Finite Group Databasebeta

← #18071370

Subgroups — #18071370

Order 4864.

536 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 83 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#14570661C211yesmaximal, characteristic
2#14564768C212yesmaximal, complemented
3#14561461C211yesmaximal, characteristic, complemented
4#14561455C212yesmaximal, complemented
5C19×#2016C211yesmaximal, characteristic, complemented
6C2×#10597393—21no—
7C2×#10597266—22no—
8#11926461—21no—
9#11926454—22no—
10#11926446C2212yes—
11#11926436—22no—
12#11926306—22no—
13#11926299C2212yes—
14C22×Q16×C19—21no—
15C2×C19×C4⋊Q8C2211yescharacteristic
16C2×C19×#103—21no—
17C19×#391C2211yescharacteristic
18C19×#336C2211yescharacteristic
19C22×Q8×C19—21no—
20C22×Q8×C19D411yescharacteristic
21C22×D76—21no—
22C22×D76—21no—
23C22×D76D412yes—
24C2×Q16×C19—42no—
25C2×Q16×C19—42no—
26C2×Q16×C19—42no—
27C22×C8×C19—21no—
28C19×C4⋊Q8—42no—
29C2×C4⋊C4×C19—22no—
30C2×C4⋊C4×C19D411yescharacteristic
31C2×C42×C19C2311yescharacteristic
32#10597393—42no—
33#10597393—42no—
34C2×(C2×D19)⋊C4—22no—
35C2×(C2×D19)⋊C4—22no—
36C2×(C2×D19)⋊C4—22no—
37C2×(C2×D19)⋊C4—22no—
38C2×C4⋊Dic19D412yes—
39C2×C4×Dic19—21no—
40C22×C19⋊C8—22no—
41C19×#103—42no—
42C19×#95—22no—
43C19⋊#95—21no—
44#10597266—44no—
45C23×D19—22no—
46C2×Q8×C19—21no—
47C2×Q8×C19—22no—
48C2×Q8×C19—41no—
49C2×Q8×C19—41no—
50C2×Q8×C19—41no—
51C2×Q8×C19—41no—
52C2×Q8×C19—41no—
53C2×Q8×C19—41no—
54C2×Q8×C19—41no—
55C2×Q8×C19D812yes—
56C22×C4×C19—21no—
57C22×C4×C19—21no—
58C22×C4×C19—41no—
59C22×C4×C19C2×D412yes—
60C22×C4×C19C2×D411yescharacteristic
61C22×Dic19—22no—
62C2×D76—22no—
63C2×D76—22no—
64C2×D76—42no—
65C2×D76—42no—
66C2×D76—42no—
67C2×D76—81no—
68C2×D76—81no—
69C2×D76—81no—
70C2×D76—82no—
71Q16×C19—48no—
72C2×C8×C19—22no—
73C2×C8×C19—41no—
74C2×C8×C19—41no—
75C4⋊C4×C19—24no—
76C4⋊C4×C19—41no—
77C4⋊C4×C19—42no—
78C42×C19—41no—
79(C2×D19)⋊C4—44no—
80(C2×D19)⋊C4—42no—
81(C2×D19)⋊C4—42no—
82(C2×D19)⋊C4—42no—
83(C2×D19)⋊C4—42no—
84(C2×D19)⋊C4—82no—
85C4⋊Dic19—42no—
86C4×Dic19—42no—
87C2×C19⋊C8—42no—
88C2×C19⋊C8—42no—
89C2×C19⋊C8—42no—
90#7758—191nomaximal, Sylow
91C23×C19#12011yescharacteristic
92C22×D19—42no—
93C22×D19—42no—
94C22×D19—42no—
95C22×D19—42no—
96C22×D19—42no—
97C22×D19—42no—
98C22×D19—42no—
99Q8×C19—42no—
100Q8×C19—42no—
101Q8×C19—42no—
102Q8×C19—81no—
103Q8×C19—81no—
104Q8×C19—81no—
105C2×C4×C19—21no—
106C2×C4×C19—22no—
107C2×C4×C19—22no—
108C2×C4×C19—21no—
109C2×C4×C19—22no—
110C2×C4×C19—41no—
111C2×C4×C19—41no—
112C2×C4×C19—41no—
113C2×C4×C19—42no—
114C2×C4×C19—42no—
115C2×C4×C19—81no—
116C2×C4×C19—81no—
117C2×C4×C19C2×D811yescharacteristic
118C2×C4×C19#13512yes—
119C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C19#13712yes—
121C2×Dic19—42no—
122C2×Dic19—42no—
123C2×Dic19—42no—
124D76—44no—
125D76—82no—
126D76—84no—
127D76—84no—
128C8×C19—42no—
129C19⋊C8—82no—
130#2733—191no—
131#2023—192no—
132#2016D1911yescharacteristic, complemented
133#1272—191no—
134#1270—192no—
135C22×C19#44711yescharacteristic
136C22×C19#45212yes—
137C22×C19#45311yescharacteristic
138C22×C19#45512yes—
139C22×C19B(4,𝔽2)11yescharacteristic
140C2×D19—82no—
141C2×D19—82no—
142C2×D19—82no—
143C2×D19—82no—
144C2×D19—82no—
145C2×D19—82no—
146C2×D19—82no—
147C4×C19—21no—
148C4×C19—21no—
149C4×C19—22no—
150C4×C19—22no—
151C4×C19—42no—
152C4×C19—82no—
153C4×C19—81no—
154Dic19—82no—
155C22×Q16—21no—
