Finite Group Databasebeta

← #14573124

Subgroups — #14573124

Order 2432.

500 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597361C211yesmaximal, characteristic, complemented
2C2×#10597357C211yesmaximal, characteristic
3#124×D19C211yesmaximal, characteristic, complemented
4C4×#64543C211yesmaximal, characteristic, complemented
5#11926769C211yesmaximal, characteristic, complemented
6#11926767C211yesmaximal, characteristic, complemented
7#11926765C211yesmaximal, characteristic, complemented
8#11926763C211yesmaximal, characteristic, complemented
9#11926761C211yesmaximal, characteristic, complemented
10#11926759C211yesmaximal, characteristic, complemented
11#11926757C211yesmaximal, characteristic, complemented
12#11926566C211yesmaximal, characteristic, complemented
13#11926551C211yesmaximal, characteristic, complemented
14#11926547C211yesmaximal, characteristic, complemented
15C19×#463C211yesmaximal, characteristic, complemented
16C2×Q8×D19C2211yescharacteristic
17C2×#64543C2211yescharacteristic
18C2×D4×D19C2211yescharacteristic
19C2×SD16×C19C2211yescharacteristic, complemented
20C2×D8×C19C2211yescharacteristic
21C19×#124C2211yescharacteristic
22C4×D4×C19C2211yescharacteristic, complemented
23#10597393C2211yescharacteristic
24C2×#64528C2211yescharacteristic, complemented
25#10597382C2211yescharacteristic
26D4×Dic19C2211yescharacteristic, complemented
27C2×#64526C2211yescharacteristic
28C2×#64526C2211yescharacteristic, complemented
29C2×#64525C2211yescharacteristic
30C4×C22⋊D19—21no—
31C2×C4×Dic19—21no—
32#10597361—24no—
33#10597357—24no—
34C2×Dic76C2211yescharacteristic, complemented
35C2×#64516C2211yescharacteristic
36C2×#64515C2211yescharacteristic
37C2×#64515C2211yescharacteristic
38#10597338C2211yescharacteristic
39#10597333C2211yescharacteristic, complemented
40#10597331—21no—
41#10597331—21no—
42(C22⋊D19)⋊C4—21no—
43C22⋊C4×D19—21no—
44C22⋊C4×D19—21no—
45#10597323—21no—
46#10597321C2211yescharacteristic
47C42×D19C2211yescharacteristic
48C4×Dic38C2211yescharacteristic, complemented
49C19×C4⋊C8C2211yescharacteristic, complemented
50C19×#103C2211yescharacteristic, complemented
51C19×#102C2211yescharacteristic
52#10597292C2211yescharacteristic, complemented
53#10597289C2211yescharacteristic
54#10597278C2211yescharacteristic
55#10597273C2211yescharacteristic, complemented
56Dic19⋊C8C2211yescharacteristic, complemented
57Dic19⋊C8C2211yescharacteristic, complemented
58#10597267C2211yescharacteristic, complemented
59#10597266C2211yescharacteristic
60C4⋊(C19⋊C8)C2211yescharacteristic, complemented
61C23×D19—21no—
62C2×Q8×C19C2311yescharacteristic
63C2×D4×C19C2311yescharacteristic
64C2×D4×C19C2311yescharacteristic
65C22×C4×C19—21no—
66C2×C22⋊D19—21no—
67C2×C22⋊D19—21no—
68C22×Dic19—21no—
69C22×Dic19—21no—
70Q8×D19—22no—
71Q8×D19—22no—
72#64543—22no—
73#64543D414yes—
74D4×D19—22no—
75D4×D19—22no—
76C2×D76C2311yescharacteristic
77C2×C4×D19—21no—
78C2×C4×D19D411yescharacteristic
79C2×C4×D19D411yescharacteristic
80C2×C4×D19C2311yescharacteristic
81C2×Dic38—21no—
82C2×Dic38C2311yescharacteristic
83C2×Dic38C2311yescharacteristic
84SD16×C19—22no—
85D8×C19—22no—
86C2×C8×C19C2311yescharacteristic
87C2×C8×C19C2311yescharacteristic
88C4⋊C4×C19C2311yescharacteristic
89C22⋊C4×C19—21no—
90C22⋊C4×C19—21no—
91C22⋊C4×C19—21no—
92C42×C19C2311yescharacteristic
93C22⋊Dic19—21no—
94C22⋊Dic19—21no—
95C22⋊Dic19—21no—
96#64528—22no—
97#64526—22no—
98#64526—22no—
99#64525—22no—
100(C2×D19)⋊C4—21no—
101(C2×D19)⋊C4—21no—
