Finite Group Databasebeta

← #18080169

Subgroups — #18080169

Order 4864.

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

normal subgroups only

This group has 576 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#14566747C211yesmaximal, characteristic, complemented
2#14562259C211yesmaximal, characteristic, complemented
3#14562143C212yesmaximal, complemented
4#14561529C212yesmaximal, complemented
5C19×#3153C211yesmaximal, characteristic
6#11926601C2212yes—
7#11926451—21no—
8#11926437—22no—
9#11926424—21no—
10C22⋊C4×Dic19—22no—
11#11926390C2212yes—
12#11926284—22no—
13#11926278—22no—
14#11926278—22no—
15C2×C19×#137—21no—
16C2×C19×AGL(1,ℤ/8)—21no—
17C19×#532C2211yescharacteristic
18C2×C19×#124C2211yescharacteristic
19C19×#497C412yescomplemented
20C19×#496C412yescomplemented
21C19×#495—22no—
22C4×M16×C19C2211yescharacteristic
23C2×#41×C19—21no—
24C22×Q8×C19D411yescharacteristic
25C22×D4×C19D411yescharacteristic
26C23×Dic19—21no—
27C19×#137—42no—
28C19×#137—42no—
29C19×AGL(1,ℤ/8)—42no—
30C19×AGL(1,ℤ/8)—42no—
31C2×Q16×C19—22no—
32C2×SD16×C19—22no—
33C2×SD16×C19—22no—
34C2×D8×C19—22no—
35C2×M16×C19—21no—
36C19×C4⋊Q8C2×C411yescharacteristic, complemented
37C19×#127C2×C411yescharacteristic, complemented
38C19×#124—21no—
39C19×#124—22no—
40C19×#124C2×C412yes—
41C19×#124D412yes—
42C19×#121—22no—
43C4×D4×C19—22no—
44C2×C22⋊C4×C19—22no—
45C2×C42×C19C2311yescharacteristic
46C2×C22⋊Dic19—22no—
47C2×C22⋊Dic19—21no—
48C2×C4⋊Dic19—21no—
49C2×C4×Dic19—22no—
50C2×C4×Dic19—21no—
51C19×#97C2×C412yescomplemented
52C4×C8×C19—21no—
53C19⋊#95—22no—
54C19⋊#95—22no—
55C19⋊#95D412yes—
56C19⋊#95D412yes—
57C22⋊(C19⋊C8)—22no—
58C4⋊(C19⋊C8)—22no—
59#10597260—22no—
60C24×C19—21no—
61#41×C19—41no—
62#41×C19—41no—
63#41×C19—41no—
64#41×C19—41no—
65C2×Q8×C19—21no—
66C2×Q8×C19—21no—
67C2×Q8×C19—41no—
68C2×Q8×C19—41no—
69C2×Q8×C19C22⋊C412yes—
70C2×D4×C19—21no—
71C2×D4×C19—22no—
72C2×D4×C19—21no—
73C2×D4×C19—41no—
74C2×D4×C19—41no—
75C2×D4×C19—41no—
76C2×D4×C19C22⋊C412yes—
77C22×C4×C19—21no—
78C22×C4×C19—41no—
79C22×C4×C19C2×D412yes—
80C22×C4×C19C2×D411yescharacteristic
81C22×Dic19—22no—
82C22×Dic19—22no—
83C22×Dic19—44no—
84C22×Dic19—81no—
85Q16×C19—44no—
86SD16×C19—44no—
87SD16×C19—44no—
88D8×C19—44no—
89M16×C19—22no—
90M16×C19—22no—
91C2×C8×C19—22no—
92C4⋊C4×C19—22no—
93C22⋊C4×C19—24no—
94C22⋊C4×C19—24no—
95C22⋊C4×C19—42no—
96C42×C19C22×C411yescharacteristic
97C42×C19C2×D411yescharacteristic
98C42×C19#4112yes—
99C22⋊Dic19—44no—
100C22⋊Dic19—81no—
101C4⋊Dic19—81no—
102C4×Dic19—44no—
103C4×Dic19—81no—
104C2×C19⋊C8—42no—
105#9441—191nomaximal, Sylow
106C23×C19—22no—
107C23×C19—42no—
108C23×C19—42no—
109C23×C19—41no—
110C23×C19—41no—
111C23×C19—41no—
112C23×C19#12011yescharacteristic
113Q8×C19—42no—
114Q8×C19—41no—
115Q8×C19—41no—
116Q8×C19—81no—
117D4×C19—42no—
118D4×C19—41no—
119D4×C19—41no—
120D4×C19—81no—
121D4×C19—82no—
122D4×C19—81no—
123D4×C19—81no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—22no—
127C2×C4×C19—42no—
128C2×C4×C19—41no—
129C2×C4×C19—41no—
130C2×C4×C19—41no—
131C2×C4×C19—81no—
132C2×C4×C19—81no—
133C2×C4×C19C2×C22⋊C411yescharacteristic
134C2×C4×C19C4×D412yes—
135C2×C4×C19#12112yes—
136C2×C4×C19#12311yescharacteristic
137C2×Dic19—24no—
138C2×Dic19—42no—
139C2×Dic19—42no—
140C2×Dic19—42no—
141C2×Dic19—42no—
142C2×Dic19—42no—
143C2×Dic19—84no—
144C8×C19—24no—
145C19⋊C8—82no—
146#3153D1911yescharacteristic
147#2372—191no—
148#1533—191no—
149#1505—192no—
150#1300—192no—
151C22×C19—22no—
152C22×C19—42no—
153C22×C19—44no—
154C22×C19—81no—
155C22×C19—81no—
156C22×C19—82no—
157C22×C19—81no—
158C22×C19—82no—
159C22×C19#38611yescharacteristic
160C22×C19#45311yescharacteristic
161C22×C19#45311yescharacteristic
162C4×C19—21no—
163C4×C19—21no—
164C4×C19—22no—
165C4×C19—22no—
166C4×C19—42no—
167C4×C19—81no—
168Dic19—44no—
169Dic19—82no—
170C2×#137—21no—
