Finite Group Databasebeta

← #18070764

Subgroups — #18070764

Order 4864.

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

normal subgroups only

This group has 594 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
1C2×#11926442C211yesmaximal, characteristic
2#14563397C211yesmaximal, characteristic
3#14561457C214yesmaximal, complemented
4C19×#1749C211yesmaximal, characteristic
5C22×C4⋊Dic19C411yescharacteristic
6C22×C4⋊Dic19C411yescharacteristic
7C22×Dic19⋊C4—21no—
8C2×C22⋊(C19⋊C8)—21no—
9C2×#10597260—21no—
10#11926442—21no—
11#11926442—21no—
12#11926442C412yes—
13#11926442C2212yes—
14C2×C19⋊#95—21no—
15#11926299C2212yes—
16C22×C42×C19C2211yescharacteristic
17C2×C19×C22⋊C8—21no—
18C2×C19×#97—21no—
19C19×#336C2212yes—
20C23×C4×C19C2×C411yescharacteristic
21C23×C4×C19D411yescharacteristic
22C23×C4×C19D411yescharacteristic
23C23×Dic19—21no—
24C23×Dic19—21no—
25C22×C8×C19—22no—
26C2×C42×C19—42no—
27C2×C42×C19C2×C411yescharacteristic
28C2×C42×C19D411yescharacteristic
29C2×C42×C19D411yescharacteristic
30C2×C42×C19C2311yescharacteristic
31C2×C4⋊Dic19—21no—
32C2×C4⋊Dic19—24no—
33C2×C4⋊Dic19—21no—
34C2×C4⋊Dic19—42no—
35C2×C4⋊Dic19C2×C412yes—
36C2×C4⋊Dic19C2×C412yes—
37C2×Dic19⋊C4—22no—
38C2×Dic19⋊C4—22no—
39C2×Dic19⋊C4—44no—
40C22×C19⋊C8—22no—
41C19×C22⋊C8—24no—
42C19×#97—42no—
43C19⋊#95—22no—
44C19⋊#95—22no—
45C22⋊(C19⋊C8)—24no—
46#10597260—42no—
47C24×C19C22⋊C411yescharacteristic
48C22×C4×C19—22no—
49C22×C4×C19—22no—
50C22×C4×C19—22no—
51C22×C4×C19—22no—
52C22×C4×C19—22no—
53C22×C4×C19—22no—
54C22×C4×C19—22no—
55C22×C4×C19—41no—
56C22×C4×C19—41no—
57C22×C4×C19C22⋊C411yescharacteristic
58C22×C4×C19C22⋊C411yescharacteristic
59C22×C4×C19C22⋊C411yescharacteristic
60C22×C4×C19C22×C411yescharacteristic
61C22×C4×C19C2×D411yescharacteristic
62C22×C4×C19C2×D411yescharacteristic
63C22×Dic19—24no—
64C22×Dic19—22no—
65C22×Dic19—22no—
66C22×Dic19—42no—
67C22×Dic19—42no—
68C22×Dic19—42no—
69C22×Dic19—42no—
70C22×Dic19—42no—
71C2×C8×C19—24no—
72C2×C8×C19—42no—
73C2×C8×C19—42no—
74C42×C19—22no—
75C42×C19—22no—
76C42×C19—41no—
77C42×C19—41no—
78C4⋊Dic19—24no—
79C4⋊Dic19—22no—
80C4⋊Dic19—42no—
81C4⋊Dic19—42no—
82C4⋊Dic19M1614yes—
83Dic19⋊C4—44no—
84Dic19⋊C4—44no—
85C2×C19⋊C8—24no—
86C2×C19⋊C8—42no—
87C2×C19⋊C8—42no—
88#7627—191nomaximal, Sylow
89C23×C19—21no—
90C23×C19—21no—
91C23×C19—21no—
92C23×C19—21no—
93C23×C19#10112yes—
94C23×C19#10412yes—
95C23×C19#10412yes—
96C23×C19C2×C22⋊C411yescharacteristic
97C2×C4×C19—28no—
98C2×C4×C19—21no—
99C2×C4×C19—21no—
100C2×C4×C19—21no—
101C2×C4×C19—21no—
102C2×C4×C19—21no—
103C2×C4×C19—21no—
104C2×C4×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—44no—
113C2×C4×C19—44no—
114C2×C4×C19#9912yes—
115C2×C4×C19C2×M1612yes—
116C2×C4×C19AGL(1,ℤ/8)12yes—
117C2×C4×C19#13712yes—
118C2×Dic19—24no—
119C2×Dic19—48no—
120C2×Dic19—42no—
121C2×Dic19—42no—
122C2×Dic19—42no—
123C2×Dic19—42no—
124C2×Dic19—42no—
125C2×Dic19—84no—
126C8×C19—44no—
127C19⋊C8—44no—
128C2×#389—191no—
129#1749—191no—
130#1749D1911yescharacteristic
131#1271—194no—
132C22×C19—22no—
133C22×C19—22no—
134C22×C19—22no—
135C22×C19—22no—
136C22×C19—22no—
137C22×C19—22no—
138C22×C19#33014yes—
139C22×C19#40711yescharacteristic
140C22×C19C2×#9911yescharacteristic
141C22×C19C2×#10111yescharacteristic
142C22×C19#41811yescharacteristic
143C22×C19#41911yescharacteristic
144C22×C19C2×#10411yescharacteristic
145C22×C19C2×#10411yescharacteristic
146C4×C19—22no—
147C4×C19—22no—
148C4×C19—22no—
149C4×C19—22no—
150C4×C19—41no—
151C4×C19—41no—
152Dic19—44no—
