Finite Group Databasebeta

← #18080331

Subgroups — #18080331

Order 4864.

576 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572664C211yesmaximal, characteristic
2#14567943C211yesmaximal, characteristic
3#14563719C212yesmaximal, complemented
4#14561502C212yesmaximal, complemented
5C19×#1799C211yesmaximal, characteristic
6C2×#10597381—21no—
7C22×C4⋊Dic19C2211yescharacteristic
8#11926616—24no—
9#11926601—21no—
10#11926508—21no—
11C2×C22⋊(C19⋊C8)C2212yes—
12#11926474C412yescomplemented
13#11926469C412yescomplemented
14#11926442—21no—
15#11926405—21no—
16#11926404—21no—
17#11926404C2211yescharacteristic
18#11926306—24no—
19C2×C4×D4×C19C2211yescharacteristic
20C2×C19×#99—21no—
21C19×#380C2212yes—
22C19×#342—21no—
23C22×D4×C19D411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C23×Dic19—21no—
27C4×D4×C19—22no—
28C4×D4×C19—22no—
29C2×C4⋊C4×C19—22no—
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C22⋊C4×C19—22no—
32C2×C22⋊C4×C19C2×C411yescharacteristic
33C2×C22⋊C4×C19D411yescharacteristic
34C2×C42×C19D411yescharacteristic
35C2×C22⋊Dic19—22no—
36C2×C22⋊Dic19—21no—
37#10597381—44no—
38C2×C4⋊Dic19—22no—
39C2×C4⋊Dic19—22no—
40C2×C4⋊Dic19—21no—
41C2×C4⋊Dic19—21no—
42C2×C4⋊Dic19C2×C412yes—
43C2×Dic19⋊C4—22no—
44C2×#64520—22no—
45C22×C19⋊C8D414yes—
46C19×#99—42no—
47C19×#95—22no—
48C19⋊#95—22no—
49C19⋊#95—22no—
50C19⋊#95C2×C412yes—
51C22⋊(C19⋊C8)—22no—
52C22⋊(C19⋊C8)—22no—
53C22⋊(C19⋊C8)—22no—
54C4⋊(C19⋊C8)—22no—
55#10597260—22no—
56C24×C19C22⋊C411yescharacteristic
57C24×C19C2×D411yescharacteristic
58C2×D4×C19—22no—
59C2×D4×C19—22no—
60C2×D4×C19—21no—
61C2×D4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—21no—
64C22×C4×C19—42no—
65C22×C4×C19—42no—
66C22×C4×C19—42no—
67C22×C4×C19C22⋊C411yescharacteristic
68C22×C4×C19C22⋊C411yescharacteristic
69C22×C4×C19C22⋊C411yescharacteristic
70C22×C4×C19C22×C411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×D412yes—
73C22×C4×C19#4112yes—
74C22×Dic19—22no—
75C22×Dic19—22no—
76C22×Dic19—42no—
77C22×Dic19—42no—
78C22×Dic19—41no—
79C22×Dic19—41no—
80C4⋊C4×C19—22no—
81C4⋊C4×C19—44no—
82C22⋊C4×C19—22no—
83C22⋊C4×C19—22no—
84C22⋊C4×C19—42no—
85C22⋊C4×C19—42no—
86C42×C19—21no—
87C42×C19—21no—
88C22⋊Dic19—44no—
89C22⋊Dic19—42no—
90C4⋊Dic19—24no—
91C4⋊Dic19—42no—
92C4⋊Dic19—41no—
93C4⋊Dic19—41no—
94Dic19⋊C4—44no—
95#64520—82no—
96C2×C19⋊C8—24no—
97C2×C19⋊C8—44no—
98#9474—191nomaximal, Sylow
99C23×C19—21no—
100C23×C19—21no—
101C23×C19—21no—
102C23×C19—41no—
103C23×C19—41no—
104C23×C19—41no—
105C23×C19—41no—
106C23×C19C2×C22⋊C411yescharacteristic
107C23×C19#12112yes—
108C23×C19AGL(1,ℤ/8)11yescharacteristic
109C23×C19AGL(1,ℤ/8)12yes—
110C23×C19#13711yescharacteristic
111D4×C19—42no—
112D4×C19—42no—
113C2×C4×C19—24no—
114C2×C4×C19—22no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—21no—
120C2×C4×C19—41no—
121C2×C4×C19—42no—
122C2×C4×C19—42no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—81no—
126C2×C4×C19—82no—
127C2×C4×C19—82no—
128C2×C4×C19—82no—
129C2×C4×C19C4×D412yes—
130C2×C4×C19#12011yescharacteristic
131C2×C4×C19#12311yescharacteristic
132C2×Dic19—42no—
133C2×Dic19—42no—
134C2×Dic19—42no—
135C2×Dic19—42no—
136C2×Dic19—42no—
137C2×Dic19—42no—
138C2×Dic19—82no—
139C2×Dic19—82no—
140C19⋊C8—44no—
141#2973—191no—
142#2486—191no—
143#1823—192no—
144#1799D1911yescharacteristic
145#1289—192no—
146C22×C19—21no—
147C22×C19—22no—
148C22×C19—21no—
149C22×C19—22no—
150C22×C19—41no—
151C22×C19—42no—
152C22×C19—41no—
153C22×C19—42no—
154C22×C19—41no—
155C22×C19—41no—
156C22×C19—41no—
157C22×C19—81no—
158C22×C19#38611yescharacteristic
159C22×C19#41711yescharacteristic
160C22×C19#41811yescharacteristic
161C22×C19#46812yes—
162C22×C19#46912yes—
163C4×C19—21no—
164C4×C19—22no—
165C4×C19—41no—
166C4×C19—41no—
