Finite Group Databasebeta

← #18080406

Subgroups — #18080406

Order 4864.

602 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 111 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#14568532C211yesmaximal, characteristic
3#14562059C212yesmaximal, complemented
4#14561495C212yesmaximal, complemented
5C19×#1800C211yesmaximal, characteristic, complemented
6C2×#10597384—21no—
7C2×C4×D76C2211yescharacteristic
8#11926622—24no—
9#11926597C2212yes—
10#11926508—22no—
11#11926469C412yes—
12#11926453C412yes—
13#11926423—22no—
14#11926410C2211yescharacteristic
15#11926401—21no—
16#11926271—24no—
17C2×C4×D4×C19C2211yescharacteristic
18C19×#423C2212yes—
19C2×C19×#100—21no—
20C19×#343—21no—
21C22×D4×C19D411yescharacteristic
22C23×C4×C19D412yes—
23C22×C22⋊D19—22no—
24C22×D76C2×C411yescharacteristic
25C22×C4×D19—21no—
26C2×M16×C19—22no—
27C4×D4×C19—22no—
28C4×D4×C19—22no—
29C2×C4⋊C4×C19D411yescharacteristic
30C2×C22⋊C4×C19C2×C412yes—
31C2×C42×C19C2311yescharacteristic
32C2×C22⋊Dic19—22no—
33#10597384—44no—
34C2×(C2×D19)⋊C4—21no—
35C2×(C2×D19)⋊C4—22no—
36C2×C4⋊Dic19—21no—
37C2×C4⋊Dic19C2×C411yescharacteristic
38C2×#64520—24no—
39C4×D76—22no—
40C4×D76—22no—
41C19×C4⋊C8—22no—
42C19×C4⋊C8—22no—
43C19×#100—42no—
44C19⋊#95—22no—
45C19⋊#95—21no—
46C19⋊#95C2×C412yes—
47C22⋊(C19⋊C8)—24no—
48C22⋊(C19⋊C8)—22no—
49C4⋊(C19⋊C8)—22no—
50C4×C19⋊C8D414yescomplemented
51C24×C19C22⋊C412yes—
52C23×D19—21no—
53C2×D4×C19—22no—
54C2×D4×C19—22no—
55C2×D4×C19—21no—
56C2×D4×C19—21no—
57C22×C4×C19—22no—
58C22×C4×C19—22no—
59C22×C4×C19—82no—
60C22×C4×C19C22⋊C412yes—
61C22×C4×C19C22×C411yescharacteristic
62C22×C4×C19C2×D411yescharacteristic
63C22×C4×C19C2×D411yescharacteristic
64C2×C22⋊D19—44no—
65C2×C22⋊D19—44no—
66C2×C22⋊D19—82no—
67C22×Dic19—21no—
68C22×Dic19—22no—
69C2×D76—22no—
70C2×D76—42no—
71C2×C4×D19—42no—
72C2×C4×D19—42no—
73C2×C4×D19—41no—
74C2×C4×D19—41no—
75M16×C19—42no—
76M16×C19—42no—
77C2×C8×C19—42no—
78C4⋊C4×C19—22no—
79C22⋊C4×C19—24no—
80C42×C19C2×D412yes—
81C42×C19#4112yes—
82C22⋊Dic19—44no—
83(C2×D19)⋊C4—41no—
84(C2×D19)⋊C4—41no—
85(C2×D19)⋊C4—82no—
86C4⋊Dic19—22no—
87C4⋊Dic19—42no—
88#64520—84no—
89C2×C19⋊C8—24no—
90#9489—191nomaximal, Sylow
91C23×C19—22no—
92C23×C19—22no—
93C23×C19—22no—
94C23×C19—42no—
95C23×C19—42no—
96C23×C19C2×C22⋊C411yescharacteristic
97C22×D19—22no—
98C22×D19—41no—
99C22×D19—41no—
100C22×D19—41no—
101C22×D19—41no—
102C22×D19—41no—
103C22×D19—41no—
104D4×C19—42no—
105D4×C19—42no—
106C2×C4×C19—22no—
107C2×C4×C19—41no—
108C2×C4×C19—41no—
109C2×C4×C19—44no—
110C2×C4×C19—42no—
111C2×C4×C19—82no—
112C2×C4×C19C4×D412yes—
113C2×C4×C19#12011yescharacteristic
114C2×C4×C19#12112yes—
115C2×C4×C19#12311yescharacteristic
116C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C19AGL(1,ℤ/8)12yes—
118C2×C4×C19#13711yescharacteristic
119C22⋊D19—88no—
120C2×Dic19—42no—
121C2×Dic19—42no—
122C2×Dic19—41no—
123C2×Dic19—41no—
124C2×Dic19—42no—
125C2×Dic19—41no—
126D76—24no—
127D76—42no—
128C4×D19—82no—
129C4×D19—82no—
130C8×C19—82no—
131C19⋊C8—44no—
132#2975—191no—
133#2535—191no—
134#1800D1911yescharacteristic, complemented
135#1486—192no—
136#1286—192no—
137C22×C19—21no—
138C22×C19—21no—
139C22×C19—44no—
140C22×C19—42no—
141C22×C19—42no—
142C22×C19—42no—
143C22×C19—82no—
144C22×C19#38611yescharacteristic
145C22×C19#41711yescharacteristic
146C22×C19#41811yescharacteristic
147C2×D19—42no—
148C2×D19—42no—
149C2×D19—42no—
150C2×D19—81no—
151C2×D19—81no—
152C2×D19—81no—
153C2×D19—81no—
154C4×C19—22no—
155C4×C19—21no—
156C4×C19—21no—
157C4×C19—42no—
158C4×C19#46812yes—
159C4×C19#46912yes—
160Dic19—82no—
161Dic19—81no—
162C2×#121—381no—
163C2×C4×D4—191no—
