Finite Group Databasebeta

← #18072909

Subgroups — #18072909

Order 4864.

942 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 942 conjugacy classes of subgroups — too many to draw. Only its 155 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
1D19×#407C212yesmaximal
2D19×#381C211yesmaximal, characteristic
3#14561544C212yesmaximal, complemented
4#14561543C211yesmaximal, characteristic, complemented
5C19×#1306C211yesmaximal, characteristic, complemented
6C23×C4×D19C2211yescharacteristic
7C2×M16×D19—22no—
8C2×C22⋊C4×D19C412yes—
9#11926508C2212yes—
10#11926507—22no—
11#11926506—22no—
12#11926506C414yescomplemented
13C22⋊C8×D19—22no—
14C22⋊C8×D19C414yescomplemented
15#11926407C2211yescharacteristic
16#11926406—22no—
17#11926405C412yes—
18#95×D19—22no—
19C19×#407C2212yes—
20C19×#381C2211yescharacteristic
21C24×D19C2×C411yescharacteristic
22C23×C4×C19C2311yescharacteristic
23C23×Dic19C2×C411yescharacteristic
24C22×C4×D19—22no—
25C22×C4×D19—44no—
26C22×C4×D19C2×C412yes—
27C22×C4×D19C2×C412yes—
28C22×C4×D19D412yes—
29C22×C4×D19D412yes—
30C22×C4×D19D412yes—
31C22×C4×D19Q812yes—
32C2×M16×C19—22no—
33C2×C22⋊C4×C19C2×C412yes—
34C2×C22⋊Dic19C2×C412yes—
35C2×(C2×D19)⋊C4—22no—
36C2×#64520—22no—
37M16×D19—48no—
38C2×#64515—24no—
39C2×C8×D19—24no—
40C22⋊C4×D19—44no—
41C19×C22⋊C8—22no—
42C19×C22⋊C8C2×C414yescomplemented
43C19×#95—22no—
44C19⋊#95—22no—
45C19⋊#95—24no—
46C22⋊(C19⋊C8)—22no—
47C22⋊(C19⋊C8)C2×C414yescomplemented
48(C2×D19)⋊C8—24no—
49(C2×D19)⋊C8—24no—
50C24×C19C22×C411yescharacteristic
51C23×D19—24no—
52C23×D19—44no—
53C23×D19C4212yes—
54C23×D19C22⋊C411yescharacteristic
55C23×D19C22⋊C411yescharacteristic
56C23×D19C4⋊C412yes—
57C22×C4×C19—22no—
58C22×C4×C19—42no—
59C22×C4×C19C22×C412yes—
60C22×C4×C19C2×D412yes—
61C22×C4×C19C2×D411yescharacteristic
62C22×C4×C19C2×Q811yescharacteristic
63C22×Dic19—22no—
64C22×Dic19—42no—
65C22×Dic19C4211yescharacteristic
66C22×Dic19C4211yescharacteristic
67C22×Dic19C22⋊C412yes—
68C22×Dic19C4⋊C412yes—
69C2×C4×D19—28no—
70C2×C4×D19—44no—
71C2×C4×D19—44no—
72C2×C4×D19—44no—
73C2×C4×D19—44no—
74C2×C4×D19—44no—
75C2×C4×D19—48no—
76C2×C4×D19—44no—
77C2×C4×D19C22⋊C412yes—
78C2×C4×D19C22⋊C412yes—
79C2×C4×D19C22⋊C412yes—
80C2×C4×D19C22⋊C412yes—
81C2×C4×D19C4⋊C412yes—
82C2×C4×D19C4⋊C412yes—
83C2×C4×D19C4⋊C412yes—
84C2×C4×D19C4⋊C412yes—
85M16×C19—44no—
86C2×C8×C19—24no—
87C22⋊C4×C19—42no—
88C22⋊Dic19—42no—
89(C2×D19)⋊C4—44no—
90#64520—44no—
91C2×C19⋊C8—24no—
92#64515—48no—
93C8×D19—48no—
94#8114—191nomaximal, Sylow
95C23×C19—22no—
96C23×C19—42no—
