Finite Group Databasebeta

← #18072335

Subgroups — #18072335

Order 4864.

608 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926568C211yesmaximal, characteristic
2#14566033C211yesmaximal, characteristic
3#14561494C214yesmaximal, complemented
4C19×#2920C211yesmaximal, characteristic
5C22×#64520—21no—
6#11926568—21no—
7#11926568—21no—
8#11926568C412yescomplemented
9#11926568C2212yes—
10C2×C4⋊(C19⋊C8)—21no—
11C2×C4⋊(C19⋊C8)C412yescomplemented
12#11926412—21no—
13#11926410C2212yes—
14#11926407C412yes—
15#11926404—21no—
16C4×C4⋊Dic19—21no—
17C4×C22⋊Dic19—21no—
18#11926390C412yes—
19C22×C42×C19C2211yescharacteristic
20C19×#432—21no—
21C19×#432—21no—
22C19×#431C412yescomplemented
23C19×#431C2212yes—
24C19×#423—21no—
25C19×#407—21no—
26C4×M16×C19C412yescomplemented
27C23×C4×C19C2×C411yescharacteristic
28C23×C4×C19D411yescharacteristic
29C23×C4×C19D411yescharacteristic
30C2×M16×C19—22no—
31C2×C42×C19C2×C411yescharacteristic
32C2×C42×C19C2×C411yescharacteristic
33C2×C42×C19C2×C411yescharacteristic
34C2×C42×C19C2×C411yescharacteristic
35C2×C42×C19C2×C411yescharacteristic
36C2×C42×C19D411yescharacteristic
37C2×C42×C19D411yescharacteristic
38C2×C42×C19D411yescharacteristic
39C2×C42×C19D411yescharacteristic
40C2×C42×C19Q811yescharacteristic
41C2×C42×C19Q811yescharacteristic
42C2×C42×C19C2311yescharacteristic
43C2×C22⋊Dic19—22no—
44C2×C4⋊Dic19—22no—
45C2×C4×Dic19—22no—
46C2×#64520—22no—
47C2×#64520—22no—
48C2×#64520—44no—
49C22×C19⋊C8—22no—
50C19×C4⋊C8—22no—
51C19×C4⋊C8—22no—
52C19×C22⋊C8—22no—
53C19×C22⋊C8—22no—
54C19×#97—22no—
55C4×C8×C19C2×C414yes—
56C19⋊#95—22no—
57C19⋊#95—22no—
58C19⋊#95—22no—
59C19⋊#95C2×C414yes—
60C4⋊(C19⋊C8)—22no—
61C4⋊(C19⋊C8)—22no—
62C4⋊(C19⋊C8)—22no—
63C4⋊(C19⋊C8)C2×C414yes—
64C24×C19C22⋊C411yescharacteristic
65C22×C4×C19—22no—
66C22×C4×C19—22no—
67C22×C4×C19—42no—
68C22×C4×C19—42no—
69C22×C4×C19C4211yescharacteristic
70C22×C4×C19C4211yescharacteristic
71C22×C4×C19C22⋊C411yescharacteristic
72C22×C4×C19C22⋊C411yescharacteristic
73C22×C4×C19C22⋊C411yescharacteristic
74C22×C4×C19C22⋊C411yescharacteristic
75C22×C4×C19C22⋊C411yescharacteristic
76C22×C4×C19C22⋊C411yescharacteristic
77C22×C4×C19C22⋊C411yescharacteristic
78C22×C4×C19C4⋊C411yescharacteristic
79C22×C4×C19C4⋊C411yescharacteristic
80C22×C4×C19C4⋊C411yescharacteristic
81C22×C4×C19C4⋊C411yescharacteristic
82C22×C4×C19C4⋊C411yescharacteristic
83C22×C4×C19C4⋊C411yescharacteristic
84C22×C4×C19C22×C411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×C4×C19C2×D411yescharacteristic
87C22×Dic19—24no—
88M16×C19—44no—
89C2×C8×C19—24no—
90C42×C19C4211yescharacteristic
91C42×C19C4211yescharacteristic
92C42×C19C22⋊C411yescharacteristic
93C42×C19C22⋊C411yescharacteristic
94C42×C19C22⋊C411yescharacteristic
95C42×C19C22⋊C411yescharacteristic
96C42×C19C4⋊C411yescharacteristic
97C42×C19C4⋊C411yescharacteristic
98C42×C19C4⋊C411yescharacteristic
99C42×C19C4⋊C411yescharacteristic
100C42×C19C4⋊C411yescharacteristic
101C42×C19C4⋊C411yescharacteristic
102C42×C19C22×C411yescharacteristic
103C42×C19C22×C411yescharacteristic
104C42×C19C2×D411yescharacteristic
105C42×C19C2×Q811yescharacteristic
106C22⋊Dic19—44no—
107C4⋊Dic19—42no—
108C4⋊Dic19—42no—
109C4×Dic19—44no—
110#64520—44no—
111#64520—44no—
