Finite Group Databasebeta

← #18070804

Subgroups — #18070804

Order 4864.

636 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 103 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#14566199C211yesmaximal, characteristic
2#14563382C212yesmaximal, complemented
3#14561456C211yesmaximal, characteristic, complemented
4#14561455C212yesmaximal, complemented
5C19×#1270C211yesmaximal, characteristic, complemented
6C2×#10597386C411yescharacteristic
7C2×D4×Dic19C411yescharacteristic
8C2×#10597339C411yescharacteristic
9C2×(C22⋊D19)⋊C4—22no—
10C2×#10597272—22no—
11#11926446C2211yescharacteristic
12#11926444—22no—
13#11926413C411yescharacteristic
14C42×Dic19C2211yescharacteristic
15#11926299C2212yes—
16#11926298—22no—
17C19×#390C2211yescharacteristic
18C19×#336C2212yes—
19C22×D4×C19C2×C411yescharacteristic
20C22×C22⋊D19—22no—
21C23×Dic19—21no—
22C22×D76C2×C411yescharacteristic
23C22×C4×D19—21no—
24C22×C8×C19—22no—
25C2×C4⋊C4×C19C2×C411yescharacteristic
26C2×C22⋊C4×C19—22no—
27C2×C42×C19C2311yescharacteristic
28C2×C22⋊Dic19—21no—
29#10597386—22no—
30#10597386—22no—
31D4×Dic19—42no—
32C2×(C2×D19)⋊C4—22no—
33C2×(C2×D19)⋊C4—21no—
34C2×C4⋊Dic19C2×C411yescharacteristic
35C2×Dic19⋊C4—22no—
36C2×C4×Dic19C2×C411yescharacteristic
37C2×C4×Dic19C2×C411yescharacteristic
38C2×C4×Dic19D412yes—
39C2×C4×Dic19D412yes—
40C22×C19⋊C8—22no—
41#10597339—42no—
42(C22⋊D19)⋊C4—44no—
43(C22⋊D19)⋊C4—44no—
44#10597272—28no—
45C24×C19—21no—
46C23×D19—21no—
47C2×D4×C19—21no—
48C2×D4×C19—41no—
49C2×D4×C19—41no—
50C2×D4×C19M1612yes—
51C22×C4×C19—21no—
52C22×C4×C19C22×C411yescharacteristic
53C22×C4×C19C2×D412yes—
54C2×C22⋊D19—28no—
55C2×C22⋊D19—44no—
56C2×C22⋊D19—44no—
57C22×Dic19—21no—
58C22×Dic19—44no—
59C22×Dic19—42no—
60C22×Dic19C22⋊C411yescharacteristic
61C22×Dic19C22⋊C411yescharacteristic
62C22×Dic19C22⋊C412yes—
63C2×D76—21no—
64C2×D76—41no—
65C2×D76—41no—
66C2×D76M1612yes—
67C2×C4×D19—44no—
68C2×C4×D19—42no—
69C2×C8×C19—24no—
70C2×C8×C19—42no—
71C2×C8×C19—42no—
72C4⋊C4×C19—41no—
73C22⋊C4×C19—42no—
74C22⋊C4×C19—42no—
75C42×C19—41no—
76C22⋊Dic19—42no—
77(C2×D19)⋊C4—42no—
78(C2×D19)⋊C4—42no—
79(C2×D19)⋊C4—42no—
80C4⋊Dic19—41no—
81Dic19⋊C4—44no—
82C4×Dic19—21no—
83C4×Dic19—21no—
84C4×Dic19—22no—
85C4×Dic19—22no—
86C4×Dic19—22no—
87C4×Dic19—24no—
88C2×C19⋊C8—24no—
89C2×C19⋊C8—42no—
90C2×C19⋊C8—42no—
91#7637—191nomaximal, Sylow
92C23×C19—22no—
93C23×C19—41no—
94C23×C19—41no—
95C23×C19—42no—
96C23×C19—42no—
97C23×C19C2×C22⋊C411yescharacteristic
98C22×D19—22no—
99C22×D19—41no—
100C22×D19—41no—
101C22×D19—42no—
102C22×D19—42no—
103D4×C19—42no—
104D4×C19—42no—
105C2×C4×C19—22no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—22no—
109C2×C4×C19—41no—
110C2×C4×C19—42no—
111C2×C4×C19C2×M1611yescharacteristic
112C2×C4×C19C2×M1611yescharacteristic
113C2×C4×C19AGL(1,ℤ/8)12yes—
114C2×C4×C19AGL(1,ℤ/8)12yes—
115C22⋊D19—416no—
116C2×Dic19—22no—
117C2×Dic19—22no—
118C2×Dic19—22no—
119C2×Dic19—21no—
120C2×Dic19—22no—
121C2×Dic19—41no—
122C2×Dic19—42no—
123C2×Dic19—84no—
124C2×Dic19#10012yes—
125C2×Dic19#10414yes—
126D76—42no—
127D76—42no—
128C4×D19—84no—
129C8×C19—44no—
130C19⋊C8—44no—
131C4×#127—191no—
132#1745—192no—
133#1270—191no—
134#1270—192no—
135#1270D1911yescharacteristic, complemented
136C22×C19—42no—
137C22×C19—44no—
138C22×C19—81no—
139C22×C19—82no—
140C22×C19—81no—
141C22×C19#40711yescharacteristic
142C22×C19#41011yescharacteristic
143C22×C19C2×#10011yescharacteristic
144C22×C19#41812yes—
145C22×C19C2×#10412yes—
146C2×D19—42no—
147C2×D19—44no—
148C2×D19—81no—
149C2×D19—82no—
150C2×D19—81no—
