Finite Group Databasebeta

← #14575175

Subgroups — #14575175

Order 2432.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597360C211yesmaximal, characteristic, complemented
2#11927213C211yesmaximal, characteristic, complemented
3#11927182C211yesmaximal, characteristic, complemented
4#11926930C211yesmaximal, characteristic, complemented
5#11926787C211yesmaximal, characteristic, complemented
6#11926780C211yesmaximal, characteristic, complemented
7#11926768C211yesmaximal, characteristic, complemented
8#11926737C211yesmaximal, characteristic, complemented
9#11926705C211yesmaximal, characteristic, complemented
10#11926689C211yesmaximal, characteristic, complemented
11#11926689C211yesmaximal, characteristic, complemented
12#11926676C211yesmaximal, characteristic, complemented
13#11926645C211yesmaximal, characteristic, complemented
14#11926615C211yesmaximal, characteristic, complemented
15C2×C19×#135C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C2×#41×C19C2211yescharacteristic, complemented
18C2×#64545C2211yescharacteristic
19C2×D4×D19C2211yescharacteristic
20C19×#135—24no—
21C2×Q16×C19C2211yescharacteristic, complemented
22C2×SD16×C19C2211yescharacteristic
23C2×SD16×C19C2211yescharacteristic, complemented
24C2×D8×C19C2211yescharacteristic
25C22×C8×C19C2211yescharacteristic, complemented
26#10597393C2211yescharacteristic
27#10597392C2211yescharacteristic
28Q8×Dic19C2211yescharacteristic, complemented
29C2×#64527C2211yescharacteristic
30C2×#64527C2211yescharacteristic, complemented
31#10597386—21no—
32#10597386C2211yescharacteristic, complemented
33#10597385—21no—
34#10597384—21no—
35#10597384C2211yescharacteristic
36#10597383—21no—
37D4×Dic19C2211yescharacteristic
38C2×#64525C2211yescharacteristic
39C2×#64525C2211yescharacteristic
40#10597376—21no—
41#10597376C2211yescharacteristic
42#10597376C2211yescharacteristic, complemented
43#10597375—21no—
44C4×C22⋊D19—21no—
45C4×C22⋊D19C2211yescharacteristic
46C2×(C2×D19)⋊C4—21no—
47#10597360—24no—
48C2×D152C2211yescharacteristic
49C2×#64515C2211yescharacteristic
50#10597292C2211yescharacteristic, complemented
51#10597292C2211yescharacteristic, complemented
52#10597289C2211yescharacteristic
53#10597289C2211yescharacteristic, complemented
54C22⋊(C19⋊C8)C2211yescharacteristic, complemented
55#10597278C2211yescharacteristic
56#10597278C2211yescharacteristic, complemented
57(C2×D19)⋊C8C2211yescharacteristic
58#10597275C2211yescharacteristic, complemented
59#10597272C2211yescharacteristic, complemented
60Dic19⋊C8C2211yescharacteristic, complemented
61C23×D19—21no—
62#41×C19—22no—
63#41×C19—22no—
64#41×C19—41no—
65#41×C19—41no—
66C2×Q8×C19C2311yescharacteristic
67C2×Q8×C19C2311yescharacteristic
68C2×D4×C19—21no—
69C2×D4×C19—21no—
70C2×D4×C19C2311yescharacteristic
71C2×D4×C19C2311yescharacteristic
72C22×C4×C19—21no—
73C22×C4×C19—21no—
74C22×C4×C19C2311yescharacteristic
75C2×C22⋊D19—21no—
76C2×C22⋊D19—21no—
77C2×C22⋊D19—21no—
78C2×C22⋊D19—21no—
79C2×C22⋊D19—21no—
80C2×C22⋊D19—21no—
81C2×C22⋊D19D411yescharacteristic
82C22×Dic19—21no—
83#64545—22no—
84#64545—41no—
85D4×D19—22no—
86D4×D19—41no—
87C2×D76—21no—
88C2×D76C2311yescharacteristic
89C2×D76C2311yescharacteristic
90C2×C4×D19—21no—
91C2×C4×D19C2311yescharacteristic
92Q16×C19—22no—
93SD16×C19—22no—
94SD16×C19D414yescomplemented
95D8×C19—22no—
96C2×C8×C19—22no—
97C2×C8×C19C2311yescharacteristic
98C2×C8×C19C2311yescharacteristic
99C22⋊Dic19—21no—
100C22⋊Dic19—21no—
101C22⋊Dic19D411yescharacteristic
102#64527—22no—
103#64527—41no—
104#64525—22no—
105#64525—41no—
106(C2×D19)⋊C4—21no—
107(C2×D19)⋊C4—21no—
108(C2×D19)⋊C4—21no—
109(C2×D19)⋊C4—21no—
110(C2×D19)⋊C4—21no—
