Finite Group Databasebeta

← #18070780

Subgroups — #18070780

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#14566122C211yesmaximal, characteristic
2#14563327C212yesmaximal, complemented
3#14561460C212yesmaximal, complemented
4#14561456C211yesmaximal, characteristic, complemented
5C19×#1270C211yesmaximal, characteristic, complemented
6C22×#64543C411yescharacteristic
7C22×#64515—22no—
8C2×#10597338C411yescharacteristic
9C2×C42×D19C2211yescharacteristic
10#11926450C2211yescharacteristic
11#11926449C411yescharacteristic
12#11926447C411yescharacteristic
13#11926420—22no—
14C22⋊C4×Dic19—22no—
15#11926299C2212yes—
16#11926298—22no—
17C19×#390C2211yescharacteristic
18C19×#336C2212yes—
19C22×D4×C19C2×C411yescharacteristic
20C22×C22⋊D19—21no—
21C23×Dic19—21no—
22C2×#64543—22no—
23C2×#64543—22no—
24C2×#64543—42no—
25C2×#64543—42no—
26C22×C4×D19C2×C411yescharacteristic
27C22×C4×D19D412yes—
28C22×Dic38C2×C411yescharacteristic
29C22×C8×C19—22no—
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C22⋊C4×C19—22no—
32C2×C42×C19C2311yescharacteristic
33C2×C22⋊Dic19—22no—
34C2×(C2×D19)⋊C4—21no—
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—
47C24×C19—21no—
48C23×D19C22⋊C411yescharacteristic
49C2×D4×C19—21no—
50C2×D4×C19—41no—
51C2×D4×C19—41no—
52C2×D4×C19M1612yescomplemented
53C22×C4×C19—21no—
54C22×C4×C19C22×C411yescharacteristic
55C22×C4×C19C2×D412yes—
56C2×C22⋊D19—24no—
57C2×C22⋊D19—42no—
58C2×C22⋊D19—42no—
59C22×Dic19—24no—
60C22×Dic19—21no—
61C22×Dic19—21no—
62C22×Dic19—42no—
63C22×Dic19—42no—
64C22×Dic19C22⋊C411yescharacteristic
65C22×Dic19C22⋊C412yes—
66#64543—48no—
67#64543—48no—
68C2×C4×D19—22no—
69C2×C4×D19—24no—
70C2×C4×D19—21no—
71C2×C4×D19—21no—
72C2×C4×D19—22no—
73C2×C4×D19—22no—
74C2×C4×D19—22no—
75C2×C4×D19—24no—
76C2×Dic38—21no—
77C2×Dic38—41no—
78C2×Dic38—41no—
79C2×Dic38M1612yescomplemented
80C2×C8×C19—24no—
81C2×C8×C19—42no—
82C2×C8×C19—42no—
83C4⋊C4×C19—41no—
84C22⋊C4×C19—42no—
85C22⋊C4×C19—42no—
86C42×C19—41no—
87C22⋊Dic19—44no—
88(C2×D19)⋊C4—42no—
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×C19—22no—
99C23×C19—41no—
100C23×C19—41no—
101C23×C19—42no—
102C23×C19—42no—
103C23×C19C2×C22⋊C411yescharacteristic
104C22×D19—21no—
105C22×D19—21no—
106C22×D19—22no—
107C22×D19—22no—
108C22×D19#9912yes—
109D4×C19—42no—
110D4×C19—42no—
111C2×C4×C19—22no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—22no—
115C2×C4×C19—41no—
116C2×C4×C19—42no—
117C2×C4×C19C2×M1611yescharacteristic
118C2×C4×C19C2×M1611yescharacteristic
119C2×C4×C19AGL(1,ℤ/8)12yes—
120C2×C4×C19#13712yes—
121C22⋊D19—48no—
122C2×Dic19—21no—
123C2×Dic19—21no—
124C2×Dic19—22no—
125C2×Dic19—22no—
126C2×Dic19—22no—
127C2×Dic19—48no—
128C2×Dic19—41no—
129C2×Dic19—41no—
130C2×Dic19—41no—
131C2×Dic19—42no—
132C2×Dic19#10012yes—
133C2×Dic19#10414yes—
134C4×D19—28no—
135C4×D19—28no—
136C4×D19—24no—
137C4×D19—24no—
138Dic38—42no—
139Dic38—42no—
140C8×C19—44no—
141C19⋊C8—44no—
142#2297—191no—
143#1728—192no—
144#1272—192no—
145#1270—191no—
146#1270D1911yescharacteristic, complemented
147C22×C19—42no—
148C22×C19—44no—
149C22×C19—81no—
150C22×C19—82no—
151C22×C19—81no—
152C22×C19#40711yescharacteristic
153C22×C19C2×#9911yescharacteristic
154C22×C19C2×#10011yescharacteristic
155C22×C19#41712yes—
156C22×C19C2×#10412yes—
157C2×D19—22no—
158C2×D19—24no—
159C2×D19—41no—
160C2×D19—42no—
161C2×D19—41no—
