Finite Group Databasebeta

← #18078282

Subgroups — #18078282

Order 4864.

756 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 135 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×#11926390C211yesmaximal, characteristic, complemented
3C2×#11926279C212yesmaximal
4#14561515C212yesmaximal, complemented
5C19×#1817C211yesmaximal, characteristic, complemented
6C2×#10597375—21no—
7C2×#10597376C2211yescharacteristic
8C22×C4×Dic19—21no—
9#11926446C412yescomplemented
10#11926442C412yescomplemented
11#11926435—22no—
12#11926423—21no—
13#11926404C2211yescharacteristic
14#11926390—24no—
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—
42C2×C4×Dic19—24no—
43C2×C4×Dic19—28no—
44C19×C22⋊C8—22no—
45C19×C22⋊C8—22no—
46C19⋊#95—24no—
47C19⋊#95—22no—
48C19⋊#95—22no—
49C19⋊#95—21no—
50C19⋊#95D414yes—
51C24×C19C2×D411yescharacteristic
52C23×D19—21no—
53C22×C4×C19—21no—
54C22×C4×C19—21no—
55C22×C4×C19—24no—
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—22no—
59C22×C4×C19—22no—
60C22×C4×C19—42no—
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—28no—
72C22×Dic19—24no—
73C22×Dic19—22no—
74C22×Dic19—21no—
75C22×Dic19—44no—
76C22×Dic19—42no—
77C22×Dic19—42no—
78C2×D76—22no—
79C2×D76—42no—
80C2×C8×C19—44no—
81C2×C8×C19—42no—
82C42×C19—24no—
83C42×C19—24no—
84C22⋊Dic19—42no—
85(C2×D19)⋊C4—44no—
86(C2×D19)⋊C4—44no—
87(C2×D19)⋊C4—42no—
88C4⋊Dic19—22no—
89C4⋊Dic19—42no—
90Dic19⋊C4—44no—
91C4×Dic19—216no—
92#9149—191nomaximal, Sylow
93C23×C19—22no—
94C23×C19—22no—
95C23×C19C2×C22⋊C411yescharacteristic
96C23×C19#12011yescharacteristic
97C23×C19#12311yescharacteristic
98C23×C19#13512yes—
99C23×C19AGL(1,ℤ/8)12yes—
100C22×D19—41no—
101C22×D19—42no—
102C22×D19—41no—
103C22×D19—41no—
104C22×D19—42no—
105C2×C4×C19—24no—
106C2×C4×C19—24no—
107C2×C4×C19—22no—
108C2×C4×C19—22no—
109C2×C4×C19—22no—
110C2×C4×C19—22no—
111C2×C4×C19—22no—
112C2×C4×C19—22no—
113C2×C4×C19—22no—
114C2×C4×C19—42no—
115C2×C4×C19—42no—
116C2×C4×C19—42no—
117C2×C4×C19—42no—
118C2×C4×C19#10414yes—
119C2×C4×C19C4×D412yes—
120C2×C4×C19#12112yes—
121C22⋊D19—82no—
122C22⋊D19—82no—
123C2×Dic19—28no—
124C2×Dic19—44no—
125C2×Dic19—48no—
126C2×Dic19—48no—
127C2×Dic19—44no—
128C2×Dic19—41no—
129C2×Dic19—42no—
130C2×Dic19—41no—
131C2×Dic19—41no—
132C2×Dic19—42no—
133C2×Dic19—42no—
134D76—82no—
135C8×C19—82no—
136#2854—191no—
137C2×#376—191no—
138#1817D1911yescharacteristic, complemented
139C2×#327—192no—
140#1294—192no—
141C22×C19—21no—
142C22×C19—21no—
143C22×C19—21no—
144C22×C19—21no—
145C22×C19—24no—
146C22×C19—24no—
147C22×C19#38611yescharacteristic
148C22×C19#41012yes—
149C22×C19#41611yescharacteristic
150C22×C19#41811yescharacteristic
151C22×C19C2×#10412yes—
152C22×C19#44912yes—
153C22×C19#48212yes—
154C2×D19—81no—
155C2×D19—81no—
156C2×D19—81no—
157C2×D19—82no—
158C2×D19—82no—
159C4×C19—24no—
160C4×C19—22no—
161C4×C19—22no—
162C4×C19—42no—
163Dic19—48no—
164Dic19—81no—
165Dic19—82no—
166C2×#123—381no—
167C2×#121—191no—
168C22×C42—381no—
169C22×C42C2×D1911yescharacteristic
170C2×C22⋊C8C2×D1912yes—
171#390—192no—
172#389—192no—
173#388—382no—
174#386—381no—
175#380—191no—
176#376—384no—
177C2×#95—192no—
178C2×#95—381no—
179#336—22no—
180#327—384no—
