Finite Group Databasebeta

← #18078322

Subgroups — #18078322

Order 4864.

648 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 127 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
2C2×#11926412C211yesmaximal, characteristic, complemented
3C2×#11926279C212yesmaximal
4#14561515C212yesmaximal, complemented
5C19×#1817C211yesmaximal, characteristic, complemented
6C2×#10597375—21no—
7C2×#10597376C2211yescharacteristic
8#11926446C412yescomplemented
9#11926442C412yescomplemented
10#11926435—22no—
11#11926423—21no—
12#11926412—24no—
13#11926404C2211yescharacteristic
14C2×C19⋊#95—21no—
15C2×C19⋊#95—21no—
16C2×C19⋊#95C2212yes—
17#11926279—24no—
18C22×C42×C19C2211yescharacteristic
19C2×C19×C22⋊C8C2212yes—
20C19×#336—22no—
21C23×C4×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×C4×C19C2311yescharacteristic
24C22×C22⋊D19—21no—
25C23×Dic19—22no—
26C22×D76C2×C411yescharacteristic
27C22×C8×C19—22no—
28C2×C42×C19—22no—
29C2×C42×C19—22no—
30C2×C42×C19C2×C412yes—
31C2×C42×C19D412yes—
32C2×C22⋊Dic19—21no—
33#10597376—22no—
34#10597376—22no—
35#10597375—44no—
36C2×(C2×D19)⋊C4—22no—
37C2×(C2×D19)⋊C4—22no—
38C2×(C2×D19)⋊C4—21no—
39C2×C4⋊Dic19C2×C411yescharacteristic
40C2×C4⋊Dic19C2×C412yes—
41C2×Dic19⋊C4—22no—
42C19×C22⋊C8—22no—
43C19×C22⋊C8—22no—
44C19⋊#95—24no—
45C19⋊#95—24no—
46C19⋊#95—22no—
47C19⋊#95—22no—
48C19⋊#95—21no—
49C19⋊#95D414yes—
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—42no—
59C22×C4×C19—42no—
60C22×C4×C19C22⋊C412yes—
61C22×C4×C19C22⋊C412yes—
62C22×C4×C19C22×C411yescharacteristic
63C22×C4×C19C2×D412yes—
64C22×C4×C19C2×D411yescharacteristic
65C22×C4×C19#4112yes—
66C2×C22⋊D19—41no—
67C2×C22⋊D19—41no—
68C2×C22⋊D19—42no—
69C2×C22⋊D19—42no—
70C22×Dic19—22no—
71C22×Dic19—21no—
72C22×Dic19—24no—
73C22×Dic19—44no—
74C22×Dic19—44no—
75C22×Dic19—42no—
76C22×Dic19—42no—
77C2×D76—22no—
78C2×D76—42no—
79C2×C8×C19—44no—
80C2×C8×C19—42no—
81C42×C19—24no—
82C42×C19—24no—
83C22⋊Dic19—42no—
84(C2×D19)⋊C4—44no—
85(C2×D19)⋊C4—44no—
86(C2×D19)⋊C4—42no—
87C4⋊Dic19—22no—
88C4⋊Dic19—42no—
89Dic19⋊C4—44no—
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×C19C4×D412yes—
118C2×C4×C19#12112yes—
119C22⋊D19—82no—
120C22⋊D19—82no—
121C2×Dic19—44no—
122C2×Dic19—44no—
123C2×Dic19—41no—
124C2×Dic19—42no—
125C2×Dic19—41no—
126C2×Dic19—41no—
127C2×Dic19—42no—
128C2×Dic19—42no—
129C2×Dic19—44no—
130C2×Dic19—84no—
131C2×Dic19—84no—
132D76—82no—
133C8×C19—82no—
134#2854—191no—
135C2×#383—191no—
136#1817D1911yescharacteristic, complemented
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—
161Dic19—84no—
162Dic19—81no—
163Dic19—82no—
164C2×#123—381no—
165C2×#121—191no—
166C22×C42C2×D1911yescharacteristic
167C2×C22⋊C8C2×D1912yes—
168#390—192no—
169#389—192no—
170#388—382no—
171#386—381no—
172#383—384no—
173#380—191no—
174C2×#95—192no—
175C2×#95—381no—
176C2×#95—381no—
177#336—22no—
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—382no—
190C23×C4D7611yescharacteristic
191C23×C4D7611yescharacteristic
192C23×C4C22×D1911yescharacteristic
193C22×C8—22no—
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×C42C22⋊D1912yes—
208C22⋊C8—22no—
209C22⋊C8—22no—
210#95—194no—
211#95—384no—
212#95—384no—
213#95—382no—
214#95—382no—
215#95—381no—
216C19#915711yescharacteristic, complemented, Sylow
217C24—381no—
218C24C2×D7611yescharacteristic
219C2×D4—382no—
220C2×D4—762no—
221C2×D4—761no—
222C2×D4—761no—
223C2×D4—762no—
224C2×D4—762no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—384no—
234C22×C4—382no—
235C22×C4—381no—
236C22×C4—764no—
237C22×C4—764no—
238C22×C4—762no—
239C22×C4—762no—
240C22×C4(C2×D19)⋊C412yes—
241C22×C4(C2×D19)⋊C412yes—
242C22×C4C2×C4×D1911yescharacteristic
243C22×C4D4×D1912yes—
244C22×C4#6454312yes—
245C22×C4C2×C22⋊D1911yescharacteristic
246C2×C8—44no—
247C2×C8—42no—
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—
264C23#1059732811yescharacteristic
265C23#1059733211yescharacteristic
266C23#1059735012yes—
267C23#1059735412yes—
268C23C2×(C2×D19)⋊C411yescharacteristic
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—764no—
287C2×C4—764no—
288C2×C4—761no—
289C2×C4—762no—
290C2×C4—761no—
291C2×C4—762no—
292C2×C4—761no—
293C2×C4—764no—
294C2×C4—762no—
295C2×C4—1524no—
296C2×C4—1524no—
297C2×C4(C22⋊D19)⋊C412yes—
298C2×C4#1059738512yes—
299C8—82no—
300C22—24no—
301C22—24no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—1521no—
307C22—1522no—
308C22—1522no—
309C22—1521no—
310C22—1521no—
311C22#1192642111yescharacteristic
312C22#1192651712yes—
313C22#1192654111yescharacteristic
314C22#1192655011yescharacteristic
315C22#1192656012yes—
316C22#1192669112yes—
317C22#1192686912yes—
318C4—22no—
319C4—22no—
320C4—42no—
321C4—42no—
322C4—1524no—
323C4—1521no—
324C4—1522no—
325C2—22no—
326C2—22no—
327C2—3041no—
328C2#1456218312yes—
329C2#1456221312yes—
330C2#1456395511yescharacteristic
331C2#1456408111yescharacteristic
332C2#1456409111yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1817C2
socleC23×C19C2×C22⋊C4
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1817D19
hypocenterC19#9157
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. C2×#11926412C2semidirect
4. #14561515C2semidirect
5. C19×#1817C2semidirect
8. #11926446C4semidirect
9. #11926442C4semidirect
136. #1817D19semidirect
216. C19#9157semidirect

Maximal subgroups

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

subgroupindex
#145719662
C2×#119264122
C2×#119262792
#145615152
C19×#18172
#915719