Finite Group Databasebeta

← #18072175

Subgroups — #18072175

Order 4864.

614 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572268C211yesmaximal, characteristic
2C2×C4×#64520C211yesmaximal, characteristic
3#14561479C214yesmaximal, complemented
4C19×#2920C211yesmaximal, characteristic
5C22×#64520C412yes—
6#11926601—21no—
7#11926601C412yes—
8#11926597—21no—
9#11926597C2212yes—
10#11926568—21no—
11#11926508C412yes—
12C4×#64520—21no—
13C4×#64520—21no—
14C4×#64520—21no—
15C4×#64520—21no—
16C4×#64520—21no—
17C2×#10597260C2212yes—
18C2×C4×C19⋊C8C412yes—
19C22×C42×C19C2211yescharacteristic
20C19×#432—21no—
21C19×#432C412yes—
22C19×#431—21no—
23C19×#431C2212yes—
24C19×#423—21no—
25C19×#407C412yes—
26C4×M16×C19—21no—
27C23×C4×C19C2×C411yescharacteristic
28C23×C4×C19C2×C411yescharacteristic
29C23×C4×C19C2×C411yescharacteristic
30C2×M16×C19—22no—
31C2×C42×C19C2×C411yescharacteristic
32C2×C42×C19C2×C411yescharacteristic
33C2×C42×C19C2×C411yescharacteristic
34C2×C42×C19D411yescharacteristic
35C2×C42×C19D411yescharacteristic
36C2×C42×C19D411yescharacteristic
37C2×C42×C19D411yescharacteristic
38C2×C42×C19D411yescharacteristic
39C2×C42×C19D411yescharacteristic
40C2×C42×C19Q811yescharacteristic
41C2×C42×C19Q811yescharacteristic
42C2×C42×C19C2311yescharacteristic
43C2×#64520—22no—
44C2×#64520—22no—
45C2×#64520—22no—
46C2×#64520—28no—
47C22×C19⋊C8C2×C414yes—
48C19×C4⋊C8—22no—
49C19×C4⋊C8—22no—
50C19×C22⋊C8—22no—
51C19×C22⋊C8C2×C414yes—
52C19×#97—22no—
53C4×C8×C19—22no—
54C22⋊(C19⋊C8)—22no—
55C22⋊(C19⋊C8)C2×C414yes—
56C4⋊(C19⋊C8)—22no—
57C4⋊(C19⋊C8)—22no—
58#10597260—22no—
59#10597260—22no—
60#10597260—22no—
61C4×C19⋊C8—22no—
62C4×C19⋊C8—22no—
63C4×C19⋊C8—22no—
64C24×C19C4211yescharacteristic
65C22×C4×C19—24no—
66C22×C4×C19—42no—
67C22×C4×C19—42no—
68C22×C4×C19C4211yescharacteristic
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×C19C4⋊C411yescharacteristic
78C22×C4×C19C4⋊C411yescharacteristic
79C22×C4×C19C4⋊C411yescharacteristic
80C22×C4×C19C4⋊C411yescharacteristic
81C22×C4×C19C4⋊C411yescharacteristic
82C22×C4×C19C4⋊C411yescharacteristic
83C22×C4×C19C22×C411yescharacteristic
84C22×C4×C19C22×C411yescharacteristic
85C22×C4×C19C22×C411yescharacteristic
86M16×C19—44no—
87C2×C8×C19—24no—
88C42×C19C22⋊C411yescharacteristic
89C42×C19C22⋊C411yescharacteristic
90C42×C19C22⋊C411yescharacteristic
91C42×C19C22⋊C411yescharacteristic
92C42×C19C22⋊C411yescharacteristic
93C42×C19C22⋊C411yescharacteristic
94C42×C19C4⋊C411yescharacteristic
95C42×C19C4⋊C411yescharacteristic
96C42×C19C4⋊C411yescharacteristic
97C42×C19C4⋊C411yescharacteristic
98C42×C19C4⋊C411yescharacteristic
99C42×C19C4⋊C411yescharacteristic
100C42×C19C2×D411yescharacteristic
101C42×C19C2×D411yescharacteristic
102C42×C19C2×D411yescharacteristic
103C42×C19C2×Q811yescharacteristic
104#64520—28no—
105#64520—28no—
106#64520—44no—
107C2×C19⋊C8—24no—
108C2×C19⋊C8—24no—
109C2×C19⋊C8—24no—
110C2×C19⋊C8M1618yescomplemented
111#7920—191nomaximal, Sylow
