Finite Group Databasebeta

← #18074589

Subgroups — #18074589

Order 4864.

884 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 884 conjugacy classes of subgroups — too many to draw. Only its 147 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#14564464C211yesmaximal, characteristic, complemented
2C4×#10597294C212yesmaximal, complemented
3#14562227C211yesmaximal, characteristic, complemented
4#14562074C212yesmaximal, complemented
5C19×#3481C211yesmaximal, characteristic
6#11926568C2211yescharacteristic, complemented
7C2×#10597294—22no—
8C2×#10597294—22no—
9C4×#64520C2212yescomplemented
10C42×Dic19C2211yescharacteristic, complemented
11#11926303—22no—
12#11926284—22no—
13Q8⋊(C19⋊C8)—22no—
14D4⋊(C19⋊C8)—22no—
15C19×#559C411yescharacteristic, complemented
16C19×#554C412yescomplemented
17C19×#553—22no—
18C19×#551—22no—
19C19×#546—22no—
20D42×C19C411yescharacteristic, complemented
21C19×#532C2211yescharacteristic
22C19×#529—22no—
23C19×#525—22no—
24C4×#41×C19C2212yes—
25C2×C4×D4×C19—22no—
26C2×#41×C19D412yes—
27C2×#41×C19D412yes—
28C22×D4×C19—22no—
29C23×C4×C19—22no—
30C19×C4⋊Q8C2×C411yescharacteristic
31C19×#127C2×C411yescharacteristic
32C19×#126—24no—
33C19×#125—22no—
34C19×#124—22no—
35C19×#124D412yes—
36C19×#123—22no—
37C19×#123—24no—
38C19×#123—22no—
39C19×C22⋊Q8—24no—
40C19×C22⋊Q8—22no—
41C19×#121—24no—
42C19×#121—22no—
43C19×#121—22no—
44C19×#120—22no—
45C19×#120—22no—
46C4×Q8×C19C2×C412yes—
47C4×Q8×C19D412yes—
48C4×D4×C19—24no—
49C4×D4×C19—24no—
50C4×D4×C19—22no—
51C4×D4×C19—22no—
52C4×D4×C19—22no—
53C4×D4×C19—22no—
54C4×D4×C19—22no—
55C4×D4×C19C2×C412yes—
56C4×D4×C19D412yes—
57C19×#117—22no—
58C19×#117—22no—
59C19×#117D412yes—
60C2×C4⋊C4×C19—22no—
61C2×C22⋊C4×C19—24no—
62C2×C42×C19—22no—
63C2×C42×C19C2311yescharacteristic
64C2×C4×Dic19—21no—
65C2×C4×Dic19—22no—
66C2×#64520—22no—
67C2×#64520—21no—
68#10597294—28no—
69#10597294—44no—
70C4⋊(C19⋊C8)—22no—
71#10597260—22no—
72C4×C19⋊C8—22no—
73C24×C19—22no—
74#41×C19—24no—
75#41×C19—42no—
76#41×C19—42no—
77#41×C19—42no—
78C2×Q8×C19C22⋊C412yes—
79C2×Q8×C19C22⋊C412yes—
80C2×D4×C19—24no—
81C2×D4×C19—22no—
82C2×D4×C19—22no—
83C2×D4×C19—22no—
84C2×D4×C19—44no—
85C2×D4×C19—44no—
86C2×D4×C19C22⋊C412yes—
87C2×D4×C19C22⋊C412yes—
88C22×C4×C19—24no—
89C22×C4×C19—22no—
90C22×C4×C19—22no—
91C22×C4×C19—22no—
92C22×C4×C19—22no—
93C22×C4×C19—22no—
94C22×C4×C19—82no—
95C22×C4×C19—82no—
96C22×C4×C19C2×D412yes—
97C22×C4×C19C2×D411yescharacteristic
98C22×Dic19—41no—
99C4⋊C4×C19—24no—
100C4⋊C4×C19—24no—
101C4⋊C4×C19—22no—
102C4⋊C4×C19—22no—
103C4⋊C4×C19—22no—
104C4⋊C4×C19C22⋊C412yes—
105C4⋊C4×C19C22⋊C412yes—
106C22⋊C4×C19—24no—
107C22⋊C4×C19—24no—
108C22⋊C4×C19—22no—
109C22⋊C4×C19—22no—
110C22⋊C4×C19—22no—
111C22⋊C4×C19—22no—
112C22⋊C4×C19—22no—
113C22⋊C4×C19—24no—
114C42×C19—22no—
115C42×C19—22no—
116C42×C19—22no—
117C42×C19C22×C411yescharacteristic
