Finite Group Databasebeta

← #18087091

Subgroups — #18087091

Order 4864.

386 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564438C211yesmaximal, characteristic
2#14564393C211yesmaximal, characteristic
3#14564354C211yesmaximal, characteristic
4C2×#11926296C211yesmaximal, characteristic
5C2×#11926290C211yesmaximal, characteristic
6#14561519C211yesmaximal, characteristic
7C19×#1988C211yesmaximal, characteristic
8C2×#10597264—21no—
9C2×C4⋊(C19⋊C8)—21no—
10C2×C4⋊(C19⋊C8)C2211yescharacteristic
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12C2×#10597292—21no—
13C2×#10597292—21no—
14C2×C4×C19⋊C8C2211yescharacteristic
15#11926414C2211yescharacteristic
16#11926306—21no—
17#11926299—21no—
18#11926296—22no—
19#11926290—22no—
20C2×C19×C4⋊Q8C2211yescharacteristic
21C2×C19×C4⋊C8C2211yescharacteristic
22C4×C4⋊C4×C19C2211yescharacteristic
23C19×#340—21no—
24C19×#340—21no—
25C22×Q8×C19—21no—
26C22×C8×C19—21no—
27C19×C4⋊Q8—21no—
28C19×C4⋊Q8—21no—
29C19×C4⋊Q8—21no—
30C19×C4⋊Q8Q812yes—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19D411yescharacteristic
34C2×C4⋊C4×C19D411yescharacteristic
35C2×C42×C19—21no—
36C2×C42×C19C2311yescharacteristic
37C2×C4⋊Dic19—21no—
38C2×C4⋊Dic19—21no—
39C2×C4⋊Dic19—21no—
40C22×C19⋊C8—21no—
41C22×C19⋊C8—21no—
42C22×C19⋊C8D411yescharacteristic
43C22×C19⋊C8D411yescharacteristic
44C19×C4⋊C8—21no—
45C19×C4⋊C8—21no—
46C19×#95—21no—
47#10597292—42no—
48#10597292—42no—
49#10597264—42no—
50C4⋊(C19⋊C8)—21no—
51C4⋊(C19⋊C8)—21no—
52C4⋊(C19⋊C8)—21no—
53C4⋊(C19⋊C8)—42no—
54C4⋊(C19⋊C8)D412yes—
55C4×C19⋊C8—21no—
56C4×C19⋊C8—21no—
57C2×Q8×C19—22no—
58C2×Q8×C19—41no—
59C2×Q8×C19—41no—
60C2×Q8×C19—41no—
61C2×Q8×C19—41no—
62C2×Q8×C19—41no—
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19—41no—
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19C2×D411yescharacteristic
68C22×C4×C19#4111yescharacteristic
69C22×Dic19—41no—
70C2×C8×C19—41no—
71C2×C8×C19—41no—
72C2×C8×C19—41no—
73C4⋊C4×C19—21no—
74C4⋊C4×C19—22no—
75C4⋊C4×C19—22no—
76C4⋊C4×C19—21no—
77C4⋊C4×C19—21no—
78C4⋊C4×C19—41no—
79C4⋊C4×C19—41no—
80C4⋊C4×C19Q1612yes—
81C42×C19—41no—
82C42×C19—41no—
83C42×C19C2×D411yescharacteristic
84C42×C19C2×Q811yescharacteristic
85C42×C19#4111yescharacteristic
86C42×C19#4111yescharacteristic
87C4⋊Dic19—41no—
88C4⋊Dic19—41no—
89C4⋊Dic19—41no—
90C4⋊Dic19—41no—
91C4⋊Dic19—81no—
92C2×C19⋊C8—21no—
93C2×C19⋊C8—21no—
94C2×C19⋊C8—21no—
95C2×C19⋊C8—22no—
96C2×C19⋊C8—21no—
97C2×C19⋊C8—21no—
98C2×C19⋊C8—41no—
99C2×C19⋊C8—41no—
100C2×C19⋊C8—41no—
101C2×C19⋊C8—41no—
102C2×C19⋊C8—41no—
103C2×C19⋊C8D812yes—
104#10592—191nomaximal, Sylow
105C23×C19#12111yescharacteristic
106Q8×C19—42no—
107Q8×C19—42no—
108Q8×C19—81no—
109Q8×C19—81no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—22no—
113C2×C4×C19—41no—
114C2×C4×C19—41no—
115C2×C4×C19—42no—
116C2×C4×C19—41no—
117C2×C4×C19—41no—
118C2×C4×C19—41no—
119C2×C4×C19—81no—
120C2×C4×C19—81no—
121C2×C4×C19#12111yescharacteristic
122C2×C4×C19#12111yescharacteristic
123C2×C4×C19C22⋊Q811yescharacteristic
124C2×C4×C19C22⋊Q811yescharacteristic
125C2×C4×C19C22⋊Q811yescharacteristic
126C2×C4×C19#12611yescharacteristic
127C2×C4×C19C2×D811yescharacteristic
128C2×C4×C19C2×Q1611yescharacteristic
129C2×C4×C19#13511yescharacteristic
130C2×C4×C19#13511yescharacteristic
131C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C19#13711yescharacteristic
134C2×C4×C19#13711yescharacteristic
135C2×Dic19—81no—
136C2×Dic19—81no—
137C2×Dic19—81no—
138C8×C19—81no—
139C19⋊C8—22no—
140C19⋊C8—42no—
141C19⋊C8—41no—
142C19⋊C8—81no—
143#1988D1911yescharacteristic
144#1956—191no—
145#1947—191no—
146#1939—191no—
147C2×#335—191no—
148C2×#332—191no—
149#1296—191no—
150C22×C19#39611yescharacteristic
151C22×C19#45911yescharacteristic
152C22×C19#46411yescharacteristic
153C22×C19#46711yescharacteristic
154C22×C19#46811yescharacteristic
155C22×C19#47111yescharacteristic
156C22×C19#47311yescharacteristic
157C4×C19—21no—
158C4×C19—21no—
159C4×C19—42no—
160C4×C19—82no—
161C4×C19—81no—
162C4×C19#46211yescharacteristic
163C4×C19#46311yescharacteristic
164C4×C19#46611yescharacteristic
165C4×C19#46811yescharacteristic
166C4×C19#47411yescharacteristic
