Finite Group Databasebeta

← #18075046

Subgroups — #18075046

Order 4864.

754 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 131 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#14563718C211yesmaximal, characteristic, complemented
2#14563712C211yesmaximal, characteristic, complemented
3#14562168C212yesmaximal, complemented
4#14562164C212yesmaximal
5C2×C19×#542C211yesmaximal, characteristic
6#11926508C2212yes—
7#11926407C2212yes—
8#11926313—21no—
9#11926313—21no—
10#11926311—21no—
11#11926311—21no—
12#11926281—24no—
13#11926278—24no—
14C19×#542—24no—
15C19×#542—24no—
16C2×C19×C4⋊Q8C411yescharacteristic, complemented
17C2×C19×#126—21no—
18C2×C19×#124—21no—
19C2×C19×#124C411yescharacteristic, complemented
20C2×C19×#123—21no—
21C2×C19×C22⋊Q8—21no—
22C2×C19×C22⋊Q8C2211yescharacteristic
23C2×C19×#121C2211yescharacteristic
24C2×C4×Q8×C19C411yescharacteristic, complemented
25C2×C4×D4×C19C411yescharacteristic, complemented
26C2×C19×#117C2211yescharacteristic
27C22×Q8×C19—21no—
28C22×Q8×C19C2×C411yescharacteristic
29C22×D4×C19—21no—
30C22×D4×C19C2×C411yescharacteristic
31C23×C4×C19—21no—
32C23×C4×C19C2311yescharacteristic
33C19×C4⋊Q8—22no—
34C19×C4⋊Q8—22no—
35C19×#126—28no—
36C19×#124—28no—
37C19×#124—22no—
38C19×#124—22no—
39C19×#123—28no—
40C19×C22⋊Q8—28no—
41C19×C22⋊Q8—22no—
42C19×C22⋊Q8D414yes—
43C19×#121—22no—
44C19×#121D414yes—
45C4×Q8×C19—22no—
46C4×Q8×C19—22no—
47C4×D4×C19—22no—
48C4×D4×C19—22no—
49C19×#117—22no—
50C19×#117—22no—
51C2×C4⋊C4×C19—21no—
52C2×C4⋊C4×C19—21no—
53C2×C4⋊C4×C19—21no—
54C2×C4⋊C4×C19C2×C411yescharacteristic
55C2×C4⋊C4×C19C2×C411yescharacteristic
56C2×C4⋊C4×C19D411yescharacteristic
57C2×C4⋊C4×C19D411yescharacteristic
58C2×C22⋊C4×C19—21no—
59C2×C22⋊C4×C19—21no—
60C2×C22⋊C4×C19—21no—
61C2×C22⋊C4×C19—21no—
62C2×C22⋊C4×C19—21no—
63C2×C22⋊C4×C19D411yescharacteristic
64C2×C22⋊C4×C19D411yescharacteristic
65C2×C42×C19—21no—
66C2×C42×C19C2×C411yescharacteristic
67C2×C42×C19C2×C411yescharacteristic
68C2×C22⋊Dic19—22no—
69C2×#64520—22no—
70C19⋊#95—22no—
71C19⋊#95—22no—
72C22⋊(C19⋊C8)—22no—
73C22⋊(C19⋊C8)—22no—
74C24×C19—21no—
75C24×C19C2×D411yescharacteristic
76C2×Q8×C19—24no—
77C2×Q8×C19—21no—
78C2×Q8×C19—42no—
79C2×Q8×C19—82no—
80C2×Q8×C19C22⋊C412yes—
81C2×D4×C19—24no—
82C2×D4×C19—21no—
83C2×D4×C19—42no—
84C2×D4×C19—82no—
85C2×D4×C19C22⋊C412yes—
86C22×C4×C19—21no—
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—24no—
90C22×C4×C19—42no—
91C22×C4×C19—82no—
92C22×C4×C19C22⋊C411yescharacteristic
93C22×C4×C19C22⋊C411yescharacteristic
94C22×C4×C19C22⋊C411yescharacteristic
95C22×C4×C19C22⋊C411yescharacteristic
96C22×C4×C19C22×C411yescharacteristic
97C22×C4×C19C2×D411yescharacteristic
98C22×C4×C19C2×D412yes—
99C22×C4×C19C2×D412yes—
100C22×Dic19—42no—
101C4⋊C4×C19—24no—
102C4⋊C4×C19—24no—
103C4⋊C4×C19—21no—
104C4⋊C4×C19—21no—
105C4⋊C4×C19—24no—
106C4⋊C4×C19—22no—
107C4⋊C4×C19—22no—
108C4⋊C4×C19C22⋊C412yes—
109C4⋊C4×C19C22⋊C412yes—
110C22⋊C4×C19—24no—
111C22⋊C4×C19—24no—
