Finite Group Databasebeta

← #18078285

Subgroups — #18078285

Order 4864.

756 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C2×#11926390C211yesmaximal, characteristic, complemented
2#14563703C211yesmaximal, characteristic, complemented
3C2×#11926278C212yesmaximal
4#14561513C212yesmaximal, complemented
5C19×#2854C211yesmaximal, characteristic
6C22×C4×Dic19—21no—
7C2×C22⋊(C19⋊C8)C2212yes—
8#11926390—24no—
9C2×C19⋊#95—21no—
10C2×C19⋊#95C2212yes—
11#11926299—22no—
12#11926278—24no—
13C2×C19×#123—21no—
14C2×C19×#121C2211yescharacteristic
15C22×C42×C19C2211yescharacteristic
16C19×#390C412yescomplemented
17C19×#389C412yescomplemented
18C19×#388—22no—
19C19×#386—21no—
20C19×#380C2211yescharacteristic
21C22×D4×C19—21no—
22C22×D4×C19C2×C411yescharacteristic
23C23×C4×C19D411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C23×Dic19—22no—
27C19×#123—44no—
28C19×#121—22no—
29C19×#121—22no—
30C2×C4⋊C4×C19—22no—
31C2×C4⋊C4×C19C2×C411yescharacteristic
32C2×C4⋊C4×C19C2×C412yes—
33C2×C22⋊C4×C19—21no—
34C2×C22⋊C4×C19—22no—
35C2×C22⋊C4×C19—22no—
36C2×C22⋊C4×C19—21no—
37C2×C42×C19—22no—
38C2×C42×C19—22no—
39C2×C42×C19C2×C412yes—
40C2×C42×C19D412yes—
41C2×C4×Dic19—24no—
42C2×C4×Dic19—28no—
43C22×C19⋊C8—22no—
44C19×#95—22no—
45C19×#95—21no—
46C19⋊#95—24no—
47C19⋊#95—22no—
48C19⋊#95D414yes—
49C22⋊(C19⋊C8)—22no—
50C22⋊(C19⋊C8)—22no—
51C24×C19—21no—
52C24×C19C2×D411yescharacteristic
53C2×D4×C19—22no—
54C2×D4×C19—42no—
55C2×D4×C19—41no—
56C2×D4×C19—41no—
57C2×D4×C19—42no—
58C2×D4×C19—42no—
59C22×C4×C19—21no—
60C22×C4×C19—21no—
61C22×C4×C19—24no—
62C22×C4×C19—21no—
63C22×C4×C19—21no—
64C22×C4×C19—22no—
65C22×C4×C19—22no—
66C22×C4×C19—22no—
67C22×C4×C19—21no—
68C22×C4×C19—42no—
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—28no—
76C22×Dic19—24no—
77C22×Dic19—44no—
78C22×Dic19—42no—
79C22×Dic19—42no—
80C4⋊C4×C19—22no—
81C4⋊C4×C19—42no—
82C4⋊C4×C19—44no—
83C22⋊C4×C19—44no—
84C22⋊C4×C19—42no—
85C22⋊C4×C19—44no—
86C22⋊C4×C19—42no—
87C42×C19—24no—
88C42×C19—24no—
89C4×Dic19—216no—
90C2×C19⋊C8—44no—
91C2×C19⋊C8—42no—
92#9149—191nomaximal, Sylow
93C23×C19—22no—
94C23×C19—22no—
95C23×C19—41no—
96C23×C19—42no—
97C23×C19—41no—
98C23×C19—41no—
99C23×C19—42no—
100C23×C19C2×C22⋊C411yescharacteristic
101C23×C19#12011yescharacteristic
102C23×C19#12311yescharacteristic
103C23×C19#13512yes—
104C23×C19AGL(1,ℤ/8)12yes—
105D4×C19—82no—
106D4×C19—82no—
107D4×C19—82no—
108C2×C4×C19—24no—
109C2×C4×C19—24no—
110C2×C4×C19—22no—
111C2×C4×C19—22no—
112C2×C4×C19—22no—
113C2×C4×C19—22no—
114C2×C4×C19—22no—
115C2×C4×C19—22no—
116C2×C4×C19—22no—
117C2×C4×C19—42no—
118C2×C4×C19—42no—
119C2×C4×C19—42no—
120C2×C4×C19—42no—
121C2×C4×C19—41no—
122C2×C4×C19—42no—
123C2×C4×C19—41no—
124C2×C4×C19—42no—
125C2×C4×C19—41no—
126C2×C4×C19—42no—
127C2×C4×C19#10414yes—
128C2×C4×C19C4×D412yes—
129C2×C4×C19#12112yes—
130C2×Dic19—28no—
131C2×Dic19—44no—
132C2×Dic19—48no—
133C2×Dic19—48no—
134C2×Dic19—44no—
135C19⋊C8—82no—
136#2854D1911yescharacteristic
137C2×#376—191no—
138#1817—191no—
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—81no—
148C22×C19—81no—
149C22×C19—81no—
150C22×C19—82no—
151C22×C19—82no—
152C22×C19#38611yescharacteristic
153C22×C19#41012yes—
154C22×C19#41611yescharacteristic
155C22×C19#41811yescharacteristic
156C22×C19C2×#10412yes—
157C22×C19#44912yes—
158C22×C19#48212yes—
159C4×C19—24no—
160C4×C19—22no—
161C4×C19—22no—
162C4×C19—42no—
163C4×C19—81no—
164C4×C19—82no—
165Dic19—48no—
166C2×#123—21no—
167C2×#121C2×D1911yescharacteristic
168C22×C42—381no—
169C22×C42C2×D1911yescharacteristic
170C2×C22⋊C8—192no—
171#390Dic1912yescomplemented
172#389Dic1912yescomplemented