118C42×C19C2×D412yes—
119C42×C19C2×D411yescharacteristic
120C4×Dic19—24no—
121C4×Dic19—22no—
122C4×Dic19—42no—
123C4×Dic19—41no—
124#64520—24no—
125#64520—42no—
126#64520—42no—
127C2×C19⋊C8—42no—
128C2×C19⋊C8—41no—
129#8440—191nomaximal, Sylow
130C23×C19—22no—
131C23×C19—22no—
132C23×C19—48no—
133C23×C19—82no—
134C23×C19#12011yescharacteristic
135Q8×C19—22no—
136Q8×C19—22no—
137Q8×C19—42no—
138D4×C19—22no—
139D4×C19—42no—
140D4×C19—44no—
141D4×C19—48no—
142D4×C19—42no—
143D4×C19—42no—
144D4×C19—82no—
145D4×C19#10414yescomplemented
146C2×C4×C19—22no—
147C2×C4×C19—22no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—22no—
151C2×C4×C19—22no—
152C2×C4×C19—22no—
153C2×C4×C19—22no—
154C2×C4×C19—44no—
155C2×C4×C19—42no—
156C2×C4×C19—42no—
157C2×C4×C19—42no—
158C2×C4×C19—42no—
159C2×C4×C19—42no—
160C2×C4×C19—42no—
161C2×C4×C19—82no—
162C2×C4×C19—84no—
163C2×C4×C19C2×C22⋊C411yescharacteristic
164C2×C4×C19C2×C22⋊C412yes—
165C2×C4×C19#12012yes—
166C2×C4×C19#12011yescharacteristic
167C2×Dic19—42no—
168C2×Dic19—44no—
169C19⋊C8—44no—
170C19⋊C8—81no—
171#3481D1911yescharacteristic
172#1962—191no—
173C4×#104—192no—
174#1525—191no—
175#1489—192no—
176C22×C19—21no—
177C22×C19—22no—
178C22×C19—24no—
179C22×C19—42no—
180C22×C19—42no—
181C22×C19—42no—
182C22×C19—44no—
183C22×C19—88no—
184C22×C19#37911yescharacteristic
185C4×C19—21no—
186C4×C19—22no—
187C4×C19—42no—
188C4×C19—42no—
189C4×C19—42no—
190C4×C19—42no—
191C4×C19C2×#10412yes—
192C4×C19#42112yes—
193C4×C19#45311yescharacteristic
194C4×C19#45511yescharacteristic
195Dic19—44no—
196#559Dic1911yescharacteristic, complemented
197#554Dic1912yescomplemented
198#553—22no—
199#551—22no—
200#546—22no—
201D42Dic1911yescharacteristic, complemented
202#532C2×D1911yescharacteristic
203#529—22no—
204#525—22no—
205C4×#41C2×D1912yes—
206C2×C4×D4—22no—
207#423—191no—
208C2×#104—382no—
209C2×#104—382no—
210C4×M16—192no—
211C43—191no—
212#339—382no—
213#329—382no—
214Q8⋊C8—382no—
215D4⋊C8—382no—
216C2×C19—41no—
217C2×C19—44no—
218C2×C19—82no—
219C2×C19#178912yes—
220C2×C19#179211yescharacteristic
221C2×#41C22⋊D1912yes—
222C2×#41C22⋊D1912yes—
223C22×D4—22no—
224C23×C4—22no—
225C2×M16—382no—
226C2×M16—381no—
227C4⋊Q8C2×Dic1911yescharacteristic
228#127C2×Dic1911yescharacteristic
229#126—24no—
230#125—22no—
231#124—22no—
232#124C22⋊D1912yes—
233#123—22no—
234#123—24no—
235#123—22no—
236C22⋊Q8—24no—
237C22⋊Q8—22no—
238#121—24no—
239#121—22no—
240#121—22no—
241#120—22no—
242#120—22no—
243C4×Q8C2×Dic1912yes—
244C4×Q8C22⋊D1912yes—
245C4×D4—24no—
246C4×D4—24no—
247C4×D4—22no—
248C4×D4—22no—
249C4×D4—22no—
250C4×D4—22no—
251C4×D4—22no—
252C4×D4C2×Dic1912yes—
253C4×D4C22⋊D1912yes—
254#117—22no—
255#117—22no—
256#117C22⋊D1912yes—
257C2×C4⋊C4—22no—
258C2×C22⋊C4—24no—
259C2×C42—22no—
260C2×C42—382no—
261C2×C42—381no—
262C2×C42C22×D1911yescharacteristic
263C4⋊C8—382no—
