Finite Group Databasebeta

← #18077603

Subgroups — #18077603

Order 4864.

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

normal subgroups only

This group has 696 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
1C2×#11926469C211yesmaximal, characteristic
2#14563719C212yesmaximal, complemented
3C2×#11926268C211yesmaximal, characteristic
4#14561513C212yesmaximal, complemented
5C19×#2312C211yesmaximal, characteristic
6C22×C4⋊Dic19C2211yescharacteristic
7C22×C22⋊Dic19—21no—
8C2×C22⋊(C19⋊C8)C2212yes—
9#11926469—22no—
10#11926469C414yescomplemented
11C2×C19⋊#95—21no—
12C2×C19⋊#95C2211yescharacteristic
13#11926306—24no—
14#11926268—22no—
15C22×C22⋊C4×C19C2211yescharacteristic
16C19×#388—24no—
17C19×#380C2212yes—
18C19×#379—21no—
19C4×C22⋊C4×C19—21no—
20C25×C19D411yescharacteristic
21C23×C4×C19D411yescharacteristic
22C23×C4×C19C2311yescharacteristic
23C23×Dic19—21no—
24C23×Dic19—21no—
25C2×C4⋊C4×C19D414yes—
26C2×C22⋊C4×C19—22no—
27C2×C22⋊C4×C19—22no—
28C2×C22⋊C4×C19—22no—
29C2×C22⋊C4×C19—22no—
30C2×C22⋊C4×C19—22no—
31C2×C22⋊C4×C19C2×C412yes—
32C2×C22⋊C4×C19D412yes—
33C2×C42×C19—22no—
34C2×C22⋊Dic19—24no—
35C2×C22⋊Dic19—44no—
36C2×C4⋊Dic19—22no—
37C2×C4⋊Dic19—22no—
38C2×C4⋊Dic19—21no—
39C2×C4⋊Dic19C2×C412yes—
40C22×C19⋊C8—22no—
41C19×#95—22no—
42C19×#95—22no—
43C19⋊#95—24no—
44C19⋊#95—21no—
45C19⋊#95C2×C412yes—
46C22⋊(C19⋊C8)—22no—
47C22⋊(C19⋊C8)—22no—
48C24×C19—21no—
49C24×C19—22no—
50C24×C19—21no—
51C24×C19—22no—
52C24×C19—42no—
53C24×C19—42no—
54C24×C19C22⋊C412yes—
55C24×C19C2×D411yescharacteristic
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—24no—
59C22×C4×C19—42no—
60C22×C4×C19—42no—
61C22×C4×C19C22⋊C412yes—
62C22×C4×C19C22×C411yescharacteristic
63C22×C4×C19C2×D411yescharacteristic
64C22×C4×C19C2×D412yes—
65C22×C4×C19#4112yes—
66C22×Dic19—22no—
67C22×Dic19—22no—
68C22×Dic19—42no—
69C22×Dic19—42no—
70C22×Dic19—41no—
71C22×Dic19—41no—
72C22×Dic19—42no—
73C22×Dic19—42no—
74C22×Dic19—42no—
75C4⋊C4×C19—44no—
76C22⋊C4×C19—24no—
77C22⋊C4×C19—24no—
78C22⋊C4×C19—42no—
79C22⋊C4×C19—42no—
80C22⋊C4×C19—82no—
81C22⋊C4×C19—82no—
82C42×C19—82no—
83C22⋊Dic19—48no—
84C4⋊Dic19—24no—
85C4⋊Dic19—42no—
86C2×C19⋊C8—44no—
87C2×C19⋊C8—42no—
88#9028—191nomaximal, Sylow
89C23×C19—22no—
90C23×C19—22no—
91C23×C19—22no—
92C23×C19—22no—
93C23×C19—22no—
94C23×C19—42no—
95C23×C19—42no—
96C23×C19—48no—
97C23×C19—42no—
98C23×C19—42no—
99C23×C19—42no—
100C23×C19—42no—
101C23×C19—81no—
102C23×C19—81no—
103C23×C19—84no—
104C23×C19C2×C22⋊C411yescharacteristic
105C23×C19#12011yescharacteristic
106C23×C19#12311yescharacteristic
107C23×C19#13512yes—
108C23×C19AGL(1,ℤ/8)12yes—
109C2×C4×C19—24no—
110C2×C4×C19—22no—
111C2×C4×C19—41no—
112C2×C4×C19—41no—
113C2×C4×C19—42no—
114C2×C4×C19—42no—
115C2×C4×C19—42no—
116C2×C4×C19—44no—
117C2×C4×C19—44no—
118C2×C4×C19—44no—
119C2×C4×C19—81no—
120C2×C4×C19C4×D412yes—
121C2×C4×C19#12112yes—
122C2×Dic19—42no—
123C2×Dic19—42no—
124C2×Dic19—42no—
125C2×Dic19—42no—
126C2×Dic19—42no—
127C2×Dic19—42no—
128C2×Dic19—84no—
129C2×Dic19—82no—
130C2×Dic19—82no—
131C19⋊C8—82no—
132C2×#397—191no—
133#2312D1911yescharacteristic
134#1823—192no—
135C2×#323—191no—
136#1294—192no—
137C22×C19—24no—
138C22×C19—24no—
139C22×C19—21no—
140C22×C19—21no—
141C22×C19—21no—
142C22×C19—21no—
143C22×C19—44no—
144C22×C19—42no—
145C22×C19—42no—
146C22×C19—42no—
147C22×C19—82no—
148C22×C19—84no—
149C22×C19—84no—
150C22×C19#38611yescharacteristic
151C22×C19#41611yescharacteristic
152C22×C19#41811yescharacteristic
153C22×C19#44912yes—
154C22×C19#45512yes—
155C22×C19#45812yes—
156C22×C19#48212yes—
157C4×C19—22no—
158C4×C19—22no—
159C4×C19—42no—
160C4×C19—84no—
161Dic19—82no—
162Dic19—82no—
