Finite Group Databasebeta

← #49130877

Subgroups — #49130877

Order 36224.

548 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583634C211yesmaximal, characteristic, complemented
2C22×#17985375C211yesmaximal, characteristic, complemented
3#31826975C211yesmaximal, characteristic, complemented
4#121×D283C211yesmaximal, characteristic, complemented
5#31826717C211yesmaximal, characteristic, complemented
6#31826715C211yesmaximal, characteristic, complemented
7#31826712C211yesmaximal, characteristic, complemented
8#31826710C211yesmaximal, characteristic, complemented
9#31826699C211yesmaximal, characteristic, complemented
10#31826694C211yesmaximal, characteristic, complemented
11#31826692C211yesmaximal, characteristic, complemented
12#31826506C211yesmaximal, characteristic, complemented
13#31826468C211yesmaximal, characteristic, complemented
14#31826463C211yesmaximal, characteristic, complemented
15#466×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C2×D4×D283—21no—
18C2×D4×D283C2211yescharacteristic
19C22×C4×D283C2211yescharacteristic
20#22583634—24no—
21C2×#17985381C2211yescharacteristic, complemented
22C2×#17985380C2211yescharacteristic, complemented
23C2×#17985377C2211yescharacteristic, complemented
24C2×#17985375—24no—
25C2×#17985375C2211yescharacteristic
26C2×#17985375C2211yescharacteristic
27C2×#17985375C2211yescharacteristic, complemented
28C2×#17985375C2211yescharacteristic, complemented
29C22×C283⋊C8C2211yescharacteristic, complemented
30#22583592—21no—
31#22583590C2211yescharacteristic, complemented
32#22583589C2211yescharacteristic, complemented
33#22583585C2211yescharacteristic
34#22583584C2211yescharacteristic
35#22583583—21no—
36#22583582—21no—
37#22583581C2211yescharacteristic
38#22583581C2211yescharacteristic, complemented
39#22583578—21no—
40D4×Dic283—21no—
41(C22⋊D283)⋊C4—21no—
42#22583568C2211yescharacteristic
43C4⋊C4×D283C2211yescharacteristic
44C22⋊C4×D283—21no—
45#22583543C2211yescharacteristic, complemented
46#22583542C2211yescharacteristic, complemented
47#22583541C2211yescharacteristic, complemented
48#22583535C2211yescharacteristic, complemented
49#22583533C2211yescharacteristic, complemented
50#22583532C2211yescharacteristic, complemented
51#22583531C2211yescharacteristic, complemented
52#22583531C2211yescharacteristic, complemented
53#22583530C2211yescharacteristic, complemented
54C2×D8×C283C2211yescharacteristic, complemented
55C22×C8×C283C2211yescharacteristic, complemented
56#121×C283C2211yescharacteristic
57#121×C283C2211yescharacteristic, complemented
58#107×C283C2211yescharacteristic, complemented
59#102×C283C2211yescharacteristic, complemented
60#102×C283C2211yescharacteristic, complemented
61C23×D283—21no—
62C23×D283D411yescharacteristic
63#17985391—22no—
64#17985391—22no—
65C2×Dic566C2311yescharacteristic
66C2×D1132—21no—
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—44no—
76C22×Dic283—21no—
77C22×Dic283D411yescharacteristic
78C2×C4×D283—22no—
