Finite Group Databasebeta

← #18078618

Subgroups — #18078618

Order 4864.

578 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 119 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#14566238C211yesmaximal, characteristic, complemented
2#14562203C212yesmaximal
3C2×#11926270C211yesmaximal, characteristic, complemented
4#14561502C212yesmaximal, complemented
5C19×#2618C211yesmaximal, characteristic
6C2×C22⋊(C19⋊C8)C2212yes—
7#11926430—24no—
8#11926407—21no—
9#11926404C2212yes—
10C4×C22⋊Dic19—21no—
11#11926278—24no—
12#11926270—22no—
13C2×C19×#123—21no—
14C2×C19×#121C2211yescharacteristic
15C22×C4⋊C4×C19C2211yescharacteristic
16C19×#398C412yescomplemented
17C19×#396—22no—
18C19×#394C412yescomplemented
19C19×#386—21no—
20C19×#380C2211yescharacteristic
21C22×D4×C19—21no—
22C22×D4×C19C2×C411yescharacteristic
23C23×C4×C19D411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C19×#123—44no—
27C19×#121—22no—
28C19×#121—22no—
29C2×C4⋊C4×C19—22no—
30C2×C4⋊C4×C19—22no—
31C2×C4⋊C4×C19—22no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19C2×C411yescharacteristic
34C2×C4⋊C4×C19C2×C412yes—
35C2×C4⋊C4×C19D412yes—
36C2×C22⋊C4×C19—21no—
37C2×C22⋊C4×C19—22no—
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19—22no—
40C2×C22⋊Dic19—22no—
41C2×C4⋊Dic19—22no—
42C2×C4×Dic19—22no—
43C22×C19⋊C8—22no—
44C19×#95—22no—
45C19×#95C2×C412yes—
46C19⋊#95—22no—
47C19⋊#95—24no—
48C19⋊#95D414yes—
49C22⋊(C19⋊C8)—22no—
50C22⋊(C19⋊C8)—22no—
51C24×C19—21no—
52C24×C19C2×D411yescharacteristic
53C2×D4×C19—22no—
54C2×D4×C19—41no—
55C2×D4×C19—41no—
56C2×D4×C19—42no—
57C2×D4×C19—42no—
58C2×D4×C19—81no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—21no—
62C22×C4×C19—22no—
63C22×C4×C19—22no—
64C22×C4×C19—21no—
65C22×C4×C19—22no—
66C22×C4×C19—21no—
67C22×C4×C19—81no—
68C22×C4×C19—81no—
69C22×C4×C19C22⋊C412yes—
70C22×C4×C19C22⋊C412yes—
71C22×C4×C19C22×C411yescharacteristic
72C22×C4×C19C2×D412yes—
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19#4112yes—
75C22×Dic19—24no—
76C4⋊C4×C19—24no—
77C4⋊C4×C19—24no—
78C4⋊C4×C19—22no—
79C4⋊C4×C19—44no—
80C4⋊C4×C19—81no—
81C22⋊C4×C19—44no—
82C22⋊C4×C19—42no—
83C22⋊C4×C19—42no—
84C22⋊C4×C19—82no—
85C22⋊Dic19—42no—
86C22⋊Dic19—42no—
87C4⋊Dic19—82no—
88C4×Dic19—82no—
89C2×C19⋊C8—42no—
90C2×C19⋊C8—82no—
91#9206—191nomaximal, Sylow
92C23×C19—41no—
93C23×C19—41no—
94C23×C19—42no—
95C23×C19—42no—
96C23×C19—41no—
97C23×C19—41no—
98C23×C19—41no—
99C23×C19C2×C22⋊C411yescharacteristic
100C23×C19#12011yescharacteristic
101C23×C19#12311yescharacteristic
102C23×C19#13512yes—
103C23×C19AGL(1,ℤ/8)12yes—
104D4×C19—82no—
105D4×C19—82no—
106D4×C19—82no—
107C2×C4×C19—22no—
108C2×C4×C19—22no—
109C2×C4×C19—22no—
110C2×C4×C19—22no—
111C2×C4×C19—42no—
112C2×C4×C19—42no—
113C2×C4×C19—41no—
114C2×C4×C19—41no—
115C2×C4×C19—42no—
116C2×C4×C19—42no—
117C2×C4×C19—42no—
118C2×C4×C19—42no—
119C2×C4×C19—42no—
120C2×C4×C19—42no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—42no—
124C2×C4×C19—41no—
125C2×C4×C19—81no—
126C2×C4×C19C4×D412yes—
127C2×C4×C19#12112yes—
128C2×Dic19—44no—
129C2×Dic19—44no—
130C2×Dic19—44no—
131C19⋊C8—82no—
132#2618D1911yescharacteristic
133#2313—191no—
134#1519—192no—
135C2×#324—191no—
136#1289—192no—
137C22×C19—21no—
138C22×C19—21no—
139C22×C19—21no—
140C22×C19—21no—
141C22×C19—21no—
142C22×C19—21no—
143C22×C19—42no—
144C22×C19—42no—
145C22×C19—82no—
146C22×C19—82no—
147C22×C19—81no—
148C22×C19—81no—
149C22×C19—81no—
150C22×C19#38611yescharacteristic
151C22×C19#41611yescharacteristic
152C22×C19#41811yescharacteristic
153C22×C19#44912yes—
154C22×C19#48212yes—
