Finite Group Databasebeta

← #18078615

Subgroups — #18078615

Order 4864.

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

normal subgroups only

This group has 578 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#14569377C211yesmaximal, characteristic
2#14566238C211yesmaximal, characteristic, complemented
3#14562204C212yesmaximal
4#14561503C212yesmaximal, complemented
5C2×C19×#324C211yesmaximal, characteristic, complemented
6C2×#10597375—21no—
7C2×#10597376C2211yescharacteristic
8#11926474C412yescomplemented
9#11926466—22no—
10#11926461C412yescomplemented
11#11926430—24no—
12#11926423—21no—
13#11926407—21no—
14#11926404C2211yescharacteristic
15#11926404C2212yes—
16C4×C22⋊Dic19—21no—
17#11926279—24no—
18C22×C4⋊C4×C19C2211yescharacteristic
19C2×C19×C22⋊C8C2212yes—
20C19×#324—22no—
21C23×C4×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C22×C22⋊D19—21no—
25C22×D76C2×C411yescharacteristic
26C22×C8×C19—22no—
27C2×C4⋊C4×C19—22no—
28C2×C4⋊C4×C19—22no—
29C2×C4⋊C4×C19C2×C412yes—
30C2×C4⋊C4×C19D412yes—
31C2×C22⋊Dic19—21no—
32C2×C22⋊Dic19—22no—
33#10597376—22no—
34#10597376—22no—
35#10597375—44no—
36C2×(C2×D19)⋊C4—22no—
37C2×(C2×D19)⋊C4—21no—
38C2×(C2×D19)⋊C4—22no—
39C2×C4⋊Dic19—22no—
40C2×C4⋊Dic19—21no—
41C2×C4⋊Dic19C2×C411yescharacteristic
42C2×Dic19⋊C4—22no—
43C2×C4×Dic19—22no—
44C19×C22⋊C8—22no—
45C19×C22⋊C8—22no—
46C19⋊#95—22no—
47C19⋊#95—24no—
48C19⋊#95—22no—
49C19⋊#95C2×C412yes—
50C19⋊#95D414yes—
51C24×C19C2×D411yescharacteristic
52C23×D19—21no—
53C22×C4×C19—21no—
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—22no—
57C22×C4×C19—22no—
58C22×C4×C19—21no—
59C22×C4×C19—81no—
60C22×C4×C19—81no—
61C22×C4×C19C22⋊C412yes—
62C22×C4×C19C22⋊C412yes—
63C22×C4×C19C22×C411yescharacteristic
64C22×C4×C19C2×D412yes—
65C22×C4×C19C2×D411yescharacteristic
66C22×C4×C19#4112yes—
67C2×C22⋊D19—41no—
68C2×C22⋊D19—41no—
69C2×C22⋊D19—42no—
70C2×C22⋊D19—42no—
71C22×Dic19—22no—
72C22×Dic19—21no—
73C22×Dic19—24no—
74C2×D76—22no—
75C2×D76—81no—
76C2×C8×C19—42no—
77C2×C8×C19—82no—
78C4⋊C4×C19—24no—
79C4⋊C4×C19—24no—
80C22⋊Dic19—42no—
81C22⋊Dic19—42no—
82C22⋊Dic19—42no—
83(C2×D19)⋊C4—44no—
84(C2×D19)⋊C4—42no—
85(C2×D19)⋊C4—82no—
86C4⋊Dic19—22no—
87C4⋊Dic19—82no—
88C4⋊Dic19—81no—
89Dic19⋊C4—44no—
90C4×Dic19—82no—
91#9206—191nomaximal, Sylow
92C23×C19—41no—
93C23×C19—41no—
94C23×C19C2×C22⋊C411yescharacteristic
95C23×C19#12011yescharacteristic
96C23×C19#12311yescharacteristic
97C23×C19#13512yes—
98C23×C19AGL(1,ℤ/8)12yes—
99C22×D19—42no—
100C22×D19—42no—
101C22×D19—41no—
102C22×D19—41no—
103C22×D19—41no—
104C2×C4×C19—22no—
105C2×C4×C19—22no—
106C2×C4×C19—22no—
107C2×C4×C19—22no—
108C2×C4×C19—42no—
109C2×C4×C19—41no—
110C2×C4×C19—42no—
111C2×C4×C19—41no—
112C2×C4×C19—42no—
113C2×C4×C19—42no—
114C2×C4×C19—42no—
115C2×C4×C19—42no—
116C2×C4×C19—81no—
117C2×C4×C19C4×D412yes—
118C2×C4×C19#12112yes—
119C22⋊D19—82no—
120C22⋊D19—82no—
121C2×Dic19—44no—
122C2×Dic19—42no—
123C2×Dic19—44no—
124C2×Dic19—42no—
125C2×Dic19—41no—
126C2×Dic19—41no—
127C2×Dic19—41no—
128C2×Dic19—42no—
129C2×Dic19—44no—
130D76—82no—
131C8×C19—82no—
132#2618—191no—
133#2313—191no—
134#1519—192no—
135C2×#324D1911yescharacteristic, complemented
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#38611yescharacteristic
146C22×C19#41611yescharacteristic
147C22×C19#41811yescharacteristic
148C22×C19#44912yes—
149C22×C19#48212yes—
150C2×D19—82no—
151C2×D19—82no—
152C2×D19—81no—
153C2×D19—81no—
154C2×D19—81no—
155C4×C19—22no—
156C4×C19—22no—
157C4×C19—42no—
