Finite Group Databasebeta

← #14573126

Subgroups — #14573126

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×#10597364C211yesmaximal, characteristic, complemented
2C2×#10597360C211yesmaximal, characteristic
3#124×D19C211yesmaximal, characteristic, complemented
4C4×#64545C211yesmaximal, characteristic, complemented
5#11926768C211yesmaximal, characteristic, complemented
6#11926766C211yesmaximal, characteristic, complemented
7#11926764C211yesmaximal, characteristic, complemented
8#11926762C211yesmaximal, characteristic, complemented
9#11926760C211yesmaximal, characteristic, complemented
10#11926758C211yesmaximal, characteristic, complemented
11#11926756C211yesmaximal, characteristic, complemented
12#11926566C211yesmaximal, characteristic, complemented
13#11926551C211yesmaximal, characteristic, complemented
14#11926547C211yesmaximal, characteristic, complemented
15C19×#464C211yesmaximal, characteristic, complemented
16C2×#64545C2211yescharacteristic
17C2×Q8×D19C2211yescharacteristic
18C2×D4×D19C2211yescharacteristic
19C2×Q16×C19C2211yescharacteristic, complemented
20C2×SD16×C19C2211yescharacteristic
21C19×#124C2211yescharacteristic
22C4×Q8×C19C2211yescharacteristic, complemented
23#10597393C2211yescharacteristic
24Q8×Dic19C2211yescharacteristic, complemented
25C2×#64528C2211yescharacteristic, complemented
26C2×#64527C2211yescharacteristic
27C2×#64527C2211yescharacteristic, complemented
28#10597382C2211yescharacteristic
29C2×#64525C2211yescharacteristic
30#10597364—24no—
31#10597360—24no—
32C2×D152C2211yescharacteristic
33C2×#64516C2211yescharacteristic, complemented
34C2×#64515C2211yescharacteristic
35C2×#64515C2211yescharacteristic
36#10597339—21no—
37#10597339C2211yescharacteristic, complemented
38#10597338—21no—
39#10597338C2211yescharacteristic
40#10597331—21no—
41#10597331—21no—
42C22⋊C4×D19—21no—
43C22⋊C4×D19—21no—
44#10597321C2211yescharacteristic
45C4×D76—21no—
46C4×D76C2211yescharacteristic, complemented
47C42×D19—21no—
48C42×D19C2211yescharacteristic
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×Q8×C19C2311yescharacteristic
64C2×D4×C19C2311yescharacteristic
65C2×C22⋊D19—21no—
66#64545—22no—
67#64545D414yes—
68Q8×D19—22no—
69Q8×D19—22no—
70D4×D19—22no—
71D4×D19—22no—
72C2×D76—21no—
73C2×D76C2311yescharacteristic
74C2×D76C2311yescharacteristic
75C2×C4×D19—21no—
76C2×C4×D19—21no—
77C2×C4×D19—21no—
78C2×C4×D19—21no—
79C2×C4×D19D411yescharacteristic
80C2×C4×D19D411yescharacteristic
81C2×C4×D19C2311yescharacteristic
82C2×Dic38—21no—
83C2×Dic38C2311yescharacteristic
84Q16×C19—22no—
85SD16×C19—22no—
86C2×C8×C19C2311yescharacteristic
87C2×C8×C19C2311yescharacteristic
88C4⋊C4×C19—21no—
89C4⋊C4×C19C2311yescharacteristic
90C22⋊C4×C19—21no—
91C22⋊C4×C19—21no—
92C42×C19—21no—
93C42×C19C2311yescharacteristic
94C22⋊Dic19—21no—
95C22⋊Dic19—21no—
96#64528—22no—
97#64527—22no—
98#64527—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—
105(C2×D19)⋊C4—21no—
106(C2×D19)⋊C4—21no—
107C4⋊Dic19—21no—
108C4⋊Dic19C2311yescharacteristic
109C4×Dic19—21no—
110C4×Dic19—21no—
111C4×Dic19D411yescharacteristic
112C4×Dic19D411yescharacteristic
113C4×Dic19C2311yescharacteristic
114C2×C19⋊C8C2311yescharacteristic
115C2×C19⋊C8C2311yescharacteristic
116D152—22no—
117#64516—22no—
118#64515—22no—
119#64515—22no—
120C23×C19—21no—
121C22×D19—21no—
122C22×D19—21no—
123C22×D19—42no—
124C22×D19—42no—
125C22×D19—42no—
126C22×D19C2×D411yescharacteristic
127Q8×C19—21no—
128Q8×C19—21no—
129Q8×C19—21no—
130Q8×C19C2×D412yes—
131D4×C19—21no—
132D4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19C2×D411yescharacteristic
137C2×C4×C19C2×D411yescharacteristic
138C2×C4×C19C2411yescharacteristic
139C22⋊D19—42no—
140C2×Dic19—21no—
141C2×Dic19—21no—
142C2×Dic19C2×D411yescharacteristic
143C2×Dic19C2×D411yescharacteristic
144C2×Dic19C2×D411yescharacteristic
145D76—24no—
146D76—21no—
147D76—21no—
148D76—21no—
149D76C2×D412yes—
150C4×D19—24no—
151C4×D19—41no—
152C4×D19—41no—
153C4×D19—42no—
154C4×D19—42no—
155C4×D19—42no—
156C4×D19C2×D412yes—
157C4×D19#4112yes—
158Dic38—21no—
159Dic38—21no—
160Dic38—42no—
161C8×C19—21no—
162C8×C19—21no—
163C19⋊C8—21no—
164C19⋊C8—21no—
165#3040—191nomaximal, Sylow
166C22×C19—41no—
167C22×C19—41no—
168C22×C19—41no—
169C22×C19C22×D411yescharacteristic
170C2×D19—21no—
171C2×D19—21no—
172C2×D19—22no—
173C2×D19—41no—
174C2×D19—41no—
175C2×D19—41no—
176C2×D19—41no—
177C2×D19—41no—
178C2×D19—84no—