111(C2×D19)⋊C4D411yescharacteristic
112C4⋊Dic19—21no—
113C4⋊Dic19C2311yescharacteristic
114C4⋊Dic19C2311yescharacteristic
115Dic19⋊C4—21no—
116Dic19⋊C4D411yescharacteristic
117C4×Dic19—21no—
118C4×Dic19C2311yescharacteristic
119C2×C19⋊C8C2311yescharacteristic
120C2×C19⋊C8C2311yescharacteristic
121D152—22no—
122#64515—22no—
123C23×C19—21no—
124C23×C19—21no—
125C23×C19C2×D411yescharacteristic
126C22×D19—21no—
127C22×D19—21no—
128C22×D19—42no—
129C22×D19—42no—
130C22×D19—81no—
131C22×D19C2×D411yescharacteristic
132Q8×C19—21no—
133Q8×C19—21no—
134Q8×C19—21no—
135Q8×C19C2×D412yes—
136D4×C19—21no—
137D4×C19—21no—
138D4×C19—21no—
139D4×C19—42no—
140D4×C19—42no—
141D4×C19C2×D412yes—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×C4×C19—42no—
147C2×C4×C19—42no—
148C2×C4×C19C2×D411yescharacteristic
149C2×C4×C19C2411yescharacteristic
150C22⋊D19—41no—
151C22⋊D19—42no—
152C22⋊D19—42no—
153C22⋊D19—81no—
154C22⋊D19—81no—
155C22⋊D19—81no—
156C22⋊D19—81no—
157C2×Dic19—21no—
158C2×Dic19—21no—
159C2×Dic19—81no—
160C2×Dic19C2×D411yescharacteristic
161C2×Dic19C2×D411yescharacteristic
162C2×Dic19C2×D411yescharacteristic
163D76—21no—
164D76—21no—
165D76—21no—
166D76—21no—
167D76—42no—
168C4×D19—21no—
169C4×D19—21no—
170C4×D19—42no—
171C8×C19—21no—
172C8×C19C2×D412yes—
173C19⋊C8—21no—
174C19⋊C8—21no—
175#3268—191nomaximal, Sylow
176C22×C19—22no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—21no—
180C22×C19—41no—
181C22×C19—41no—
182C22×C19—41no—
183C22×C19—41no—
184C22×C19—41no—
185C22×C19C22×D411yescharacteristic
186C2×D19—21no—
187C2×D19—21no—
188C2×D19—21no—
189C2×D19—41no—
190C2×D19—41no—
191C2×D19—41no—
192C2×D19—41no—
193C2×D19—41no—
194C2×D19—41no—
195C2×D19—84no—
196C4×C19—22no—
197C4×C19—21no—
198C4×C19—41no—
199C4×C19C22×D411yescharacteristic
200C4×C19H(5,𝔽2)11yescharacteristic
201Dic19—21no—
202Dic19—21no—
203Dic19—21no—
204Dic19—41no—
205Dic19—41no—
206C2×AGL(1,ℤ/8)—191no—
207C2×#135D1911yescharacteristic, complemented
208#550—191no—
209#546—191no—
210#496—191no—
211#468—191no—
212#466—191no—
213#464—191no—
214#459—191no—
215#452—191no—
216#449—191no—
217#449—191no—
218#447—191no—
219#440—191no—
220#435—191no—
221C2×C19—42no—
222C2×C19—41no—
223C2×C19—81no—
224C2×C19D4211yescharacteristic
225C2×C19#57511yescharacteristic
226C2×C19#57611yescharacteristic
227D19—41no—
228D19—81no—
229D19—81no—
230C2×#41—191no—
231C2×#41C2×D1911yescharacteristic
232C2×#41C2×D1911yescharacteristic, complemented
233C22×D4—191no—
234AGL(1,ℤ/8)—384no—
235#135—24no—
236C2×Q16C2×D1911yescharacteristic, complemented
237C2×SD16—191no—
238C2×SD16—191no—
239C2×SD16C2×D1911yescharacteristic
240C2×SD16C2×D1911yescharacteristic, complemented
241C2×D8—191no—
242C2×D8—191no—
243C2×D8—191no—
244C2×D8C2×D1911yescharacteristic
245C2×M16—191no—
246C22×C8C2×D1911yescharacteristic, complemented
247#127—191no—
248#127—381no—
249#124—191no—
250#123—381no—
251C22⋊Q8—191no—
252#121—191no—
253#121—191no—
254#121—191no—
255#121—381no—
256#121—381no—
257#121—381no—
258#120—381no—
259C4×Q8—191no—
260C4×D4—191no—
261C4×D4—191no—
262C4×D4—381no—
263C2×C22⋊C4—381no—
264#107—191no—
265C4⋊C8—191no—
266#103—191no—
267#103—191no—
268#102—191no—
269#102—191no—
270#102—191no—
271#102—191no—
272C22⋊C8—191no—
273C22⋊C8—191no—
274#97—191no—
275C19#326811yescharacteristic, complemented, Sylow
276C24—381no—
277#41—22no—
278#41—22no—
279#41—41no—
280#41—41no—
281#41—382no—
282#41—761no—
283C2×Q8C22×D1911yescharacteristic
284C2×Q8C22×D1911yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—191no—
288C2×D4—191no—
289C2×D4—191no—
290C2×D4—381no—
291C2×D4—381no—
292C2×D4—381no—
293C2×D4—381no—
294C2×D4—382no—
295C2×D4—381no—
