Finite Group Databasebeta

← #49132898

Subgroups — #49132898

Order 36224.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583639C211yesmaximal, characteristic, complemented
2C2×#22583634C211yesmaximal, characteristic, complemented
3#31827123C211yesmaximal, characteristic, complemented
4#31827110C211yesmaximal, characteristic, complemented
5#31826847C211yesmaximal, characteristic, complemented
6#31826722C211yesmaximal, characteristic, complemented
7#31826717C211yesmaximal, characteristic, complemented
8#31826688C211yesmaximal, characteristic, complemented
9#31826628C211yesmaximal, characteristic, complemented
10#31826614C211yesmaximal, characteristic, complemented
11#31826607C211yesmaximal, characteristic, complemented
12#31826605C211yesmaximal, characteristic, complemented
13C4×#17985380C211yesmaximal, characteristic, complemented
14#31826542C211yesmaximal, characteristic, complemented
15#463×C283C211yesmaximal, characteristic, complemented
16C2×#17985391C2211yescharacteristic
17C2×#17985391C2211yescharacteristic
18C2×Q8×D283C2211yescharacteristic, complemented
19C2×D4×D283C2211yescharacteristic
20#22583639—24no—
21#22583634—24no—
22C2×Dic1132C2211yescharacteristic, complemented
23C2×#17985382C2211yescharacteristic, complemented
24C2×#17985381C2211yescharacteristic
25C2×#17985380C2211yescharacteristic
26C2×#17985380C2211yescharacteristic, complemented
27C2×#17985379C2211yescharacteristic
28C2×#17985377C2211yescharacteristic
29C2×#17985375C2211yescharacteristic
30C2×#17985375C2211yescharacteristic, complemented
31#22583598C2211yescharacteristic
32#22583596—21no—
33#22583594—21no—
34#22583590C2211yescharacteristic
35#22583587—21no—
36#22583586C2211yescharacteristic
37#22583585C2211yescharacteristic
38#22583584—21no—
39#22583583—21no—
40#22583581C2211yescharacteristic, complemented
41#22583580—21no—
42C4×Dic566C2211yescharacteristic, complemented
43C4×D1132C2211yescharacteristic
44(C22⋊D283)⋊C4—21no—
45C2×(C2×D283)⋊C4—21no—
46#22583541C2211yescharacteristic, complemented
47#22583535C2211yescharacteristic, complemented
48#22583533C2211yescharacteristic, complemented
49#22583532C2211yescharacteristic
50#22583531C2211yescharacteristic
51(C2×D283)⋊C8C2211yescharacteristic
52(C2×D283)⋊C8C2211yescharacteristic, complemented
53C4×C283⋊C8C2211yescharacteristic, complemented
54C2×SD16×C283C2211yescharacteristic
55C2×D8×C283C2211yescharacteristic
56#124×C283C2211yescharacteristic, complemented
57C4×D4×C283C2211yescharacteristic
58C4⋊C8×C283C2211yescharacteristic, complemented
59#103×C283C2211yescharacteristic, complemented
60#102×C283C2211yescharacteristic, complemented
61C23×D283—21no—
62#17985391—22no—
63#17985391—22no—
64#17985391—41no—
65#17985391—41no—
66C2×Dic566—21no—
67C2×Dic566C2311yescharacteristic
68C2×Dic566C2311yescharacteristic
