Finite Group Databasebeta

← #49130759

Subgroups — #49130759

Order 36224.

526 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583634C211yesmaximal, characteristic, complemented
2C2×D8×D283C211yesmaximal, characteristic, complemented
3#31827028C211yesmaximal, characteristic, complemented
4#31826937C211yesmaximal, characteristic, complemented
5#31826681C211yesmaximal, characteristic, complemented
6#31826680C211yesmaximal, characteristic, complemented
7#31826679C211yesmaximal, characteristic, complemented
8#31826678C211yesmaximal, characteristic, complemented
9#31826659C211yesmaximal, characteristic, complemented
10#31826658C211yesmaximal, characteristic, complemented
11#31826657C211yesmaximal, characteristic, complemented
12#31826490C211yesmaximal, characteristic, complemented
13#31826468C211yesmaximal, characteristic, complemented
14#31826458C211yesmaximal, characteristic, complemented
15#459×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C2×D4×D283C2211yescharacteristic
18C2×D4×D283C2211yescharacteristic
19#22583634—24no—
20C2×#17985381C2211yescharacteristic, complemented
21C2×#17985380C2211yescharacteristic, complemented
22C2×D2264C2211yescharacteristic
23C2×#17985377C2211yescharacteristic
24C2×#17985377C2211yescharacteristic
25C2×#17985377C2211yescharacteristic, complemented
26D8×D283—24no—
27C2×#17985375C2211yescharacteristic
28C2×C8×D283C2211yescharacteristic
29#22583606C2211yescharacteristic, complemented
30#22583598C2211yescharacteristic, complemented
31#22583597C2211yescharacteristic, complemented
32#22583582—21no—
33#22583582—21no—
34#22583578—21no—
35#22583578—21no—
36C4×D1132C2211yescharacteristic, complemented
37D4×Dic283C2211yescharacteristic, complemented
38#22583572C2211yescharacteristic, complemented
39C4×C22⋊D283—21no—
40(C22⋊D283)⋊C4—21no—
41#22583568C2211yescharacteristic
42#22583567C2211yescharacteristic
43C2×(C2×D283)⋊C4—21no—
44C22⋊C4×D283—21no—
45C4⋊(C283⋊C8)C2211yescharacteristic, complemented
46Dic283⋊C8C2211yescharacteristic, complemented
47Dic283⋊C8C2211yescharacteristic, complemented
48#22583535C2211yescharacteristic, complemented
49#22583533C2211yescharacteristic, complemented
50#22583532C2211yescharacteristic, complemented
51#22583531C2211yescharacteristic, complemented
52#22583531C2211yescharacteristic, complemented
53#22583530C2211yescharacteristic, complemented
54C2×D8×C283C2211yescharacteristic
55C2×D8×C283C2211yescharacteristic, complemented
56#127×C283C2211yescharacteristic, complemented
57C4×D4×C283C2211yescharacteristic, complemented
58C4⋊C8×C283C2211yescharacteristic, complemented
59#102×C283C2211yescharacteristic, complemented
60#102×C283C2211yescharacteristic, complemented
61C23×D283—21no—
62C23×D283—21no—
63#17985391—22no—
64#17985391—22no—
65C2×Dic566C2311yescharacteristic
66C2×D1132C2311yescharacteristic
67C2×D1132C2311yescharacteristic
68C2×C22⋊D283—21no—
