Finite Group Databasebeta

← #14575177

Subgroups — #14575177

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
2C2×#10597362C211yesmaximal, characteristic, complemented
3#11927216C211yesmaximal, characteristic, complemented
4#11927189C211yesmaximal, characteristic, complemented
5#11926933C211yesmaximal, characteristic, complemented
6#11926791C211yesmaximal, characteristic, complemented
7#11926781C211yesmaximal, characteristic, complemented
8#11926766C211yesmaximal, characteristic, complemented
9#11926739C211yesmaximal, characteristic, complemented
10#11926709C211yesmaximal, characteristic, complemented
11#11926692C211yesmaximal, characteristic, complemented
12#11926690C211yesmaximal, characteristic, complemented
13#11926679C211yesmaximal, characteristic, complemented
14#11926617C211yesmaximal, characteristic, complemented
15C19×#440C211yesmaximal, characteristic, complemented
16C2×#64545C2211yescharacteristic
17C2×#64545C2211yescharacteristic, complemented
18C2×#64543C2211yescharacteristic
19C2×D4×D19C2211yescharacteristic
20C2×SD16×C19C2211yescharacteristic
21C4×Q8×C19C2211yescharacteristic, complemented
22C4×D4×C19C2211yescharacteristic
23C2×#64528C2211yescharacteristic, complemented
24C2×#64527C2211yescharacteristic
25C2×#64525C2211yescharacteristic
26C2×#64525C2211yescharacteristic
27#10597376—21no—
28C2×(C2×D19)⋊C4—21no—
29#10597362—24no—
30#10597360—24no—
31C2×D152C2211yescharacteristic
32C2×D152C2211yescharacteristic
33C2×#64516C2211yescharacteristic, complemented
34C2×#64516C2211yescharacteristic, complemented
35C2×#64515C2211yescharacteristic
36C2×C8×D19C2211yescharacteristic, complemented
37#10597343C2211yescharacteristic
38#10597341—21no—
39#10597341—21no—
40#10597341C2211yescharacteristic
41#10597341C2211yescharacteristic
42#10597341C2211yescharacteristic, complemented
43#10597332—21no—
44#10597328—21no—
45#10597321C2211yescharacteristic
46#10597320—21no—
47#10597320C2211yescharacteristic, complemented
48C4×D76—21no—
49C4×D76C2211yescharacteristic
50C19×#107C2211yescharacteristic, complemented
51C19×#103C2211yescharacteristic, complemented
52C19×#102C2211yescharacteristic
53C19×#97C2211yescharacteristic, complemented
54(C2×D19)⋊C8C2211yescharacteristic
55(C2×D19)⋊C8C2211yescharacteristic, complemented
56#10597267C2211yescharacteristic, complemented
57#10597266C2211yescharacteristic
58#10597266C2211yescharacteristic, complemented
59#10597266C2211yescharacteristic, complemented
60C4⋊(C19⋊C8)C2211yescharacteristic, complemented
61C23×D19—21no—
62C2×Q8×C19C2311yescharacteristic
63C2×D4×C19C2311yescharacteristic
64C22×C4×C19—21no—
65C2×C22⋊D19—21no—
66C2×C22⋊D19—21no—
67C22×Dic19—21no—
68#64545—22no—
69#64545—22no—
70#64545—41no—
71#64545—41no—
72#64543—22no—
73#64543—41no—
74D4×D19—22no—
75D4×D19—41no—
76C2×D76—21no—
77C2×D76—21no—
78C2×D76—21no—
79C2×D76—21no—
80C2×D76—21no—
81C2×D76—21no—
82C2×D76—21no—
83C2×D76D411yescharacteristic
84C2×D76C2311yescharacteristic
85C2×D76C2311yescharacteristic
86C2×D76C2311yescharacteristic
87C2×C4×D19—21no—
88C2×C4×D19—21no—
89C2×C4×D19C2311yescharacteristic
90C2×C4×D19C2311yescharacteristic
91C2×Dic38C2311yescharacteristic
92SD16×C19D414yescomplemented
93C2×C8×C19C2311yescharacteristic
94C2×C8×C19C2311yescharacteristic
95C4⋊C4×C19—21no—
