Finite Group Databasebeta

← #18072330

Subgroups — #18072330

Order 4864.

634 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572268C211yesmaximal, characteristic
2#14572268C211yesmaximal, characteristic
3#14561493C214yesmaximal, complemented
4C2×C19×#382C211yesmaximal, characteristic
5#11926601—21no—
6#11926601—21no—
7#11926601—21no—
8#11926601C412yescomplemented
9#11926597—21no—
10#11926597C412yescomplemented
11#11926597C412yescomplemented
12#11926597C2212yes—
13#11926568—21no—
14#11926568C2212yes—
15#11926508—21no—
16#11926508—21no—
17C4×#64520—21no—
18C4×#64520C412yescomplemented
19C22×C4⋊C4×C19—21no—
20C22×C42×C19C2211yescharacteristic
21C19×#382—21no—
22C19×#382—21no—
23C19×#382C412yes—
24C19×#382C2212yes—
25C2×C19×#95—21no—
26C2×C19×#95C412yes—
27C23×C4×C19—22no—
28C23×C4×C19C2×C411yescharacteristic
29C23×C4×C19D411yescharacteristic
30C23×C4×C19D411yescharacteristic
31C2×C4⋊C4×C19—22no—
32C2×C4⋊C4×C19—22no—
33C2×C4⋊C4×C19—44no—
34C2×C42×C19C2×C411yescharacteristic
35C2×C42×C19C2×C411yescharacteristic
36C2×C42×C19C2×C411yescharacteristic
37C2×C42×C19C2×C411yescharacteristic
38C2×C42×C19C2×C411yescharacteristic
39C2×C42×C19D411yescharacteristic
40C2×C42×C19D411yescharacteristic
41C2×C42×C19D411yescharacteristic
42C2×C42×C19D411yescharacteristic
43C2×C42×C19Q811yescharacteristic
44C2×C42×C19Q811yescharacteristic
45C2×C42×C19C2311yescharacteristic
46C2×#64520—22no—
47C2×#64520—22no—
48C19×#95—22no—
49C19×#95—22no—
50C19×#95—22no—
51C19×#95C2×C414yes—
52C22⋊(C19⋊C8)—22no—
53C22⋊(C19⋊C8)—22no—
54C22⋊(C19⋊C8)—22no—
55C22⋊(C19⋊C8)—22no—
56C4⋊(C19⋊C8)—22no—
57C4⋊(C19⋊C8)—22no—
58C4⋊(C19⋊C8)—22no—
59C4⋊(C19⋊C8)C2×C414yescomplemented
60#10597260—22no—
61#10597260—22no—
62C4×C19⋊C8—22no—
63C4×C19⋊C8C2×C414yescomplemented
64C24×C19C22⋊C411yescharacteristic
65C22×C4×C19—22no—
66C22×C4×C19—22no—
67C22×C4×C19—24no—
68C22×C4×C19—42no—
69C22×C4×C19—42no—
70C22×C4×C19—44no—
71C22×C4×C19—44no—
72C22×C4×C19—44no—
73C22×C4×C19C4211yescharacteristic
74C22×C4×C19C4211yescharacteristic
75C22×C4×C19C22⋊C411yescharacteristic
76C22×C4×C19C22⋊C411yescharacteristic
77C22×C4×C19C22⋊C411yescharacteristic
78C22×C4×C19C22⋊C411yescharacteristic
79C22×C4×C19C22⋊C411yescharacteristic
80C22×C4×C19C22⋊C411yescharacteristic
81C22×C4×C19C22⋊C411yescharacteristic
82C22×C4×C19C4⋊C411yescharacteristic
83C22×C4×C19C4⋊C411yescharacteristic
84C22×C4×C19C4⋊C411yescharacteristic
85C22×C4×C19C4⋊C411yescharacteristic
86C22×C4×C19C4⋊C411yescharacteristic
87C22×C4×C19C4⋊C411yescharacteristic
88C22×C4×C19C22×C411yescharacteristic
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C4⋊C4×C19—44no—
92C4⋊C4×C19—44no—
93C42×C19C4211yescharacteristic
94C42×C19C4211yescharacteristic
95C42×C19C22⋊C411yescharacteristic
96C42×C19C22⋊C411yescharacteristic
97C42×C19C22⋊C411yescharacteristic
98C42×C19C22⋊C411yescharacteristic
99C42×C19C4⋊C411yescharacteristic
100C42×C19C4⋊C411yescharacteristic
101C42×C19C4⋊C411yescharacteristic
102C42×C19C4⋊C411yescharacteristic
103C42×C19C4⋊C411yescharacteristic
104C42×C19C4⋊C411yescharacteristic
105C42×C19C22×C411yescharacteristic
106C42×C19C22×C411yescharacteristic
107C42×C19C2×D411yescharacteristic
108C42×C19C2×Q811yescharacteristic
109#64520—44no—
110#64520—42no—
111#64520—42no—
112C2×C19⋊C8—24no—
113C2×C19⋊C8—24no—