112C22⋊C4×C19—24no—
113C22⋊C4×C19—24no—
114C22⋊C4×C19—22no—
115C22⋊C4×C19—22no—
116C22⋊C4×C19—24no—
117C42×C19—24no—
118C42×C19—21no—
119C42×C19—21no—
120C42×C19—21no—
121C42×C19—21no—
122C22⋊Dic19—44no—
123#64520—44no—
124C2×C19⋊C8—42no—
125#8519—191nomaximal, Sylow
126C23×C19—22no—
127C23×C19—22no—
128C23×C19—41no—
129C23×C19—41no—
130C23×C19—42no—
131C23×C19—42no—
132C23×C19—42no—
133C23×C19C2×C22⋊C411yescharacteristic
134C23×C19#12012yes—
135Q8×C19—42no—
136Q8×C19—42no—
137Q8×C19—84no—
138D4×C19—42no—
139D4×C19—42no—
140D4×C19—84no—
141C2×C4×C19—22no—
142C2×C4×C19—22no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—22no—
146C2×C4×C19—21no—
147C2×C4×C19—21no—
148C2×C4×C19—22no—
149C2×C4×C19—22no—
150C2×C4×C19—42no—
151C2×C4×C19—42no—
152C2×C4×C19—42no—
153C2×C4×C19—42no—
154C2×C4×C19—42no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—84no—
160C2×C4×C19C2×C22⋊C411yescharacteristic
161C2×C4×C19C2×C22⋊C411yescharacteristic
162C2×C4×C19#12012yes—
163C2×Dic19—82no—
164C2×Dic19—82no—
165C2×Dic19—82no—
166C19⋊C8—82no—
167C2×#542D1911yescharacteristic
168#1822—191no—
169#1820—191no—
170#1511—192no—
171#1510—192no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19—22no—
175C22×C19—22no—
176C22×C19—22no—
177C22×C19—42no—
178C22×C19—42no—
179C22×C19—42no—
180C22×C19—82no—
181C22×C19—84no—
182C22×C19#37911yescharacteristic
183C22×C19#41012yes—
184C4×C19—22no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—42no—
188C4×C19—42no—
189C4×C19—41no—
190C4×C19—41no—
191C4×C19—41no—
192C4×C19—41no—
193C4×C19—42no—
194Dic19—162no—
195#542—24no—
196#542—24no—
197C2×C4⋊Q8Dic1911yescharacteristic, complemented
198C2×#126—21no—
199C2×#124—21no—
200C2×#124Dic1911yescharacteristic, complemented
201C2×#123—21no—
202C2×C22⋊Q8—21no—
203C2×C22⋊Q8C2×D1911yescharacteristic
204C2×#121C2×D1911yescharacteristic
205C2×C4×Q8Dic1911yescharacteristic, complemented
206C2×C4×D4Dic1911yescharacteristic, complemented
207C2×#117C2×D1911yescharacteristic
208#407—192no—
209#381—192no—
210#343—381no—
211#343—381no—
212#342—381no—
213#342—381no—
214#328—384no—
215#327—384no—
216C2×C19—22no—
217C2×C19—42no—
218C2×C19—82no—
219C2×C19#178211yescharacteristic
220C2×C19#179511yescharacteristic
221C2×C19#179611yescharacteristic
222C22×Q8—21no—
223C22×Q8C2×Dic1911yescharacteristic
224C22×D4—21no—
225C22×D4C2×Dic1911yescharacteristic
226C23×C4—21no—
227C23×C4C22×D1911yescharacteristic
228C2×M16—382no—
229C4⋊Q8—22no—
230C4⋊Q8—22no—
231#126—28no—
232#124—28no—
233#124—22no—
234#124—22no—
235#123—28no—
236C22⋊Q8—28no—
237C22⋊Q8—22no—
238C22⋊Q8C22⋊D1914yes—
239#121—22no—
240#121C22⋊D1914yes—
241C4×Q8—22no—
242C4×Q8—22no—
243C4×D4—22no—
244C4×D4—22no—
245#117—22no—
246#117—22no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4C2×Dic1911yescharacteristic
251C2×C4⋊C4C2×Dic1911yescharacteristic
252C2×C4⋊C4C22⋊D1911yescharacteristic
253C2×C4⋊C4C22⋊D1911yescharacteristic
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—382no—
