Finite Group Databasebeta

← #18087010

Subgroups — #18087010

Order 4864.

442 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14568666C211yesmaximal, characteristic
2#14564391C211yesmaximal, characteristic
3#14563794C211yesmaximal, characteristic
4#14561519C211yesmaximal, characteristic
5#14561476C211yesmaximal, characteristic
6#14561474C211yesmaximal, characteristic
7C19×#1948C211yesmaximal, characteristic
8C2×#10597336—21no—
9C2×#10597264—21no—
10C2×#10597264—22no—
11C2×C4⋊(C19⋊C8)C2211yescharacteristic
12C2×C4×C19⋊C8C2211yescharacteristic
13#11926476—22no—
14#11926443—21no—
15#11926442—21no—
16#11926414—21no—
17#11926414C2211yescharacteristic
18C4×C4⋊Dic19C2211yescharacteristic
19#11926306—21no—
20C2×C19×#106—21no—
21C2×C19×C4⋊C8C2211yescharacteristic
22C19×#384C2211yescharacteristic
23C4×C4⋊C4×C19C2211yescharacteristic
24C19×#340—21no—
25C22×C8×C19—21no—
26C2×C4⋊C4×C19—21no—
27C2×C4⋊C4×C19—21no—
28C2×C4⋊C4×C19—21no—
29C2×C4⋊C4×C19D411yescharacteristic
30C2×C4⋊C4×C19D411yescharacteristic
31C2×C42×C19—21no—
32C2×C42×C19C2311yescharacteristic
33C2×C4⋊Dic19—22no—
34C2×C4⋊Dic19—21no—
35C2×C4⋊Dic19—21no—
36C2×C4⋊Dic19—22no—
37C2×C4⋊Dic19D411yescharacteristic
38C2×C4⋊Dic19D411yescharacteristic
39C2×C4⋊Dic19D412yes—
40C2×Dic19⋊C4—22no—
41C2×C4×Dic19—21no—
42C22×C19⋊C8—21no—
43C22×C19⋊C8—21no—
44#10597336—42no—
45#10597336—42no—
46C19×#106—42no—
47C19×C4⋊C8—21no—
48C19×C4⋊C8Q812yes—
49C19×#95—21no—
50C19⋊#95—22no—
51C19⋊#95—21no—
52#10597264—44no—
53#10597264—42no—
54C4⋊(C19⋊C8)—21no—
55C4⋊(C19⋊C8)Q812yes—
56C4×C19⋊C8—21no—
57C4×C19⋊C8Q812yes—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—41no—
61C22×C4×C19C2×D411yescharacteristic
62C22×C4×C19C2×D411yescharacteristic
63C22×C4×C19C2×D411yescharacteristic
64C22×Dic19—21no—
65C22×Dic19—21no—
66C22×Dic19—22no—
67C2×C8×C19—22no—
68C2×C8×C19—41no—
69C2×C8×C19—41no—
70C4⋊C4×C19—21no—
71C4⋊C4×C19—21no—
72C4⋊C4×C19—42no—
73C4⋊C4×C19—41no—
74C4⋊C4×C19—41no—
75C4⋊C4×C19—41no—
76C4⋊C4×C19—41no—
77C4⋊C4×C19D812yes—
78C4⋊C4×C19Q1612yes—
79C42×C19—41no—
80C42×C19—41no—
81C42×C19C2×Q811yescharacteristic
82C42×C19C2×Q811yescharacteristic
83C42×C19C2×Q811yescharacteristic
84C42×C19#4111yescharacteristic
85C4⋊Dic19—21no—
86C4⋊Dic19—21no—
87C4⋊Dic19—21no—
88C4⋊Dic19—21no—
89C4⋊Dic19—44no—
90C4⋊Dic19—41no—
91C4⋊Dic19—41no—
92C4⋊Dic19—41no—
93C4⋊Dic19—41no—
94C4⋊Dic19—42no—
95C4⋊Dic19—82no—
96Dic19⋊C4—44no—
97C4×Dic19—41no—
98C4×Dic19—41no—
99C2×C19⋊C8—22no—
100C2×C19⋊C8—22no—
101C2×C19⋊C8—22no—
102C2×C19⋊C8—22no—
103C2×C19⋊C8—41no—
104C2×C19⋊C8—41no—
105#10579—191nomaximal, Sylow
106C23×C19#12011yescharacteristic
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—22no—
110C2×C4×C19—22no—
111C2×C4×C19—41no—
112C2×C4×C19—41no—
113C2×C4×C19—41no—
114C2×C4×C19—41no—
115C2×C4×C19—81no—
116C2×C4×C19—81no—
