Finite Group Databasebeta

← #18077614

Subgroups — #18077614

Order 4864.

484 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 111 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#14572720C211yesmaximal, characteristic
2C4×#10597293C211yesmaximal, characteristic
3#14562082C212yesmaximal
4#14561528C212yesmaximal
5C19×#2399C211yesmaximal, characteristic
6#11926675—24no—
7#11926601—21no—
8#11926601C2212yes—
9#11926597—21no—
10C2×#10597293—21no—
11C4×#64520C2212yes—
12#11926313—21no—
13Q8⋊(C19⋊C8)—24no—
14C2×C4×Q8×C19C2211yescharacteristic
15C2×C4×Q8×C19C2211yescharacteristic
16C19×#398—21no—
17C19×#398C411yescharacteristic
18C19×#398C411yescharacteristic
19C19×#395—21no—
20C19×#395C411yescharacteristic
21C19×#395C411yescharacteristic
22C4×C4⋊C4×C19—21no—
23C4×C4⋊C4×C19—21no—
24C19×#376C2211yescharacteristic
25C22×Q8×C19C2×C411yescharacteristic
26C22×Q8×C19D411yescharacteristic
27C4×Q8×C19—22no—
28C4×Q8×C19—22no—
29C4×Q8×C19—22no—
30C4×Q8×C19—22no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—21no—
35C2×C4⋊C4×C19—21no—
36C2×C4⋊C4×C19C2×C411yescharacteristic
37C2×C4⋊C4×C19C2×C411yescharacteristic
38C2×C4⋊C4×C19C2×C411yescharacteristic
39C2×C4⋊C4×C19D411yescharacteristic
40C2×C42×C19—21no—
41C2×C42×C19—21no—
42C2×C42×C19D411yescharacteristic
43C2×C42×C19D411yescharacteristic
44C2×C42×C19C2311yescharacteristic
45C2×#64520—22no—
46C19×#95—21no—
47C19×#95—21no—
48C19×#95—21no—
49C19×#95—21no—
50C19×#95—21no—
51C19×#95C2×C411yescharacteristic
52C19×#95C2×C411yescharacteristic
53#10597293—24no—
54C22⋊(C19⋊C8)—22no—
55C4⋊(C19⋊C8)—22no—
56C4⋊(C19⋊C8)—22no—
57C4⋊(C19⋊C8)D414yes—
58#10597260—22no—
59#10597260—22no—
60#10597260—22no—
61C4×C19⋊C8—22no—
62C4×C19⋊C8—22no—
63C2×Q8×C19—22no—
64C2×Q8×C19—22no—
65C2×Q8×C19—22no—
66C2×Q8×C19—41no—
67C2×Q8×C19—42no—
68C22×C4×C19—21no—
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19C22⋊C411yescharacteristic
73C22×C4×C19C22⋊C411yescharacteristic
74C22×C4×C19C22⋊C411yescharacteristic
75C22×C4×C19C22⋊C411yescharacteristic
76C22×C4×C19C22×C411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C4⋊C4×C19—22no—
80C4⋊C4×C19—22no—
81C4⋊C4×C19—22no—
82C4⋊C4×C19—22no—
83C4⋊C4×C19—42no—
84C4⋊C4×C19—42no—
85C4⋊C4×C19—42no—
86C4⋊C4×C19—42no—
87C4⋊C4×C19—42no—
88C42×C19—24no—
89C42×C19—21no—
90C42×C19—21no—
91C42×C19—21no—
92C42×C19—21no—
93C42×C19—41no—
94C42×C19—41no—
95C42×C19C2×D412yes—
96C42×C19#4112yes—
97#64520—24no—
98#64520—42no—
99C2×C19⋊C8—24no—
100C2×C19⋊C8—42no—
101#9030—191nomaximal, Sylow
102C23×C19C2×C22⋊C411yescharacteristic
103Q8×C19—24no—
104Q8×C19—44no—
105Q8×C19—42no—
106C2×C4×C19—21no—
107C2×C4×C19—21no—
108C2×C4×C19—21no—
109C2×C4×C19—21no—
110C2×C4×C19—22no—
111C2×C4×C19—22no—
112C2×C4×C19—22no—
113C2×C4×C19—22no—
114C2×C4×C19—21no—
115C2×C4×C19—21no—
116C2×C4×C19—21no—
117C2×C4×C19—21no—
118C2×C4×C19—21no—
119C2×C4×C19—41no—
120C2×C4×C19—41no—
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#10412yes—
132C2×C4×C19C4×D412yes—
133C2×C4×C19#12011yescharacteristic
134C2×C4×C19#12112yes—
135C2×C4×C19#12311yescharacteristic
136C19⋊C8—44no—
137C19⋊C8—44no—
138#2983—191no—
139#2399D1911yescharacteristic
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—42no—