171C2×AGL(1,ℤ/8)—21no—
172#532C2×D1911yescharacteristic
173C2×#124C2×D1911yescharacteristic
174#497Dic1912yescomplemented
175#496Dic1912yescomplemented
176#495—22no—
177#432—192no—
178C4×M16C2×D1911yescharacteristic
179#391—381no—
180#388—382no—
181#386—381no—
182C4×C22⋊C4—382no—
183#376—192no—
184#329—382no—
185#327—382no—
186#327—382no—
187C2×C19—21no—
188C2×C19—21no—
189C2×C19—82no—
190C2×C19—161no—
191C2×C19#188711yescharacteristic
192C2×C19#190612yes—
193C2×#41—21no—
194C22×Q8C22⋊D1911yescharacteristic
195C22×D4C22⋊D1911yescharacteristic
196C23×C4—381no—
197#137—42no—
198#137—42no—
199AGL(1,ℤ/8)—42no—
200AGL(1,ℤ/8)—42no—
201C2×Q16—22no—
202C2×SD16—22no—
203C2×SD16—22no—
204C2×D8—22no—
205C2×M16—21no—
206C4⋊Q8C2×Dic1911yescharacteristic, complemented
207#127C2×Dic1911yescharacteristic, complemented
208#124—22no—
209#124—21no—
210#124C2×Dic1912yes—
211#124C22⋊D1912yes—
212#121—22no—
213C4×D4—22no—
214C2×C4⋊C4—381no—
215C2×C22⋊C4—22no—
216C2×C22⋊C4—382no—
217C2×C22⋊C4—381no—
218C2×C42—382no—
219C2×C42—381no—
220C2×C42C22×D1911yescharacteristic
221C4⋊C8—382no—
222C22⋊C8—382no—
223#97—382no—
224#97C2×Dic1912yescomplemented
225C4×C8—21no—
226#95—192no—
227#95—192no—
228#95—382no—
229#95—382no—
230C19#944111yescharacteristic, complemented, Sylow
231C24—21no—
232#41—41no—
233#41—41no—
234#41—41no—
235#41—41no—
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8C22⋊Dic1912yes—
241C2×D4—22no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4C22⋊Dic1912yes—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—382no—
251C22×C4—382no—
252C22×C4—764no—
253C22×C4—1521no—
254C22×C4D4×D1912yes—
255C22×C4C2×C22⋊D1911yescharacteristic
256Q16—44no—
257SD16—44no—
258SD16—44no—
259D8—44no—
260M16—22no—
261M16—22no—
262C2×C8—22no—
263C2×C8—762no—
264C4⋊C4—22no—
265C4⋊C4—1521no—
266C22⋊C4—24no—
267C22⋊C4—24no—
268C22⋊C4—42no—
269C22⋊C4—764no—
270C22⋊C4—1521no—
271C42—764no—
272C42—1521no—
273C42#6454312yes—
274C42C22×Dic1911yescharacteristic
275C42C2×C22⋊D1911yescharacteristic
276C23—22no—
277C23—42no—
278C23—42no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23#1059738311yescharacteristic
283Q8—42no—
284Q8—41no—
285Q8—41no—
286Q8—81no—
287D4—42no—
288D4—41no—
289D4—41no—
290D4—81no—
291D4—82no—
292D4—81no—
293D4—81no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—384no—
304C2×C4—762no—
305C2×C4—762no—
306C2×C4—762no—
307C2×C4—762no—
308C2×C4—762no—
309C2×C4—1524no—
310C2×C4D4×Dic1912yes—
311C2×C4#1059738111yescharacteristic
312C2×C4#1059738512yes—
313C2×C4C2×C22⋊Dic1911yescharacteristic
314C8—24no—
315C8—1522no—
316C22—22no—
317C22—44no—
318C22—42no—
319C22—81no—
320C22—81no—
321C22—82no—
322C22—82no—
323C22—81no—
324C22#1192642411yescharacteristic
325C22#1192671111yescharacteristic
326C22#1192671111yescharacteristic
327C4—22no—
328C4—22no—
329C4—21no—
330C4—21no—
331C4—42no—
332C4—81no—
333C4—764no—
334C4—1522no—
335C2—21no—
336C2—21no—
337C2—82no—
338C2—161no—
339C2#1456403411yescharacteristic
340C2#1456413812yes—
subgroupG/H
centerC22#11926424
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3153C2
socleC22×C19#386
cosocleC2×C42×C19C23
hypercenter#3153D19
hypocenterC19#9441
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3153

Complements

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

NH ≅ G/Ntype
1. #14566747C2semidirect
2. #14562259C2semidirect
3. #14562143C2semidirect
4. #14561529C2semidirect
19. C19×#497C4semidirect
20. C19×#496C4semidirect
36. C19×C4⋊Q8C2×C4semidirect
37. C19×#127C2×C4semidirect
51. C19×#97C2×C4semidirect
174. #497Dic19semidirect
175. #496Dic19semidirect
206. C4⋊Q8C2×Dic19semidirect
207. #127C2×Dic19semidirect
224. #97C2×Dic19semidirect
230. C19#9441semidirect

Maximal subgroups

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

subgroupindex
#145667472
#145622592
#145621432
#145615292
C19×#31532
#944119