Finite Group Databasebeta

← #49131738

Subgroups — #49131738

Order 36224.

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

normal subgroups only

This group has 564 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×#22583640C211yesmaximal, characteristic, complemented
2C2×#22583635C211yesmaximal, characteristic, complemented
3C22×#17985381C211yesmaximal, characteristic, complemented
4#31827036C211yesmaximal, characteristic, complemented
5#31827029C211yesmaximal, characteristic, complemented
6#31826858C212yesmaximal, complemented
7#31826853C212yesmaximal, complemented
8#31826846C212yesmaximal, complemented
9#31826836C212yesmaximal, complemented
10#31826420C211yesmaximal, characteristic, complemented
11C2×#135×C283C211yesmaximal, characteristic, complemented
12C22×Dic566C2211yescharacteristic
13C22×D1132C2211yescharacteristic
14#22583640—24no—
15#22583635—24no—
16C2×#17985382C2212yescomplemented
17C2×#17985381—24no—
18C2×#17985381C2212yes—
19C2×#17985381C2212yes—
20C2×#17985380C2212yescomplemented
21C2×#17985379C2212yes—
22C2×#17985377C2212yes—
23C2×#17985376C2211yescharacteristic
24#22583608C2212yescomplemented
25#22583606C2212yes—
26#22583599C2212yes—
27#22583597C2212yescomplemented
28#22583591—22no—
29#22583589—22no—
30#22583584—22no—
31#22583578—22no—
32#22583569C2211yescharacteristic
33#22583520C2212yescomplemented
34C8×Dic283C2212yescomplemented
35C2×#41×C283C2211yescharacteristic
36C2×#41×C283C2211yescharacteristic
37#135×C283—24no—
38C2×Q16×C283C2211yescharacteristic, complemented
39C2×SD16×C283C2211yescharacteristic, complemented
40C2×SD16×C283C2211yescharacteristic, complemented
41C2×D8×C283C2211yescharacteristic, complemented
42C22×C8×C283C2211yescharacteristic
43C23×D283—21no—
44C2×Dic566—21no—
45C2×Dic566—22no—
46C2×Dic566—22no—
47C2×Dic566C2312yes—
48C2×D1132—22no—
49C2×D1132—22no—
50C2×D1132—21no—
51C2×D1132C2312yes—
52C2×C22⋊D283—24no—
53C22×Dic283—21no—
54#17985382—24no—
55#17985381—24no—
56#17985381—24no—
57#17985380—24no—
58#17985379—24no—
59#17985377—24no—
60#17985376D414yescomplemented
61C2×C283⋊C8C2312yes—
62C4⋊Dic283D412yes—
63Dic283⋊C4—24no—
64C22⋊Dic283—24no—
65C22⋊Dic283D412yes—
66(C2×D283)⋊C4—24no—
67C4×Dic283C2312yes—
68#41×C283—22no—
69#41×C283—22no—
70#41×C283—22no—
71#41×C283—22no—
72C2×Q8×C283C2311yescharacteristic
73C2×Q8×C283C2311yescharacteristic
74C2×D4×C283—21no—
75C2×D4×C283—21no—
76C2×D4×C283C2311yescharacteristic
77C2×D4×C283C2311yescharacteristic
78C22×C4×C283—21no—
79C22×C4×C283—21no—
80C22×C4×C283C2311yescharacteristic
81Q16×C283—22no—
82SD16×C283—22no—
83SD16×C283—22no—
84D8×C283—22no—
85C2×C8×C283D414yescomplemented
86C2×C8×C283C2311yescharacteristic
87C2×C8×C283C2311yescharacteristic
88C22×D283—22no—
89C22×D283—42no—
90C22×D283—82no—
91Dic566—22no—
92Dic566—22no—
93Dic566—42no—
94D1132—22no—
95D1132—22no—
96D1132—42no—
97C22⋊D283—84no—
98C2×Dic283—22no—
99C2×Dic283—42no—
100C2×Dic283C2×D414yes—
101C283⋊C8C2×D414yes—
102C23×C283—21no—
103C23×C283—21no—
104C23×C283C2×D411yescharacteristic
105Q8×C283—21no—
106Q8×C283—21no—
107Q8×C283—21no—
108Q8×C283—21no—
109D4×C283—21no—
110D4×C283—21no—
111D4×C283—21no—
112D4×C283—21no—
113D4×C283—42no—
114D4×C283—42no—
115C2×C4×C283—21no—
116C2×C4×C283—21no—
117C2×C4×C283—42no—
118C2×C4×C283—42no—
119C2×C4×C283C2×D411yescharacteristic
120C2×C4×C283C2×D412yes—
121C2×C4×C283C2×D412yes—
122C2×C4×C283C2411yescharacteristic
123C8×C283C2×D412yes—
124C8×C283C2×D412yes—
125C22×C283—22no—
126C22×C283—41no—
127C22×C283—41no—
128C22×C283—42no—
129C22×C283—42no—
130C22×C283#12712yes—
131C22×C283C22×D411yescharacteristic
132C2×D283—42no—
133C2×D283—44no—
134C2×D283—84no—
135C4×C283—41no—
136C4×C283—41no—
137C4×C283#12712yes—
138C4×C283C22×D411yescharacteristic
139C4×C283C22×D411yescharacteristic
140Dic283—24no—
141Dic283—42no—
142C2×C283—22no—
143C2×C283—81no—
144C2×C283—81no—
145C2×C283C2×#12711yescharacteristic
146C2×C283#57712yes—
147D283—82no—
148C283#315411yescharacteristic, complemented, Sylow
149#3154—2831nomaximal, Sylow
150C2×#137—2831no—
