Finite Group Databasebeta

← #18078324

Subgroups — #18078324

Order 4864.

648 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 131 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#14571966C211yesmaximal, characteristic
2#14563703C211yesmaximal, characteristic, complemented
3C2×#11926277C212yesmaximal
4#14561514C212yesmaximal, complemented
5C2×C19×#383C211yesmaximal, characteristic, complemented
6C2×#10597375—21no—
7C2×#10597376C2211yescharacteristic
8C2×C22⋊(C19⋊C8)C2212yes—
9#11926446C412yescomplemented
10#11926442C412yescomplemented
11#11926435—22no—
12#11926423—21no—
13#11926404C2211yescharacteristic
14#11926299—22no—
15#11926277—24no—
16C22×C42×C19C2211yescharacteristic
17C19×#383—24no—
18C2×C19×#95—21no—
19C2×C19×#95—21no—
20C2×C19×#95C2212yes—
21C23×C4×C19—22no—
22C23×C4×C19D411yescharacteristic
23C23×C4×C19D411yescharacteristic
24C23×C4×C19C2311yescharacteristic
25C22×C22⋊D19—21no—
26C22×D76C2×C411yescharacteristic
27C2×C42×C19—22no—
28C2×C42×C19—22no—
29C2×C42×C19C2×C412yes—
30C2×C42×C19D412yes—
31C2×C22⋊Dic19—21no—
32#10597376—22no—
33#10597376—22no—
34#10597375—44no—
35C2×(C2×D19)⋊C4—22no—
36C2×(C2×D19)⋊C4—22no—
37C2×(C2×D19)⋊C4—21no—
38C2×C4⋊Dic19C2×C411yescharacteristic
39C2×C4⋊Dic19C2×C412yes—
40C2×Dic19⋊C4—22no—
41C22×C19⋊C8—22no—
42C19×#95—24no—
43C19×#95—24no—
44C19×#95—22no—
45C19×#95D414yes—
46C19⋊#95—22no—
47C19⋊#95—21no—
48C22⋊(C19⋊C8)—22no—
49C22⋊(C19⋊C8)—22no—
50C24×C19C2×D411yescharacteristic
51C23×D19—21no—
52C22×C4×C19—21no—
53C22×C4×C19—21no—
54C22×C4×C19—21no—
55C22×C4×C19—21no—
56C22×C4×C19—22no—
57C22×C4×C19—22no—
58C22×C4×C19—24no—
59C22×C4×C19—42no—
60C22×C4×C19—42no—
61C22×C4×C19—44no—
62C22×C4×C19—44no—
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—41no—
72C2×C22⋊D19—41no—
73C2×C22⋊D19—42no—
74C2×C22⋊D19—42no—
75C22×Dic19—22no—
76C22×Dic19—21no—
77C2×D76—22no—
78C2×D76—42no—
79C42×C19—24no—
80C42×C19—24no—
81C22⋊Dic19—42no—
82(C2×D19)⋊C4—44no—
83(C2×D19)⋊C4—44no—
84(C2×D19)⋊C4—42no—
85C4⋊Dic19—22no—
86C4⋊Dic19—42no—
87Dic19⋊C4—44no—
88C2×C19⋊C8—44no—
89C2×C19⋊C8—42no—
90#9157—191nomaximal, Sylow
91C23×C19—22no—
92C23×C19—22no—
93C23×C19C2×C22⋊C411yescharacteristic
94C23×C19#12011yescharacteristic
95C23×C19#12311yescharacteristic
96C23×C19#13512yes—
97C23×C19AGL(1,ℤ/8)12yes—
98C22×D19—41no—
99C22×D19—42no—
100C22×D19—41no—
101C22×D19—41no—
102C22×D19—42no—
103C2×C4×C19—22no—
104C2×C4×C19—22no—
105C2×C4×C19—22no—
106C2×C4×C19—22no—
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—42no—
114C2×C4×C19—42no—
115C2×C4×C19—42no—
116C2×C4×C19—42no—
117C2×C4×C19—44no—
118C2×C4×C19—44no—
119C2×C4×C19—44no—
120C2×C4×C19—84no—
121C2×C4×C19—84no—
122C2×C4×C19C4×D412yes—
123C2×C4×C19#12112yes—
124C22⋊D19—82no—
125C22⋊D19—82no—
126C2×Dic19—41no—
127C2×Dic19—42no—
128C2×Dic19—41no—
129C2×Dic19—41no—
130C2×Dic19—42no—
131C2×Dic19—42no—
132D76—82no—
133C19⋊C8—82no—
134#2854—191no—
135C2×#383D1911yescharacteristic, complemented
136#1817—191no—
137C2×#327—192no—
138#1294—192no—
139C22×C19—21no—
140C22×C19—21no—
141C22×C19—21no—
142C22×C19—21no—
143C22×C19—24no—
144C22×C19—24no—
145C22×C19#38611yescharacteristic
146C22×C19#41012yes—
147C22×C19#41611yescharacteristic
148C22×C19#41811yescharacteristic
149C22×C19#42112yes—
150C22×C19#44912yes—
151C22×C19#48212yes—
152C2×D19—81no—
153C2×D19—81no—
154C2×D19—81no—
155C2×D19—82no—
156C2×D19—82no—
157C4×C19—22no—
158C4×C19—22no—
159C4×C19—42no—
160C4×C19—42no—
161C4×C19—84no—
162Dic19—81no—
163Dic19—82no—