153C4×C19—42no—
154C4×C19—41no—
155C4×C19—41no—
156C4×C19—41no—
157C4×C19—42no—
158C4×C19—81no—
159C4×C19#45612yes—
160C2×C4×Q8C2×D1911yescharacteristic
161C2×C4×Q8C2×D1911yescharacteristic
162#446—384no—
163#432—192no—
164#432—381no—
165#431—381no—
166C2×#101—381no—
167C4×M16—192no—
168#398—21no—
169#398Dic1911yescharacteristic
170#398Dic1911yescharacteristic
171#395—21no—
172#395Dic1911yescharacteristic
173#395Dic1911yescharacteristic
174C4×C4⋊C4—21no—
175C4×C4⋊C4—21no—
176#376C2×D1911yescharacteristic
177#343—381no—
178Q8⋊C8—384no—
179C2×C19—21no—
180C2×C19—21no—
181C2×C19#187111yescharacteristic
182C2×C19#188611yescharacteristic
183C2×C19#189111yescharacteristic
184C22×Q8C2×Dic1911yescharacteristic
185C22×Q8C22⋊D1911yescharacteristic
186C2×M16—382no—
187C4×Q8—22no—
188C4×Q8—22no—
189C4×Q8—22no—
190C4×Q8—22no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4C2×Dic1911yescharacteristic
197C2×C4⋊C4C2×Dic1911yescharacteristic
198C2×C4⋊C4C2×Dic1911yescharacteristic
199C2×C4⋊C4C22⋊D1911yescharacteristic
200C2×C42—21no—
201C2×C42—21no—
202C2×C42C22⋊D1911yescharacteristic
203C2×C42C22⋊D1911yescharacteristic
204C2×C42C22×D1911yescharacteristic
205C4⋊C8—194no—
206C4⋊C8—382no—
207C4⋊C8—382no—
208#101—384no—
209C22⋊C8—382no—
210#97—382no—
211#97—382no—
212#97—382no—
213C4×C8—382no—
214C4×C8—382no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95C2×Dic1911yescharacteristic
221#95C2×Dic1911yescharacteristic
222C19#903011yescharacteristic, complemented, Sylow
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—42no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4C22⋊Dic1911yescharacteristic
233C22×C4C22⋊Dic1911yescharacteristic
234C22×C4C22⋊Dic1911yescharacteristic
235C22×C4C22⋊Dic1911yescharacteristic
236C22×C4C22×Dic1911yescharacteristic
237C22×C4C2×C22⋊D1911yescharacteristic
238C22×C4C2×C22⋊D1911yescharacteristic
239M16—384no—
240M16—762no—
241C2×C8—384no—
242C2×C8—762no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C42—24no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C42—41no—
258C42—41no—
259C42D4×D1912yes—
260C42#6454312yes—
261C23C2×C22⋊Dic1911yescharacteristic
262Q8—24no—
263Q8—44no—
264Q8—42no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4#1059729412yes—
291C2×C4D4×Dic1912yes—
292C2×C4#1059738111yescharacteristic
293C2×C4#1059738311yescharacteristic
294C2×C4#1059738512yes—
295C8—764no—
296C8—764no—
297C22—21no—
298C22—21no—
299C22#1192642411yescharacteristic
300C22C2×#1059729411yescharacteristic
301C22#1192656111yescharacteristic
302C4—22no—
303C4—22no—
304C4—21no—
305C4—22no—
306C4—42no—
307C4—42no—
308C4—41no—
309C4—42no—
310C4—41no—
311C4—41no—
312C4—81no—
313C4#1192672612yes—
314C2—21no—
315C2—21no—
316C2#1456393811yescharacteristic
317C2#1456402911yescharacteristic
318C2#1456405411yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2399C2
socleC22×C19#386
prime radicalC23×C19C2×C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2399D19
hypocenterC19#9030
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2399

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
#145727202
C4×#105972932
#145620822
#145615282
C19×#23992
#903019