Finite Group Databasebeta

← #18080419

Subgroups — #18080419

Order 4864.

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

normal subgroups only

This group has 544 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#14572054C211yesmaximal, characteristic
2#14562082C212yesmaximal, complemented
3#14561969C211yesmaximal, characteristic
4#14561499C212yesmaximal, complemented
5C19×#2599C211yesmaximal, characteristic
6C22×#64520—21no—
7#11926601C2212yes—
8#11926500—24no—
9C4×#64520—21no—
10C4×#64520C2212yes—
11Q8⋊(C19⋊C8)—24no—
12#11926270—21no—
13#11926268—21no—
14C2×C4×Q8×C19C2211yescharacteristic
15C2×C19×#117C2211yescharacteristic
16C19×#398C411yescharacteristic
17C19×#397C411yescharacteristic
18C19×#395C411yescharacteristic
19C19×#393C411yescharacteristic
20C19×#388—21no—
21C19×#387—21no—
22C19×#387—21no—
23C19×#385—21no—
24C19×#383C2211yescharacteristic
25C22×Q8×C19C2×C411yescharacteristic
26C23×C4×C19D411yescharacteristic
27C4×Q8×C19—22no—
28C4×Q8×C19—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×C19D411yescharacteristic
37C2×C22⋊C4×C19—21no—
38C2×C22⋊C4×C19—21no—
39C2×C22⋊C4×C19C2×C411yescharacteristic
40C2×C22⋊C4×C19D411yescharacteristic
41C2×C42×C19—21no—
42C2×C42×C19D411yescharacteristic
43C2×C42×C19C2311yescharacteristic
44C2×#64520—24no—
45C2×#64520—24no—
46C2×#64520—22no—
47C2×#64520—22no—
48C22×C19⋊C8—22no—
49C19×#95—21no—
50C19×#95—21no—
51C19×#95—21no—
52C19×#95—21no—
53C19×#95—21no—
54C19×#95—21no—
55C19×#95C2×C411yescharacteristic
56C19×#95C2×C411yescharacteristic
57C22⋊(C19⋊C8)—22no—
58C4⋊(C19⋊C8)—22no—
59#10597260—22no—
60#10597260—22no—
61#10597260—22no—
62C4×C19⋊C8—22no—
63C4×C19⋊C8D414yes—
64C24×C19C22⋊C411yescharacteristic
65C2×Q8×C19—22no—
66C2×Q8×C19—42no—
67C22×C4×C19—22no—
68C22×C4×C19—22no—
69C22×C4×C19—21no—
70C22×C4×C19—21no—
71C22×C4×C19—21no—
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19—21no—
75C22×C4×C19C22⋊C411yescharacteristic
76C22×C4×C19C22⋊C411yescharacteristic
77C22×C4×C19C22⋊C411yescharacteristic
78C22×C4×C19C22×C411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19C2×D411yescharacteristic
81C4⋊C4×C19—22no—
82C4⋊C4×C19—22no—
83C4⋊C4×C19—22no—
84C4⋊C4×C19—42no—
85C4⋊C4×C19—42no—
86C4⋊C4×C19—41no—
87C4⋊C4×C19—41no—
88C22⋊C4×C19—22no—
89C22⋊C4×C19—22no—
90C22⋊C4×C19—42no—
91C22⋊C4×C19—42no—
92C42×C19—21no—
93C42×C19—21no—
94C42×C19—42no—
95C42×C19C2×D412yes—
96C42×C19#4112yes—
97#64520—28no—
98#64520—24no—
99#64520—24no—
100C2×C19⋊C8—28no—
101C2×C19⋊C8—24no—
102C2×C19⋊C8—42no—
103#9491—191nomaximal, Sylow
104C23×C19—21no—
105C23×C19—21no—
106C23×C19—41no—
107C23×C19—41no—
108C23×C19#10412yes—
109C23×C19C2×C22⋊C411yescharacteristic
110Q8×C19—24no—
111Q8×C19—42no—
112C2×C4×C19—22no—
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—22no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
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×C19—41no—
137C2×C4×C19#10412yes—
138C2×C4×C19C4×D412yes—
139C2×C4×C19#12011yescharacteristic
140C2×C4×C19#12112yes—
141C2×C4×C19#12311yescharacteristic
142C19⋊C8—28no—
143C19⋊C8—82no—
144#2873—191no—
145#2599D1911yescharacteristic
146#1491—192no—
147#1464—191no—
148#1288—192no—
149C22×C19—21no—
150C22×C19—21no—
151C22×C19—22no—
152C22×C19—42no—
153C22×C19—41no—
154C22×C19—41no—
155C22×C19—81no—
156C22×C19#38611yescharacteristic
157C22×C19C2×#10411yescharacteristic
158C22×C19C2×#10411yescharacteristic
159C4×C19—22no—
160C4×C19—21no—
161C4×C19—22no—
162C4×C19—21no—
163C4×C19—22no—
164C4×C19—41no—
165C4×C19—42no—
166C4×C19—41no—
167C4×C19—81no—
168C4×C19—81no—
169C4×C19—81no—
170C22×M16—381no—
171C2×C4×Q8C2×D1911yescharacteristic
