Finite Group Databasebeta

← #18087272

Subgroups — #18087272

Order 4864.

366 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#14564570C211yesmaximal, characteristic
2#14563791C211yesmaximal, characteristic
3#14563641C211yesmaximal, characteristic
4#14563637C211yesmaximal, characteristic
5#14561519C211yesmaximal, characteristic
6#14561469C211yesmaximal, characteristic
7C19×#1296C211yesmaximal, characteristic
8C2×C4×Dic38C2211yescharacteristic
9C2×#10597265—21no—
10C2×#10597265—21no—
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12C2×#10597273—21no—
13C2×#10597267—21no—
14C2×C4×C19⋊C8C2211yescharacteristic
15#11926414C2211yescharacteristic
16#11926307—21no—
17#11926306—21no—
18#11926298—21no—
19#11926298—21no—
20C2×C19×C4⋊C8C2211yescharacteristic
21C2×C19×C4⋊C8C2211yescharacteristic
22C19×#384C2211yescharacteristic
23C22×Dic38D411yescharacteristic
24C22×C8×C19—21no—
25C22×C8×C19—21no—
26C2×C4⋊C4×C19—21no—
27C2×C4⋊C4×C19—21no—
28C2×C4⋊C4×C19—21no—
29C2×C42×C19C2311yescharacteristic
30C2×C4⋊Dic19—21no—
31C2×C4⋊Dic19—21no—
32C2×C4⋊Dic19—21no—
33C2×C4⋊Dic19D411yescharacteristic
34C2×Dic19⋊C4—21no—
35C2×C4×Dic19—21no—
36C22×C19⋊C8—21no—
37C22×C19⋊C8D411yescharacteristic
38C22×C19⋊C8D411yescharacteristic
39C4×Dic38—21no—
40C4×Dic38—21no—
41C4×Dic38—21no—
42C4×Dic38—21no—
43C19×C4⋊C8—21no—
44C19×C4⋊C8—21no—
45C19×C4⋊C8—21no—
46C19×C4⋊C8—21no—
47#10597273—42no—
48#10597267—42no—
49#10597265—42no—
50#10597265—42no—
51C4⋊(C19⋊C8)—21no—
52C4⋊(C19⋊C8)—21no—
53C4×C19⋊C8—21no—
54C4×C19⋊C8—21no—
55C22×C4×C19—41no—
56C22×C4×C19C2×D411yescharacteristic
57C22×C4×C19C2×D411yescharacteristic
58C22×C4×C19#4111yescharacteristic
59C22×Dic19—21no—
60C22×Dic19—21no—
61C22×Dic19—41no—
62C2×Dic38—21no—
63C2×Dic38—21no—
64C2×Dic38—21no—
65C2×Dic38—21no—
66C2×Dic38—21no—
67C2×Dic38SD1612yes—
68C2×C8×C19—41no—
69C2×C8×C19—41no—
70C2×C8×C19—41no—
71C2×C8×C19—41no—
72C2×C8×C19—41no—
73C2×C8×C19—41no—
74C4⋊C4×C19—41no—
75C4⋊C4×C19—41no—
76C4⋊C4×C19—41no—
77C4⋊C4×C19—41no—
78C4⋊C4×C19—81no—
79C42×C19#4111yescharacteristic
80C42×C19#4111yescharacteristic
81C42×C19#4111yescharacteristic
82C42×C19#4111yescharacteristic
83C4⋊Dic19—21no—
84C4⋊Dic19—21no—
85C4⋊Dic19—41no—
86C4⋊Dic19—41no—
87C4⋊Dic19—41no—
88C4⋊Dic19—41no—
89C4⋊Dic19—81no—
90Dic19⋊C4—41no—
91Dic19⋊C4—41no—
92C4×Dic19—41no—
93C4×Dic19—41no—
94C2×C19⋊C8—21no—
95C2×C19⋊C8—21no—
96C2×C19⋊C8—21no—
97C2×C19⋊C8—21no—
98C2×C19⋊C8—41no—
99C2×C19⋊C8—41no—
100C2×C19⋊C8—41no—
101C2×C19⋊C8SD1612yes—
102C2×C19⋊C8Q1612yes—
103#10620—191nomaximal, Sylow
104C23×C19#12111yescharacteristic
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—81no—
108C2×C4×C19—81no—
109C2×C4×C19—81no—
110C2×C4×C19#12311yescharacteristic
111C2×C4×C19#12311yescharacteristic
