Finite Group Databasebeta

← #18071130

Subgroups — #18071130

Order 4864.

500 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 111 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#14563329C211yesmaximal, characteristic
3#14561459C212yesmaximal, complemented
4#14561457C212yesmaximal, complemented
5C19×#1797C211yesmaximal, characteristic
6C22×#64520—21no—
7C2×#10597316C411yescharacteristic
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—
42C2×#64520—24no—
43C2×#64520—42no—
44C2×#64520—42no—
45C22×C19⋊C8—22no—
46#10597316—42no—
47C19×C4⋊C8—42no—
48C19×C22⋊C8—42no—
49C19⋊#95—21no—
50C19⋊#95—21no—
51C19⋊#95—21no—
52C19⋊#95—21no—
53C19⋊#95—21no—
54C19⋊#95—21no—
55C24×C19C22⋊C411yescharacteristic
56C22×C4×C19—22no—
57C22×C4×C19—22no—
58C22×C4×C19—21no—
59C22×C4×C19—21no—
60C22×C4×C19—22no—
61C22×C4×C19—22no—
62C22×C4×C19—21no—
63C22×C4×C19—21no—
64C22×C4×C19—41no—
65C22×C4×C19—41no—
66C22×C4×C19—41no—
67C22×C4×C19C22⋊C411yescharacteristic
68C22×C4×C19C22⋊C411yescharacteristic
69C22×C4×C19C22⋊C411yescharacteristic
70C22×C4×C19C22×C411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×Dic19—21no—
74C22×Dic19—21no—
75C22×Dic19—21no—
76C22×Dic19—21no—
77C2×C8×C19—42no—
78C2×C8×C19—42no—
79C2×C8×C19—42no—
80C42×C19—22no—
81C42×C19—22no—
82C42×C19—41no—
83C42×C19—41no—
84C22⋊Dic19—42no—
85C22⋊Dic19—42no—
86C4⋊Dic19—22no—
87C4⋊Dic19—22no—
88C4⋊Dic19—41no—
89C4⋊Dic19—41no—
90Dic19⋊C4—42no—
91Dic19⋊C4—42no—
92Dic19⋊C4—41no—
93Dic19⋊C4—41no—
94Dic19⋊C4—41no—
95Dic19⋊C4—41no—
96#64520—48no—
97C2×C19⋊C8—24no—
98C2×C19⋊C8—42no—
99C2×C19⋊C8—42no—
100#7711—191nomaximal, Sylow
101C23×C19—21no—
102C23×C19—21no—
103C23×C19—21no—
104C23×C19—21no—
105C23×C19—21no—
106C23×C19—21no—
107C23×C19#10412yes—
108C23×C19C2×C22⋊C411yescharacteristic
109C2×C4×C19—24no—
110C2×C4×C19—24no—
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—21no—
119C2×C4×C19—21no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—44no—
125C2×C4×C19—42no—
126C2×C4×C19—42no—
127C2×C4×C19#9912yes—
128C2×C4×C19#10112yes—
129C2×C4×C19#13112yes—
130C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C19#13711yescharacteristic
133C2×C4×C19#13711yescharacteristic
134C2×Dic19—41no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137C2×Dic19—41no—
138C2×Dic19—41no—
139C2×Dic19—41no—
140C2×Dic19—41no—
141C2×Dic19—41no—
142C2×Dic19—41no—
143C2×Dic19—41no—
144C2×Dic19—41no—
145C2×Dic19—41no—
146C8×C19—82no—
147C19⋊C8—44no—
148#2851—191no—
149#1797D1911yescharacteristic
150#1728—191no—
151#1271—192no—
152#1271—192no—
153C22×C19—22no—
154C22×C19—22no—
155C22×C19—22no—
156C22×C19—41no—
157C22×C19—41no—
158C22×C19—41no—
159C22×C19—41no—
160C22×C19#40811yescharacteristic
161C22×C19C2×#9911yescharacteristic
162C22×C19C2×#10111yescharacteristic
163C22×C19#41711yescharacteristic
164C22×C19#41711yescharacteristic
165C22×C19C2×#10411yescharacteristic
166C22×C19#42111yescharacteristic
167C4×C19—22no—
168C4×C19—22no—
169C4×C19—21no—
170C4×C19—22no—
171C4×C19—21no—
172C4×C19—21no—
173C4×C19—21no—
174C4×C19—41no—
175Dic19—81no—
176Dic19—81no—
177Dic19—81no—
178Dic19—81no—
179C22×M16—381no—
180C2×#125—191no—
181C22×C42C2×D1911yescharacteristic
182C2×C4⋊C8—21no—
183C2×C22⋊C8—21no—
184#389—191no—
185#389—191no—
186#387—381no—
187#387—381no—
188#385—381no—
189#385—381no—
190#382—191no—
191#380—191no—
192#380—191no—
193#336—192no—
194#336—381no—
195#336C2×D1912yes—
196C2×C19—42no—