167C4×C19#47711yescharacteristic
168C4×C19#47811yescharacteristic
169C4×C19#47911yescharacteristic
170Dic19—161no—
171C2×C4⋊Q8C2×D1911yescharacteristic
172C2×#107—381no—
173C2×C4⋊C8—191no—
174C2×C4⋊C8—191no—
175C2×C4⋊C8—381no—
176C2×C4⋊C8C2×D1911yescharacteristic
177C2×#103—381no—
178C2×#103—381no—
179C2×C4×C8—191no—
180#384—191no—
181C4×C4⋊C4C2×D1911yescharacteristic
182#340—21no—
183#340—21no—
184#340—381no—
185#336—381no—
186#335—382no—
187#332—382no—
188C2×C19#166911yescharacteristic
189C2×C19#168411yescharacteristic
190C2×C19#168511yescharacteristic
191C2×C19#170011yescharacteristic
192C2×C19#206411yescharacteristic
193C2×C19#206711yescharacteristic
194C2×C19#206811yescharacteristic
195C22×Q8—21no—
196C22×C8—21no—
197C22×C8—191no—
198C22×C8—191no—
199C22×C8—381no—
200C22×C8—381no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8Dic3812yes—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—381no—
208C2×C4⋊C4—381no—
209C2×C4⋊C4—381no—
210C2×C4⋊C4C22⋊D1911yescharacteristic
211C2×C4⋊C4C22⋊D1911yescharacteristic
212C2×C42—21no—
213C2×C42C22×D1911yescharacteristic
214#107—762no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—192no—
218C4⋊C8—381no—
219C4⋊C8—381no—
220C4⋊C8—381no—
221C4⋊C8—762no—
222#103—762no—
223#103—762no—
224C4×C8—381no—
225C4×C8—381no—
226#95—21no—
227C19#1059211yescharacteristic, complemented, Sylow
228C2×Q8—22no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—41no—
237C22×C4—761no—
238C22×C4D4×D1911yescharacteristic
239C22×C4#6454311yescharacteristic
240C22×C4C2×C22⋊D1911yescharacteristic
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—192no—
245C2×C8—381no—
246C2×C8—381no—
247C2×C8—382no—
248C2×C8—381no—
249C2×C8—381no—
250C2×C8—381no—
251C2×C8—761no—
252C2×C8—761no—
253C2×C8—761no—
254C2×C8—761no—
255C2×C8—761no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—761no—
264C4⋊C4—761no—
265C4⋊C4—761no—
266C4⋊C4—761no—
267C4⋊C4—1521no—
268C4⋊C4#6452812yes—
269C42—41no—
270C42—41no—
271C42C2×Dic3811yescharacteristic
272C42#6454111yescharacteristic
273C42D4×D1911yescharacteristic
274C42#6454311yescharacteristic
275C23#1059738511yescharacteristic
276Q8—42no—
277Q8—42no—
278Q8—81no—
279Q8—81no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—1521no—
292C2×C4—1521no—
293C2×C4—1521no—
294C2×C4#1059732411yescharacteristic
295C2×C4#1059732411yescharacteristic
296C2×C4#1059732511yescharacteristic
297C2×C4#1059733011yescharacteristic
298C2×C4D8×D1911yescharacteristic
299C2×C4#1059735711yescharacteristic
300C2×C4#1059736111yescharacteristic
301C2×C4#1059736211yescharacteristic
302C2×C4#1059737011yescharacteristic
303C2×C4#1059738411yescharacteristic
304C2×C4#1059738811yescharacteristic
305C2×C4C2×#6452811yescharacteristic
306C2×C4#1059739511yescharacteristic
307C2×C4#1059739611yescharacteristic
308C8—81no—
309C8—382no—
310C8—761no—
311C8—762no—
312C8—1521no—
313C22#1192646711yescharacteristic
314C22#1192673711yescharacteristic
315C22#1192676411yescharacteristic
316C22#1192678311yescharacteristic
317C22#1192679211yescharacteristic
318C22#1192680911yescharacteristic
319C22#1192681711yescharacteristic
320C4—21no—
321C4—21no—
322C4—42no—
323C4—81no—
324C4—82no—
325C4—3041no—
326C4#1192675111yescharacteristic
327C4#1192675611yescharacteristic
328C4#1192677911yescharacteristic
329C4#1192678911yescharacteristic
330C4#1192682211yescharacteristic
331C4#1192683911yescharacteristic
332C4#1192684611yescharacteristic
333C4#1192685111yescharacteristic
334C2#1456299811yescharacteristic
335C2#1456309111yescharacteristic
336C2#1456310211yescharacteristic
337C2#1456318711yescharacteristic
338C2#1456500211yescharacteristic
339C2#1456501911yescharacteristic
340C2#1456503011yescharacteristic
subgroupG/H
centerC23#10597385
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1988C2
socle, prime radicalC23×C19#121
hypercenter#1988D19
hypocenterC19#10592
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
227. C19#10592semidirect

Maximal subgroups

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

subgroupindex
#145644382
#145643932
#145643542
C2×#119262962
C2×#119262902
#145615192
C19×#19882
#1059219