151C2×AGL(1,ℤ/8)—2831no—
152C2×#135D28311yescharacteristic, complemented
153C22×SD16—2831no—
154#536—2831no—
155#535—2831no—
156#497—2832no—
157#496—2832no—
158#495—2832no—
159#492—2832no—
160#405—2831no—
161C2×#41C2×D28311yescharacteristic
162C2×#41C2×D28311yescharacteristic
163C22×Q8—2831no—
164C22×D4—2831no—
165#137—5664no—
166AGL(1,ℤ/8)—5664no—
167#135—24no—
168C2×Q16—2832no—
169C2×Q16C2×D28311yescharacteristic, complemented
170C2×SD16—2832no—
171C2×SD16—2832no—
172C2×SD16—2832no—
173C2×SD16—2832no—
174C2×SD16—5664no—
175C2×SD16C2×D28311yescharacteristic, complemented
176C2×SD16C2×D28311yescharacteristic, complemented
177C2×D8—2832no—
178C2×D8C2×D28311yescharacteristic, complemented
179C2×M16—2831no—
180C22×C8C2×D28311yescharacteristic
181C4⋊Q8—2832no—
182#127—2832no—
183#124—2832no—
184#124—2832no—
185#123—5662no—
186C22⋊Q8—5662no—
187#121—5662no—
188#120—5662no—
189#117—2831no—
190#97—2832no—
191C4×C8—2832no—
192C24—5661no—
193#41—22no—
194#41—22no—
195#41—22no—
196#41—22no—
197C2×Q8—2832no—
198C2×Q8—5661no—
199C2×Q8—5662no—
200C2×Q8—5662no—
201C2×Q8C22×D28311yescharacteristic
202C2×Q8C22×D28311yescharacteristic
203C2×D4—21no—
204C2×D4—21no—
205C2×D4—2832no—
206C2×D4—5664no—
207C2×D4—5662no—
208C2×D4—5661no—
209C2×D4—5662no—
210C2×D4C22×D28311yescharacteristic
211C2×D4C22×D28311yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—5661no—
215C22×C4C22×D28311yescharacteristic
216Q16—22no—
217Q16—5664no—
218SD16—22no—
219SD16—22no—
220SD16—5664no—
221SD16—5664no—
222SD16—5664no—
223SD16—5664no—
224D8—22no—
225D8—5664no—
226M16—2834no—
227C2×C8—2832no—
228C2×C8C22⋊D28314yescomplemented
229C2×C8C22×D28311yescharacteristic
230C2×C8C22×D28311yescharacteristic
231C4⋊C4—2832no—
232C4⋊C4—5664no—
233C22⋊C4—2832no—
234C22⋊C4—5664no—
235C22⋊C4—5664no—
236C42—2832no—
237C23—21no—
238C23—21no—
239C23—5662no—
240C23—11322no—
241C23—22642no—
242C23D4×D28311yescharacteristic
243Q8—21no—
244Q8—21no—
245Q8—21no—
246Q8—21no—
247Q8—5662no—
248Q8—5662no—
249Q8—11322no—
250D4—21no—
251D4—21no—
252D4—21no—
253D4—21no—
254D4—42no—
255D4—42no—
256D4—5662no—
257D4—5662no—
258D4—11322no—
259D4—22644no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—2834no—
265C2×C4—5662no—
266C2×C4—11322no—
267C2×C4D4×D28311yescharacteristic
268C2×C4D4×D28312yes—
269C2×C4C2×C22⋊D28312yes—
270C2×C4C23×D28311yescharacteristic
271C8—2834no—
272C8C2×C22⋊D28312yes—
273C8C2×C22⋊D28312yes—
274C22—22no—
275C22—41no—
276C22—41no—
277C22—42no—
278C22—42no—
279C22—11322no—
280C22—11324no—
281C22—22644no—
282C22#2258360612yes—
283C22C2×D4×D28311yescharacteristic
284C4—41no—
285C4—41no—
286C4—5664no—
287C4—11322no—
288C4#2258360612yes—
289C4C2×D4×D28311yescharacteristic
290C4C22×C22⋊D28311yescharacteristic
291C2—22no—
292C2—81no—
293C2—81no—
294C2—22642no—
295C2C2×#2258360611yescharacteristic
296C2#3182727212yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#135×C283C2
socleC22×C283C22×D4
hypercenterC2×#135D283
hypocenterC283#3154
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#22583640C2semidirect
2. C2×#22583635C2semidirect
3. C22×#17985381C2semidirect
4. #31827036C2semidirect
5. #31827029C2semidirect
6. #31826858C2semidirect
7. #31826853C2semidirect
8. #31826846C2semidirect
9. #31826836C2semidirect
10. #31826420C2semidirect
11. C2×#135×C283C2semidirect
16. C2×#17985382C22semidirect
20. C2×#17985380C22semidirect
24. #22583608C22semidirect
27. #22583597C22semidirect
33. #22583520C22semidirect
34. C8×Dic283C22semidirect
38. C2×Q16×C283C22semidirect
39. C2×SD16×C283C22semidirect
40. C2×SD16×C283C22semidirect
41. C2×D8×C283C22semidirect
60. #17985376D4semidirect
85. C2×C8×C283D4semidirect
148. C283#3154semidirect
152. C2×#135D283semidirect
169. C2×Q16C2×D283semidirect
175. C2×SD16C2×D283semidirect
176. C2×SD16C2×D283semidirect
178. C2×D8C2×D283semidirect
228. C2×C8C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836402
C2×#225836352
C22×#179853812
#318270362
#318270292
#318268582
#318268532
#318268462
#318268362
#318264202
C2×#135×C2832
#3154283