Finite Group Databasebeta

← #18070658

Subgroups — #18070658

Order 4864.

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

normal subgroups only

This group has 608 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#14566199C211yesmaximal, characteristic
2#14563777C212yesmaximal, complemented
3#14561456C211yesmaximal, characteristic, complemented
4#14561455C212yesmaximal, complemented
5C19×#1270C211yesmaximal, characteristic, complemented
6C2×#10597386C411yescharacteristic
7C2×D4×Dic19C411yescharacteristic
8C2×#10597339C411yescharacteristic
9C2×(C22⋊D19)⋊C4—22no—
10#11926446C2211yescharacteristic
11#11926444—22no—
12#11926413C411yescharacteristic
13C42×Dic19C2211yescharacteristic
14#11926299C2212yes—
15#11926298—22no—
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#10597386C814yescomplemented
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—
44C24×C19—21no—
45C23×D19—21no—
46C2×D4×C19—21no—
47C2×D4×C19—41no—
48C2×D4×C19—41no—
49C2×D4×C19C2×C812yes—
50C22×C4×C19—21no—
51C22×C4×C19C22×C411yescharacteristic
52C22×C4×C19C2×D412yes—
53C2×C22⋊D19—28no—
54C2×C22⋊D19—44no—
55C2×C22⋊D19—44no—
56C22×Dic19—21no—
57C22×Dic19—44no—
58C22×Dic19—42no—
59C22×Dic19C22⋊C411yescharacteristic
60C22×Dic19C22⋊C412yes—
61C22×Dic19C22⋊C411yescharacteristic
62C2×D76—21no—
63C2×D76—41no—
64C2×D76—41no—
65C2×D76C2×C812yes—
66C2×C4×D19—44no—
67C2×C4×D19—42no—
68C2×C8×C19—42no—
69C2×C8×C19—42no—
70C2×C8×C19—42no—
71C4⋊C4×C19—41no—
72C22⋊C4×C19—42no—
73C22⋊C4×C19—42no—
74C42×C19—41no—
75C22⋊Dic19—42no—
76(C2×D19)⋊C4—42no—
77(C2×D19)⋊C4—42no—
78(C2×D19)⋊C4—42no—
79C4⋊Dic19—41no—
80Dic19⋊C4—44no—
81C4×Dic19—22no—
82C4×Dic19—22no—
83C4×Dic19—22no—
84C4×Dic19—42no—
85C4×Dic19C2×C812yes—
86C4×Dic19M1612yes—
87C2×C19⋊C8—42no—
88C2×C19⋊C8—42no—
89C2×C19⋊C8—42no—
90#7603—191nomaximal, Sylow
91C23×C19—22no—
92C23×C19—41no—
93C23×C19—41no—
94C23×C19—42no—
95C23×C19—42no—
96C23×C19C2×C22⋊C411yescharacteristic
97C22×D19—22no—
98C22×D19—41no—
99C22×D19—41no—
100C22×D19—42no—
101C22×D19—42no—
102D4×C19—42no—
103D4×C19—42no—
104C2×C4×C19—22no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—22no—
108C2×C4×C19—41no—
109C2×C4×C19—42no—
110C2×C4×C19C22×C811yescharacteristic
111C2×C4×C19C2×M1611yescharacteristic
112C2×C4×C19AGL(1,ℤ/8)12yes—
113C2×C4×C19AGL(1,ℤ/8)12yes—
114C22⋊D19—416no—
115C2×Dic19—22no—
116C2×Dic19—22no—
117C2×Dic19—22no—
118C2×Dic19—21no—
119C2×Dic19—22no—
120C2×Dic19—41no—
121C2×Dic19—42no—
122C2×Dic19—84no—
123C2×Dic19C22⋊C814yes—
124C2×Dic19#10012yes—
125D76—42no—
126D76—42no—
127C4×D19—84no—
128C8×C19—82no—
129C19⋊C8—82no—
130C4×#127—191no—
131#1839—192no—
132#1270—191no—
133#1270—192no—
134#1270D1911yescharacteristic, complemented
135C22×C19—42no—
136C22×C19—44no—
137C22×C19—81no—
138C22×C19—81no—
139C22×C19—82no—
140C22×C19C2×C22⋊C811yescharacteristic
141C22×C19#41011yescharacteristic
142C22×C19C2×#10011yescharacteristic
143C22×C19#41812yes—
144C22×C19#42112yes—
145C2×D19—42no—
146C2×D19—44no—
147C2×D19—81no—
148C2×D19—81no—
149C2×D19—82no—
150C4×C19—21no—
151C4×C19—21no—
152C4×C19—22no—
153C4×C19—22no—
154C4×C19—81no—
155Dic19—22no—
156Dic19—24no—
157Dic19—41no—
158Dic19—81no—
159C2×#127—191no—
160C2×C4×D4—191no—
161C2×C4×D4—191no—
162C2×C4×D4—382no—
163#390—191no—
164#390—382no—
165#390C2×D1911yescharacteristic
166#384—191no—
167C43—191no—
