Finite Group Databasebeta

← #18073087

Subgroups — #18073087

Order 4864.

582 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
1C2×D4×C19⋊C8C211yesmaximal, characteristic
2#14563413C212yesmaximal, complemented
3#14561953C211yesmaximal, characteristic
4#14561483C212yesmaximal, complemented
5C4×C19×#99C211yesmaximal, characteristic
6C23×C19⋊C8C411yescharacteristic, complemented
7C23×C19⋊C8C2211yescharacteristic
8D4×C19⋊C8—22no—
9D4×C19⋊C8—22no—
10C2×C4⋊(C19⋊C8)C411yescharacteristic, complemented
11C2×C22⋊(C19⋊C8)C411yescharacteristic, complemented
12C2×C22⋊(C19⋊C8)C2211yescharacteristic
13C2×C22⋊(C19⋊C8)C2212yes—
14C2×#10597260—22no—
15C2×C4×C19⋊C8C411yescharacteristic, complemented
16#11926299—22no—
17#11926270C412yescomplemented
18#11926268C412yescomplemented
19C2×C4×D4×C19C2211yescharacteristic
20C2×C19×#99C412yes—
21C4×C22⋊C4×C19C2212yes—
22C19×#342C412yes—
23C22×D4×C19C2×C411yescharacteristic
24C23×C4×C19C2×C411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C4×D4×C19—22no—
27C4×D4×C19—22no—
28C2×C4⋊C4×C19C2×C411yescharacteristic
29C2×C22⋊C4×C19C2×C414yes—
30C2×C22⋊C4×C19C2×C411yescharacteristic
31C2×C22⋊C4×C19C2×C411yescharacteristic
32C2×C42×C19—22no—
33C2×C42×C19C2×C411yescharacteristic
34C22×C19⋊C8—22no—
35C22×C19⋊C8—21no—
36C22×C19⋊C8—21no—
37C22×C19⋊C8—42no—
38C22×C19⋊C8—42no—
39C22×C19⋊C8C2×C411yescharacteristic
40C22×C19⋊C8C2×C411yescharacteristic
41C22×C19⋊C8C2×C411yescharacteristic
42C22×C19⋊C8C2×C411yescharacteristic
43C22×C19⋊C8D412yes—
44C22×C19⋊C8D412yes—
45C19×#99—24no—
46C19×#95—22no—
47C22⋊(C19⋊C8)—22no—
48C22⋊(C19⋊C8)—22no—
49C22⋊(C19⋊C8)—22no—
50C22⋊(C19⋊C8)C2×C414yes—
51C4⋊(C19⋊C8)—22no—
52#10597260—44no—
53C4×C19⋊C8—21no—
54C4×C19⋊C8—21no—
55C24×C19C4211yescharacteristic
56C24×C19C22×C411yescharacteristic
57C2×D4×C19—22no—
58C2×D4×C19—22no—
59C2×D4×C19M1614yes—
60C22×C4×C19—21no—
61C22×C4×C19—21no—
62C22×C4×C19—24no—
63C22×C4×C19—41no—
64C22×C4×C19—41no—
65C22×C4×C19—41no—
66C22×C4×C19—41no—
67C22×C4×C19C4211yescharacteristic
68C22×C4×C19C4211yescharacteristic
69C22×C4×C19C4211yescharacteristic
70C22×C4×C19C22×C411yescharacteristic
71C22×C4×C19C22×C411yescharacteristic
72C22×C4×C19C2×D412yes—
73C22×C4×C19#4112yes—
74C4⋊C4×C19—22no—
75C22⋊C4×C19—22no—
76C22⋊C4×C19—22no—
77C22⋊C4×C19—24no—
78C22⋊C4×C19—24no—
79C42×C19—21no—
80C42×C19—21no—
81C42×C19—42no—
82C42×C19—42no—
83C2×C19⋊C8—24no—
84C2×C19⋊C8—22no—
85C2×C19⋊C8—21no—
86C2×C19⋊C8—21no—
87C2×C19⋊C8—24no—
88C2×C19⋊C8—41no—
89C2×C19⋊C8—42no—
90C2×C19⋊C8—42no—
91C2×C19⋊C8—42no—
92C2×C19⋊C8—42no—
93C2×C19⋊C8—42no—
94C2×C19⋊C8—41no—
95C2×C19⋊C8—41no—
96C2×C19⋊C8C22⋊C411yescharacteristic
97C2×C19⋊C8C22⋊C412yes—
