Finite Group Databasebeta

← #49130552

Subgroups — #49130552

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×#22583641C211yesmaximal, characteristic, complemented
3#31827039C211yesmaximal, characteristic, complemented
4#31826626C214yesmaximal, complemented
5#31826619C214yesmaximal, complemented
6#31826474C211yesmaximal, characteristic, complemented
7#31826462C211yesmaximal, characteristic, complemented
8#31826431C211yesmaximal, characteristic, complemented
9C22×Q16×C283C211yesmaximal, characteristic, complemented
10#22583658—24no—
11#22583658—24no—
12C2×#17985393—21no—
13C2×#17985393C2212yes—
14C2×#17985392—22no—
15C2×#17985392C2211yescharacteristic
16C2×#17985392C2211yescharacteristic
17C2×Q8×D283—21no—
18C2×Q8×D283C2212yes—
19#22583641—24no—
20C2×#17985382C2212yes—
21C2×#17985379C2212yes—
22C2×#17985376C2211yescharacteristic
23#22583608—21no—
24#22583599—21no—
25#22583593—22no—
26#22583586C2214yes—
27#22583569C2211yescharacteristic
28#22583535C2212yes—
29#22583534C2214yes—
30#22583532C2212yes—
31(C2×D283)⋊C8C2214yes—
32C22×Q8×C283C2211yescharacteristic
33C22×Q8×C283C2211yescharacteristic
34C2×Q16×C283—24no—
35C2×Q16×C283C2214yes—
36C22×C8×C283C2211yescharacteristic
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×Dic566D411yescharacteristic
47C2×Dic566C2311yescharacteristic
48Q8×D283—28no—
49Q8×D283—24no—
50Q8×D283—24no—
51C2×D1132—22no—
52C2×D1132D411yescharacteristic
53C2×D1132C2311yescharacteristic
54C2×C22⋊D283—21no—
55C2×C22⋊D283D412yes—
56C2×C4×D283—22no—
57C2×C4×D283—22no—
58C2×C4×D283—21no—
59C2×C4×D283C2312yes—
60#17985382—24no—
61#17985379—24no—
62#17985376—22no—
63C2×C283⋊C8C2312yes—
64C4⋊Dic283C2312yes—
65Dic283⋊C4—24no—
66C22⋊Dic283—21no—
67(C2×D283)⋊C4—24no—
68C4×Dic283—21no—
69C2×Q8×C283—21no—
70C2×Q8×C283—22no—
71C2×Q8×C283—21no—
72C2×Q8×C283—22no—
73C2×Q8×C283—22no—
74C2×Q8×C283D414yes—
75C2×Q8×C283C2312yes—
76C2×Q8×C283C2312yes—
77C22×C4×C283—21no—
78C22×C4×C283—21no—
79C22×C4×C283C2311yescharacteristic
80Q16×C283—28no—
81C2×C8×C283—22no—
82C2×C8×C283C2312yes—
83C22×D283—21no—
84C22×D283C2×D412yes—
85Dic566—28no—
86Dic566—22no—
87Dic566—21no—
88Dic566C2×D412yes—
89D1132—28no—
90D1132—22no—
91D1132—21no—
92D1132C2×D412yes—
93C22⋊D283—24no—
94C22⋊D283—24no—
95C2×Dic283—21no—
96C2×Dic283—22no—
97C2×Dic283C2×D412yes—
98C4×D283—28no—
99C4×D283—28no—
100C4×D283—24no—
101C4×D283—22no—
102C4×D283—22no—
103C283⋊C8—22no—
104C23×C283C2×D411yescharacteristic
105Q8×C283—24no—
106Q8×C283—22no—
107Q8×C283—22no—
108Q8×C283—22no—
109Q8×C283—42no—
110Q8×C283C2×D414yes—
111C2×C4×C283—24no—
112C2×C4×C283—22no—
113C2×C4×C283—22no—
114C2×C4×C283—42no—
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×Q16D28311yescharacteristic, complemented
145#536—2831no—
146#452—2834no—
