Finite Group Databasebeta

← #14575178

Subgroups — #14575178

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×#10597395C211yesmaximal, characteristic, complemented
2C2×#10597365C211yesmaximal, characteristic, complemented
3#11927213C211yesmaximal, characteristic, complemented
4#11927185C211yesmaximal, characteristic, complemented
5#11926930C211yesmaximal, characteristic, complemented
6#11926792C211yesmaximal, characteristic, complemented
7#11926779C211yesmaximal, characteristic, complemented
8#11926768C211yesmaximal, characteristic, complemented
9#11926738C211yesmaximal, characteristic, complemented
10#11926692C211yesmaximal, characteristic, complemented
11#11926688C211yesmaximal, characteristic, complemented
12#11926680C211yesmaximal, characteristic, complemented
13#11926647C211yesmaximal, characteristic, complemented
14#11926618C211yesmaximal, characteristic, complemented
15C19×#452C211yesmaximal, characteristic, complemented
16C2×#41×C19C2211yescharacteristic
17C2×#64545C2211yescharacteristic
18C2×#64545C2211yescharacteristic, complemented
19C22×D76C2211yescharacteristic
20C2×Q16×C19C2211yescharacteristic, complemented
21C2×SD16×C19C2211yescharacteristic, complemented
22C19×C22⋊Q8C2211yescharacteristic
23#10597395—24no—
24#10597393C2211yescharacteristic
25Q8×Dic19C2211yescharacteristic, complemented
26C2×#64527C2211yescharacteristic
27C2×#64527C2211yescharacteristic
28C2×#64527C2211yescharacteristic, complemented
29#10597386—21no—
30#10597386C2211yescharacteristic, complemented
31#10597384—21no—
32#10597384C2211yescharacteristic, complemented
33C2×#64525C2211yescharacteristic
34C2×#64525C2211yescharacteristic
35#10597376—21no—
36#10597376C2211yescharacteristic
37C4×C22⋊D19—21no—
38C4×C22⋊D19C2211yescharacteristic
39C2×#64520C2211yescharacteristic
40#10597365—24no—
41C2×D152C2211yescharacteristic
42C2×D152C2211yescharacteristic
43C2×C8×D19C2211yescharacteristic, complemented
44#10597341—21no—
45#10597341C2211yescharacteristic
46#10597340—21no—
47#10597339C2211yescharacteristic
48#10597328—21no—
49C22⋊C4×D19—21no—
50C19×#103C2211yescharacteristic, complemented
51C19×#102C2211yescharacteristic, complemented
52C19×C22⋊C8C2211yescharacteristic
53#10597292C2211yescharacteristic, complemented
54#10597278C2211yescharacteristic
55#10597278C2211yescharacteristic
56(C2×D19)⋊C8C2211yescharacteristic, complemented
57#10597272C2211yescharacteristic, complemented
58Dic19⋊C8C2211yescharacteristic, complemented
59#10597266C2211yescharacteristic, complemented
60#10597264C2211yescharacteristic, complemented
61C23×D19—21no—
62#41×C19—22no—
63#41×C19—41no—
64C2×Q8×C19C2311yescharacteristic
65C2×Q8×C19C2311yescharacteristic
66C2×D4×C19—21no—
67C2×D4×C19C2311yescharacteristic
68C22×C4×C19—21no—
69C22×C4×C19C2311yescharacteristic
70C2×C22⋊D19—21no—
71C2×C22⋊D19—21no—
72C2×C22⋊D19—21no—
73C2×C22⋊D19—21no—
74C2×C22⋊D19D411yescharacteristic
75#64545—22no—
76#64545—22no—
77#64545—41no—
78#64545—41no—
79C2×D76—22no—
80C2×D76—21no—
81C2×D76—21no—
82C2×D76—21no—
83C2×D76—21no—
84C2×D76—41no—
85C2×D76C2311yescharacteristic
86C2×D76C2311yescharacteristic
87C2×D76C2311yescharacteristic
88C2×C4×D19—21no—
89C2×C4×D19—21no—
90C2×C4×D19—21no—
91C2×C4×D19C2311yescharacteristic
92Q16×C19—22no—
93SD16×C19—41no—
94C2×C8×C19C2311yescharacteristic
95C2×C8×C19C2311yescharacteristic
96C4⋊C4×C19—21no—
97C4⋊C4×C19C2311yescharacteristic
98C22⋊C4×C19—21no—
99C22⋊Dic19—21no—
100C22⋊Dic19D411yescharacteristic
101#64527—22no—
102#64527—22no—
103#64527D414yescomplemented
104#64525—22no—
105#64525—22no—
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
114Dic19⋊C4D411yescharacteristic
115C4×Dic19—21no—
116C4×Dic19C2311yescharacteristic
117#64520—22no—
118C2×C19⋊C8C2311yescharacteristic
119C2×C19⋊C8C2311yescharacteristic
120D152—22no—
121D152—41no—
122C8×D19—22no—
123C23×C19—21no—
124C23×C19C2×D411yescharacteristic
125C22×D19—21no—
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—42no—
139C2×C4×C19—21no—
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—81no—
150C22⋊D19—81no—
151C22⋊D19—81no—
152C2×Dic19—21no—
153C2×Dic19C2×D411yescharacteristic
154C2×Dic19C2×D411yescharacteristic
155C2×Dic19C2×D411yescharacteristic
156D76—21no—
157D76—21no—
158D76—21no—
159D76—21no—
160D76—21no—
161D76—42no—
162D76—42no—
163D76—42no—
164D76—81no—
165D76C2×D412yes—
166C4×D19—21no—
167C4×D19—21no—
168C4×D19—42no—
169C4×D19—42no—
170C4×D19—81no—
171C8×C19—21no—
172C8×C19—21no—
173C19⋊C8—21no—
174C19⋊C8C2×D412yes—
175#3268—191nomaximal, Sylow
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—21no—
