Finite Group Databasebeta

← #49130976

Subgroups — #49130976

Order 36224.

452 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31827264C211yesmaximal, characteristic, complemented
2#31827261C211yesmaximal, characteristic, complemented
3C2×#22583631C211yesmaximal, characteristic, complemented
4#131×D283C211yesmaximal, characteristic, complemented
5#31826739C211yesmaximal, characteristic, complemented
6#31826738C211yesmaximal, characteristic, complemented
7#31826734C211yesmaximal, characteristic, complemented
8#31826733C211yesmaximal, characteristic, complemented
9#31826729C211yesmaximal, characteristic, complemented
10#31826728C211yesmaximal, characteristic, complemented
11#31826725C211yesmaximal, characteristic, complemented
12#108×D283C211yesmaximal, characteristic, complemented
13#31826448C211yesmaximal, characteristic, complemented
14#31826446C211yesmaximal, characteristic, complemented
15#471×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×#17985391C2211yescharacteristic
18#41×D283C2211yescharacteristic
19#22583643C2211yescharacteristic
20#22583642—21no—
21#22583641C2211yescharacteristic
22#22583640C2211yescharacteristic
23#22583639—21no—
24#22583638C2211yescharacteristic
25#22583637—21no—
26#22583636C2211yescharacteristic
27#22583635C2211yescharacteristic
28#22583634—21no—
29#22583633—21no—
30#22583631—21no—
31#22583631—21no—
32#22583631—21no—
33#22583631—21no—
34#22583631—21no—
35#22583631—21no—
36#22583629—21no—
37C2×#17985382C2211yescharacteristic, complemented
38C2×#17985381C2211yescharacteristic, complemented
39C2×#17985377C2211yescharacteristic, complemented
40#22583618—21no—
41#22583618C2211yescharacteristic
42#22583617C2211yescharacteristic
43#22583616—21no—
44#22583616C2211yescharacteristic
45M16×D283—21no—
46M16×D283C2211yescharacteristic
47M16×D283C2211yescharacteristic
48M16×D283C2211yescharacteristic
49C2×C8×D283—21no—
50C2×C8×D283C2211yescharacteristic
51#22583546C2211yescharacteristic, complemented
52#22583545C2211yescharacteristic, complemented
53#22583545C2211yescharacteristic, complemented
54#22583529C2211yescharacteristic, complemented
55#22583528C2211yescharacteristic, complemented
56#22583528C2211yescharacteristic, complemented
57#22583527C2211yescharacteristic, complemented
58#22583526C2211yescharacteristic, complemented
59#22583526C2211yescharacteristic, complemented
60#137×C283C2211yescharacteristic
61AGL(1,ℤ/8)×C283C2211yescharacteristic
62C2×SD16×C283C2211yescharacteristic, complemented
63#131×C283C2211yescharacteristic
64#108×C283C2211yescharacteristic, complemented
65#101×C283C2211yescharacteristic, complemented
66#100×C283C2211yescharacteristic, complemented
67#17985393—21no—
68#17985393—21no—
69#17985393—21no—
70#17985393—21no—
71#17985393D411yescharacteristic
72#17985392—21no—
73#17985392C2311yescharacteristic
74#17985391—21no—
75#17985391—21no—
76#17985391—21no—
77#17985391—21no—
78#17985391—21no—
79#17985391D411yescharacteristic
