C2×C4#1059739412yes—
301C2×C4#1059739511yescharacteristic
302C2×C4#1059739612yes—
303C2×C4#1059739711yescharacteristic
304C8—1522no—
305C8—1522no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22—81no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22#1192651111yescharacteristic
314C22#1192651811yescharacteristic
315C22C2×#1059729011yescharacteristic
316C22#1192654011yescharacteristic
317C22#1192654511yescharacteristic
318C22#1192656111yescharacteristic
319C22#1192656111yescharacteristic
320C4—22no—
321C4—21no—
322C4—21no—
323C4—22no—
324C4—22no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—81no—
331C2—161no—
332C2#1456198711yescharacteristic
333C2#1456204311yescharacteristic
334C2#1456210011yescharacteristic
335C2#1456217311yescharacteristic
336C2#1456221211yescharacteristic
337C2#1456227011yescharacteristic
338C2#1456233011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2861C2
socleC23×C19C2×C22⋊C4
prime radicalC22×D4×C19C2×C4
cosocleC2×C42×C19C23
hypercenter#2861D19
hypocenterC19#7716
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C43 ◁ #2861

Complements

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

NH ≅ G/Ntype
1. #14563778C2semidirect
2. #14563752C2semidirect
3. #14561461C2semidirect
220. C19#7716semidirect

Maximal subgroups

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

subgroupindex
#145637782
#145637522
#145614612
#145614562
C19×#28612
#771619