69C2×C22⋊D283—21no—
70C2×C22⋊D283—21no—
71C2×C22⋊D283—21no—
72C2×C22⋊D283—21no—
73D4×D283—22no—
74D4×D283—22no—
75D4×D283—22no—
76D4×D283D414yescomplemented
77C22×Dic283—21no—
78C22×Dic283—21no—
79C2×C4×D283—21no—
80C2×C4×D283—21no—
81C2×C4×D283C2311yescharacteristic
82#17985381—22no—
83#17985380—22no—
84D2264—22no—
85#17985377—22no—
86#17985377—22no—
87#17985377—22no—
88#17985375—22no—
89C2×C283⋊C8C2311yescharacteristic
90C2×C283⋊C8C2311yescharacteristic
91C8×D283—22no—
92C4⋊Dic283C2311yescharacteristic
93Dic283⋊C4D411yescharacteristic
94Dic283⋊C4D411yescharacteristic
95C22⋊Dic283—21no—
96C22⋊Dic283—21no—
97C22⋊Dic283—21no—
98(C2×D283)⋊C4—21no—
99(C2×D283)⋊C4—21no—
100(C2×D283)⋊C4—21no—
101(C2×D283)⋊C4—21no—
102(C2×D283)⋊C4—21no—
103(C2×D283)⋊C4D411yescharacteristic
104(C2×D283)⋊C4D411yescharacteristic
105C4×Dic283—21no—
106C4×Dic283C2311yescharacteristic
107C2×D4×C283—21no—
108C2×D4×C283—21no—
109C2×D4×C283C2311yescharacteristic
110C2×D4×C283C2311yescharacteristic
111C2×D4×C283C2311yescharacteristic
112C22×C4×C283—21no—
113D8×C283—22no—
114D8×C283—22no—
115C2×C8×C283C2311yescharacteristic
116C2×C8×C283C2311yescharacteristic
117C4⋊C4×C283C2311yescharacteristic
118C22⋊C4×C283—21no—
119C42×C283C2311yescharacteristic
120C22×D283—21no—
121C22×D283—24no—
122C22×D283—21no—
123C22×D283—42no—
124C22×D283—81no—
125C22×D283—81no—
126C22×D283—81no—
127C22×D283—81no—
128C22×D283C2×D411yescharacteristic
129Dic566—21no—
130Dic566—21no—
131D1132—21no—
132D1132—21no—
133D1132—21no—
134D1132C2×D412yes—
135C22⋊D283—24no—
136C22⋊D283—42no—
137C22⋊D283—42no—
138C22⋊D283—81no—
139C22⋊D283—81no—
140C2×Dic283—21no—
141C2×Dic283—21no—
142C2×Dic283—42no—
143C2×Dic283—81no—
144C2×Dic283C2×D411yescharacteristic
145C2×Dic283C2×D411yescharacteristic
146C2×Dic283C2×D411yescharacteristic
147C4×D283—81no—
148C4×D283—81no—
149C4×D283C2×D412yes—
150C4×D283#4112yes—
151C283⋊C8—21no—
152C283⋊C8—21no—
153C23×C283—21no—
154C23×C283—21no—
155C23×C283—21no—
156D4×C283—21no—
157D4×C283—21no—
158D4×C283—21no—
159D4×C283—21no—
160D4×C283—21no—
161D4×C283—81no—
162D4×C283—81no—
163D4×C283C2×D412yes—
164C2×C4×C283—21no—
165C2×C4×C283—81no—
166C2×C4×C283C2×D411yescharacteristic
167C2×C4×C283C2×D411yescharacteristic
168C2×C4×C283C2411yescharacteristic
169C8×C283—21no—
170C8×C283—21no—
171C22×C283—22no—
172C22×C283—41no—
173C22×C283—41no—
174C22×C283—41no—
175C22×C283—41no—
176C22×C283—41no—
177C22×C283—41no—
178C22×C283—41no—
179C22×C283—41no—
180C22×C283C22×D411yescharacteristic
181C2×D283—21no—
182C2×D283—21no—
183C2×D283—22no—
184C2×D283—41no—
185C2×D283—41no—
186C2×D283—41no—
187C2×D283—41no—
188C2×D283—41no—
189C2×D283—84no—
190C2×D283—84no—
191C2×D283#12112yes—
192C4×C283—21no—
193C4×C283—21no—
194C4×C283—41no—
195C4×C283C22×D411yescharacteristic
196C4×C283C2×#4111yescharacteristic
197Dic283—21no—
198Dic283—21no—
199Dic283—41no—
200Dic283—41no—
201Dic283#12112yes—
