Finite Group Databasebeta

← #18080184

Subgroups — #18080184

Order 4864.

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

normal subgroups only

This group has 474 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#14572273C211yesmaximal, characteristic
2#14563712C211yesmaximal, characteristic
3#14562168C212yesmaximal
4#14561488C212yesmaximal
5C19×#2499C211yesmaximal, characteristic
6#11926605—24no—
7#11926568—21no—
8#11926508C2212yes—
9C4×#64520—21no—
10#11926407C2212yes—
11#11926311—21no—
12#11926311—21no—
13#11926281—24no—
14C2×C19×C22⋊Q8C2211yescharacteristic
15C2×C19×#117C2211yescharacteristic
16C19×#397—21no—
17C19×#397—21no—
18C19×#391C411yescharacteristic, complemented
19C19×#391C411yescharacteristic, complemented
20C19×#387—21no—
21C19×#387—21no—
22C19×#384C411yescharacteristic, complemented
23C19×#382C411yescharacteristic, complemented
24C4×C22⋊C4×C19C2211yescharacteristic
25C22×Q8×C19C2×C411yescharacteristic
26C23×C4×C19C2311yescharacteristic
27C19×C22⋊Q8—22no—
28C19×C22⋊Q8—22no—
29C19×#117—22no—
30C19×#117—22no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19C2×C411yescharacteristic
35C2×C4⋊C4×C19C2×C411yescharacteristic
36C2×C4⋊C4×C19C2×C411yescharacteristic
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19D411yescharacteristic
40C2×C22⋊C4×C19D411yescharacteristic
41C2×C42×C19C2×C411yescharacteristic
42C2×C42×C19C2×C411yescharacteristic
43C2×C42×C19D411yescharacteristic
44C2×C42×C19D411yescharacteristic
45C2×C22⋊Dic19—22no—
46C2×#64520—22no—
47C19×#95—21no—
48C19×#95—21no—
49C19×#95—21no—
50C19×#95—21no—
51C19×#95—21no—
52C19×#95—21no—
53C19×#95—21no—
54C19⋊#95—22no—
55C19⋊#95—22no—
56C22⋊(C19⋊C8)—22no—
57C22⋊(C19⋊C8)D414yes—
58C4⋊(C19⋊C8)—24no—
59#10597260—22no—
60C4×C19⋊C8—22no—
61C24×C19C2×D411yescharacteristic
62C2×Q8×C19—22no—
63C2×Q8×C19—41no—
64C2×Q8×C19—41no—
65C22×C4×C19—21no—
66C22×C4×C19—21no—
67C22×C4×C19—21no—
68C22×C4×C19—21no—
69C22×C4×C19—41no—
70C22×C4×C19—41no—
71C22×C4×C19C22⋊C411yescharacteristic
72C22×C4×C19C22⋊C411yescharacteristic
73C22×C4×C19C22⋊C411yescharacteristic
74C22×C4×C19C22⋊C411yescharacteristic
75C22×C4×C19C22×C411yescharacteristic
76C22×C4×C19C2×D412yes—
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19#4112yes—
79C22×Dic19—42no—
80C4⋊C4×C19—22no—
81C4⋊C4×C19—22no—
82C4⋊C4×C19—22no—
83C4⋊C4×C19—42no—
84C4⋊C4×C19—42no—
85C4⋊C4×C19—41no—
86C4⋊C4×C19—41no—
87C22⋊C4×C19—22no—
88C22⋊C4×C19—22no—
89C22⋊C4×C19—42no—
90C22⋊C4×C19—42no—
91C42×C19—21no—
92C42×C19—21no—
93C42×C19—21no—
94C42×C19—21no—
95C42×C19—41no—
96C42×C19—41no—
97C22⋊Dic19—42no—
98C22⋊Dic19—42no—
99#64520—42no—
100#64520—42no—
101C2×C19⋊C8—24no—
102#9444—191nomaximal, Sylow
103C23×C19—21no—
104C23×C19—21no—
105C23×C19—41no—
106C23×C19—41no—
107C23×C19C2×C22⋊C411yescharacteristic
108C23×C19#12112yes—
109Q8×C19—82no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—22no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—42no—
120C2×C4×C19—42no—
121C2×C4×C19—41no—
122C2×C4×C19—41no—
123C2×C4×C19—41no—
124C2×C4×C19—41no—
125C2×C4×C19—41no—
126C2×C4×C19—41no—
127C2×C4×C19—41no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—41no—
132C2×C4×C19—41no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19C4×D412yes—
137C2×C4×C19#12011yescharacteristic
138C2×C4×C19#12311yescharacteristic
139C2×Dic19—82no—
140C2×Dic19—82no—
141C2×Dic19—82no—
142C19⋊C8—44no—
143#2921—191no—
144#2499D1911yescharacteristic
145#1820—191no—
146#1511—192no—
147#1284—192no—
148C22×C19—21no—
149C22×C19—21no—
150C22×C19—22no—
151C22×C19—22no—
152C22×C19—22no—
153C22×C19—81no—
154C22×C19—81no—
155C22×C19#38611yescharacteristic
156C22×C19#41011yescharacteristic
157C22×C19#41011yescharacteristic
158C4×C19—21no—