69Q8×D283—22no—
70Q8×D283—41no—
71C2×D1132—21no—
72C2×D1132D411yescharacteristic
73C2×D1132C2311yescharacteristic
74C2×C22⋊D283—21no—
75C2×C22⋊D283—21no—
76C2×C22⋊D283—21no—
77C2×C22⋊D283—21no—
78D4×D283—22no—
79D4×D283—41no—
80C22×Dic283—21no—
81C22×Dic283—21no—
82C2×C4×D283—21no—
83C2×C4×D283C2311yescharacteristic
84C2×C4×D283C2311yescharacteristic
85Dic1132—22no—
86#17985382—22no—
87#17985381—22no—
88#17985380—41no—
89#17985380D414yescomplemented
90#17985379—41no—
91#17985377—22no—
92#17985375—22no—
93#17985375—22no—
94C2×C283⋊C8C2311yescharacteristic
95C2×C283⋊C8C2311yescharacteristic
96C4⋊Dic283—21no—
97C4⋊Dic283D411yescharacteristic
98C4⋊Dic283C2311yescharacteristic
99Dic283⋊C4—21no—
100Dic283⋊C4—21no—
101C22⋊Dic283—21no—
102(C2×D283)⋊C4—21no—
103(C2×D283)⋊C4—21no—
104(C2×D283)⋊C4—21no—
105(C2×D283)⋊C4—21no—
106(C2×D283)⋊C4—21no—
107(C2×D283)⋊C4D411yescharacteristic
108(C2×D283)⋊C4D411yescharacteristic
109C4×Dic283—21no—
110C2×Q8×C283C2311yescharacteristic
111C2×D4×C283C2311yescharacteristic
112C2×D4×C283C2311yescharacteristic
113C22×C4×C283—21no—
114SD16×C283—22no—
115D8×C283—22no—
116C2×C8×C283C2311yescharacteristic
117C2×C8×C283C2311yescharacteristic
118C4⋊C4×C283C2311yescharacteristic
119C22⋊C4×C283—21no—
120C22⋊C4×C283—21no—
121C22⋊C4×C283—21no—
122C42×C283C2311yescharacteristic
123C22×D283—21no—
124C22×D283—42no—
125C22×D283—42no—
126C22×D283—81no—
127C22×D283C2×D411yescharacteristic
128C22×D283C2×D411yescharacteristic
129Dic566—21no—
130Dic566—21no—
131Dic566—21no—
132Dic566—42no—
133Dic566C2×D412yes—
134D1132—21no—
135D1132—21no—
136D1132—41no—
137D1132—81no—
138C22⋊D283—42no—
139C22⋊D283—42no—
140C22⋊D283—42no—
141C22⋊D283—42no—
142C2×Dic283—21no—
143C2×Dic283—21no—
144C2×Dic283—21no—
145C2×Dic283—42no—
146C2×Dic283—42no—
147C2×Dic283C2×D411yescharacteristic
148C2×Dic283C2×D411yescharacteristic
149C4×D283—21no—
150C4×D283—21no—
151C4×D283—21no—
152C4×D283—21no—
153C4×D283—42no—
154C283⋊C8—21no—
155C283⋊C8C2×D412yes—
156C23×C283—21no—
157C23×C283—21no—
158Q8×C283—21no—
159Q8×C283—21no—
160D4×C283—21no—
161D4×C283—21no—
162D4×C283—21no—
163D4×C283C2×D412yes—
164C2×C4×C283—21no—
165C2×C4×C283—21no—
166C2×C4×C283—81no—
167C2×C4×C283C2×D411yescharacteristic
168C2×C4×C283C2×D411yescharacteristic
169C2×C4×C283C2411yescharacteristic
170C8×C283—21no—
171C8×C283—21no—
172C22×C283—22no—
173C22×C283—41no—
174C22×C283—41no—
175C22×C283—41no—
176C22×C283—41no—
177C22×C283—41no—
178C22×C283C22×D411yescharacteristic
179C2×D283—21no—
180C2×D283—21no—
181C2×D283—21no—
182C2×D283—21no—
183C2×D283—21no—
184C2×D283—21no—
185C2×D283—41no—
186C2×D283—41no—
187C2×D283—41no—
188C2×D283—84no—
189C4×C283—21no—
190C4×C283—21no—
191C4×C283—41no—
192C4×C283—41no—
193C4×C283C22×D411yescharacteristic
194C4×C283H(5,𝔽2)11yescharacteristic
