Finite Group Databasebeta

← #18075182

Subgroups — #18075182

Order 4864.

778 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 778 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C22×#10597335C211yesmaximal, characteristic
2#14563713C212yesmaximal
3#14561965C211yesmaximal, characteristic
4#14561964C212yesmaximal
5C19×#1463C211yesmaximal, characteristic
6C2×#10597335—24no—
7C2×#10597335—24no—
8C2×#10597335—22no—
9C2×#10597335—22no—
10C22×C4⋊Dic19C2211yescharacteristic
11C22×Dic19⋊C4C411yescharacteristic
12C22×Dic19⋊C4C411yescharacteristic
13C22×Dic19⋊C4C411yescharacteristic
14C22×Dic19⋊C4C2211yescharacteristic
15C22×C4×Dic19C411yescharacteristic
16#11926508C2212yes—
17#11926312—24no—
18#11926270—22no—
19#11926269—24no—
20C22×C4⋊C4×C19C2211yescharacteristic
21C19×#407C2212yes—
22C19×#324—22no—
23C23×C4×C19C2×C411yescharacteristic
24C23×C4×C19C2×C411yescharacteristic
25C23×C4×C19C2311yescharacteristic
26C23×Dic19C2×C411yescharacteristic
27C23×Dic19C2×C411yescharacteristic
28C23×Dic19C2×C411yescharacteristic
29C23×Dic19C2×C411yescharacteristic
30C2×M16×C19—22no—
31C2×C4⋊C4×C19—22no—
32C2×C4⋊C4×C19—22no—
33C2×C4⋊C4×C19D412yes—
34C2×C4⋊C4×C19D412yes—
35C2×C4⋊Dic19—21no—
36C2×C4⋊Dic19—22no—
37C2×C4⋊Dic19—21no—
38C2×C4⋊Dic19D414yes—
39C2×Dic19⋊C4—22no—
40C2×Dic19⋊C4—22no—
41C2×Dic19⋊C4—22no—
42C2×Dic19⋊C4—21no—
43C2×Dic19⋊C4—22no—
44C2×Dic19⋊C4—21no—
45C2×Dic19⋊C4—22no—
46C2×Dic19⋊C4—22no—
47C2×Dic19⋊C4—22no—
48C2×Dic19⋊C4—22no—
49C2×Dic19⋊C4—22no—
50C2×Dic19⋊C4—22no—
51C2×Dic19⋊C4D414yes—
52C2×C4×Dic19—22no—
53C2×C4×Dic19—22no—
54C2×C4×Dic19—22no—
55C2×#64520—22no—
56#10597335—216no—
57#10597335—216no—
58C19×C22⋊C8—22no—
59C19×C22⋊C8—22no—
60C22⋊(C19⋊C8)—22no—
61C22⋊(C19⋊C8)—22no—
62C24×C19C22×C411yescharacteristic
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19—21no—
66C22×C4×C19—21no—
67C22×C4×C19—42no—
68C22×C4×C19—42no—
69C22×C4×C19—42no—
70C22×C4×C19C22⋊C412yes—
71C22×C4×C19C22⋊C412yes—
72C22×C4×C19C2×D411yescharacteristic
73C22×C4×C19C2×D412yes—
74C22×C4×C19C2×D412yes—
75C22×C4×C19C2×D411yescharacteristic
76C22×Dic19—21no—
77C22×Dic19—21no—
78C22×Dic19—24no—
79C22×Dic19—21no—
80C22×Dic19—21no—
81C22×Dic19—21no—
82C22×Dic19—21no—
83C22×Dic19—21no—
84C22×Dic19—21no—
85C22×Dic19—42no—
86C22×Dic19—42no—
87C22×Dic19—42no—
88C22×Dic19C22⋊C412yes—
89C22×Dic19C22⋊C412yes—
90C22×Dic19C22⋊C412yes—
91C22×Dic19C22⋊C412yes—
92M16×C19—44no—
93C2×C8×C19—42no—
94C4⋊C4×C19—24no—
95C4⋊C4×C19—24no—
96C4⋊Dic19—24no—
97C4⋊Dic19—24no—
98Dic19⋊C4—28no—
99Dic19⋊C4—28no—
100Dic19⋊C4—28no—
101Dic19⋊C4—24no—
102Dic19⋊C4—24no—
103C4×Dic19—28no—
104#64520—44no—
105C2×C19⋊C8—42no—
106#8554—191nomaximal, Sylow
107C23×C19—22no—
108C23×C19—22no—
109C23×C19—22no—
110C23×C19C2×C22⋊C411yescharacteristic
111C23×C19C2×C22⋊C411yescharacteristic
112C23×C19C2×C22⋊C411yescharacteristic
113C2×C4×C19—24no—
114C2×C4×C19—22no—
115C2×C4×C19—22no—
116C2×C4×C19—24no—
117C2×C4×C19—41no—
118C2×C4×C19—42no—
119C2×C4×C19—41no—
120C2×C4×C19—42no—
121C2×C4×C19—42no—
122C2×C4×C19—42no—
123C2×C4×C19—42no—
124C2×C4×C19—42no—
125C2×C4×C19#12012yes—
126C2×C4×C19#12012yes—
127C2×Dic19—24no—
128C2×Dic19—24no—
129C2×Dic19—22no—
130C2×Dic19—22no—
131C2×Dic19—22no—
132C2×Dic19—22no—
133C2×Dic19—22no—
134C2×Dic19—42no—
135C2×Dic19—42no—
136C2×Dic19—42no—
137C2×Dic19—42no—
138C2×Dic19—42no—
139C2×Dic19—42no—
140C2×Dic19—42no—
141C2×Dic19—42no—
142C2×Dic19—42no—
143C2×Dic19#10114yes—
144C8×C19—82no—
145C19⋊C8—82no—
146C22×#125—191no—
147#1821—192no—
148#1463—192no—
149#1463—191no—
150#1463D1911yescharacteristic
151C22×C19—28no—
152C22×C19—21no—
153C22×C19—21no—
154C22×C19—21no—
155C22×C19—21no—
156C22×C19—21no—
157C22×C19—21no—
158C22×C19#37911yescharacteristic