173#388—22no—
174#386—21no—
175#380C2×D1911yescharacteristic
176#376—384no—
177C2×#95—192no—
178C2×#95—381no—
179#336—382no—
180#327—384no—
181C2×C19—22no—
182C2×C19—22no—
183C2×C19—161no—
184C2×C19#150012yes—
185C2×C19#150512yes—
186C2×C19#187511yescharacteristic
187C2×C19#189611yescharacteristic
188C2×C19#189911yescharacteristic
189C22×D4—21no—
190C22×D4C2×Dic1911yescharacteristic
191C23×C4—382no—
192C23×C4C22⋊D1911yescharacteristic
193C23×C4C22⋊D1911yescharacteristic
194C23×C4C22×D1911yescharacteristic
195C22×C8—382no—
196#123—44no—
197#121—22no—
198#121—22no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4C2×Dic1911yescharacteristic
201C2×C4⋊C4C2×Dic1912yes—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—21no—
206C2×C42—22no—
207C2×C42—22no—
208C2×C42—384no—
209C2×C42—388no—
210C2×C42C2×Dic1912yes—
211C2×C42C22⋊D1912yes—
212C22⋊C8—382no—
213C22⋊C8—382no—
214#95—22no—
215#95—21no—
216#95—194no—
217#95—384no—
218#95—382no—
219C19#914911yescharacteristic, complemented, Sylow
220C24—21no—
221C24C2×C22⋊D1911yescharacteristic
222C2×D4—22no—
223C2×D4—42no—
224C2×D4—42no—
225C2×D4—41no—
226C2×D4—41no—
227C2×D4—42no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—24no—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—42no—
238C22×C4—388no—
239C22×C4—384no—
240C22×C4—764no—
241C22×C4—762no—
242C22×C4—762no—
243C22×C4C22⋊Dic1912yes—
244C22×C4C22⋊Dic1912yes—
245C22×C4D4×D1912yes—
246C22×C4#6454312yes—
247C22×C4C22×Dic1911yescharacteristic
248C22×C4C2×C22⋊D1911yescharacteristic
249C2×C8—764no—
250C2×C8—762no—
251C4⋊C4—22no—
252C4⋊C4—42no—
253C4⋊C4—44no—
254C22⋊C4—44no—
255C22⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—44no—
258C42—24no—
259C42—24no—
260C42—3816no—
261C23—22no—
262C23—22no—
263C23—41no—
264C23—41no—
265C23—42no—
266C23—41no—
267C23—42no—
268C23#1059737812yes—
269C23#1059738111yescharacteristic
270C23#1059738311yescharacteristic
271C23#1059739612yes—
272C23C2×C22⋊Dic1911yescharacteristic
273D4—82no—
274D4—82no—
275D4—82no—
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—41no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—388no—
296C2×C4—768no—
297C2×C4—768no—
298C2×C4—764no—
299C2×C4—764no—
300C2×C4#1059729414yes—
301C2×C4D4×Dic1912yes—
302C2×C4#1059738512yes—
303C8—1522no—
304C22—24no—
305C22—24no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—82no—
311C22—82no—
312C22—81no—
313C22—81no—
314C22—81no—
315C22#1192642411yescharacteristic
316C22#1192651812yes—
317C22#1192654011yescharacteristic
318C22#1192654911yescharacteristic
319C22C2×#1059729412yes—
320C22#1192668712yes—
321C22#1192686512yes—
322C4—24no—
323C4—22no—
324C4—22no—
325C4—42no—
326C4—82no—
327C4—81no—
328C4—768no—
329C2—22no—
330C2—22no—
331C2—161no—
332C2#1456212112yes—
333C2#1456214312yes—
334C2#1456395811yescharacteristic
335C2#1456407911yescharacteristic
336C2#1456409411yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic19
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2854C2
socleC23×C19C2×C22⋊C4
prime radicalC2×C19×#121C22
cosocleC23×C4×C19C23
hypercenter#2854D19
hypocenterC19#9149
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2854

Complements

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

NH ≅ G/Ntype
1. C2×#11926390C2semidirect
2. #14563703C2semidirect
4. #14561513C2semidirect
16. C19×#390C4semidirect
17. C19×#389C4semidirect
171. #390Dic19semidirect
172. #389Dic19semidirect
219. C19#9149semidirect

Maximal subgroups

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

subgroupindex
C2×#119263902
#145637032
C2×#119262782
#145615132
C19×#28542
#914919