202C2×C283—42no—
203C2×C283—81no—
204C2×C283—81no—
205C2×C283C2×#12111yescharacteristic
206C2×C283#57611yescharacteristic
207C2×C283#57611yescharacteristic
208D283—22no—
209D283—42no—
210D283—81no—
211C283#304111yescharacteristic, complemented, Sylow
212#3041—2831nomaximal, Sylow
213C2×AGL(1,ℤ/8)—2831no—
214C22×D8—2831no—
215#535—2831no—
216#518—2831no—
217#463—2831no—
218#463—2831no—
219#463—2831no—
220#463—2831no—
221#459—2831no—
222#459—2831no—
223#459—2831no—
224#459D28311yescharacteristic, complemented
225#424—2831no—
226#418—2831no—
227#416—2831no—
228C2×#41—2831no—
229C22×D4—2831no—
230C22×D4—2831no—
231AGL(1,ℤ/8)—5664no—
232C2×SD16—2831no—
233C2×SD16—2831no—
234C2×D8—2831no—
235C2×D8—2831no—
236C2×D8—2831no—
237C2×D8—2831no—
238C2×D8—5664no—
239C2×D8C2×D28311yescharacteristic
240C2×D8C2×D28311yescharacteristic, complemented
241C2×M16—2831no—
242C22×C8—2831no—
243#127—2831no—
244#127C2×D28311yescharacteristic, complemented
245#124—2831no—
246#124—2831no—
247#121—5661no—
248#121—5661no—
249#120—5661no—
250#120—5661no—
251C4×D4—2831no—
252C4×D4—2831no—
253C4×D4—2831no—
254C4×D4—5661no—
255C4×D4—5661no—
256C4×D4C2×D28311yescharacteristic, complemented
257#117—2831no—
258#117—2831no—
259C2×C22⋊C4—5661no—
260C2×C22⋊C4—5661no—
261C4⋊C8—2831no—
262C4⋊C8—2831no—
263C4⋊C8—2831no—
264C4⋊C8C2×D28311yescharacteristic, complemented
265#103—2831no—
266#103—2831no—
267#102—2831no—
268#102—2831no—
269#102—2831no—
270#102—2831no—
271#102C2×D28311yescharacteristic, complemented
272#102C2×D28311yescharacteristic, complemented
273C24—5661no—
274C24—5661no—
275#41—5662no—
276#41—5662no—
277C2×Q8—2831no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—2834no—
281C2×D4—2831no—
282C2×D4—2831no—
283C2×D4—5662no—
284C2×D4—5662no—
285C2×D4—5662no—
286C2×D4—5661no—
287C2×D4—5661no—
288C2×D4—5661no—
289C2×D4—5661no—
290C2×D4—5661no—
291C2×D4C22×D28311yescharacteristic
292C2×D4C22×D28311yescharacteristic
293C2×D4C22×D28311yescharacteristic
294C22×C4—21no—
295C22×C4—2831no—
296C22×C4—5661no—
297C22×C4—5661no—
298C22×C4—5661no—
299C22×C4—5661no—
300SD16—5662no—
301SD16—5662no—
302D8—22no—
303D8—22no—
304D8—5662no—
305D8—5662no—
306D8—5662no—
307D8—5662no—
308M16—5662no—
309C2×C8—2831no—
310C2×C8—2831no—
311C2×C8—5662no—
312C2×C8C22×D28311yescharacteristic
313C2×C8C22×D28311yescharacteristic
314C4⋊C4—2831no—
315C4⋊C4—2831no—
316C4⋊C4—2831no—
317C4⋊C4C22×D28311yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—2831no—
320C22⋊C4—2831no—
321C22⋊C4—5661no—
322C22⋊C4—5661no—
323C22⋊C4—5661no—
324C22⋊C4—5661no—
325C22⋊C4—5661no—
326C22⋊C4—5661no—
327C22⋊C4—5661no—
328C22⋊C4—5661no—
329C42—2831no—
330C42—5661no—
331C42C22×D28311yescharacteristic
332C23—21no—
333C23—21no—
334C23—21no—
335C23—2831no—
336C23—5664no—
337C23—5661no—
338C23—5661no—
339C23—11322no—
340C23—22641no—
341C23—22641no—
342C23—22641no—
343C23—22641no—
344Q8—5661no—
