Finite Group Databasebeta

← #18080849

Subgroups — #18080849

Order 4864.

398 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564588C211yesmaximal, characteristic
2#14564391C211yesmaximal, characteristic
3C8×C4⋊Dic19C211yesmaximal, characteristic
4C2×#11926290C211yesmaximal, characteristic
5#14561518C211yesmaximal, characteristic
6#14561470C211yesmaximal, characteristic
7C19×#1956C211yesmaximal, characteristic
8C2×#10597264—21no—
9C2×C4⋊(C19⋊C8)C2211yescharacteristic
10C2×C4⋊(C19⋊C8)C2211yescharacteristic
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12C2×C8×Dic19—21no—
13C4×C4⋊Dic19C2211yescharacteristic
14#11926306—21no—
15#11926306—21no—
16#11926306—21no—
17#11926298—21no—
18#11926290C414yescomplemented
19C2×C19×C4⋊Q8C2211yescharacteristic
20C2×C19×#103—21no—
21C2×C19×#103—21no—
22C2×C4×C8×C19C2211yescharacteristic
23C19×#384C2211yescharacteristic
24C22×Q8×C19—21no—
25C22×C8×C19D411yescharacteristic
26C22×C8×C19D411yescharacteristic
27C19×C4⋊Q8—21no—
28C19×C4⋊Q8—21no—
29C19×C4⋊Q8—21no—
30C19×C4⋊Q8C2×C412yes—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19—21no—
36C2×C42×C19C2311yescharacteristic
37C2×C4⋊Dic19D411yescharacteristic
38C2×C4⋊Dic19D411yescharacteristic
39C2×C4×Dic19—21no—
40C22×C19⋊C8—21no—
41C22×C19⋊C8—21no—
42C22×C19⋊C8—21no—
43C19×#103—42no—
44C19×#103—42no—
45C4×C8×C19—21no—
46C4×C8×C19—21no—
47C19⋊#95—21no—
48C8×Dic19—42no—
49#10597264—42no—
50C4⋊(C19⋊C8)—21no—
51C4⋊(C19⋊C8)—21no—
52C4⋊(C19⋊C8)—21no—
53C4⋊(C19⋊C8)—21no—
54C4⋊(C19⋊C8)C2×C412yes—
55C4⋊(C19⋊C8)C2×C412yes—
56C2×Q8×C19—22no—
57C2×Q8×C19—41no—
58C2×Q8×C19—41no—
59C2×Q8×C19—41no—
60C2×Q8×C19—41no—
61C2×Q8×C19—41no—
62C22×C4×C19—41no—
63C22×C4×C19—41no—
64C22×C4×C19C2×D411yescharacteristic
65C22×C4×C19C2×D411yescharacteristic
66C22×C4×C19#4111yescharacteristic
67C22×Dic19—21no—
68C22×Dic19—21no—
69C2×C8×C19—21no—
70C2×C8×C19—21no—
71C2×C8×C19—21no—
72C2×C8×C19—21no—
73C2×C8×C19—21no—
74C2×C8×C19D812yes—
75C4⋊C4×C19—22no—
76C4⋊C4×C19—22no—
77C4⋊C4×C19—41no—
78C4⋊C4×C19—41no—
79C4⋊C4×C19—41no—
80C4⋊C4×C19—41no—
81C4⋊C4×C19—41no—
82C4⋊C4×C19—41no—
83C4⋊C4×C19—81no—
84C42×C19C22×C411yescharacteristic
85C42×C19#4111yescharacteristic
86C42×C19#4111yescharacteristic
87C42×C19#4111yescharacteristic
88C4⋊Dic19—21no—
89C4⋊Dic19—21no—
90C4⋊Dic19SD1612yes—
91C4⋊Dic19Q1612yes—
92C4×Dic19—41no—
93C4×Dic19—41no—
94C2×C19⋊C8—22no—
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—
103#9561—191nomaximal, Sylow
104C23×C19#12111yescharacteristic
105Q8×C19—42no—
106Q8×C19—42no—
107Q8×C19—81no—
108Q8×C19—81no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—42no—
112C2×C4×C19—81no—
113C2×C4×C19—81no—
114C2×C4×C19—81no—
115C2×C4×C19—81no—
116C2×C4×C19—81no—
117C2×C4×C19#11711yescharacteristic
118C2×C4×C19C4×D411yescharacteristic
119C2×C4×C19C4×D411yescharacteristic
120C2×C4×C19#12311yescharacteristic
121C2×C4×C19#12411yescharacteristic
122C2×C4×C19#12611yescharacteristic
123C2×C4×C19C2×D811yescharacteristic
124C2×C4×C19C2×SD1611yescharacteristic
125C2×C4×C19C2×Q1611yescharacteristic
126C2×C4×C19#13511yescharacteristic
127C2×C4×C19#13511yescharacteristic
128C2×C4×C19#13511yescharacteristic
129C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C19#13711yescharacteristic
131C2×Dic19—22no—
132C2×Dic19—22no—
133C2×Dic19—41no—
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137C8×C19—22no—
138C8×C19—41no—
139C19⋊C8—42no—
140C19⋊C8—42no—
141C19⋊C8—81no—
142#1988—191no—
143#1956D1911yescharacteristic
144#1947—191no—
145C8×C4⋊C4—191no—
146C2×#332—191no—
147#1296—191no—
148#1277—191no—
149C22×C19#38811yescharacteristic
150C22×C19#45911yescharacteristic
151C22×C19#46411yescharacteristic
152C22×C19#46511yescharacteristic
153C22×C19#46711yescharacteristic
154C22×C19#47111yescharacteristic
155C22×C19#47311yescharacteristic
156C4×C19—21no—
157C4×C19—21no—
158C4×C19—82no—
159C4×C19—161no—
160C4×C19C4×D811yescharacteristic
161C4×C19C4×SD1611yescharacteristic
162C4×C19C4×Q1611yescharacteristic
163C4×C19#44011yescharacteristic
164C4×C19#48011yescharacteristic
165C4×C19#48211yescharacteristic