163C22×C4⋊C4—191no—
164C22×C22⋊C4—381no—
165C22×C22⋊C4C2×D1911yescharacteristic
166C2×C22⋊C8—192no—
167#397—194no—
168#397—382no—
169#388—24no—
170#380C2×D1912yes—
171#379—21no—
172C4×C22⋊C4—21no—
173C2×#95—191no—
174C2×#95—381no—
175#340—384no—
176#323—382no—
177C2×C19—21no—
178C2×C19—21no—
179C2×C19—22no—
180C2×C19—82no—
181C2×C19#161214yes—
182C2×C19#187511yescharacteristic
183C2×C19#188511yescharacteristic
184C2×C19#189011yescharacteristic
185C25C22⋊D1911yescharacteristic
186C23×C4—381no—
187C23×C4—381no—
188C23×C4C22⋊D1911yescharacteristic
189C23×C4C22×D1911yescharacteristic
190C22×C8—382no—
191C2×C4⋊C4—192no—
192C2×C4⋊C4—382no—
193C2×C4⋊C4—382no—
194C2×C4⋊C4—381no—
195C2×C4⋊C4C22⋊D1914yes—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—384no—
202C2×C22⋊C4—764no—
203C2×C22⋊C4C4×D1912yes—
204C2×C22⋊C4D7612yes—
205C2×C42—22no—
206C22⋊C8—382no—
207C22⋊C8—382no—
208#95—22no—
209#95—22no—
210#95—192no—
211#95—384no—
212#95—381no—
213C19#902811yescharacteristic, complemented, Sylow
214C24—22no—
215C24—21no—
216C24—22no—
217C24—21no—
218C24—42no—
219C24—42no—
220C24(C2×D19)⋊C412yes—
221C24C2×C22⋊D1911yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—24no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—382no—
228C22×C4—382no—
229C22×C4—762no—
230C22×C4—762no—
231C22×C4—762no—
232C22×C4—762no—
233C22×C4—762no—
234C22×C4—761no—
235C22×C4—761no—
236C22×C4(C2×D19)⋊C412yes—
237C22×C4C2×C4×D1911yescharacteristic
238C22×C4C2×D7611yescharacteristic
239C22×C4#6454112yes—
240C22×C4C2×C22⋊D1912yes—
241C2×C8—764no—
242C2×C8—762no—
243C4⋊C4—44no—
244C4⋊C4—384no—
245C4⋊C4—762no—
246C22⋊C4—24no—
247C22⋊C4—24no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—82no—
251C22⋊C4—82no—
252C22⋊C4—768no—
253C42—82no—
254C23—22no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—22no—
259C23—42no—
260C23—42no—
261C23—48no—
262C23—42no—
263C23—42no—
264C23—42no—
265C23—42no—
266C23—81no—
267C23—81no—
268C23—84no—
269C23C2×(C2×D19)⋊C411yescharacteristic
270C23#1059737511yescharacteristic
271C23#1059739512yes—
272C23#1059739612yes—
273C23#1059739911yescharacteristic
274C2×C4—24no—
275C2×C4—22no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—44no—
282C2×C4—44no—
283C2×C4—44no—
284C2×C4—81no—
285C2×C4—762no—
286C2×C4—762no—
287C2×C4—762no—
288C2×C4—762no—
289C2×C4—762no—
290C2×C4—762no—
291C2×C4—1524no—
292C2×C4—1522no—
293C2×C4—1522no—
294C2×C4C4×C22⋊D1912yes—
295C2×C4#1059737612yes—
296C8—1522no—
297C22—24no—
298C22—24no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—44no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—82no—
308C22—84no—
309C22—84no—
310C22#1192642311yescharacteristic
311C22#1192653811yescharacteristic
312C22#1192654811yescharacteristic
313C22#1192668912yes—
314C22#1192672212yes—
315C22#1192673412yes—
316C22#1192686812yes—
317C4—22no—
318C4—22no—
319C4—42no—
320C4—84no—
321C4—1522no—
322C4—1522no—
323C2—21no—
324C2—21no—
325C2—22no—
326C2—82no—
327C2#1456264914yes—
328C2#1456395711yescharacteristic
329C2#1456402311yescharacteristic
330C2#1456404811yescharacteristic
subgroupG/H
centerC23#10597399
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2312C2
socleC23×C19#120
prime radicalC25×C19D4
cosocleC23×C4×C19C23
hypercenter#2312D19
hypocenterC19#9028
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2312

Complements

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

NH ≅ G/Ntype
2. #14563719C2semidirect
4. #14561513C2semidirect
10. #11926469C4semidirect
213. C19#9028semidirect

Maximal subgroups

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

subgroupindex
C2×#119264692
#145637192
C2×#119262682
#145615132
C19×#23122
#902819