Finite Group Databasebeta

← #18081110

Subgroups — #18081110

Order 4864.

378 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564354C211yesmaximal, characteristic
2#14564351C211yesmaximal, characteristic
3C4×#10597265C211yesmaximal, characteristic
4C2×#11926296C211yesmaximal, characteristic
5C2×#11926265C211yesmaximal, characteristic
6#14561475C211yesmaximal, characteristic
7C19×#1279C211yesmaximal, characteristic
8C2×#10597265C411yescharacteristic
9C2×#10597265C411yescharacteristic
10C2×C4⋊(C19⋊C8)—21no—
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12C2×Dic19⋊C8—21no—
13C2×C4×C19⋊C8C2211yescharacteristic
14C2×C4×C19⋊C8C2211yescharacteristic
15C4×C4⋊Dic19C2211yescharacteristic
16#11926306C411yescharacteristic
17#11926306C411yescharacteristic
18#11926299—21no—
19#11926298—21no—
20#11926296—22no—
21#11926265—22no—
22C2×C19×C4⋊C8C2211yescharacteristic
23C2×C4×C8×C19C2211yescharacteristic
24C4×C4⋊C4×C19C2211yescharacteristic
25C22×C8×C19—21no—
26C22×C8×C19—21no—
27C2×C4⋊C4×C19C2×C411yescharacteristic
28C2×C4⋊C4×C19C2×C411yescharacteristic
29C2×C42×C19—21no—
30C2×C42×C19C2311yescharacteristic
31C2×C4⋊Dic19C2×C411yescharacteristic
32C2×C4⋊Dic19C2×C411yescharacteristic
33C2×C4×Dic19—21no—
34C22×C19⋊C8—21no—
35C22×C19⋊C8C2×C411yescharacteristic
36C22×C19⋊C8C2×C411yescharacteristic
37C22×C19⋊C8D411yescharacteristic
38C22×C19⋊C8D411yescharacteristic
39C19×C4⋊C8—21no—
40C19×C4⋊C8—21no—
41C4×C8×C19—21no—
42C4×C8×C19Q812yes—
43C19×#95—21no—
44C19⋊#95—21no—
45Dic19⋊C8—42no—
46#10597265—22no—
47#10597265—22no—
48C4⋊(C19⋊C8)—21no—
49C4⋊(C19⋊C8)—21no—
50C4⋊(C19⋊C8)—42no—
51C4×C19⋊C8—21no—
52C4×C19⋊C8—21no—
53C4×C19⋊C8D412yes—
54C4×C19⋊C8Q812yes—
55C22×C4×C19—21no—
56C22×C4×C19—21no—
57C22×C4×C19C22×C411yescharacteristic
58C22×C4×C19C2×D411yescharacteristic
59C22×C4×C19#4111yescharacteristic
60C22×Dic19—21no—
61C22×Dic19—21no—
62C2×C8×C19—22no—
63C2×C8×C19—22no—
64C2×C8×C19—22no—
65C2×C8×C19—41no—
66C2×C8×C19—41no—
67C2×C8×C19—41no—
68C4⋊C4×C19—21no—
69C4⋊C4×C19—21no—
70C4⋊C4×C19—21no—
71C4⋊C4×C19M1612yes—
72C42×C19—41no—
73C42×C19—41no—
74C42×C19C2×D411yescharacteristic
75C42×C19C2×Q811yescharacteristic
76C42×C19C2×Q811yescharacteristic
77C42×C19#4111yescharacteristic
78C4⋊Dic19—21no—
79C4⋊Dic19—21no—
80C4⋊Dic19—21no—
81C4⋊Dic19M1612yes—
82C4×Dic19—41no—
83C4×Dic19—41no—
84C2×C19⋊C8—21no—
85C2×C19⋊C8—21no—
86C2×C19⋊C8—21no—
87C2×C19⋊C8—21no—
88C2×C19⋊C8—21no—
89C2×C19⋊C8—21no—
90C2×C19⋊C8—21no—
91C2×C19⋊C8—21no—
92C2×C19⋊C8—21no—
93C2×C19⋊C8—21no—
94C2×C19⋊C8—41no—
95C2×C19⋊C8—41no—
96C2×C19⋊C8—41no—
97C2×C19⋊C8C4⋊C412yes—
98C2×C19⋊C8C4⋊C412yes—
99#9600—191nomaximal, Sylow
100C23×C19C4×D411yescharacteristic
101C2×C4×C19—21no—
102C2×C4×C19—21no—
103C2×C4×C19—22no—
104C2×C4×C19—41no—
105C2×C4×C19—41no—
106C2×C4×C19—41no—
