Finite Group Databasebeta

← #14575265

Subgroups — #14575265

Order 2432.

498 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×#10597364C211yesmaximal, characteristic, complemented
2C2×#10597357C211yesmaximal, characteristic, complemented
3#11927202C211yesmaximal, characteristic, complemented
4#11927187C211yesmaximal, characteristic, complemented
5#11926799C211yesmaximal, characteristic, complemented
6#11926794C211yesmaximal, characteristic, complemented
7#11926763C211yesmaximal, characteristic, complemented
8#11926756C211yesmaximal, characteristic, complemented
9#11926703C211yesmaximal, characteristic, complemented
10#11926693C211yesmaximal, characteristic, complemented
11#11926688C211yesmaximal, characteristic, complemented
12#11926681C211yesmaximal, characteristic, complemented
13C4×#64516C211yesmaximal, characteristic, complemented
14#11926623C211yesmaximal, characteristic, complemented
15C19×#495C211yesmaximal, characteristic, complemented
16C2×#64545C2211yescharacteristic
17C2×Q8×D19C2211yescharacteristic, complemented
18C2×#64543C2211yescharacteristic
19C2×D4×D19C2211yescharacteristic
20C2×Q16×C19C2211yescharacteristic, complemented
21C2×SD16×C19C2211yescharacteristic
22C2×SD16×C19C2211yescharacteristic, complemented
23C2×D8×C19C2211yescharacteristic
24C19×#124C2211yescharacteristic
25C19×#124C2211yescharacteristic, complemented
26#10597392C2211yescharacteristic
27#10597392C2211yescharacteristic
28C2×#64528C2211yescharacteristic, complemented
29C2×#64527C2211yescharacteristic
30#10597384C2211yescharacteristic
31#10597384C2211yescharacteristic, complemented
32C2×#64526C2211yescharacteristic
33C2×#64525C2211yescharacteristic
34#10597364—24no—
35#10597357—24no—
36C2×#64516C2211yescharacteristic
37C2×#64515C2211yescharacteristic
38C2×#64515C2211yescharacteristic, complemented
39#10597331—21no—
40#10597330—21no—
41#10597330—21no—
42#10597329—21no—
43#10597328—21no—
44(C22⋊D19)⋊C4—21no—
45C22⋊C4×D19—21no—
46#10597324—21no—
47C4×D76C2211yescharacteristic
48C4×D76C2211yescharacteristic
49C4×Dic38C2211yescharacteristic, complemented
50C4×C8×C19C2211yescharacteristic, complemented
51#10597292C2211yescharacteristic, complemented
52#10597292C2211yescharacteristic, complemented
53#10597289C2211yescharacteristic
54#10597289C2211yescharacteristic, complemented
55#10597278C2211yescharacteristic
56(C2×D19)⋊C8C2211yescharacteristic
57(C2×D19)⋊C8C2211yescharacteristic, complemented
58#10597274C2211yescharacteristic, complemented
59#10597273C2211yescharacteristic, complemented
60C4⋊(C19⋊C8)C2211yescharacteristic, complemented
61C23×D19—21no—
62C2×Q8×C19C2311yescharacteristic
63C2×Q8×C19C2311yescharacteristic
64C2×D4×C19C2311yescharacteristic
65C2×D4×C19C2311yescharacteristic
66C2×C22⋊D19—21no—
67C2×C22⋊D19—21no—
68C2×C22⋊D19—21no—
69C2×C22⋊D19—21no—
70C22×Dic19—21no—
71#64545—22no—
72#64545—41no—
73Q8×D19—22no—
74Q8×D19—41no—
75#64543—22no—
76#64543—41no—
77D4×D19—22no—
78D4×D19—41no—
79C2×D76—21no—
80C2×D76D411yescharacteristic
81C2×D76C2311yescharacteristic
82C2×C4×D19—21no—
83C2×C4×D19—21no—
84C2×C4×D19—21no—
85C2×C4×D19C2311yescharacteristic
86C2×C4×D19C2311yescharacteristic
87C2×Dic38—21no—
88C2×Dic38C2311yescharacteristic
89Q16×C19—22no—
90SD16×C19—41no—
91SD16×C19—41no—
92D8×C19—22no—
93C2×C8×C19C2311yescharacteristic
94C2×C8×C19C2311yescharacteristic
95C22⋊C4×C19—21no—
96C22⋊C4×C19—21no—
97C22⋊C4×C19—21no—
98C22⋊C4×C19—21no—
99C42×C19C2311yescharacteristic
100C22⋊Dic19—21no—
101C22⋊Dic19—21no—
102#64528—22no—
103#64527—22no—
104#64526—22no—