80C2×Dic566C2311yescharacteristic
81Q8×D283D411yescharacteristic
82C2×D1132—21no—
83C2×D1132C2311yescharacteristic
84C2×C22⋊D283—21no—
85D4×D283—21no—
86D4×D283D411yescharacteristic
87C22×Dic283—21no—
88C2×C4×D283—21no—
89C2×C4×D283—21no—
90C2×C4×D283C2311yescharacteristic
91Dic1132—21no—
92#17985382—21no—
93#17985382—21no—
94#17985382—21no—
95#17985382—21no—
96#17985381—21no—
97#17985381—21no—
98#17985381—21no—
99#17985381—21no—
100#17985380—21no—
101#17985380—21no—
102#17985379—21no—
103#17985379—21no—
104D2264—21no—
105#17985377—21no—
106#17985377—21no—
107#17985377—21no—
108#17985377—21no—
109#17985376—21no—
110#17985376C2311yescharacteristic
111#17985376C2311yescharacteristic
112#17985376C2311yescharacteristic
113#17985375—21no—
114#17985375—21no—
115#17985375—21no—
116#17985375—21no—
117#17985375—21no—
118C2×C283⋊C8—21no—
119C2×C283⋊C8C2311yescharacteristic
120C8×D283—21no—
121C8×D283—21no—
122C8×D283—21no—
123C8×D283—21no—
124C8×D283—21no—
125C8×D283D411yescharacteristic
126C8×D283D411yescharacteristic
127C8×D283D411yescharacteristic
128C8×D283D411yescharacteristic
129#41×C283C2311yescharacteristic
130C2×Q8×C283C2311yescharacteristic
131C2×D4×C283C2311yescharacteristic
132Q16×C283—21no—
133SD16×C283—21no—
134SD16×C283—21no—
135SD16×C283—21no—
136SD16×C283—21no—
137D8×C283—21no—
138M16×C283—21no—
139M16×C283C2311yescharacteristic
140M16×C283C2311yescharacteristic
141M16×C283C2311yescharacteristic
142C2×C8×C283—21no—
143C2×C8×C283C2311yescharacteristic
144C22×D283—21no—
145C22×D283—21no—
146C22×D283#4111yescharacteristic
147Dic566—21no—
148Dic566—21no—
149Dic566—21no—
150Dic566C2×D411yescharacteristic
151D1132—21no—
152D1132—21no—
153D1132—21no—
154D1132—41no—
155D1132—41no—
156D1132C2×D411yescharacteristic
157C22⋊D283—21no—
158C22⋊D283—21no—
159C22⋊D283—21no—
160C22⋊D283—41no—
161C22⋊D283—41no—
162C2×Dic283—21no—
163C2×Dic283—21no—
164C2×Dic283—41no—
165C2×Dic283—41no—
166C2×Dic283#4111yescharacteristic
167C4×D283—21no—
168C4×D283—21no—
169C4×D283—21no—
170C4×D283—41no—
171C4×D283—41no—
172C4×D283C2×D411yescharacteristic
173C4×D283C2×D411yescharacteristic
174C4×D283C2×D411yescharacteristic
175C4×D283C2×D411yescharacteristic
176C283⋊C8—21no—
177C283⋊C8—21no—
178C283⋊C8—21no—
179C283⋊C8C2×D411yescharacteristic
180C283⋊C8C2×D411yescharacteristic
181C23×C283—21no—
182Q8×C283—21no—
183Q8×C283—21no—
184Q8×C283C2×D411yescharacteristic
185D4×C283—21no—
186D4×C283—21no—
187D4×C283—21no—
188D4×C283C2×D411yescharacteristic
189C2×C4×C283—21no—
190C2×C4×C283—21no—
191C2×C4×C283C2411yescharacteristic
192C8×C283—21no—
193C8×C283—21no—
194C8×C283—21no—
195C8×C283C2×D411yescharacteristic
196C8×C283C2×D411yescharacteristic
197C22×C283—21no—
198C22×C283—41no—
199C22×C283—81no—
200C22×C283C2×#4111yescharacteristic
201C2×D283—21no—
202C2×D283—41no—
203C2×D283—42no—
204C2×D283—41no—
205C2×D283—81no—
206C2×D283#12111yescharacteristic
207C2×D283#12111yescharacteristic
208C4×C283—21no—
