Finite Group Databasebeta

← #18080409

Subgroups — #18080409

Order 4864.

602 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 119 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#14572676C211yesmaximal, characteristic, complemented
2#14563627C211yesmaximal, characteristic, complemented
3#14562060C212yesmaximal, complemented
4#14561493C212yesmaximal, complemented
5C19×#2535C211yesmaximal, characteristic
6#11926622—24no—
7#11926597C2212yes—
8#11926568C2212yes—
9C2×#10597290—21no—
10#11926508—22no—
11#11926313—21no—
12D4⋊(C19⋊C8)—24no—
13C2×C19×#121—21no—
14C2×C4×D4×C19C2211yescharacteristic
15C2×C4×D4×C19C2211yescharacteristic
16C19×#397C412yes—
17C19×#392C412yes—
18C19×#386—22no—
19C19×#382C2211yescharacteristic
20C19×#380—21no—
21C22×D4×C19—22no—
22C22×D4×C19C2×C411yescharacteristic
23C22×D4×C19D411yescharacteristic
24C23×C4×C19—21no—
25C23×C4×C19D412yes—
26C19×#121—44no—
27C4×D4×C19—22no—
28C4×D4×C19—22no—
29C4×D4×C19—22no—
30C4×D4×C19—22no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19C2×C411yescharacteristic
33C2×C4⋊C4×C19D411yescharacteristic
34C2×C22⋊C4×C19—22no—
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—22no—
37C2×C22⋊C4×C19C2×C412yes—
38C2×C42×C19C2311yescharacteristic
39C2×#64520—24no—
40C2×#64520—22no—
41C19×#95—22no—
42C19×#95—21no—
43C19×#95C2×C412yes—
44#10597290—42no—
45C22⋊(C19⋊C8)—24no—
46C22⋊(C19⋊C8)—22no—
47C4⋊(C19⋊C8)—22no—
48C4⋊(C19⋊C8)—22no—
49C4⋊(C19⋊C8)—22no—
50C4×C19⋊C8D414yescomplemented
51C24×C19—21no—
52C24×C19C22⋊C412yes—
53C2×D4×C19—22no—
54C2×D4×C19—22no—
55C2×D4×C19—22no—
56C2×D4×C19—21no—
57C2×D4×C19—21no—
58C2×D4×C19—42no—
59C2×D4×C19—44no—
60C2×D4×C19—44no—
61C2×D4×C19—82no—
62C22×C4×C19—22no—
63C22×C4×C19—22no—
64C22×C4×C19—21no—
65C22×C4×C19—22no—
66C22×C4×C19—42no—
67C22×C4×C19—42no—
68C22×C4×C19—41no—
69C22×C4×C19—41no—
70C22×C4×C19—82no—
71C22×C4×C19C22⋊C412yes—
72C22×C4×C19C22×C411yescharacteristic
73C22×C4×C19C2×D411yescharacteristic
74C22×C4×C19C2×D411yescharacteristic
75C4⋊C4×C19—22no—
76C4⋊C4×C19—22no—
77C4⋊C4×C19—42no—
78C22⋊C4×C19—24no—
79C22⋊C4×C19—44no—
80C22⋊C4×C19—41no—
81C22⋊C4×C19—41no—
82C22⋊C4×C19—82no—
83C42×C19C2×D412yes—
84C42×C19#4112yes—
85#64520—42no—
86#64520—42no—
87#64520—84no—
88C2×C19⋊C8—24no—
89C2×C19⋊C8—42no—
90#9489—191nomaximal, Sylow
91C23×C19—22no—
92C23×C19—22no—
93C23×C19—22no—
94C23×C19—22no—
95C23×C19—42no—
96C23×C19—42no—
97C23×C19—41no—
98C23×C19—41no—
99C23×C19—41no—
100C23×C19—41no—
101C23×C19—41no—
102C23×C19—41no—
103C23×C19C2×C22⋊C411yescharacteristic
104D4×C19—24no—
105D4×C19—42no—
106D4×C19—42no—
107D4×C19—42no—
108D4×C19—88no—
109C2×C4×C19—22no—
110C2×C4×C19—41no—
111C2×C4×C19—41no—
112C2×C4×C19—44no—
113C2×C4×C19—42no—
114C2×C4×C19—42no—
115C2×C4×C19—42no—
116C2×C4×C19—41no—
117C2×C4×C19—41no—
118C2×C4×C19—41no—
119C2×C4×C19—42no—
120C2×C4×C19—82no—
121C2×C4×C19—82no—
122C2×C4×C19—82no—
123C2×C4×C19C4×D412yes—
124C2×C4×C19#12011yescharacteristic
125C2×C4×C19#12112yes—
126C2×C4×C19#12311yescharacteristic
127C2×C4×C19AGL(1,ℤ/8)12yes—
128C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C19#13711yescharacteristic
130C19⋊C8—44no—
131C19⋊C8—82no—
132#2975—191no—
133#2535D1911yescharacteristic
134#1800—191no—
135#1486—192no—
136#1286—192no—
137C22×C19—21no—
138C22×C19—21no—
139C22×C19—42no—
140C22×C19—44no—
141C22×C19—42no—
142C22×C19—42no—
143C22×C19—42no—
144C22×C19—42no—
145C22×C19—42no—
146C22×C19—82no—
147C22×C19—81no—
148C22×C19—81no—
149C22×C19—81no—
150C22×C19—81no—
151C22×C19#38611yescharacteristic
152C22×C19#41711yescharacteristic
153C22×C19#41811yescharacteristic
154C4×C19—22no—