264#104—388no—
265#104—764no—
266#97—382no—
267C4×C8—382no—
268C19#844011yescharacteristic, complemented, Sylow
269C24—22no—
270#41—24no—
271#41—42no—
272#41—42no—
273#41—42no—
274C2×Q8C22⋊Dic1912yes—
275C2×Q8C22⋊Dic1912yes—
276C2×D4—24no—
277C2×D4—22no—
278C2×D4—22no—
279C2×D4—22no—
280C2×D4—44no—
281C2×D4—44no—
282C2×D4C22⋊Dic1912yes—
283C2×D4C22⋊Dic1912yes—
284C22×C4—24no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—82no—
291C22×C4—82no—
292C22×C4—761no—
293C22×C4C2×C22⋊D1912yes—
294C22×C4C2×C22⋊D1911yescharacteristic
295M16—384no—
296M16—762no—
297M16—762no—
298C2×C8—762no—
299C2×C8—761no—
300C4⋊C4—24no—
301C4⋊C4—24no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4C22⋊Dic1912yes—
306C4⋊C4C22⋊Dic1912yes—
307C22⋊C4—24no—
308C22⋊C4—24no—
309C22⋊C4—22no—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—24no—
315C42—22no—
316C42—22no—
317C42—22no—
318C42—384no—
319C42—382no—
320C42—762no—
321C42—761no—
322C42C22×Dic1911yescharacteristic
323C42C2×C22⋊D1911yescharacteristic
324C42C2×C22⋊D1912yes—
325C23—22no—
326C23—22no—
327C23—48no—
328C23—82no—
329C23#1059739911yescharacteristic
330Q8—22no—
331Q8—22no—
332Q8—42no—
333D4—22no—
334D4—42no—
335D4—44no—
336D4—48no—
337D4—42no—
338D4—42no—
339D4—82no—
340D4#1059729414yescomplemented
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—82no—
357C2×C4—84no—
358C2×C4—762no—
359C2×C4—764no—
360C2×C4C2×C22⋊Dic1911yescharacteristic
361C2×C4C2×C22⋊Dic1912yes—
362C2×C4#1059739912yes—
363C2×C4#1059739911yescharacteristic
364C8—764no—
365C8—1521no—
366C22—21no—
367C22—22no—
368C22—24no—
369C22—42no—
370C22—42no—
371C22—42no—
372C22—44no—
373C22—88no—
374C22#1192640011yescharacteristic
375C4—21no—
376C4—22no—
377C4—42no—
378C4—42no—
379C4—42no—
380C4—42no—
381C4—764no—
382C4C2×#1059729412yes—
383C4#1192656112yes—
384C4#1192671211yescharacteristic
385C4#1192672211yescharacteristic
386C2—41no—
387C2—44no—
388C2—82no—
389C2#1456357912yes—
390C2#1456358911yescharacteristic
subgroupG/H
centerC2×C4#10597399
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3481C2
socleC22×C19#379
cosocleC2×C42×C19C23
hypercenter#3481D19
hypocenterC19#8440
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3481

Complements

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

NH ≅ G/Ntype
1. #14564464C2semidirect
2. C4×#10597294C2semidirect
3. #14562227C2semidirect
4. #14562074C2semidirect
6. #11926568C22semidirect
9. C4×#64520C22semidirect
10. C42×Dic19C22semidirect
15. C19×#559C4semidirect
16. C19×#554C4semidirect
20. D42×C19C4semidirect
145. D4×C19#104semidirect
196. #559Dic19semidirect
197. #554Dic19semidirect
201. D42Dic19semidirect
268. C19#8440semidirect
340. D4#10597294semidirect

Maximal subgroups

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

subgroupindex
#145644642
C4×#105972942
#145622272
#145620742
C19×#34812
#844019