Finite Group Databasebeta

← #18080343

Subgroups — #18080343

Order 4864.

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

normal subgroups only

This group has 818 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#14566970C211yesmaximal, characteristic
2#14563580C212yesmaximal
3#14561965C211yesmaximal, characteristic, complemented
4#14561488C212yesmaximal, complemented
5C19×#2274C211yesmaximal, characteristic, complemented
6C22×#64541C2211yescharacteristic
7C2×#10597375—21no—
8C2×#10597262—24no—
9#11926508C2212yes—
10#11926464C412yescomplemented
11#11926461C412yescomplemented
12#11926423—21no—
13#11926415—22no—
14#11926407C2211yescharacteristic
15#11926270—22no—
16C2×C19×#117—21no—
17C22×C4⋊C4×C19C2211yescharacteristic
18C4×C4⋊C4×C19—24no—
19C4×C22⋊C4×C19—21no—
20C4×C22⋊C4×C19C2212yes—
21C23×C4×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C22×C22⋊D19—21no—
25C2×#64541—22no—
26C2×#64541—22no—
27C2×#64541—44no—
28C22×D76C2×C411yescharacteristic
29C22×C4×D19—21no—
30C22×Dic38C2×C411yescharacteristic
31C19×#117—28no—
32C2×C4⋊C4×C19—22no—
33C2×C4⋊C4×C19—22no—
34C2×C4⋊C4×C19—22no—
35C2×C4⋊C4×C19C2×C412yes—
36C2×C4⋊C4×C19D412yes—
37C2×C22⋊C4×C19—22no—
38C2×C42×C19—22no—
39C2×C42×C19—22no—
40C2×C42×C19D414yes—
41C2×C22⋊Dic19—21no—
42#10597375—44no—
43C2×(C2×D19)⋊C4—22no—
44C2×(C2×D19)⋊C4—22no—
45C2×Dic19⋊C4—22no—
46C2×#64520—22no—
47C19×#95—22no—
48C19×#95—22no—
49C19⋊#95—22no—
50C19⋊#95—21no—
51C19⋊#95C2×C412yes—
52C22⋊(C19⋊C8)—22no—
53C22⋊(C19⋊C8)—22no—
54#10597262—48no—
55C24×C19C2×D411yescharacteristic
56C23×D19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—21no—
59C22×C4×C19—24no—
60C22×C4×C19—24no—
61C22×C4×C19—21no—
62C22×C4×C19—21no—
63C22×C4×C19—42no—
64C22×C4×C19—42no—
65C22×C4×C19C22⋊C412yes—
66C22×C4×C19C22⋊C412yes—
67C22×C4×C19C22×C411yescharacteristic
68C22×C4×C19C2×D411yescharacteristic
69C22×C4×C19C2×D412yes—
70C22×C4×C19#4112yes—
71C2×C22⋊D19—24no—
72C2×C22⋊D19—42no—
73C2×C22⋊D19—41no—
74C2×C22⋊D19—41no—
75C22×Dic19—21no—
76C22×Dic19—22no—
77#64541—28no—
78#64541—44no—
79#64541—44no—
80#64541—44no—
81C2×D76—22no—
82C2×D76—42no—
83C2×C4×D19—42no—
84C2×C4×D19—42no—
85C2×C4×D19—42no—
86C2×Dic38—22no—
87C2×Dic38—42no—
88C4⋊C4×C19—28no—
89C4⋊C4×C19—24no—
90C4⋊C4×C19—24no—
91C22⋊C4×C19—28no—
92C42×C19—28no—
93C42×C19—44no—
94C42×C19—82no—
95C22⋊Dic19—42no—
96(C2×D19)⋊C4—44no—
97(C2×D19)⋊C4—44no—
98Dic19⋊C4—44no—
99#64520—44no—
100C2×C19⋊C8—42no—
101#9476—191nomaximal, Sylow
102C23×C19—22no—
103C23×C19—22no—
104C23×C19—41no—
105C23×C19C2×C22⋊C411yescharacteristic
106C23×C19#12011yescharacteristic
107C23×C19#12311yescharacteristic
108C22×D19—22no—
109C22×D19—41no—
110C22×D19—42no—
111C22×D19—41no—
112C22×D19—42no—
113C2×C4×C19—22no—
114C2×C4×C19—22no—
115C2×C4×C19—24no—
116C2×C4×C19—22no—
117C2×C4×C19—22no—
118C2×C4×C19—24no—
119C2×C4×C19—28no—
120C2×C4×C19—22no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—42no—
124C2×C4×C19—44no—
125C2×C4×C19—44no—
126C2×C4×C19—42no—
127C2×C4×C19—42no—
128C2×C4×C19—81no—
129C2×C4×C19#10414yescomplemented
130C2×C4×C19C4×D412yes—
131C2×C4×C19#12112yes—
132C22⋊D19—44no—
133C22⋊D19—44no—
134C2×Dic19—22no—
135C2×Dic19—41no—
136C2×Dic19—41no—
137C2×Dic19—42no—
138C2×Dic19—42no—
139C2×Dic19—42no—
140D76—24no—
141D76—42no—
142C4×D19—48no—
143Dic38—24no—
144Dic38—42no—
145C19⋊C8—82no—
146#2406—191no—
147#2274D1911yescharacteristic, complemented
148#1789—192no—
149#1463—191no—
150#1284—192no—
151C22×C19—21no—
152C22×C19—21no—
153C22×C19—21no—
154C22×C19—21no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19—44no—
159C22×C19#38611yescharacteristic
160C22×C19C2×#10412yes—
161C22×C19B(4,𝔽2)12yes—
162C2×D19—44no—
163C2×D19—42no—
164C2×D19—82no—
165C2×D19—81no—
166C2×D19—81no—
167C4×C19—22no—
168C4×C19—22no—
169C4×C19—24no—
170C4×C19—48no—