98C2×C19⋊C8C22⋊C411yescharacteristic
99#8160—191nomaximal, Sylow
100C23×C19—21no—
101C23×C19—21no—
102C23×C19—41no—
103C23×C19—41no—
104C23×C19—41no—
105C23×C19—41no—
106C23×C19#9712yescomplemented
107C23×C19C2×C4211yescharacteristic
108C23×C19C4×D412yes—
109C23×C19C2×M1612yes—
110C23×C19#13112yes—
111D4×C19—28no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—22no—
115C2×C4×C19—21no—
116C2×C4×C19—22no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—41no—
121C2×C4×C19—42no—
122C2×C4×C19—42no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—44no—
128C2×C4×C19—44no—
129C2×C4×C19—44no—
130C2×C4×C19#9712yescomplemented
131C2×C4×C19C2×C22⋊C411yescharacteristic
132C2×C4×C19#11711yescharacteristic
133C2×C4×C19C4×D412yes—
134C19⋊C8—21no—
135C19⋊C8—22no—
136C19⋊C8—44no—
137C19⋊C8—41no—
138C19⋊C8—41no—
139C19⋊C8#9912yescomplemented
140C2×C8×D4—191no—
141C4×#99D1911yescharacteristic
142#1752—192no—
143#1459—191no—
144#1282—192no—
145C22×C19—22no—
146C22×C19—21no—
147C22×C19—22no—
148C22×C19—21no—
149C22×C19—22no—
150C22×C19—42no—
151C22×C19—42no—
152C22×C19—42no—
153C22×C19—42no—
154C22×C19—41no—
155C22×C19—41no—
156C22×C19C4×C22⋊C411yescharacteristic
157C22×C19C2×#9711yescharacteristic
158C22×C19#40511yescharacteristic
159C22×C19#43514yes—
160C4×C19—22no—
161C4×C19—22no—
162C4×C19—21no—
163C4×C19—41no—
164C4×C19—41no—
165C4×C19—84no—
166C4×C19C2×#9911yescharacteristic
167C4×C19#41011yescharacteristic
168C23×C8—191no—
169C23×C8—191no—
170C2×C4×D4C2×D1911yescharacteristic
171C8×D4—382no—
172C8×D4—382no—
173C2×C4⋊C8—191no—
174C2×#99Dic1912yes—
175C2×C22⋊C8—192no—
176C2×C22⋊C8—191no—
177C2×C22⋊C8—191no—
178C2×#97—382no—
179C2×C4×C8—191no—
180C4×C22⋊C4C2×D1912yes—
181#342Dic1912yes—
182#336—382no—
183#324—192no—
184#323—192no—
185C2×C19—24no—
186C2×C19—21no—
187C2×C19—21no—
188C2×C19—42no—
189C2×C19#175211yescharacteristic
190C2×C19C4×#9911yescharacteristic
191C2×C19#175711yescharacteristic
192C22×D4C2×Dic1911yescharacteristic
193C23×C4C4×D1911yescharacteristic
194C23×C4C22×D1911yescharacteristic
195C22×C8—191no—
196C22×C8—192no—
197C22×C8—191no—
198C22×C8—192no—
199C22×C8—191no—
200C22×C8—191no—
201C22×C8—381no—
202C22×C8—381no—
203C22×C8—382no—
204C22×C8—762no—
205C22×C8—762no—
206C4×D4—22no—
207C4×D4—22no—
208C2×C4⋊C4C4×D1911yescharacteristic
209C2×C22⋊C4C4×D1911yescharacteristic
210C2×C22⋊C4C2×Dic1914yes—
211C2×C22⋊C4C2×Dic1911yescharacteristic
212C2×C42—22no—
213C2×C42C4×D1911yescharacteristic
214C4⋊C8—382no—
215#99—24no—
216C22⋊C8—194no—
217C22⋊C8—382no—
218C22⋊C8—382no—
219C22⋊C8—382no—
220#97—764no—
221C4×C8—381no—
222C4×C8—381no—
223#95—22no—
224C19#816011yescharacteristic, complemented, Sylow