197C2×C19#147211yescharacteristic
198C2×C19#148311yescharacteristic
199C2×C19#149511yescharacteristic
200C2×C19#150411yescharacteristic
201C2×C19#151311yescharacteristic
202C2×C19#152811yescharacteristic
203C2×C19#156111yescharacteristic
204C23×C4C4×D1911yescharacteristic
205C23×C4D7611yescharacteristic
206C23×C4C22⋊D1911yescharacteristic
207C2×M16—384no—
208C2×M16—762no—
209C2×M16—762no—
210C22×C8—22no—
211C22×C8—382no—
212#125—762no—
213C2×C4⋊C4—191no—
214C2×C4⋊C4—191no—
215C2×C4⋊C4—191no—
216C2×C4⋊C4—191no—
217C2×C4⋊C4—381no—
218C2×C4⋊C4—381no—
219C2×C4⋊C4—381no—
220C2×C4⋊C4—381no—
221C2×C22⋊C4—381no—
222C2×C22⋊C4—381no—
223C2×C42—42no—
224C2×C42C4×D1911yescharacteristic
225C2×C42D7611yescharacteristic
226C2×C42C22⋊D1911yescharacteristic
227C2×C42C22×D1911yescharacteristic
228C4⋊C8—42no—
229C22⋊C8—42no—
230#95—381no—
231#95—381no—
232#95—381no—
233#95—381no—
234#95—381no—
235#95—381no—
236C19#771111yescharacteristic, complemented, Sylow
237C24(C2×D19)⋊C411yescharacteristic
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—381no—
250C22×C4—381no—
251C22×C4—381no—
252C22×C4—381no—
253C22×C4(C2×D19)⋊C411yescharacteristic
254C22×C4(C2×D19)⋊C411yescharacteristic
255C22×C4(C2×D19)⋊C411yescharacteristic
256C22×C4C2×C4×D1911yescharacteristic
257C22×C4C2×D7611yescharacteristic
258C22×C4C2×C22⋊D1911yescharacteristic
259M16—768no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—384no—
264C2×C8—762no—
265C2×C8—762no—
266C4⋊C4—382no—
267C4⋊C4—382no—
268C4⋊C4—761no—
269C4⋊C4—761no—
270C4⋊C4—762no—
271C4⋊C4—761no—
272C4⋊C4—761no—
273C4⋊C4—762no—
274C4⋊C4—761no—
275C4⋊C4—761no—
276C22⋊C4—762no—
277C22⋊C4—762no—
278C42—22no—
279C42—22no—
280C42—41no—
281C42—41no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23#1059728212yes—
289C23C2×(C2×D19)⋊C411yescharacteristic
290C2×C4—24no—
291C2×C4—24no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—44no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—761no—
309C2×C4—761no—
310C2×C4—761no—
311C2×C4—761no—
312C2×C4—761no—
313C2×C4—761no—
314C2×C4—761no—
315C2×C4—761no—
316C2×C4—761no—
317C2×C4—761no—
318C2×C4—761no—
319C2×C4—761no—
320C2×C4#1059726312yes—
321C2×C4#1059728112yes—
322C2×C4#1059734712yes—
323C2×C4#1059735411yescharacteristic
324C2×C4#1059735511yescharacteristic
325C2×C4#1059737811yescharacteristic
326C2×C4#1059738811yescharacteristic
327C8—82no—
328C8—764no—
329C22—22no—
330C22—22no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22#1192651011yescharacteristic
337C22C2×#1059726311yescharacteristic
338C22C2×#1059728111yescharacteristic
339C22#1192654311yescharacteristic
340C22#1192654611yescharacteristic
341C22C2×#1059728211yescharacteristic
342C22#1192656211yescharacteristic
343C4—21no—
344C4—22no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—22no—
349C4—22no—
350C4—41no—
351C4—1521no—
352C4—1521no—
353C4—1521no—
354C4—1521no—
355C2—42no—
356C2#1456199811yescharacteristic
357C2#1456204611yescharacteristic
358C2#1456210111yescharacteristic
359C2#1456214011yescharacteristic
360C2#1456217611yescharacteristic
361C2#1456223811yescharacteristic
362C2#1456237211yescharacteristic
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#7711
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
236. C19#7711semidirect

Maximal subgroups

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

subgroupindex
#145719452
#145633292
#145614592
#145614572
C19×#17972
#771119