Finite Group Databasebeta

← #18081608

Subgroups — #18081608

Order 4864.

478 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572012C211yesmaximal, characteristic
2#14563751C211yesmaximal, characteristic
3C4⋊C8×Dic19C211yesmaximal, characteristic
4C2×#11926291C211yesmaximal, characteristic
5C2×#11926290C211yesmaximal, characteristic
6C2×#11926289C211yesmaximal, characteristic
7C2×C19×#332C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9C2×C4⋊(C19⋊C8)C2211yescharacteristic
10C2×C4⋊(C19⋊C8)C2211yescharacteristic
11C2×C8×Dic19—21no—
12#11926451—22no—
13#11926449—21no—
14#11926449—21no—
15#11926409C414yes—
16C42×Dic19C2211yescharacteristic
17#11926298—21no—
18#11926298—22no—
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
37C2×C4⋊Dic19—21no—
38C2×C4⋊Dic19C2×C412yes—
39C2×C4×Dic19C2×C412yes—
40C2×C4×Dic19D411yescharacteristic
41C2×C4×Dic19D412yes—
42C2×C4×Dic19D411yescharacteristic
43C22×C19⋊C8—21no—
44C22×C19⋊C8—21no—
45#10597315—21no—
46#10597315—21no—
47#10597315—21no—
48#10597315—21no—
49C19×C4⋊C8—21no—
50C19×C4⋊C8—21no—
51C19×C4⋊C8—21no—
52C19×C4⋊C8D412yes—
53C19⋊#95—24no—
54C19⋊#95—24no—
55C8×Dic19—42no—
56C4⋊(C19⋊C8)—21no—
57C4⋊(C19⋊C8)—21no—
58C4⋊(C19⋊C8)—21no—
59C4⋊(C19⋊C8)D412yes—
60C2×Q8×C19—41no—
61C2×Q8×C19—41no—
62C2×Q8×C19—42no—
63C2×Q8×C19—42no—
64C22×C4×C19—22no—
65C22×C4×C19C22×C411yescharacteristic
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19C2×D411yescharacteristic
68C22×Dic19—22no—
69C22×Dic19C22⋊C412yes—
70C22×Dic19C22⋊C412yes—
71C2×Dic38—41no—
72C2×Dic38—41no—
73C2×Dic38—41no—
74C2×Dic38—41no—
75C2×Dic38—41no—
76C2×Dic38—41no—
77C2×C8×C19—22no—
78C2×C8×C19—41no—
79C2×C8×C19—41no—
80C2×C8×C19—41no—
81C2×C8×C19—42no—
82C4⋊C4×C19—22no—
83C4⋊C4×C19—22no—
84C4⋊C4×C19—41no—
85C4⋊C4×C19—41no—
86C42×C19C2×D411yescharacteristic
87C42×C19C2×D411yescharacteristic
88C42×C19#4111yescharacteristic
89C42×C19#4111yescharacteristic
90C4⋊Dic19—22no—
91C4⋊Dic19—22no—
92C4⋊Dic19—41no—
93C4⋊Dic19—41no—
94C4×Dic19—22no—
95C4×Dic19—22no—
96C4×Dic19—21no—
97C4×Dic19—21no—
98C4×Dic19—21no—
99C4×Dic19—21no—
100C4×Dic19—24no—
101C2×C19⋊C8—22no—
102C2×C19⋊C8—41no—
103C2×C19⋊C8—41no—
104C2×C19⋊C8—41no—
105C2×C19⋊C8—42no—
106#9700—191nomaximal, Sylow
107C23×C19C2×C22⋊C411yescharacteristic
108Q8×C19—82no—
109Q8×C19—81no—
110Q8×C19—81no—
111C2×C4×C19—22no—
112C2×C4×C19—42no—
113C2×C4×C19—44no—
114C2×C4×C19C4×D411yescharacteristic
115C2×C4×C19C4×D411yescharacteristic
116C2×C4×C19#12111yescharacteristic
117C2×C4×C19#12111yescharacteristic
118C2×C4×C19#12411yescharacteristic
119C2×C4×C19#12711yescharacteristic
120C2×C4×C19#13512yes—
121C2×C4×C19#13511yescharacteristic
122C2×C4×C19#13512yes—
123C2×C4×C19#13511yescharacteristic
124C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C19#13711yescharacteristic
126C2×Dic19—22no—
127C2×Dic19—22no—
128C2×Dic19—22no—
129C2×Dic19—22no—
130C2×Dic19—22no—
131C2×Dic19—42no—
132C2×Dic19—42no—
133C2×Dic19—42no—
134C2×Dic19#10114yes—
135Dic38—81no—
136Dic38—81no—
137Dic38—81no—
138Dic38—81no—
139C8×C19—42no—
140C8×C19—81no—
141C19⋊C8—42no—
142C19⋊C8—81no—
143#2862—191no—
144#1831—191no—
145C4×C4⋊C8—191no—
146C2×#332—191no—
147C2×#332—191no—
148C2×#332—191no—
149C2×#332D1911yescharacteristic
150C22×C19#39011yescharacteristic
151C22×C19C2×#10112yes—
152C22×C19#41612yes—
153C22×C19#41611yescharacteristic
154C22×C19#41711yescharacteristic
155C4×C19—21no—
156C4×C19—21no—
157C4×C19—82no—
158C4×C19#46311yescharacteristic
159C4×C19#46311yescharacteristic
160C4×C19#46411yescharacteristic
161C4×C19#46411yescharacteristic
162C4×C19#48812yes—
163C4×C19#49511yescharacteristic
164C4×C19#49511yescharacteristic
165Dic19—24no—
166Dic19—42no—
167Dic19—82no—
168C2×C4⋊Q8—191no—