107C2×C4×C19—41no—
108C2×C4×C19—41no—
109C2×C4×C19C2×C4⋊C411yescharacteristic
110C2×C4×C19C4×Q811yescharacteristic
111C2×C4×C19#12111yescharacteristic
112C2×C4×C19C22⋊Q811yescharacteristic
113C2×C4×C19#12511yescharacteristic
114C2×C4×C19C4⋊Q811yescharacteristic
115C2×C4×C19C2×M1611yescharacteristic
116C2×C4×C19C2×M1611yescharacteristic
117C2×C4×C19#13111yescharacteristic
118C2×C4×C19#13111yescharacteristic
119C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C19#13711yescharacteristic
122C2×C4×C19#13711yescharacteristic
123C2×Dic19—22no—
124C2×Dic19—41no—
125C2×Dic19—41no—
126C2×Dic19—41no—
127C2×Dic19—41no—
128C2×Dic19—41no—
129C8×C19—24no—
130C8×C19—81no—
131C19⋊C8—22no—
132C19⋊C8—22no—
133C19⋊C8—41no—
134C19⋊C8—41no—
135C19⋊C8—81no—
136#1939—191no—
137#1939—191no—
138C4×#106—191no—
139C2×#335—191no—
140C2×#322—191no—
141#1279—191no—
142#1279D1911yescharacteristic
143C22×C19#38911yescharacteristic
144C22×C19#43511yescharacteristic
145C22×C19#43511yescharacteristic
146C22×C19#44011yescharacteristic
147C22×C19#44011yescharacteristic
148C22×C19#44311yescharacteristic
149C22×C19#44311yescharacteristic
150C4×C19—21no—
151C4×C19—21no—
152C4×C19—42no—
153C4×C19—81no—
154C4×C19#42311yescharacteristic
155C4×C19#42411yescharacteristic
156C4×C19#44611yescharacteristic
157C4×C19#44611yescharacteristic
158C4×C19#46911yescharacteristic
159C4×C19#47011yescharacteristic
160C4×C19#50111yescharacteristic
161C4×C19#50111yescharacteristic
162Dic19—42no—
163Dic19—81no—
164C2×#106—191no—
165C2×#106—191no—
166C2×C4⋊C8—191no—
167C2×C4⋊C8—381no—
168C2×C4⋊C8—381no—
169C2×C4⋊C8C2×D1911yescharacteristic
170C2×C4×C8—191no—
171C2×C4×C8—191no—
172C2×C4×C8C2×D1911yescharacteristic
173C4×C4⋊C4—191no—
174C4×C4⋊C4C2×D1911yescharacteristic
175#340—191no—
176#340—191no—
177#336—381no—
178#336—381no—
179#335—382no—
180#322—382no—
181C2×C19#158511yescharacteristic
182C2×C19#158511yescharacteristic
183C2×C19#158811yescharacteristic
184C2×C19#158811yescharacteristic
185C2×C19#194011yescharacteristic
186C2×C19#194411yescharacteristic
187C2×C19#194511yescharacteristic
188C22×C8—21no—
189C22×C8—21no—
190C22×C8—191no—
191C22×C8—191no—
192C22×C8—191no—
193C22×C8—191no—
194C22×C8—381no—
195C2×C4⋊C4—191no—
196C2×C4⋊C4—191no—
197C2×C4⋊C4C4×D1911yescharacteristic
198C2×C4⋊C4C4×D1911yescharacteristic
199C2×C42—21no—
200C2×C42—381no—
201C2×C42C22×D1911yescharacteristic
202#106—382no—
203#106—382no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—381no—
207C4⋊C8—381no—
208C4⋊C8—762no—
209C4⋊C8—762no—
210C4×C8—21no—
211C4×C8—192no—
212C4×C8—192no—
213C4×C8—381no—
214C4×C8—381no—
215C4×C8Dic3812yes—
216#95—21no—
217#95—381no—
218C19#960011yescharacteristic, complemented, Sylow
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—381no—
222C22×C4—381no—