260C2×C22⋊C4C22⋊D1911yescharacteristic
261C2×C22⋊C4C22⋊D1911yescharacteristic
262C2×C42—21no—
263C2×C42C2×Dic1911yescharacteristic
264C2×C42C2×Dic1911yescharacteristic
265C22⋊C8—382no—
266C22⋊C8—382no—
267#95—382no—
268#95—382no—
269C19#851911yescharacteristic, complemented, Sylow
270C24—21no—
271C24C2×C22⋊D1911yescharacteristic
272C2×Q8—24no—
273C2×Q8—21no—
274C2×Q8—42no—
275C2×Q8—82no—
276C2×Q8C22⋊Dic1912yes—
277C2×D4—24no—
278C2×D4—21no—
279C2×D4—42no—
280C2×D4—82no—
281C2×D4C22⋊Dic1912yes—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—24no—
286C22×C4—42no—
287C22×C4—82no—
288C22×C4—762no—
289C22×C4C22⋊Dic1911yescharacteristic
290C22×C4C22⋊Dic1911yescharacteristic
291C22×C4C22⋊Dic1911yescharacteristic
292C22×C4C22⋊Dic1911yescharacteristic
293C22×C4C22×Dic1911yescharacteristic
294C22×C4C2×C22⋊D1911yescharacteristic
295C22×C4C2×C22⋊D1912yes—
296C22×C4C2×C22⋊D1912yes—
297M16—764no—
298C2×C8—762no—
299C4⋊C4—24no—
300C4⋊C4—24no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—24no—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4C22⋊Dic1912yes—
307C4⋊C4C22⋊Dic1912yes—
308C22⋊C4—24no—
309C22⋊C4—24no—
310C22⋊C4—24no—
311C22⋊C4—24no—
312C22⋊C4—22no—
313C22⋊C4—22no—
314C22⋊C4—24no—
315C22⋊C4—764no—
316C42—24no—
317C42—21no—
318C42—21no—
319C42—21no—
320C42—21no—
321C23—22no—
322C23—22no—
323C23—41no—
324C23—41no—
325C23—42no—
326C23—42no—
327C23—42no—
328C23C2×C22⋊Dic1911yescharacteristic
329C23#1059739912yes—
330Q8—42no—
331Q8—42no—
332Q8—84no—
333D4—42no—
334D4—42no—
335D4—84no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—84no—
355C2×C4—1522no—
356C2×C4—1522no—
357C2×C4—1522no—
358C2×C4C2×C22⋊Dic1911yescharacteristic
359C2×C4C2×C22⋊Dic1911yescharacteristic
360C2×C4#1059739912yes—
361C8—1522no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—42no—
368C22—42no—
369C22—42no—
370C22—82no—
371C22—84no—
372C22#1192640011yescharacteristic
373C22#1192651812yes—
374C4—22no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—42no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—42no—
384C4—3042no—
385C2—22no—
386C2—42no—
387C2—82no—
388C2#1456355311yescharacteristic
389C2#1456360511yescharacteristic
390C2#1456361011yescharacteristic
subgroupG/H
centerC22#11926400
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#542C2
socleC22×C19#379
prime radicalC2×C19×#121C22
cosocleC23×C4×C19C23
hypercenterC2×#542D19
hypocenterC19#8519
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. #14563718C2semidirect
2. #14563712C2semidirect
3. #14562168C2semidirect
16. C2×C19×C4⋊Q8C4semidirect
19. C2×C19×#124C4semidirect
24. C2×C4×Q8×C19C4semidirect
25. C2×C4×D4×C19C4semidirect
197. C2×C4⋊Q8Dic19semidirect
200. C2×#124Dic19semidirect
205. C2×C4×Q8Dic19semidirect
206. C2×C4×D4Dic19semidirect
269. C19#8519semidirect

Maximal subgroups

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

subgroupindex
#145637182
#145637122
#145621682
#145621642
C2×C19×#5422
#851919