296C2×D4—381no—
297C2×D4—381no—
298C2×D4—761no—
299C2×D4C22×D1911yescharacteristic
300C2×D4C22×D1911yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—191no—
304C22×C4—381no—
305C22×C4—381no—
306C22×C4C22×D1911yescharacteristic
307Q16—22no—
308SD16—22no—
309SD16—382no—
310SD16—761no—
311SD16C22⋊D1914yescomplemented
312D8—22no—
313D8—382no—
314D8—382no—
315D8—761no—
316M16—382no—
317C2×C8—22no—
318C2×C8—191no—
319C2×C8—191no—
320C2×C8C22×D1911yescharacteristic
321C2×C8C22×D1911yescharacteristic
322C4⋊C4—191no—
323C4⋊C4—191no—
324C4⋊C4—191no—
325C4⋊C4—381no—
326C4⋊C4—381no—
327C22⋊C4—191no—
328C22⋊C4—191no—
329C22⋊C4—381no—
330C22⋊C4—381no—
331C22⋊C4—381no—
332C22⋊C4—381no—
333C22⋊C4—381no—
334C22⋊C4—381no—
335C22⋊C4—381no—
336C42—191no—
337C42—381no—
338C23—21no—
339C23—21no—
340C23—191no—
341C23—381no—
342C23—381no—
343C23—762no—
344C23—762no—
345C23—1521no—
346C23D4×D1911yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—21no—
350Q8C2×C22⋊D1912yes—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—42no—
355D4—42no—
356D4—381no—
357D4—381no—
358D4—381no—
359D4—381no—
360D4—762no—
361D4—761no—
362D4—762no—
363D4—762no—
364D4—1521no—
365D4—1521no—
366D4—1521no—
367D4—1521no—
368D4C2×C22⋊D1912yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—191no—
376C2×C4—191no—
377C2×C4—191no—
378C2×C4—381no—
379C2×C4—381no—
380C2×C4—381no—
381C2×C4—381no—
382C2×C4—762no—
383C2×C4—1521no—
384C2×C4D4×D1911yescharacteristic
385C2×C4C23×D1911yescharacteristic
386C8—21no—
387C8—381no—
388C8—381no—
389C8C2×C22⋊D1912yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—22no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—381no—
400C22—381no—
401C22—381no—
402C22—761no—
403C22—761no—
404C22—761no—
405C22—761no—
406C22—761no—
407C22—761no—
408C22—1524no—
409C22C2×D4×D1911yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—381no—
414C4—381no—
415C4—381no—
416C4—761no—
417C4—761no—
418C4#1059743011yescharacteristic
419C4C22×C22⋊D1911yescharacteristic
420C2—41no—
421C2—42no—
422C2—81no—
423C2—761no—
424C2—1521no—
425C2—1521no—
426C2D4×C22⋊D1911yescharacteristic
427C2#1192734111yescharacteristic
428C2#1192734611yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC2×C19×#135C2
socleC22×C19C22×D4
hypercenterC2×#135D19
hypocenterC19#3268
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#10597360C2semidirect
2. #11927213C2semidirect
3. #11927182C2semidirect
4. #11926930C2semidirect
5. #11926787C2semidirect
6. #11926780C2semidirect
7. #11926768C2semidirect
8. #11926737C2semidirect
9. #11926705C2semidirect
10. #11926689C2semidirect
11. #11926689C2semidirect
12. #11926676C2semidirect
13. #11926645C2semidirect
14. #11926615C2semidirect
15. C2×C19×#135C2semidirect
17. C2×#41×C19C22semidirect
21. C2×Q16×C19C22semidirect
23. C2×SD16×C19C22semidirect
25. C22×C8×C19C22semidirect
28. Q8×Dic19C22semidirect
30. C2×#64527C22semidirect
32. #10597386C22semidirect
42. #10597376C22semidirect
50. #10597292C22semidirect
51. #10597292C22semidirect
53. #10597289C22semidirect
54. C22⋊(C19⋊C8)C22semidirect
56. #10597278C22semidirect
58. #10597275C22semidirect
59. #10597272C22semidirect
60. Dic19⋊C8C22semidirect
94. SD16×C19D4semidirect
207. C2×#135D19semidirect
232. C2×#41C2×D19semidirect
236. C2×Q16C2×D19semidirect
240. C2×SD16C2×D19semidirect
246. C22×C8C2×D19semidirect
275. C19#3268semidirect
311. SD16C22⋊D19semidirect

Maximal subgroups

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

subgroupindex
C2×#105973602
#119272132
#119271822
#119269302
#119267872
#119267802
#119267682
#119267372
#119267052
#119266892
#119266762
#119266452
#119266152
C2×C19×#1352
#326819