Finite Group Databasebeta

← #18087305

Subgroups — #18087305

Order 4864.

350 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564570C211yesmaximal, characteristic
2#14563762C211yesmaximal, characteristic
3#14563641C211yesmaximal, characteristic
4#14563637C211yesmaximal, characteristic
5#14561519C211yesmaximal, characteristic
6#14561469C211yesmaximal, characteristic
7C19×#1296C211yesmaximal, characteristic
8C2×C4×Dic38C2211yescharacteristic
9C2×C4⋊(C19⋊C8)C2211yescharacteristic
10C2×#10597273—21no—
11C2×#10597267—21no—
12C2×C4×C19⋊C8C2211yescharacteristic
13#11926414C2211yescharacteristic
14#11926307—21no—
15#11926306—21no—
16#11926306—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—
49C4⋊(C19⋊C8)—21no—
50C4⋊(C19⋊C8)—21no—
51C4×C19⋊C8—21no—
52C4×C19⋊C8—21no—
53C22×C4×C19—41no—
54C22×C4×C19C2×D411yescharacteristic
55C22×C4×C19C2×D411yescharacteristic
56C22×C4×C19#4111yescharacteristic
57C22×Dic19—21no—
58C22×Dic19—21no—
59C22×Dic19—41no—
60C2×Dic38—21no—
61C2×Dic38—21no—
62C2×Dic38—21no—
63C2×Dic38—21no—
64C2×Dic38—21no—
65C2×Dic38SD1612yes—
66C2×C8×C19—41no—
67C2×C8×C19—41no—
68C2×C8×C19—41no—
69C2×C8×C19—41no—
70C2×C8×C19—41no—
71C2×C8×C19—41no—
72C4⋊C4×C19—41no—
73C4⋊C4×C19—41no—
74C4⋊C4×C19—41no—
75C4⋊C4×C19—41no—
76C4⋊C4×C19—81no—
77C42×C19#4111yescharacteristic
78C42×C19#4111yescharacteristic
79C42×C19#4111yescharacteristic
80C42×C19#4111yescharacteristic
81C4⋊Dic19—21no—
82C4⋊Dic19—21no—
83C4⋊Dic19—41no—
84C4⋊Dic19—41no—
85C4⋊Dic19—41no—
86C4⋊Dic19—41no—
87C4⋊Dic19—81no—
88Dic19⋊C4—41no—
89Dic19⋊C4—41no—
90C4×Dic19—41no—
91C4×Dic19—41no—
92C2×C19⋊C8—21no—
93C2×C19⋊C8—21no—
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—
101#10626—191nomaximal, Sylow
102C23×C19#12111yescharacteristic
103C2×C4×C19—21no—
104C2×C4×C19—21no—
105C2×C4×C19—81no—
106C2×C4×C19—81no—
107C2×C4×C19—81no—
108C2×C4×C19#12311yescharacteristic
109C2×C4×C19#12311yescharacteristic
110C2×C4×C19#12311yescharacteristic
111C2×C4×C19#12411yescharacteristic
112C2×C4×C19#12611yescharacteristic
113C2×C4×C19#12611yescharacteristic
114C2×C4×C19C2×SD1611yescharacteristic
115C2×C4×C19#13511yescharacteristic
116C2×C4×C19#13511yescharacteristic
117C2×C4×C19#13511yescharacteristic
118C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C19#13711yescharacteristic
120C2×C4×C19#13711yescharacteristic
121C2×C4×C19#13711yescharacteristic
122C2×Dic19—22no—
123C2×Dic19—41no—
124C2×Dic19—41no—
125C2×Dic19—41no—
126C2×Dic19—41no—
127C2×Dic19—41no—
128C2×Dic19—81no—
129C2×Dic19—81no—
130C2×Dic19—81no—
131Dic38—22no—
132Dic38—22no—
133Dic38—41no—
134Dic38—41no—
135C8×C19—81no—
136C8×C19—81no—
137C19⋊C8—41no—
138C19⋊C8—41no—
139C19⋊C8—81no—
140#1984—191no—
141#1834—191no—
142#1803—191no—
143#1803—191no—
144#1296—191no—
145#1296D1911yescharacteristic
146#1277—191no—
147C22×C19#39711yescharacteristic
148C22×C19#46411yescharacteristic
149C22×C19#46411yescharacteristic
150C22×C19#46511yescharacteristic
151C22×C19#46811yescharacteristic
152C22×C19#47211yescharacteristic
153C22×C19#47311yescharacteristic
154C4×C19—21no—
155C4×C19—21no—
156C4×C19—161no—
157C4×C19#48111yescharacteristic
158C4×C19#48211yescharacteristic
159C4×C19#48311yescharacteristic
160C4×C19#48511yescharacteristic
161C4×C19#48511yescharacteristic
162C4×C19#48511yescharacteristic
163C4×C19#48811yescharacteristic
164C4×C19#49111yescharacteristic
165Dic19—42no—
166Dic19—81no—
167Dic19—161no—
168C2×C4×Q8—191no—
169C2×C4⋊C8—191no—
170C2×C4⋊C8C2×D1911yescharacteristic
171C2×C4⋊C8C2×D1911yescharacteristic
172C2×#103—381no—
173C2×#103—381no—
174C2×C4×C8—191no—
175#384—191no—
176#384C2×D1911yescharacteristic
177#340—381no—
178#340—381no—
179#340—381no—
180#340—381no—
181#336—381no—
182#336—381no—