209C4×C283—41no—
210C4×C283C22×D411yescharacteristic
211C4×C283C22×D411yescharacteristic
212Dic283—21no—
213Dic283—41no—
214Dic283#12111yescharacteristic
215Dic283#12111yescharacteristic
216C2×C283—21no—
217C2×C283—41no—
218C2×C283—81no—
219C2×C283C2×#12111yescharacteristic
220D283—21no—
221D283—21no—
222D283—41no—
223D283—81no—
224C283#306711yescharacteristic, complemented, Sylow
225#3067—2831nomaximal, Sylow
226#575—2831no—
227#575—2831no—
228C2×#135—2831no—
229C2×#131—2831no—
230#473—2831no—
231#473—2831no—
232#472—2831no—
233#472—2831no—
234#471—2831no—
235#471—2831no—
236#471—2831no—
237#471D28311yescharacteristic, complemented
238C2×#108—2831no—
239#413—2831no—
240#413—2831no—
241C2×#41—2831no—
242C2×#41—2831no—
243C2×#41—2831no—
244#137—2831no—
245#137—2831no—
246#137—2831no—
247#137—5661no—
248#137—5661no—
249#137C2×D28311yescharacteristic
250AGL(1,ℤ/8)—2831no—
251AGL(1,ℤ/8)—2831no—
252AGL(1,ℤ/8)—2831no—
253AGL(1,ℤ/8)—5661no—
254AGL(1,ℤ/8)—5661no—
255AGL(1,ℤ/8)C2×D28311yescharacteristic
256#135—5661no—
257#135—5661no—
258#135—5661no—
259#135—5661no—
260#135—5661no—
261#135—5661no—
262#135—5661no—
263#135—5661no—
264C2×Q16—2831no—
265C2×SD16—2831no—
266C2×SD16C2×D28311yescharacteristic, complemented
267C2×D8—2831no—
268#131—2831no—
269#131—2831no—
270#131—2831no—
271#131—5661no—
272#131—5661no—
273#131C2×D28311yescharacteristic
274C2×M16—2831no—
275C2×M16—2831no—
276C2×M16—2831no—
277C2×M16—5661no—
278C22×C8—2831no—
279C22×C8—5661no—
280#108—2831no—
281#108—2831no—
282#108—2831no—
283#108C2×D28311yescharacteristic, complemented
284#101—2831no—
285#101—2831no—
286#101—2831no—
287#101C2×D28311yescharacteristic, complemented
288#100—2831no—
289#100—2831no—
290#100—2831no—
291#100C2×D28311yescharacteristic, complemented
292#41—2831no—
293#41—2831no—
294#41—2831no—
295#41—5661no—
296#41—5661no—
297#41—5661no—
298#41—5661no—
299#41—5661no—
300#41—5661no—
301#41—5661no—
302#41—5661no—
303#41—5661no—
304#41—5661no—
305#41C22×D28311yescharacteristic
306C2×Q8—2831no—
307C2×Q8—2831no—
308C2×Q8C22×D28311yescharacteristic
309C2×D4—2831no—
310C2×D4—2831no—
311C2×D4—5661no—
312C2×D4—5661no—
313C2×D4—5661no—
314C2×D4C22×D28311yescharacteristic
315C22×C4—2831no—
316C22×C4—5661no—
317C22×C4—5661no—
318C22×C4—5661no—
319Q16—21no—
320Q16—5661no—
321Q16—5661no—
322Q16—5661no—
323Q16—5661no—
324Q16—5661no—
325SD16—21no—
326SD16—21no—
327SD16—21no—
328SD16—21no—
329SD16—5661no—
330SD16—5661no—
331SD16—5661no—
332SD16—5661no—
333SD16—5661no—
334SD16—5661no—
335SD16—5661no—
336SD16—5661no—
337D8—21no—
338D8—5661no—
339D8—5661no—
340D8—5661no—
341D8—5661no—
342D8—5661no—
343M16—21no—
344M16—2831no—
345M16—2831no—
346M16—2831no—
347M16—5661no—
348M16—5661no—
349M16—5661no—
350M16—5661no—
351M16—5661no—
352M16—5661no—
353M16C22×D28311yescharacteristic
354M16C22×D28311yescharacteristic
355M16C22×D28311yescharacteristic
356C2×C8—21no—
357C2×C8—2831no—
358C2×C8—2831no—
359C2×C8—2831no—