225C24C4×Dic1911yescharacteristic
226C24C22×Dic1911yescharacteristic
227C2×D4—22no—
228C2×D4—22no—
229C2×D4#6452014yes—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—24no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4C4×Dic1911yescharacteristic
238C22×C4C4×Dic1911yescharacteristic
239C22×C4C4×Dic1911yescharacteristic
240C22×C4C2×C4×D1911yescharacteristic
241C22×C4C2×C4×D1911yescharacteristic
242C22×C4D4×D1912yes—
243C22×C4#6454312yes—
244C2×C8—191no—
245C2×C8—191no—
246C2×C8—192no—
247C2×C8—384no—
248C2×C8—382no—
249C2×C8—381no—
250C2×C8—381no—
251C2×C8—384no—
252C2×C8—762no—
253C2×C8—762no—
254C2×C8—761no—
255C2×C8—762no—
256C2×C8—762no—
257C2×C8—762no—
258C2×C8—761no—
259C2×C8—761no—
260C4⋊C4—22no—
261C22⋊C4—22no—
262C22⋊C4—22no—
263C22⋊C4—24no—
264C22⋊C4—24no—
265C42—21no—
266C42—21no—
267C42—42no—
268C42—42no—
269C23—21no—
270C23—21no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23#1059726012yescomplemented
276C23C2×#6452012yes—
277C23C2×C4×Dic1911yescharacteristic
278C23D4×Dic1912yes—
279C23#1059739412yes—
280D4—28no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4#1059726012yescomplemented
300C2×C4#1059732311yescharacteristic
301C2×C4C22⋊C4×D1911yescharacteristic
302C2×C4(C22⋊D19)⋊C412yes—
303C8—192no—
304C8—381no—
305C8—382no—
306C8—764no—
307C8—761no—
308C8—761no—
309C22—22no—
310C22—21no—
311C22—22no—
312C22—21no—
313C22—22no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—41no—
319C22—41no—
320C22C22⋊C4×Dic1911yescharacteristic
321C22C2×#1059726011yescharacteristic
322C22#1192650011yescharacteristic
323C22#1192661614yes—
324C4—22no—
325C4—22no—
326C4—21no—
327C4—41no—
328C4—41no—
329C4—84no—
330C4#99×D1911yescharacteristic
331C4#1192651611yescharacteristic
332C2—24no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2#1456341311yescharacteristic
337C2#99×Dic1911yescharacteristic
338C2#1456343711yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D19
commutatorC23×C19C2×C42
FrattiniC23×C4C22×D19
FittingC4×C19×#99C2
socleC22×C19C4×C22⋊C4
prime radicalC22×D4×C19C2×C4
cosocleC23×C4×C19C23
hypercenterC4×#99D19
hypocenterC19#8160
LCSG ▷ C23×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #14563413C2semidirect
4. #14561483C2semidirect
6. C23×C19⋊C8C4semidirect
10. C2×C4⋊(C19⋊C8)C4semidirect
11. C2×C22⋊(C19⋊C8)C4semidirect
15. C2×C4×C19⋊C8C4semidirect
17. #11926270C4semidirect
18. #11926268C4semidirect
106. C23×C19#97semidirect
130. C2×C4×C19#97semidirect
139. C19⋊C8#99semidirect
224. C19#8160semidirect
275. C23#10597260semidirect
299. C2×C4#10597260semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C19⋊C82
#145634132
#145619532
#145614832
C4×C19×#992
#816019