Finite Group Databasebeta

← #18071372

Subgroups — #18071372

Order 4864.

536 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 87 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#14564771C212yesmaximal, complemented
2#14564734C211yesmaximal, characteristic, complemented
3#14561461C211yesmaximal, characteristic, complemented
4#14561456C212yesmaximal, complemented
5C19×#2733C211yesmaximal, characteristic
6C22×#64528—21no—
7C2×#10597315C2211yescharacteristic
8C2×#10597267—21no—
9C2×#10597289—22no—
10#11926306—22no—
11#11926299C2211yescharacteristic
12#11926299C2212yes—
13C2×C19×#124—21no—
14C19×#394—21no—
15C19×#392—22no—
16C19×#391C2211yescharacteristic
17C19×#390C2212yes—
18C19×#388—22no—
19C22×Q8×C19D411yescharacteristic
20C22×D4×C19—21no—
21C22×D4×C19—21no—
22C22×D4×C19D412yes—
23C22×Dic38—21no—
24C19×#124—42no—
25C19×#124—42no—
26C2×C4⋊C4×C19D411yescharacteristic
27C2×C4⋊C4×C19D412yes—
28C2×C22⋊C4×C19—22no—
29C2×C22⋊C4×C19—22no—
30C2×C22⋊C4×C19—22no—
31C2×C22⋊C4×C19—22no—
32C2×C42×C19—21no—
33C2×C42×C19C2311yescharacteristic
34C2×#64528—42no—
35C2×#64528—42no—
36C2×#64528—42no—
37C2×C4⋊Dic19—22no—
38C22×C19⋊C8—21no—
39C22×C19⋊C8—22no—
40#10597315—42no—
41C19×#95—21no—
42C19×#95—22no—
43#10597289—44no—
44#10597267—42no—
45C24×C19—22no—
46C2×Q8×C19—21no—
47C2×Q8×C19—41no—
48C2×Q8×C19—41no—
49C2×Q8×C19D812yes—
50C2×D4×C19—22no—
51C2×D4×C19—22no—
52C2×D4×C19—42no—
53C2×D4×C19—42no—
54C2×D4×C19—42no—
55C2×D4×C19—81no—
56C2×D4×C19—81no—
57C2×D4×C19—81no—
58C2×D4×C19—82no—
59C22×C4×C19—21no—
60C22×C4×C19—22no—
61C22×C4×C19—21no—
62C22×C4×C19C2×D411yescharacteristic
63C22×C4×C19C2×D412yes—
64C22×Dic19—41no—
65C2×Dic38—22no—
66C2×Dic38—41no—
67C2×Dic38—41no—
68C2×Dic38—41no—
69C2×Dic38—41no—
70C2×Dic38—41no—
71C4⋊C4×C19—42no—
72C4⋊C4×C19—41no—
73C22⋊C4×C19—44no—
74C22⋊C4×C19—42no—
75C22⋊C4×C19—42no—
76C22⋊C4×C19—42no—
77C22⋊C4×C19—42no—
78C22⋊C4×C19—82no—
79C42×C19—41no—
80C42×C19—42no—
81#64528—48no—
82C4⋊Dic19—24no—
83C4⋊Dic19—42no—
84C2×C19⋊C8—22no—
85C2×C19⋊C8—41no—
86C2×C19⋊C8—41no—
87C2×C19⋊C8—42no—
88C2×C19⋊C8—42no—
89C2×C19⋊C8—42no—
90#7758—191nomaximal, Sylow
91C23×C19—42no—
92C23×C19—42no—
93C23×C19—42no—
94C23×C19—42no—
95C23×C19—42no—
96C23×C19—42no—
97C23×C19—42no—
98C23×C19#12011yescharacteristic
99Q8×C19—42no—
100Q8×C19—81no—
101D4×C19—44no—
102D4×C19—82no—
103D4×C19—84no—
104D4×C19—84no—
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—42no—
113C2×C4×C19—42no—
114C2×C4×C19—41no—
115C2×C4×C19—42no—
116C2×C4×C19—42no—
117C2×C4×C19C2×D811yescharacteristic
118C2×C4×C19#13512yes—
119C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C19#13712yes—
121C2×Dic19—42no—
122C2×Dic19—81no—
123C2×Dic19—81no—
124Dic38—42no—
125Dic38—42no—
126Dic38—81no—
127Dic38—81no—
128C19⋊C8—42no—
129C19⋊C8—82no—
130#2733D1911yescharacteristic
131#2023—192no—
132#2016—191no—
133#1272—191no—
134#1270—192no—
135C22×C19—82no—
136C22×C19—82no—
137C22×C19—82no—
138C22×C19—82no—
139C22×C19—82no—
140C22×C19—82no—
141C22×C19—82no—
142C22×C19#44711yescharacteristic
143C22×C19#45212yes—
144C22×C19#45311yescharacteristic
145C22×C19#45512yes—
146C22×C19B(4,𝔽2)11yescharacteristic
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—381no—
156C2×C4⋊Q8—191no—