117C2×C4×C19—81no—
118C2×C4×C19C22⋊Q811yescharacteristic
119C2×C4×C19C22⋊Q811yescharacteristic
120C2×C4×C19C22⋊Q811yescharacteristic
121C2×C4×C19C4⋊Q811yescharacteristic
122C2×C4×C19C4⋊Q811yescharacteristic
123C2×C4×C19C4⋊Q811yescharacteristic
124C2×C4×C19C2×D811yescharacteristic
125C2×C4×C19C2×Q1611yescharacteristic
126C2×C4×C19#13511yescharacteristic
127C2×C4×C19#13511yescharacteristic
128C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C19#13711yescharacteristic
131C2×C4×C19#13711yescharacteristic
132C2×Dic19—41no—
133C2×Dic19—41no—
134C2×Dic19—42no—
135C2×Dic19—41no—
136C2×Dic19—42no—
137C2×Dic19—41no—
138C2×Dic19—42no—
139C2×Dic19—41no—
140C2×Dic19—41no—
141C8×C19—42no—
142C19⋊C8—24no—
143C19⋊C8—42no—
144#2552—191no—
145#1948D1911yescharacteristic
146#1947—191no—
147#1845—191no—
148#1296—191no—
149#1279—191no—
150#1279—191no—
151C22×C19#39511yescharacteristic
152C22×C19#44711yescharacteristic
153C22×C19#44911yescharacteristic
154C22×C19#45111yescharacteristic
155C22×C19#45211yescharacteristic
156C22×C19#45311yescharacteristic
157C22×C19#45611yescharacteristic
158C4×C19—21no—
159C4×C19—21no—
160C4×C19—42no—
161C4×C19—42no—
162C4×C19—161no—
163C4×C19#47411yescharacteristic
164C4×C19#47711yescharacteristic
165C4×C19#47811yescharacteristic
166C4×C19#47911yescharacteristic
167C4×C19#49911yescharacteristic
168C4×C19#50011yescharacteristic
169C4×C19#50111yescharacteristic
170C4×C19#50111yescharacteristic
171Dic19—81no—
172Dic19—82no—
173Dic19—81no—
174C2×#125—381no—
175C2×#107—382no—
176C2×#107—381no—
177C2×#106—21no—
178C2×C4⋊C8—191no—
179C2×C4⋊C8C2×D1911yescharacteristic
180C2×C4×C8—191no—
181#398—382no—
182#389—381no—
183#389—381no—
184#384—191no—
185#384—381no—
186#384C2×D1911yescharacteristic
187C4×C4⋊C4—191no—
188C4×C4⋊C4C2×D1911yescharacteristic
189#340—21no—
190#340—381no—
191C2×C19#162111yescharacteristic
192C2×C19#163211yescharacteristic
193C2×C19#164711yescharacteristic
194C2×C19#164811yescharacteristic
195C2×C19#205711yescharacteristic
196C2×C19#205911yescharacteristic
197C2×C19#206011yescharacteristic
198C22×C8—21no—
199C22×C8—381no—
200C22×C8—381no—
201#125—762no—
202#125—762no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—191no—
207C2×C4⋊C4—191no—
208C2×C4⋊C4—192no—
209C2×C4⋊C4—382no—
210C2×C4⋊C4—382no—
211C2×C4⋊C4—381no—
212C2×C4⋊C4—381no—
213C2×C4⋊C4—382no—
214C2×C4⋊C4C22⋊D1911yescharacteristic
215C2×C4⋊C4C22⋊D1911yescharacteristic
216C2×C42—21no—
217C2×C42—381no—
218C2×C42C22×D1911yescharacteristic
219#107—762no—
220#107—764no—
221#106—42no—
222C4⋊C8—21no—
223C4⋊C8—192no—
224C4⋊C8—381no—
225C4⋊C8Dic3812yes—
226C4×C8—192no—
227C4×C8—381no—
228#95—21no—
229#95—382no—
230#95—381no—
231C19#1057911yescharacteristic, complemented, Sylow
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—41no—
235C22×C4—381no—
