Finite Group Databasebeta

← #18071225

Subgroups — #18071225

Order 4864.

450 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 107 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#14571945C211yesmaximal, characteristic
2#14563703C211yesmaximal, characteristic
3#14561459C212yesmaximal, complemented
4#14561457C212yesmaximal, complemented
5C19×#1797C211yesmaximal, characteristic
6C2×#10597316C411yescharacteristic
7C2×C22⋊(C19⋊C8)—21no—
8#11926442C2211yescharacteristic
9#11926442C2211yescharacteristic
10#11926428—21no—
11#11926428—21no—
12#11926417—21no—
13#11926417—21no—
14#11926410C411yescharacteristic
15#11926404C411yescharacteristic
16#11926404C411yescharacteristic
17#11926299—21no—
18#11926299C2212yes—
19C22×C42×C19C2211yescharacteristic
20C2×C19×C4⋊C8—21no—
21C2×C19×C22⋊C8—21no—
22C19×#336C2212yes—
23C23×C4×C19C2×C411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19D411yescharacteristic
26C22×C8×C19—22no—
27C2×C42×C19—42no—
28C2×C42×C19C2×C411yescharacteristic
29C2×C42×C19D411yescharacteristic
30C2×C42×C19D411yescharacteristic
31C2×C42×C19C2311yescharacteristic
32C2×C22⋊Dic19—21no—
33C2×C22⋊Dic19—21no—
34C2×C4⋊Dic19C2×C411yescharacteristic
35C2×C4⋊Dic19C2×C411yescharacteristic
36C2×C4⋊Dic19C2×C411yescharacteristic
37C2×C4⋊Dic19C2×C411yescharacteristic
38C2×Dic19⋊C4—21no—
39C2×Dic19⋊C4—21no—
40C2×Dic19⋊C4—21no—
41C2×Dic19⋊C4—21no—
42C22×C19⋊C8—22no—
43#10597316—42no—
44C19×C4⋊C8—42no—
45C19×C22⋊C8—42no—
46C19⋊#95—21no—
47C19⋊#95—21no—
48C19⋊#95—21no—
49C19⋊#95—21no—
50C19⋊#95—21no—
51C19⋊#95—21no—
52C22⋊(C19⋊C8)—42no—
53C24×C19C22⋊C411yescharacteristic
54C22×C4×C19—22no—
55C22×C4×C19—22no—
56C22×C4×C19—22no—
57C22×C4×C19—22no—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—41no—
61C22×C4×C19—41no—
62C22×C4×C19—41no—
63C22×C4×C19—41no—
64C22×C4×C19C22⋊C411yescharacteristic
65C22×C4×C19C22⋊C411yescharacteristic
66C22×C4×C19C22⋊C411yescharacteristic
67C22×C4×C19C22×C411yescharacteristic
68C22×C4×C19C2×D411yescharacteristic
69C22×C4×C19C2×D411yescharacteristic
70C22×Dic19—21no—
71C22×Dic19—21no—
72C22×Dic19—21no—
73C22×Dic19—21no—
74C2×C8×C19—42no—
75C2×C8×C19—42no—
76C2×C8×C19—42no—
77C42×C19—22no—
78C42×C19—22no—
79C42×C19—41no—
80C42×C19—41no—
81C22⋊Dic19—42no—
82C22⋊Dic19—42no—
83C4⋊Dic19—22no—
84C4⋊Dic19—22no—
85C4⋊Dic19—41no—
86C4⋊Dic19—41no—
87Dic19⋊C4—42no—
88Dic19⋊C4—42no—
89Dic19⋊C4—42no—
90Dic19⋊C4—41no—
91Dic19⋊C4—41no—
92C2×C19⋊C8—42no—
93C2×C19⋊C8—42no—
94C2×C19⋊C8—42no—
95#7731—191nomaximal, Sylow
96C23×C19—21no—
97C23×C19—21no—
98C23×C19—21no—
99C23×C19—21no—
100C23×C19—21no—
101C23×C19—21no—
102C23×C19#10112yes—
103C23×C19C2×C22⋊C411yescharacteristic
104C2×C4×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—44no—
119C2×C4×C19—44no—
120C2×C4×C19—42no—
121C2×C4×C19—42no—
122C2×C4×C19#9912yes—
123C2×C4×C19#13112yes—
124C2×C4×C19#13512yes—
125C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C19#13711yescharacteristic
127C2×Dic19—41no—
128C2×Dic19—41no—
129C2×Dic19—41no—
130C2×Dic19—41no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—41no—
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137C2×Dic19—41no—
138C2×Dic19—41no—
139C8×C19—82no—
140C19⋊C8—82no—
141#2851—191no—
142#1817—191no—
143#1797D1911yescharacteristic
144#1271—192no—
145#1271—192no—
146C22×C19—22no—
147C22×C19—22no—
148C22×C19—22no—
149C22×C19—41no—
150C22×C19—41no—
151C22×C19—41no—
152C22×C19—41no—
153C22×C19#40811yescharacteristic
154C22×C19C2×#9911yescharacteristic
155C22×C19C2×#10111yescharacteristic
156C22×C19#41611yescharacteristic
157C22×C19#41711yescharacteristic
158C22×C19#42111yescharacteristic
159C22×C19#42111yescharacteristic
160C4×C19—22no—
161C4×C19—21no—
162C4×C19—21no—
163C4×C19—22no—
164C4×C19—22no—
165C4×C19—41no—