79C2×C4×D283—22no—
80C2×C4×D283—21no—
81C2×C4×D283D411yescharacteristic
82C2×C4×D283D411yescharacteristic
83C2×C4×D283C2311yescharacteristic
84C2×C4×D283C2311yescharacteristic
85#17985381—22no—
86#17985380—22no—
87#17985377—22no—
88#17985375—22no—
89#17985375—22no—
90#17985375—22no—
91#17985375D414yescomplemented
92C2×C283⋊C8—22no—
93C2×C283⋊C8C2311yescharacteristic
94C2×C283⋊C8C2311yescharacteristic
95C4⋊Dic283—21no—
96C4⋊Dic283C2311yescharacteristic
97C4⋊Dic283C2311yescharacteristic
98Dic283⋊C4—21no—
99Dic283⋊C4—21no—
100C22⋊Dic283—21no—
101C22⋊Dic283—21no—
102C22⋊Dic283—21no—
103(C2×D283)⋊C4—21no—
104(C2×D283)⋊C4—21no—
105(C2×D283)⋊C4—21no—
106(C2×D283)⋊C4—21no—
107C4×Dic283—21no—
108C2×D4×C283—21no—
109C2×D4×C283—21no—
110C2×D4×C283C2311yescharacteristic
111C2×D4×C283C2311yescharacteristic
112C22×C4×C283C2311yescharacteristic
113D8×C283—22no—
114C2×C8×C283—22no—
115C2×C8×C283C2311yescharacteristic
116C2×C8×C283C2311yescharacteristic
117C4⋊C4×C283C2311yescharacteristic
118C4⋊C4×C283C2311yescharacteristic
119C22⋊C4×C283—21no—
120C22⋊C4×C283—21no—
121C22×D283—22no—
122C22×D283—22no—
123C22×D283—21no—
124C22×D283—41no—
125C22×D283—42no—
126C22×D283—42no—
127C22×D283—42no—
128C22×D283C2×D411yescharacteristic
129C22×D283C2×D411yescharacteristic
130Dic566—21no—
131Dic566—21no—
132D1132—21no—
133D1132—21no—
134D1132—42no—
135C22⋊D283—42no—
136C22⋊D283—42no—
137C22⋊D283—42no—
138C22⋊D283—42no—
139C22⋊D283—42no—
140C2×Dic283—22no—
141C2×Dic283—21no—
142C2×Dic283—21no—
143C2×Dic283—21no—
144C2×Dic283—42no—
145C2×Dic283C2×D411yescharacteristic
146C2×Dic283C2×D411yescharacteristic
147C4×D283—22no—
148C4×D283—21no—
149C4×D283—21no—
150C4×D283—22no—
151C4×D283—42no—
152C4×D283C2×D412yes—
153C4×D283#4112yes—
154C283⋊C8—21no—
155C283⋊C8C2×D412yescomplemented
156C23×C283—21no—
157C23×C283—21no—
158C23×C283C2×D411yescharacteristic
159D4×C283—21no—
160D4×C283—21no—
161D4×C283—21no—
162D4×C283—21no—
163D4×C283—42no—
164D4×C283—42no—
165C2×C4×C283—21no—
166C2×C4×C283—21no—
167C2×C4×C283—21no—
168C2×C4×C283—21no—
169C2×C4×C283C2×D411yescharacteristic
170C2×C4×C283C2411yescharacteristic
171C8×C283—21no—
172C8×C283C2×D412yescomplemented
173C22×C283—21no—
174C22×C283—21no—
175C22×C283—41no—
176C22×C283—41no—
177C22×C283—41no—
178C22×C283—41no—
179C22×C283—41no—
180C22×C283—41no—
181C22×C283AGL(1,ℤ/8)12yescomplemented
182C22×C283C22×D411yescharacteristic
183C2×D283—21no—
184C2×D283—21no—
185C2×D283—21no—
186C2×D283—21no—
187C2×D283—21no—
188C2×D283—44no—
189C2×D283—41no—
190C2×D283—41no—
191C2×D283—41no—
192C2×D283—84no—
193C2×D283#12112yes—
194C4×C283—21no—
195C4×C283—41no—
196C4×C283—41no—
197C4×C283C22×D411yescharacteristic
198C4×C283C2×#4111yescharacteristic
199Dic283—21no—
200Dic283—41no—
201Dic283—41no—
202Dic283—41no—
203Dic283#12112yes—
204C2×C283—22no—
205C2×C283—81no—
206C2×C283—81no—
207C2×C283C2×#12111yescharacteristic
208C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
209C2×C283#57511yescharacteristic
210D283—22no—