162C4×C19—21no—
163C4×C19—21no—
164C4×C19—22no—
165C4×C19—22no—
166C4×C19—81no—
167Dic19—22no—
168Dic19—24no—
169Dic19—42no—
170Dic19—81no—
171C22×#41—191no—
172C22×M16—382no—
173C2×#117—191no—
174C22×C42—191no—
175#391—191no—
176#391—191no—
177#390—191no—
178#390C2×D1911yescharacteristic
179#386—382no—
180C4×C22⋊C4—382no—
181#336—192no—
182#336—382no—
183#336C2×D1912yes—
184C2×C19—82no—
185C2×C19#146211yescharacteristic
186C2×C19#148912yes—
187C2×C19#150412yes—
188C2×C19#152511yescharacteristic
189C2×C19#156011yescharacteristic
190D19—42no—
191C2×#41—382no—
192C2×#41—382no—
193C2×#41—762no—
194C2×#41—762no—
195C22×Q8—191no—
196C22×D4—381no—
197C22×D4C4×D1911yescharacteristic
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—22no—
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—382no—
218#95—382no—
219C19#763111yescharacteristic, complemented, Sylow
220C24—21no—
221C24—191no—
222#41—768no—
223#41—768no—
224C2×Q8—192no—
225C2×Q8—381no—
226C2×Q8—761no—
227C2×Q8—761no—
228C2×D4—21no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4—384no—
232C2×D4—762no—
233C2×D4—762no—
234C2×D4#6451512yescomplemented
235C22×C4—21no—
236C22×C4—192no—
237C22×C4—191no—
238C22×C4—382no—
239C22×C4—384no—
240C22×C4—384no—
241C22×C4—382no—
242C22×C4—381no—
243C22×C4—381no—
244C22×C4—382no—
245C22×C4—382no—
246C22×C4—384no—
247C22×C4—381no—
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—42no—
263C22⋊C4—42no—
264C22⋊C4—762no—
265C22⋊C4—764no—
266C42—41no—
267C42—762no—
268C42—761no—
269C42—762no—
270C23—22no—
271C23—42no—
272C23—42no—
273C23—41no—
274C23—41no—
275C23—192no—
276C23—382no—
277C23—382no—
278C23—381no—
279C23—381no—
280C23C22⋊C4×D1911yescharacteristic
281Q8—762no—
282Q8—762no—
283D4—42no—
284D4—42no—
285D4—768no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—194no—
293C2×C4—192no—
294C2×C4—388no—
295C2×C4—384no—
296C2×C4—384no—
297C2×C4—388no—
298C2×C4—382no—
299C2×C4—381no—
300C2×C4—381no—
301C2×C4—382no—
302C2×C4—382no—
303C2×C4—768no—
304C2×C4—761no—
305C2×C4—761no—
306C2×C4—762no—
307C2×C4—761no—
308C2×C4C2×#6451511yescharacteristic
309C2×C4M16×D1911yescharacteristic
310C2×C4#1059735712yes—
311C2×C4#1059736112yes—
312C8—44no—
313C8—764no—
314C22—44no—
315C22—42no—
316C22—81no—
317C22—82no—
318C22—81no—
319C22—384no—
320C22—382no—
321C22—762no—
322C22—761no—
323C22—761no—
324C22#1192650611yescharacteristic
325C22#99×D1911yescharacteristic
326C22#100×D1911yescharacteristic
327C22#1192654212yes—
328C22#104×D1912yes—
329C4—22no—
330C4—22no—
331C4—21no—
332C4—21no—
333C4—81no—
334C4—384no—
335C4—382no—
336C4—762no—
337C4—1521no—
338C2—82no—
339C2—762no—
340C2#1456196011yescharacteristic
341C2#1456207112yes—
342C2#1456213612yes—
343C2#1456222511yescharacteristic
344C2#1456236711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1270C2
socleC23×C19C2×C22⋊C4
prime radicalC22×#64543C4
cosocleC2×C42×C19C23
hypercenter#1270D19
hypocenterC19#7631
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. #14563327C2semidirect
3. #14561460C2semidirect
4. #14561456C2semidirect
5. C19×#1270C2semidirect
52. C2×D4×C19M16semidirect
79. C2×Dic38M16semidirect
146. #1270D19semidirect
219. C19#7631semidirect
234. C2×D4#64515semidirect

Maximal subgroups

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

subgroupindex
#145661222
#145633272
#145614602
#145614562
C19×#12702
#763119