171C4×C19—42no—
172Dic19—42no—
173Dic19—82no—
174C22×#41—191no—
175C2×#123—381no—
176C2×#117—21no—
177C22×C4⋊C4C2×D1911yescharacteristic
178C2×#104—384no—
179#407—192no—
180#395—192no—
181#394—192no—
182#386—381no—
183#385—382no—
184#381—191no—
185C4×C4⋊C4—24no—
186C4×C22⋊C4—21no—
187C4×C22⋊C4C2×D1912yes—
188#324—382no—
189C2×C19—22no—
190C2×C19—22no—
191C2×C19—41no—
192C2×C19#188911yescharacteristic
193C2×C19#189611yescharacteristic
194C2×C19#191211yescharacteristic
195D19—82no—
196C2×#41—382no—
197C2×#41—382no—
198C2×#41—764no—
199C22×Q8—191no—
200C22×D4—191no—
201C22×D4—381no—
202C23×C4—381no—
203C23×C4C22⋊D1911yescharacteristic
204C23×C4C22⋊D1911yescharacteristic
205C23×C4C22×D1911yescharacteristic
206C2×M16—382no—
207#123—764no—
208#117—28no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—382no—
213C2×C4⋊C4C4×D1912yes—
214C2×C4⋊C4D7612yes—
215C2×C22⋊C4—22no—
216C2×C22⋊C4—381no—
217C2×C22⋊C4—382no—
218C2×C22⋊C4—382no—
219C2×C42—22no—
220C2×C42—22no—
221C2×C42C22⋊D1914yes—
222#104—768no—
223C22⋊C8—382no—
224C22⋊C8—382no—
225#95—22no—
226#95—22no—
227#95—192no—
228#95—382no—
229#95—381no—
230C19#947611yescharacteristic, complemented, Sylow
231C24—381no—
232C24C2×C22⋊D1911yescharacteristic
233#41—388no—
234#41—764no—
235#41—764no—
236#41—764no—
237C2×Q8—382no—
238C2×Q8—762no—
239C2×D4—384no—
240C2×D4—382no—
241C2×D4—762no—
242C2×D4—762no—
243C2×D4—761no—
244C2×D4—761no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—24no—
248C22×C4—24no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—381no—
254C22×C4—382no—
255C22×C4—762no—
256C22×C4—762no—
257C22×C4—762no—
258C22×C4(C2×D19)⋊C412yes—
259C22×C4(C2×D19)⋊C412yes—
260C22×C4C2×C4×D1911yescharacteristic
261C22×C4C2×D7611yescharacteristic
262C22×C4#6454112yes—
263C22×C4C2×C22⋊D1912yes—
264M16—764no—
265C2×C8—762no—
266C4⋊C4—28no—
267C4⋊C4—24no—
268C4⋊C4—24no—
269C4⋊C4—764no—
270C22⋊C4—28no—
271C22⋊C4—764no—
272C22⋊C4—762no—
273C22⋊C4—764no—
274C42—28no—
275C42—44no—
276C42—82no—
277C23—22no—
278C23—22no—
279C23—41no—
280C23—382no—
281C23—761no—
282C23—762no—
283C23—762no—
284C23—761no—
285C23C2×(C2×D19)⋊C411yescharacteristic
286C23#1059737511yescharacteristic
287C23#1059739911yescharacteristic
288Q8—384no—
289Q8—762no—
290D4—384no—
291D4—762no—
292D4—764no—
293D4—764no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—28no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—81no—
310C2×C4—382no—
311C2×C4—768no—
312C2×C4—761no—
313C2×C4—761no—
314C2×C4—762no—
315C2×C4—762no—
316C2×C4—762no—
317C2×C4#1059726214yescomplemented
318C2×C4C4×C22⋊D1912yes—
319C2×C4#1059737612yes—
320C8—1522no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—44no—
329C22—764no—
330C22—762no—
331C22—1522no—
332C22—1521no—
333C22—1521no—
334C22#1192642311yescharacteristic
335C22C2×#1059726212yes—
336C22#1192673112yes—
337C4—22no—
338C4—22no—
339C4—24no—
340C4—48no—
341C4—42no—
342C4—762no—
343C4—1522no—
344C2—22no—
345C2—22no—
346C2—41no—
347C2—1522no—
348C2#1456404311yescharacteristic
349C2#1456407811yescharacteristic
350C2#1456417211yescharacteristic
subgroupG/H
centerC22#11926423
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2274C2
socleC22×C19#386
prime radicalC22×#64541C22
cosocleC23×C4×C19C23
hypercenter#2274D19
hypocenterC19#9476
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2274

Complements

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

NH ≅ G/Ntype
3. #14561965C2semidirect
4. #14561488C2semidirect
5. C19×#2274C2semidirect
10. #11926464C4semidirect
11. #11926461C4semidirect
129. C2×C4×C19#104semidirect
147. #2274D19semidirect
230. C19#9476semidirect
317. C2×C4#10597262semidirect

Maximal subgroups

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

subgroupindex
#145669702
#145635802
#145619652
#145614882
C19×#22742
#947619