Finite Group Databasebeta

← #49130570

Subgroups — #49130570

Order 36224.

764 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22583655C211yesmaximal, characteristic, complemented
2C2×#22583636C211yesmaximal, characteristic, complemented
3C2×#22583632C211yesmaximal, characteristic, complemented
4#31827046C211yesmaximal, characteristic, complemented
5#31826628C212yesmaximal, complemented
6#31826617C212yesmaximal, complemented
7#31826611C212yesmaximal, complemented
8#31826600C212yesmaximal, complemented
9#31826464C211yesmaximal, characteristic, complemented
10#31826431C211yesmaximal, characteristic, complemented
11C2×#102×C283C211yesmaximal, characteristic, complemented
12#22583655—24no—
13#22583655—24no—
14C2×#17985392C2211yescharacteristic
15C2×#17985392C2211yescharacteristic
16C2×#17985392C2211yescharacteristic, complemented
17C2×#17985391—21no—
18C2×#17985391C2212yes—
19C22×C22⋊D283—22no—
20C2×D4×D283—21no—
21C2×D4×D283C2212yes—
22#22583636—24no—
23#22583632—24no—
24C2×Dic1132C2211yescharacteristic, complemented
25C2×#17985381C2211yescharacteristic, complemented
26C2×#17985381C2211yescharacteristic, complemented
27C2×#17985380C2212yescomplemented
28C2×D2264C2211yescharacteristic, complemented
29C2×#17985377C2212yescomplemented
30C2×#17985376C2211yescharacteristic, complemented
31#22583590—21no—
32#22583590C2212yescomplemented
33#22583585—21no—
34#22583585C2212yescomplemented
35#22583584—22no—
36#22583533C2212yescomplemented
37#22583530C2212yescomplemented
38(C2×D283)⋊C8C2212yescomplemented
39(C2×D283)⋊C8C2212yescomplemented
40C22×D4×C283C2211yescharacteristic
41C22×C8×C283C2211yescharacteristic, complemented
42C2×C4⋊C4×C283C2211yescharacteristic, complemented
43#102×C283C2212yescomplemented
44#102×C283C2212yescomplemented
45C23×D283—22no—
46#17985392—22no—
47#17985392—22no—
48#17985392—22no—
49#17985392—22no—
50#17985392—22no—
51#17985392D414yescomplemented
52#17985391—28no—
53#17985391—24no—
54#17985391—24no—
55C2×Dic566D411yescharacteristic
56C2×Dic566C2311yescharacteristic
57C2×Dic566C2311yescharacteristic
58C2×D1132—22no—
59C2×D1132D411yescharacteristic
60C2×D1132C2311yescharacteristic
61C2×D1132C2311yescharacteristic
62C2×C22⋊D283—216no—
63C2×C22⋊D283—22no—
64C2×C22⋊D283—22no—
65C2×C22⋊D283—21no—
66C2×C22⋊D283—21no—
67C2×C22⋊D283D412yes—
68D4×D283—28no—
69D4×D283—24no—
70D4×D283—24no—
71C22×Dic283—22no—
72C2×C4×D283—21no—
73C2×C4×D283—21no—
74C2×C4×D283C2312yes—
75Dic1132—22no—
76#17985381—22no—
77#17985381—22no—
78#17985380—24no—
79D2264—22no—
80#17985377—24no—
81#17985376—22no—
82C2×C283⋊C8C2312yes—
83C4⋊Dic283—22no—
84(C2×D283)⋊C4—22no—
85(C2×D283)⋊C4—22no—
86C24×C283—21no—
87C2×D4×C283—21no—
88C2×D4×C283—22no—
89C2×D4×C283D414yescomplemented
90C2×D4×C283C2312yes—
91C22×C4×C283—21no—
92C22×C4×C283C2311yescharacteristic
93C2×C8×C283—22no—
94C2×C8×C283C2311yescharacteristic
95C2×C8×C283C2311yescharacteristic
96C4⋊C4×C283—21no—
97C4⋊C4×C283C2312yes—
98C22×D283—21no—
99C22×D283—28no—
100C22×D283—21no—
101C22×D283—82no—
102C22×D283—82no—
103C22×D283C2×D412yes—
104Dic566—22no—
105Dic566—21no—
106Dic566—21no—
107Dic566—21no—
