Finite Group Databasebeta

← #18087070

Subgroups — #18087070

Order 4864.

370 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564597C211yesmaximal, characteristic
2#14564393C211yesmaximal, characteristic
3#14564354C211yesmaximal, characteristic
4C2×#11926294C211yesmaximal, characteristic
5C2×#11926293C211yesmaximal, characteristic
6#14561519C211yesmaximal, characteristic
7C19×#1987C211yesmaximal, characteristic
8C2×#10597264—21no—
9C2×C4⋊(C19⋊C8)—21no—
10C2×C4⋊(C19⋊C8)C2211yescharacteristic
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12C2×C4×C19⋊C8C2211yescharacteristic
13#11926414C2211yescharacteristic
14#11926306—21no—
15#11926306—21no—
16#11926306—21no—
17#11926299—21no—
18#11926294—22no—
19#11926293—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#10597264—42no—
48C4⋊(C19⋊C8)—21no—
49C4⋊(C19⋊C8)—21no—
50C4⋊(C19⋊C8)—21no—
51C4⋊(C19⋊C8)—42no—
52C4⋊(C19⋊C8)D412yes—
53C4×C19⋊C8—21no—
54C4×C19⋊C8—21no—
55C2×Q8×C19—22no—
56C2×Q8×C19—41no—
57C2×Q8×C19—81no—
58C2×Q8×C19—81no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—41no—
62C22×C4×C19C2×D411yescharacteristic
63C22×C4×C19C2×D411yescharacteristic
64C22×C4×C19#4111yescharacteristic
65C22×Dic19—41no—
66C2×C8×C19—41no—
67C2×C8×C19—41no—
68C2×C8×C19—41no—
69C4⋊C4×C19—21no—
70C4⋊C4×C19—22no—
71C4⋊C4×C19—22no—
72C4⋊C4×C19—21no—
73C4⋊C4×C19—21no—
74C4⋊C4×C19—41no—
75C4⋊C4×C19—41no—
76C4⋊C4×C19SD1612yes—
77C42×C19—41no—
78C42×C19—41no—
79C42×C19C2×D411yescharacteristic
80C42×C19C2×Q811yescharacteristic
81C42×C19#4111yescharacteristic
82C42×C19#4111yescharacteristic
83C4⋊Dic19—41no—
84C4⋊Dic19—41no—
85C4⋊Dic19—41no—
86C4⋊Dic19—41no—
87C4⋊Dic19—81no—
88C2×C19⋊C8—21no—
89C2×C19⋊C8—21no—
90C2×C19⋊C8—21no—
91C2×C19⋊C8—22no—
92C2×C19⋊C8—21no—
93C2×C19⋊C8—21no—
94C2×C19⋊C8—41no—
95C2×C19⋊C8—41no—
96C2×C19⋊C8—41no—
97C2×C19⋊C8—41no—
98C2×C19⋊C8—41no—
99C2×C19⋊C8Q1612yes—
100#10589—191nomaximal, Sylow
101C23×C19#12111yescharacteristic
102Q8×C19—82no—
103Q8×C19—82no—
104C2×C4×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19—22no—
107C2×C4×C19—41no—
108C2×C4×C19—41no—
109C2×C4×C19—42no—
110C2×C4×C19—41no—
111C2×C4×C19—41no—
112C2×C4×C19—41no—
113C2×C4×C19—81no—
114C2×C4×C19—81no—
115C2×C4×C19#12111yescharacteristic
116C2×C4×C19#12111yescharacteristic
117C2×C4×C19C22⋊Q811yescharacteristic
118C2×C4×C19C22⋊Q811yescharacteristic
119C2×C4×C19C22⋊Q811yescharacteristic
120C2×C4×C19#12611yescharacteristic
121C2×C4×C19C2×SD1611yescharacteristic
122C2×C4×C19C2×Q1611yescharacteristic
123C2×C4×C19#13511yescharacteristic
124C2×C4×C19#13511yescharacteristic
125C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C19#13711yescharacteristic
127C2×C4×C19#13711yescharacteristic
128C2×C4×C19#13711yescharacteristic
129C2×Dic19—81no—
130C2×Dic19—81no—
131C2×Dic19—81no—
132C8×C19—81no—
133C19⋊C8—22no—
134C19⋊C8—42no—
135C19⋊C8—41no—
136C19⋊C8—81no—
137#1990—191no—
138#1987D1911yescharacteristic
139#1947—191no—
140#1939—191no—
141C2×#334—191no—
142C2×#333—191no—
143#1296—191no—
144C22×C19#39611yescharacteristic
145C22×C19#46211yescharacteristic
146C22×C19#46311yescharacteristic
147C22×C19#46511yescharacteristic
148C22×C19#47011yescharacteristic
149C22×C19#47111yescharacteristic
150C22×C19#47211yescharacteristic
151C4×C19—21no—
152C4×C19—21no—
153C4×C19—42no—
154C4×C19—82no—
155C4×C19—81no—
156C4×C19#46111yescharacteristic
157C4×C19#46411yescharacteristic
158C4×C19#46711yescharacteristic
159C4×C19#46811yescharacteristic
160C4×C19#47511yescharacteristic
161C4×C19#47711yescharacteristic
162C4×C19#47911yescharacteristic
163C4×C19#47911yescharacteristic
164Dic19—161no—
165C2×C4⋊Q8C2×D1911yescharacteristic
166C2×#107—381no—
167C2×C4⋊C8—191no—
168C2×C4⋊C8—191no—
169C2×C4⋊C8—381no—
170C2×C4⋊C8C2×D1911yescharacteristic
171C2×C4×C8—191no—
172#384—191no—