164C2×#123—381no—
165C2×#121—191no—
166C22×C42C2×D1911yescharacteristic
167C2×C22⋊C8—192no—
168#390—192no—
169#389—192no—
170#388—382no—
171#386—381no—
172#383—24no—
173#380—191no—
174C2×#95—21no—
175C2×#95—21no—
176C2×#95C2×D1912yes—
177#336—382no—
178#327—384no—
179C2×C19—22no—
180C2×C19—22no—
181C2×C19#151412yes—
182C2×C19#152112yes—
183C2×C19#187511yescharacteristic
184C2×C19#189711yescharacteristic
185C2×C19#189911yescharacteristic
186D19—161no—
187C22×D4—191no—
188C22×D4—381no—
189C23×C4—22no—
190C23×C4C22⋊D1911yescharacteristic
191C23×C4C22⋊D1911yescharacteristic
192C23×C4C22×D1911yescharacteristic
193C22×C8—382no—
194#123—764no—
195#121—382no—
196#121—382no—
197C2×C4⋊C4—191no—
198C2×C4⋊C4—192no—
199C2×C4⋊C4—382no—
200C2×C22⋊C4—381no—
201C2×C22⋊C4—382no—
202C2×C22⋊C4—382no—
203C2×C22⋊C4—381no—
204C2×C42—22no—
205C2×C42—22no—
206C2×C42C4×D1912yes—
207C2×C42D7612yes—
208C22⋊C8—382no—
209C22⋊C8—382no—
210#95—24no—
211#95—24no—
212#95—22no—
213#95—382no—
214#95—381no—
215#95C22⋊D1914yes—
216C19#915711yescharacteristic, complemented, Sylow
217C24—381no—
218C24C2×C22⋊D1911yescharacteristic
219C2×D4—382no—
220C2×D4—762no—
221C2×D4—762no—
222C2×D4—762no—
223C2×D4—761no—
224C2×D4—761no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—24no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—44no—
235C22×C4—44no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—382no—
239C22×C4—381no—
240C22×C4(C2×D19)⋊C412yes—
241C22×C4(C2×D19)⋊C412yes—
242C22×C4C2×C4×D1911yescharacteristic
243C22×C4C2×D7611yescharacteristic
244C22×C4#6454112yes—
245C22×C4C2×C22⋊D1912yes—
246C2×C8—764no—
247C2×C8—762no—
248C4⋊C4—382no—
249C4⋊C4—762no—
250C4⋊C4—764no—
251C22⋊C4—764no—
252C22⋊C4—764no—
253C22⋊C4—762no—
254C22⋊C4—762no—
255C42—24no—
256C42—24no—
257C23—22no—
258C23—22no—
259C23—761no—
260C23—761no—
261C23—762no—
262C23—761no—
263C23—762no—
264C23C2×(C2×D19)⋊C411yescharacteristic
265C23#1059737511yescharacteristic
266C23#1059739512yes—
267C23#1059739612yes—
268C23#1059739911yescharacteristic
269D4—1522no—
270D4—1522no—
271D4—1522no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—44no—
289C2×C4—84no—
290C2×C4—84no—
291C2×C4—761no—
292C2×C4—762no—
293C2×C4—761no—
294C2×C4—762no—
295C2×C4—761no—
296C2×C4—762no—
297C2×C4C4×C22⋊D1912yes—
298C2×C4#1059737612yes—
299C8—1522no—
300C22—24no—
301C22—24no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—1521no—
307C22—1522no—
308C22—1522no—
309C22—1521no—
310C22—1521no—
311C22#1192642311yescharacteristic
312C22#1192651712yes—
313C22#1192653811yescharacteristic
314C22#1192654811yescharacteristic
315C22#1192656212yes—
316C22#1192668912yes—
317C22#1192686812yes—
318C4—22no—
319C4—22no—
320C4—42no—
321C4—42no—
322C4—84no—
323C4—1521no—
324C4—1522no—
325C2—22no—
326C2—22no—
327C2—3041no—
328C2#1456218112yes—
329C2#1456221012yes—
330C2#1456395711yescharacteristic
331C2#1456408311yescharacteristic
332C2#1456409311yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#383C2
socleC23×C19C2×C22⋊C4
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenterC2×#383D19
hypocenterC19#9157
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
2. #14563703C2semidirect
4. #14561514C2semidirect
5. C2×C19×#383C2semidirect
9. #11926446C4semidirect
10. #11926442C4semidirect
135. C2×#383D19semidirect
216. C19#9157semidirect

Maximal subgroups

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

subgroupindex
#145719662
#145637032
C2×#119262772
#145615142
C2×C19×#3832
#915719