114#7959—191nomaximal, Sylow
115C23×C19—22no—
116C23×C19—22no—
117C23×C19—21no—
118C23×C19—21no—
119C23×C19#9511yescharacteristic
120C23×C19#9511yescharacteristic
121C23×C19C2×C22⋊C411yescharacteristic
122C2×C4×C19—22no—
123C2×C4×C19—22no—
124C2×C4×C19—22no—
125C2×C4×C19—22no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—22no—
129C2×C4×C19—22no—
130C2×C4×C19—22no—
131C2×C4×C19—22no—
132C2×C4×C19—41no—
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—44no—
141C2×C4×C19—44no—
142C2×C4×C19—44no—
143C2×C4×C19—88no—
144C2×C4×C19#9511yescharacteristic
145C2×C4×C19#9511yescharacteristic
146C2×C4×C19#9511yescharacteristic
147C2×C4×C19#9511yescharacteristic
148C2×C4×C19#9511yescharacteristic
149C2×C4×C19#9511yescharacteristic
150C2×C4×C19C2×C4211yescharacteristic
151C2×C4×C19C2×C22⋊C411yescharacteristic
152C2×C4×C19C2×C22⋊C411yescharacteristic
153C2×C4×C19C2×C4⋊C411yescharacteristic
154C2×C4×C19C2×C4⋊C411yescharacteristic
155C2×C4×C19C2×C4⋊C411yescharacteristic
156C2×C4×C19AGL(1,ℤ/8)12yes—
157C2×C4×C19#13712yes—
158C19⋊C8—44no—
159C19⋊C8—44no—
160#2920—191no—
161#2920—191no—
162C2×#382D1911yescharacteristic
163#1286—194no—
164C22×C19—24no—
165C22×C19—24no—
166C22×C19—21no—
167C22×C19—21no—
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—21no—
171C22×C19—21no—
172C22×C19H(3,ℤ/4)12yes—
173C22×C19#34412yes—
174C22×C19C2×#9511yescharacteristic
175C22×C19#41811yescharacteristic
176C22×C19#41911yescharacteristic
177C4×C19—21no—
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—21no—
183C4×C19—21no—
184C4×C19—21no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—84no—
188C4×C19#41712yes—
189C4×C19#42812yes—
190C22×C4⋊C4—21no—
191C22×C42C2×D1911yescharacteristic
192#432—192no—
193#432—381no—
194#432—381no—
195#432—381no—
196#431—192no—
197#431—192no—
198#431—192no—
199#431—381no—
200#423—192no—
201#423—381no—
202#407—381no—
203#407—381no—
204C4×M16—192no—
205C4×M16—381no—
206#382—21no—
207#382—21no—
208#382Dic1912yes—
209#382C2×D1912yes—
210C2×#95—21no—
211C2×#95Dic1912yes—
212C2×C19—21no—
213C2×C19—22no—
214C2×C19—22no—
215C2×C19—21no—
216C2×C19C2×H(3,ℤ/4)11yescharacteristic
217C2×C19#173611yescharacteristic
218C2×C19C2×#34411yescharacteristic
219C23×C4—22no—
220C23×C4C2×Dic1911yescharacteristic
221C23×C4C22⋊D1911yescharacteristic
222C23×C4C22⋊D1911yescharacteristic
223C2×M16—382no—
224C2×M16—382no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—44no—
228C2×C42Dic3811yescharacteristic
229C2×C42Dic3811yescharacteristic
230C2×C42C4×D1911yescharacteristic
231C2×C42C4×D1911yescharacteristic
232C2×C42C4×D1911yescharacteristic
233C2×C42C4×D1911yescharacteristic
234C2×C42D7611yescharacteristic
235C2×C42D7611yescharacteristic
236C2×C42C2×Dic1911yescharacteristic
237C2×C42C22⋊D1911yescharacteristic
238C2×C42C22⋊D1911yescharacteristic
239C2×C42C22×D1911yescharacteristic
240C4⋊C8—194no—
241C4⋊C8—382no—
242C4⋊C8—382no—
243C4⋊C8—382no—
244C22⋊C8—382no—
245C22⋊C8—382no—
246C22⋊C8—382no—
247C22⋊C8—382no—
248#97—382no—
249#97—382no—
250C4×C8—194no—
251C4×C8—382no—
252#95—22no—
253#95—22no—
254#95—22no—
255#95C2×Dic1914yes—
256C19#795911yescharacteristic, complemented, Sylow
257C24C22⋊Dic1911yescharacteristic
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—24no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—44no—
