Finite Group Databasebeta

← #18087267

Subgroups — #18087267

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#14564571C211yesmaximal, characteristic
2#14563637C211yesmaximal, characteristic
3#14563637C211yesmaximal, characteristic
4#14561518C211yesmaximal, characteristic
5#14561518C211yesmaximal, characteristic
6#14561470C211yesmaximal, characteristic
7C19×#1844C211yesmaximal, characteristic
8C2×C4×Dic38C2211yescharacteristic
9C2×C4⋊(C19⋊C8)C2211yescharacteristic
10C2×C4⋊(C19⋊C8)C2211yescharacteristic
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12C2×#10597267—21no—
13C2×#10597267—21no—
14#11926306—21no—
15#11926306—21no—
16#11926298—21no—
17#11926298—21no—
18C2×C19×#106—21no—
19C2×C19×#106—21no—
20C2×C4×C8×C19C2211yescharacteristic
21C19×#384C2211yescharacteristic
22C19×#384C2211yescharacteristic
23C22×Dic38D411yescharacteristic
24C22×C8×C19D411yescharacteristic
25C22×C8×C19D411yescharacteristic
26C2×C4⋊C4×C19—21no—
27C2×C4⋊C4×C19—21no—
28C2×C4⋊C4×C19—21no—
29C2×C4⋊C4×C19—21no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C42×C19C2311yescharacteristic
33C2×C4⋊Dic19D411yescharacteristic
34C2×Dic19⋊C4—21no—
35C2×C4×Dic19—21no—
36C22×C19⋊C8—21no—
37C22×C19⋊C8—21no—
38C22×C19⋊C8—21no—
39C4×Dic38—21no—
40C4×Dic38—21no—
41C4×Dic38—21no—
42C4×Dic38—21no—
43C19×#106—42no—
44C19×#106—42no—
45C4×C8×C19—21no—
46C4×C8×C19—21no—
47#10597267—42no—
48#10597267—42no—
49C4⋊(C19⋊C8)—21no—
50C4⋊(C19⋊C8)—21no—
51C4⋊(C19⋊C8)—21no—
52C4⋊(C19⋊C8)—21no—
53C4⋊(C19⋊C8)—21no—
54C4⋊(C19⋊C8)—21no—
55C22×C4×C19—41no—
56C22×C4×C19—41no—
57C22×C4×C19C2×D411yescharacteristic
58C22×C4×C19C2×D411yescharacteristic
59C22×C4×C19#4111yescharacteristic
60C22×Dic19—21no—
61C22×Dic19—21no—
62C2×Dic38—21no—
63C2×Dic38—21no—
64C2×Dic38—21no—
65C2×Dic38—21no—
66C2×Dic38—21no—
67C2×Dic38SD1612yes—
68C2×C8×C19—21no—
69C2×C8×C19—21no—
70C2×C8×C19—21no—
71C2×C8×C19—21no—
72C2×C8×C19SD1612yes—
73C2×C8×C19Q1612yes—
74C4⋊C4×C19—41no—
75C4⋊C4×C19—41no—
76C4⋊C4×C19—41no—
77C4⋊C4×C19—41no—
78C4⋊C4×C19—41no—
79C4⋊C4×C19—41no—
80C4⋊C4×C19—41no—
81C4⋊C4×C19—41no—
82C4⋊C4×C19—81no—
83C4⋊C4×C19—81no—
84C42×C19#4111yescharacteristic
85C42×C19#4111yescharacteristic
86C42×C19#4111yescharacteristic
87C42×C19#4111yescharacteristic
88C4⋊Dic19—21no—
89C4⋊Dic19—21no—
90Dic19⋊C4—41no—
91Dic19⋊C4—41no—
92C4×Dic19—41no—
93C4×Dic19—41no—
94C2×C19⋊C8—41no—
95C2×C19⋊C8—41no—
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#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—81no—
111C2×C4×C19—81no—
112C2×C4×C19—81no—
113C2×C4×C19#12311yescharacteristic
114C2×C4×C19#12311yescharacteristic
115C2×C4×C19#12311yescharacteristic
116C2×C4×C19#12411yescharacteristic
117C2×C4×C19#12611yescharacteristic
118C2×C4×C19#12611yescharacteristic
119C2×C4×C19C2×SD1611yescharacteristic
120C2×C4×C19C2×SD1611yescharacteristic
121C2×C4×C19C2×Q1611yescharacteristic
122C2×C4×C19#13511yescharacteristic
123C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C19#13711yescharacteristic
126C2×C4×C19#13711yescharacteristic
127C2×Dic19—22no—
128C2×Dic19—41no—
129C2×Dic19—41no—
130C2×Dic19—41no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133Dic38—22no—
134Dic38—22no—
135Dic38—41no—
136Dic38—41no—
137C8×C19—22no—
138C8×C19—22no—
139C19⋊C8—81no—
140C19⋊C8—81no—
141C19⋊C8—81no—
142#1984—191no—
143#1844D1911yescharacteristic
144#1803—191no—
145#1803—191no—
146#1296—191no—
147#1296—191no—
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—161no—
160C4×C19#48111yescharacteristic
161C4×C19#48211yescharacteristic
162C4×C19#48311yescharacteristic
163C4×C19#48311yescharacteristic
164C4×C19#48411yescharacteristic
