Finite Group Databasebeta

← #14575345

Subgroups — #14575345

Order 2432.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597396C211yesmaximal, characteristic, complemented
2C2×SD16×D19C211yesmaximal, characteristic, complemented
3#11927201C211yesmaximal, characteristic, complemented
4#11927191C211yesmaximal, characteristic, complemented
5#11926927C211yesmaximal, characteristic, complemented
6#11926772C211yesmaximal, characteristic, complemented
7#11926771C211yesmaximal, characteristic, complemented
8#11926764C211yesmaximal, characteristic, complemented
9#11926758C211yesmaximal, characteristic, complemented
10#11926708C211yesmaximal, characteristic, complemented
11#11926701C211yesmaximal, characteristic, complemented
12#11926676C211yesmaximal, characteristic, complemented
13#11926629C211yesmaximal, characteristic, complemented
14(C22⋊D19)⋊C8C211yesmaximal, characteristic, complemented
15C19×#449C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic, complemented
17C2×Q8×D19C2211yescharacteristic
18C2×D4×D19C2211yescharacteristic
19C2×#64541C2211yescharacteristic
20C2×SD16×C19C2211yescharacteristic
21C2×D8×C19C2211yescharacteristic
22C19×#121C2211yescharacteristic
23#10597396—24no—
24Q8×Dic19C2211yescharacteristic, complemented
25C2×#64528C2211yescharacteristic, complemented
26C2×#64527C2211yescharacteristic
27#10597384—21no—
28#10597384—21no—
29#10597384C2211yescharacteristic
30#10597383—21no—
31#10597382—21no—
32#10597382C2211yescharacteristic
33#10597382C2211yescharacteristic, complemented
34C2×#64526C2211yescharacteristic
35C2×#64526C2211yescharacteristic, complemented
36C2×#64525C2211yescharacteristic
37C4×C22⋊D19—21no—
38C4×C22⋊D19C2211yescharacteristic
39#10597370—21no—
40#10597370C2211yescharacteristic, complemented
41C22×C19⋊C8C2211yescharacteristic, complemented
42SD16×D19—24no—
43C2×Dic76C2211yescharacteristic, complemented
44C2×#64516C2211yescharacteristic
45C2×C8×D19C2211yescharacteristic
46#10597343C2211yescharacteristic
47#10597339C2211yescharacteristic
48#10597329—21no—
49C22⋊C4×D19—21no—
50C19×#103C2211yescharacteristic, complemented
51C19×#102C2211yescharacteristic, complemented
52C19×C22⋊C8C2211yescharacteristic, complemented
53#10597289C2211yescharacteristic
54#10597278C2211yescharacteristic
55(C2×D19)⋊C8C2211yescharacteristic
56#10597273C2211yescharacteristic, complemented
57Dic19⋊C8C2211yescharacteristic, complemented
58C8×Dic19C2211yescharacteristic, complemented
59#10597267C2211yescharacteristic, complemented
60#10597265C2211yescharacteristic, complemented
61C23×D19—21no—
62#41×C19—22no—
63#41×C19—41no—
64C2×Q8×C19C2311yescharacteristic
65C2×D4×C19—21no—
66C2×D4×C19—21no—
67C2×D4×C19C2311yescharacteristic
68C2×D4×C19C2311yescharacteristic
69C22×C4×C19—21no—
70C22×C4×C19C2311yescharacteristic
71C2×C22⋊D19—21no—
72C2×C22⋊D19—21no—
73C2×C22⋊D19—21no—
74C2×C22⋊D19D411yescharacteristic
75Q8×D19—22no—
76Q8×D19—41no—
77D4×D19—22no—
78D4×D19—41no—
79#64541—22no—
80#64541—41no—
81C2×D76C2311yescharacteristic
82C2×C4×D19—21no—
83C2×C4×D19—21no—
84C2×C4×D19—21no—
85C2×C4×D19C2311yescharacteristic
86C2×Dic38—21no—
87C2×Dic38C2311yescharacteristic
88C2×Dic38C2311yescharacteristic
89SD16×C19—22no—
90D8×C19—41no—
91C2×C8×C19C2311yescharacteristic
92C2×C8×C19C2311yescharacteristic
93C4⋊C4×C19C2311yescharacteristic
94C22⋊C4×C19—21no—
95C22⋊Dic19—21no—
96C22⋊Dic19—21no—
97C22⋊Dic19—21no—
98C22⋊Dic19—21no—
99C22⋊Dic19—21no—
100C22⋊Dic19—21no—
101C22⋊Dic19D411yescharacteristic
102#64528—22no—
103#64527D414yescomplemented
104#64526—22no—
105#64526—22no—
