Finite Group Databasebeta

← #18077613

Subgroups — #18077613

Order 4864.

484 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 107 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#14566926C211yesmaximal, characteristic
2C4×#10597293C211yesmaximal, characteristic
3#14562081C212yesmaximal
4#14561527C212yesmaximal
5C19×#2983C211yesmaximal, characteristic
6C2×C4×Dic38C2211yescharacteristic
7C2×#10597293—21no—
8C4×#64520C2212yes—
9#11926475—21no—
10#11926474C411yescharacteristic
11#11926474C411yescharacteristic
12#11926464C411yescharacteristic
13#11926464C411yescharacteristic
14#11926463—21no—
15C4×Dic19⋊C4—21no—
16C4×Dic19⋊C4—21no—
17#11926390C2211yescharacteristic
18#11926313—21no—
19#11926274—24no—
20C2×C4×Q8×C19C2211yescharacteristic
21C19×#446—24no—
22C19×#432—21no—
23C19×#432C2212yes—
24C19×#431—21no—
25C22×Q8×C19D411yescharacteristic
26C22×Dic38C2×C411yescharacteristic
27C4×Q8×C19—22no—
28C4×Q8×C19—22no—
29C2×C4⋊C4×C19C2×C411yescharacteristic
30C2×C4⋊C4×C19C2×C411yescharacteristic
31C2×C4⋊C4×C19D411yescharacteristic
32C2×C42×C19D411yescharacteristic
33C2×C42×C19D411yescharacteristic
34C2×C42×C19C2311yescharacteristic
35C2×C4⋊Dic19C2×C411yescharacteristic
36C2×Dic19⋊C4—21no—
37C2×Dic19⋊C4—21no—
38C2×Dic19⋊C4—21no—
39C2×Dic19⋊C4—21no—
40C2×Dic19⋊C4—21no—
41C2×C4×Dic19—21no—
42C2×C4×Dic19—21no—
43C2×#64520—22no—
44C4×Dic38—22no—
45C4×Dic38—22no—
46C19×C4⋊C8—22no—
47C19×C4⋊C8—22no—
48C19×C4⋊C8D414yes—
49C19×C22⋊C8—22no—
50C19×#97—22no—
51C19×#97—22no—
52C4×C8×C19—22no—
53#10597293—24no—
54C19⋊#95—21no—
55C19⋊#95—21no—
56C19⋊#95—21no—
57C19⋊#95—21no—
58C19⋊#95—21no—
59C19⋊#95C2×C411yescharacteristic
60C19⋊#95C2×C411yescharacteristic
61#10597260—22no—
62C4×C19⋊C8—22no—
63C2×Q8×C19—22no—
64C2×Q8×C19—22no—
65C2×Q8×C19—41no—
66C22×C4×C19C22⋊C411yescharacteristic
67C22×C4×C19C22⋊C411yescharacteristic
68C22×C4×C19C22⋊C411yescharacteristic
69C22×C4×C19C22⋊C411yescharacteristic
70C22×C4×C19C22×C411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C22×Dic19—21no—
74C22×Dic19—21no—
75C22×Dic19—21no—
76C22×Dic19—21no—
77C2×Dic38—22no—
78C2×Dic38—42no—
79C2×C8×C19—24no—
80C4⋊C4×C19—22no—
81C4⋊C4×C19—22no—
82C4⋊C4×C19—22no—
83C42×C19—21no—
84C42×C19—21no—
85C42×C19—21no—
86C42×C19—21no—
87C42×C19C2×D412yes—
88C42×C19#4112yes—
89C4⋊Dic19—22no—
90Dic19⋊C4—42no—
91Dic19⋊C4—42no—
92Dic19⋊C4—42no—
93Dic19⋊C4—42no—
94Dic19⋊C4—42no—
95C4×Dic19—24no—
96C4×Dic19—41no—
97C4×Dic19—41no—
98#64520—24no—
99#64520—42no—
100C2×C19⋊C8—42no—
101#9030—191nomaximal, Sylow
102C23×C19C2×C22⋊C411yescharacteristic
103Q8×C19—44no—
104C2×C4×C19—21no—
105C2×C4×C19—21no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—22no—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—21no—
114C2×C4×C19—41no—
115C2×C4×C19—41no—
116C2×C4×C19—41no—
117C2×C4×C19#10412yes—
118C2×C4×C19C4×D412yes—
119C2×C4×C19#12011yescharacteristic
120C2×C4×C19#12112yes—
121C2×C4×C19#12311yescharacteristic
122C2×Dic19—22no—
123C2×Dic19—22no—
124C2×Dic19—22no—
125C2×Dic19—41no—
126C2×Dic19—41no—
127C2×Dic19—41no—
128C2×Dic19—41no—
129C2×Dic19—41no—
130C2×Dic19—41no—
131C2×Dic19—41no—
132C2×Dic19—41no—
133C2×Dic19—41no—
134Dic38—24no—
135Dic38—42no—
136C8×C19—44no—
137C19⋊C8—44no—
138#2983D1911yescharacteristic
139#2399—191no—
140C4×#101—191no—
141#1491—192no—
142#1300—192no—
143C22×C19—21no—
144C22×C19—21no—
145C22×C19#38611yescharacteristic
146C22×C19C2×#10411yescharacteristic
147C22×C19#42111yescharacteristic
148C4×C19—22no—
149C4×C19—22no—
150C4×C19—21no—
151C4×C19—22no—
152C4×C19—41no—