155C4×C19—21no—
156C4×C19—21no—
157C4×C19—42no—
158C4×C19—82no—
159C4×C19—81no—
160C4×C19#46812yes—
161C4×C19#46912yes—
162C2×#121—21no—
163C2×C4×D4C2×D1911yescharacteristic
164C2×C4×D4C2×D1911yescharacteristic
165#436—384no—
166#431—192no—
167#423—192no—
168C2×#100—381no—
169#407—382no—
170#397Dic1912yes—
171#392Dic1912yes—
172#386—22no—
173#382C2×D1911yescharacteristic
174#380—21no—
175#343—381no—
176D4⋊C8—384no—
177C2×C19—21no—
178C2×C19—21no—
179C2×C19—82no—
180C2×C19—82no—
181C2×C19#189111yescharacteristic
182C2×C19#189511yescharacteristic
183C2×C19#191111yescharacteristic
184C22×D4—22no—
185C22×D4C2×Dic1911yescharacteristic
186C22×D4C22⋊D1911yescharacteristic
187C23×C4—21no—
188C23×C4C22⋊D1912yes—
189C2×M16—384no—
190C2×M16—382no—
191#121—44no—
192C4×D4—22no—
193C4×D4—22no—
194C4×D4—22no—
195C4×D4—22no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4C2×Dic1911yescharacteristic
198C2×C4⋊C4C22⋊D1911yescharacteristic
199C2×C22⋊C4—22no—
200C2×C22⋊C4—21no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4C2×Dic1912yes—
203C2×C42C22×D1911yescharacteristic
204C4⋊C8—382no—
205C4⋊C8—382no—
206C4⋊C8—382no—
207#100—762no—
208C22⋊C8—384no—
209C22⋊C8—382no—
210C4×C8—194no—
211#95—22no—
212#95—21no—
213#95C2×Dic1912yes—
214C19#948911yescharacteristic, complemented, Sylow
215C24—21no—
216C24C22⋊Dic1912yes—
217C2×D4—22no—
218C2×D4—22no—
219C2×D4—22no—
220C2×D4—21no—
221C2×D4—21no—
222C2×D4—42no—
223C2×D4—44no—
224C2×D4—44no—
225C2×D4—82no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—82no—
235C22×C4C22⋊Dic1912yes—
236C22×C4C22×Dic1911yescharacteristic
237C22×C4C2×C22⋊D1911yescharacteristic
238C22×C4C2×C22⋊D1911yescharacteristic
239M16—762no—
240M16—762no—
241M16—1524no—
242C2×C8—384no—
243C2×C8—762no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—42no—
247C22⋊C4—24no—
248C22⋊C4—44no—
249C22⋊C4—41no—
250C22⋊C4—41no—
251C22⋊C4—82no—
252C42D4×D1912yes—
253C42#6454312yes—
254C23—22no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—42no—
259C23—42no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23C2×C22⋊Dic1911yescharacteristic
267D4—24no—
268D4—42no—
269D4—42no—
270D4—42no—
271D4—88no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—44no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—82no—
284C2×C4—82no—
285C2×C4—82no—
286C2×C4#1059737812yes—
287C2×C4D4×Dic1912yes—
288C2×C4#1059738111yescharacteristic
289C2×C4#1059738311yescharacteristic
290C2×C4#1059738512yes—
291C2×C4#1059739511yescharacteristic
292C2×C4#1059739711yescharacteristic
293C8—764no—
294C8—1522no—
295C22—21no—
296C22—21no—
297C22—42no—
298C22—44no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—42no—
303C22—42no—
304C22—82no—
305C22—81no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22#1192642411yescharacteristic
310C22#1192654511yescharacteristic
311C22#1192654911yescharacteristic
312C4—21no—
313C4—21no—
314C4—22no—
315C4—42no—
316C4—82no—
317C4—81no—
318C4#1192678812yes—
319C4#1192679512yes—
320C2—21no—
321C2—21no—
322C2—82no—
323C2—82no—
324C2#1456405411yescharacteristic
325C2#1456407411yescharacteristic
326C2#1456416811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#2535C2
socleC22×C19#386
cosocleC2×C42×C19C23
hypercenter#2535D19
hypocenterC19#9489
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. #14572676C2semidirect
2. #14563627C2semidirect
3. #14562060C2semidirect
4. #14561493C2semidirect
50. C4×C19⋊C8D4semidirect
214. C19#9489semidirect

Maximal subgroups

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

subgroupindex
#145726762
#145636272
#145620602
#145614932
C19×#25352
#948919