Finite Group Databasebeta

← #18081571

Subgroups — #18081571

Order 4864.

570 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572031C211yesmaximal, characteristic
2#14563786C211yesmaximal, characteristic
3C4⋊C8×Dic19C211yesmaximal, characteristic
4C2×#11926291C211yesmaximal, characteristic
5C2×#11926290C211yesmaximal, characteristic
6C2×#11926289C211yesmaximal, characteristic
7C2×C19×#332C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9C2×#10597390—22no—
10C2×C4⋊(C19⋊C8)C2211yescharacteristic
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12C2×Dic19⋊C8—22no—
13C2×C8×Dic19—21no—
14#11926413—21no—
15#11926413—21no—
16#11926413C414yes—
17C42×Dic19C2211yescharacteristic
18#11926298—21no—
19#11926291—22no—
20#11926290—22no—
21#11926289—22no—
22C2×C19×C4⋊Q8C2211yescharacteristic
23C2×C19×C4⋊C8C2211yescharacteristic
24C2×C19×C4⋊C8C2211yescharacteristic
25C19×#332—22no—
26C22×Q8×C19—21no—
27C22×Dic38—21no—
28C22×C8×C19—21no—
29C22×C8×C19—21no—
30C19×C4⋊Q8—21no—
31C19×C4⋊Q8—21no—
32C19×C4⋊Q8—21no—
33C19×C4⋊Q8—21no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19C2×C412yes—
36C2×C42×C19C2311yescharacteristic
37#10597390—44no—
38#10597390—44no—
39C2×C4⋊Dic19—21no—
40C2×C4⋊Dic19C2×C412yes—
41C2×Dic19⋊C4—24no—
42C2×Dic19⋊C4—24no—
43C2×C4×Dic19C2×C412yes—
44C2×C4×Dic19D411yescharacteristic
45C2×C4×Dic19D412yes—
46C2×C4×Dic19D411yescharacteristic
47C22×C19⋊C8—21no—
48C22×C19⋊C8—21no—
49#10597315—21no—
50#10597315—21no—
51#10597315—21no—
52#10597315—21no—
53C19×C4⋊C8—21no—
54C19×C4⋊C8—21no—
55C19×C4⋊C8—21no—
56C19×C4⋊C8D412yes—
57Dic19⋊C8—44no—
58C8×Dic19—42no—
59C4⋊(C19⋊C8)—21no—
60C4⋊(C19⋊C8)—21no—
61C4⋊(C19⋊C8)—21no—
62C4⋊(C19⋊C8)D412yes—
63C2×Q8×C19—41no—
64C2×Q8×C19—41no—
65C2×Q8×C19—42no—
66C2×Q8×C19—42no—
67C22×C4×C19—22no—
68C22×C4×C19C22×C411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×C4×C19C2×D411yescharacteristic
71C22×Dic19—22no—
72C22×Dic19C22⋊C412yes—
73C22×Dic19C22⋊C412yes—
74C2×Dic38—41no—
75C2×Dic38—41no—
76C2×Dic38—42no—
77C2×Dic38—42no—
78C2×C8×C19—22no—
79C2×C8×C19—41no—
80C2×C8×C19—41no—
81C2×C8×C19—41no—
82C2×C8×C19—42no—
83C4⋊C4×C19—22no—
84C4⋊C4×C19—22no—
85C4⋊C4×C19—41no—
86C4⋊C4×C19—41no—
87C42×C19C2×D411yescharacteristic
88C42×C19C2×D411yescharacteristic
89C42×C19#4111yescharacteristic
90C42×C19#4111yescharacteristic
91C4⋊Dic19—22no—
92C4⋊Dic19—22no—
93C4⋊Dic19—41no—
94C4⋊Dic19—41no—
95Dic19⋊C4—48no—
96Dic19⋊C4—48no—
97C4×Dic19—21no—
98C4×Dic19—21no—
99C4×Dic19—24no—
100C4×Dic19D814yes—
101C4×Dic19SD1614yes—
102C4×Dic19SD1612yes—
103C4×Dic19Q1612yes—
104C2×C19⋊C8—22no—
105C2×C19⋊C8—41no—
106C2×C19⋊C8—41no—
107C2×C19⋊C8—41no—
108C2×C19⋊C8—42no—
