Finite Group Databasebeta

← #49130762

Subgroups — #49130762

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×#22583637C211yesmaximal, characteristic, complemented
2C2×D8×D283C211yesmaximal, characteristic, complemented
3#31827033C211yesmaximal, characteristic, complemented
4#31826937C211yesmaximal, characteristic, complemented
5#31826683C211yesmaximal, characteristic, complemented
6#31826682C211yesmaximal, characteristic, complemented
7#31826677C211yesmaximal, characteristic, complemented
8#31826661C211yesmaximal, characteristic, complemented
9#31826660C211yesmaximal, characteristic, complemented
10#31826659C211yesmaximal, characteristic, complemented
11#31826658C211yesmaximal, characteristic, complemented
12#31826490C211yesmaximal, characteristic, complemented
13#31826468C211yesmaximal, characteristic, complemented
14#31826460C211yesmaximal, characteristic, complemented
15#463×C283C211yesmaximal, characteristic, complemented
16C2×#17985393C2211yescharacteristic
17C2×D4×D283C2211yescharacteristic
18C2×D4×D283C2211yescharacteristic
19#22583637—24no—
20C2×#17985379C2211yescharacteristic, complemented
21C2×D2264C2211yescharacteristic
22C2×D2264C2211yescharacteristic, complemented
23C2×#17985377C2211yescharacteristic
24C2×#17985377C2211yescharacteristic
25C2×#17985377C2211yescharacteristic, complemented
26D8×D283—24no—
27C2×#17985375C2211yescharacteristic
28C2×C8×D283C2211yescharacteristic
29#22583607C2211yescharacteristic, complemented
30#22583606C2211yescharacteristic, complemented
31#22583599C2211yescharacteristic, complemented
32#22583583—21no—
33#22583583—21no—
34#22583580—21no—
35#22583580—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#22583534C2211yescharacteristic, complemented
49#22583532C2211yescharacteristic, complemented
50#22583532C2211yescharacteristic, complemented
51#22583531C2211yescharacteristic, complemented
52#22583530C2211yescharacteristic, complemented
53#22583530C2211yescharacteristic, complemented
54C2×SD16×C283C2211yescharacteristic, complemented
55C2×D8×C283C2211yescharacteristic
56#124×C283C2211yescharacteristic, complemented
57C4×D4×C283C2211yescharacteristic, complemented
58C4⋊C8×C283C2211yescharacteristic, complemented
59#103×C283C2211yescharacteristic, complemented
60#102×C283C2211yescharacteristic, complemented
61C23×D283—21no—
62C23×D283—21no—
63#17985393—22no—
64#17985393—22no—
65C2×D1132—21no—
66C2×D1132—21no—
67C2×D1132—21no—
68C2×D1132C2311yescharacteristic
69C2×D1132C2311yescharacteristic
70C2×D1132C2311yescharacteristic
71C2×C22⋊D283—21no—
72C2×C22⋊D283—21no—
73C2×C22⋊D283—21no—
74C2×C22⋊D283—21no—
75D4×D283—22no—
76D4×D283—22no—
77D4×D283—22no—
78D4×D283D414yescomplemented
79C22×Dic283—21no—
80C2×C4×D283—21no—
81C2×C4×D283—21no—
82C2×C4×D283—21no—
83C2×C4×D283C2311yescharacteristic
84#17985379—22no—
85D2264—22no—
86D2264—22no—
87#17985377—22no—
88#17985377—22no—
89#17985377—22no—
90#17985375—22no—
91C2×C283⋊C8C2311yescharacteristic
92C2×C283⋊C8C2311yescharacteristic
93C8×D283—22no—
94C4⋊Dic283C2311yescharacteristic
95Dic283⋊C4D411yescharacteristic
96Dic283⋊C4D411yescharacteristic
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×Q8×C283C2311yescharacteristic
108C2×D4×C283C2311yescharacteristic
109C2×D4×C283C2311yescharacteristic
110C22×C4×C283—21no—
111SD16×C283—22no—
112D8×C283—22no—
113C2×C8×C283C2311yescharacteristic
114C2×C8×C283C2311yescharacteristic
115C4⋊C4×C283C2311yescharacteristic
116C22⋊C4×C283—21no—
117C22⋊C4×C283—21no—
118C22⋊C4×C283—21no—
119C42×C283C2311yescharacteristic
120C22×D283—21no—
121C22×D283—24no—
122C22×D283—21no—
123C22×D283—21no—
124C22×D283—42no—
125C22×D283—81no—
126C22×D283—81no—
127C22×D283—81no—
128C22×D283—81no—
129C22×D283C2×D411yescharacteristic
130D1132—21no—
131D1132—21no—
132D1132—21no—
133D1132—21no—
134D1132—21no—
135D1132—42no—
136D1132—81no—
137D1132—81no—
138D1132C2×D412yes—
139C22⋊D283—24no—
140C22⋊D283—42no—
141C22⋊D283—81no—
142C22⋊D283—81no—
143C2×Dic283—21no—
144C2×Dic283—81no—
145C2×Dic283C2×D411yescharacteristic
146C2×Dic283C2×D411yescharacteristic
147C2×Dic283C2×D411yescharacteristic
148C4×D283—42no—
149C4×D283—81no—
150C4×D283—81no—
151C4×D283C2×D412yes—
152C4×D283#4112yes—
153C283⋊C8—21no—
154C283⋊C8—21no—
155C23×C283—21no—
156C23×C283—21no—
157Q8×C283—21no—
158Q8×C283—21no—
159D4×C283—21no—
160D4×C283—21no—
161D4×C283—21no—
162D4×C283C2×D412yes—
163C2×C4×C283—21no—
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×C283C22×D411yescharacteristic
178C2×D283—21no—
179C2×D283—21no—
180C2×D283—22no—
181C2×D283—41no—
182C2×D283—41no—