102(C2×D19)⋊C4—21no—
103(C2×D19)⋊C4—21no—
104(C2×D19)⋊C4—21no—
105C4⋊Dic19C2311yescharacteristic
106Dic19⋊C4—21no—
107Dic19⋊C4—21no—
108C4×Dic19—21no—
109C4×Dic19—21no—
110C4×Dic19—21no—
111C4×Dic19D411yescharacteristic
112C4×Dic19D411yescharacteristic
113C4×Dic19C2311yescharacteristic
114C2×C19⋊C8C2311yescharacteristic
115C2×C19⋊C8C2311yescharacteristic
116Dic76—22no—
117#64516—22no—
118#64515—22no—
119#64515—22no—
120C23×C19—21no—
121C23×C19—21no—
122C22×D19—21no—
123C22×D19—42no—
124C22×D19—42no—
125C22×D19—42no—
126C22×D19C2×D411yescharacteristic
127Q8×C19—21no—
128Q8×C19—21no—
129D4×C19—21no—
130D4×C19—21no—
131D4×C19—21no—
132D4×C19C2×D412yes—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—42no—
136C2×C4×C19C2×D411yescharacteristic
137C2×C4×C19C2×D411yescharacteristic
138C2×C4×C19C2411yescharacteristic
139C22⋊D19—24no—
140C22⋊D19—42no—
141C2×Dic19—21no—
142C2×Dic19—24no—
143C2×Dic19—21no—
144C2×Dic19—21no—
145C2×Dic19—42no—
146C2×Dic19C2×D411yescharacteristic
147C2×Dic19C2×D411yescharacteristic
148C2×Dic19C2×D411yescharacteristic
149D76—21no—
150D76—21no—
151C4×D19—41no—
152C4×D19—41no—
153C4×D19—42no—
154C4×D19C2×D412yes—
155C4×D19#4112yes—
156Dic38—21no—
157Dic38—21no—
158Dic38—21no—
159Dic38—42no—
160Dic38C2×D412yes—
161C8×C19—21no—
162C8×C19—21no—
163C19⋊C8—21no—
164C19⋊C8—21no—
165#3040—191nomaximal, Sylow
166C22×C19—22no—
167C22×C19—41no—
168C22×C19—41no—
169C22×C19—41no—
170C22×C19—41no—
171C22×C19—41no—
172C22×C19C22×D411yescharacteristic
173C2×D19—21no—
174C2×D19—21no—
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—41no—
178C2×D19—84no—
179C2×D19#12112yes—
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—41no—
183C4×C19—41no—
184C4×C19C22×D411yescharacteristic
185C4×C19C2×#4111yescharacteristic
186Dic19—22no—
187Dic19—21no—
188Dic19—21no—
189Dic19—41no—
190Dic19—41no—
191Dic19#12112yes—
192C2×#137—191no—
193C2×AGL(1,ℤ/8)—191no—
194C2×#124—191no—
195C4×#41—191no—
196#464—191no—
197#464—191no—
198#464—191no—
199#464—191no—
200#463—191no—
201#463—191no—
202#463—191no—
203#463D1911yescharacteristic, complemented
204#423—191no—
205#419—191no—
206#418—191no—
207C2×C19—42no—
208C2×C19—81no—
209C2×C19C2×#12111yescharacteristic
210C2×C19#57511yescharacteristic
211C2×C19#57511yescharacteristic
212D19—22no—
213D19—81no—
214C2×#41—191no—
215C22×Q8—191no—
216C22×D4—191no—
217#137—384no—
218AGL(1,ℤ/8)—384no—
219C2×Q16—191no—
220C2×Q16—191no—
221C2×SD16—191no—
222C2×SD16—191no—
223C2×SD16—191no—
224C2×SD16C2×D1911yescharacteristic, complemented
225C2×D8—191no—
226C2×D8C2×D1911yescharacteristic
227C2×M16—191no—
228C2×M16—191no—
229#124—191no—
230#124—191no—
231#124—191no—
232#124—381no—
233#124—381no—
234#124C2×D1911yescharacteristic
235C4×Q8—191no—
236C4×Q8—191no—
237C4×D4—191no—
238C4×D4—381no—
239C4×D4—381no—
240C4×D4C2×D1911yescharacteristic, complemented
241#117—191no—
242#117—381no—
243C2×C22⋊C4—381no—
244C2×C22⋊C4—381no—
245C2×C42—191no—
246C2×C42—381no—
247C4⋊C8—191no—
248C4⋊C8—191no—
249C4⋊C8—191no—
250C4⋊C8C2×D1911yescharacteristic, complemented
251#103—191no—
252#103—191no—
253#103—191no—
254#103C2×D1911yescharacteristic, complemented
255#102—191no—
256#102—191no—
257#102—191no—
258#102C2×D1911yescharacteristic
259C19#304011yescharacteristic, complemented, Sylow
260C24—381no—
261#41—194no—
262#41—382no—
263C2×Q8—191no—
264C2×Q8—191no—
265C2×Q8—381no—
266C2×Q8—382no—
267C2×Q8—382no—
268C2×Q8C22×D1911yescharacteristic
269C2×D4—191no—
270C2×D4—382no—