183C2×C19#167811yescharacteristic
184C2×C19#168011yescharacteristic
185C2×C19#169811yescharacteristic
186C2×C19#170011yescharacteristic
187C2×C19#207411yescharacteristic
188C2×C19#207711yescharacteristic
189C2×C19#207811yescharacteristic
190C22×Q8—191no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—191no—
194C22×C8—191no—
195C22×C8—381no—
196C4×Q8—381no—
197C4×Q8—381no—
198C4×Q8—381no—
199C4×Q8—381no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—191no—
204C2×C4⋊C4—381no—
205C2×C4⋊C4—381no—
206C2×C4⋊C4—381no—
207C2×C4⋊C4—381no—
208C2×C42—381no—
209C2×C42C22×D1911yescharacteristic
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—381no—
215C4⋊C8—381no—
216#103—762no—
217#103—762no—
218C4×C8—381no—
219C4×C8—381no—
220C19#1062611yescharacteristic, complemented, Sylow
221C2×Q8—192no—
222C2×Q8—381no—
223C2×Q8—381no—
224C2×Q8—381no—
225C2×Q8—381no—
226C2×Q8—381no—
227C22×C4—41no—
228C22×C4—381no—
229C22×C4—381no—
230C22×C4—761no—
231C22×C4#6454111yescharacteristic
232C22×C4D4×D1911yescharacteristic
233C22×C4D4×D1911yescharacteristic
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—381no—
241C2×C8—381no—
242C2×C8—381no—
243C2×C8—381no—
244C2×C8—381no—
245C2×C8—381no—
246C2×C8—761no—
247C2×C8—761no—
248C2×C8—761no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—81no—
254C4⋊C4—381no—
255C4⋊C4—381no—
256C4⋊C4—761no—
257C4⋊C4—761no—
258C4⋊C4—761no—
259C4⋊C4—761no—
260C4⋊C4—761no—
261C4⋊C4—761no—
262C4⋊C4—1521no—
263C42—761no—
264C42—761no—
265C42#6454111yescharacteristic
266C42#6454111yescharacteristic
267C42#6454311yescharacteristic
268C42#6454511yescharacteristic
269C23#1059733011yescharacteristic
270Q8—382no—
271Q8—382no—
272Q8—761no—
273Q8—761no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—382no—
280C2×C4—761no—
281C2×C4—761no—
282C2×C4—761no—
283C2×C4—761no—
284C2×C4—761no—
285C2×C4—1521no—
286C2×C4—1521no—
287C2×C4—1521no—
288C2×C4#1059732211yescharacteristic
289C2×C4#1059732911yescharacteristic
290C2×C4#1059733111yescharacteristic
291C2×C4#1059734011yescharacteristic
292C2×C4#1059734011yescharacteristic
293C2×C4#1059734411yescharacteristic
294C2×C4#1059735811yescharacteristic
295C2×C4#1059735811yescharacteristic
296C2×C4SD16×D1911yescharacteristic
297C2×C4#1059736011yescharacteristic
298C2×C4#1059736111yescharacteristic
299C2×C4#1059736211yescharacteristic
300C2×C4#1059736411yescharacteristic
301C2×C4#1059736411yescharacteristic
302C8—81no—
303C8—81no—
304C8—761no—
305C8—761no—
306C8—1521no—
307C22#1192647311yescharacteristic
308C22#1192676511yescharacteristic
309C22#1192676911yescharacteristic
310C22#1192677211yescharacteristic
311C22#1192679311yescharacteristic
312C22#1192681311yescharacteristic
313C22#1192681811yescharacteristic
314C4—21no—
315C4—21no—
316C4—161no—
317C4—3041no—
318C4—762no—
319C4—1521no—
320C4#1192686411yescharacteristic
321C4#1192686611yescharacteristic
322C4#1192687311yescharacteristic
323C4#1192688711yescharacteristic
324C4#1192688711yescharacteristic
325C4#1192688811yescharacteristic
326C4#1192689711yescharacteristic
327C4#1192691111yescharacteristic
328C2#1456305011yescharacteristic
329C2#1456306811yescharacteristic
330C2#1456317811yescharacteristic
331C2#1456318811yescharacteristic
332C2#1456505711yescharacteristic
333C2#1456507311yescharacteristic
334C2#1456507911yescharacteristic
subgroupG/H
centerC23#10597330
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1296C2
socle, prime radicalC23×C19#121
hypercenter#1296D19
hypocenterC19#10626
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
220. C19#10626semidirect

Maximal subgroups

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

subgroupindex
#145645702
#145637622
#145636412
#145636372
#145615192
#145614692
C19×#12962
#1062619