97C23×C19C2×C4211yescharacteristic
98C23×C19C2×C22⋊C411yescharacteristic
99C23×C19C2×C4⋊C411yescharacteristic
100C22×D19—22no—
101C22×D19—24no—
102C22×D19—24no—
103C22×D19—24no—
104C22×D19—24no—
105C22×D19—24no—
106C22×D19—42no—
107C22×D19—42no—
108C22×D19—42no—
109C22×D19—416no—
110C22×D19#9512yes—
111C22×D19#9512yes—
112C22×D19#9914yes—
113C2×C4×C19—24no—
114C2×C4×C19—42no—
115C2×C4×C19—41no—
116C2×C4×C19—41no—
117C2×C4×C19—44no—
118C2×C4×C19—42no—
119C2×C4×C19C2×C22⋊C412yes—
120C2×C4×C19C2×C4⋊C412yes—
121C2×Dic19—24no—
122C2×Dic19—41no—
123C2×Dic19—41no—
124C2×Dic19—42no—
125C2×Dic19—44no—
126C2×Dic19—42no—
127C2×Dic19#9512yes—
128C2×Dic19#9512yes—
129C4×D19—24no—
130C4×D19—24no—
131C4×D19—24no—
132C4×D19—24no—
133C4×D19—42no—
134C4×D19—42no—
135C4×D19—42no—
136C4×D19—42no—
137C4×D19—88no—
138C8×C19—44no—
139C19⋊C8—44no—
140C2×#407—192no—
141C2×#381—191no—
142#1306—192no—
143#1306—191no—
144#1306D1911yescharacteristic, complemented
145C22×C19—22no—
146C22×C19—21no—
147C22×C19—21no—
148C22×C19—22no—
149C22×C19—22no—
150C22×C19—44no—
151C22×C19C2×#9511yescharacteristic
152C22×C19C2×#9912yes—
153C2×D19—28no—
154C2×D19—22no—
155C2×D19—22no—
156C2×D19—22no—
157C2×D19—22no—
158C2×D19—44no—
159C2×D19—48no—
160C2×D19—48no—
161C2×D19#34214yes—
162C2×D19#34414yes—
163C4×C19—22no—
164C4×C19—22no—
165C4×C19—82no—
166Dic19—22no—
167Dic19—22no—
168Dic19—82no—
169C24×C4—191no—
170C22×M16—382no—
171C22×C22⋊C4—192no—
172#407—192no—
173#407—194no—
174#407—382no—
175#407—382no—
176#407C2×D1912yes—
177C2×C22⋊C8—194no—
178C2×C22⋊C8—382no—
179#381—191no—
180#381—192no—
181#381—382no—
182#381C2×D1911yescharacteristic
183C2×#95—382no—
184C2×C19—22no—
185C2×C19—41no—
186C2×C19—41no—
187C2×C19C2×#34211yescharacteristic
188C2×C19C2×#34412yes—
189D19—24no—
190D19—24no—
191C25—191no—
192C23×C4—191no—
193C23×C4—192no—
194C23×C4—192no—
195C23×C4—192no—
196C23×C4—192no—
197C23×C4—192no—
198C23×C4—192no—
199C23×C4—382no—
200C23×C4—764no—
201C23×C4C22×D1911yescharacteristic
202C2×M16—22no—
203C2×M16—384no—
204C2×M16—382no—
205C2×M16—768no—
206C22×C8—384no—
207C2×C22⋊C4—192no—
208C2×C22⋊C4—382no—
209C2×C22⋊C4—764no—
210C2×C22⋊C4C4×D1912yes—
211C22⋊C8—22no—
212C22⋊C8—194no—
213C22⋊C8—384no—
214C22⋊C8—384no—
215C22⋊C8—382no—
216C22⋊C8C4×D1914yescomplemented
217#95—22no—
218#95—384no—
219#95—382no—
220C19#811411yescharacteristic, complemented, Sylow
221C24—191no—
222C24—191no—
223C24—192no—
224C24—192no—
225C24—384no—
226C24—764no—
227C24C2×C4×D1911yescharacteristic
228C22×C4—22no—
229C22×C4—42no—
