Finite Group Databasebeta

← #49119764

Subgroups — #49119764

Order 36224.

334 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 65 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
1#31826978C211yesmaximal, characteristic
2#31826427C211yesmaximal, characteristic, complemented
3#95×D283C211yesmaximal, characteristic, complemented
4#31826202C211yesmaximal, characteristic, complemented
5#31826200C211yesmaximal, characteristic, complemented
6#31826198C211yesmaximal, characteristic, complemented
7#328×C283C211yesmaximal, characteristic, complemented
8C2×#17985393C411yescharacteristic, complemented
9C22×C4×D283—21no—
10C22×C4×D283C2211yescharacteristic
11C2×#17985375—21no—
12#22583595—21no—
13#22583586C411yescharacteristic, complemented
14#22583585C411yescharacteristic, complemented
15#22583584C2211yescharacteristic
16#22583580—21no—
17#22583572—21no—
18(C22⋊D283)⋊C4—21no—
19#22583568C411yescharacteristic, complemented
20C22⋊(C283⋊C8)C2211yescharacteristic
21(C2×D283)⋊C8—21no—
22C283⋊#95—21no—
23C283⋊#95C2211yescharacteristic
24C22⋊Q8×C283C2211yescharacteristic
25C22⋊C8×C283C2211yescharacteristic
26#95×C283C2211yescharacteristic
27C23×D283D411yescharacteristic
28#17985393—42no—
29C2×D1132—21no—
30C2×D1132—21no—
31C2×D1132C2×C411yescharacteristic, complemented
32C2×C22⋊D283—21no—
33C22×Dic283—21no—
34C22×Dic283D411yescharacteristic
35C2×C4×D283—24no—
36C2×C4×D283—21no—
37C2×C4×D283—42no—
38C2×C4×D283—42no—
39C2×C4×D283—42no—
40C2×C4×D283C2×C411yescharacteristic
41C2×C4×D283C2×C411yescharacteristic
42C2×C4×D283D411yescharacteristic
43C2×C4×D283D411yescharacteristic
44#17985375—42no—
45C2×C283⋊C8—21no—
46C4⋊Dic283C2×C411yescharacteristic, complemented
47Dic283⋊C4—21no—
48(C2×D283)⋊C4—21no—
49(C2×D283)⋊C4—21no—
50(C2×D283)⋊C4—21no—
51(C2×D283)⋊C4—21no—
52C4×Dic283—21no—
53C2×Q8×C283C2×C411yescharacteristic, complemented
54C22×C4×C283—21no—
55C22×C4×C283C2311yescharacteristic
56C2×C8×C283—21no—
57C4⋊C4×C283—21no—
58C4⋊C4×C283C2×C411yescharacteristic, complemented
59C22⋊C4×C283—21no—
60C22×D283—21no—
61C22×D283—21no—
62C22×D283—22no—
63C22×D283—22no—
64C22×D283—21no—
65C22×D283C22⋊C411yescharacteristic
66C22×D283C22⋊C411yescharacteristic
67D1132—41no—
68D1132—42no—
69D1132—42no—
70C22⋊D283—41no—
71C22⋊D283—41no—
72C2×Dic283—22no—
73C2×Dic283—21no—
74C2×Dic283—41no—
75C2×Dic283—41no—
76C2×Dic283—41no—
77C2×Dic283C22⋊C411yescharacteristic
78C2×Dic283C22⋊C411yescharacteristic
79C4×D283—22no—
80C4×D283—22no—
81C4×D283—41no—
82C4×D283—41no—
83C4×D283—42no—
84C4×D283—48no—
85C283⋊C8—41no—
86C23×C283C2×D411yescharacteristic
87Q8×C283—41no—
88C2×C4×C283—22no—
89C2×C4×C283—21no—
90C2×C4×C283—21no—
91C2×C4×C283—41no—
92C2×C4×C283—41no—
93C2×C4×C283—41no—
94C2×C4×C283C22×C411yescharacteristic
95C2×C4×C283C2×D411yescharacteristic
96C8×C283—41no—
97C22×C283—21no—
98C22×C283—21no—
99C22×C283C2×C22⋊C411yescharacteristic
100C22×C283AGL(1,ℤ/8)11yescharacteristic
101C22×C283#13711yescharacteristic
102C2×D283—24no—
103C2×D283—24no—
104C2×D283—21no—
105C2×D283—21no—
106C2×D283—21no—
107C2×D283—21no—
108C2×D283—41no—
109C2×D283—41no—
110C2×D283—41no—
111C2×D283#9912yes—
112C2×D283#10412yes—
113C4×C283—21no—
114C4×C283—21no—
115C4×C283—42no—
116C4×C283—41no—
117C4×C283—41no—
118Dic283—21no—
119Dic283—21no—
120Dic283—42no—
121Dic283—41no—
122C2×C283—21no—
123C2×C283—21no—
124C2×C283C2×#9911yescharacteristic
125C2×C283#41711yescharacteristic
126C2×C283C2×#10411yescharacteristic
