Finite Group Databasebeta

← #14575179

Subgroups — #14575179

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×#10597357C211yesmaximal, characteristic, complemented
2C2×#10597396C211yesmaximal, characteristic, complemented
3#11927212C211yesmaximal, characteristic, complemented
4#11927182C211yesmaximal, characteristic, complemented
5#11926930C211yesmaximal, characteristic, complemented
6#11926793C211yesmaximal, characteristic, complemented
7#11926778C211yesmaximal, characteristic, complemented
8#11926769C211yesmaximal, characteristic, complemented
9#11926737C211yesmaximal, characteristic, complemented
10#11926703C211yesmaximal, characteristic, complemented
11#11926691C211yesmaximal, characteristic, complemented
12#11926679C211yesmaximal, characteristic, complemented
13#11926641C211yesmaximal, characteristic, complemented
14#11926612C211yesmaximal, characteristic, complemented
15C19×#449C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C2×#64543C2211yescharacteristic
18C2×D4×D19C2211yescharacteristic
19C2×#64541C2211yescharacteristic, complemented
20C2×SD16×C19C2211yescharacteristic, complemented
21C2×D8×C19C2211yescharacteristic
22C19×#121C2211yescharacteristic, complemented
23#10597396—24no—
24#10597393C2211yescharacteristic
25#10597392C2211yescharacteristic
26C2×#64528C2211yescharacteristic, complemented
27C2×#64527C2211yescharacteristic, complemented
28#10597386—21no—
29#10597386C2211yescharacteristic, complemented
30#10597385—21no—
31#10597385—21no—
32#10597383—21no—
33D4×Dic19C2211yescharacteristic
34C2×#64526C2211yescharacteristic
35C2×#64525C2211yescharacteristic
36C2×#64525C2211yescharacteristic
37#10597376C2211yescharacteristic
38#10597375—21no—
39C4×C22⋊D19C2211yescharacteristic
40C2×(C2×D19)⋊C4—21no—
41C22×C19⋊C8C2211yescharacteristic, complemented
42#10597357—24no—
43C2×D152C2211yescharacteristic
44C2×#64516C2211yescharacteristic
45C2×#64515C2211yescharacteristic
46#10597341C2211yescharacteristic
47#10597333C2211yescharacteristic, complemented
48#10597330—21no—
49(C22⋊D19)⋊C4—21no—
50C19×#103C2211yescharacteristic, complemented
51C19×#102C2211yescharacteristic
52C19×C22⋊C8C2211yescharacteristic, complemented
53#10597289C2211yescharacteristic, complemented
54#10597278C2211yescharacteristic, complemented
55(C2×D19)⋊C8C2211yescharacteristic
56#10597273C2211yescharacteristic, complemented
57#10597272C2211yescharacteristic, complemented
58Dic19⋊C8C2211yescharacteristic, complemented
59#10597266C2211yescharacteristic
60#10597264C2211yescharacteristic, 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⋊D19—21no—
75C2×C22⋊D19—21no—
76C2×C22⋊D19—21no—
77C2×C22⋊D19D411yescharacteristic
78C22×Dic19—21no—
79C22×Dic19—21no—
80#64543—22no—
81#64543—41no—
82D4×D19—22no—
83D4×D19—41no—
84#64541—22no—
85#64541—41no—
86C2×D76—21no—
87C2×D76C2311yescharacteristic
88C2×D76C2311yescharacteristic
89C2×C4×D19—21no—
90C2×C4×D19C2311yescharacteristic
91C2×Dic38C2311yescharacteristic
92SD16×C19—41no—
93D8×C19—22no—
94C2×C8×C19C2311yescharacteristic
95C2×C8×C19C2311yescharacteristic
96C4⋊C4×C19C2311yescharacteristic
97C22⋊C4×C19—21no—
98C22⋊Dic19—21no—
99C22⋊Dic19D411yescharacteristic
100#64528—22no—
101#64527—22no—
102#64526D414yescomplemented
103#64525—22no—
104#64525—22no—
105(C2×D19)⋊C4—21no—
106(C2×D19)⋊C4—21no—
107(C2×D19)⋊C4—21no—
108(C2×D19)⋊C4—21no—
109(C2×D19)⋊C4—21no—
110(C2×D19)⋊C4D411yescharacteristic
111C4⋊Dic19C2311yescharacteristic
112Dic19⋊C4—21no—
113Dic19⋊C4—21no—
114Dic19⋊C4D411yescharacteristic
115C4×Dic19—21no—
116C4×Dic19C2311yescharacteristic
117C2×C19⋊C8—22no—
118C2×C19⋊C8C2311yescharacteristic
119C2×C19⋊C8C2311yescharacteristic
120D152—41no—
121#64516—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—
134D4×C19—21no—
135D4×C19—21no—
136D4×C19—21no—
137D4×C19—42no—
138D4×C19—81no—
139D4×C19C2×D412yes—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—42no—
145C2×C4×C19C2×D411yescharacteristic
146C2×C4×C19C2411yescharacteristic
147C22⋊D19—41no—
148C22⋊D19—42no—
149C22⋊D19—42no—
150C22⋊D19—42no—
151C22⋊D19—42no—
152C22⋊D19—81no—
153C22⋊D19—81no—
154C2×Dic19—21no—
155C2×Dic19—21no—
156C2×Dic19—42no—
157C2×Dic19—81no—
158C2×Dic19C2×D411yescharacteristic
159C2×Dic19C2×D411yescharacteristic
160C2×Dic19C2×D411yescharacteristic
161D76—21no—
162D76—21no—
163D76—21no—
164D76—21no—
165D76—81no—
166C4×D19—21no—
167C4×D19—21no—
168C4×D19—42no—
169Dic38—21no—
170Dic38C2×D412yes—
171C8×C19—21no—
172C8×C19—21no—
173C19⋊C8—21no—
174C19⋊C8C2×D412yes—