271C2×D4—382no—
272C2×D4—381no—
273C2×D4—381no—
274C2×D4C22×D1911yescharacteristic
275C2×D4C22×D1911yescharacteristic
276C22×C4—21no—
277C22×C4—191no—
278C22×C4—191no—
279C22×C4—191no—
280C22×C4—381no—
281C22×C4—381no—
282C22×C4—381no—
283Q16—382no—
284Q16—382no—
285SD16—22no—
286SD16—382no—
287SD16—382no—
288SD16—382no—
289D8—22no—
290D8—382no—
291M16—382no—
292M16—382no—
293C2×C8—191no—
294C2×C8—191no—
295C2×C8C22×D1911yescharacteristic
296C2×C8C22×D1911yescharacteristic
297C4⋊C4—191no—
298C4⋊C4—381no—
299C4⋊C4—381no—
300C4⋊C4C22×D1911yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—381no—
305C22⋊C4—381no—
306C22⋊C4—381no—
307C22⋊C4—381no—
308C22⋊C4—381no—
309C22⋊C4—381no—
310C22⋊C4—381no—
311C22⋊C4—381no—
312C42—191no—
313C42—191no—
314C42—191no—
315C42—381no—
316C42—381no—
317C42—381no—
318C42C22×D1911yescharacteristic
319C23—21no—
320C23—21no—
321C23—191no—
322C23—381no—
323C23—762no—
324C23—762no—
325C23—762no—
326Q8—21no—
327Q8—21no—
328Q8—192no—
329Q8—381no—
330Q8—381no—
331Q8—381no—
332Q8—762no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—384no—
337D4—381no—
338D4—381no—
339D4—762no—
340D4D4×D1912yes—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—191no—
345C2×C4—192no—
346C2×C4—192no—
347C2×C4—191no—
348C2×C4—191no—
349C2×C4—384no—
350C2×C4—381no—
351C2×C4—381no—
352C2×C4—381no—
353C2×C4—761no—
354C2×C4—761no—
355C2×C4—762no—
356C2×C4—762no—
357C2×C4D4×D1911yescharacteristic
358C2×C4D4×D1911yescharacteristic
359C2×C4C23×D1911yescharacteristic
360C8—21no—
361C8—21no—
362C8—381no—
363C8—381no—
364C22—22no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—192no—
371C22—381no—
372C22—381no—
373C22—761no—
374C22—761no—
375C22—761no—
376C22—1524no—
377C22C2×D4×D1911yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—192no—
383C4—381no—
384C4—381no—
385C4—382no—
386C4—761no—
387C4—761no—
388C4C2×D4×D1911yescharacteristic
389C4#41×D1911yescharacteristic
390C2—42no—
391C2—81no—
392C2—382no—
393C2—1521no—
394C2#121×D1911yescharacteristic
395C2#1192734011yescharacteristic
396C2#1192734111yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#463C2
socleC22×C19C22×D4
prime radicalC2×#10597357C2
hypercenter#463D19
hypocenterC19#3040
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#10597361C2semidirect
3. #124×D19C2semidirect
4. C4×#64543C2semidirect
5. #11926769C2semidirect
6. #11926767C2semidirect
7. #11926765C2semidirect
8. #11926763C2semidirect
9. #11926761C2semidirect
10. #11926759C2semidirect
11. #11926757C2semidirect
12. #11926566C2semidirect
13. #11926551C2semidirect
14. #11926547C2semidirect
15. C19×#463C2semidirect
19. C2×SD16×C19C22semidirect
22. C4×D4×C19C22semidirect
24. C2×#64528C22semidirect
26. D4×Dic19C22semidirect
28. C2×#64526C22semidirect
34. C2×Dic76C22semidirect
39. #10597333C22semidirect
48. C4×Dic38C22semidirect
49. C19×C4⋊C8C22semidirect
50. C19×#103C22semidirect
52. #10597292C22semidirect
55. #10597273C22semidirect
56. Dic19⋊C8C22semidirect
57. Dic19⋊C8C22semidirect
58. #10597267C22semidirect
60. C4⋊(C19⋊C8)C22semidirect
203. #463D19semidirect
224. C2×SD16C2×D19semidirect
240. C4×D4C2×D19semidirect
250. C4⋊C8C2×D19semidirect
254. #103C2×D19semidirect
259. C19#3040semidirect

Maximal subgroups

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

subgroupindex
C2×#105973612
C2×#105973572
#124×D192
C4×#645432
#119267692
#119267672
#119267652
#119267632
#119267612
#119267592
#119267572
#119265662
#119265512
#119265472
C19×#4632
#304019