Finite Group Databasebeta

← #49130557

Subgroups — #49130557

Order 36224.

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

normal subgroups only

This group has 700 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×#22583658C211yesmaximal, characteristic
2C2×#22583643C211yesmaximal, characteristic, complemented
3C22×#17985382C211yesmaximal, characteristic, complemented
4#31827041C211yesmaximal, characteristic, complemented
5#31826630C214yesmaximal, complemented
6#31826622C214yesmaximal, complemented
7#31826459C211yesmaximal, characteristic, complemented
8#31826433C211yesmaximal, characteristic, complemented
9#419×C283C211yesmaximal, characteristic, complemented
10#22583658—24no—
11#22583658—24no—
12C2×#17985393—21no—
13C2×#17985393C2212yes—
14C2×#17985392—22no—
15C2×#17985392C2211yescharacteristic
16C2×#17985392C2211yescharacteristic
17C22×Dic566C2211yescharacteristic
18C2×Q8×D283—21no—
19C2×Q8×D283C2212yes—
20#22583643—24no—
21C2×Dic1132C2212yes—
22C2×#17985382—24no—
23C2×#17985382C2214yes—
24C2×#17985381C2212yes—
25C22×C283⋊C8C2211yescharacteristic
26#22583610—21no—
27#22583598—21no—
28#22583594—22no—
29#22583590C2214yes—
30#22583533C2212yes—
31#22583530C2212yes—
32(C2×D283)⋊C8C2214yes—
33C22×Q8×C283C2211yescharacteristic
34C2×M16×C283C2211yescharacteristic
35#117×C283C2211yescharacteristic
36#103×C283C2214yes—
37#17985393—28no—
38#17985393—24no—
39#17985393—24no—
40#17985392—216no—
41#17985392—22no—
42#17985392—22no—
43#17985392—22no—
44#17985392D414yes—
45C2×Dic566—22no—
46C2×Dic566—21no—
47C2×Dic566—22no—
48C2×Dic566—22no—
49C2×Dic566D411yescharacteristic
50C2×Dic566C2312yes—
51C2×Dic566C2311yescharacteristic
52Q8×D283—28no—
53Q8×D283—24no—
54Q8×D283—24no—
55C2×D1132—22no—
56C2×D1132D411yescharacteristic
57C2×D1132C2311yescharacteristic
58C2×C22⋊D283—21no—
59C2×C22⋊D283D412yes—
60C22×Dic283—21no—
61C2×C4×D283—22no—
62C2×C4×D283—22no—
63C2×C4×D283—21no—
64C2×C4×D283C2312yes—
65Dic1132—24no—
66#17985382—28no—
67#17985381—24no—
68C2×C283⋊C8—22no—
69C2×C283⋊C8C2312yes—
70C4⋊Dic283—24no—
71(C2×D283)⋊C4—24no—
72C2×Q8×C283—21no—
73C2×Q8×C283—22no—
74C2×Q8×C283D414yes—
75C2×Q8×C283C2312yes—
76C22×C4×C283—21no—
77C22×C4×C283C2311yescharacteristic
78M16×C283—22no—
79C2×C8×C283C2312yes—
80C4⋊C4×C283C2312yes—
81C22⋊C4×C283—21no—
82C42×C283—21no—
83C22×D283—21no—
84C22×D283C2×D412yes—
85Dic566—28no—
86Dic566—22no—
87Dic566—21no—
88Dic566—22no—
89Dic566—22no—
90Dic566—42no—
91Dic566C2×D412yes—
92D1132—28no—
93D1132—22no—
94D1132—21no—
95D1132C2×D412yes—
96C22⋊D283—24no—
97C22⋊D283—24no—
98C2×Dic283—21no—
99C2×Dic283—22no—
100C2×Dic283—42no—
101C2×Dic283C2×D412yes—
102C4×D283—28no—
103C4×D283—28no—
104C4×D283—24no—
105C4×D283—22no—
106C4×D283—22no—
107C283⋊C8—22no—
108C23×C283C2×D411yescharacteristic
109Q8×C283—24no—
110Q8×C283—22no—
111Q8×C283C2×D414yes—
112C2×C4×C283—24no—
113C2×C4×C283—22no—
114C2×C4×C283—22no—
115C2×C4×C283C2×D411yescharacteristic
116C2×C4×C283C2×D412yes—
117C2×C4×C283C2×D412yes—
118C2×C4×C283C2411yescharacteristic
119C8×C283—22no—
120C22×C283—22no—
121C22×C283#12012yes—
122C22×C283C22×D411yescharacteristic
123C2×D283—22no—
124C2×D283—22no—
125C2×D283—24no—
126C2×D283—42no—
127C4×C283—24no—
128C4×C283—42no—
129C4×C283#12012yes—
130C4×C283C22×D411yescharacteristic
131C4×C283C22×D411yescharacteristic
132Dic283—22no—
133Dic283—22no—
134Dic283—42no—