166C4×C19—41no—
167Dic19—81no—
168Dic19—81no—
169Dic19—81no—
170Dic19—81no—
171C2×#125—191no—
172C22×C42C2×D1911yescharacteristic
173C2×C4⋊C8—21no—
174C2×C22⋊C8—21no—
175C2×C22⋊C8—381no—
176#389—191no—
177#389—191no—
178#387—381no—
179#387—381no—
180#385—381no—
181#385—381no—
182#382—191no—
183#380—191no—
184#380—191no—
185#336—192no—
186#336—381no—
187#336C2×D1912yes—
188C2×C19—42no—
189C2×C19#147211yescharacteristic
190C2×C19#148211yescharacteristic
191C2×C19#149511yescharacteristic
192C2×C19#151311yescharacteristic
193C2×C19#151611yescharacteristic
194C2×C19#153411yescharacteristic
195C2×C19#155211yescharacteristic
196C23×C4C4×D1911yescharacteristic
197C23×C4D7611yescharacteristic
198C23×C4C22⋊D1911yescharacteristic
199C22×C8—22no—
200C22×C8—382no—
201#125—762no—
202C2×C4⋊C4—191no—
203C2×C4⋊C4—191no—
204C2×C4⋊C4—191no—
205C2×C4⋊C4—191no—
206C2×C4⋊C4—381no—
207C2×C4⋊C4—381no—
208C2×C4⋊C4—381no—
209C2×C4⋊C4—381no—
210C2×C22⋊C4—381no—
211C2×C22⋊C4—381no—
212C2×C42—42no—
213C2×C42C4×D1911yescharacteristic
214C2×C42D7611yescharacteristic
215C2×C42C22⋊D1911yescharacteristic
216C2×C42C22×D1911yescharacteristic
217C4⋊C8—42no—
218C22⋊C8—42no—
219C22⋊C8—762no—
220#95—381no—
221#95—381no—
222#95—381no—
223#95—381no—
224#95—381no—
225#95—381no—
226C19#773111yescharacteristic, complemented, Sylow
227C24(C2×D19)⋊C411yescharacteristic
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—381no—
239C22×C4—381no—
240C22×C4—381no—
241C22×C4—381no—
242C22×C4(C2×D19)⋊C411yescharacteristic
243C22×C4(C2×D19)⋊C411yescharacteristic
244C22×C4(C2×D19)⋊C411yescharacteristic
245C22×C4C2×C4×D1911yescharacteristic
246C22×C4C2×D7611yescharacteristic
247C22×C4C2×C22⋊D1911yescharacteristic
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—762no—
252C2×C8—762no—
253C2×C8—762no—
254C4⋊C4—382no—
255C4⋊C4—382no—
256C4⋊C4—761no—
257C4⋊C4—761no—
258C4⋊C4—762no—
259C4⋊C4—761no—
260C4⋊C4—761no—
261C4⋊C4—762no—
262C4⋊C4—762no—
263C22⋊C4—762no—
264C22⋊C4—762no—
265C42—22no—
266C42—22no—
267C42—41no—
268C42—41no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23#1059728112yes—
276C23C2×(C2×D19)⋊C411yescharacteristic
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—44no—
292C2×C4—44no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—761no—
296C2×C4—761no—
297C2×C4—761no—
298C2×C4—761no—
299C2×C4—761no—
300C2×C4—761no—
301C2×C4—761no—
302C2×C4—761no—
303C2×C4—761no—
304C2×C4—761no—
305C2×C4—761no—
306C2×C4—761no—
307C2×C4#1059726312yes—
308C2×C4#1059735012yes—
309C2×C4#1059735312yes—
310C2×C4#1059737811yescharacteristic
311C2×C4#1059738811yescharacteristic
312C8—82no—
313C8—1522no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22#1192651211yescharacteristic
322C22C2×#1059726311yescharacteristic
323C22C2×#1059728111yescharacteristic
324C22#1192654111yescharacteristic
325C22#1192654311yescharacteristic
326C22#1192656011yescharacteristic
327C22#1192656211yescharacteristic
328C4—21no—
329C4—21no—
330C4—22no—
331C4—22no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—1521no—
336C4—1521no—
337C4—1521no—
338C4—1521no—
339C2—42no—
340C2#1456200011yescharacteristic
341C2#1456204411yescharacteristic
342C2#1456209811yescharacteristic
343C2#1456217611yescharacteristic
344C2#1456219211yescharacteristic
345C2#1456226111yescharacteristic
346C2#1456233311yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1797C2
socleC23×C19C2×C22⋊C4
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1797D19
hypocenterC19#7731
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. #14561459C2semidirect
4. #14561457C2semidirect
226. C19#7731semidirect

Maximal subgroups

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

subgroupindex
#145719452
#145637032
#145614592
#145614572
C19×#17972
#773119