166C4×C19#48711yescharacteristic
167C4×C19#48811yescharacteristic
168Dic19—42no—
169Dic19—42no—
170C2×C4⋊Q8C2×D1911yescharacteristic
171C2×#107—381no—
172C2×C4⋊C8—191no—
173C2×C4⋊C8—191no—
174C2×C4⋊C8—191no—
175C2×#103—21no—
176C2×#103—21no—
177C2×C4×C8—381no—
178C2×C4×C8C2×D1911yescharacteristic
179#384C2×D1911yescharacteristic
180C4×C4⋊C4—191no—
181#340—381no—
182#340—381no—
183#340—381no—
184#336—381no—
185#332—194no—
186C2×C19#166511yescharacteristic
187C2×C19#166911yescharacteristic
188C2×C19#168011yescharacteristic
189C2×C19#168411yescharacteristic
190C2×C19#192511yescharacteristic
191C2×C19#193011yescharacteristic
192C2×C19#193311yescharacteristic
193C22×Q8—21no—
194C22×C8—381no—
195C22×C8—381no—
196C22×C8—381no—
197C22×C8C22⋊D1911yescharacteristic
198C22×C8C22⋊D1911yescharacteristic
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8C4×D1912yes—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—191no—
209C2×C4⋊C4—191no—
210C2×C42—381no—
211C2×C42C22×D1911yescharacteristic
212#107—762no—
213C4⋊C8—192no—
214C4⋊C8—192no—
215C4⋊C8—381no—
216C4⋊C8—381no—
217C4⋊C8—381no—
218C4⋊C8—381no—
219#103—42no—
220#103—42no—
221C4×C8—21no—
222C4×C8—21no—
223C4×C8—762no—
224#95—381no—
225C19#956111yescharacteristic, complemented, Sylow
226C2×Q8—22no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—381no—
235C22×C4—381no—
236C22×C4D4×D1911yescharacteristic
237C22×C4#6454311yescharacteristic
238C22×C4C2×C22⋊D1911yescharacteristic
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—382no—
245C2×C8—382no—
246C2×C8—761no—
247C2×C8—761no—
248C2×C8—761no—
249C2×C8—761no—
250C2×C8—761no—
251C2×C8—761no—
252C2×C8—761no—
253C2×C8#6452512yes—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—81no—
263C4⋊C4—192no—
264C4⋊C4—192no—
265C4⋊C4—381no—
266C4⋊C4—381no—
267C42—761no—
268C42—761no—
269C42C2×C4×D1911yescharacteristic
270C42#6454111yescharacteristic
271C42#6454311yescharacteristic
272C42#6454311yescharacteristic
273C23#1059738411yescharacteristic
274Q8—42no—
275Q8—42no—
276Q8—81no—
277Q8—81no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—382no—
287C2×C4—382no—
288C2×C4—761no—
289C2×C4—761no—
290C2×C4—761no—
291C2×C4—761no—
292C2×C4#1059732311yescharacteristic
293C2×C4#1059732511yescharacteristic
294C2×C4(C22⋊D19)⋊C411yescharacteristic
295C2×C4#1059733111yescharacteristic
296C2×C4SD16×D1911yescharacteristic
297C2×C4#1059736211yescharacteristic
298C2×C4Q16×D1911yescharacteristic
299C2×C4#1059736511yescharacteristic
300C2×C4C4×C22⋊D1911yescharacteristic
301C2×C4C2×#6452511yescharacteristic
302C2×C4#1059737811yescharacteristic
303C2×C4#1059738111yescharacteristic
304C2×C4#1059739611yescharacteristic
305C2×C4#1059739711yescharacteristic
306C8—22no—
307C8—41no—
308C8—762no—
309C8—762no—
310C8—1521no—
311C22#1192643211yescharacteristic
312C22#1192673611yescharacteristic
313C22#1192676311yescharacteristic
314C22#1192677011yescharacteristic
315C22#1192678211yescharacteristic
316C22#1192680411yescharacteristic
317C22#1192681611yescharacteristic
318C4—21no—
319C4—21no—
320C4—82no—
321C4—161no—
322C4—762no—
323C4—762no—
324C4C4×#6452511yescharacteristic
325C4#1192662911yescharacteristic
326C4#1192663611yescharacteristic
327C4#1192664411yescharacteristic
328C4#1192685511yescharacteristic
329C4#1192686511yescharacteristic
330C4#1192689311yescharacteristic
331C4#1192690011yescharacteristic
332C2#1456297311yescharacteristic
333C2#1456299711yescharacteristic
334C2#1456306211yescharacteristic
335C2#1456309011yescharacteristic
336C2#1456425211yescharacteristic
337C2#1456428711yescharacteristic
338C2#1456430811yescharacteristic
subgroupG/H
centerC23#10597384
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1956C2
socle, prime radicalC23×C19#121
cosocleC2×C42×C19C23
hypercenter#1956D19
hypocenterC19#9561
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
18. #11926290C4semidirect
225. C19#9561semidirect

Maximal subgroups

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

subgroupindex
#145645882
#145643912
C8×C4⋊Dic192
C2×#119262902
#145615182
#145614702
C19×#19562
#956119