164C2×C4×D4C2×D1911yescharacteristic
165#436—384no—
166#431—192no—
167#423C2×D1912yes—
168C2×#100—21no—
169#407—382no—
170#397—192no—
171#392—192no—
172#386—382no—
173#382—191no—
174#380—381no—
175#343—21no—
176D4⋊C8—384no—
177C2×C19—21no—
178C2×C19—21no—
179C2×C19—82no—
180C2×C19#189111yescharacteristic
181C2×C19#189511yescharacteristic
182C2×C19#191111yescharacteristic
183D19—82no—
184C22×D4—191no—
185C22×D4—382no—
186C22×D4C22⋊D1911yescharacteristic
187C23×C4—381no—
188C23×C4D7612yes—
189C2×M16—22no—
190C2×M16—384no—
191#121—764no—
192C4×D4—22no—
193C4×D4—22no—
194C4×D4—382no—
195C4×D4—382no—
196C2×C4⋊C4—191no—
197C2×C4⋊C4—381no—
198C2×C4⋊C4C22⋊D1911yescharacteristic
199C2×C22⋊C4—382no—
200C2×C22⋊C4—381no—
201C2×C22⋊C4—382no—
202C2×C22⋊C4C4×D1912yes—
203C2×C42C22×D1911yescharacteristic
204C4⋊C8—22no—
205C4⋊C8—22no—
206C4⋊C8—382no—
207#100—42no—
208C22⋊C8—384no—
209C22⋊C8—382no—
210C4×C8—194no—
211#95—192no—
212#95—382no—
213#95—381no—
214C19#948911yescharacteristic, complemented, Sylow
215C24—381no—
216C24(C2×D19)⋊C412yes—
217C2×D4—21no—
218C2×D4—22no—
219C2×D4—21no—
220C2×D4—22no—
221C2×D4—382no—
222C2×D4—762no—
223C2×D4—764no—
224C2×D4—764no—
225C2×D4—1522no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—82no—
229C22×C4—382no—
230C22×C4—381no—
231C22×C4—761no—
232C22×C4—762no—
233C22×C4—761no—
234C22×C4—762no—
235C22×C4(C2×D19)⋊C412yes—
236C22×C4C2×C4×D1911yescharacteristic
237C22×C4C2×D7611yescharacteristic
238C22×C4C2×C22⋊D1911yescharacteristic
239M16—42no—
240M16—42no—
241M16—1524no—
242C2×C8—42no—
243C2×C8—384no—
244C4⋊C4—22no—
245C4⋊C4—382no—
246C4⋊C4—762no—
247C22⋊C4—24no—
248C22⋊C4—764no—
249C22⋊C4—761no—
250C22⋊C4—761no—
251C22⋊C4—1522no—
252C42D4×D1912yes—
253C42#6454312yes—
254C23—22no—
255C23—22no—
256C23—22no—
257C23—42no—
258C23—42no—
259C23—382no—
260C23—761no—
261C23—761no—
262C23—761no—
263C23—761no—
264C23—761no—
265C23—761no—
266C23C2×(C2×D19)⋊C411yescharacteristic
267D4—42no—
268D4—42no—
269D4—384no—
270D4—762no—
271D4—1528no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—44no—
276C2×C4—42no—
277C2×C4—82no—
278C2×C4—762no—
279C2×C4—762no—
280C2×C4—761no—
281C2×C4—761no—
282C2×C4—762no—
283C2×C4—761no—
284C2×C4—1522no—
285C2×C4—1522no—
286C2×C4(C22⋊D19)⋊C412yes—
287C2×C4#1059732811yescharacteristic
288C2×C4#1059733211yescharacteristic
289C2×C4#1059737811yescharacteristic
290C2×C4#1059738512yes—
291C2×C4#1059738811yescharacteristic
292C2×C4#1059739512yes—
293C8—82no—
294C8—764no—
295C22—21no—
296C22—21no—
297C22—44no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—82no—
302C22—762no—
303C22—762no—
304C22—762no—
305C22—1521no—
306C22—1521no—
307C22—1521no—
308C22—1521no—
309C22#1192642111yescharacteristic
310C22#1192654311yescharacteristic
311C22#1192654811yescharacteristic
312C4—21no—
313C4—21no—
314C4—22no—
315C4—42no—
316C4—1522no—
317C4—1521no—
318C4#1192679212yes—
319C4#1192679512yes—
320C2—21no—
321C2—21no—
322C2—82no—
323C2—1522no—
324C2#1456405111yescharacteristic
325C2#1456407111yescharacteristic
326C2#1456416511yescharacteristic
subgroupG/H
centerC22#11926421
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1800C2
socleC22×C19#386
prime radical#14568532C2
cosocleC2×C42×C19C23
hypercenter#1800D19
hypocenterC19#9489
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
1. #14572676C2semidirect
3. #14562059C2semidirect
4. #14561495C2semidirect
5. C19×#1800C2semidirect
50. C4×C19⋊C8D4semidirect
134. #1800D19semidirect
214. C19#9489semidirect

Maximal subgroups

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

subgroupindex
#145726762
#145685322
#145620592
#145614952
C19×#18002
#948919