264C22×C4—44no—
265C22×C4—44no—
266C22×C4C4×Dic1911yescharacteristic
267C22×C4C4×Dic1911yescharacteristic
268C22×C4Dic19⋊C411yescharacteristic
269C22×C4Dic19⋊C411yescharacteristic
270C22×C4Dic19⋊C411yescharacteristic
271C22×C4Dic19⋊C411yescharacteristic
272C22×C4C4⋊Dic1911yescharacteristic
273C22×C4C4⋊Dic1911yescharacteristic
274C22×C4(C2×D19)⋊C411yescharacteristic
275C22×C4(C2×D19)⋊C411yescharacteristic
276C22×C4(C2×D19)⋊C411yescharacteristic
277C22×C4(C2×D19)⋊C411yescharacteristic
278C22×C4C22⋊Dic1911yescharacteristic
279C22×C4C22⋊Dic1911yescharacteristic
280C22×C4C22⋊Dic1911yescharacteristic
281C22×C4C22×Dic1911yescharacteristic
282C22×C4C2×C22⋊D1911yescharacteristic
283C22×C4C2×C22⋊D1911yescharacteristic
284M16—764no—
285M16—762no—
286M16—762no—
287C2×C8—384no—
288C2×C8—384no—
289C4⋊C4—44no—
290C4⋊C4—44no—
291C42C4×Dic1911yescharacteristic
292C42C4×Dic1911yescharacteristic
293C42Dic19⋊C411yescharacteristic
294C42Dic19⋊C411yescharacteristic
295C42Dic19⋊C411yescharacteristic
296C42Dic19⋊C411yescharacteristic
297C42C4⋊Dic1911yescharacteristic
298C42C4⋊Dic1911yescharacteristic
299C42(C2×D19)⋊C411yescharacteristic
300C42(C2×D19)⋊C411yescharacteristic
301C42(C2×D19)⋊C411yescharacteristic
302C42(C2×D19)⋊C411yescharacteristic
303C42C2×Dic3811yescharacteristic
304C42C2×C4×D1911yescharacteristic
305C42C2×C4×D1911yescharacteristic
306C42C2×D7611yescharacteristic
307C23—21no—
308C23—21no—
309C23—22no—
310C23—22no—
311C23C19⋊#9511yescharacteristic
312C23C19⋊#9511yescharacteristic
313C23C2×C22⋊Dic1911yescharacteristic
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—44no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—88no—
336C2×C4C19⋊#9511yescharacteristic
337C2×C4C19⋊#9511yescharacteristic
338C2×C4C19⋊#9511yescharacteristic
339C2×C4C19⋊#9511yescharacteristic
340C2×C4C19⋊#9511yescharacteristic
341C2×C4C19⋊#9511yescharacteristic
342C2×C4C2×C4×Dic1911yescharacteristic
343C2×C4C2×Dic19⋊C411yescharacteristic
344C2×C4C2×Dic19⋊C411yescharacteristic
345C2×C4C2×C4⋊Dic1911yescharacteristic
346C2×C4C2×(C2×D19)⋊C411yescharacteristic
347C2×C4C2×(C2×D19)⋊C411yescharacteristic
348C2×C4#1059737812yes—
349C2×C4#1059738812yes—
350C8—764no—
351C8—764no—
352C22—24no—
353C22—24no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22#1192630012yes—
361C22#1192631412yes—
362C22C2×C19⋊#9511yescharacteristic
363C22#1192654911yescharacteristic
364C22#1192655311yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—84no—
376C4#1192654312yes—
377C4#1192658412yes—
378C2—21no—
379C2—21no—
380C2—22no—
381C2—22no—
382C2C2×#1192630011yescharacteristic
383C2#1456335411yescharacteristic
384C2C2×#1192631411yescharacteristic
subgroupG/H
centerC22C2×C19⋊#95
commutatorC2×C4×C19C2×C42
FrattiniC2×C42C22×D19
FittingC2×C19×#382C2
socleC22×C19C2×#95
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenterC2×#382D19
hypocenterC19#7959
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
3. #14561493C2semidirect
8. #11926601C4semidirect
10. #11926597C4semidirect
11. #11926597C4semidirect
18. C4×#64520C4semidirect
59. C4⋊(C19⋊C8)C2×C4semidirect
63. C4×C19⋊C8C2×C4semidirect
256. C19#7959semidirect

Maximal subgroups

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

subgroupindex
#145722682
#145614932
C2×C19×#3822
#795919