112C2×C19⋊C8—24no—
113C2×C19⋊C8—44no—
114#7960—191nomaximal, Sylow
115C23×C19—22no—
116C23×C19—22no—
117C23×C19—41no—
118C23×C19#9511yescharacteristic
119C23×C19#9511yescharacteristic
120C23×C19C2×C22⋊C411yescharacteristic
121C2×C4×C19—22no—
122C2×C4×C19—22no—
123C2×C4×C19—22no—
124C2×C4×C19—22no—
125C2×C4×C19—22no—
126C2×C4×C19—22no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—22no—
132C2×C4×C19—22no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19—41no—
140C2×C4×C19#9511yescharacteristic
141C2×C4×C19#9511yescharacteristic
142C2×C4×C19#9511yescharacteristic
143C2×C4×C19#9511yescharacteristic
144C2×C4×C19#9511yescharacteristic
145C2×C4×C19#9511yescharacteristic
146C2×C4×C19C2×C4211yescharacteristic
147C2×C4×C19C2×C22⋊C411yescharacteristic
148C2×C4×C19C2×C22⋊C411yescharacteristic
149C2×C4×C19C2×C4⋊C411yescharacteristic
150C2×C4×C19C2×C4⋊C411yescharacteristic
151C2×C4×C19C2×C4⋊C411yescharacteristic
152C2×C4×C19AGL(1,ℤ/8)12yes—
153C2×C4×C19#13712yes—
154C2×Dic19—44no—
155C2×Dic19—44no—
156C2×Dic19—44no—
157C8×C19—44no—
158C19⋊C8—44no—
159#2920D1911yescharacteristic
160C2×#423—191no—
161#2283—191no—
162#1286—194no—
163C22×C19—21no—
164C22×C19—21no—
165C22×C19—21no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—44no—
171C22×C19#34412yes—
172C22×C19C2×#9511yescharacteristic
173C22×C19#41712yes—
174C4×C19—21no—
175C4×C19—21no—
176C4×C19—21no—
177C4×C19—21no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—21no—
183C4×C19H(3,ℤ/4)12yes—
184C4×C19#41811yescharacteristic
185C4×C19#41911yescharacteristic
186C4×C19#42812yes—
187Dic19—84no—
188C22×M16—381no—
189C22×C42C2×D1911yescharacteristic
190#432—21no—
191#432—21no—
192#431Dic1912yescomplemented
193#431C2×D1912yes—
194#423—21no—
195#423—192no—
196#423—192no—
197#423—381no—
198#423—381no—
199C2×C4⋊C8—192no—
200C2×C4⋊C8—381no—
201#407—21no—
202C4×M16Dic1912yescomplemented
203#383—381no—
204#382—192no—
205#381—192no—
206#380—381no—
207C4×C4⋊C4—381no—
208C4×C22⋊C4—381no—
209#376—192no—
210C2×C19—22no—
211C2×C19—22no—
212C2×C19—41no—
213C2×C19C2×H(3,ℤ/4)11yescharacteristic
214C2×C19#173611yescharacteristic
215C2×C19C2×#34411yescharacteristic
216C23×C4C4×D1911yescharacteristic
217C23×C4D7611yescharacteristic
218C23×C4C22⋊D1911yescharacteristic
219C2×M16—22no—
220C2×M16—382no—
221C2×M16—382no—
222C2×M16—764no—
223C22×C8—382no—
224C2×C4⋊C4—382no—
225C2×C22⋊C4—382no—
226C2×C42—382no—
227C2×C42Dic3811yescharacteristic
228C2×C42Dic3811yescharacteristic
229C2×C42C4×D1911yescharacteristic
230C2×C42C4×D1911yescharacteristic
231C2×C42C4×D1911yescharacteristic
232C2×C42D7611yescharacteristic
233C2×C42C2×Dic1911yescharacteristic
234C2×C42C2×Dic1911yescharacteristic
235C2×C42C22⋊D1911yescharacteristic
236C2×C42C22⋊D1911yescharacteristic
237C2×C42C22⋊D1911yescharacteristic
238C2×C42C22×D1911yescharacteristic
239C4⋊C8—22no—
240C4⋊C8—22no—
241C4⋊C8—194no—
242C4⋊C8—382no—
243C4⋊C8—382no—
244C4⋊C8—382no—
245C22⋊C8—22no—
246C22⋊C8—22no—
247#97—22no—
248C4×C8C2×Dic1914yes—
249#95—194no—
250#95—382no—
251#95—382no—
252#95—382no—
253C19#796011yescharacteristic, complemented, Sylow
254C24(C2×D19)⋊C411yescharacteristic
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—384no—
260C22×C4C4×Dic1911yescharacteristic
