Finite Group Databasebeta

← #18070782

Subgroups — #18070782

Order 4864.

730 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 105 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#14566124C211yesmaximal, characteristic
2#14563327C212yesmaximal, complemented
3#14561461C211yesmaximal, characteristic, complemented
4#14561455C212yesmaximal, complemented
5C19×#1272C211yesmaximal, characteristic, complemented
6C22×#64545C411yescharacteristic
7C22×#64515—22no—
8C2×#10597338C411yescharacteristic
9C2×C42×D19C2211yescharacteristic
10#11926451C411yescharacteristic
11#11926446C2211yescharacteristic
12#11926445C411yescharacteristic
13#11926422—22no—
14#11926391—22no—
15#11926299C2212yes—
16#11926298—22no—
17C19×#391C2211yescharacteristic
18C19×#336C2212yes—
19C22×Q8×C19C2×C411yescharacteristic
20C2×#64545—22no—
21C2×#64545—22no—
22C2×#64545—42no—
23C2×#64545—42no—
24C22×D76—21no—
25C22×D76C2×C411yescharacteristic
26C22×C4×D19—21no—
27C22×C4×D19C2×C411yescharacteristic
28C22×C4×D19D412yes—
29C22×C8×C19—22no—
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C42×C19C2311yescharacteristic
32C2×(C2×D19)⋊C4—21no—
33C2×(C2×D19)⋊C4—22no—
34C2×(C2×D19)⋊C4—22no—
35C2×C4⋊Dic19C2×C411yescharacteristic
36C2×C4×Dic19—21no—
37C2×C4×Dic19C2×C411yescharacteristic
38C2×C4×Dic19D412yes—
39C22×C19⋊C8—22no—
40C2×#64515—28no—
41C2×#64515—44no—
42C2×#64515—44no—
43#10597338—42no—
44C42×D19—42no—
45C19×#95—22no—
46C19⋊#95—22no—
47C23×D19—21no—
48C23×D19C22⋊C411yescharacteristic
49C2×Q8×C19—21no—
50C2×Q8×C19—41no—
51C2×Q8×C19—41no—
52C2×Q8×C19M1612yescomplemented
53C22×C4×C19—21no—
54C22×C4×C19—21no—
55C22×C4×C19C22×C411yescharacteristic
56C22×C4×C19C2×D412yes—
57C22×Dic19—21no—
58C22×Dic19C22⋊C411yescharacteristic
59C22×Dic19C22⋊C412yes—
60#64545—48no—
61#64545—48no—
62C2×D76—24no—
63C2×D76—21no—
64C2×D76—41no—
65C2×D76—41no—
66C2×D76—42no—
67C2×D76—42no—
68C2×D76M1612yescomplemented
69C2×C4×D19—22no—
70C2×C4×D19—24no—
71C2×C4×D19—21no—
72C2×C4×D19—21no—
73C2×C4×D19—22no—
74C2×C4×D19—22no—
75C2×C4×D19—22no—
76C2×C4×D19—24no—
77C2×C4×D19—24no—
78C2×C4×D19—42no—
79C2×C4×D19—42no—
80C2×C8×C19—24no—
81C2×C8×C19—42no—
82C2×C8×C19—42no—
83C4⋊C4×C19—41no—
84C42×C19—41no—
85(C2×D19)⋊C4—42no—
86(C2×D19)⋊C4—42no—
87(C2×D19)⋊C4—42no—
88(C2×D19)⋊C4—44no—
89C4⋊Dic19—41no—
90C4×Dic19—41no—
91C4×Dic19—42no—
92C4×Dic19—42no—
93C2×C19⋊C8—24no—
94C2×C19⋊C8—42no—
95C2×C19⋊C8—42no—
96#64515—416no—
97#7631—191nomaximal, Sylow
98C23×C19C2×C22⋊C411yescharacteristic
99C22×D19—21no—
100C22×D19—21no—
101C22×D19—22no—
102C22×D19—22no—
103C22×D19—22no—
104C22×D19—41no—
105C22×D19—41no—
106C22×D19—42no—
107C22×D19—42no—
108C22×D19#9912yes—
109Q8×C19—42no—
110Q8×C19—42no—
111C2×C4×C19—22no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—22no—
115C2×C4×C19—22no—
116C2×C4×C19—41no—
117C2×C4×C19—41no—
118C2×C4×C19—41no—
119C2×C4×C19—42no—
120C2×C4×C19C2×M1611yescharacteristic
121C2×C4×C19C2×M1611yescharacteristic
122C2×C4×C19AGL(1,ℤ/8)12yes—
123C2×C4×C19#13712yes—
124C2×Dic19—21no—
125C2×Dic19—21no—
126C2×Dic19—22no—
127C2×Dic19—22no—
128C2×Dic19—41no—
129C2×Dic19—42no—
130C2×Dic19#10012yes—
131C2×Dic19#10414yes—
132D76—42no—
133D76—42no—
134D76—48no—
135C4×D19—28no—
136C4×D19—28no—
137C4×D19—24no—
138C4×D19—24no—
139C4×D19—48no—
140C8×C19—44no—
141C19⋊C8—44no—
142#2297—191no—
143#1728—192no—
144#1272—191no—
145#1272D1911yescharacteristic, complemented
146#1270—192no—
147C22×C19#40711yescharacteristic
148C22×C19C2×#9911yescharacteristic
149C22×C19C2×#10011yescharacteristic
150C22×C19#41712yes—
151C22×C19C2×#10412yes—
152C2×D19—22no—
153C2×D19—24no—
154C2×D19—41no—
155C2×D19—42no—
156C2×D19—41no—
157C2×D19—42no—
158C2×D19—44no—
159C2×D19—81no—
160C2×D19—82no—
161C2×D19—81no—
162C4×C19—21no—
163C4×C19—21no—
164C4×C19—22no—
165C4×C19—22no—
166C4×C19—42no—