109#9692—191nomaximal, Sylow
110C23×C19C2×C22⋊C411yescharacteristic
111Q8×C19—82no—
112Q8×C19—81no—
113Q8×C19—81no—
114C2×C4×C19—22no—
115C2×C4×C19—42no—
116C2×C4×C19—44no—
117C2×C4×C19C4×D411yescharacteristic
118C2×C4×C19C4×D411yescharacteristic
119C2×C4×C19#12111yescharacteristic
120C2×C4×C19#12111yescharacteristic
121C2×C4×C19#12411yescharacteristic
122C2×C4×C19#12711yescharacteristic
123C2×C4×C19C2×D812yes—
124C2×C4×C19C2×SD1611yescharacteristic
125C2×C4×C19C2×SD1612yes—
126C2×C4×C19C2×Q1611yescharacteristic
127C2×C4×C19#13711yescharacteristic
128C2×C4×C19#13711yescharacteristic
129C2×Dic19—22no—
130C2×Dic19—22no—
131C2×Dic19—42no—
132C2×Dic19—44no—
133C2×Dic19#10114yes—
134C2×Dic19#10214yes—
135C2×Dic19#10214yes—
136C2×Dic19#10314yes—
137Dic38—82no—
138Dic38—81no—
139Dic38—81no—
140C8×C19—42no—
141C8×C19—81no—
142C19⋊C8—42no—
143C19⋊C8—81no—
144#2868—191no—
145#1842—191no—
146C4×C4⋊C8—191no—
147C2×#332—191no—
148C2×#332—191no—
149C2×#332—191no—
150C2×#332D1911yescharacteristic
151C22×C19#39011yescharacteristic
152C22×C19C2×#10112yes—
153C22×C19C2×#10212yes—
154C22×C19C2×#10311yescharacteristic
155C22×C19#41911yescharacteristic
156C4×C19—21no—
157C4×C19—21no—
158C4×C19—82no—
159C4×C19#46111yescharacteristic
160C4×C19#46111yescharacteristic
161C4×C19#46211yescharacteristic
162C4×C19#46211yescharacteristic
163C4×C19#48612yes—
164C4×C19#49211yescharacteristic
165C4×C19#49311yescharacteristic
166Dic19—24no—
167Dic19—82no—
168Dic19#33218yescomplemented
169C2×C4⋊Q8—191no—
170C2×C4⋊Q8—382no—
171C2×C4⋊Q8C2×D1911yescharacteristic
172C2×C4⋊C8—191no—
173C2×C4⋊C8—191no—
174C2×C4⋊C8—382no—
175C2×C4⋊C8C2×D1911yescharacteristic
176C2×C4⋊C8C2×D1911yescharacteristic
177C2×C4×C8—381no—
178#384—194no—
179#384—381no—
180#384—381no—
181C43—191no—
182#336—381no—
183#332—22no—
184#332—382no—
185#332—382no—
186#332—382no—
187C2×C19C2×#33212yes—
188C2×C19#154612yes—
189C2×C19#195711yescharacteristic
190C2×C19#196611yescharacteristic
191C2×C19#198111yescharacteristic
192C22×Q8—21no—
193C22×Q8—381no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—381no—
197C22×C8—381no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—381no—
203C4⋊Q8—381no—
204C4⋊Q8—381no—
205C4⋊Q8—381no—
206C4⋊Q8—764no—
207C4⋊Q8—764no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—192no—
210C2×C4⋊C4—384no—
211C2×C4⋊C4—384no—
212C2×C4⋊C4—381no—
213C2×C4⋊C4C4×D1912yes—
214C2×C42—192no—
215C2×C42—191no—
216C2×C42—192no—
217C2×C42—191no—
218C2×C42C22×D1911yescharacteristic
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—192no—
223C4⋊C8—381no—
224C4⋊C8—381no—
225C4⋊C8—381no—
226C4⋊C8—764no—
227C4⋊C8C22⋊D1912yes—
228C4×C8—762no—