153Dic19—82no—
154C22×C4⋊C4—191no—
155C22×C4⋊C4—191no—
156C22×C4⋊C4—381no—
157C22×C42C2×D1911yescharacteristic
158C2×C22⋊C8—21no—
159C2×C22⋊C8—381no—
160C2×#97—21no—
161C2×#97—381no—
162#389—192no—
163#389—192no—
164#389—381no—
165#389—381no—
166C2×#95—381no—
167#336—192no—
168#336C2×D1912yes—
169C2×C19—24no—
170C2×C19#146311yescharacteristic
171C2×C19#149011yescharacteristic
172C2×C19#149111yescharacteristic
173C2×C19#150711yescharacteristic
174C2×C19#150811yescharacteristic
175C2×C19C2×#33011yescharacteristic
176C2×C19#155611yescharacteristic
177C23×C4—381no—
178C23×C4—381no—
179C23×C4C4×D1911yescharacteristic
180C23×C4D7611yescharacteristic
181C23×C4C22⋊D1911yescharacteristic
182C22×C8—22no—
183C22×C8—382no—
184C2×C4⋊C4—192no—
185C2×C4⋊C4—192no—
186C2×C4⋊C4—384no—
187C2×C4⋊C4—381no—
188C2×C4⋊C4—381no—
189C2×C4⋊C4—382no—
190C2×C4⋊C4—382no—
191C2×C4⋊C4—764no—
192C2×C4⋊C4—762no—
193C2×C42—42no—
194C2×C42C4×D1911yescharacteristic
195C2×C42D7611yescharacteristic
196C2×C42C22⋊D1911yescharacteristic
197C2×C42C22×D1911yescharacteristic
198C22⋊C8—24no—
199C22⋊C8—384no—
200#97—42no—
201#97—762no—
202#95—382no—
203#95—382no—
204C19#762711yescharacteristic, complemented, Sylow
205C24(C2×D19)⋊C411yescharacteristic
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—384no—
216C22×C4—382no—
217C22×C4—382no—
218C22×C4—762no—
219C22×C4—762no—
220C22×C4—762no—
221C22×C4—762no—
222C22×C4—762no—
223C22×C4(C2×D19)⋊C411yescharacteristic
224C22×C4(C2×D19)⋊C411yescharacteristic
225C22×C4(C2×D19)⋊C411yescharacteristic
226C22×C4C2×C4×D1911yescharacteristic
227C22×C4C2×D7611yescharacteristic
228C22×C4C2×C22⋊D1911yescharacteristic
229C2×C8—24no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—384no—
233C2×C8—762no—
234C2×C8—762no—
235C4⋊C4—194no—
236C4⋊C4—384no—
237C4⋊C4—382no—
238C4⋊C4—762no—
239C4⋊C4—764no—
240C4⋊C4—762no—
241C4⋊C4—764no—
242C42—22no—
243C42—22no—
244C42—41no—
245C42—41no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23#1059726212yes—
251C23#1059728112yes—
252C23#1059728212yes—
253C23C2×(C2×D19)⋊C411yescharacteristic
254C2×C4—28no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—44no—
270C2×C4—44no—
271C2×C4—384no—
272C2×C4—768no—
273C2×C4—762no—
274C2×C4—762no—
275C2×C4—762no—
276C2×C4—762no—
277C2×C4—762no—
278C2×C4—1524no—
279C2×C4#1059726312yes—
280C2×C4M16×D1912yes—
281C2×C4#1059735412yes—
282C2×C4#1059739712yes—
283C8—44no—
284C8—764no—
285C22—22no—
286C22—22no—
287C22—22no—
288C22—22no—
289C22—22no—
290C22—22no—
291C22#1192628514yes—
292C22#1192650711yescharacteristic
293C22C2×#1059726311yescharacteristic
294C22C2×#1059728111yescharacteristic
295C22#1192655011yescharacteristic
296C22#1192655211yescharacteristic
297C22C2×#1059728211yescharacteristic
298C22C2×#1059726211yescharacteristic
299C4—22no—
300C4—22no—
301C4—22no—
302C4—22no—
303C4—41no—
304C4—41no—
305C4—764no—
306C4—1522no—
307C2—24no—
308C2#1456196411yescharacteristic
309C2#1456207911yescharacteristic
310C2#1456208111yescharacteristic
311C2#1456215211yescharacteristic
312C2#1456215411yescharacteristic
313C2C2×#1192628511yescharacteristic
314C2#1456235111yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1749C2
socleC23×C19C2×C22⋊C4
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#1749D19
hypocenterC19#7627
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
3. #14561457C2semidirect
204. C19#7627semidirect

Maximal subgroups

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

subgroupindex
C2×#119264422
#145633972
#145614572
C19×#17492
#762719