108Dic566C2×D412yes—
109D1132—22no—
110D1132—21no—
111D1132—21no—
112D1132—21no—
113D1132—82no—
114D1132C2×D412yes—
115C22⋊D283—28no—
116C22⋊D283—28no—
117C22⋊D283—24no—
118C22⋊D283—24no—
119C22⋊D283—42no—
120C2×Dic283—28no—
121C2×Dic283—21no—
122C2×Dic283—21no—
123C2×Dic283C2×D412yes—
124C4×D283—24no—
125C4×D283—22no—
126C4×D283—22no—
127C4×D283—42no—
128C283⋊C8—22no—
129C23×C283—22no—
130C23×C283—24no—
131C23×C283—81no—
132C23×C283—81no—
133C23×C283C2×D411yescharacteristic
134D4×C283—24no—
135D4×C283—22no—
136D4×C283C2×D414yes—
137C2×C4×C283—22no—
138C2×C4×C283—81no—
139C2×C4×C283C2×D411yescharacteristic
140C2×C4×C283C2×D412yes—
141C2×C4×C283C2×D412yes—
142C2×C4×C283C2411yescharacteristic
143C8×C283—21no—
144C8×C283—21no—
145C22×C283—21no—
146C22×C283—21no—
147C22×C283—24no—
148C22×C283—42no—
149C22×C283—42no—
150C22×C283—84no—
151C22×C283#12012yes—
152C22×C283C22×D411yescharacteristic
153C2×D283—22no—
154C2×D283—22no—
155C2×D283—22no—
156C2×D283—22no—
157C2×D283—41no—
158C2×D283—41no—
159C2×D283—41no—
160C2×D283—41no—
161C2×D283—41no—
162C2×D283—88no—
163C4×C283—42no—
164C4×C283#12012yes—
165C4×C283C22×D411yescharacteristic
166C4×C283C22×D411yescharacteristic
167Dic283—22no—
168Dic283—22no—
169Dic283—41no—
170C2×C283—22no—
171C2×C283—44no—
172C2×C283C2×#12011yescharacteristic
173C2×C283#57611yescharacteristic
174C2×C283#57711yescharacteristic
175D283—42no—
176D283—42no—
177D283—81no—
178C283#301211yescharacteristic, complemented, Sylow
179#3012—2831nomaximal, Sylow
180C2×H(5,𝔽2)—2831no—
181C2×AGL(1,ℤ/8)—2831no—
182C2×#135—2831no—
183#537—2831no—
184#452—2832no—
185#450—2832no—
186#449—2832no—
187#447—2832no—
188#417—2831no—
189C2×#102D28311yescharacteristic, complemented
190#408—2831no—
191H(5,𝔽2)—5664no—
192H(5,𝔽2)—5664no—
193C2×#41—2831no—
194C2×#41—2832no—
195C2×#41—2831no—
196C2×#41—2831no—
197C2×#41—5661no—
198C22×D4—2832no—
199C22×D4—5661no—
200C22×D4—5662no—
201C22×D4C2×D28311yescharacteristic
202AGL(1,ℤ/8)—5664no—
203#135—5664no—
204C2×Q16—2831no—
205C2×SD16—2832no—
206C2×SD16—2831no—
207C2×SD16—2831no—
208C2×D8—2832no—
209C2×D8—2831no—
210C2×M16—2831no—
211C22×C8C2×D28311yescharacteristic, complemented
212C22⋊Q8—2832no—
213C22⋊Q8—5661no—
214#121—2832no—
215#121—5661no—
216#121—5662no—
217C2×C4⋊C4C2×D28311yescharacteristic, complemented
218#103—2832no—
219#102—2832no—
220#102C2×D28312yescomplemented
221#102C2×D28312yescomplemented
222C22⋊C8—2832no—
223C22⋊C8—2832no—
224C24—21no—
225C24—5662no—
226#41—2834no—
227#41—5664no—
228#41—5668no—
229#41—5664no—
230#41—5662no—
231#41—5662no—
232#41—5662no—
233#41—5662no—
234#41—5662no—
235C2×Q8—2831no—
236C2×Q8—2831no—
237C2×Q8—2831no—
238C2×D4—21no—
239C2×D4—22no—
240C2×D4—2832no—
241C2×D4—2831no—
242C2×D4—2831no—
243C2×D4—2831no—
244C2×D4—5662no—
245C2×D4—5662no—
246C2×D4—5664no—
247C2×D4—5668no—
248C2×D4—5662no—
249C2×D4—56616no—
250C2×D4—5661no—
251C2×D4—5664no—
252C2×D4—5661no—
253C2×D4D113214yescomplemented
254C2×D4C22×D28312yes—
255C22×C4—21no—
256C22×C4—2832no—
257C22×C4—5662no—
258C22×C4—5661no—
259C22×C4—5661no—
260C22×C4C22×D28311yescharacteristic
261Q16—5662no—
262SD16—5662no—