159C22×C19#41012yes—
160C22×C19C2×#10112yes—
161C22×C19#41312yes—
162C4×C19—22no—
163C4×C19—22no—
164C4×C19—42no—
165C4×C19—42no—
166Dic19—24no—
167Dic19—42no—
168Dic19—42no—
169Dic19—42no—
170C2×#125—384no—
171C2×#125—384no—
172C2×#125—382no—
173C2×#125—382no—
174C22×C4⋊C4—191no—
175C22×C4⋊C4—191no—
176C22×C4⋊C4—191no—
177C22×C4⋊C4—191no—
178C22×C4⋊C4—191no—
179C22×C4⋊C4C2×D1911yescharacteristic
180C22×C42—191no—
181#407—192no—
182#407C2×D1912yes—
183#343—384no—
184#324—22no—
185#324—384no—
186#324—382no—
187C2×C19—22no—
188C2×C19—22no—
189C2×C19—22no—
190C2×C19#178211yescharacteristic
191C2×C19#178411yescharacteristic
192C2×C19#178511yescharacteristic
193C23×C4—191no—
194C23×C4—191no—
195C23×C4—191no—
196C23×C4—191no—
197C23×C4C4×D1911yescharacteristic
198C23×C4C4×D1911yescharacteristic
199C23×C4C22×D1911yescharacteristic
200C2×M16—22no—
201C2×M16—382no—
202#125—3816no—
203#125—3816no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—194no—
207C2×C4⋊C4—194no—
208C2×C4⋊C4—382no—
209C2×C4⋊C4—382no—
210C2×C4⋊C4—382no—
211C2×C4⋊C4—382no—
212C2×C4⋊C4—382no—
213C2×C4⋊C4—382no—
214C2×C4⋊C4—382no—
215C2×C4⋊C4—382no—
216C2×C4⋊C4—382no—
217C2×C4⋊C4—381no—
218C2×C4⋊C4—381no—
219C2×C4⋊C4—382no—
220C2×C4⋊C4—382no—
221C2×C4⋊C4—381no—
222C2×C4⋊C4—381no—
223C2×C4⋊C4D7612yes—
224C2×C4⋊C4C22⋊D1912yes—
225C2×C42—382no—
226C2×C42—382no—
227C2×C42—382no—
228C22⋊C8—22no—
229C22⋊C8—22no—
230C22⋊C8—382no—
231C22⋊C8—382no—
232C19#855411yescharacteristic, complemented, Sylow
233C24C2×C4×D1911yescharacteristic
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—192no—
242C22×C4—192no—
243C22×C4—192no—
244C22×C4—192no—
245C22×C4—384no—
246C22×C4—381no—
247C22×C4—381no—
248C22×C4—381no—
249C22×C4—381no—
250C22×C4—381no—
251C22×C4—381no—
252C22×C4—381no—
253C22×C4—381no—
254C22×C4—762no—
255C22×C4—762no—
256C22×C4—762no—
257C22×C4(C2×D19)⋊C412yes—
258C22×C4(C2×D19)⋊C412yes—
259C22×C4C2×D7611yescharacteristic
260C22×C4D4×D1912yes—
261C22×C4D4×D1912yes—
262C22×C4C2×C22⋊D1911yescharacteristic
263M16—44no—
264M16—764no—
265C2×C8—42no—
266C2×C8—762no—
267C4⋊C4—24no—
268C4⋊C4—24no—
269C4⋊C4—388no—
270C4⋊C4—388no—
271C4⋊C4—388no—
272C4⋊C4—384no—
273C4⋊C4—384no—
274C4⋊C4—384no—
275C4⋊C4—384no—
276C42—388no—
277C23—22no—
278C23—22no—
279C23—22no—
280C23C22⋊C4×D1911yescharacteristic
281C23C22⋊C4×D1911yescharacteristic
282C23C2×(C2×D19)⋊C411yescharacteristic
283C2×C4—24no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—24no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—194no—
296C2×C4—384no—
297C2×C4—384no—
298C2×C4—382no—
299C2×C4—382no—
300C2×C4—382no—
301C2×C4—382no—
302C2×C4—382no—
303C2×C4—762no—
304C2×C4—762no—
305C2×C4—762no—
306C2×C4—762no—
307C2×C4—762no—
308C2×C4—762no—
309C2×C4—762no—
310C2×C4—762no—
311C2×C4—762no—
312C2×C4#1059732812yes—
313C2×C4#1059738312yes—
314C8—82no—
315C8—1522no—
316C22—28no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22#1192639911yescharacteristic
324C22#1192651612yes—
325C22#101×D1912yes—
326C22#1192652612yes—
327C4—22no—
328C4—22no—
329C4—42no—
330C4—42no—
331C4—384no—
332C4—762no—
333C4—762no—
334C4—762no—
335C2—22no—
336C2—22no—
337C2—22no—
338C2#1456355111yescharacteristic
339C2#1456355711yescharacteristic
340C2#1456356111yescharacteristic
subgroupG/H
centerC22#11926399
commutator, prime radicalC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1463C2
socleC22×C19#379
cosocleC23×C4×C19C23
hypercenter#1463D19
hypocenterC19#8554
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
232. C19#8554semidirect

Maximal subgroups

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

subgroupindex
C22×#105973352
#145637132
#145619652
#145619642
C19×#14632
#855419