96C4⋊C4×C19C2311yescharacteristic
97C4⋊C4×C19C2311yescharacteristic
98C22⋊C4×C19—21no—
99C42×C19—21no—
100C42×C19C2311yescharacteristic
101#64528—22no—
102#64527—22no—
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)⋊C4—21no—
111(C2×D19)⋊C4D411yescharacteristic
112(C2×D19)⋊C4D411yescharacteristic
113C4⋊Dic19—21no—
114C4⋊Dic19D411yescharacteristic
115C2×C19⋊C8C2311yescharacteristic
116C2×C19⋊C8C2311yescharacteristic
117D152—22no—
118D152—41no—
119#64516—22no—
120#64516—41no—
121#64515—22no—
122C8×D19—22no—
123C23×C19—21no—
124C22×D19—21no—
125C22×D19—21no—
126C22×D19—21no—
127C22×D19—42no—
128C22×D19—42no—
129C22×D19—81no—
130C22×D19C2×D411yescharacteristic
131C22×D19C2×D411yescharacteristic
132Q8×C19—21no—
133Q8×C19C2×D412yes—
134D4×C19—21no—
135D4×C19C2×D412yes—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—81no—
140C2×C4×C19C2×D411yescharacteristic
141C2×C4×C19C2×D411yescharacteristic
142C2×C4×C19C2411yescharacteristic
143C22⋊D19—42no—
144C22⋊D19—42no—
145C2×Dic19—21no—
146C2×Dic19—42no—
147C2×Dic19C2×D411yescharacteristic
148C2×Dic19C2×D411yescharacteristic
149D76—21no—
150D76—21no—
151D76—21no—
152D76—21no—
153D76—21no—
154D76—21no—
155D76—41no—
156D76—42no—
157D76—42no—
158D76—42no—
159D76—81no—
160D76—81no—
161D76—81no—
162D76—81no—
163C4×D19—21no—
164C4×D19—21no—
165C4×D19—21no—
166C4×D19—21no—
167C4×D19—42no—
168C4×D19—42no—
169Dic38—21no—
170Dic38—21no—
171C8×C19—21no—
172C8×C19C2×D412yes—
173C19⋊C8—21no—
174C19⋊C8—21no—
175#3268—191nomaximal, Sylow
176C22×C19—22no—
177C22×C19—41no—
178C22×C19—41no—
179C22×C19C22×D411yescharacteristic
180C2×D19—21no—
181C2×D19—21no—
182C2×D19—21no—
183C2×D19—21no—
184C2×D19—21no—
185C2×D19—21no—
186C2×D19—41no—
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—21no—
199C4×C19—41no—
200C4×C19—41no—
201C4×C19C22×D411yescharacteristic
202C4×C19H(5,𝔽2)11yescharacteristic
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#449—191no—
218#447—191no—
219#440D1911yescharacteristic, complemented
220#435—191no—
221C2×C19—42no—
222C2×C19D4211yescharacteristic
223C2×C19#57511yescharacteristic
224C2×C19#57611yescharacteristic
225D19—41no—
226D19—41no—
227D19—81no—
228D19—81no—
229D19—81no—
230C2×#41—191no—
231C2×#41—191no—
232C2×#41—191no—
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
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⋊Q8—191no—
252#121—191no—
253#121—191no—
254#121—191no—
255#121—381no—
256#121—381no—
257#121—381no—
258#120—381no—
259C4×Q8C2×D1911yescharacteristic, complemented
260C4×D4—191no—
261C4×D4—381no—
262C4×D4C2×D1911yescharacteristic
263C2×C22⋊C4—381no—
264#107C2×D1911yescharacteristic, complemented
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⋊C8—191no—
274#97C2×D1911yescharacteristic, complemented
275C19#326811yescharacteristic, complemented, Sylow
276C24—381no—
277#41—382no—
278#41—382no—
279#41—382no—
280#41—761no—
281#41—761no—
282#41—761no—
283C2×Q8—191no—
284C2×Q8C22×D1911yescharacteristic
285C2×D4—191no—
286C2×D4—191no—
287C2×D4—191no—
288C2×D4—191no—
289C2×D4—381no—
290C2×D4—381no—
291C2×D4—381no—
292C2×D4—381no—
293C2×D4—381no—
294C2×D4—381no—
295C2×D4—382no—
296C2×D4—381no—
297C2×D4—381no—
298C2×D4—381no—
299C2×D4—761no—
300C2×D4C22×D1911yescharacteristic
301C22×C4—21no—
302C22×C4—191no—
303C22×C4—191no—
304C22×C4—381no—