135C2×C283—22no—
136C2×C283C2×#12011yescharacteristic
137C2×C283#57812yes—
138D283—42no—
139D283—42no—
140C283#301111yescharacteristic, complemented, Sylow
141#3011—2831nomaximal, Sylow
142C2×2−1+4—2831no—
143C2×#137—2831no—
144C22×Q16—2831no—
145#536—2831no—
146#452—2834no—
147#451—2834no—
148#419D28311yescharacteristic, complemented
149#416—2831no—
150#408—2831no—
1512−1+4—5664no—
1522−1+4—5664no—
153C2×#41—2831no—
154C2×#41—2832no—
155C2×#41—2831no—
156C2×#41—5662no—
157C2×#41—5661no—
158C22×Q8—2832no—
159C22×Q8—2831no—
160C22×Q8—5661no—
161C22×Q8C2×D28311yescharacteristic
162#137—5664no—
163C2×Q16—2834no—
164C2×Q16—2832no—
165C2×Q16—5664no—
166C2×SD16—2832no—
167C2×M16C2×D28311yescharacteristic
168C22×C8—2831no—
169C4⋊Q8—5661no—
170#124—5661no—
171#123—5662no—
172C22⋊Q8—2834no—
173#117C2×D28311yescharacteristic
174#103—2832no—
175#103C2×D28314yes—
176#102—2832no—
177C22⋊C8—2834no—
178#41—2834no—
179#41—56616no—
180#41—5664no—
181#41—5668no—
182#41—5664no—
183#41—5662no—
184#41—5662no—
185#41—5662no—
186C2×Q8—21no—
187C2×Q8—22no—
188C2×Q8—2831no—
189C2×Q8—2831no—
190C2×Q8—2832no—
191C2×Q8—5662no—
192C2×Q8—5664no—
193C2×Q8—5668no—
194C2×Q8—5664no—
195C2×Q8—5661no—
196C2×Q8—5662no—
197C2×Q8—5662no—
198C2×Q8D113214yes—
199C2×Q8C22×D28312yes—
200C2×D4—2832no—
201C2×D4—2831no—
202C2×D4—2831no—
203C2×D4—5662no—
204C2×D4—5661no—
205C22×C4—21no—
206C22×C4—2832no—
207C22×C4—5662no—
208C22×C4—5662no—
209C22×C4—5661no—
210C22×C4—5661no—
211C22×C4C22×D28311yescharacteristic
212Q16—5664no—
213Q16—5668no—
214SD16—5664no—
215M16—22no—
216C2×C8—2832no—
217C2×C8—5662no—
218C2×C8C22×D28312yes—
219C4⋊C4—5664no—
220C4⋊C4C22×D28312yes—
221C22⋊C4—21no—
222C22⋊C4—5664no—
223C42—21no—
224C23—2832no—
225C23—5661no—
226C23D4×D28311yescharacteristic
227Q8—24no—
228Q8—22no—
229Q8—2832no—
230Q8—5668no—
231Q8—5662no—
232Q8—5661no—
233Q8—5662no—
234Q8—5662no—
235Q8—11322no—
236Q8C2×D113214yes—
237D4—2832no—
238D4—5668no—
239D4—5664no—
240D4—5664no—
241D4—5662no—
242D4—5661no—
243C2×C4—24no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—2832no—
247C2×C4—5668no—
248C2×C4—5668no—
249C2×C4—5661no—
250C2×C4—5664no—
251C2×C4—5662no—
252C2×C4—5662no—
253C2×C4—5662no—
254C2×C4—11322no—
255C2×C4D4×D28311yescharacteristic
256C2×C4D4×D28312yes—
257C2×C4C2×D113212yes—
258C2×C4C23×D28311yescharacteristic
259C8—22no—
260C8—5662no—
261C22—22no—
262C22—5662no—
263C22—5662no—
264C22—5664no—
265C22—11322no—
266C22#2258358012yes—
267C22C2×D4×D28311yescharacteristic
268C4—24no—
269C4—42no—
270C4—5662no—
271C4—5662no—
272C4—11322no—
273C4#2258358012yes—
274C4C2×D4×D28311yescharacteristic
275C4C22×D113211yescharacteristic
276C2—22no—
277C2—11322no—
278C2—11322no—
279C2C2×#2258358011yescharacteristic
280C2#3182728112yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#419×C283C2
socleC22×C283C22×D4
prime radicalC2×#22583658C2
hypercenter#419D283
hypocenterC283#3011
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
2. C2×#22583643C2semidirect
3. C22×#17985382C2semidirect
4. #31827041C2semidirect
5. #31826630C2semidirect
6. #31826622C2semidirect
7. #31826459C2semidirect
8. #31826433C2semidirect
9. #419×C283C2semidirect
140. C283#3011semidirect
148. #419D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836582
C2×#225836432
C22×#179853822
#318270412
#318266302
#318266222
#318264592
#318264332
#419×C2832
#3011283