Finite Group Databasebeta

← #18073618

Subgroups — #18073618

Order 4864.

462 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14563502C211yesmaximal, characteristic, complemented
2#14562284C211yesmaximal, characteristic
3#14562130C211yesmaximal, characteristic
4#14561927C211yesmaximal, characteristic, complemented
5#14561536C211yesmaximal, characteristic, complemented
6#14561530C211yesmaximal, characteristic, complemented
7C19×#2931C211yesmaximal, characteristic
8#11926597C2211yescharacteristic
9#11926597C2211yescharacteristic
10C2×C4⋊(C19⋊C8)C2211yescharacteristic
11C2×#10597272—21no—
12C4×C4⋊Dic19C2211yescharacteristic
13#11926298—21no—
14#11926290C412yescomplemented
15#11926288C412yescomplemented
16#11926278C414yes—
17#11926266—21no—
18#11926266—21no—
19C2×C19×#131—21no—
20C19×#532C2211yescharacteristic
21C19×#436—21no—
22C19×#436C412yescomplemented
23C8×D4×C19—21no—
24C8×D4×C19C412yescomplemented
25C19×#423C2211yescharacteristic
26C19×#408—21no—
27C2×C4×C8×C19C2211yescharacteristic
28C2×#41×C19—21no—
29C19×#131—42no—
30C19×#131—42no—
31C2×M16×C19—21no—
32C2×M16×C19—22no—
33C22×C8×C19—22no—
34C22×C8×C19D411yescharacteristic
35C22×C8×C19D411yescharacteristic
36C19×C4⋊Q8C2×C411yescharacteristic
37C19×#127C2×C411yescharacteristic
38C19×#124—21no—
39C19×#121—21no—
40C19×#121C2×C412yes—
41C4×D4×C19—21no—
42C4×D4×C19C2×C412yes—
43C2×C42×C19C2311yescharacteristic
44C2×C4⋊Dic19—21no—
45C2×C4×Dic19—21no—
46C22×C19⋊C8—21no—
47C19×C4⋊C8—21no—
48C19×C4⋊C8C2×C412yes—
49C19×C22⋊C8—22no—
50C19×C22⋊C8—22no—
51C4×C8×C19C2×C411yescharacteristic
52C4×C8×C19C2×C411yescharacteristic
53C4×C8×C19D411yescharacteristic
54C4×C8×C19D411yescharacteristic
55C19⋊#95C2×C412yes—
56C22⋊(C19⋊C8)—21no—
57C22⋊(C19⋊C8)C2×C412yes—
58#10597272—42no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)—21no—
61C4⋊(C19⋊C8)C2×C412yes—
62C4⋊(C19⋊C8)C2×C412yes—
63C4×C19⋊C8—21no—
64C4×C19⋊C8—21no—
65#41×C19—41no—
66#41×C19—41no—
67#41×C19—41no—
68#41×C19—41no—
69C2×Q8×C19—21no—
70C2×D4×C19—22no—
71C2×D4×C19—21no—
72C2×D4×C19—21no—
73C2×D4×C19C4212yes—
74C22×C4×C19—22no—
75C22×C4×C19C22×C411yescharacteristic
76C22×C4×C19C2×D411yescharacteristic
77C22×C4×C19#4111yescharacteristic
78C22×Dic19—22no—
79M16×C19—44no—
80M16×C19—41no—
81M16×C19—41no—
82C2×C8×C19—21no—
83C2×C8×C19—21no—
84C2×C8×C19—21no—
85C2×C8×C19—21no—
86C2×C8×C19—22no—
87C2×C8×C19—44no—
88C2×C8×C19C22⋊C411yescharacteristic
89C2×C8×C19C22⋊C411yescharacteristic
90C2×C8×C19C22⋊C411yescharacteristic
91C2×C8×C19C22⋊C411yescharacteristic
92C4⋊C4×C19—21no—
93C4⋊C4×C19C4212yes—
94C22⋊C4×C19—22no—
95C22⋊C4×C19—22no—
96C42×C19C22×C411yescharacteristic
97C42×C19C22×C411yescharacteristic
98C42×C19C2×D411yescharacteristic
99C42×C19#4111yescharacteristic
100C4⋊Dic19—42no—
101C4×Dic19—41no—
102C4×Dic19—41no—
103C2×C19⋊C8—22no—
104C2×C19⋊C8—22no—
105C2×C19⋊C8—22no—
106C2×C19⋊C8—41no—