236C22×C4—381no—
237C22×C4—382no—
238C22×C4D4×D1911yescharacteristic
239C22×C4D4×D1911yescharacteristic
240C22×C4C2×C22⋊D1911yescharacteristic
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—382no—
245C2×C8—382no—
246C2×C8—382no—
247C2×C8—382no—
248C2×C8—761no—
249C2×C8—761no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—42no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—381no—
258C4⋊C4—381no—
259C4⋊C4—381no—
260C4⋊C4—381no—
261C4⋊C4—762no—
262C4⋊C4—764no—
263C4⋊C4—764no—
264C4⋊C4—761no—
265C4⋊C4—761no—
266C4⋊C4—761no—
267C4⋊C4—761no—
268C4⋊C4—1522no—
269C4⋊C4#6452512yes—
270C4⋊C4#6452812yes—
271C42—41no—
272C42—41no—
273C42—761no—
274C42—761no—
275C42C2×Dic3811yescharacteristic
276C42#6454111yescharacteristic
277C42Q8×D1911yescharacteristic
278C42Q8×D1911yescharacteristic
279C23#1059738311yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—761no—
292C2×C4—761no—
293C2×C4—762no—
294C2×C4—761no—
295C2×C4—762no—
296C2×C4—761no—
297C2×C4—762no—
298C2×C4—761no—
299C2×C4—761no—
300C2×C4#1059733411yescharacteristic
301C2×C4#1059733411yescharacteristic
302C2×C4#1059734211yescharacteristic
303C2×C4#1059734211yescharacteristic
304C2×C4#1059736011yescharacteristic
305C2×C4#1059736111yescharacteristic
306C2×C4#1059736211yescharacteristic
307C2×C4#1059736211yescharacteristic
308C2×C4#1059737011yescharacteristic
309C2×C4C2×#6452511yescharacteristic
310C2×C4C2×#6452811yescharacteristic
311C2×C4#1059739011yescharacteristic
312C2×C4#1059739511yescharacteristic
313C2×C4#1059739711yescharacteristic
314C8—42no—
315C8—384no—
316C8—762no—
317C22#1192646411yescharacteristic
318C22#1192667711yescharacteristic
319C22#1192668811yescharacteristic
320C22#1192669911yescharacteristic
321C22#1192670311yescharacteristic
322C22#1192671011yescharacteristic
323C22#1192672511yescharacteristic
324C4—21no—
325C4—21no—
326C4—42no—
327C4—42no—
328C4—161no—
329C4—1521no—
330C4—1521no—
331C4—1522no—
332C4#1192682411yescharacteristic
333C4#1192683911yescharacteristic
334C4#1192684311yescharacteristic
335C4#1192685411yescharacteristic
336C4#1192694411yescharacteristic
337C4#1192694711yescharacteristic
338C4#1192695111yescharacteristic
339C4#1192695411yescharacteristic
340C2#1456269811yescharacteristic
341C2#1456276711yescharacteristic
342C2#1456286811yescharacteristic
343C2#1456287611yescharacteristic
344C2#1456496311yescharacteristic
345C2#1456497511yescharacteristic
346C2#1456497811yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1948C2
socle, prime radicalC23×C19#120
hypercenter#1948D19
hypocenterC19#10579
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
231. C19#10579semidirect

Maximal subgroups

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

subgroupindex
#145686662
#145643912
#145637942
#145615192
#145614762
#145614742
C19×#19482
#1057919