263SD16—5662no—
264SD16—5664no—
265D8—5662no—
266D8—5664no—
267M16—5662no—
268C2×C8—22no—
269C2×C8—2832no—
270C2×C8C22×D28311yescharacteristic
271C2×C8C22×D28311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—5662no—
274C4⋊C4C22×D28312yes—
275C22⋊C4—5662no—
276C22⋊C4—5662no—
277C23—22no—
278C23—24no—
279C23—81no—
280C23—81no—
281C23—2832no—
282C23—5668no—
283C23—5661no—
284C23—5661no—
285C23—22642no—
286C23—22642no—
287C23D4×D28311yescharacteristic
288Q8—2832no—
289Q8—5662no—
290Q8—5661no—
291Q8—5661no—
292Q8—5661no—
293D4—24no—
294D4—22no—
295D4—2832no—
296D4—5668no—
297D4—5668no—
298D4—5664no—
299D4—5664no—
300D4—5662no—
301D4—5661no—
302D4—5661no—
303D4—5661no—
304D4—11322no—
305D4—22642no—
306D4C2×D113214yes—
307C2×C4—22no—
308C2×C4—81no—
309C2×C4—2832no—
310C2×C4—5668no—
311C2×C4—5661no—
312C2×C4—5664no—
313C2×C4—5662no—
314C2×C4—5662no—
315C2×C4—5661no—
316C2×C4—11322no—
317C2×C4D4×D28311yescharacteristic
318C2×C4D4×D28312yes—
319C2×C4C2×D113212yes—
320C2×C4C23×D28311yescharacteristic
321C8—21no—
322C8—21no—
323C8—5662no—
324C22—21no—
325C22—21no—
326C22—24no—
327C22—42no—
328C22—42no—
329C22—84no—
330C22—5662no—
331C22—5662no—
332C22—5662no—
333C22—5662no—
334C22—11321no—
335C22—11321no—
336C22—11321no—
337C22—11321no—
338C22—11321no—
339C22—22648no—
340C22#2258358012yes—
341C22C2×D4×D28311yescharacteristic
342C4—42no—
343C4—5662no—
344C4—5662no—
345C4—11321no—
346C4#2258358012yes—
347C4C2×D4×D28311yescharacteristic
348C4C22×D113211yescharacteristic
349C2—22no—
350C2—44no—
351C2—11322no—
352C2—11322no—
353C2—22641no—
354C2C2×#2258358011yescharacteristic
355C2#3182726611yescharacteristic
356C2#3182727111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#102×C283C2
socleC22×C283C22×D4
hypercenterC2×#102D283
hypocenterC283#3012
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#22583655C2semidirect
2. C2×#22583636C2semidirect
3. C2×#22583632C2semidirect
4. #31827046C2semidirect
5. #31826628C2semidirect
6. #31826617C2semidirect
7. #31826611C2semidirect
8. #31826600C2semidirect
9. #31826464C2semidirect
10. #31826431C2semidirect
11. C2×#102×C283C2semidirect
16. C2×#17985392C22semidirect
24. C2×Dic1132C22semidirect
25. C2×#17985381C22semidirect
26. C2×#17985381C22semidirect
27. C2×#17985380C22semidirect
28. C2×D2264C22semidirect
29. C2×#17985377C22semidirect
30. C2×#17985376C22semidirect
32. #22583590C22semidirect
34. #22583585C22semidirect
36. #22583533C22semidirect
37. #22583530C22semidirect
38. (C2×D283)⋊C8C22semidirect
39. (C2×D283)⋊C8C22semidirect
41. C22×C8×C283C22semidirect
42. C2×C4⋊C4×C283C22semidirect
43. #102×C283C22semidirect
44. #102×C283C22semidirect
51. #17985392D4semidirect
89. C2×D4×C283D4semidirect
178. C283#3012semidirect
189. C2×#102D283semidirect
211. C22×C8C2×D283semidirect
217. C2×C4⋊C4C2×D283semidirect
220. #102C2×D283semidirect
221. #102C2×D283semidirect
253. C2×D4D1132semidirect

Maximal subgroups

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

subgroupindex
C2×#225836552
C2×#225836362
C2×#225836322
#318270462
#318266282
#318266172
#318266112
#318266002
#318264642
#318264312
C2×#102×C2832
#3012283