Finite Group Databasebeta

← #18080534

Subgroups — #18080534

Order 4864.

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

normal subgroups only

This group has 478 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#14563718C211yesmaximal, characteristic
3#14561965C212yesmaximal
4#14561543C212yesmaximal
5C19×#2484C211yesmaximal, characteristic
6#11926605—24no—
7#11926568—21no—
8#11926508C2212yes—
9#11926508C2212yes—
10C4×#64520—21no—
11#11926313—21no—
12#11926313—21no—
13#11926270—24no—
14C2×C19×#117C2211yescharacteristic
15C22×C4⋊C4×C19C2211yescharacteristic
16C19×#400—21no—
17C19×#398—21no—
18C19×#387—21no—
19C19×#387—21no—
20C19×#385C411yescharacteristic
21C19×#385C411yescharacteristic
22C19×#381C411yescharacteristic
23C19×#381C411yescharacteristic
24C19×#381C2211yescharacteristic
25C23×C4×C19C2×C411yescharacteristic
26C23×C4×C19C2×C411yescharacteristic
27C23×C4×C19C2311yescharacteristic
28C19×#117—22no—
29C19×#117—22no—
30C2×C4⋊C4×C19—21no—
31C2×C4⋊C4×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—22no—
35C2×C4⋊C4×C19—22no—
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C4⋊C4×C19D411yescharacteristic
38C2×C22⋊C4×C19C2×C411yescharacteristic
39C2×C22⋊C4×C19C2×C411yescharacteristic
40C2×C22⋊C4×C19C2×C411yescharacteristic
41C2×C22⋊C4×C19C2×C411yescharacteristic
42C2×C42×C19D411yescharacteristic
43C2×C42×C19D411yescharacteristic
44C2×#64520—22no—
45C2×#64520—22no—
46C19×#95—21no—
47C19×#95—21no—
48C19×#95—21no—
49C19×#95—21no—
50C19×#95—21no—
51C19×#95—21no—
52C19×#95—21no—
53C19×#95—21no—
54C22⋊(C19⋊C8)—22no—
55C22⋊(C19⋊C8)—22no—
56C22⋊(C19⋊C8)—22no—
57C22⋊(C19⋊C8)D414yes—
58C4⋊(C19⋊C8)—24no—
59#10597260—22no—
60C4×C19⋊C8—22no—
61C24×C19C22×C411yescharacteristic
62C22×C4×C19—21no—
63C22×C4×C19—22no—
64C22×C4×C19—21no—
65C22×C4×C19—21no—
66C22×C4×C19—21no—
67C22×C4×C19—22no—
68C22×C4×C19—42no—
69C22×C4×C19—41no—
70C22×C4×C19—41no—
71C22×C4×C19—41no—
72C22×C4×C19—41no—
73C22×C4×C19C22⋊C411yescharacteristic
74C22×C4×C19C22⋊C411yescharacteristic
75C22×C4×C19C22⋊C411yescharacteristic
76C22×C4×C19C22⋊C411yescharacteristic
77C22×C4×C19C2×D412yes—
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19#4112yes—
81C4⋊C4×C19—22no—
82C4⋊C4×C19—22no—
83C4⋊C4×C19—42no—
84C4⋊C4×C19—42no—
85C4⋊C4×C19—41no—
86C4⋊C4×C19—42no—
87C4⋊C4×C19—41no—
88C22⋊C4×C19—22no—
89C22⋊C4×C19—22no—
90C22⋊C4×C19—41no—
91C22⋊C4×C19—41no—
92C42×C19—21no—
93C42×C19—21no—
94C42×C19—21no—
95C42×C19—21no—
96#64520—42no—
97#64520—42no—
98#64520—42no—
99#64520—42no—
100C2×C19⋊C8—24no—
101C2×C19⋊C8—42no—
102#9514—191nomaximal, Sylow
103C23×C19—21no—
104C23×C19—21no—
105C23×C19—41no—
106C23×C19—41no—
107C23×C19C2×C22⋊C411yescharacteristic
108C23×C19C4×D412yes—
109C2×C4×C19—21no—
110C2×C4×C19—21no—
111C2×C4×C19—21no—
112C2×C4×C19—21no—
113C2×C4×C19—22no—
114C2×C4×C19—24no—
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—42no—
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×C19—41no—
137C2×C4×C19—82no—
138C2×C4×C19#12011yescharacteristic
139C2×C4×C19#12112yes—
140C2×C4×C19#12311yescharacteristic
141C19⋊C8—44no—
142C19⋊C8—82no—
143#2921—191no—
144#2484D1911yescharacteristic
145#1822—191no—
146#1463—192no—
147#1306—192no—
148C22×C19—21no—
149C22×C19—21no—
150C22×C19—22no—
151C22×C19—22no—
152C22×C19—22no—
153C22×C19—42no—
154C22×C19—42no—
