Finite Group Databasebeta

← #49130799

Subgroups — #49130799

Order 36224.

504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22583638C211yesmaximal, characteristic, complemented
2C2×#22583630C211yesmaximal, characteristic, complemented
3#31827029C211yesmaximal, characteristic, complemented
4#31826946C211yesmaximal, characteristic, complemented
5#31826690C212yesmaximal, complemented
6#31826683C212yesmaximal, complemented
7#31826664C212yesmaximal, complemented
8#31826659C212yesmaximal, complemented
9#31826493C211yesmaximal, characteristic, complemented
10C2×#22583530C211yesmaximal, characteristic, complemented
11#417×C283C211yesmaximal, characteristic, complemented
12C2×#17985392C2211yescharacteristic
13C22×D1132C2211yescharacteristic
14#22583638—24no—
15#22583630—24no—
16C2×#17985382C2211yescharacteristic, complemented
17C2×#17985381C2212yes—
18C2×#17985380C2211yescharacteristic, complemented
19C2×#17985379C2211yescharacteristic, complemented
20C2×D2264C2212yes—
21C2×#17985377C2211yescharacteristic, complemented
22C22×C283⋊C8C2211yescharacteristic
23#22583606C2212yes—
24#22583599C2212yes—
25#22583584—21no—
26#22583584—21no—
27#22583578—22no—
28#22583575C2212yescomplemented
29#22583572C2212yescomplemented
30C4×C22⋊D283—22no—
31#22583569C2211yescharacteristic
32#22583568—21no—
33C4⋊C4×D283—21no—
34Dic283⋊C8C2212yescomplemented
35Dic283⋊C8C2212yescomplemented
36#22583530C2212yes—
37#22583530C2212yes—
38C2×#41×C283C2211yescharacteristic
39C2×M16×C283C2211yescharacteristic
40C2×C4⋊C4×C283C2211yescharacteristic
41#103×C283C2212yescomplemented
42#102×C283C2212yescomplemented
43C23×D283—21no—
44#17985392—22no—
45#17985392D414yescomplemented
46C2×Dic566C2311yescharacteristic
47C2×D1132—22no—
48C2×D1132—21no—
49C2×D1132—22no—
50C2×D1132C2312yes—
51C2×D1132C2311yescharacteristic
52C2×C22⋊D283—22no—
53C2×C22⋊D283—22no—
54C2×C22⋊D283—21no—
55C2×C4×D283—22no—
56C2×C4×D283—21no—
57#17985382—22no—
58#17985381—24no—
59#17985380—22no—
60#17985379—22no—
61D2264—24no—
62#17985377—22no—
63C2×C283⋊C8—22no—
64C2×C283⋊C8C2311yescharacteristic
65C2×C283⋊C8C2311yescharacteristic
66C4⋊Dic283D411yescharacteristic
67C4⋊Dic283D411yescharacteristic
68Dic283⋊C4—22no—
69C22⋊Dic283D412yes—
70(C2×D283)⋊C4—22no—
71(C2×D283)⋊C4—22no—
72(C2×D283)⋊C4—22no—
73C4×Dic283—22no—
74C4×Dic283C2312yes—
75#41×C283—22no—
76#41×C283—22no—
77C2×Q8×C283C2311yescharacteristic
78C2×D4×C283—21no—
79C2×D4×C283C2311yescharacteristic
80C22×C4×C283—21no—
81C22×C4×C283—21no—
82C22×C4×C283C2311yescharacteristic
83M16×C283—22no—
84C2×C8×C283C2312yes—
85C4⋊C4×C283—21no—
86C4⋊C4×C283C2312yes—
87C22×D283—21no—
88C22×D283—22no—
89C22×D283—42no—
90C22×D283—81no—
91C22×D283—81no—
92Dic566—21no—
93Dic566C2×D412yes—
94D1132—22no—
95D1132—21no—
96D1132—22no—
97D1132—42no—
98D1132C2×D412yes—
99C22⋊D283—24no—
100C22⋊D283—82no—
101C22⋊D283—82no—
102C2×Dic283—21no—
103C2×Dic283C2×D412yes—
104C2×Dic283C2×D412yes—
105C4×D283—24no—
106C4×D283—82no—
107C283⋊C8—21no—
108C283⋊C8—21no—
109C23×C283—21no—
110C23×C283C2×D411yescharacteristic
111Q8×C283—21no—
112Q8×C283—21no—
113D4×C283—21no—
114D4×C283—21no—
115D4×C283—42no—
116C2×C4×C283—22no—
117C2×C4×C283—21no—
118C2×C4×C283—42no—
119C2×C4×C283—81no—
120C2×C4×C283C2×D411yescharacteristic
121C2×C4×C283C2×D412yes—
122C2×C4×C283#4112yes—
123C2×C4×C283C2411yescharacteristic
124C8×C283—22no—
125C22×C283—21no—
126C22×C283—21no—
127C22×C283—41no—
128C22×C283—41no—
129C22×C283—41no—
130C22×C283#12112yes—
131C22×C283C22×D411yescharacteristic
132C2×D283—22no—
133C2×D283—41no—
134C2×D283—41no—
135C2×D283—42no—
136C2×D283—42no—
137C2×D283—42no—
138C2×D283—84no—
139C4×C283—41no—
140C4×C283—42no—
141C4×C283#12112yes—
142C4×C283C22×D411yescharacteristic
143C4×C283C2×#4111yescharacteristic
144Dic283—22no—
145Dic283—22no—
146Dic283—22no—
147C2×C283—22no—
148C2×C283—81no—
149C2×C283C2×#12111yescharacteristic
150C2×C283#57611yescharacteristic
151C2×C283#57711yescharacteristic
152D283—42no—