106#64525—22no—
107(C2×D19)⋊C4—21no—
108(C2×D19)⋊C4—21no—
109(C2×D19)⋊C4D411yescharacteristic
110C4⋊Dic19—21no—
111C4⋊Dic19—21no—
112C4⋊Dic19C2311yescharacteristic
113Dic19⋊C4—21no—
114Dic19⋊C4D411yescharacteristic
115C4×Dic19—21no—
116C4×Dic19C2311yescharacteristic
117C2×C19⋊C8—22no—
118C2×C19⋊C8C2311yescharacteristic
119C2×C19⋊C8C2311yescharacteristic
120Dic76—41no—
121#64516—22no—
122C8×D19—22no—
123C23×C19—21no—
124C23×C19—21no—
125C23×C19C2×D411yescharacteristic
126C22×D19—21no—
127C22×D19—42no—
128C22×D19—42no—
129C22×D19—81no—
130C22×D19C2×D411yescharacteristic
131Q8×C19—21no—
132Q8×C19C2×D412yes—
133D4×C19—21no—
134D4×C19—21no—
135D4×C19—21no—
136D4×C19—21no—
137D4×C19—42no—
138D4×C19—81no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—42no—
144C2×C4×C19C2×D411yescharacteristic
145C2×C4×C19C2411yescharacteristic
146C22⋊D19—22no—
147C22⋊D19—42no—
148C22⋊D19—42no—
149C22⋊D19—42no—
150C2×Dic19—21no—
151C2×Dic19—21no—
152C2×Dic19—21no—
153C2×Dic19C2×D411yescharacteristic
154C2×Dic19C2×D411yescharacteristic
155C2×Dic19C2×D411yescharacteristic
156D76—21no—
157D76C2×D412yes—
158C4×D19—21no—
159C4×D19—21no—
160C4×D19—42no—
161C4×D19—42no—
162C4×D19—81no—
163Dic38—21no—
164Dic38—21no—
165Dic38—21no—
166Dic38—21no—
167Dic38—42no—
168C8×C19—21no—
169C8×C19—21no—
170C19⋊C8—21no—
171C19⋊C8C2×D412yes—
172#3282—191nomaximal, Sylow
173C22×C19—21no—
174C22×C19—21no—
175C22×C19—21no—
176C22×C19—41no—
177C22×C19—41no—
178C22×C19—41no—
179C22×C19—41no—
180C22×C19—41no—
181C22×C19—41no—
182C22×C19C22×D411yescharacteristic
183C2×D19—21no—
184C2×D19—21no—
185C2×D19—22no—
186C2×D19—41no—
187C2×D19—41no—
188C2×D19—84no—
189C2×D19#13512yescomplemented
190C4×C19—22no—
191C4×C19—21no—
192C4×C19—41no—
193C4×C19C22×D411yescharacteristic
194C4×C19H(5,𝔽2)11yescharacteristic
195Dic19—21no—
196Dic19—21no—
197Dic19—21no—
198Dic19—41no—
199Dic19—41no—
200Dic19—41no—
201C2×#135—191no—
202C22×SD16—191no—
203#548—191no—
204#546—191no—
205#495—191no—
206#465—191no—
207#465—191no—
208#464—191no—
209#463—191no—
210#452—191no—
211#451—191no—
212#449D1911yescharacteristic, complemented
213#447—191no—
214C4×SD16—191no—
215C8×D4—191no—
216C2×C19—41no—
217C2×C19—81no—
218C2×C19—81no—
219C2×C19D4211yescharacteristic
220C2×C19C2×#13511yescharacteristic
221C2×C19#57711yescharacteristic
222D19—22no—
223D19—42no—
224C2×#41—191no—
225C2×#41C2×D1911yescharacteristic, complemented
226C22×Q8—191no—
227C22×D4—191no—
228#135—384no—
229C2×Q16—191no—
230C2×Q16—191no—
231C2×SD16—191no—
232C2×SD16—191no—
233C2×SD16—191no—
234C2×SD16—191no—
235C2×SD16—384no—
236C2×SD16C2×D1911yescharacteristic
237C2×D8—191no—
238C2×D8C2×D1911yescharacteristic
239C22×C8—191no—
240C22×C8—191no—
241#124—191no—
242#124—191no—
243#124—381no—
244#123—381no—
245C22⋊Q8—191no—
246C22⋊Q8—191no—
247C22⋊Q8—381no—
248#121—191no—
249#121—381no—
250#121—381no—
251#121C2×D1911yescharacteristic
252#120—381no—
253C4×Q8—191no—
254C4×D4—191no—
255C4×D4—191no—
256C4×D4—381no—
257C2×C22⋊C4—381no—
258#106—191no—
259C4⋊C8—191no—
260#103—191no—
261#103—191no—
262#103C2×D1911yescharacteristic, complemented
263#102—191no—
264#102—191no—
265#102C2×D1911yescharacteristic, complemented
266C22⋊C8—191no—
267C22⋊C8C2×D1911yescharacteristic, complemented
268C4×C8—191no—
269C19#328211yescharacteristic, complemented, Sylow
270C24—381no—
271#41—22no—
272#41—41no—
273#41—382no—
274#41—761no—
275C2×Q8—191no—
276C2×Q8—191no—
277C2×Q8—381no—
278C2×Q8—382no—
279C2×Q8—761no—
280C2×Q8C22×D1911yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—191no—
284C2×D4—191no—
285C2×D4—381no—