195Dic283—21no—
196Dic283—21no—
197Dic283—22no—
198Dic283—41no—
199Dic283—41no—
200C2×C283—42no—
201C2×C283—81no—
202C2×C283D4211yescharacteristic
203C2×C283#57511yescharacteristic
204C2×C283#57711yescharacteristic
205D283—41no—
206D283—41no—
207D283—81no—
208C283#327511yescharacteristic, complemented, Sylow
209#3275—2831nomaximal, Sylow
210C2×#137—2831no—
211C2×AGL(1,ℤ/8)—2831no—
212#548—2831no—
213#546—2831no—
214#495—2831no—
215#470—2831no—
216#469—2831no—
217#464—2831no—
218#463D28311yescharacteristic, complemented
219#452—2831no—
220#450—2831no—
221#449—2831no—
222#448—2831no—
223C4×SD16—2831no—
224#436—2831no—
225C2×#41—2831no—
226C2×#41—2831no—
227C22×Q8—2831no—
228C22×D4—2831no—
229#137—5664no—
230AGL(1,ℤ/8)—5664no—
231C2×Q16—2831no—
232C2×Q16—2831no—
233C2×SD16—2831no—
234C2×SD16—2831no—
235C2×SD16—2831no—
236C2×SD16—2831no—
237C2×SD16C2×D28311yescharacteristic
238C2×D8—2831no—
239C2×D8C2×D28311yescharacteristic
240C2×M16—2831no—
241C2×M16—2831no—
242#124—2831no—
243#124—5661no—
244#124C2×D28311yescharacteristic, complemented
245#123—5661no—
246C22⋊Q8—2831no—
247C22⋊Q8—2831no—
248C22⋊Q8—5661no—
249#121—2831no—
250#121—2831no—
251#121—5661no—
252#121—5661no—
253#120—5661no—
254C4×Q8—2831no—
255C4×D4—2831no—
256C4×D4—5661no—
257C4×D4C2×D28311yescharacteristic
258C2×C22⋊C4—5661no—
259#106—2831no—
260C4⋊C8C2×D28311yescharacteristic, complemented
261#103—2831no—
262#103—2831no—
263#103C2×D28311yescharacteristic, complemented
264#102—2831no—
265#102—2831no—
266#102C2×D28311yescharacteristic, complemented
267C22⋊C8—2831no—
268C22⋊C8—2831no—
269C4×C8—2831no—
270C24—5661no—
271#41—5662no—
272#41—5662no—
273#41—11321no—
274#41—11321no—
275C2×Q8—2831no—
276C2×Q8—2831no—
277C2×Q8—5661no—
278C2×Q8—5662no—
279C2×Q8—11321no—
280C2×Q8C22×D28311yescharacteristic
281C2×D4—2831no—
282C2×D4—2831no—
283C2×D4—5661no—
284C2×D4—5661no—
285C2×D4—5662no—
286C2×D4—5661no—
287C2×D4—5661no—
288C2×D4—5661no—
289C2×D4—11321no—
290C2×D4C22×D28311yescharacteristic
291C2×D4C22×D28311yescharacteristic
292C22×C4—21no—
293C22×C4—2831no—
294C22×C4—2831no—
295C22×C4—5661no—
296C22×C4—5661no—
297C22×C4—5661no—
298Q16—5662no—
299Q16—5662no—
300SD16—22no—
301SD16—2834no—
302SD16—5662no—
303SD16—11321no—
304SD16—11321no—
305D8—22no—
306D8—5662no—
307M16—5662no—
308M16—5662no—
309C2×C8—2831no—
310C2×C8—2831no—
311C2×C8C22×D28311yescharacteristic
312C2×C8C22×D28311yescharacteristic
313C4⋊C4—2831no—
314C4⋊C4—2831no—
315C4⋊C4—5661no—
316C4⋊C4—5661no—
317C4⋊C4—5661no—
318C4⋊C4C22×D28311yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—2831no—
323C22⋊C4—2831no—
324C22⋊C4—5661no—
325C22⋊C4—5661no—
326C22⋊C4—5661no—
327C22⋊C4—5661no—
328C22⋊C4—5661no—
329C22⋊C4—5661no—
330C42—5661no—
331C42C22×D28311yescharacteristic
332C23—21no—
333C23—21no—