107C2×C19⋊C8—41no—
108#8253—191nomaximal, Sylow
109C23×C19—22no—
110C23×C19C4×D411yescharacteristic
111Q8×C19—41no—
112Q8×C19—41no—
113D4×C19—42no—
114D4×C19—42no—
115D4×C19—42no—
116D4×C19—41no—
117D4×C19—41no—
118D4×C19—42no—
119C2×C4×C19—22no—
120C2×C4×C19—22no—
121C2×C4×C19—41no—
122C2×C4×C19—42no—
123C2×C4×C19—42no—
124C2×C4×C19C2×C4211yescharacteristic
125C2×C4×C19C2×C22⋊C411yescharacteristic
126C2×C4×C19#11711yescharacteristic
127C2×C4×C19C4×D411yescharacteristic
128C2×C4×C19C4×D411yescharacteristic
129C2×C4×C19C4×D411yescharacteristic
130C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C19#13711yescharacteristic
134C2×Dic19—42no—
135C2×Dic19—42no—
136C2×Dic19—42no—
137C8×C19—21no—
138C8×C19—21no—
139C8×C19—21no—
140C8×C19—21no—
141C8×C19—42no—
142C19⋊C8—42no—
143C19⋊C8—42no—
144C19⋊C8—42no—
145#2931D1911yescharacteristic
146#1770—191no—
147#1540—191no—
148#1502—191no—
149#1452—191no—
150#1303—191no—
151#1301—191no—
152C22×C19—21no—
153C22×C19—21no—
154C22×C19—42no—
155C22×C19—42no—
156C22×C19—42no—
157C22×C19C4×C22⋊C411yescharacteristic
158C22×C19#44011yescharacteristic
159C22×C19#44211yescharacteristic
160C4×C19—21no—
161C4×C19—21no—
162C4×C19—21no—
163C4×C19—42no—
164C4×C19#41711yescharacteristic
165C4×C19#41811yescharacteristic
166C4×C19#44011yescharacteristic
167C4×C19#44211yescharacteristic
168C4×C19#44412yes—
169Dic19—82no—
170C2×#131—21no—
171#532C2×D1911yescharacteristic
172#436—21no—
173#436Dic1912yescomplemented
174C8×D4—21no—
175C8×D4Dic1912yescomplemented
176#431—191no—
177#431—191no—
178#423C2×D1911yescharacteristic
179C2×C4⋊C8—191no—
180#408—21no—
181C2×#97—381no—
182C2×C4×C8C2×D1911yescharacteristic
183C4×C4⋊C4—191no—
184#336—381no—
185#332—192no—
186#331—192no—
187#327—194no—
188#322—381no—
189#322—381no—
190C2×C19—21no—
191C2×C19—21no—
192C2×C19—82no—
193C2×C19#175711yescharacteristic
194C2×C19#176211yescharacteristic
195C2×C19#176511yescharacteristic
196C2×#41—21no—
197#131—42no—
198#131—42no—
199C2×M16—21no—
200C2×M16—22no—
201C22×C8—22no—
202C22×C8—381no—
203C22×C8C22⋊D1911yescharacteristic
204C22×C8C22⋊D1911yescharacteristic
205C4⋊Q8C4×D1911yescharacteristic
206#127C4×D1911yescharacteristic
207#124—21no—
208#121—21no—
209#121C4×D1912yes—
210C4×D4—21no—
211C4×D4C2×Dic1912yes—
212C2×C4⋊C4—381no—
213C2×C42—381no—
214C2×C42C22×D1911yescharacteristic
215C4⋊C8—21no—
216C4⋊C8—192no—
217C4⋊C8—192no—
218C4⋊C8—381no—
219C4⋊C8—381no—
220C4⋊C8C2×Dic1912yes—
221C22⋊C8—22no—
222C22⋊C8—22no—
223C22⋊C8—192no—
224C22⋊C8—381no—
225#97—762no—
226C4×C8—381no—
227C4×C8—381no—
228C4×C8C2×Dic1911yescharacteristic
229C4×C8C2×Dic1911yescharacteristic
230C4×C8C22⋊D1911yescharacteristic
231C4×C8C22⋊D1911yescharacteristic
232#95—192no—
233C19#825311yescharacteristic, complemented, Sylow
234#41—41no—
235#41—41no—
236#41—41no—
237#41—41no—
238C2×Q8—21no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4C4×Dic1912yes—