345Q8—5661no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—81no—
352D4—81no—
353D4—2832no—
354D4—5664no—
355D4—5661no—
356D4—5661no—
357D4—5661no—
358D4—11322no—
359D4—11322no—
360D4—22641no—
361D4—22641no—
362D4D4×D28312yes—
363C2×C4—21no—
364C2×C4—81no—
365C2×C4—2831no—
366C2×C4—2832no—
367C2×C4—2832no—
368C2×C4—2831no—
369C2×C4—2831no—
370C2×C4—5661no—
371C2×C4—5661no—
372C2×C4—11322no—
373C2×C4—22641no—
374C2×C4—22641no—
375C2×C4—22641no—
376C2×C4D4×D28311yescharacteristic
377C2×C4D4×D28311yescharacteristic
378C2×C4C23×D28311yescharacteristic
379C8—21no—
380C8—21no—
381C8—5661no—
382C8—5661no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—2832no—
393C22—5661no—
394C22—5661no—
395C22—5662no—
396C22—11321no—
397C22—11321no—
398C22—11321no—
399C22—11321no—
400C22—11321no—
401C22—22644no—
402C22—22644no—
403C22C2×D4×D28311yescharacteristic
404C4—21no—
405C4—21no—
406C4—41no—
407C4—2832no—
408C4—5661no—
409C4—5661no—
410C4—11321no—
411C4—11321no—
412C4C2×D4×D28311yescharacteristic
413C4#41×D28311yescharacteristic
414C2—42no—
415C2—81no—
416C2—81no—
417C2—5662no—
418C2—11322no—
419C2—22641no—
420C2#121×D28311yescharacteristic
421C2#3182726611yescharacteristic
422C2#3182726911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#459×C283C2
socleC22×C283C22×D4
hypercenter#459D283
hypocenterC283#3041
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#22583634C2semidirect
2. C2×D8×D283C2semidirect
3. #31827028C2semidirect
4. #31826937C2semidirect
5. #31826681C2semidirect
6. #31826680C2semidirect
7. #31826679C2semidirect
8. #31826678C2semidirect
9. #31826659C2semidirect
10. #31826658C2semidirect
11. #31826657C2semidirect
12. #31826490C2semidirect
13. #31826468C2semidirect
14. #31826458C2semidirect
15. #459×C283C2semidirect
20. C2×#17985381C22semidirect
21. C2×#17985380C22semidirect
25. C2×#17985377C22semidirect
29. #22583606C22semidirect
30. #22583598C22semidirect
31. #22583597C22semidirect
36. C4×D1132C22semidirect
37. D4×Dic283C22semidirect
38. #22583572C22semidirect
45. C4⋊(C283⋊C8)C22semidirect
46. Dic283⋊C8C22semidirect
47. Dic283⋊C8C22semidirect
48. #22583535C22semidirect
49. #22583533C22semidirect
50. #22583532C22semidirect
51. #22583531C22semidirect
52. #22583531C22semidirect
53. #22583530C22semidirect
55. C2×D8×C283C22semidirect
56. #127×C283C22semidirect
57. C4×D4×C283C22semidirect
58. C4⋊C8×C283C22semidirect
59. #102×C283C22semidirect
60. #102×C283C22semidirect
76. D4×D283D4semidirect
211. C283#3041semidirect
224. #459D283semidirect
240. C2×D8C2×D283semidirect
244. #127C2×D283semidirect
256. C4×D4C2×D283semidirect
264. C4⋊C8C2×D283semidirect
271. #102C2×D283semidirect
272. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836342
C2×D8×D2832
#318270282
#318269372
#318266812
#318266802
#318266792
#318266782
#318266592
#318266582
#318266572
#318264902
#318264682
#318264582
#459×C2832
#3041283