229C19#969211yescharacteristic, complemented, Sylow
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—42no—
233C2×Q8—42no—
234C2×Q8—761no—
235C2×Q8—761no—
236C2×Q8—762no—
237C2×Q8—762no—
238C22×C4—22no—
239C22×C4—192no—
240C22×C4—192no—
241C22×C4—382no—
242C22×C4C2×C4×D1911yescharacteristic
243C22×C4D4×D1911yescharacteristic
244C22×C4D4×D1911yescharacteristic
245C2×C8—22no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—42no—
250C2×C8—382no—
251C2×C8—761no—
252C2×C8—761no—
253C2×C8—761no—
254C2×C8—762no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—382no—
260C4⋊C4—382no—
261C4⋊C4—768no—
262C4⋊C4—768no—
263C4⋊C4—761no—
264C4⋊C4—761no—
265C42—194no—
266C42—192no—
267C42—194no—
268C42—192no—
269C42—384no—
270C42—381no—
271C42—381no—
272C42#6454111yescharacteristic
273C42D4×D1911yescharacteristic
274C42#6454311yescharacteristic
275C42C2×C22⋊D1911yescharacteristic
276C23C22⋊C4×D1911yescharacteristic
277Q8—82no—
278Q8—81no—
279Q8—81no—
280Q8—1522no—
281Q8—1521no—
282Q8—1521no—
283C2×C4—22no—
284C2×C4—44no—
285C2×C4—42no—
286C2×C4—194no—
287C2×C4—194no—
288C2×C4—194no—
289C2×C4—194no—
290C2×C4—382no—
291C2×C4—382no—
292C2×C4—764no—
293C2×C4—762no—
294C2×C4(C22⋊D19)⋊C411yescharacteristic
295C2×C4#1059733011yescharacteristic
296C2×C4#1059733111yescharacteristic
297C2×C4D8×D1912yes—
298C2×C4SD16×D1912yes—
299C2×C4SD16×D1911yescharacteristic
300C2×C4#1059736111yescharacteristic
301C2×C4Q16×D1911yescharacteristic
302C2×C4#1059736411yescharacteristic
303C2×C4C4×C22⋊D1911yescharacteristic
304C2×C4#1059738511yescharacteristic
305C2×C4#1059738611yescharacteristic
306C8—42no—
307C8—81no—
308C8—762no—
309C8—1521no—
310C22#1192644411yescharacteristic
311C22#101×D1912yes—
312C22#102×D1912yes—
313C22#103×D1911yescharacteristic
314C22#1192655111yescharacteristic
315C4—21no—
316C4—21no—
317C4—82no—
318C4—198no—
319C4—384no—
320C4—1522no—
321C4#1192674711yescharacteristic
322C4#1192674811yescharacteristic
323C4#1192675211yescharacteristic
324C4#1192675311yescharacteristic
325C4#1192688912yes—
326C4#1192691511yescharacteristic
327C4#1192691911yescharacteristic
328C2D19×#33212yes—
329C2#1456230512yes—
330C2#1456443911yescharacteristic
331C2#1456447711yescharacteristic
332C2#1456455611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC2×C19×#332C2
socle, prime radicalC23×C19C2×C22⋊C4
cosocleC2×C42×C19C23
hypercenterC2×#332D19
hypocenterC19#9692
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
168. Dic19#332semidirect
229. C19#9692semidirect

Maximal subgroups

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

subgroupindex
#145720312
#145637862
C4⋊C8×Dic192
C2×#119262912
C2×#119262902
C2×#119262892
C2×C19×#3322
#969219