179C22×C19—41no—
180C22×C19—41no—
181C22×C19—41no—
182C22×C19C22×D411yescharacteristic
183C2×D19—21no—
184C2×D19—22no—
185C2×D19—21no—
186C2×D19—21no—
187C2×D19—41no—
188C2×D19—41no—
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×C19—41no—
200C4×C19C22×D411yescharacteristic
201C4×C19H(5,𝔽2)11yescharacteristic
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#452D1911yescharacteristic, complemented
216#449—191no—
217#449—191no—
218#447—191no—
219#440—191no—
220#435—191no—
221C2×C19—41no—
222C2×C19—81no—
223C2×C19D4211yescharacteristic
224C2×C19#57511yescharacteristic
225C2×C19#57611yescharacteristic
226D19—41no—
227D19—42no—
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×Q16C2×D1911yescharacteristic, complemented
237C2×SD16—191no—
238C2×SD16—191no—
239C2×SD16—191no—
240C2×SD16C2×D1911yescharacteristic, complemented
241C2×D8—191no—
242C2×D8—191no—
243C2×D8—191no—
244C2×D8—191no—
245C2×M16—191no—
246C22×C8—191no—
247#127—191no—
248#127—381no—
249#124—191no—
250#123—381no—
251C22⋊Q8C2×D1911yescharacteristic
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#103C2×D1911yescharacteristic, complemented
268#102—191no—
269#102—191no—
270#102—191no—
271#102C2×D1911yescharacteristic, complemented
272C22⋊C8—191no—
273C22⋊C8C2×D1911yescharacteristic
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×Q8C22×D1911yescharacteristic
284C2×Q8C22×D1911yescharacteristic
285C2×D4—21no—
286C2×D4—191no—
287C2×D4—191no—
288C2×D4—191no—
289C2×D4—191no—
290C2×D4—382no—
291C2×D4—381no—
292C2×D4—381no—
293C2×D4—381no—
294C2×D4—381no—
295C2×D4—381no—
296C2×D4—381no—
297C2×D4—381no—
298C2×D4—381no—
299C2×D4—761no—
300C2×D4C22×D1911yescharacteristic
301C22×C4—21no—
302C22×C4—191no—
303C22×C4—381no—
304C22×C4—381no—
305C22×C4—381no—
306C22×C4C22×D1911yescharacteristic
307Q16—22no—
308SD16—41no—
309SD16—194no—
310SD16—382no—
311SD16—382no—
312D8—382no—
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—21no—
323C4⋊C4—191no—
324C4⋊C4—191no—
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—191no—
340C23—381no—
341C23—381no—
342C23—381no—
343C23—762no—
344C23—762no—
345C23—1521no—
346C23D4×D1911yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—21no—
350Q8D4×D1912yes—
351D4—21no—
352D4—21no—
353D4—42no—
354D4—192no—
355D4—381no—
356D4—381no—
357D4—381no—
358D4—381no—
359D4—381no—
360D4—762no—
361D4—762no—
362D4—762no—
363D4—761no—
364D4—762no—
365D4—1521no—
366D4—1521no—
367D4—1521no—
368D4—1521no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—191no—
376C2×C4—191no—
377C2×C4—191no—
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—41no—
394C22—41no—
395C22—41no—
396C22—381no—
397C22—381no—
398C22—381no—
399C22—382no—
400C22—761no—
401C22—761no—
402C22—761no—
403C22—761no—
404C22—761no—
405C22—761no—
406C22—761no—
407C22—761no—
408C22—1524no—
409C22C2×D4×D1911yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—41no—
414C4—381no—
415C4—381no—
416C4—381no—
417C4—761no—
418C4C2×D4×D1911yescharacteristic
419C4#1059743011yescharacteristic
420C2—41no—
421C2—81no—
422C2—761no—
423C2—762no—
424C2—1521no—
425C2—1521no—
426C2#1192717611yescharacteristic
427C2#1192734311yescharacteristic
428C2#1192734611yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#452C2
socleC22×C19C22×D4
hypercenter#452D19
hypocenterC19#3268
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×#10597395C2semidirect
2. C2×#10597365C2semidirect
3. #11927213C2semidirect
4. #11927185C2semidirect
5. #11926930C2semidirect
6. #11926792C2semidirect
7. #11926779C2semidirect
8. #11926768C2semidirect
9. #11926738C2semidirect
10. #11926692C2semidirect
11. #11926688C2semidirect
12. #11926680C2semidirect
13. #11926647C2semidirect
14. #11926618C2semidirect
15. C19×#452C2semidirect
18. C2×#64545C22semidirect
20. C2×Q16×C19C22semidirect
21. C2×SD16×C19C22semidirect
25. Q8×Dic19C22semidirect
28. C2×#64527C22semidirect
30. #10597386C22semidirect
32. #10597384C22semidirect
43. C2×C8×D19C22semidirect
50. C19×#103C22semidirect
51. C19×#102C22semidirect
53. #10597292C22semidirect
56. (C2×D19)⋊C8C22semidirect
57. #10597272C22semidirect
58. Dic19⋊C8C22semidirect
59. #10597266C22semidirect
60. #10597264C22semidirect
103. #64527D4semidirect
215. #452D19semidirect
236. C2×Q16C2×D19semidirect
240. C2×SD16C2×D19semidirect
267. #103C2×D19semidirect
271. #102C2×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×#105973952
C2×#105973652
#119272132
#119271852
#119269302
#119267922
#119267792
#119267682
#119267382
#119266922
#119266882
#119266802
#119266472
#119266182
C19×#4522
#326819