156C2×C4⋊Q8C2×D1911yescharacteristic
157C2×#124—381no—
158C2×#103—21no—
159C2×#102—382no—
160#394—381no—
161#392—382no—
162#391C2×D1911yescharacteristic
163#390—192no—
164#388—382no—
165#340—382no—
166#336—192no—
167#336C2×D1911yescharacteristic
168C2×C19#159511yescharacteristic
169C2×C19#160612yes—
170C2×C19#163411yescharacteristic
171C2×C19#164112yes—
172C2×C19#165911yescharacteristic
173D19—162no—
174C22×Q8—21no—
175C22×Q8C22⋊D1911yescharacteristic
176C22×D4—192no—
177C22×D4—381no—
178C22×D4—381no—
179C2×Q16—42no—
180C2×Q16—42no—
181C2×Q16—42no—
182C22×C8—21no—
183C22×C8—382no—
184C4⋊Q8—42no—
185#124—762no—
186#124—762no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—192no—
189C2×C4⋊C4C22⋊D1911yescharacteristic
190C2×C22⋊C4—382no—
191C2×C22⋊C4—382no—
192C2×C22⋊C4—382no—
193C2×C22⋊C4—382no—
194C2×C42—381no—
195C2×C42C22×D1911yescharacteristic
196#103—42no—
197#102—764no—
198#95—22no—
199#95—381no—
200C19#775811yescharacteristic, complemented, Sylow
201C24—382no—
202C2×Q8—21no—
203C2×Q8—22no—
204C2×Q8—41no—
205C2×Q8—41no—
206C2×Q8—41no—
207C2×Q8—41no—
208C2×Q8—41no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8#6452512yes—
212C2×D4—382no—
213C2×D4—382no—
214C2×D4—762no—
215C2×D4—762no—
216C2×D4—762no—
217C2×D4—1521no—
218C2×D4—1521no—
219C2×D4—1521no—
220C2×D4—1522no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—41no—
224C22×C4—382no—
225C22×C4D4×D1912yes—
226C22×C4C2×C22⋊D1911yescharacteristic
227Q16—48no—
228C2×C8—22no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—762no—
232C2×C8—762no—
233C2×C8—762no—
234C4⋊C4—24no—
235C4⋊C4—41no—
236C4⋊C4—42no—
237C4⋊C4—762no—
238C22⋊C4—764no—
239C22⋊C4—762no—
240C22⋊C4—762no—
241C22⋊C4—762no—
242C22⋊C4—762no—
243C22⋊C4—1522no—
244C42—41no—
245C42—762no—
246C23—762no—
247C23—762no—
248C23—762no—
249C23—762no—
250C23—762no—
251C23—762no—
252C23—762no—
253C23#1059738311yescharacteristic
254Q8—42no—
255Q8—42no—
256Q8—42no—
257Q8—81no—
258Q8—81no—
259Q8—81no—
260D4—764no—
261D4—1522no—
262D4—1524no—
263D4—1524no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4—762no—
277C2×C4—762no—
278C2×C4—762no—
279C2×C4#1059736412yes—
280C2×C4#1059736512yes—
281C2×C4C2×#6452511yescharacteristic
282C2×C4#1059739511yescharacteristic
283C8—42no—
284C8—1522no—
285C22—1522no—
286C22—1522no—
287C22—1522no—
288C22—1522no—
289C22—1522no—
290C22—1522no—
291C22—1522no—
292C22#1192667711yescharacteristic
293C22#1192670512yes—
294C22#1192671111yescharacteristic
295C22#1192672012yes—
296C22#1192673011yescharacteristic
297C4—22no—
298C4—22no—
299C4—21no—
300C4—21no—
301C4—42no—
302C4—81no—
303C4—82no—
304C4—1522no—
305C2—3042no—
306C2#1456255211yescharacteristic
307C2#1456261412yes—
308C2#1456277811yescharacteristic
309C2#1456282612yes—
310C2#1456293911yescharacteristic
subgroupG/H
centerC23#10597383
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2016C2
socleC23×C19#120
prime radical#14570661C2
hypercenter#2016D19
hypocenterC19#7758
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2016

Complements

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

NH ≅ G/Ntype
2. #14564768C2semidirect
3. #14561461C2semidirect
4. #14561455C2semidirect
5. C19×#2016C2semidirect
132. #2016D19semidirect
200. C19#7758semidirect

Maximal subgroups

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

subgroupindex
#145706612
#145647682
#145614612
#145614552
C19×#20162
#775819