173C4×C4⋊C4C2×D1911yescharacteristic
174#340—21no—
175#340—21no—
176#340—381no—
177#340—381no—
178#340—381no—
179#336—381no—
180#334—382no—
181#333—382no—
182C2×C19#167211yescharacteristic
183C2×C19#167711yescharacteristic
184C2×C19#169611yescharacteristic
185C2×C19#170311yescharacteristic
186C2×C19#206311yescharacteristic
187C2×C19#206611yescharacteristic
188C2×C19#206811yescharacteristic
189C22×Q8—21no—
190C22×C8—21no—
191C22×C8—191no—
192C22×C8—191no—
193C22×C8—381no—
194C22×C8—381no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8Dic3812yes—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—381no—
202C2×C4⋊C4—381no—
203C2×C4⋊C4—381no—
204C2×C4⋊C4C22⋊D1911yescharacteristic
205C2×C4⋊C4C22⋊D1911yescharacteristic
206C2×C42—21no—
207C2×C42C22×D1911yescharacteristic
208#107—762no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—192no—
212C4⋊C8—381no—
213C4⋊C8—381no—
214C4⋊C8—381no—
215C4⋊C8—762no—
216C4×C8—381no—
217C4×C8—381no—
218#95—21no—
219C19#1058911yescharacteristic, complemented, Sylow
220C2×Q8—22no—
221C2×Q8—41no—
222C2×Q8—81no—
223C2×Q8—81no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—41no—
227C22×C4—761no—
228C22×C4D4×D1911yescharacteristic
229C22×C4#6454311yescharacteristic
230C22×C4C2×C22⋊D1911yescharacteristic
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—192no—
235C2×C8—381no—
236C2×C8—381no—
237C2×C8—382no—
238C2×C8—381no—
239C2×C8—381no—
240C2×C8—381no—
241C2×C8—761no—
242C2×C8—761no—
243C2×C8—761no—
244C2×C8—761no—
245C2×C8—761no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—761no—
254C4⋊C4—761no—
255C4⋊C4—761no—
256C4⋊C4—761no—
257C4⋊C4—1521no—
258C4⋊C4#6452712yes—
259C42—41no—
260C42—41no—
261C42C2×Dic3811yescharacteristic
262C42#6454111yescharacteristic
263C42D4×D1911yescharacteristic
264C42#6454311yescharacteristic
265C23#1059738511yescharacteristic
266Q8—82no—
267Q8—82no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—1521no—
280C2×C4—1521no—
281C2×C4—1521no—
282C2×C4#1059732411yescharacteristic
283C2×C4#1059732411yescharacteristic
284C2×C4#1059732511yescharacteristic
285C2×C4#1059733011yescharacteristic
286C2×C4#1059736011yescharacteristic
287C2×C4#1059736211yescharacteristic
288C2×C4Q16×D1911yescharacteristic
289C2×C4#1059736411yescharacteristic
290C2×C4#1059737011yescharacteristic
291C2×C4#1059738411yescharacteristic
292C2×C4C2×#6452711yescharacteristic
293C2×C4#1059738811yescharacteristic
294C2×C4#1059739611yescharacteristic
295C2×C4#1059739711yescharacteristic
296C8—81no—
297C8—382no—
298C8—761no—
299C8—762no—
300C8—1521no—
301C22#1192646711yescharacteristic
302C22#1192675211yescharacteristic
303C22#1192676111yescharacteristic
304C22#1192677511yescharacteristic
305C22#1192680011yescharacteristic
306C22#1192680511yescharacteristic
307C22#1192681211yescharacteristic
308C4—21no—
309C4—21no—
310C4—42no—
311C4—82no—
312C4—81no—
313C4—3041no—
314C4#1192674611yescharacteristic
315C4#1192676311yescharacteristic
316C4#1192678411yescharacteristic
317C4#1192679311yescharacteristic
318C4#1192682911yescharacteristic
319C4#1192683711yescharacteristic
320C4#1192684911yescharacteristic
321C4#1192685111yescharacteristic
322C2#1456301911yescharacteristic
323C2#1456304611yescharacteristic
324C2#1456316111yescharacteristic
325C2#1456321211yescharacteristic
326C2#1456499511yescharacteristic
327C2#1456501611yescharacteristic
328C2#1456502611yescharacteristic
subgroupG/H
centerC23#10597385
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1987C2
socle, prime radicalC23×C19#121
hypercenter#1987D19
hypocenterC19#10589
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
219. C19#10589semidirect

Maximal subgroups

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

subgroupindex
#145645972
#145643932
#145643542
C2×#119262942
C2×#119262932
#145615192
C19×#19872
#1058919