334C23—2831no—
335C23—2831no—
336C23—5661no—
337C23—11322no—
338C23—11322no—
339C23—22641no—
340Q8—21no—
341Q8—21no—
342Q8—2832no—
343Q8—5661no—
344Q8—5661no—
345Q8—5661no—
346Q8—11322no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—5661no—
351D4—5661no—
352D4—11321no—
353D4—11322no—
354D4—11322no—
355D4—11322no—
356D4—11322no—
357D4—22641no—
358D4D4×D28312yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—81no—
362C2×C4—2831no—
363C2×C4—2831no—
364C2×C4—5661no—
365C2×C4—5661no—
366C2×C4—5661no—
367C2×C4—5661no—
368C2×C4—5661no—
369C2×C4—5661no—
370C2×C4—5661no—
371C2×C4—11322no—
372C2×C4—11322no—
373C2×C4—11322no—
374C2×C4D4×D28311yescharacteristic
375C2×C4D4×D28311yescharacteristic
376C2×C4C23×D28311yescharacteristic
377C8—21no—
378C8—21no—
379C8—2832no—
380C8—5661no—
381C22—22no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—5661no—
388C22—5661no—
389C22—5661no—
390C22—5661no—
391C22—5661no—
392C22—5661no—
393C22—11321no—
394C22—11321no—
395C22—11321no—
396C22—22644no—
397C22C2×D4×D28311yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—5661no—
403C4—5661no—
404C4—5662no—
405C4—11321no—
406C4—11321no—
407C4C2×D4×D28311yescharacteristic
408C4#2258365611yescharacteristic
409C2—42no—
410C2—81no—
411C2—11321no—
412C2—11321no—
413C2—22641no—
414C2#3182709911yescharacteristic
415C2#3182726211yescharacteristic
416C2#3182727511yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#463×C283C2
socleC22×C283C22×D4
hypercenter#463D283
hypocenterC283#3275
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×#22583639C2semidirect
2. C2×#22583634C2semidirect
3. #31827123C2semidirect
4. #31827110C2semidirect
5. #31826847C2semidirect
6. #31826722C2semidirect
7. #31826717C2semidirect
8. #31826688C2semidirect
9. #31826628C2semidirect
10. #31826614C2semidirect
11. #31826607C2semidirect
12. #31826605C2semidirect
13. C4×#17985380C2semidirect
14. #31826542C2semidirect
15. #463×C283C2semidirect
18. C2×Q8×D283C22semidirect
22. C2×Dic1132C22semidirect
23. C2×#17985382C22semidirect
26. C2×#17985380C22semidirect
30. C2×#17985375C22semidirect
40. #22583581C22semidirect
42. C4×Dic566C22semidirect
46. #22583541C22semidirect
47. #22583535C22semidirect
48. #22583533C22semidirect
52. (C2×D283)⋊C8C22semidirect
53. C4×C283⋊C8C22semidirect
56. #124×C283C22semidirect
58. C4⋊C8×C283C22semidirect
59. #103×C283C22semidirect
60. #102×C283C22semidirect
89. #17985380D4semidirect
208. C283#3275semidirect
218. #463D283semidirect
244. #124C2×D283semidirect
260. C4⋊C8C2×D283semidirect
263. #103C2×D283semidirect
266. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836392
C2×#225836342
#318271232
#318271102
#318268472
#318267222
#318267172
#318266882
#318266282
#318266142
#318266072
#318266052
C4×#179853802
#318265422
#463×C2832
#3275283