Finite Group Databasebeta

← #18087075

Subgroups — #18087075

Order 4864.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564559C211yesmaximal, characteristic
2#14564391C211yesmaximal, characteristic
3#14564353C211yesmaximal, characteristic
4C2×#11926295C211yesmaximal, characteristic
5C2×#11926290C211yesmaximal, characteristic
6#14561518C211yesmaximal, characteristic
7C19×#1990C211yesmaximal, characteristic
8C2×#10597264—21no—
9C2×C4⋊(C19⋊C8)C2211yescharacteristic
10C2×C4⋊(C19⋊C8)C2211yescharacteristic
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12C2×Dic19⋊C8—21no—
13C2×#10597292—21no—
14C2×#10597292—21no—
15C4×C4⋊Dic19C2211yescharacteristic
16#11926306—21no—
17#11926298—21no—
18#11926295—22no—
19#11926290—22no—
20C2×C19×C4⋊Q8C2211yescharacteristic
21C2×C4×C8×C19C2211yescharacteristic
22C19×#384C2211yescharacteristic
23C19×#340—21no—
24C19×#340—21no—
25C22×Q8×C19—21no—
26C22×C8×C19D411yescharacteristic
27C22×C8×C19D411yescharacteristic
28C19×C4⋊Q8—21no—
29C19×C4⋊Q8—21no—
30C19×C4⋊Q8—21no—
31C19×C4⋊Q8Q812yes—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19—21no—
37C2×C42×C19C2311yescharacteristic
38C2×C4⋊Dic19D411yescharacteristic
39C2×C4⋊Dic19D411yescharacteristic
40C2×C4×Dic19—21no—
41C22×C19⋊C8—21no—
42C22×C19⋊C8—21no—
43C22×C19⋊C8—21no—
44C4×C8×C19—21no—
45C4×C8×C19—21no—
46#10597292—42no—
47#10597292—42no—
48C19⋊#95—21no—
49Dic19⋊C8—42no—
50#10597264—42no—
51C4⋊(C19⋊C8)—21no—
52C4⋊(C19⋊C8)—21no—
53C4⋊(C19⋊C8)—21no—
54C4⋊(C19⋊C8)—21no—
55C4⋊(C19⋊C8)—21no—
56C4⋊(C19⋊C8)D412yes—
57C2×Q8×C19—22no—
58C2×Q8×C19—41no—
59C2×Q8×C19—41no—
60C2×Q8×C19—41no—
61C2×Q8×C19—41no—
62C2×Q8×C19—41no—
63C22×C4×C19—41no—
64C22×C4×C19—41no—
65C22×C4×C19C2×D411yescharacteristic
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19#4111yescharacteristic
68C22×Dic19—21no—
69C22×Dic19—21no—
70C2×C8×C19—21no—
71C2×C8×C19—21no—
72C2×C8×C19—21no—
73C2×C8×C19—21no—
74C2×C8×C19—21no—
75C2×C8×C19Q1612yes—
76C4⋊C4×C19—22no—
77C4⋊C4×C19—22no—
78C4⋊C4×C19—41no—
79C4⋊C4×C19—41no—
80C4⋊C4×C19—41no—
81C4⋊C4×C19—41no—
82C4⋊C4×C19—41no—
83C4⋊C4×C19—41no—
84C4⋊C4×C19—81no—
85C42×C19C2×D411yescharacteristic
86C42×C19C2×Q811yescharacteristic
87C42×C19#4111yescharacteristic
88C42×C19#4111yescharacteristic
89C4⋊Dic19—21no—
90C4⋊Dic19—21no—
91C4⋊Dic19—21no—
92C4⋊Dic19SD1612yes—
93C4×Dic19—41no—
94C4×Dic19—41no—
95C2×C19⋊C8—22no—
96C2×C19⋊C8—41no—
97C2×C19⋊C8—41no—
98C2×C19⋊C8—41no—
99C2×C19⋊C8—41no—
100C2×C19⋊C8—41no—
101C2×C19⋊C8—41no—
102C2×C19⋊C8—41no—
103C2×C19⋊C8—41no—
104#10590—191nomaximal, Sylow
105C23×C19#12111yescharacteristic
106Q8×C19—42no—
107Q8×C19—42no—
108Q8×C19—81no—
109Q8×C19—81no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—42no—
113C2×C4×C19—81no—
114C2×C4×C19—81no—
115C2×C4×C19—81no—
116C2×C4×C19—81no—
117C2×C4×C19—81no—
118C2×C4×C19#12111yescharacteristic
119C2×C4×C19#12111yescharacteristic
120C2×C4×C19C22⋊Q811yescharacteristic
121C2×C4×C19C22⋊Q811yescharacteristic
122C2×C4×C19C22⋊Q811yescharacteristic
123C2×C4×C19#12611yescharacteristic
124C2×C4×C19C2×SD1611yescharacteristic
125C2×C4×C19C2×Q1611yescharacteristic
126C2×C4×C19#13511yescharacteristic
127C2×C4×C19#13511yescharacteristic
128C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C19#13711yescharacteristic
132C2×Dic19—22no—
133C2×Dic19—41no—
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137C2×Dic19—41no—
138C8×C19—22no—
139C8×C19—41no—
140C19⋊C8—42no—
141C19⋊C8—81no—
142C19⋊C8—81no—
143#1990D1911yescharacteristic
144#1981—191no—
145#1947—191no—
146#1939—191no—
147C2×#334—191no—
148C2×#332—191no—
149#1296—191no—
150C22×C19#39611yescharacteristic
151C22×C19#46211yescharacteristic
152C22×C19#46311yescharacteristic
153C22×C19#46511yescharacteristic
154C22×C19#46911yescharacteristic
155C22×C19#47111yescharacteristic
156C22×C19#47311yescharacteristic
157C4×C19—21no—
158C4×C19—21no—
159C4×C19—82no—
160C4×C19—161no—
161C4×C19#46011yescharacteristic
162C4×C19#46311yescharacteristic
163C4×C19#46711yescharacteristic
164C4×C19#46811yescharacteristic
165C4×C19#47611yescharacteristic