168#336—192no—
169#336—382no—
170#336—382no—
171#336C2×D1912yes—
172C2×C19—82no—
173C2×C19#146011yescharacteristic
174C2×C19#147812yes—
175C2×C19#151412yes—
176C2×C19#153611yescharacteristic
177C2×C19#155511yescharacteristic
178D19—82no—
179C22×D4—191no—
180C22×D4—382no—
181C22×D4C4×D1911yescharacteristic
182C23×C4—381no—
183C23×C4—381no—
184C22×C8—22no—
185C22×C8—382no—
186#127—194no—
187#127—382no—
188C4×D4—764no—
189C4×D4—764no—
190C4×D4—762no—
191C4×D4—762no—
192C2×C4⋊C4—191no—
193C2×C4⋊C4—382no—
194C2×C4⋊C4C4×D1911yescharacteristic
195C2×C22⋊C4—22no—
196C2×C22⋊C4—381no—
197C2×C22⋊C4—381no—
198C2×C22⋊C4—382no—
199C2×C42—191no—
200C2×C42—191no—
201C2×C42—192no—
202C2×C42—192no—
203C2×C42C22×D1911yescharacteristic
204C19#760311yescharacteristic, complemented, Sylow
205C24—21no—
206C24—381no—
207C2×D4—21no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—192no—
211C2×D4—388no—
212C2×D4—381no—
213C2×D4—761no—
214C2×D4—761no—
215C2×D4—764no—
216C2×D4—764no—
217C2×D4C8×D1912yes—
218C22×C4—21no—
219C22×C4—192no—
220C22×C4—191no—
221C22×C4—191no—
222C22×C4—381no—
223C22×C4—762no—
224C22×C4—764no—
225C22×C4—762no—
226C22×C4—764no—
227C22×C4C2×C4×D1911yescharacteristic
228C22×C4D4×D1912yes—
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—762no—
233C2×C8—762no—
234C2×C8—762no—
235C4⋊C4—41no—
236C4⋊C4—761no—
237C4⋊C4—764no—
238C22⋊C4—42no—
239C22⋊C4—42no—
240C22⋊C4—762no—
241C22⋊C4—762no—
242C22⋊C4—762no—
243C22⋊C4—762no—
244C42—41no—
245C42—192no—
246C42—192no—
247C42—382no—
248C42—382no—
249C42—382no—
250C42—762no—
251C23—22no—
252C23—42no—
253C23—42no—
254C23—41no—
255C23—41no—
256C23—382no—
257C23—762no—
258C23—762no—
259C23—761no—
260C23—761no—
261C23C22⋊C4×D1911yescharacteristic
262D4—42no—
263D4—42no—
264D4—762no—
265D4—762no—
266D4—7616no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—194no—
274C2×C4—192no—
275C2×C4—382no—
276C2×C4—382no—
277C2×C4—382no—
278C2×C4—382no—
279C2×C4—381no—
280C2×C4—762no—
281C2×C4—761no—
282C2×C4—1524no—
283C2×C4—1524no—
284C2×C4C2×C8×D1911yescharacteristic
285C2×C4M16×D1911yescharacteristic
286C2×C4#1059735712yes—
287C2×C4#1059736012yes—
288C8—82no—
289C8—1522no—
290C22—42no—
291C22—44no—
292C22—81no—
293C22—82no—
294C22—81no—
295C22—762no—
296C22—764no—
297C22—1521no—
298C22—1522no—
299C22—1521no—
300C22C22⋊C8×D1911yescharacteristic
301C22#1192651611yescharacteristic
302C22#100×D1911yescharacteristic
303C22#1192654712yes—
304C22#1192655912yes—
305C4—22no—
306C4—22no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—382no—
311C4—384no—
312C4—761no—
313C4—1521no—
314C2—82no—
315C2—1522no—
316C2#1456195411yescharacteristic
317C2#1456202412yes—
318C2#1456218012yes—
319C2#1456226811yescharacteristic
320C2#1456234711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC2×C4×C19C22×C8
FrattiniC2×C42C22×D19
FittingC19×#1270C2
socleC23×C19C2×C22⋊C4
prime radicalC2×#10597386C4
cosocleC2×C42×C19C23
hypercenter#1270D19
hypocenterC19#7603
LCSG ▷ C2×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. #14563777C2semidirect
3. #14561456C2semidirect
4. #14561455C2semidirect
5. C19×#1270C2semidirect
30. #10597386C8semidirect
134. #1270D19semidirect
204. C19#7603semidirect

Maximal subgroups

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

subgroupindex
#145661992
#145637772
#145614562
#145614552
C19×#12702
#760319