151C4×C19—21no—
152C4×C19—21no—
153C4×C19—22no—
154C4×C19—22no—
155C4×C19—81no—
156Dic19—22no—
157Dic19—24no—
158Dic19—41no—
159Dic19—81no—
160C2×#127—191no—
161C2×C4×D4—191no—
162C2×C4×D4—191no—
163C2×C4×D4—382no—
164C2×#97—382no—
165#390—191no—
166#390—382no—
167#390C2×D1911yescharacteristic
168#384—191no—
169C43—191no—
170#336—192no—
171#336—382no—
172#336C2×D1912yes—
173C2×C19—82no—
174C2×C19#146611yescharacteristic
175C2×C19#149012yes—
176C2×C19#150512yes—
177C2×C19#152511yescharacteristic
178C2×C19#155511yescharacteristic
179D19—82no—
180C22×D4—191no—
181C22×D4—382no—
182C22×D4C4×D1911yescharacteristic
183C23×C4—381no—
184C23×C4—381no—
185C22×C8—22no—
186C22×C8—382no—
187#127—382no—
188#127—382no—
189C4×D4—764no—
190C4×D4—764no—
191C4×D4—762no—
192C4×D4—762no—
193C2×C4⋊C4—191no—
194C2×C4⋊C4—382no—
195C2×C4⋊C4C4×D1911yescharacteristic
196C2×C22⋊C4—22no—
197C2×C22⋊C4—381no—
198C2×C22⋊C4—381no—
199C2×C22⋊C4—382no—
200C2×C42—191no—
201C2×C42—191no—
202C2×C42—192no—
203C2×C42—192no—
204C2×C42C22×D1911yescharacteristic
205#97—388no—
206C19#763711yescharacteristic, complemented, Sylow
207C24—21no—
208C24—381no—
209C2×D4—21no—
210C2×D4—41no—
211C2×D4—41no—
212C2×D4—192no—
213C2×D4—388no—
214C2×D4—381no—
215C2×D4—761no—
216C2×D4—761no—
217C2×D4—764no—
218C2×D4—764no—
219C2×D4#6451512yes—
220C22×C4—21no—
221C22×C4—192no—
222C22×C4—191no—
223C22×C4—191no—
224C22×C4—381no—
225C22×C4—762no—
226C22×C4—764no—
227C22×C4—762no—
228C22×C4—764no—
229C22×C4C2×C4×D1911yescharacteristic
230C22×C4D4×D1912yes—
231C2×C8—24no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—384no—
235C2×C8—762no—
236C2×C8—762no—
237C4⋊C4—41no—
238C4⋊C4—761no—
239C4⋊C4—764no—
240C22⋊C4—42no—
241C22⋊C4—42no—
242C22⋊C4—762no—
243C22⋊C4—762no—
244C22⋊C4—762no—
245C22⋊C4—762no—
246C42—41no—
247C42—384no—
248C42—382no—
249C42—381no—
250C42—381no—
251C42—382no—
252C42—382no—
253C23—22no—
254C23—42no—
255C23—42no—
256C23—41no—
257C23—41no—
258C23—382no—
259C23—762no—
260C23—762no—
261C23—761no—
262C23—761no—
263C23C22⋊C4×D1911yescharacteristic
264D4—42no—
265D4—42no—
266D4—762no—
267D4—762no—
268D4—7616no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—194no—
276C2×C4—192no—
277C2×C4—382no—
278C2×C4—382no—
279C2×C4—382no—
280C2×C4—382no—
281C2×C4—381no—
282C2×C4—762no—
283C2×C4—761no—
284C2×C4—1524no—
285C2×C4—1524no—
286C2×C4C2×#6451511yescharacteristic
287C2×C4M16×D1911yescharacteristic
288C2×C4#1059735712yes—
289C2×C4#1059736012yes—
290C8—44no—
291C8—764no—
292C22—44no—
293C22—42no—
294C22—81no—
295C22—82no—
296C22—81no—
297C22—764no—
298C22—762no—
299C22—1521no—
300C22—1522no—
301C22—1521no—
302C22#1192650611yescharacteristic
303C22#1192651611yescharacteristic
304C22#100×D1911yescharacteristic
305C22#1192654712yes—
306C22#104×D1912yes—
307C4—22no—
308C4—22no—
309C4—21no—
310C4—21no—
311C4—81no—
312C4—384no—
313C4—382no—
314C4—761no—
315C4—1521no—
316C2—82no—
317C2—1522no—
318C2#1456197411yescharacteristic
319C2#1456207612yes—
320C2#1456214112yes—
321C2#1456222511yescharacteristic
322C2#1456234711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1270C2
socleC23×C19C2×C22⋊C4
prime radicalC2×#10597386C4
cosocleC2×C42×C19C23
hypercenter#1270D19
hypocenterC19#7637
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #14563382C2semidirect
3. #14561456C2semidirect
4. #14561455C2semidirect
5. C19×#1270C2semidirect
135. #1270D19semidirect
206. C19#7637semidirect

Maximal subgroups

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

subgroupindex
#145661992
#145633822
#145614562
#145614552
C19×#12702
#763719