112C23×C19—22no—
113C23×C19—41no—
114C23×C19—41no—
115C23×C19#9511yescharacteristic
116C23×C19#9511yescharacteristic
117C23×C19C2×C4211yescharacteristic
118C2×C4×C19—22no—
119C2×C4×C19—22no—
120C2×C4×C19—22no—
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—22no—
128C2×C4×C19—22no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19#9511yescharacteristic
136C2×C4×C19#9511yescharacteristic
137C2×C4×C19#9511yescharacteristic
138C2×C4×C19#9511yescharacteristic
139C2×C4×C19#9511yescharacteristic
140C2×C4×C19#9511yescharacteristic
141C2×C4×C19C2×C22⋊C411yescharacteristic
142C2×C4×C19C2×C22⋊C411yescharacteristic
143C2×C4×C19C2×C22⋊C411yescharacteristic
144C2×C4×C19C2×C4⋊C411yescharacteristic
145C2×C4×C19C2×C4⋊C411yescharacteristic
146C2×C4×C19C2×C4⋊C411yescharacteristic
147C2×C4×C19C2×M1614yes—
148C8×C19—44no—
149C19⋊C8—28no—
150C19⋊C8—44no—
151#2920—191no—
152#2920D1911yescharacteristic
153C2×C4×M16—191no—
154#1281—194no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—21no—
159C22×C19—21no—
160C22×C19—21no—
161C22×C19—21no—
162C22×C19—21no—
163C22×C19—44no—
164C22×C19C2×#9511yescharacteristic
165C22×C19C4×M1612yes—
166C4×C19—21no—
167C4×C19—21no—
168C4×C19—21no—
169C4×C19—21no—
170C4×C19—21no—
171C4×C19—21no—
172C4×C19—21no—
173C4×C19—21no—
174C4×C19#34412yes—
175C4×C19#34412yes—
176C4×C19#40712yes—
177C4×C19#42312yes—
178C22×M16—192no—
179C22×C42C2×D1911yescharacteristic
180#432—21no—
181#432—192no—
182#432—381no—
183#432Dic1912yes—
184#431—21no—
185#431—192no—
186#431—381no—
187#431C2×D1912yes—
188#423—21no—
189#423—381no—
190#407—192no—
191#407Dic1912yes—
192C4×M16—21no—
193C4×M16—381no—
194C4×M16—381no—
195C4×M16—381no—
196C4×M16—381no—
197C4×M16—381no—
198C2×#97—192no—
199C2×C4×C8—192no—
200C2×C19—22no—
201C2×C19—41no—
202C2×C19—41no—
203C2×C19#172811yescharacteristic
204C2×C19C2×#34411yescharacteristic
205C2×C19C2×#34411yescharacteristic
206C23×C4C4×D1911yescharacteristic
207C23×C4C4×D1911yescharacteristic
208C23×C4C2×Dic1911yescharacteristic
209C2×M16—22no—
210C2×M16—388no—
211C2×M16—382no—
212C2×M16—382no—
213C2×M16—382no—
214C22×C8—194no—
215C2×C42Dic3811yescharacteristic
216C2×C42Dic3811yescharacteristic
217C2×C42C4×D1911yescharacteristic
218C2×C42C4×D1911yescharacteristic
219C2×C42D7611yescharacteristic
220C2×C42D7611yescharacteristic
221C2×C42C2×Dic1911yescharacteristic
222C2×C42C22⋊D1911yescharacteristic
223C2×C42C22⋊D1911yescharacteristic
224C2×C42C22⋊D1911yescharacteristic
225C2×C42C22⋊D1911yescharacteristic
226C2×C42C22×D1911yescharacteristic
227C4⋊C8—22no—
228C4⋊C8—22no—
229C4⋊C8—382no—
230C4⋊C8—382no—
231C22⋊C8—22no—
232C22⋊C8—194no—
233C22⋊C8—382no—
234C22⋊C8C2×Dic1914yes—
235#97—22no—
236#97—382no—
237#97—382no—
238#97—382no—
239C4×C8—22no—
240C4×C8—382no—
241C4×C8—382no—
242C4×C8—382no—
243C19#792011yescharacteristic, complemented, Sylow
244C24C4×Dic1911yescharacteristic
245C22×C4—24no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4C4×Dic1911yescharacteristic