158C4×C19—42no—
159Dic19—82no—
160Dic19—84no—
161Dic19—81no—
162C2×#123—381no—
163C2×#121—191no—
164C22×C4⋊C4C2×D1911yescharacteristic
165C2×C22⋊C8C2×D1912yes—
166#398—192no—
167#396—382no—
168#394—192no—
169#387—384no—
170#386—381no—
171#381—381no—
172#380—191no—
173#380—192no—
174C4×C22⋊C4—381no—
175#327—384no—
176#324—22no—
177C2×C19—21no—
178C2×C19—22no—
179C2×C19—21no—
180C2×C19—22no—
181C2×C19#187511yescharacteristic
182C2×C19#191211yescharacteristic
183C2×C19#191311yescharacteristic
184D19—161no—
185C22×D4—191no—
186C22×D4—381no—
187C23×C4D7611yescharacteristic
188C23×C4D7611yescharacteristic
189C23×C4C22×D1911yescharacteristic
190C22×C8—22no—
191#123—764no—
192#121—382no—
193#121—382no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—191no—
197C2×C4⋊C4—382no—
198C2×C4⋊C4—382no—
199C2×C4⋊C4—381no—
200C2×C4⋊C4C4×D1912yes—
201C2×C4⋊C4C22⋊D1912yes—
202C2×C22⋊C4—381no—
203C2×C22⋊C4—382no—
204C2×C22⋊C4—382no—
205C2×C22⋊C4—381no—
206C2×C22⋊C4—382no—
207C2×C42—382no—
208C22⋊C8—22no—
209C22⋊C8—22no—
210#95—192no—
211#95—194no—
212#95—382no—
213#95—384no—
214#95—382no—
215C19#920611yescharacteristic, complemented, Sylow
216C24—381no—
217C24C2×D7611yescharacteristic
218C2×D4—382no—
219C2×D4—761no—
220C2×D4—761no—
221C2×D4—762no—
222C2×D4—762no—
223C2×D4—1521no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—81no—
231C22×C4—81no—
232C22×C4—384no—
233C22×C4—382no—
234C22×C4—381no—
235C22×C4(C2×D19)⋊C412yes—
236C22×C4(C2×D19)⋊C412yes—
237C22×C4C2×C4×D1911yescharacteristic
238C22×C4D4×D1912yes—
239C22×C4#6454312yes—
240C22×C4C2×C22⋊D1911yescharacteristic
241C2×C8—42no—
242C2×C8—82no—
243C4⋊C4—24no—
244C4⋊C4—24no—
245C4⋊C4—382no—
246C4⋊C4—764no—
247C4⋊C4—1522no—
248C4⋊C4—1521no—
249C22⋊C4—764no—
250C22⋊C4—762no—
251C22⋊C4—762no—
252C22⋊C4—762no—
253C22⋊C4—762no—
254C22⋊C4—1522no—
255C42—1522no—
256C23—41no—
257C23—41no—
258C23—762no—
259C23—762no—
260C23—761no—
261C23—761no—
262C23—761no—
263C23#1059732811yescharacteristic
264C23#1059733211yescharacteristic
265C23#1059735012yes—
266C23#1059735412yes—
267C23C2×(C2×D19)⋊C411yescharacteristic
268D4—1522no—
269D4—1522no—
270D4—1522no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—81no—
284C2×C4—764no—
285C2×C4—762no—
286C2×C4—764no—
287C2×C4—762no—
288C2×C4—761no—
289C2×C4—762no—
290C2×C4—761no—
291C2×C4—761no—
292C2×C4—764no—
293C2×C4(C22⋊D19)⋊C412yes—
294C2×C4#1059738512yes—
295C8—82no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—42no—
303C22—42no—
304C22—1522no—
305C22—1522no—
306C22—1521no—
307C22—1521no—
308C22—1521no—
309C22#1192642111yescharacteristic
310C22#1192654111yescharacteristic
311C22#1192655011yescharacteristic
312C22#1192669112yes—
313C22#1192686912yes—
314C4—22no—
315C4—22no—
316C4—42no—
317C4—42no—
318C4—1522no—
319C4—1524no—
320C4—1521no—
321C2—21no—
322C2—22no—
323C2—21no—
324C2—22no—
325C2—3041no—
326C2#1456395511yescharacteristic
327C2#1456417011yescharacteristic
328C2#1456417511yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#324C2
socleC22×C19#386
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenterC2×#324D19
hypocenterC19#9206
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #14566238C2semidirect
4. #14561503C2semidirect
5. C2×C19×#324C2semidirect
8. #11926474C4semidirect
10. #11926461C4semidirect
135. C2×#324D19semidirect
215. C19#9206semidirect

Maximal subgroups

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

subgroupindex
#145693772
#145662382
#145622042
#145615032
C2×C19×#3242
#920619