127D283—22no—
128D283—22no—
129D283—81no—
130C283#150411yescharacteristic, complemented, Sylow
131#1504—2831nomaximal, Sylow
132#525—2831no—
133#407—2831no—
134C2×#95—2831no—
135#328—2831no—
136#328D28311yescharacteristic, complemented
137#327—2831no—
138#327—2831no—
139C2×#41—2831no—
140C23×C4—2831no—
141C23×C4—5661no—
142C2×M16—5661no—
143#123—5661no—
144C22⋊Q8—2831no—
145C22⋊Q8C2×D28311yescharacteristic
146#121—2831no—
147#121—2831no—
148#120—5661no—
149C4×D4—5661no—
150C4×D4—5661no—
151#117—2831no—
152C22⋊C8—2831no—
153C22⋊C8—5661no—
154C22⋊C8C2×D28311yescharacteristic
155#95—2831no—
156#95—5661no—
157#95C2×D28311yescharacteristic
158C24—2831no—
159#41—11322no—
160C2×Q8C4×D28311yescharacteristic, complemented
161C2×D4—2831no—
162C2×D4—5661no—
163C2×D4—5661no—
164C2×D4—5661no—
165C22×C4—21no—
166C22×C4—2831no—
167C22×C4—2831no—
168C22×C4—2831no—
169C22×C4—2831no—
170C22×C4—2831no—
171C22×C4—5661no—
172C22×C4—5664no—
173C22×C4—5661no—
174C22×C4—11322no—
175C22×C4—11322no—
176C22×C4—11322no—
177C22×C4C22×D28311yescharacteristic
178M16—11322no—
179C2×C8—21no—
180C2×C8—5661no—
181C4⋊C4—21no—
182C4⋊C4—2831no—
183C4⋊C4—5661no—
184C4⋊C4C4×D28311yescharacteristic, complemented
185C22⋊C4—21no—
186C22⋊C4—5661no—
187C22⋊C4—5661no—
188C22⋊C4—5661no—
189C22⋊C4—5661no—
190C42—5661no—
191C23—2831no—
192C23—2831no—
193C23—5662no—
194C23—5662no—
195C23—5661no—
196C23—5661no—
197C23—5661no—
198C23D4×D28311yescharacteristic
199Q8—41no—
200D4—11321no—
201D4—11322no—
202D4—11322no—
203D4—11321no—
204D4—11321no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—2831no—
212C2×C4—2831no—
213C2×C4—5662no—
214C2×C4—5662no—
215C2×C4—5662no—
216C2×C4—5661no—
217C2×C4—11321no—
218C2×C4—11321no—
219C2×C4—11322no—
220C2×C4—11328no—
221C2×C4—11321no—
222C2×C4—11321no—
223C2×C4—11321no—
224C2×C4C2×C4×D28311yescharacteristic
225C2×C4D4×D28311yescharacteristic
226C8—41no—
227C8—11321no—
228C22—21no—
229C22—21no—
230C22—2832no—
231C22—2832no—
232C22—5664no—
233C22—5664no—
234C22—5661no—
235C22—5661no—
236C22—5661no—
237C22—5661no—
238C22—11321no—
239C22—11321no—
240C22—11321no—
241C22C22⋊C4×D28311yescharacteristic
242C22#2258363711yescharacteristic
243C22#2258364211yescharacteristic
244C4—21no—
245C4—21no—
246C4—42no—
247C4—41no—
248C4—41no—
249C4—5661no—
250C4—5661no—
251C4—11322no—
252C4—11321no—
253C2—21no—
254C2—21no—
255C2—5662no—
256C2—5662no—
257C2—22641no—
258C2#99×D28311yescharacteristic
259C2#3182646511yescharacteristic
260C2#104×D28311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D283
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#328×C283C2
socleC22×C283C2×C22⋊C4
prime radical#31826978C2
cosocleC22×C4×C283C23
hypercenter#328D283
hypocenterC283#1504
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #31826427C2semidirect
3. #95×D283C2semidirect
4. #31826202C2semidirect
5. #31826200C2semidirect
6. #31826198C2semidirect
7. #328×C283C2semidirect
8. C2×#17985393C4semidirect
13. #22583586C4semidirect
14. #22583585C4semidirect
19. #22583568C4semidirect
31. C2×D1132C2×C4semidirect
46. C4⋊Dic283C2×C4semidirect
53. C2×Q8×C283C2×C4semidirect
58. C4⋊C4×C283C2×C4semidirect
130. C283#1504semidirect
136. #328D283semidirect
160. C2×Q8C4×D283semidirect
184. C4⋊C4C4×D283semidirect

Maximal subgroups

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

subgroupindex
#318269782
#318264272
#95×D2832
#318262022
#318262002
#318261982
#328×C2832
#1504283