167C4×C19—41no—
168C4×C19—162no—
169C4×C19#45812yes—
170Dic19—82no—
171Dic19—82no—
172C2×#123—381no—
173C2×C4×D4C2×D1911yescharacteristic
174C22×C4⋊C4—191no—
175#435—384no—
176#432—381no—
177C2×#99—21no—
178#407—381no—
179C2×C22⋊C8—192no—
180#398—192no—
181#397—192no—
182#389—381no—
183#381—381no—
184#380—191no—
185#380—381no—
186#380C2×D1912yes—
187#342—21no—
188#340—384no—
189C2×C19—21no—
190C2×C19—22no—
191C2×C19—21no—
192C2×C19—22no—
193C2×C19—81no—
194C2×C19#189011yescharacteristic
195C2×C19#189511yescharacteristic
196C2×C19#190911yescharacteristic
197C22×D4C22⋊D1911yescharacteristic
198C23×C4—381no—
199C23×C4D7611yescharacteristic
200C23×C4C22×D1911yescharacteristic
201C2×M16—382no—
202C22×C8—194no—
203#123—764no—
204C4×D4—22no—
205C4×D4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—192no—
208C2×C4⋊C4—382no—
209C2×C4⋊C4—382no—
210C2×C4⋊C4—382no—
211C2×C4⋊C4—381no—
212C2×C4⋊C4—381no—
213C2×C4⋊C4C4×D1911yescharacteristic
214C2×C22⋊C4—22no—
215C2×C22⋊C4—382no—
216C2×C22⋊C4—381no—
217C2×C22⋊C4C4×D1911yescharacteristic
218C2×C22⋊C4C22⋊D1911yescharacteristic
219C2×C42D7611yescharacteristic
220C4⋊C8—382no—
221#99—42no—
222C22⋊C8—382no—
223C22⋊C8—382no—
224C22⋊C8—382no—
225#97—382no—
226#95—22no—
227#95—192no—
228#95—382no—
229#95—382no—
230C19#947411yescharacteristic, complemented, Sylow
231C24(C2×D19)⋊C411yescharacteristic
232C24C2×C22⋊D1911yescharacteristic
233C2×D4—21no—
234C2×D4—22no—
235C2×D4—21no—
236C2×D4—22no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—382no—
243C22×C4—382no—
244C22×C4—761no—
245C22×C4—762no—
246C22×C4—761no—
247C22×C4—762no—
248C22×C4(C2×D19)⋊C411yescharacteristic
249C22×C4(C2×D19)⋊C411yescharacteristic
250C22×C4(C2×D19)⋊C411yescharacteristic
251C22×C4C2×C4×D1911yescharacteristic
252C22×C4C2×D7611yescharacteristic
253C22×C4D4×D1912yes—
254C22×C4#6454312yes—
255M16—1522no—
256C2×C8—384no—
257C2×C8—764no—
258C4⋊C4—22no—
259C4⋊C4—44no—
260C4⋊C4—384no—
261C4⋊C4—764no—
262C4⋊C4—762no—
263C4⋊C4—761no—
264C4⋊C4—761no—
265C22⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—42no—
268C22⋊C4—42no—
269C22⋊C4—764no—
270C22⋊C4—762no—
271C42—21no—
272C42—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23C2×(C2×D19)⋊C411yescharacteristic
281C23#1059737811yescharacteristic
282C23#1059738512yes—
283C23#1059738811yescharacteristic
284C23#1059739512yes—
285D4—42no—
286D4—42no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4—762no—
304C2×C4—762no—
305C2×C4—762no—
306C2×C4—762no—
307C2×C4—762no—
308C2×C4—762no—
309C2×C4—1522no—
310C2×C4—1522no—
311C2×C4(C22⋊D19)⋊C412yes—
312C2×C4#1059732811yescharacteristic
313C2×C4#1059733211yescharacteristic
314C8—764no—
315C22—21no—
316C22—22no—
317C22—21no—
318C22—22no—
319C22—41no—
320C22—41no—
321C22—42no—
322C22—42no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22#1192642111yescharacteristic
328C22#1192654311yescharacteristic
329C22#1192654811yescharacteristic
330C22#1192679212yes—
331C22#1192679512yes—
332C4—21no—
333C4—22no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—162no—
338C4—1522no—
339C4—1522no—
340C4#1192673512yes—
341C2—22no—
342C2—21no—
343C2—21no—
344C2—22no—
345C2—81no—
346C2#1456404611yescharacteristic
347C2#1456407111yescharacteristic
348C2#1456415511yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1799C2
socleC22×C19#386
prime radicalC22×D4×C19D4
cosocleC23×C4×C19C23
hypercenter#1799D19
hypocenterC19#9474
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #14563719C2semidirect
4. #14561502C2semidirect
12. #11926474C4semidirect
13. #11926469C4semidirect
230. C19#9474semidirect

Maximal subgroups

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

subgroupindex
#145726642
#145679432
#145637192
#145615022
C19×#17992
#947419