243C22×C4—22no—
244C22×C4—382no—
245C22×C4C2×C4×D1911yescharacteristic
246C22×C4#6454111yescharacteristic
247C22×C4C2×C22⋊D1911yescharacteristic
248M16—44no—
249M16—41no—
250M16—41no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—22no—
256C2×C8—44no—
257C2×C8—382no—
258C2×C8—382no—
259C2×C8—382no—
260C2×C8—761no—
261C2×C8—761no—
262C2×C8C22⋊Dic1911yescharacteristic
263C2×C8C22⋊Dic1911yescharacteristic
264C2×C8C22⋊Dic1911yescharacteristic
265C2×C8C22⋊Dic1911yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—762no—
268C4⋊C4C4×Dic1912yes—
269C22⋊C4—22no—
270C22⋊C4—22no—
271C42—761no—
272C42—761no—
273C42C2×C4×D1911yescharacteristic
274C42#6454111yescharacteristic
275C42C22×Dic1911yescharacteristic
276C42C2×C22⋊D1911yescharacteristic
277C23—22no—
278C23C4×C22⋊D1911yescharacteristic
279Q8—41no—
280Q8—41no—
281D4—42no—
282D4—42no—
283D4—42no—
284D4—41no—
285D4—41no—
286D4—42no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—762no—
293C2×C4—762no—
294C2×C4—762no—
295C2×C4C2×C4×Dic1911yescharacteristic
296C2×C4#1059737211yescharacteristic
297C2×C4C4×C22⋊D1911yescharacteristic
298C2×C4C4×C22⋊D1911yescharacteristic
299C2×C4C4×C22⋊D1911yescharacteristic
300C2×C4#1059737811yescharacteristic
301C2×C4#1059737811yescharacteristic
302C2×C4#1059739511yescharacteristic
303C2×C4#1059739711yescharacteristic
304C2×C4C2×C22⋊Dic1911yescharacteristic
305C8—21no—
306C8—21no—
307C8—21no—
308C8—21no—
309C8—42no—
310C8—762no—
311C8—762no—
312C8—762no—
313C22—21no—
314C22—21no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22C4×C22⋊Dic1911yescharacteristic
319C22#1192664411yescharacteristic
320C22#1192665411yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—42no—
325C4—1522no—
326C4#1192654511yescharacteristic
327C4#1192654911yescharacteristic
328C4#1192664411yescharacteristic
329C4#1192665411yescharacteristic
330C4#1192666412yes—
331C2—21no—
332C2—21no—
333C2—82no—
334C2#1456343511yescharacteristic
335C2#1456346011yescharacteristic
336C2#1456347711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊Dic19
commutatorC2×C4×C19C2×C42
FrattiniC2×C42C22×D19
FittingC19×#2931C2
socleC22×C19C4×C22⋊C4
prime radicalC19×#532C22
cosocleC2×C42×C19C23
hypercenter#2931D19
hypocenterC19#8253
LCSG ▷ C2×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #2931

Complements

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

NH ≅ G/Ntype
1. #14563502C2semidirect
4. #14561927C2semidirect
5. #14561536C2semidirect
6. #14561530C2semidirect
14. #11926290C4semidirect
15. #11926288C4semidirect
22. C19×#436C4semidirect
24. C8×D4×C19C4semidirect
173. #436Dic19semidirect
175. C8×D4Dic19semidirect
233. C19#8253semidirect

Maximal subgroups

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

subgroupindex
#145635022
#145622842
#145621302
#145619272
#145615362
#145615302
C19×#29312
#825319