249C22×C4C4×Dic1911yescharacteristic
250C22×C4C4×Dic1911yescharacteristic
251C22×C4Dic19⋊C411yescharacteristic
252C22×C4Dic19⋊C411yescharacteristic
253C22×C4Dic19⋊C411yescharacteristic
254C22×C4Dic19⋊C411yescharacteristic
255C22×C4C4⋊Dic1911yescharacteristic
256C22×C4C4⋊Dic1911yescharacteristic
257C22×C4(C2×D19)⋊C411yescharacteristic
258C22×C4(C2×D19)⋊C411yescharacteristic
259C22×C4(C2×D19)⋊C411yescharacteristic
260C22×C4(C2×D19)⋊C411yescharacteristic
261C22×C4C22⋊Dic1911yescharacteristic
262C22×C4C22⋊Dic1911yescharacteristic
263C22×C4C2×C4×D1911yescharacteristic
264C22×C4C2×C4×D1911yescharacteristic
265C22×C4C22×Dic1911yescharacteristic
266M16—44no—
267M16—388no—
268M16—388no—
269M16—764no—
270C2×C8—24no—
271C2×C8—198no—
272C2×C8—384no—
273C2×C8—384no—
274C2×C8—384no—
275C42Dic19⋊C411yescharacteristic
276C42Dic19⋊C411yescharacteristic
277C42Dic19⋊C411yescharacteristic
278C42Dic19⋊C411yescharacteristic
279C42C4⋊Dic1911yescharacteristic
280C42C4⋊Dic1911yescharacteristic
281C42(C2×D19)⋊C411yescharacteristic
282C42(C2×D19)⋊C411yescharacteristic
283C42(C2×D19)⋊C411yescharacteristic
284C42(C2×D19)⋊C411yescharacteristic
285C42C22⋊Dic1911yescharacteristic
286C42C22⋊Dic1911yescharacteristic
287C42C2×Dic3811yescharacteristic
288C42C2×D7611yescharacteristic
289C42C2×C22⋊D1911yescharacteristic
290C42C2×C22⋊D1911yescharacteristic
291C23—22no—
292C23—41no—
293C23—41no—
294C23C19⋊#9511yescharacteristic
295C23C19⋊#9511yescharacteristic
296C23C2×C4×Dic1911yescharacteristic
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4C19⋊#9511yescharacteristic
315C2×C4C19⋊#9511yescharacteristic
316C2×C4C19⋊#9511yescharacteristic
317C2×C4C19⋊#9511yescharacteristic
318C2×C4C19⋊#9511yescharacteristic
319C2×C4C19⋊#9511yescharacteristic
320C2×C4M16×D1914yes—
321C2×C4C2×Dic19⋊C411yescharacteristic
322C2×C4C2×Dic19⋊C411yescharacteristic
323C2×C4C2×C4⋊Dic1911yescharacteristic
324C2×C4C2×(C2×D19)⋊C411yescharacteristic
325C2×C4C2×(C2×D19)⋊C411yescharacteristic
326C2×C4C2×C22⋊Dic1911yescharacteristic
327C8—44no—
328C8—388no—
329C8—764no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—44no—
339C22C2×C19⋊#9511yescharacteristic
340C22M16×Dic1912yes—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4#1192631412yes—
350C4#1192631612yes—
351C4#1192650712yes—
352C4#1192656712yes—
353C2—22no—
354C2—41no—
355C2—41no—
356C2#1456332811yescharacteristic
357C2C2×#1192631411yescharacteristic
358C2C2×#1192631611yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D19)⋊C4
commutatorC23×C19C2×C42
FrattiniC2×C42C22×D19
FittingC19×#2920C2
socleC22×C19C2×#95
prime radicalC24×C19C42
cosocleC2×C42×C19C23
hypercenter#2920D19
hypocenterC19#7920
LCSG ▷ C23×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
3. #14561479C2semidirect
110. C2×C19⋊C8M16semidirect
243. C19#7920semidirect

Maximal subgroups

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

subgroupindex
#145722682
C2×C4×#645202
#145614792
C19×#29202
#792019