181C2×C19—22no—
182C2×C19—22no—
183C2×C19#150012yes—
184C2×C19#150512yes—
185C2×C19#187511yescharacteristic
186C2×C19#189611yescharacteristic
187C2×C19#189911yescharacteristic
188D19—161no—
189C22×D4—191no—
190C22×D4—381no—
191C23×C4—382no—
192C23×C4D7611yescharacteristic
193C23×C4D7611yescharacteristic
194C23×C4C22×D1911yescharacteristic
195C22×C8—22no—
196#123—764no—
197#121—382no—
198#121—382no—
199C2×C4⋊C4—191no—
200C2×C4⋊C4—192no—
201C2×C4⋊C4—382no—
202C2×C22⋊C4—381no—
203C2×C22⋊C4—382no—
204C2×C22⋊C4—382no—
205C2×C22⋊C4—381no—
206C2×C42—22no—
207C2×C42—22no—
208C2×C42—384no—
209C2×C42—388no—
210C2×C42C4×D1912yes—
211C2×C42C22⋊D1912yes—
212C22⋊C8—22no—
213C22⋊C8—22no—
214#95—194no—
215#95—384no—
216#95—382no—
217#95—382no—
218#95—381no—
219C19#914911yescharacteristic, complemented, Sylow
220C24—381no—
221C24C2×D7611yescharacteristic
222C2×D4—382no—
223C2×D4—762no—
224C2×D4—761no—
225C2×D4—761no—
226C2×D4—762no—
227C2×D4—762no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—24no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—42no—
236C22×C4—388no—
237C22×C4—384no—
238C22×C4—382no—
239C22×C4—381no—
240C22×C4—764no—
241C22×C4—762no—
242C22×C4—762no—
243C22×C4(C2×D19)⋊C412yes—
244C22×C4(C2×D19)⋊C412yes—
245C22×C4C2×C4×D1911yescharacteristic
246C22×C4D4×D1912yes—
247C22×C4#6454312yes—
248C22×C4C2×C22⋊D1911yescharacteristic
249C2×C8—44no—
250C2×C8—42no—
251C4⋊C4—382no—
252C4⋊C4—762no—
253C4⋊C4—764no—
254C22⋊C4—764no—
255C22⋊C4—762no—
256C22⋊C4—762no—
257C22⋊C4—764no—
258C42—24no—
259C42—24no—
260C42—3816no—
261C23—22no—
262C23—22no—
263C23—761no—
264C23—761no—
265C23—762no—
266C23—761no—
267C23—762no—
268C23#1059732811yescharacteristic
269C23#1059733211yescharacteristic
270C23#1059735012yes—
271C23#1059735412yes—
272C23C2×(C2×D19)⋊C411yescharacteristic
273D4—1522no—
274D4—1522no—
275D4—1522no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—388no—
290C2×C4—768no—
291C2×C4—768no—
292C2×C4—764no—
293C2×C4—764no—
294C2×C4—761no—
295C2×C4—762no—
296C2×C4—761no—
297C2×C4—762no—
298C2×C4—761no—
299C2×C4—762no—
300C2×C4#1059728214yes—
301C2×C4(C22⋊D19)⋊C412yes—
302C2×C4#1059738512yes—
303C8—82no—
304C22—24no—
305C22—24no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—1522no—
311C22—1522no—
312C22—1521no—
313C22—1521no—
314C22—1521no—
315C22#1192642111yescharacteristic
316C22#1192651712yes—
317C22#1192654111yescharacteristic
318C22#1192655011yescharacteristic
319C22C2×#1059728212yes—
320C22#1192669112yes—
321C22#1192686912yes—
322C4—24no—
323C4—22no—
324C4—22no—
325C4—42no—
326C4—768no—
327C4—1522no—
328C4—1521no—
329C2—22no—
330C2—22no—
331C2—3041no—
332C2#1456212212yes—
333C2#1456214412yes—
334C2#1456395511yescharacteristic
335C2#1456407611yescharacteristic
336C2#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#9149
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×#11926390C2semidirect
4. #14561515C2semidirect
5. C19×#1817C2semidirect
9. #11926446C4semidirect
10. #11926442C4semidirect
138. #1817D19semidirect
219. C19#9149semidirect

Maximal subgroups

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

subgroupindex
#145719662
C2×#119263902
C2×#119262792
#145615152
C19×#18172
#914919