211D283—41no—
212D283—81no—
213C283#305511yescharacteristic, complemented, Sylow
214#3055—2831nomaximal, Sylow
215C2×AGL(1,ℤ/8)—2831no—
216C22×M16—2831no—
217#525—2831no—
218C2×#121—2831no—
219#469—2831no—
220#469—2831no—
221#468—2831no—
222#468—2831no—
223#466—2831no—
224#466D28311yescharacteristic, complemented
225#465—2831no—
226#465—2831no—
227#428—2831no—
228#418—2831no—
229#417—2831no—
230C2×#41—2831no—
231C22×D4—2831no—
232C22×D4—5661no—
233C23×C4—2831no—
234AGL(1,ℤ/8)—5664no—
235C2×SD16—2831no—
236C2×SD16—2831no—
237C2×D8—2831no—
238C2×D8C2×D28311yescharacteristic, complemented
239C2×M16—2831no—
240C2×M16—2831no—
241C2×M16—2831no—
242C2×M16—2831no—
243C2×M16—5664no—
244C22×C8—2831no—
245C22×C8C2×D28311yescharacteristic, complemented
246#123—5661no—
247C22⋊Q8—2831no—
248C22⋊Q8—2831no—
249#121—2831no—
250#121—2831no—
251#121—2831no—
252#121—2831no—
253#121—5661no—
254#121—5661no—
255#121C2×D28311yescharacteristic
256#121C2×D28311yescharacteristic, complemented
257#120—5661no—
258C4×D4—5661no—
259C4×D4—5661no—
260#117—2831no—
261C2×C4⋊C4—2831no—
262C2×C22⋊C4—5661no—
263#107—2831no—
264#107C2×D28311yescharacteristic, complemented
265#106—2831no—
266#106—2831no—
267#103—2831no—
268#103—2831no—
269#102—2831no—
270#102—2831no—
271#102—2831no—
272#102—2831no—
273#102C2×D28311yescharacteristic, complemented
274#102C2×D28311yescharacteristic, complemented
275C24—2831no—
276C24—5661no—
277#41—5662no—
278#41—5662no—
279C2×Q8—2831no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—2831no—
283C2×D4—5661no—
284C2×D4—5662no—
285C2×D4—5662no—
286C2×D4—5661no—
287C2×D4—5661no—
288C2×D4—5661no—
289C2×D4—5661no—
290C2×D4—5661no—
291C2×D4—11324no—
292C2×D4C22×D28311yescharacteristic
293C2×D4C22×D28311yescharacteristic
294C22×C4—2831no—
295C22×C4—2831no—
296C22×C4—2831no—
297C22×C4—2831no—
298C22×C4—2831no—
299C22×C4—5662no—
300C22×C4—5662no—
301C22×C4—5661no—
302C22×C4—5661no—
303C22×C4C22×D28311yescharacteristic
304SD16—5662no—
305SD16—5662no—
306D8—22no—
307D8—5662no—
308M16—2834no—
309M16—5662no—
310M16—5662no—
311M16—5662no—
312C2×C8—22no—
313C2×C8—2831no—
314C2×C8—2831no—
315C2×C8—5662no—
316C2×C8C22×D28311yescharacteristic
317C2×C8C22×D28311yescharacteristic
318C4⋊C4—2831no—
319C4⋊C4—2831no—
320C4⋊C4—5661no—
321C4⋊C4—5661no—
322C4⋊C4—5661no—
323C4⋊C4C22×D28311yescharacteristic
324C4⋊C4C22×D28311yescharacteristic
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—5661no—
328C22⋊C4—5661no—
329C22⋊C4—5661no—
330C22⋊C4—5661no—
331C22⋊C4—5661no—
332C22⋊C4—5661no—
333C22⋊C4—5661no—
334C42—5661no—
335C23—21no—
336C23—21no—
337C23—2831no—
338C23—2831no—
339C23—5662no—
340C23—5662no—
341C23—5661no—
342C23—11321no—
343C23—11322no—
344C23—11322no—
345C23—11322no—
346C23D4×D28311yescharacteristic
347Q8—5661no—
348Q8—5661no—
349D4—21no—
350D4—21no—
351D4—21no—
352D4—21no—
353D4—42no—
354D4—42no—
355D4—5661no—
356D4—5661no—
357D4—11322no—
358D4—11322no—
359D4—11322no—
360D4—11322no—
361D4—11322no—