230C22×C4—192no—
231C22×C4—191no—
232C22×C4—191no—
233C22×C4—192no—
234C22×C4—192no—
235C22×C4—192no—
236C22×C4—192no—
237C22×C4—192no—
238C22×C4—192no—
239C22×C4—192no—
240C22×C4—192no—
241C22×C4—192no—
242C22×C4—388no—
243C22×C4—382no—
244C22×C4—764no—
245C22×C4—764no—
246C22×C4—764no—
247C22×C4—764no—
248C22×C4—764no—
249C22×C4—764no—
250C22×C4—768no—
251C22×C4—762no—
252C22×C4C2×C4×D1912yes—
253C22×C4D4×D1912yes—
254C22×C4D4×D1911yescharacteristic
255C22×C4Q8×D1911yescharacteristic
256M16—44no—
257M16—768no—
258M16—764no—
259C2×C8—24no—
260C2×C8—384no—
261C2×C8—768no—
262C22⋊C4—42no—
263C22⋊C4—764no—
264C22⋊C4—762no—
265C23—22no—
266C23—42no—
267C23—192no—
268C23—192no—
269C23—194no—
270C23—384no—
271C23—384no—
272C23—384no—
273C23—384no—
274C23—384no—
275C23—382no—
276C23—762no—
277C23—762no—
278C23—762no—
279C23—7616no—
280C23C42×D1911yescharacteristic
281C23C22⋊C4×D1911yescharacteristic
282C23C4⋊C4×D1911yescharacteristic
283C2×C4—24no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—44no—
288C2×C4—42no—
289C2×C4—192no—
290C2×C4—192no—
291C2×C4—384no—
292C2×C4—384no—
293C2×C4—384no—
294C2×C4—384no—
295C2×C4—384no—
296C2×C4—762no—
297C2×C4—762no—
298C2×C4—762no—
299C2×C4—762no—
300C2×C4—761no—
301C2×C4—761no—
302C2×C4—762no—
303C2×C4—764no—
304C2×C4—762no—
305C2×C4—1528no—
306C2×C4C22⋊C4×D1912yes—
307C2×C4C4⋊C4×D1912yes—
308C8—44no—
309C8—764no—
310C22—22no—
311C22—21no—
312C22—21no—
313C22—22no—
314C22—22no—
315C22—44no—
316C22—194no—
317C22—194no—
318C22—388no—
319C22—382no—
320C22—382no—
321C22—382no—
322C22—382no—
323C22—764no—
324C22—768no—
325C22—768no—
326C22#95×D1911yescharacteristic
327C22#99×D1912yes—
328C4—22no—
329C4—22no—
330C4—82no—
331C4—382no—
332C4—382no—
333C4—1522no—
334C2—22no—
335C2—41no—
336C2—41no—
337C2—384no—
338C2—384no—
339C2D19×#34211yescharacteristic
340C2D19×#34412yes—
subgroupG/H
centerC22#95×D19
commutatorC23×C19C2×C42
FrattiniC23×C4C22×D19
FittingC19×#1306C2
socleC22×C19C2×#95
prime radicalC24×D19C2×C4
cosocleC23×C4×C19C23
hypercenter#1306D19
hypocenterC19#8114
LCSG ▷ C23×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
3. #14561544C2semidirect
4. #14561543C2semidirect
5. C19×#1306C2semidirect
12. #11926506C4semidirect
14. C22⋊C8×D19C4semidirect
42. C19×C22⋊C8C2×C4semidirect
47. C22⋊(C19⋊C8)C2×C4semidirect
144. #1306D19semidirect
216. C22⋊C8C4×D19semidirect
220. C19#8114semidirect

Maximal subgroups

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

subgroupindex
D19×#4072
D19×#3812
#145615442
#145615432
C19×#13062
#811419