165C4×C19#48511yescharacteristic
166C4×C19#48711yescharacteristic
167C4×C19#48911yescharacteristic
168Dic19—42no—
169Dic19—81no—
170C2×C4×Q8—191no—
171C2×#106—21no—
172C2×#106—21no—
173C2×C4⋊C8—191no—
174C2×C4⋊C8—191no—
175C2×C4⋊C8—191no—
176C2×#103—381no—
177C2×#103—381no—
178C2×C4×C8C2×D1911yescharacteristic
179#384C2×D1911yescharacteristic
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—381no—
194C22×C8—381no—
195C22×C8—381no—
196C22×C8C22⋊D1911yescharacteristic
197C22×C8C22⋊D1911yescharacteristic
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—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—191no—
209C2×C4⋊C4—381no—
210C2×C42—381no—
211C2×C42C22×D1911yescharacteristic
212#106—42no—
213#106—42no—
214C4⋊C8—381no—
215C4⋊C8—381no—
216C4⋊C8—381no—
217C4⋊C8—381no—
218C4⋊C8—381no—
219C4⋊C8—381no—
220#103—762no—
221#103—762no—
222C4×C8—21no—
223C4×C8—21no—
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—41no—
233C22×C4—381no—
234C22×C4—381no—
235C22×C4D4×D1911yescharacteristic
236C22×C4#6454311yescharacteristic
237C22×C4C2×C22⋊D1911yescharacteristic
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—761no—
243C2×C8—761no—
244C2×C8—761no—
245C2×C8—761no—
246C2×C8—761no—
247C2×C8—761no—
248C2×C8—761no—
249C2×C8—761no—
250C2×C8—761no—
251C2×C8#6452612yes—
252C2×C8#6452812yes—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—81no—
262C4⋊C4—81no—
263C4⋊C4—381no—
264C4⋊C4—381no—
265C4⋊C4—761no—
266C4⋊C4—761no—
267C42—761no—
268C42—761no—
269C42#6454111yescharacteristic
270C42#6454111yescharacteristic
271C42#6454511yescharacteristic
272C42#6454511yescharacteristic
273C23#1059738411yescharacteristic
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—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—382no—
287C2×C4—761no—
288C2×C4—761no—
289C2×C4—761no—
290C2×C4—761no—
291C2×C4—761no—
292C2×C4#1059734011yescharacteristic
293C2×C4#1059734011yescharacteristic
294C2×C4#1059734411yescharacteristic
295C2×C4#1059734411yescharacteristic
296C2×C4SD16×D1911yescharacteristic
297C2×C4#1059736011yescharacteristic
298C2×C4#1059736111yescharacteristic
299C2×C4#1059736211yescharacteristic
300C2×C4#1059737511yescharacteristic
301C2×C4#1059737811yescharacteristic
302C2×C4C2×#6452611yescharacteristic
303C2×C4#1059738811yescharacteristic
304C2×C4C2×#6452811yescharacteristic
305C2×C4#1059739311yescharacteristic
306C8—22no—
307C8—22no—
308C8—1521no—
309C8—1521no—
310C8—1521no—
311C22#1192647011yescharacteristic
312C22#1192674111yescharacteristic
313C22#1192675111yescharacteristic
314C22#1192677011yescharacteristic
315C22#1192678711yescharacteristic
316C22#1192680411yescharacteristic
317C22#1192680411yescharacteristic
318C4—21no—
319C4—21no—
320C4—161no—
321C4—161no—
322C4—762no—
323C4—1521no—
324C4#1192686411yescharacteristic
325C4#1192687011yescharacteristic
326C4#1192687411yescharacteristic
327C4#1192687611yescharacteristic
328C4#1192687911yescharacteristic
329C4#1192688811yescharacteristic
330C4#1192689611yescharacteristic
331C4#1192690611yescharacteristic
332C2#1456298011yescharacteristic
333C2#1456301411yescharacteristic
334C2#1456310411yescharacteristic
335C2#1456313811yescharacteristic
336C2#1456504411yescharacteristic
337C2#1456506911yescharacteristic
338C2#1456508111yescharacteristic
subgroupG/H
centerC23#10597384
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1844C2
socle, prime radicalC23×C19#121
hypercenter#1844D19
hypocenterC19#10620
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1844

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
#145645712
#145636372
#145615182
#145614702
C19×#18442
#1062019