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—
169C2×#117C2×D1911yescharacteristic
170C22×C4⋊C4C2×D1911yescharacteristic
171#433—384no—
172#423—381no—
173#407—192no—
174#407—192no—
175C4×M16—381no—
176#400—21no—
177#398—21no—
178#387—21no—
179#387—21no—
180#385Dic1911yescharacteristic
181#385Dic1911yescharacteristic
182#381Dic1911yescharacteristic
183#381Dic1911yescharacteristic
184#381C2×D1911yescharacteristic
185#343—381no—
186#343—381no—
187#324—384no—
188C2×C19—21no—
189C2×C19—21no—
190C2×C19—42no—
191C2×C19#189111yescharacteristic
192C2×C19#189911yescharacteristic
193C2×C19#191511yescharacteristic
194C23×C4C2×Dic1911yescharacteristic
195C23×C4C2×Dic1911yescharacteristic
196C23×C4C22×D1911yescharacteristic
197C2×M16—382no—
198C2×M16—382no—
199#117—22no—
200#117—22no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4C22⋊D1911yescharacteristic
208C2×C4⋊C4C22⋊D1911yescharacteristic
209C2×C22⋊C4C2×Dic1911yescharacteristic
210C2×C22⋊C4C2×Dic1911yescharacteristic
211C2×C22⋊C4C2×Dic1911yescharacteristic
212C2×C22⋊C4C2×Dic1911yescharacteristic
213C2×C42C22⋊D1911yescharacteristic
214C2×C42C22⋊D1911yescharacteristic
215C4⋊C8—384no—
216C22⋊C8—194no—
217C22⋊C8—382no—
218C22⋊C8—382no—
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—21no—
230C19#951411yescharacteristic, complemented, Sylow
231C24C22×Dic1911yescharacteristic
232C22×C4—22no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—42no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4C22⋊Dic1911yescharacteristic
244C22×C4C22⋊Dic1911yescharacteristic
245C22×C4C22⋊Dic1911yescharacteristic
246C22×C4C22⋊Dic1911yescharacteristic
247C22×C4D4×D1912yes—
248C22×C4#6454312yes—
249C22×C4C2×C22⋊D1911yescharacteristic
250C22×C4C2×C22⋊D1911yescharacteristic
251M16—762no—
252M16—762no—
253M16—762no—
254M16—762no—
255C2×C8—384no—
256C2×C8—762no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—42no—
264C22⋊C4—22no—
265C22⋊C4—22no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—21no—
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23D4×Dic1912yes—
277C23C2×C22⋊Dic1911yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—42no—
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—82no—
307C2×C4#1059738111yescharacteristic
308C2×C4#1059738311yescharacteristic
309C2×C4#1059738512yes—
310C8—764no—
311C8—1522no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—42no—
318C22—42no—
319C22#1192642411yescharacteristic
320C22#1192651811yescharacteristic
321C22#1192651811yescharacteristic
322C4—21no—
323C4—22no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—42no—
328C4—41no—
329C4—41no—
330C4—81no—
331C4—81no—
332C4—81no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2#1456405411yescharacteristic
337C2#1456409411yescharacteristic
338C2#1456418811yescharacteristic
subgroupG/H
centerC22#11926424
commutator, prime radicalC24×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#2484C2
socleC22×C19#386
cosocleC23×C4×C19C23
hypercenter#2484D19
hypocenterC19#9514
LCSG ▷ C24×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2484

Complements

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

NH ≅ G/Ntype
230. C19#9514semidirect

Maximal subgroups

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

subgroupindex
#145722732
#145637182
#145619652
#145615432
C19×#24842
#951419