166C4×C19#47711yescharacteristic
167C4×C19#47811yescharacteristic
168C4×C19#47911yescharacteristic
169Dic19—42no—
170Dic19—81no—
171C2×C4⋊Q8C2×D1911yescharacteristic
172C2×#107—381no—
173C2×C4⋊C8—191no—
174C2×C4⋊C8—191no—
175C2×C4⋊C8—191no—
176C2×C4⋊C8—381no—
177C2×#103—381no—
178C2×#103—381no—
179C2×C4×C8C2×D1911yescharacteristic
180#384C2×D1911yescharacteristic
181C4×C4⋊C4—191no—
182#340—21no—
183#340—21no—
184#340—381no—
185#336—381no—
186#334—382no—
187#332—382no—
188C2×C19#167211yescharacteristic
189C2×C19#167911yescharacteristic
190C2×C19#169411yescharacteristic
191C2×C19#170111yescharacteristic
192C2×C19#206411yescharacteristic
193C2×C19#206511yescharacteristic
194C2×C19#206811yescharacteristic
195C22×Q8—21no—
196C22×C8—381no—
197C22×C8—381no—
198C22×C8—381no—
199C22×C8C22⋊D1911yescharacteristic
200C22×C8C22⋊D1911yescharacteristic
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8Dic3812yes—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—191no—
211C2×C4⋊C4—191no—
212C2×C42—381no—
213C2×C42C22×D1911yescharacteristic
214#107—762no—
215C4⋊C8—192no—
216C4⋊C8—381no—
217C4⋊C8—381no—
218C4⋊C8—381no—
219C4⋊C8—381no—
220C4⋊C8—381no—
221C4⋊C8—762no—
222#103—762no—
223#103—762no—
224C4×C8—21no—
225C4×C8—21no—
226#95—381no—
227C19#1059011yescharacteristic, complemented, Sylow
228C2×Q8—22no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—381no—
237C22×C4—381no—
238C22×C4D4×D1911yescharacteristic
239C22×C4#6454311yescharacteristic
240C22×C4C2×C22⋊D1911yescharacteristic
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—382no—
247C2×C8—761no—
248C2×C8—761no—
249C2×C8—761no—
250C2×C8—761no—
251C2×C8—761no—
252C2×C8—761no—
253C2×C8—761no—
254C2×C8—761no—
255C2×C8#6452812yes—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—81no—
265C4⋊C4—192no—
266C4⋊C4—381no—
267C4⋊C4—381no—
268C4⋊C4—381no—
269C42—761no—
270C42—761no—
271C42C2×Dic3811yescharacteristic
272C42#6454111yescharacteristic
273C42D4×D1911yescharacteristic
274C42#6454311yescharacteristic
275C23#1059738411yescharacteristic
276Q8—42no—
277Q8—42no—
278Q8—81no—
279Q8—81no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—382no—
289C2×C4—761no—
290C2×C4—761no—
291C2×C4—761no—
292C2×C4—761no—
293C2×C4—761no—
294C2×C4#1059732411yescharacteristic
295C2×C4#1059732411yescharacteristic
296C2×C4#1059732511yescharacteristic
297C2×C4#1059733011yescharacteristic
298C2×C4#1059735711yescharacteristic
299C2×C4#1059735711yescharacteristic
300C2×C4SD16×D1911yescharacteristic
301C2×C4#1059736211yescharacteristic
302C2×C4#1059737011yescharacteristic
303C2×C4#1059738511yescharacteristic
304C2×C4#1059738811yescharacteristic
305C2×C4C2×#6452811yescharacteristic
306C2×C4#1059739511yescharacteristic
307C2×C4#1059739611yescharacteristic
308C8—22no—
309C8—41no—
310C8—762no—
311C8—1521no—
312C8—1521no—
313C22#1192646711yescharacteristic
314C22#1192675111yescharacteristic
315C22#1192675611yescharacteristic
316C22#1192677011yescharacteristic
317C22#1192679411yescharacteristic
318C22#1192680411yescharacteristic
319C22#1192681611yescharacteristic
320C4—21no—
321C4—21no—
322C4—82no—
323C4—161no—
324C4—762no—
325C4—1521no—
326C4#1192674311yescharacteristic
327C4#1192675811yescharacteristic
328C4#1192678311yescharacteristic
329C4#1192679211yescharacteristic
330C4#1192683211yescharacteristic
331C4#1192683911yescharacteristic
332C4#1192684611yescharacteristic
333C4#1192685111yescharacteristic
334C2#1456301411yescharacteristic
335C2#1456305511yescharacteristic
336C2#1456315011yescharacteristic
337C2#1456319311yescharacteristic
338C2#1456500011yescharacteristic
339C2#1456500711yescharacteristic
340C2#1456503011yescharacteristic
subgroupG/H
centerC23#10597384
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1990C2
socle, prime radicalC23×C19#121
hypercenter#1990D19
hypocenterC19#10590
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
227. C19#10590semidirect

Maximal subgroups

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

subgroupindex
#145645592
#145643912
#145643532
C2×#119262952
C2×#119262902
#145615182
C19×#19902
#1059019