305C22×C4—381no—
306C22×C4—381no—
307Q16—382no—
308SD16—382no—
309SD16—382no—
310SD16—761no—
311SD16D7614yescomplemented
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—381no—
325C4⋊C4C22×D1911yescharacteristic
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—21no—
337C42C22×D1911yescharacteristic
338C23—21no—
339C23—191no—
340C23—191no—
341C23—381no—
342C23—381no—
343C23—381no—
344C23—762no—
345C23—762no—
346C23—1521no—
347Q8—21no—
348Q8—381no—
349Q8—381no—
350Q8C2×D7612yes—
351D4—21no—
352D4—381no—
353D4—381no—
354D4—381no—
355D4—381no—
356D4—381no—
357D4—381no—
358D4—761no—
359D4—762no—
360D4—762no—
361D4—762no—
362D4—762no—
363D4—762no—
364D4—1521no—
365D4—1521no—
366D4—1521no—
367D4—1521no—
368D4C2×D7612yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—191no—
374C2×C4—191no—
375C2×C4—381no—
376C2×C4—381no—
377C2×C4—381no—
378C2×C4—381no—
379C2×C4—381no—
380C2×C4—762no—
381C2×C4—762no—
382C2×C4—762no—
383C2×C4D4×D1911yescharacteristic
384C2×C4D4×D1911yescharacteristic
385C2×C4C23×D1911yescharacteristic
386C8—21no—
387C8—381no—
388C8—381no—
389C8C2×D7612yes—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—381no—
394C22—381no—
395C22—381no—
396C22—381no—
397C22—381no—
398C22—381no—
399C22—761no—
400C22—761no—
401C22—761no—
402C22—761no—
403C22—761no—
404C22—761no—
405C22—761no—
406C22—761no—
407C22—761no—
408C22—1524no—
409C22C2×D4×D1911yescharacteristic
410C4—21no—
411C4—21no—
412C4—22no—
413C4—41no—
414C4—41no—
415C4—381no—
416C4—381no—
417C4—761no—
418C4C22×D7611yescharacteristic
419C4#1059743511yescharacteristic
420C2—42no—
421C2—761no—
422C2—761no—
423C2—1521no—
424C2—1521no—
425C2—1521no—
426C2D4×D7611yescharacteristic
427C2#1192734311yescharacteristic
428C2#1192734811yescharacteristic
subgroupG/H
centerC22C2×D4×D19
commutator, cosocleC2×C4×C19C24
FrattiniC2×C4C23×D19
FittingC19×#440C2
socleC22×C19C22×D4
hypercenter#440D19
hypocenterC19#3268
LCSG ▷ C2×C4×C19 ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. C2×#10597360C2semidirect
2. C2×#10597362C2semidirect
3. #11927216C2semidirect
4. #11927189C2semidirect
5. #11926933C2semidirect
6. #11926791C2semidirect
7. #11926781C2semidirect
8. #11926766C2semidirect
9. #11926739C2semidirect
10. #11926709C2semidirect
11. #11926692C2semidirect
12. #11926690C2semidirect
13. #11926679C2semidirect
14. #11926617C2semidirect
15. C19×#440C2semidirect
17. C2×#64545C22semidirect
21. C4×Q8×C19C22semidirect
23. C2×#64528C22semidirect
33. C2×#64516C22semidirect
34. C2×#64516C22semidirect
36. C2×C8×D19C22semidirect
42. #10597341C22semidirect
47. #10597320C22semidirect
50. C19×#107C22semidirect
51. C19×#103C22semidirect
53. C19×#97C22semidirect
55. (C2×D19)⋊C8C22semidirect
56. #10597267C22semidirect
58. #10597266C22semidirect
59. #10597266C22semidirect
60. C4⋊(C19⋊C8)C22semidirect
92. SD16×C19D4semidirect
219. #440D19semidirect
259. C4×Q8C2×D19semidirect
264. #107C2×D19semidirect
267. #103C2×D19semidirect
274. #97C2×D19semidirect
275. C19#3268semidirect
311. SD16D76semidirect

Maximal subgroups

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

subgroupindex
C2×#105973602
C2×#105973622
#119272162
#119271892
#119269332
#119267912
#119267812
#119267662
#119267392
#119267092
#119266922
#119266902
#119266792
#119266172
C19×#4402
#326819