157C2×#124—21no—
158C2×#103—381no—
159C2×#102—382no—
160#394—21no—
161#392—22no—
162#391C2×D1911yescharacteristic
163#390C2×D1912yes—
164#388—22no—
165#340—382no—
166#336—191no—
167#336—192no—
168C2×C19—162no—
169C2×C19#159511yescharacteristic
170C2×C19#160612yes—
171C2×C19#163411yescharacteristic
172C2×C19#164112yes—
173C2×C19#165911yescharacteristic
174C22×Q8—381no—
175C22×Q8C22⋊D1911yescharacteristic
176C22×D4—21no—
177C22×D4—21no—
178C22×D4C22⋊D1912yes—
179C2×Q16—762no—
180C2×Q16—762no—
181C2×Q16—762no—
182C22×C8—381no—
183C22×C8—382no—
184C4⋊Q8—762no—
185#124—42no—
186#124—42no—
187C2×C4⋊C4—382no—
188C2×C4⋊C4C22⋊D1912yes—
189C2×C4⋊C4C22⋊D1911yescharacteristic
190C2×C22⋊C4—22no—
191C2×C22⋊C4—22no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C42—21no—
195C2×C42C22×D1911yescharacteristic
196#103—762no—
197#102—764no—
198#95—21no—
199#95—22no—
200C19#775811yescharacteristic, complemented, Sylow
201C24—22no—
202C2×Q8—21no—
203C2×Q8—41no—
204C2×Q8—41no—
205C2×Q8—382no—
206C2×Q8—761no—
207C2×Q8—761no—
208C2×Q8—761no—
209C2×Q8—761no—
210C2×Q8—761no—
211C2×Q8#6452512yes—
212C2×D4—22no—
213C2×D4—22no—
214C2×D4—42no—
215C2×D4—42no—
216C2×D4—42no—
217C2×D4—81no—
218C2×D4—81no—
219C2×D4—81no—
220C2×D4—82no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—761no—
225C22×C4C2×C22⋊D1911yescharacteristic
226C22×C4C2×C22⋊D1912yes—
227Q16—768no—
228C2×C8—382no—
229C2×C8—761no—
230C2×C8—761no—
231C2×C8—762no—
232C2×C8—762no—
233C2×C8—762no—
234C4⋊C4—41no—
235C4⋊C4—42no—
236C4⋊C4—384no—
237C4⋊C4—762no—
238C22⋊C4—44no—
239C22⋊C4—42no—
240C22⋊C4—42no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C22⋊C4—82no—
244C42—41no—
245C42—42no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23—42no—
250C23—42no—
251C23—42no—
252C23—42no—
253C23#1059739911yescharacteristic
254Q8—42no—
255Q8—81no—
256Q8—762no—
257Q8—762no—
258Q8—1521no—
259Q8—1521no—
260D4—44no—
261D4—82no—
262D4—84no—
263D4—84no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—762no—
277C2×C4—1521no—
278C2×C4—1521no—
279C2×C4C2×#6452511yescharacteristic
280C2×C4#1059737811yescharacteristic
281C2×C4#1059739612yes—
282C2×C4#1059739712yes—
283C8—762no—
284C8—1522no—
285C22—82no—
286C22—82no—
287C22—82no—
288C22—82no—
289C22—82no—
290C22—82no—
291C22—82no—
292C22#1192667811yescharacteristic
293C22#1192670612yes—
294C22#1192671211yescharacteristic
295C22#1192672212yes—
296C22#1192673111yescharacteristic
297C4—22no—
298C4—22no—
299C4—21no—
300C4—21no—
301C4—42no—
302C4—82no—
303C4—81no—
304C4—1522no—
305C2—162no—
306C2#1456255311yescharacteristic
307C2#1456261512yes—
308C2#1456278011yescharacteristic
309C2#1456282812yes—
310C2#1456294111yescharacteristic
subgroupG/H
centerC23#10597399
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#2733C2
socleC23×C19#120
hypercenter#2733D19
hypocenterC19#7758
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2733

Complements

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

NH ≅ G/Ntype
1. #14564771C2semidirect
2. #14564734C2semidirect
3. #14561461C2semidirect
4. #14561456C2semidirect
200. C19#7758semidirect

Maximal subgroups

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

subgroupindex
#145647712
#145647342
#145614612
#145614562
C19×#27332
#775819