179C2×D19#12112yes—
180C4×C19—22no—
181C4×C19—21no—
182C4×C19—21no—
183C4×C19—41no—
184C4×C19—41no—
185C4×C19C22×D411yescharacteristic
186C4×C19C2×#4111yescharacteristic
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#464D1911yescharacteristic, complemented
200#463—191no—
201#463—191no—
202#463—191no—
203#463—191no—
204#423—191no—
205#419—191no—
206#418—191no—
207C2×C19—81no—
208C2×C19C2×#12111yescharacteristic
209C2×C19#57511yescharacteristic
210C2×C19#57511yescharacteristic
211D19—22no—
212D19—42no—
213D19—81no—
214C2×#41—191no—
215C22×Q8—191no—
216C22×D4—191no—
217#137—384no—
218AGL(1,ℤ/8)—384no—
219C2×Q16—191no—
220C2×Q16C2×D1911yescharacteristic, complemented
221C2×SD16—191no—
222C2×SD16—191no—
223C2×SD16—191no—
224C2×SD16C2×D1911yescharacteristic
225C2×D8—191no—
226C2×D8—191no—
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×Q8C2×D1911yescharacteristic, complemented
237C4×D4—191no—
238C4×D4—191no—
239C4×D4—381no—
240C4×D4—381no—
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—381no—
265C2×Q8—382no—
266C2×Q8—382no—
267C2×Q8C22×D1911yescharacteristic
268C2×Q8C22×D1911yescharacteristic
269C2×D4—191no—
270C2×D4—191no—
271C2×D4—381no—
272C2×D4—382no—
273C2×D4—382no—
274C2×D4—381no—
275C2×D4C22×D1911yescharacteristic
276C22×C4—191no—
277C22×C4—191no—
278C22×C4—191no—
279C22×C4—381no—
280C22×C4—381no—
281C22×C4—381no—
282C22×C4—381no—
283Q16—22no—
284Q16—382no—
285SD16—22no—
286SD16—382no—
287SD16—382no—
288SD16—382no—
289D8—382no—
290D8—382no—
291M16—382no—
292M16—382no—
293C2×C8—191no—
294C2×C8—191no—
295C2×C8C22×D1911yescharacteristic
296C2×C8C22×D1911yescharacteristic
297C4⋊C4—21no—
298C4⋊C4—191no—
299C4⋊C4—381no—
300C4⋊C4C22×D1911yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—381no—
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—21no—
313C42—191no—
314C42—191no—
315C42—191no—
316C42—381no—
317C42—381no—
318C42C22×D1911yescharacteristic
319C23—21no—
320C23—191no—
321C23—381no—
322C23—381no—
323C23—762no—
324C23—762no—
325C23—762no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—381no—
330Q8—381no—
331Q8—762no—
332Q8D4×D1912yes—
333D4—21no—
334D4—21no—
335D4—192no—
336D4—384no—
337D4—381no—
338D4—381no—
339D4—381no—
340D4—762no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
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—761no—
353C2×C4—761no—
354C2×C4—762no—
355C2×C4—762no—
356C2×C4—762no—
357C2×C4D4×D1911yescharacteristic
358C2×C4D4×D1911yescharacteristic
359C2×C4C23×D1911yescharacteristic
360C8—21no—
361C8—21no—
362C8—381no—
363C8—381no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—192no—
368C22—381no—
369C22—381no—
370C22—382no—
371C22—761no—
372C22—761no—
373C22—761no—
374C22—761no—
375C22—761no—
376C22—1524no—
377C22C2×D4×D1911yescharacteristic
378C4—21no—
379C4—21no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—192no—
384C4—381no—
385C4—381no—
386C4—761no—
387C4—761no—
388C4C2×D4×D1911yescharacteristic
389C4#41×D1911yescharacteristic
390C2—81no—
391C2—382no—
392C2—762no—
393C2—1521no—
394C2#121×D1911yescharacteristic
395C2#1192734111yescharacteristic
396C2#1192734311yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#464C2
socleC22×C19C22×D4
prime radicalC2×#10597360C2
hypercenter#464D19
hypocenterC19#3040
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#10597364C2semidirect
3. #124×D19C2semidirect
4. C4×#64545C2semidirect
5. #11926768C2semidirect
6. #11926766C2semidirect
7. #11926764C2semidirect
8. #11926762C2semidirect
9. #11926760C2semidirect
10. #11926758C2semidirect
11. #11926756C2semidirect
12. #11926566C2semidirect
13. #11926551C2semidirect
14. #11926547C2semidirect
15. C19×#464C2semidirect
19. C2×Q16×C19C22semidirect
22. C4×Q8×C19C22semidirect
24. Q8×Dic19C22semidirect
25. C2×#64528C22semidirect
27. C2×#64527C22semidirect
33. C2×#64516C22semidirect
37. #10597339C22semidirect
46. C4×D76C22semidirect
49. C19×C4⋊C8C22semidirect
50. C19×#103C22semidirect
52. #10597292C22semidirect
55. #10597273C22semidirect
56. Dic19⋊C8C22semidirect
57. Dic19⋊C8C22semidirect
58. #10597267C22semidirect
60. C4⋊(C19⋊C8)C22semidirect
199. #464D19semidirect
220. C2×Q16C2×D19semidirect
236. C4×Q8C2×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×#105973642
C2×#105973602
#124×D192
C4×#645452
#119267682
#119267662
#119267642
#119267622
#119267602
#119267582
#119267562
#119265662
#119265512
#119265472
C19×#4642
#304019