Finite Group Databasebeta

← #49130497

Subgroups — #49130497

Order 36224.

738 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×Q8×D283C211yesmaximal, characteristic, complemented
2C2×#22583643C211yesmaximal, characteristic, complemented
3C2×#22583641C211yesmaximal, characteristic, complemented
4#31826977C211yesmaximal, characteristic
5#31826622C214yesmaximal, complemented
6#31826605C214yesmaximal, complemented
7#31826473C211yesmaximal, characteristic, complemented
8#31826428C211yesmaximal, characteristic, complemented
9#419×C283C211yesmaximal, characteristic, complemented
10C2×#17985392C2211yescharacteristic
11C22×Dic566—21no—
12C22×Dic566C2211yescharacteristic
13C2×Q8×D283—24no—
14C2×Q8×D283—22no—
15C2×Q8×D283—24no—
16C2×Q8×D283C2214yes—
17C22×C4×D283—21no—
18C22×C4×D283C2211yescharacteristic
19#22583643—24no—
20#22583641—24no—
21C2×Dic1132C2212yescomplemented
22C2×#17985382C2212yescomplemented
23C2×#17985381C2212yescomplemented
24C2×#17985379C2212yescomplemented
25C2×#17985376C2211yescharacteristic
26#22583594—21no—
27#22583590C2212yes—
28#22583585C2212yes—
29#22583580—21no—
30C4×D1132—22no—
31#22583533C2214yescomplemented
32(C2×D283)⋊C8C2214yes—
33C22×Q8×C283C2211yescharacteristic
34C2×M16×C283C2211yescharacteristic
35#117×C283C2211yescharacteristic
36#103×C283C2214yescomplemented
37C23×D283D411yescharacteristic
38#17985392—22no—
39#17985392—22no—
40C2×Dic566—28no—
41C2×Dic566—24no—
42C2×Dic566—21no—
43C2×Dic566—22no—
44C2×Dic566D414yescomplemented
45C2×Dic566C2311yescharacteristic
46C2×Dic566C2312yes—
47Q8×D283—216no—
48Q8×D283—28no—
49Q8×D283—28no—
50C2×D1132—22no—
51C2×D1132C2311yescharacteristic
52C2×C22⋊D283—21no—
53C22×Dic283—21no—
54C22×Dic283D411yescharacteristic
55C2×C4×D283—28no—
56C2×C4×D283—24no—
57C2×C4×D283—22no—
58C2×C4×D283—22no—
59C2×C4×D283—21no—
60C2×C4×D283D412yes—
61C2×C4×D283C2312yes—
62Dic1132—24no—
63#17985382—24no—
64#17985381—24no—
65#17985379—24no—
66#17985376—22no—
67C2×C283⋊C8C2312yes—
68C4⋊Dic283—22no—
69(C2×D283)⋊C4—22no—
70(C2×D283)⋊C4—22no—
71C2×Q8×C283—22no—
72C2×Q8×C283—21no—
73C2×Q8×C283D414yescomplemented
74C2×Q8×C283C2312yes—
75C22×C4×C283—21no—
76C22×C4×C283C2311yescharacteristic
77M16×C283—22no—
78C2×C8×C283C2312yes—
79C4⋊C4×C283C2312yes—
80C22⋊C4×C283—21no—
81C42×C283—21no—
82C22×D283—22no—
83C22×D283—24no—
84C22×D283—21no—
85C22×D283C2×D412yes—
86Dic566—216no—
87Dic566—24no—
88Dic566—22no—
89Dic566—21no—
90Dic566—21no—
91Dic566C2×D414yes—
92D1132—21no—
93D1132—21no—
94D1132—44no—
95C22⋊D283—42no—
96C2×Dic283—24no—
97C2×Dic283—22no—
98C2×Dic283—22no—
99C2×Dic283—21no—
100C2×Dic283C2×D412yes—
101C4×D283—216no—
102C4×D283—24no—
103C4×D283—22no—
104C4×D283—22no—
105C4×D283—42no—
106C283⋊C8—22no—
107C23×C283C2×D411yescharacteristic
108Q8×C283—24no—
109Q8×C283—22no—
110Q8×C283C2×D414yes—
111C2×C4×C283—24no—
112C2×C4×C283—22no—
113C2×C4×C283—22no—
114C2×C4×C283C2×D411yescharacteristic
115C2×C4×C283C2×D412yes—
116C2×C4×C283C2×D412yes—
117C2×C4×C283C2411yescharacteristic
118C8×C283—22no—
119C22×C283—22no—
120C22×C283#12012yes—
121C22×C283C22×D411yescharacteristic
122C2×D283—28no—
123C2×D283—22no—
124C2×D283—22no—
125C2×D283—41no—
126C2×D283—42no—
127C2×D283#13714yescomplemented
128C4×C283—24no—
129C4×C283—42no—
130C4×C283#12012yes—
131C4×C283C22×D411yescharacteristic
132C4×C283C22×D411yescharacteristic
133Dic283—24no—
134Dic283—22no—
135Dic283—41no—
136C2×C283—22no—
137C2×C283C2×#12011yescharacteristic
138C2×C283C2×#13712yes—
139D283—24no—
140D283—81no—
141C283#300411yescharacteristic, complemented, Sylow