112C2×C4×C19#12311yescharacteristic
113C2×C4×C19#12411yescharacteristic
114C2×C4×C19#12611yescharacteristic
115C2×C4×C19#12611yescharacteristic
116C2×C4×C19C2×SD1611yescharacteristic
117C2×C4×C19C2×SD1611yescharacteristic
118C2×C4×C19C2×Q1611yescharacteristic
119C2×C4×C19#13511yescharacteristic
120C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C19#13711yescharacteristic
123C2×C4×C19#13711yescharacteristic
124C2×Dic19—22no—
125C2×Dic19—41no—
126C2×Dic19—41no—
127C2×Dic19—41no—
128C2×Dic19—41no—
129C2×Dic19—41no—
130C2×Dic19—81no—
131C2×Dic19—81no—
132C2×Dic19—81no—
133Dic38—22no—
134Dic38—22no—
135Dic38—41no—
136Dic38—41no—
137C8×C19—81no—
138C8×C19—81no—
139C19⋊C8—22no—
140C19⋊C8—22no—
141C19⋊C8—81no—
142#1984—191no—
143#1844—191no—
144#1803—191no—
145#1803—191no—
146#1296—191no—
147#1296D1911yescharacteristic
148#1277—191no—
149C22×C19#39711yescharacteristic
150C22×C19#46011yescharacteristic
151C22×C19#46211yescharacteristic
152C22×C19#46511yescharacteristic
153C22×C19#46811yescharacteristic
154C22×C19#47111yescharacteristic
155C22×C19#47111yescharacteristic
156C4×C19—21no—
157C4×C19—21no—
158C4×C19—161no—
159C4×C19#48111yescharacteristic
160C4×C19#48211yescharacteristic
161C4×C19#48311yescharacteristic
162C4×C19#48311yescharacteristic
163C4×C19#48411yescharacteristic
164C4×C19#48511yescharacteristic
165C4×C19#48711yescharacteristic
166C4×C19#48911yescharacteristic
167Dic19—42no—
168Dic19—81no—
169Dic19—161no—
170C2×C4×Q8—191no—
171C2×#106—381no—
172C2×#106—381no—
173C2×C4⋊C8—191no—
174C2×C4⋊C8C2×D1911yescharacteristic
175C2×C4⋊C8C2×D1911yescharacteristic
176C2×#103—381no—
177C2×#103—381no—
178C2×C4×C8—191no—
179#384—191no—
180#384C2×D1911yescharacteristic
181#340—381no—
182#340—381no—
183#336—381no—
184#336—381no—
185C2×C19#166611yescharacteristic
186C2×C19#167211yescharacteristic
187C2×C19#168611yescharacteristic
188C2×C19#169211yescharacteristic
189C2×C19#207211yescharacteristic
190C2×C19#207711yescharacteristic
191C2×C19#207911yescharacteristic
192C22×Q8—191no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—191no—
196C22×C8—191no—
197C22×C8—381no—
198C4×Q8—381no—
199C4×Q8—381no—
200C4×Q8—381no—
201C4×Q8—381no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—191no—
206C2×C4⋊C4—381no—
207C2×C4⋊C4—381no—
208C2×C4⋊C4—381no—
209C2×C4⋊C4—381no—
210C2×C42—381no—
211C2×C42C22×D1911yescharacteristic
212#106—762no—
213#106—762no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—381no—
219C4⋊C8—381no—
220#103—762no—
221#103—762no—
222C4×C8—381no—
223C4×C8—381no—
224C19#1062011yescharacteristic, complemented, Sylow
225C2×Q8—192no—
226C2×Q8—381no—
227C2×Q8—381no—
228C2×Q8—381no—
229C2×Q8—381no—
230C2×Q8—381no—
231C22×C4—41no—
232C22×C4—381no—
233C22×C4—381no—
234C22×C4—761no—