105#64525—22no—
106(C2×D19)⋊C4—21no—
107(C2×D19)⋊C4—21no—
108(C2×D19)⋊C4—21no—
109(C2×D19)⋊C4D411yescharacteristic
110(C2×D19)⋊C4D411yescharacteristic
111C4⋊Dic19D411yescharacteristic
112C4⋊Dic19C2311yescharacteristic
113C4⋊Dic19C2311yescharacteristic
114Dic19⋊C4—21no—
115Dic19⋊C4—21no—
116Dic19⋊C4—21no—
117C4×Dic19—21no—
118C2×C19⋊C8C2311yescharacteristic
119C2×C19⋊C8C2311yescharacteristic
120#64516D414yescomplemented
121#64515—22no—
122#64515—22no—
123C23×C19—21no—
124C23×C19—21no—
125C22×D19—21no—
126C22×D19—42no—
127C22×D19—42no—
128C22×D19—81no—
129C22×D19C2×D411yescharacteristic
130C22×D19C2×D411yescharacteristic
131Q8×C19—21no—
132Q8×C19—21no—
133Q8×C19—21no—
134Q8×C19—21no—
135D4×C19—21no—
136D4×C19—21no—
137D4×C19—21no—
138D4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19C2×D411yescharacteristic
142C2×C4×C19C2×D411yescharacteristic
143C2×C4×C19C2411yescharacteristic
144C22⋊D19—42no—
145C22⋊D19—42no—
146C22⋊D19—42no—
147C22⋊D19—81no—
148C2×Dic19—21no—
149C2×Dic19—21no—
150C2×Dic19—21no—
151C2×Dic19—42no—
152C2×Dic19C2×D411yescharacteristic
153C2×Dic19C2×D411yescharacteristic
154D76—21no—
155D76—41no—
156D76—42no—
157D76C2×D412yes—
158C4×D19—21no—
159C4×D19—21no—
160C4×D19—21no—
161C4×D19—21no—
162C4×D19—42no—
163C4×D19—42no—
164C4×D19—81no—
165Dic38—21no—
166Dic38—42no—
167Dic38C2×D412yes—
168C8×C19—21no—
169C8×C19C2×D412yes—
170C19⋊C8—21no—
171C19⋊C8—21no—
172#3275—191nomaximal, Sylow
173C22×C19—41no—
174C22×C19—41no—
175C22×C19—41no—
176C22×C19—41no—
177C22×C19—41no—
178C22×C19—41no—
179C22×C19C22×D411yescharacteristic
180C2×D19—21no—
181C2×D19—21no—
182C2×D19—22no—
183C2×D19—21no—
184C2×D19—21no—
185C2×D19—21no—
186C2×D19—21no—
187C2×D19—41no—
188C2×D19—41no—
189C2×D19—84no—
190C4×C19—21no—
191C4×C19—21no—
192C4×C19—41no—
193C4×C19—41no—
194C4×C19C22×D411yescharacteristic
195C4×C19H(5,𝔽2)11yescharacteristic
196Dic19—22no—
197Dic19—21no—
198Dic19—21no—
199Dic19—41no—
200Dic19—41no—
201C2×#137—191no—
202C2×AGL(1,ℤ/8)—191no—
203#548—191no—
204#546—191no—
205#495D1911yescharacteristic, complemented
206#470—191no—
207#469—191no—
208#464—191no—
209#463—191no—
210#452—191no—
211#450—191no—
212#449—191no—
213#448—191no—
214C4×SD16—191no—
215#436—191no—
216C2×C19—81no—
217C2×C19—81no—
218C2×C19D4211yescharacteristic
219C2×C19#57511yescharacteristic
220C2×C19#57711yescharacteristic
221D19—41no—
222D19—41no—
223D19—42no—
224C2×#41—191no—
225C2×#41—191no—
226C22×Q8—191no—
227C22×D4—191no—
228#137—384no—
229AGL(1,ℤ/8)—384no—
230C2×Q16—191no—
231C2×Q16C2×D1911yescharacteristic, complemented
232C2×SD16—191no—
233C2×SD16—191no—
234C2×SD16—191no—
235C2×SD16C2×D1911yescharacteristic
236C2×SD16C2×D1911yescharacteristic, complemented
237C2×D8—191no—
238C2×D8C2×D1911yescharacteristic
239C2×M16—191no—
240C2×M16—191no—
241#124—381no—
242#124C2×D1911yescharacteristic
243#124C2×D1911yescharacteristic, complemented
244#123—381no—
245C22⋊Q8—191no—
246C22⋊Q8—191no—
247C22⋊Q8—381no—
248#121—191no—
249#121—191no—
250#121—381no—
251#121—381no—
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#103—191no—
263#102—191no—
264#102—191no—
265#102—191no—
266C22⋊C8—191no—
267C22⋊C8—191no—
268C4×C8C2×D1911yescharacteristic, complemented
269C19#327511yescharacteristic, complemented, Sylow
270C24—381no—
271#41—382no—
272#41—382no—
273#41—761no—
274#41—761no—
275C2×Q8—191no—
276C2×Q8—381no—
277C2×Q8—382no—
278C2×Q8—761no—
279C2×Q8C22×D1911yescharacteristic
280C2×Q8C22×D1911yescharacteristic
281C2×D4—191no—
282C2×D4—191no—
283C2×D4—381no—
284C2×D4—381no—
285C2×D4—382no—
286C2×D4—381no—