147#451—2834no—
148#419—2831no—
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—5661no—
160C22×Q8C2×D28311yescharacteristic
161C22×Q8C2×D28311yescharacteristic
162#137—5664no—
163C2×Q16—24no—
164C2×Q16—2832no—
165C2×Q16C2×D28314yes—
166C2×SD16—2832no—
167C2×M16—2831no—
168C22×C8C2×D28311yescharacteristic
169C4⋊Q8—5661no—
170#124—5661no—
171#123—5662no—
172C22⋊Q8—2834no—
173#117—2831no—
174#103—2834no—
175#103—2832no—
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—21no—
189C2×Q8—22no—
190C2×Q8—22no—
191C2×Q8—2831no—
192C2×Q8—2831no—
193C2×Q8—5662no—
194C2×Q8—5664no—
195C2×Q8—5668no—
196C2×Q8—5664no—
197C2×Q8C22⋊D28314yes—
198C2×Q8C22×D28312yes—
199C2×Q8C22×D28312yes—
200C2×D4—2832no—
201C2×D4—2831no—
202C2×D4—2831no—
203C2×D4—5662no—
204C2×D4—5661no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—2832no—
208C22×C4—5662no—
209C22×C4—5662no—
210C22×C4—5661no—
211C22×C4C22×D28311yescharacteristic
212Q16—28no—
213Q16—5664no—
214SD16—5664no—
215M16—5662no—
216C2×C8—22no—
217C2×C8—2832no—
218C2×C8C22×D28312yes—
219C4⋊C4—2832no—
220C4⋊C4—5664no—
221C22⋊C4—5664no—
222C22⋊C4—5661no—
223C42—5661no—
224C23—2832no—
225C23—5661no—
226C23D4×D28311yescharacteristic
227Q8—24no—
228Q8—22no—
229Q8—22no—
230Q8—22no—
231Q8—42no—
232Q8—2832no—
233Q8—5668no—
234Q8—5662no—
235Q8—5661no—
236Q8C2×C22⋊D28314yes—
237D4—2832no—
238D4—5668no—
239D4—5664no—
240D4—5664no—
241D4—5662no—
242D4—5661no—
243C2×C4—24no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—2832no—
248C2×C4—5668no—
249C2×C4—5668no—
250C2×C4—5661no—
251C2×C4—5664no—
252C2×C4—5662no—
253C2×C4—5662no—
254C2×C4—5662no—
255C2×C4D4×D28311yescharacteristic
256C2×C4D4×D28312yes—
257C2×C4C2×C22⋊D28312yes—
258C2×C4C23×D28311yescharacteristic
259C8—22no—
260C8—5662no—
261C22—22no—
262C22—5662no—
263C22—5662no—
264C22—5664no—
265C22—11322no—
266C22#2258357812yes—
267C22C2×D4×D28311yescharacteristic
268C4—24no—
269C4—42no—
270C4—5662no—
271C4—5662no—
272C4—11322no—
273C4#2258357812yes—
274C4C2×D4×D28311yescharacteristic
275C4C22×C22⋊D28311yescharacteristic
276C2—22no—
277C2—11322no—
278C2—11322no—
279C2C2×#2258357811yescharacteristic
280C2#3182727812yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC22×Q16×C283C2
socleC22×C283C22×D4
prime radicalC2×#22583658C2
hypercenterC22×Q16D283
hypocenterC283#3011
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#22583641C2semidirect
3. #31827039C2semidirect
4. #31826626C2semidirect
5. #31826619C2semidirect
6. #31826474C2semidirect
7. #31826462C2semidirect
8. #31826431C2semidirect
9. C22×Q16×C283C2semidirect
140. C283#3011semidirect
144. C22×Q16D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836582
C2×#225836412
#318270392
#318266262
#318266192
#318264742
#318264622
#318264312
C22×Q16×C2832
#3011283