169C2×C4⋊Q8C2×D1911yescharacteristic
170C2×C4⋊C8—191no—
171C2×C4⋊C8—191no—
172C2×C4⋊C8C2×D1911yescharacteristic
173C2×C4⋊C8C2×D1911yescharacteristic
174C2×C4×C8—381no—
175#391—381no—
176#391—381no—
177#391—382no—
178#382—194no—
179C43—191no—
180#336—382no—
181#336—381no—
182#332—22no—
183#332—382no—
184#332—382no—
185#332—382no—
186C2×C19#154412yes—
187C2×C19#155212yes—
188C2×C19#195811yescharacteristic
189C2×C19#196611yescharacteristic
190C2×C19#198311yescharacteristic
191C22×Q8—21no—
192C22×Q8—381no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—381no—
196C22×C8—381no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—381no—
202C4⋊Q8—381no—
203C4⋊Q8—381no—
204C4⋊Q8—381no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—192no—
207C2×C4⋊C4—381no—
208C2×C4⋊C4C4×D1912yes—
209C2×C42—192no—
210C2×C42—192no—
211C2×C42—191no—
212C2×C42—191no—
213C2×C42C22×D1911yescharacteristic
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—192no—
218C4⋊C8—381no—
219C4⋊C8—381no—
220C4⋊C8—381no—
221C4⋊C8C22⋊D1912yes—
222C4×C8—762no—
223#95—384no—
224#95—384no—
225C19#970011yescharacteristic, complemented, Sylow
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—42no—
229C2×Q8—42no—
230C2×Q8—761no—
231C2×Q8—761no—
232C2×Q8—761no—
233C2×Q8—761no—
234C2×Q8—761no—
235C2×Q8—761no—
236C22×C4—22no—
237C22×C4—192no—
238C22×C4—192no—
239C22×C4—382no—
240C22×C4C2×C4×D1911yescharacteristic
241C22×C4D4×D1911yescharacteristic
242C22×C4D4×D1911yescharacteristic
243C2×C8—22no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—42no—
248C2×C8—382no—
249C2×C8—761no—
250C2×C8—761no—
251C2×C8—761no—
252C2×C8—762no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—382no—
258C4⋊C4—382no—
259C4⋊C4—761no—
260C4⋊C4—761no—
261C42—384no—
262C42—382no—
263C42—381no—
264C42—382no—
265C42—381no—
266C42—381no—
267C42—381no—
268C42#6454111yescharacteristic
269C42D4×D1911yescharacteristic
270C42#6454311yescharacteristic
271C42C2×C22⋊D1911yescharacteristic
272C23C22⋊C4×D1911yescharacteristic
273Q8—82no—
274Q8—81no—
275Q8—81no—
276Q8—1521no—
277Q8—1521no—
278Q8—1521no—
279Q8—1521no—
280C2×C4—22no—
281C2×C4—44no—
282C2×C4—42no—
283C2×C4—194no—
284C2×C4—382no—
285C2×C4—382no—
286C2×C4—382no—
287C2×C4—382no—
288C2×C4—382no—
289C2×C4—762no—
290C2×C4—762no—
291C2×C4—762no—
292C2×C4(C22⋊D19)⋊C411yescharacteristic
293C2×C4#1059733011yescharacteristic
294C2×C4#1059733111yescharacteristic
295C2×C4#1059735812yes—
296C2×C4#1059736011yescharacteristic
297C2×C4#1059736212yes—
298C2×C4#1059736211yescharacteristic
299C2×C4#1059736411yescharacteristic
300C2×C4#1059736511yescharacteristic
301C2×C4C4×C22⋊D1911yescharacteristic
302C2×C4#1059738511yescharacteristic
303C2×C4#1059738611yescharacteristic
304C8—42no—
305C8—81no—
306C8—762no—
307C8—1521no—
308C22#1192644411yescharacteristic
309C22#101×D1912yes—
310C22#1192653712yes—
311C22#1192653911yescharacteristic
312C22#1192654411yescharacteristic
313C4—21no—
314C4—21no—
315C4—82no—
316C4—384no—
317C4—762no—
318C4—1522no—
319C4#1192676111yescharacteristic
320C4#1192676211yescharacteristic
321C4#1192676811yescharacteristic
322C4#1192676911yescharacteristic
323C4#1192689712yes—
324C4#1192692511yescharacteristic
325C4#1192692711yescharacteristic
326C2#1456229812yes—
327C2#1456233212yes—
328C2#1456444511yescharacteristic
329C2#1456447711yescharacteristic
330C2#1456456411yescharacteristic
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#9700
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
225. C19#9700semidirect

Maximal subgroups

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

subgroupindex
#145720122
#145637512
C4⋊C8×Dic192
C2×#119262912
C2×#119262902
C2×#119262892
C2×C19×#3322
#970019