286C2×D4—382no—
287C2×D4—381no—
288C2×D4—381no—
289C2×D4—761no—
290C2×D4C22×D1911yescharacteristic
291C2×D4C22×D1911yescharacteristic
292C22×C4—21no—
293C22×C4—191no—
294C22×C4—381no—
295C22×C4—381no—
296C22×C4—381no—
297C22×C4C22×D1911yescharacteristic
298Q16—382no—
299Q16—761no—
300SD16—22no—
301SD16—194no—
302SD16—382no—
303SD16—382no—
304SD16—382no—
305D8—41no—
306D8—382no—
307C2×C8—191no—
308C2×C8—191no—
309C2×C8—382no—
310C2×C8—382no—
311C2×C8C22×D1911yescharacteristic
312C2×C8C22×D1911yescharacteristic
313C4⋊C4—191no—
314C4⋊C4—191no—
315C4⋊C4—381no—
316C4⋊C4—381no—
317C4⋊C4—381no—
318C4⋊C4C22×D1911yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—191no—
321C22⋊C4—191no—
322C22⋊C4—381no—
323C22⋊C4—381no—
324C22⋊C4—381no—
325C22⋊C4—381no—
326C22⋊C4—381no—
327C22⋊C4—381no—
328C22⋊C4—381no—
329C22⋊C4—381no—
330C42—191no—
331C42—381no—
332C23—21no—
333C23—21no—
334C23—191no—
335C23—381no—
336C23—762no—
337C23—762no—
338C23—1521no—
339C23D4×D1911yescharacteristic
340Q8—21no—
341Q8—381no—
342Q8—381no—
343Q8—381no—
344Q8—381no—
345Q8—762no—
346Q8D4×D1912yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—42no—
352D4—81no—
353D4—192no—
354D4—382no—
355D4—381no—
356D4—762no—
357D4—762no—
358D4—762no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—42no—
364C2×C4—191no—
365C2×C4—191no—
366C2×C4—191no—
367C2×C4—381no—
368C2×C4—381no—
369C2×C4—381no—
370C2×C4—381no—
371C2×C4—381no—
372C2×C4—762no—
373C2×C4—762no—
374C2×C4—1521no—
375C2×C4D4×D1911yescharacteristic
376C2×C4C23×D1911yescharacteristic
377C8—21no—
378C8—21no—
379C8—192no—
380C8—381no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—192no—
391C22—381no—
392C22—381no—
393C22—382no—
394C22—761no—
395C22—761no—
396C22—1524no—
397C22C2×D4×D1911yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—381no—
402C4—381no—
403C4—381no—
404C4—761no—
405C4—761no—
406C4—761no—
407C4C2×D4×D1911yescharacteristic
408C4#1059743011yescharacteristic
409C2—41no—
410C2—81no—
411C2—81no—
412C2—382no—
413C2—762no—
414C2#1192717611yescharacteristic
415C2#135×D1911yescharacteristic
416C2#1192735411yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#449C2
socleC22×C19C22×D4
hypercenter#449D19
hypocenterC19#3282
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#10597396C2semidirect
2. C2×SD16×D19C2semidirect
3. #11927201C2semidirect
4. #11927191C2semidirect
5. #11926927C2semidirect
6. #11926772C2semidirect
7. #11926771C2semidirect
8. #11926764C2semidirect
9. #11926758C2semidirect
10. #11926708C2semidirect
11. #11926701C2semidirect
12. #11926676C2semidirect
13. #11926629C2semidirect
14. (C22⋊D19)⋊C8C2semidirect
15. C19×#449C2semidirect
16. C2×#41×C19C22semidirect
24. Q8×Dic19C22semidirect
25. C2×#64528C22semidirect
33. #10597382C22semidirect
35. C2×#64526C22semidirect
40. #10597370C22semidirect
41. C22×C19⋊C8C22semidirect
43. C2×Dic76C22semidirect
50. C19×#103C22semidirect
51. C19×#102C22semidirect
52. C19×C22⋊C8C22semidirect
56. #10597273C22semidirect
57. Dic19⋊C8C22semidirect
58. C8×Dic19C22semidirect
59. #10597267C22semidirect
60. #10597265C22semidirect
103. #64527D4semidirect
189. C2×D19#135semidirect
212. #449D19semidirect
225. C2×#41C2×D19semidirect
262. #103C2×D19semidirect
265. #102C2×D19semidirect
267. C22⋊C8C2×D19semidirect
269. C19#3282semidirect

Maximal subgroups

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

subgroupindex
C2×#105973962
C2×SD16×D192
#119272012
#119271912
#119269272
#119267722
#119267712
#119267642
#119267582
#119267082
#119267012
#119266762
#119266292
(C22⋊D19)⋊C82
C19×#4492
#328219