223C22×C4C2×C4×D1911yescharacteristic
224C22×C4D4×D1911yescharacteristic
225C22×C4#6454311yescharacteristic
226C2×C8—22no—
227C2×C8—22no—
228C2×C8—22no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—192no—
233C2×C8—192no—
234C2×C8—381no—
235C2×C8—381no—
236C2×C8—381no—
237C2×C8—381no—
238C2×C8—381no—
239C2×C8—381no—
240C2×C8—381no—
241C2×C8—381no—
242C2×C8—381no—
243C2×C8—381no—
244C2×C8—761no—
245C2×C8—761no—
246C2×C8—761no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—192no—
251C4⋊C4—381no—
252C4⋊C4—381no—
253C4⋊C4—381no—
254C4⋊C4#6451512yes—
255C42—41no—
256C42—41no—
257C42—761no—
258C42—761no—
259C42C2×Dic3811yescharacteristic
260C42#6454111yescharacteristic
261C42D4×D1911yescharacteristic
262C42Q8×D1911yescharacteristic
263C23(C22⋊D19)⋊C411yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—382no—
273C2×C4—761no—
274C2×C4—761no—
275C2×C4—761no—
276C2×C4—761no—
277C2×C4—761no—
278C2×C4C4×Dic3811yescharacteristic
279C2×C4#1059732411yescharacteristic
280C2×C4#1059733011yescharacteristic
281C2×C4#1059733411yescharacteristic
282C2×C4#1059733511yescharacteristic
283C2×C4C4⋊C4×D1911yescharacteristic
284C2×C4C2×#6451511yescharacteristic
285C2×C4#1059734711yescharacteristic
286C2×C4M16×D1911yescharacteristic
287C2×C4#1059735311yescharacteristic
288C2×C4#1059735711yescharacteristic
289C2×C4#1059736011yescharacteristic
290C2×C4#1059736111yescharacteristic
291C2×C4#1059736411yescharacteristic
292C8—24no—
293C8—81no—
294C8—382no—
295C8—382no—
296C8—761no—
297C8—761no—
298C8—1521no—
299C22#1192644111yescharacteristic
300C22#1192661211yescharacteristic
301C22#1192661811yescharacteristic
302C22#1192664111yescharacteristic
303C22#1192664711yescharacteristic
304C22#1192665811yescharacteristic
305C22#1192665811yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—81no—
310C4—762no—
311C4—1521no—
312C4#1192656611yescharacteristic
313C4#1192656911yescharacteristic
314C4#1192667211yescharacteristic
315C4#1192667411yescharacteristic
316C4#1192679611yescharacteristic
317C4#1192680111yescharacteristic
318C4#1192695111yescharacteristic
319C4#1192695211yescharacteristic
320C2#1456248911yescharacteristic
321C2#1456249511yescharacteristic
322C2#1456251011yescharacteristic
323C2#1456251611yescharacteristic
324C2#1456435711yescharacteristic
325C2#1456437711yescharacteristic
326C2#1456438211yescharacteristic
subgroupG/H
centerC22×C4D4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1279C2
socle, prime radicalC23×C19C4×D4
cosocleC2×C42×C19C23
hypercenter#1279D19
hypocenterC19#9600
LCSG ▷ C22×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
218. C19#9600semidirect

Maximal subgroups

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

subgroupindex
#145643542
#145643512
C4×#105972652
C2×#119262962
C2×#119262652
#145614752
C19×#12792
#960019