142#3004—2831nomaximal, Sylow
143C23×Q8—2831no—
144C2×#137—2831no—
145C2×#137—2831no—
146#525—2831no—
147#451—2834no—
148#448—2834no—
149#419—2831no—
150#419D28311yescharacteristic, complemented
151#407—2831no—
152C2×#41—2831no—
153C22×Q8—2834no—
154C22×Q8—2831no—
155C22×Q8—5661no—
156C22×Q8—5662no—
157C22×Q8—5664no—
158C22×Q8—5664no—
159C22×Q8C2×D28311yescharacteristic
160C23×C4—2831no—
161C23×C4—5661no—
162#137—5664no—
163#137—5664no—
164C2×Q16—2832no—
165C2×Q16—2832no—
166C2×SD16—2832no—
167C2×SD16—2832no—
168C2×M16—2831no—
169C2×M16C2×D28311yescharacteristic
170#123—5661no—
171C22⋊Q8—2832no—
172#121—2832no—
173#120—5661no—
174C4×D4—5662no—
175#117C2×D28311yescharacteristic
176#103—2834no—
177#103C2×D28314yescomplemented
178C22⋊C8—2834no—
179C24—2831no—
180#41—5662no—
181#41—5662no—
182C2×Q8—22no—
183C2×Q8—21no—
184C2×Q8—2834no—
185C2×Q8—2832no—
186C2×Q8—2831no—
187C2×Q8—5664no—
188C2×Q8—5668no—
189C2×Q8—5668no—
190C2×Q8—56616no—
191C2×Q8—5668no—
192C2×Q8—5661no—
193C2×Q8—5662no—
194C2×Q8D113214yescomplemented
195C2×Q8C22×D28312yes—
196C2×D4—2831no—
197C2×D4—5662no—
198C2×D4—5661no—
199C22×C4—21no—
200C22×C4—2831no—
201C22×C4—2832no—
202C22×C4—2832no—
203C22×C4—5664no—
204C22×C4—5668no—
205C22×C4—5661no—
206C22×C4—5662no—
207C22×C4—5662no—
208C22×C4—5661no—
209C22×C4C22×D28311yescharacteristic
210Q16—5664no—
211Q16—5664no—
212SD16—5664no—
213SD16—5664no—
214M16—22no—
215M16—5662no—
216C2×C8—2832no—
217C2×C8C22×D28312yes—
218C4⋊C4—5662no—
219C4⋊C4C22×D28312yes—
220C22⋊C4—21no—
221C22⋊C4—5662no—
222C22⋊C4—5662no—
223C42—21no—
224C23—2832no—
225C23—5664no—
226C23—5662no—
227C23—5661no—
228C23D4×D28311yescharacteristic
229Q8—24no—
230Q8—22no—
231Q8—2834no—
232Q8—56616no—
233Q8—5664no—
234Q8—5662no—
235Q8—5661no—
236Q8—5661no—
237Q8C2×D113214yes—
238D4—5661no—
239D4—5661no—
240D4—11324no—
241D4—11322no—
242C2×C4—24no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—2832no—
246C2×C4—56616no—
247C2×C4—5662no—
248C2×C4—5664no—
249C2×C4—5662no—
250C2×C4—5664no—
251C2×C4—5662no—
252C2×C4—5662no—
253C2×C4—5661no—
254C2×C4—11322no—
255C2×C4D4×D28311yescharacteristic
256C2×C4D4×D28312yes—
257C2×C4C2×D113212yes—
258C2×C4C23×D28311yescharacteristic
259C8—22no—
260C8—5662no—
261C22—22no—
262C22—2834no—
263C22—5668no—
264C22—5662no—
265C22—5662no—
266C22—11321no—
267C22—11322no—
268C22#2258358012yes—
269C22C2×D4×D28311yescharacteristic
270C4—24no—
271C4—42no—
272C4—5662no—
273C4—5664no—
274C4—11321no—
275C4#2258358012yes—
276C4C2×D4×D28311yescharacteristic
277C4C22×D113211yescharacteristic
278C2—22no—
279C2—5664no—
280C2—22641no—
281C2C2×#2258358011yescharacteristic
282C2#137×D28312yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#419×C283C2
socleC22×C283C22×D4
prime radical#31826977C2
hypercenter#419D283
hypocenterC283#3004
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D283C2semidirect
2. C2×#22583643C2semidirect
3. C2×#22583641C2semidirect
5. #31826622C2semidirect
6. #31826605C2semidirect
7. #31826473C2semidirect
8. #31826428C2semidirect
9. #419×C283C2semidirect
21. C2×Dic1132C22semidirect
22. C2×#17985382C22semidirect
23. C2×#17985381C22semidirect
24. C2×#17985379C22semidirect
31. #22583533C22semidirect
36. #103×C283C22semidirect
44. C2×Dic566D4semidirect
73. C2×Q8×C283D4semidirect
127. C2×D283#137semidirect
141. C283#3004semidirect
150. #419D283semidirect
177. #103C2×D283semidirect
194. C2×Q8D1132semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D2832
C2×#225836432
C2×#225836412
#318269772
#318266222
#318266052
#318264732
#318264282
#419×C2832
#3004283