153C4×C19—41no—
154C4×C19—41no—
155C4×C19#45612yes—
156Dic19—42no—
157Dic19—42no—
158Dic19—42no—
159Dic19—81no—
160C2×C4×Q8—191no—
161C2×C4×Q8C2×D1911yescharacteristic
162#446—24no—
163#432—21no—
164#432C2×D1912yes—
165#431—21no—
166C2×#101—381no—
167C4×M16—192no—
168#398—191no—
169#398—191no—
170#398—381no—
171#395—191no—
172#395—191no—
173#395—381no—
174C4×C4⋊C4—381no—
175C4×C4⋊C4—381no—
176#376—191no—
177#343—381no—
178Q8⋊C8—384no—
179C2×C19—21no—
180C2×C19—21no—
181C2×C19#187111yescharacteristic
182C2×C19#188611yescharacteristic
183C2×C19#189111yescharacteristic
184C22×Q8—191no—
185C22×Q8D7611yescharacteristic
186C2×M16—382no—
187C4×Q8—22no—
188C4×Q8—22no—
189C4×Q8—382no—
190C4×Q8—382no—
191C2×C4⋊C4—191no—
192C2×C4⋊C4—381no—
193C2×C4⋊C4—381no—
194C2×C4⋊C4—381no—
195C2×C4⋊C4—381no—
196C2×C4⋊C4—381no—
197C2×C4⋊C4C4×D1911yescharacteristic
198C2×C4⋊C4C4×D1911yescharacteristic
199C2×C4⋊C4D7611yescharacteristic
200C2×C42—381no—
201C2×C42—381no—
202C2×C42C22⋊D1911yescharacteristic
203C2×C42C22⋊D1911yescharacteristic
204C2×C42C22×D1911yescharacteristic
205C4⋊C8—22no—
206C4⋊C8—22no—
207C4⋊C8C22⋊D1914yes—
208#101—384no—
209C22⋊C8—22no—
210#97—22no—
211#97—22no—
212#97—382no—
213C4×C8—22no—
214C4×C8—382no—
215#95—191no—
216#95—191no—
217#95—381no—
218#95—381no—
219#95—381no—
220#95—381no—
221#95—381no—
222C19#903011yescharacteristic, complemented, Sylow
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—41no—
226C2×Q8—382no—
227C2×Q8—762no—
228C22×C4—381no—
229C22×C4—381no—
230C22×C4—381no—
231C22×C4—381no—
232C22×C4(C2×D19)⋊C411yescharacteristic
233C22×C4(C2×D19)⋊C411yescharacteristic
234C22×C4(C2×D19)⋊C411yescharacteristic
235C22×C4(C2×D19)⋊C411yescharacteristic
236C22×C4C2×C4×D1911yescharacteristic
237C22×C4C2×D7611yescharacteristic
238C22×C4C2×C22⋊D1911yescharacteristic
239M16—384no—
240M16—762no—
241C2×C8—24no—
242C2×C8—762no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—382no—
247C4⋊C4—762no—
248C4⋊C4—762no—
249C4⋊C4—762no—
250C4⋊C4—762no—
251C4⋊C4—762no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—384no—
257C42—761no—
258C42—761no—
259C42#6454112yes—
260C42C2×C22⋊D1912yes—
261C23C2×(C2×D19)⋊C411yescharacteristic
262Q8—44no—
263Q8—384no—
264Q8—762no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—382no—
279C2×C4—382no—
280C2×C4—382no—
281C2×C4—761no—
282C2×C4—761no—
283C2×C4—761no—
284C2×C4—761no—
285C2×C4—761no—
286C2×C4—761no—
287C2×C4—761no—
288C2×C4—761no—
289C2×C4—761no—
290C2×C4#1059728212yes—
291C2×C4C4×C22⋊D1912yes—
292C2×C4#1059737511yescharacteristic
293C2×C4#1059737612yes—
294C2×C4#1059739911yescharacteristic
295C8—44no—
296C8—764no—
297C22—21no—
298C22—21no—
299C22#1192642311yescharacteristic
300C22C2×#1059728211yescharacteristic
301C22#1192656011yescharacteristic
302C4—22no—
303C4—22no—
304C4—21no—
305C4—22no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—762no—
310C4—762no—
311C4—762no—
312C4—1521no—
313C4#1192672712yes—
314C2—21no—
315C2—21no—
316C2#1456393711yescharacteristic
317C2#1456402811yescharacteristic
318C2#1456405311yescharacteristic
subgroupG/H
centerC2×C4#10597399
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2983C2
socleC22×C19#386
prime radicalC23×C19C2×C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2983D19
hypocenterC19#9030
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
222. C19#9030semidirect

Maximal subgroups

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

subgroupindex
#145669262
C4×#105972932
#145620812
#145615272
C19×#29832
#903019