287C2×D4—381no—
288C2×D4—381no—
289C2×D4—761no—
290C2×D4C22×D1911yescharacteristic
291C2×D4C22×D1911yescharacteristic
292C22×C4—191no—
293C22×C4—191no—
294C22×C4—381no—
295C22×C4—381no—
296C22×C4—381no—
297C22×C4—381no—
298Q16—22no—
299Q16—382no—
300SD16—41no—
301SD16—41no—
302SD16—194no—
303SD16—382no—
304SD16—382no—
305D8—22no—
306D8—382no—
307M16—382no—
308M16—382no—
309C2×C8—191no—
310C2×C8—191no—
311C2×C8C22×D1911yescharacteristic
312C2×C8C22×D1911yescharacteristic
313C4⋊C4—191no—
314C4⋊C4—191no—
315C4⋊C4—191no—
316C4⋊C4—381no—
317C4⋊C4—381no—
318C4⋊C4—381no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—191no—
324C22⋊C4—191no—
325C22⋊C4—381no—
326C22⋊C4—381no—
327C22⋊C4—381no—
328C22⋊C4—381no—
329C22⋊C4—381no—
330C42—381no—
331C42C22×D1911yescharacteristic
332C23—21no—
333C23—21no—
334C23—191no—
335C23—191no—
336C23—381no—
337C23—762no—
338C23—762no—
339C23—1521no—
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—192no—
345Q8—381no—
346Q8—762no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—192no—
352D4—381no—
353D4—761no—
354D4—762no—
355D4—762no—
356D4—762no—
357D4—762no—
358D4—1521no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—191no—
362C2×C4—191no—
363C2×C4—381no—
364C2×C4—381no—
365C2×C4—381no—
366C2×C4—381no—
367C2×C4—381no—
368C2×C4—381no—
369C2×C4—381no—
370C2×C4—762no—
371C2×C4—762no—
372C2×C4—762no—
373C2×C4—1521no—
374C2×C4D4×D1911yescharacteristic
375C2×C4D4×D1911yescharacteristic
376C2×C4C23×D1911yescharacteristic
377C8—21no—
378C8—381no—
379C8—381no—
380C8D4×D1912yes—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—381no—
388C22—381no—
389C22—381no—
390C22—381no—
391C22—381no—
392C22—381no—
393C22—382no—
394C22—761no—
395C22—761no—
396C22—1524no—
397C22C2×D4×D1911yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—381no—
403C4—381no—
404C4—382no—
405C4—761no—
406C4—761no—
407C4C2×D4×D1911yescharacteristic
408C4#1059743011yescharacteristic
409C2—81no—
410C2—81no—
411C2—761no—
412C2—761no—
413C2—762no—
414C2#1192717911yescharacteristic
415C2#1192734111yescharacteristic
416C2#1192735111yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#495C2
socleC22×C19C22×D4
hypercenter#495D19
hypocenterC19#3275
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#10597364C2semidirect
2. C2×#10597357C2semidirect
3. #11927202C2semidirect
4. #11927187C2semidirect
5. #11926799C2semidirect
6. #11926794C2semidirect
7. #11926763C2semidirect
8. #11926756C2semidirect
9. #11926703C2semidirect
10. #11926693C2semidirect
11. #11926688C2semidirect
12. #11926681C2semidirect
13. C4×#64516C2semidirect
14. #11926623C2semidirect
15. C19×#495C2semidirect
17. C2×Q8×D19C22semidirect
20. C2×Q16×C19C22semidirect
22. C2×SD16×C19C22semidirect
25. C19×#124C22semidirect
28. C2×#64528C22semidirect
31. #10597384C22semidirect
38. C2×#64515C22semidirect
49. C4×Dic38C22semidirect
50. C4×C8×C19C22semidirect
51. #10597292C22semidirect
52. #10597292C22semidirect
54. #10597289C22semidirect
57. (C2×D19)⋊C8C22semidirect
58. #10597274C22semidirect
59. #10597273C22semidirect
60. C4⋊(C19⋊C8)C22semidirect
120. #64516D4semidirect
205. #495D19semidirect
231. C2×Q16C2×D19semidirect
236. C2×SD16C2×D19semidirect
243. #124C2×D19semidirect
268. C4×C8C2×D19semidirect
269. C19#3275semidirect

Maximal subgroups

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

subgroupindex
C2×#105973642
C2×#105973572
#119272022
#119271872
#119267992
#119267942
#119267632
#119267562
#119267032
#119266932
#119266882
#119266812
C4×#645162
#119266232
C19×#4952
#327519