153D283—82no—
154C283#304511yescharacteristic, complemented, Sylow
155#3045—2831nomaximal, Sylow
156C2×AGL(1,ℤ/8)—2831no—
157C2×#135—2831no—
158#535—2831no—
159#520—2831no—
160#464—2832no—
161#463—2832no—
162#460—2832no—
163#459—2832no—
164#424—2831no—
165#417D28311yescharacteristic, complemented
166C2×#102—2831no—
167C2×#41—2831no—
168C2×#41C2×D28311yescharacteristic
169C22×D4—2831no—
170AGL(1,ℤ/8)—5664no—
171#135—5664no—
172C2×Q16—2831no—
173C2×SD16—2831no—
174C2×SD16—2831no—
175C2×SD16—2832no—
176C2×D8—2831no—
177C2×D8—2832no—
178C2×M16C2×D28311yescharacteristic
179C22×C8—2831no—
180#127—2832no—
181#124—2832no—
182#121—5661no—
183#121—5661no—
184#120—5662no—
185C4×Q8—2832no—
186C4×D4—2832no—
187C4×D4—5662no—
188#117—2831no—
189#117—5661no—
190C2×C4⋊C4—5661no—
191C2×C4⋊C4C2×D28311yescharacteristic
192C4⋊C8—2832no—
193C4⋊C8—2832no—
194#103C2×D28312yescomplemented
195#102—2832no—
196#102—2832no—
197#102C2×D28312yescomplemented
198C24—5661no—
199#41—22no—
200#41—22no—
201#41—2834no—
202#41—5662no—
203C2×Q8—2831no—
204C2×Q8C22×D28311yescharacteristic
205C2×D4—21no—
206C2×D4—2831no—
207C2×D4—2832no—
208C2×D4—5662no—
209C2×D4—5662no—
210C2×D4—5661no—
211C2×D4—5662no—
212C2×D4—5661no—
213C2×D4—5662no—
214C2×D4C22×D28311yescharacteristic
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—5662no—
218C22×C4—5661no—
219C22×C4C22×D28311yescharacteristic
220Q16—5662no—
221SD16—5664no—
222SD16—5662no—
223SD16—5662no—
224D8—5664no—
225D8—5662no—
226M16—22no—
227C2×C8—2831no—
228C2×C8—2831no—
229C2×C8—5662no—
230C2×C8C22×D28312yes—
231C4⋊C4—21no—
232C4⋊C4—2831no—
233C4⋊C4—2831no—
234C4⋊C4—5662no—
235C4⋊C4C22×D28312yes—
236C22⋊C4—2832no—
237C22⋊C4—5662no—
238C22⋊C4—5662no—
239C22⋊C4—5662no—
240C42—2832no—
241C42—5662no—
242C23—21no—
243C23—5661no—
244C23—5662no—
245C23—11322no—
246C23—22641no—
247C23—22641no—
248C23D4×D28311yescharacteristic
249Q8—21no—
250Q8—21no—
251Q8—2832no—
252Q8—5661no—
253D4—21no—
254D4—21no—
255D4—42no—
256D4—2832no—
257D4—5664no—
258D4—5662no—
259D4—5661no—
260D4—5662no—
261D4—11322no—
262D4—22642no—
263D4—22642no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—81no—
268C2×C4—2832no—
269C2×C4—2832no—
270C2×C4—5661no—
271C2×C4—5664no—
272C2×C4—22642no—
273C2×C4D4×D28311yescharacteristic
274C2×C4D4×D28312yes—
275C2×C4#1798539212yes—
276C2×C4C23×D28311yescharacteristic
277C8—22no—
278C8—5661no—
279C8—5661no—
280C22—21no—
281C22—21no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—5662no—
286C22—11321no—
287C22—11321no—
288C22—11322no—
289C22—11322no—
290C22—11322no—
291C22—22644no—
292C22#2258358312yes—
293C22C2×D4×D28311yescharacteristic
294C4—41no—
295C4—42no—
296C4—5662no—
297C4—5662no—
298C4—5662no—
299C4#2258358312yes—
300C4C2×D4×D28311yescharacteristic
301C4C2×#1798539211yescharacteristic
302C2—22no—
303C2—81no—
304C2—11322no—
305C2—22642no—
306C2C2×#2258358311yescharacteristic
307C2#3182726911yescharacteristic
308C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#417×C283C2
socleC22×C283C22×D4
hypercenter#417D283
hypocenterC283#3045
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#22583638C2semidirect
2. C2×#22583630C2semidirect
3. #31827029C2semidirect
4. #31826946C2semidirect
5. #31826690C2semidirect
6. #31826683C2semidirect
7. #31826664C2semidirect
8. #31826659C2semidirect
9. #31826493C2semidirect
10. C2×#22583530C2semidirect
11. #417×C283C2semidirect
16. C2×#17985382C22semidirect
18. C2×#17985380C22semidirect
19. C2×#17985379C22semidirect
21. C2×#17985377C22semidirect
28. #22583575C22semidirect
29. #22583572C22semidirect
34. Dic283⋊C8C22semidirect
35. Dic283⋊C8C22semidirect
41. #103×C283C22semidirect
42. #102×C283C22semidirect
45. #17985392D4semidirect
154. C283#3045semidirect
165. #417D283semidirect
194. #103C2×D283semidirect
197. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836382
C2×#225836302
#318270292
#318269462
#318266902
#318266832
#318266642
#318266592
#318264932
C2×#225835302
#417×C2832
#3045283