167C4×C19—81no—
168Dic19—22no—
169Dic19—24no—
170Dic19—81no—
171C22×#41—191no—
172C22×M16—382no—
173C2×#117—191no—
174C22×C42—191no—
175#391—191no—
176#391C2×D1911yescharacteristic
177#390—191no—
178#390—191no—
179#386—382no—
180C4×C22⋊C4—382no—
181#336—192no—
182#336—382no—
183#336C2×D1912yes—
184C2×C19#146211yescharacteristic
185C2×C19#148912yes—
186C2×C19#150412yes—
187C2×C19#152511yescharacteristic
188C2×C19#156011yescharacteristic
189D19—42no—
190D19—82no—
191C2×#41—382no—
192C2×#41—382no—
193C2×#41—762no—
194C2×#41—762no—
195C22×Q8C4×D1911yescharacteristic
196C22×D4—191no—
197C22×D4—381no—
198C23×C4—191no—
199C23×C4—192no—
200C23×C4—381no—
201C2×M16—388no—
202C2×M16—764no—
203C2×M16—764no—
204C22×C8—22no—
205C22×C8—382no—
206#117—762no—
207C2×C4⋊C4—191no—
208C2×C4⋊C4C4×D1911yescharacteristic
209C2×C22⋊C4—382no—
210C2×C22⋊C4—381no—
211C2×C22⋊C4—382no—
212C2×C42—191no—
213C2×C42—192no—
214C2×C42—381no—
215C2×C42—762no—
216C2×C42C22×D1911yescharacteristic
217#95—22no—
218#95—382no—
219C19#763111yescharacteristic, complemented, Sylow
220C24—191no—
221C24—381no—
222#41—768no—
223#41—768no—
224C2×Q8—21no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8#6451512yescomplemented
228C2×D4—192no—
229C2×D4—384no—
230C2×D4—381no—
231C2×D4—761no—
232C2×D4—761no—
233C2×D4—762no—
234C2×D4—762no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—192no—
238C22×C4—191no—
239C22×C4—382no—
240C22×C4—384no—
241C22×C4—384no—
242C22×C4—382no—
243C22×C4—384no—
244C22×C4—381no—
245C22×C4—381no—
246C22×C4—382no—
247C22×C4—382no—
248C22×C4—381no—
249C22×C4—762no—
250C22×C4—762no—
251C22×C4C2×C4×D1911yescharacteristic
252C22×C4D4×D1912yes—
253M16—7616no—
254C2×C8—24no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—384no—
258C2×C8—762no—
259C2×C8—762no—
260C4⋊C4—41no—
261C4⋊C4—761no—
262C22⋊C4—764no—
263C22⋊C4—762no—
264C22⋊C4—762no—
265C22⋊C4—762no—
266C42—41no—
267C42—762no—
268C42—761no—
269C42—762no—
270C23—192no—
271C23—382no—
272C23—382no—
273C23—381no—
274C23—381no—
275C23—382no—
276C23—762no—
277C23—762no—
278C23—761no—
279C23—761no—
280C23C22⋊C4×D1911yescharacteristic
281Q8—42no—
282Q8—42no—
283D4—762no—
284D4—762no—
285D4—768no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—22no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—194no—
296C2×C4—192no—
297C2×C4—388no—
298C2×C4—384no—
299C2×C4—384no—
300C2×C4—388no—
301C2×C4—382no—
302C2×C4—381no—
303C2×C4—381no—
304C2×C4—382no—
305C2×C4—768no—
306C2×C4—762no—
307C2×C4—761no—
308C2×C4C2×#6451511yescharacteristic
309C2×C4M16×D1911yescharacteristic
310C2×C4#1059736012yes—
311C2×C4#1059736412yes—
312C8—44no—
313C8—764no—
314C22—384no—
315C22—382no—
316C22—762no—
317C22—761no—
318C22—761no—
319C22—764no—
320C22—762no—
321C22—1521no—
322C22—1522no—
323C22—1521no—
324C22#1192650611yescharacteristic
325C22#99×D1911yescharacteristic
326C22#100×D1911yescharacteristic
327C22#1192654412yes—
328C22#104×D1912yes—
329C4—22no—
330C4—22no—
331C4—21no—
332C4—21no—
333C4—42no—
334C4—81no—
335C4—384no—
336C4—382no—
337C4—1521no—
338C2—762no—
339C2—1522no—
340C2#1456196011yescharacteristic
341C2#1456207312yes—
342C2#1456213812yes—
343C2#1456222511yescharacteristic
344C2#1456236911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1272C2
socleC23×C19C2×C22⋊C4
prime radicalC22×#64545C4
cosocleC2×C42×C19C23
hypercenter#1272D19
hypocenterC19#7631
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
2. #14563327C2semidirect
3. #14561461C2semidirect
4. #14561455C2semidirect
5. C19×#1272C2semidirect
52. C2×Q8×C19M16semidirect
68. C2×D76M16semidirect
145. #1272D19semidirect
219. C19#7631semidirect
227. C2×Q8#64515semidirect

Maximal subgroups

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

subgroupindex
#145661242
#145633272
#145614612
#145614552
C19×#12722
#763119