235C22×C4#6454111yescharacteristic
236C22×C4D4×D1911yescharacteristic
237C22×C4D4×D1911yescharacteristic
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—192no—
245C2×C8—192no—
246C2×C8—381no—
247C2×C8—381no—
248C2×C8—381no—
249C2×C8—381no—
250C2×C8—761no—
251C2×C8—761no—
252C2×C8—761no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—81no—
258C4⋊C4—381no—
259C4⋊C4—381no—
260C4⋊C4—761no—
261C4⋊C4—761no—
262C4⋊C4—761no—
263C4⋊C4—761no—
264C4⋊C4—761no—
265C4⋊C4—761no—
266C4⋊C4—1521no—
267C42—761no—
268C42—761no—
269C42#6454111yescharacteristic
270C42#6454111yescharacteristic
271C42#6454311yescharacteristic
272C42#6454511yescharacteristic
273C23#1059733011yescharacteristic
274Q8—382no—
275Q8—382no—
276Q8—761no—
277Q8—761no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—382no—
284C2×C4—761no—
285C2×C4—761no—
286C2×C4—761no—
287C2×C4—761no—
288C2×C4—761no—
289C2×C4—1521no—
290C2×C4—1521no—
291C2×C4—1521no—
292C2×C4#1059732211yescharacteristic
293C2×C4#1059732911yescharacteristic
294C2×C4#1059733111yescharacteristic
295C2×C4#1059734011yescharacteristic
296C2×C4#1059734011yescharacteristic
297C2×C4#1059734411yescharacteristic
298C2×C4#1059735711yescharacteristic
299C2×C4#1059735711yescharacteristic
300C2×C4SD16×D1911yescharacteristic
301C2×C4SD16×D1911yescharacteristic
302C2×C4#1059736111yescharacteristic
303C2×C4#1059736111yescharacteristic
304C2×C4Q16×D1911yescharacteristic
305C2×C4#1059736511yescharacteristic
306C8—81no—
307C8—81no—
308C8—382no—
309C8—382no—
310C8—1521no—
311C22#1192647311yescharacteristic
312C22#1192674311yescharacteristic
313C22#1192675311yescharacteristic
314C22#1192677611yescharacteristic
315C22#1192678911yescharacteristic
316C22#1192680611yescharacteristic
317C22#1192681011yescharacteristic
318C4—21no—
319C4—21no—
320C4—161no—
321C4—3041no—
322C4—762no—
323C4—1521no—
324C4#1192686111yescharacteristic
325C4#1192687111yescharacteristic
326C4#1192687611yescharacteristic
327C4#1192687611yescharacteristic
328C4#1192688111yescharacteristic
329C4#1192688411yescharacteristic
330C4#1192689311yescharacteristic
331C4#1192690211yescharacteristic
332C2#1456298611yescharacteristic
333C2#1456302011yescharacteristic
334C2#1456310611yescharacteristic
335C2#1456314011yescharacteristic
336C2#1456504711yescharacteristic
337C2#1456507411yescharacteristic
338C2#1456508411yescharacteristic
subgroupG/H
centerC23#10597330
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1296C2
socle, prime radicalC23×C19#121
hypercenter#1296D19
hypocenterC19#10620
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
224. C19#10620semidirect

Maximal subgroups

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

subgroupindex
#145645702
#145637912
#145636412
#145636372
#145615192
#145614692
C19×#12962
#1062019