155C4×C19—22no—
156C4×C19—22no—
157C4×C19—42no—
158C4×C19—42no—
159C4×C19—82no—
160C4×C19—81no—
161Dic19—84no—
162C2×#123—21no—
163C2×#121C2×D1911yescharacteristic
164C22×C4⋊C4C2×D1911yescharacteristic
165C2×C22⋊C8—192no—
166#398Dic1912yescomplemented
167#396—22no—
168#394Dic1912yescomplemented
169#387—384no—
170#386—21no—
171#381—381no—
172#380—192no—
173#380C2×D1911yescharacteristic
174C4×C22⋊C4—381no—
175#327—384no—
176#324—382no—
177C2×C19—22no—
178C2×C19—21no—
179C2×C19—21no—
180C2×C19—22no—
181C2×C19—161no—
182C2×C19#187511yescharacteristic
183C2×C19#191211yescharacteristic
184C2×C19#191311yescharacteristic
185C22×D4—21no—
186C22×D4C2×Dic1911yescharacteristic
187C23×C4C22⋊D1911yescharacteristic
188C23×C4C22⋊D1911yescharacteristic
189C23×C4C22×D1911yescharacteristic
190C22×C8—382no—
191#123—44no—
192#121—22no—
193#121—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—382no—
199C2×C4⋊C4C2×Dic1911yescharacteristic
200C2×C4⋊C4C2×Dic1912yes—
201C2×C4⋊C4C22⋊D1912yes—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4—382no—
207C2×C42—382no—
208C22⋊C8—382no—
209C22⋊C8—382no—
210#95—22no—
211#95—194no—
212#95—382no—
213#95—384no—
214#95C2×Dic1912yes—
215C19#920611yescharacteristic, complemented, Sylow
216C24—21no—
217C24C2×C22⋊D1911yescharacteristic
218C2×D4—22no—
219C2×D4—42no—
220C2×D4—41no—
221C2×D4—41no—
222C2×D4—42no—
223C2×D4—81no—
224C22×C4—22no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—22no—
232C22×C4—81no—
233C22×C4—81no—
234C22×C4—384no—
235C22×C4C22⋊Dic1912yes—
236C22×C4C22⋊Dic1912yes—
237C22×C4D4×D1912yes—
238C22×C4#6454312yes—
239C22×C4C22×Dic1911yescharacteristic
240C22×C4C2×C22⋊D1911yescharacteristic
241C2×C8—762no—
242C2×C8—1522no—
243C4⋊C4—24no—
244C4⋊C4—24no—
245C4⋊C4—22no—
246C4⋊C4—44no—
247C4⋊C4—81no—
248C4⋊C4—1522no—
249C22⋊C4—44no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—82no—
253C22⋊C4—762no—
254C22⋊C4—762no—
255C42—1522no—
256C23—41no—
257C23—41no—
258C23—42no—
259C23—42no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23#1059737812yes—
264C23#1059738111yescharacteristic
265C23#1059738311yescharacteristic
266C23#1059739612yes—
267C23C2×C22⋊Dic1911yescharacteristic
268D4—82no—
269D4—82no—
270D4—82no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—81no—
290C2×C4—764no—
291C2×C4—764no—
292C2×C4—764no—
293C2×C4D4×Dic1912yes—
294C2×C4#1059738512yes—
295C8—1522no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—42no—
303C22—42no—
304C22—82no—
305C22—82no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22#1192642411yescharacteristic
310C22#1192654011yescharacteristic
311C22#1192654911yescharacteristic
312C22#1192668712yes—
313C22#1192686512yes—
314C4—22no—
315C4—22no—
316C4—42no—
317C4—42no—
318C4—82no—
319C4—81no—
320C4—1524no—
321C2—21no—
322C2—22no—
323C2—21no—
324C2—22no—
325C2—161no—
326C2#1456395811yescharacteristic
327C2#1456417311yescharacteristic
328C2#1456417811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2618C2
socleC22×C19#386
prime radicalC2×C19×#121C22
cosocleC23×C4×C19C23
hypercenter#2618D19
hypocenterC19#9206
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2618

Complements

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

NH ≅ G/Ntype
1. #14566238C2semidirect
3. C2×#11926270C2semidirect
4. #14561502C2semidirect
16. C19×#398C4semidirect
18. C19×#394C4semidirect
166. #398Dic19semidirect
168. #394Dic19semidirect
215. C19#9206semidirect

Maximal subgroups

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

subgroupindex
#145662382
#145622032
C2×#119262702
#145615022
C19×#26182
#920619