183C2×D283—41no—
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×C283—41no—
196C4×C283C22×D411yescharacteristic
197C4×C283C2×#4111yescharacteristic
198Dic283—21no—
199Dic283—21no—
200Dic283—41no—
201Dic283#12112yes—
202C2×C283—42no—
203C2×C283—81no—
204C2×C283C2×#12111yescharacteristic
205C2×C283#57611yescharacteristic
206C2×C283#57611yescharacteristic
207D283—22no—
208D283—42no—
209D283—81no—
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#463D28311yescharacteristic, complemented
221#459—2831no—
222#459—2831no—
223#459—2831no—
224#459—2831no—
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×SD16C2×D28311yescharacteristic, complemented
234C2×D8—2831no—
235C2×D8—2831no—
236C2×D8—2831no—
237C2×D8—2831no—
238C2×D8—2831no—
239C2×D8—5664no—
240C2×D8C2×D28311yescharacteristic
241C2×M16—2831no—
242C22×C8—2831no—
243#127—2831no—
244#127—2831no—
245#124—2831no—
246#124C2×D28311yescharacteristic, complemented
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#103C2×D28311yescharacteristic, complemented
267#102—2831no—
268#102—2831no—
269#102—2831no—
270#102—2831no—
271#102—2831no—
272#102C2×D28311yescharacteristic, complemented
273C24—5661no—
274C24—5661no—
275#41—5662no—
276#41—5662no—
277C2×Q8C22×D28311yescharacteristic
278C2×D4—2834no—
279C2×D4—2831no—
280C2×D4—2831no—
281C2×D4—2831no—
282C2×D4—5661no—
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×D4—5661no—
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—22no—
301SD16—5662no—
302D8—22no—
303D8—5662no—
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—21no—
320C22⋊C4—21no—
321C22⋊C4—2831no—
322C22⋊C4—2831no—
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—2831no—
335C23—5664no—
336C23—5661no—
337C23—5661no—
338C23—5661no—
339C23—11322no—
340C23—22641no—
341C23—22641no—
342C23—22641no—
343C23—22641no—
344Q8—21no—
345Q8—21no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—2832no—
350D4—5664no—
351D4—5661no—
352D4—5661no—
353D4—5661no—
354D4—5661no—
355D4—5661no—
356D4—11322no—
357D4—11322no—
358D4—22641no—
359D4—22641no—
360D4—22641no—
361D4—22641no—
362D4D4×D28312yes—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—81no—
366C2×C4—2831no—
367C2×C4—2832no—
368C2×C4—2832no—
369C2×C4—2831no—
370C2×C4—2831no—
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—2832no—
390C22—5661no—
391C22—5661no—
392C22—5662no—
393C22—11321no—
394C22—11321no—
395C22—11321no—
396C22—11321no—
397C22—11321no—
398C22—11321no—
399C22—11321no—
400C22—11321no—
401C22—22644no—
402C22—22644no—
403C22C2×D4×D28311yescharacteristic
404C4—21no—
405C4—21no—
406C4—41no—
407C4—41no—
408C4—2832no—
409C4—5661no—
410C4—5661no—
411C4—11321no—
412C4C2×D4×D28311yescharacteristic
413C4#41×D28311yescharacteristic
414C2—42no—
415C2—81no—
416C2—5662no—
417C2—11322no—
418C2—22641no—
419C2—22641no—
420C2#121×D28311yescharacteristic
421C2#3182726711yescharacteristic
422C2#3182726911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#463×C283C2
socleC22×C283C22×D4
hypercenter#463D283
hypocenterC283#3041
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#22583637C2semidirect
2. C2×D8×D283C2semidirect
3. #31827033C2semidirect
4. #31826937C2semidirect
5. #31826683C2semidirect
6. #31826682C2semidirect
7. #31826677C2semidirect
8. #31826661C2semidirect
9. #31826660C2semidirect
10. #31826659C2semidirect
11. #31826658C2semidirect
12. #31826490C2semidirect
13. #31826468C2semidirect
14. #31826460C2semidirect
15. #463×C283C2semidirect
20. C2×#17985379C22semidirect
22. C2×D2264C22semidirect
25. C2×#17985377C22semidirect
29. #22583607C22semidirect
30. #22583606C22semidirect
31. #22583599C22semidirect
36. C4×D1132C22semidirect
37. D4×Dic283C22semidirect
38. #22583572C22semidirect
45. C4⋊(C283⋊C8)C22semidirect
46. Dic283⋊C8C22semidirect
47. Dic283⋊C8C22semidirect
48. #22583534C22semidirect
49. #22583532C22semidirect
50. #22583532C22semidirect
51. #22583531C22semidirect
52. #22583530C22semidirect
53. #22583530C22semidirect
54. C2×SD16×C283C22semidirect
56. #124×C283C22semidirect
57. C4×D4×C283C22semidirect
58. C4⋊C8×C283C22semidirect
59. #103×C283C22semidirect
60. #102×C283C22semidirect
78. D4×D283D4semidirect
211. C283#3041semidirect
220. #463D283semidirect
233. C2×SD16C2×D283semidirect
246. #124C2×D283semidirect
256. C4×D4C2×D283semidirect
264. C4⋊C8C2×D283semidirect
266. #103C2×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×#225836372
C2×D8×D2832
#318270332
#318269372
#318266832
#318266822
#318266772
#318266612
#318266602
#318266592
#318266582
#318264902
#318264682
#318264602
#463×C2832
#3041283