175#3268—191nomaximal, Sylow
176C22×C19—21no—
177C22×C19—22no—
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—21no—
197C4×C19—41no—
198C4×C19—41no—
199C4×C19C22×D411yescharacteristic
200C4×C19H(5,𝔽2)11yescharacteristic
201Dic19—22no—
202Dic19—21no—
203Dic19—21no—
204Dic19—21no—
205Dic19—41no—
206C2×AGL(1,ℤ/8)—191no—
207C2×#135—191no—
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#449D1911yescharacteristic, complemented
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×#41—191no—
232C2×#41C2×D1911yescharacteristic
233C22×D4—191no—
234AGL(1,ℤ/8)—384no—
235#135—384no—
236C2×Q16—191no—
237C2×SD16—191no—
238C2×SD16—191no—
239C2×SD16—191no—
240C2×SD16C2×D1911yescharacteristic, complemented
241C2×D8—191no—
242C2×D8—191no—
243C2×D8—191no—
244C2×D8C2×D1911yescharacteristic
245C2×M16—191no—
246C22×C8—191no—
247#127—191no—
248#127—381no—
249#124—191no—
250#123—381no—
251C22⋊Q8—191no—
252#121—191no—
253#121—191no—
254#121—381no—
255#121—381no—
256#121—381no—
257#121C2×D1911yescharacteristic, complemented
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#103C2×D1911yescharacteristic, complemented
268#102—191no—
269#102—191no—
270#102—191no—
271#102C2×D1911yescharacteristic
272C22⋊C8—191no—
273C22⋊C8C2×D1911yescharacteristic, complemented
274#97—191no—
275C19#326811yescharacteristic, complemented, Sylow
276C24—381no—
277#41—22no—
278#41—41no—
279#41—382no—
280#41—382no—
281#41—761no—
282#41—761no—
283C2×Q8—191no—
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—191no—
303C22×C4—381no—
304C22×C4—381no—
305C22×C4—381no—
306C22×C4C22×D1911yescharacteristic
307Q16—382no—
308SD16—41no—
309SD16—194no—
310SD16—382no—
311SD16—382no—
312D8—22no—
313D8—382no—
314D8—382no—
315D8—761no—
316M16—382no—
317C2×C8—191no—
318C2×C8—191no—
319C2×C8—382no—
320C2×C8C22×D1911yescharacteristic
321C2×C8C22×D1911yescharacteristic
322C4⋊C4—191no—
323C4⋊C4—191no—
324C4⋊C4—381no—
325C4⋊C4—381no—
326C4⋊C4C22×D1911yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—191no—
329C22⋊C4—191no—
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—192no—
350Q8—381no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—42no—
355D4—81no—
356D4—381no—
357D4—381no—
358D4—381no—
359D4—381no—
360D4—761no—
361D4—762no—
362D4—762no—
363D4—762no—
364D4—762no—
365D4—1521no—
366D4—1521no—
367D4—1521no—
368D4D4×D1912yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—42no—
374C2×C4—191no—
375C2×C4—191no—
376C2×C4—191no—
377C2×C4—381no—
378C2×C4—381no—
379C2×C4—381no—
380C2×C4—381no—
381C2×C4—762no—
382C2×C4—762no—
383C2×C4—1521no—
384C2×C4D4×D1911yescharacteristic
385C2×C4C23×D1911yescharacteristic
386C8—21no—
387C8—21no—
388C8—192no—
389C8—381no—
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—41no—
412C4—41no—
413C4—381no—
414C4—381no—
415C4—381no—
416C4—382no—
417C4—761no—
418C4C2×D4×D1911yescharacteristic
419C4#1059743011yescharacteristic
420C2—41no—
421C2—42no—
422C2—81no—
423C2—761no—
424C2—1521no—
425C2—1521no—
426C2#1192717611yescharacteristic
427C2#1192734111yescharacteristic
428C2#1192734811yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#449C2
socleC22×C19C22×D4
hypercenter#449D19
hypocenterC19#3268
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×#10597357C2semidirect
2. C2×#10597396C2semidirect
3. #11927212C2semidirect
4. #11927182C2semidirect
5. #11926930C2semidirect
6. #11926793C2semidirect
7. #11926778C2semidirect
8. #11926769C2semidirect
9. #11926737C2semidirect
10. #11926703C2semidirect
11. #11926691C2semidirect
12. #11926679C2semidirect
13. #11926641C2semidirect
14. #11926612C2semidirect
15. C19×#449C2semidirect
19. C2×#64541C22semidirect
20. C2×SD16×C19C22semidirect
22. C19×#121C22semidirect
26. C2×#64528C22semidirect
27. C2×#64527C22semidirect
29. #10597386C22semidirect
41. C22×C19⋊C8C22semidirect
47. #10597333C22semidirect
50. C19×#103C22semidirect
52. C19×C22⋊C8C22semidirect
53. #10597289C22semidirect
54. #10597278C22semidirect
56. #10597273C22semidirect
57. #10597272C22semidirect
58. Dic19⋊C8C22semidirect
60. #10597264C22semidirect
102. #64526D4semidirect
217. #449D19semidirect
240. C2×SD16C2×D19semidirect
257. #121C2×D19semidirect
267. #103C2×D19semidirect
273. C22⋊C8C2×D19semidirect
275. C19#3268semidirect

Maximal subgroups

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

subgroupindex
C2×#105973572
C2×#105973962
#119272122
#119271822
#119269302
#119267932
#119267782
#119267692
#119267372
#119267032
#119266912
#119266792
#119266412
#119266122
C19×#4492
#326819