159C4×C19—22no—
160C4×C19—21no—
161C4×C19—42no—
162C4×C19—41no—
163C4×C19—41no—
164C4×C19—41no—
165C4×C19—41no—
166C4×C19—81no—
167C4×C19—81no—
168C4×C19—81no—
169Dic19—162no—
170C2×C22⋊Q8C2×D1911yescharacteristic
171C2×#117C2×D1911yescharacteristic
172#433—384no—
173#423—381no—
174#407—192no—
175C4×M16—381no—
176#397—21no—
177#397—21no—
178#391Dic1911yescharacteristic, complemented
179#391Dic1911yescharacteristic, complemented
180#387—21no—
181#387—21no—
182#384Dic1911yescharacteristic, complemented
183#382Dic1911yescharacteristic, complemented
184#381—192no—
185C4×C22⋊C4C2×D1911yescharacteristic
186#342—381no—
187#342—381no—
188#328—384no—
189C2×C19—21no—
190C2×C19—21no—
191C2×C19—42no—
192C2×C19#188411yescharacteristic
193C2×C19#189911yescharacteristic
194C2×C19#190911yescharacteristic
195C22×Q8C2×Dic1911yescharacteristic
196C23×C4C22×D1911yescharacteristic
197C2×M16—382no—
198C22⋊Q8—22no—
199C22⋊Q8—22no—
200#117—22no—
201#117—22no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C2×Dic1911yescharacteristic
206C2×C4⋊C4C2×Dic1911yescharacteristic
207C2×C4⋊C4C2×Dic1911yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—382no—
211C2×C22⋊C4C22⋊D1911yescharacteristic
212C2×C22⋊C4C22⋊D1911yescharacteristic
213C2×C42C2×Dic1911yescharacteristic
214C2×C42C2×Dic1911yescharacteristic
215C2×C42C22⋊D1911yescharacteristic
216C2×C42C22⋊D1911yescharacteristic
217C4⋊C8—384no—
218C22⋊C8—194no—
219C22⋊C8—382no—
220#97—382no—
221C4×C8—382no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—382no—
230#95—382no—
231C19#944411yescharacteristic, complemented, Sylow
232C24C2×C22⋊D1911yescharacteristic
233C2×Q8—22no—
234C2×Q8—41no—
235C2×Q8—41no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—762no—
243C22×C4C22⋊Dic1911yescharacteristic
244C22×C4C22⋊Dic1911yescharacteristic
245C22×C4C22⋊Dic1911yescharacteristic
246C22×C4C22⋊Dic1911yescharacteristic
247C22×C4D4×D1912yes—
248C22×C4#6454312yes—
249C22×C4C22×Dic1911yescharacteristic
250C22×C4C2×C22⋊D1911yescharacteristic
251M16—762no—
252M16—762no—
253C2×C8—384no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C22⋊C4—22no—
262C22⋊C4—22no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—762no—
266C22⋊C4—762no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—41no—
272C42—41no—
273C23—21no—
274C23—21no—
275C23—41no—
276C23—41no—
277C23#1059738512yes—
278C23C2×C22⋊Dic1911yescharacteristic
279Q8—82no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—1522no—
307C2×C4—1522no—
308C2×C4—1522no—
309C2×C4D4×Dic1912yes—
310C2×C4#1059738111yescharacteristic
311C2×C4#1059738311yescharacteristic
312C8—764no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—81no—
319C22—81no—
320C22#1192642411yescharacteristic
321C22#1192651811yescharacteristic
322C22#1192651811yescharacteristic
323C4—21no—
324C4—22no—
325C4—21no—
326C4—42no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—81no—
332C4—81no—
333C4—81no—
334C4—3042no—
335C2—21no—
336C2—21no—
337C2—42no—
338C2#1456401911yescharacteristic
339C2#1456409411yescharacteristic
340C2#1456415811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2499C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenter#2499D19
hypocenterC19#9444
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2499

Complements

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

NH ≅ G/Ntype
18. C19×#391C4semidirect
19. C19×#391C4semidirect
22. C19×#384C4semidirect
23. C19×#382C4semidirect
178. #391Dic19semidirect
179. #391Dic19semidirect
182. #384Dic19semidirect
183. #382Dic19semidirect
231. C19#9444semidirect

Maximal subgroups

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

subgroupindex
#145722732
#145637122
#145621682
#145614882
C19×#24992
#944419