362D4—11322no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—2831no—
368C2×C4—2832no—
369C2×C4—2832no—
370C2×C4—2831no—
371C2×C4—5662no—
372C2×C4—5662no—
373C2×C4—5662no—
374C2×C4—5661no—
375C2×C4—5661no—
376C2×C4—5661no—
377C2×C4—5661no—
378C2×C4—5661no—
379C2×C4—11322no—
380C2×C4—11322no—
381C2×C4D4×D28311yescharacteristic
382C2×C4C23×D28311yescharacteristic
383C8—21no—
384C8—2832no—
385C8—5661no—
386C8D4×D28312yescomplemented
387C22—21no—
388C22—21no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—2832no—
396C22—5661no—
397C22—5661no—
398C22—5661no—
399C22—5661no—
400C22—5661no—
401C22—11324no—
402C22—11321no—
403C22—11321no—
404C22—11321no—
405C22—22644no—
406C22#2258363412yescomplemented
407C22C2×D4×D28311yescharacteristic
408C4—21no—
409C4—41no—
410C4—41no—
411C4—2832no—
412C4—5661no—
413C4—11321no—
414C4—11321no—
415C4—11321no—
416C4C2×D4×D28311yescharacteristic
417C4#41×D28311yescharacteristic
418C2—22no—
419C2—81no—
420C2—81no—
421C2—5662no—
422C2—11321no—
423C2—22641no—
424C2#121×D28311yescharacteristic
425C2C2×#2258363411yescharacteristic
426C2#3182726211yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#466×C283C2
socleC22×C283C22×D4
hypercenter#466D283
hypocenterC283#3055
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#22583634C2semidirect
2. C22×#17985375C2semidirect
3. #31826975C2semidirect
4. #121×D283C2semidirect
5. #31826717C2semidirect
6. #31826715C2semidirect
7. #31826712C2semidirect
8. #31826710C2semidirect
9. #31826699C2semidirect
10. #31826694C2semidirect
11. #31826692C2semidirect
12. #31826506C2semidirect
13. #31826468C2semidirect
14. #31826463C2semidirect
15. #466×C283C2semidirect
21. C2×#17985381C22semidirect
22. C2×#17985380C22semidirect
23. C2×#17985377C22semidirect
27. C2×#17985375C22semidirect
28. C2×#17985375C22semidirect
29. C22×C283⋊C8C22semidirect
31. #22583590C22semidirect
32. #22583589C22semidirect
38. #22583581C22semidirect
45. #22583543C22semidirect
46. #22583542C22semidirect
47. #22583541C22semidirect
48. #22583535C22semidirect
49. #22583533C22semidirect
50. #22583532C22semidirect
51. #22583531C22semidirect
52. #22583531C22semidirect
53. #22583530C22semidirect
54. C2×D8×C283C22semidirect
55. C22×C8×C283C22semidirect
57. #121×C283C22semidirect
58. #107×C283C22semidirect
59. #102×C283C22semidirect
60. #102×C283C22semidirect
91. #17985375D4semidirect
155. C283⋊C8C2×D4semidirect
172. C8×C283C2×D4semidirect
181. C22×C283AGL(1,ℤ/8)semidirect
213. C283#3055semidirect
224. #466D283semidirect
238. C2×D8C2×D283semidirect
245. C22×C8C2×D283semidirect
256. #121C2×D283semidirect
264. #107C2×D283semidirect
273. #102C2×D283semidirect
274. #102C2×D283semidirect
386. C8D4×D283semidirect
406. C22#22583634semidirect

Maximal subgroups

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

subgroupindex
C2×#225836342
C22×#179853752
#318269752
#121×D2832
#318267172
#318267152
#318267122
#318267102
#318266992
#318266942
#318266922
#318265062
#318264682
#318264632
#466×C2832
#3055283