261C22×C4C4×Dic1911yescharacteristic
262C22×C4Dic19⋊C411yescharacteristic
263C22×C4Dic19⋊C411yescharacteristic
264C22×C4Dic19⋊C411yescharacteristic
265C22×C4Dic19⋊C411yescharacteristic
266C22×C4C4⋊Dic1911yescharacteristic
267C22×C4C4⋊Dic1911yescharacteristic
268C22×C4(C2×D19)⋊C411yescharacteristic
269C22×C4(C2×D19)⋊C411yescharacteristic
270C22×C4(C2×D19)⋊C411yescharacteristic
271C22×C4(C2×D19)⋊C411yescharacteristic
272C22×C4(C2×D19)⋊C411yescharacteristic
273C22×C4C22⋊Dic1911yescharacteristic
274C22×C4C22⋊Dic1911yescharacteristic
275C22×C4C2×C4×D1911yescharacteristic
276C22×C4C2×D7611yescharacteristic
277C22×C4C2×C22⋊D1911yescharacteristic
278M16—44no—
279M16—764no—
280M16—764no—
281C2×C8—24no—
282C2×C8—384no—
283C2×C8—764no—
284C4⋊C4—762no—
285C4⋊C4—762no—
286C22⋊C4—764no—
287C42—764no—
288C42C4×Dic1911yescharacteristic
289C42C4×Dic1911yescharacteristic
290C42Dic19⋊C411yescharacteristic
291C42Dic19⋊C411yescharacteristic
292C42Dic19⋊C411yescharacteristic
293C42Dic19⋊C411yescharacteristic
294C42C4⋊Dic1911yescharacteristic
295C42C4⋊Dic1911yescharacteristic
296C42(C2×D19)⋊C411yescharacteristic
297C42(C2×D19)⋊C411yescharacteristic
298C42C22⋊Dic1911yescharacteristic
299C42C22⋊Dic1911yescharacteristic
300C42C2×Dic3811yescharacteristic
301C42C2×C4×D1911yescharacteristic
302C42C22×Dic1911yescharacteristic
303C42C2×C22⋊D1911yescharacteristic
304C23—22no—
305C23—22no—
306C23—41no—
307C23C19⋊#9511yescharacteristic
308C23C19⋊#9511yescharacteristic
309C23C2×(C2×D19)⋊C411yescharacteristic
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—764no—
330C2×C4—764no—
331C2×C4—764no—
332C2×C4C19⋊#9511yescharacteristic
333C2×C4C19⋊#9511yescharacteristic
334C2×C4C19⋊#9511yescharacteristic
335C2×C4C19⋊#9511yescharacteristic
336C2×C4C19⋊#9511yescharacteristic
337C2×C4C19⋊#9511yescharacteristic
338C2×C4#1059735412yes—
339C2×C4#1059735512yes—
340C2×C4C2×C4×Dic1911yescharacteristic
341C2×C4C2×Dic19⋊C411yescharacteristic
342C2×C4C2×Dic19⋊C411yescharacteristic
343C2×C4C2×C4⋊Dic1911yescharacteristic
344C2×C4C2×(C2×D19)⋊C411yescharacteristic
345C2×C4C2×C22⋊Dic1911yescharacteristic
346C8—44no—
347C8—764no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—44no—
356C22#1192631512yes—
357C22C2×C19⋊#9511yescharacteristic
358C22#1192654612yes—
359C4—21no—
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—1524no—
369C4#1192630012yes—
370C4#1192655011yescharacteristic
371C4#1192655411yescharacteristic
372C4#1192658612yes—
373C2—22no—
374C2—22no—
375C2—41no—
376C2C2×#1192630011yescharacteristic
377C2#1456335511yescharacteristic
378C2C2×#1192631511yescharacteristic
subgroupG/H
centerC22C2×C19⋊#95
commutatorC2×C4×C19C2×C42
FrattiniC2×C42C22×D19
FittingC19×#2920C2
socleC22×C19C2×#95
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2920D19
hypocenterC19#7960
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
3. #14561494C2semidirect
8. #11926568C4semidirect
11. C2×C4⋊(C19⋊C8)C4semidirect
22. C19×#431C4semidirect
26. C4×M16×C19C4semidirect
192. #431Dic19semidirect
202. C4×M16Dic19semidirect
253. C19#7960semidirect

Maximal subgroups

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

subgroupindex
C2×#119265682
#145660332
#145614942
C19×#29202
#796019