172C2×#117C2×D1911yescharacteristic
173#432—192no—
174#405—384no—
175C4×M16—192no—
176C4×M16—381no—
177#398Dic1911yescharacteristic
178#397Dic1911yescharacteristic
179#395Dic1911yescharacteristic
180#393Dic1911yescharacteristic
181#388—21no—
182#387—21no—
183#387—21no—
184#385—21no—
185#383C2×D1911yescharacteristic
186Q8⋊C8—384no—
187#324—381no—
188#323—381no—
189C2×C19—21no—
190C2×C19—21no—
191C2×C19—42no—
192C2×C19#189111yescharacteristic
193C2×C19#189611yescharacteristic
194C2×C19#190911yescharacteristic
195C22×Q8C2×Dic1911yescharacteristic
196C23×C4C22⋊D1911yescharacteristic
197C2×M16—382no—
198C2×M16—384no—
199C2×M16—384no—
200C2×M16—382no—
201C22×C8—382no—
202C4×Q8—22no—
203C4×Q8—22no—
204#117—22no—
205#117—22no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4C2×Dic1911yescharacteristic
210C2×C4⋊C4C2×Dic1911yescharacteristic
211C2×C4⋊C4C22⋊D1911yescharacteristic
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4C2×Dic1911yescharacteristic
215C2×C22⋊C4C22⋊D1911yescharacteristic
216C2×C42—21no—
217C2×C42C22⋊D1911yescharacteristic
218C2×C42C22×D1911yescharacteristic
219C4⋊C8—382no—
220C22⋊C8—382no—
221#97—382no—
222#97—382no—
223#97—382no—
224C4×C8—194no—
225C4×C8—382no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95C2×Dic1911yescharacteristic
233#95C2×Dic1911yescharacteristic
234C19#949111yescharacteristic, complemented, Sylow
235C24C22⋊Dic1911yescharacteristic
236C2×Q8—22no—
237C2×Q8—42no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—22no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4C22⋊Dic1911yescharacteristic
247C22×C4C22⋊Dic1911yescharacteristic
248C22×C4C22⋊Dic1911yescharacteristic
249C22×C4C22×Dic1911yescharacteristic
250C22×C4C2×C22⋊D1911yescharacteristic
251C22×C4C2×C22⋊D1911yescharacteristic
252M16—388no—
253M16—384no—
254M16—384no—
255C2×C8—388no—
256C2×C8—384no—
257C2×C8—762no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—42no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—42no—
265C22⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—42no—
268C22⋊C4—42no—
269C42—21no—
270C42—21no—
271C42—42no—
272C42D4×D1912yes—
273C42#6454312yes—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23#1059729412yes—
279C23C2×C22⋊Dic1911yescharacteristic
280Q8—24no—
281Q8—42no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—24no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—21no—
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—41no—
307C2×C4#1059729412yes—
308C2×C4D4×Dic1912yes—
309C2×C4#1059738111yescharacteristic
310C2×C4#1059738311yescharacteristic
311C2×C4#1059738512yes—
312C8—388no—
313C8—1522no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—42no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22#1192642411yescharacteristic
322C22C2×#1059729411yescharacteristic
323C22C2×#1059729411yescharacteristic
324C4—22no—
325C4—22no—
326C4—21no—
327C4—21no—
328C4—22no—
329C4—41no—
330C4—42no—
331C4—41no—
332C4—81no—
333C4—81no—
334C4—81no—
335C2—21no—
336C2—21no—
337C2—42no—
338C2#1456405411yescharacteristic
339C2#1456407911yescharacteristic
340C2#1456415811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#2599C2
socleC22×C19#386
prime radicalC24×C19C22⋊C4
cosocleC2×C42×C19C23
hypercenter#2599D19
hypocenterC19#9491
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2599

Complements

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

NH ≅ G/Ntype
2. #14562082C2semidirect
4. #14561499C2semidirect
234. C19#9491semidirect

Maximal subgroups

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

subgroupindex
#145720542
#145620822
#145619692
#145614992
C19×#25992
#949119