360C2×C8—2831no—
361C2×C8—2831no—
362C2×C8—5661no—
363C2×C8—5661no—
364C2×C8—5661no—
365C2×C8—5661no—
366C2×C8—5661no—
367C2×C8—5661no—
368C2×C8C22×D28311yescharacteristic
369C23—21no—
370C23—2831no—
371C23—5661no—
372C23—5661no—
373Q8—21no—
374Q8—21no—
375Q8—2831no—
376Q8—5661no—
377Q8—5661no—
378Q8—5661no—
379Q8D4×D28311yescharacteristic
380D4—21no—
381D4—21no—
382D4—21no—
383D4—2831no—
384D4—5661no—
385D4—5661no—
386D4—5661no—
387D4—5661no—
388D4—5661no—
389D4—5661no—
390D4—11321no—
391D4—11321no—
392D4—11321no—
393D4—11321no—
394D4D4×D28311yescharacteristic
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—2831no—
398C2×C4—2831no—
399C2×C4—2831no—
400C2×C4—2831no—
401C2×C4—2831no—
402C2×C4—5661no—
403C2×C4—5661no—
404C2×C4—5661no—
405C2×C4—5661no—
406C2×C4—5661no—
407C2×C4—11321no—
408C2×C4—11321no—
409C2×C4—11321no—
410C2×C4—11321no—
411C2×C4C23×D28311yescharacteristic
412C8—21no—
413C8—21no—
414C8—21no—
415C8—2831no—
416C8—2831no—
417C8—5661no—
418C8—5661no—
419C8—5661no—
420C8D4×D28311yescharacteristic
421C8D4×D28311yescharacteristic
422C22—21no—
423C22—41no—
424C22—81no—
425C22—2831no—
426C22—2831no—
427C22—5661no—
428C22—11321no—
429C22—11322no—
430C22—11321no—
431C22—22641no—
432C22#41×D28311yescharacteristic
433C4—21no—
434C4—41no—
435C4—2831no—
436C4—2831no—
437C4—5661no—
438C4—11321no—
439C4C2×D4×D28311yescharacteristic
440C4C2×D4×D28311yescharacteristic
441C2—21no—
442C2—41no—
443C2—81no—
444C2—5661no—
445C2—5661no—
446C2—11321no—
447C2—22641no—
448C2#121×D28311yescharacteristic
subgroupG/H
centerC2#121×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#471×C283C2
socleC2×C283C2×#121
hypercenter#471D283
hypocenterC283#3067
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #31827264C2semidirect
2. #31827261C2semidirect
3. C2×#22583631C2semidirect
4. #131×D283C2semidirect
5. #31826739C2semidirect
6. #31826738C2semidirect
7. #31826734C2semidirect
8. #31826733C2semidirect
9. #31826729C2semidirect
10. #31826728C2semidirect
11. #31826725C2semidirect
12. #108×D283C2semidirect
13. #31826448C2semidirect
14. #31826446C2semidirect
15. #471×C283C2semidirect
37. C2×#17985382C22semidirect
38. C2×#17985381C22semidirect
39. C2×#17985377C22semidirect
51. #22583546C22semidirect
52. #22583545C22semidirect
53. #22583545C22semidirect
54. #22583529C22semidirect
55. #22583528C22semidirect
56. #22583528C22semidirect
57. #22583527C22semidirect
58. #22583526C22semidirect
59. #22583526C22semidirect
62. C2×SD16×C283C22semidirect
64. #108×C283C22semidirect
65. #101×C283C22semidirect
66. #100×C283C22semidirect
224. C283#3067semidirect
237. #471D283semidirect
266. C2×SD16C2×D283semidirect
283. #108C2×D283semidirect
287. #101C2×D283semidirect
291. #100C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318272642
#318272612
C2×#225836312
#131×D2832
#318267392
#318267382
#318267342
#318267332
#318267292
#318267282
#318267252
#108×D2832
#318264482
#318264462
#471×C2832
#3067283