Finite Group Databasebeta

← #49119751

Subgroups — #49119751

Order 36224.

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

normal subgroups only

This group has 304 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
2C22⋊C8×D283C211yesmaximal, characteristic, complemented
3#31826312C211yesmaximal, characteristic, complemented
4#31826202C211yesmaximal, characteristic, complemented
5#31826200C211yesmaximal, characteristic, complemented
6#31826198C211yesmaximal, characteristic, complemented
7#328×C283C211yesmaximal, characteristic, complemented
8C2×#17985393C411yescharacteristic, complemented
9C22×C4×D283C2211yescharacteristic
10C2×C8×D283—21no—
11#22583595—21no—
12#22583586C411yescharacteristic, complemented
13#22583585C411yescharacteristic, complemented
14#22583584C2211yescharacteristic
15#22583580—21no—
16#22583572—21no—
17(C22⋊D283)⋊C4—21no—
18#22583568C411yescharacteristic, complemented
19C2×(C2×D283)⋊C4—21no—
20C2×C4×Dic283—21no—
21C22⋊(C283⋊C8)C2211yescharacteristic
22(C2×D283)⋊C8—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
32C2×C22⋊D283—21no—
33C22×Dic283—21no—
34C22×Dic283D411yescharacteristic
35C2×C4×D283—21no—
36C2×C4×D283—42no—
37C2×C4×D283C2×C411yescharacteristic
38C2×C4×D283C2×C411yescharacteristic
39C2×C4×D283D411yescharacteristic
40C2×C4×D283D411yescharacteristic
41C2×C283⋊C8—21no—
42C8×D283—42no—
43C4⋊Dic283C2×C411yescharacteristic
44Dic283⋊C4—21no—
45(C2×D283)⋊C4—24no—
46(C2×D283)⋊C4—21no—
47(C2×D283)⋊C4—21no—
48(C2×D283)⋊C4—21no—
49(C2×D283)⋊C4—21no—
50C4×Dic283—21no—
51C4×Dic283—42no—
52C2×Q8×C283C2×C411yescharacteristic
53C22×C4×C283—21no—
54C22×C4×C283C2311yescharacteristic
55C2×C8×C283—21no—
56C4⋊C4×C283—21no—
57C4⋊C4×C283C2×C411yescharacteristic
58C22⋊C4×C283—21no—
59C22×D283—21no—
60C22×D283—21no—
61C22×D283—22no—
62C22×D283—21no—
63C22×D283—41no—
64C22×D283C22⋊C411yescharacteristic
65C22×D283C22⋊C411yescharacteristic
66D1132—41no—
67D1132—42no—
68D1132—42no—
69C22⋊D283—41no—
70C22⋊D283—41no—
71C2×Dic283—22no—
72C2×Dic283—22no—
73C2×Dic283—21no—
74C2×Dic283—41no—
75C2×Dic283—41no—
76C2×Dic283C22⋊C411yescharacteristic
77C2×Dic283C22⋊C411yescharacteristic
78C4×D283—22no—
79C4×D283—22no—
80C4×D283—41no—
81C4×D283—41no—
82C4×D283—42no—
83C283⋊C8—41no—
84C23×C283C2×D411yescharacteristic
85Q8×C283—41no—
86C2×C4×C283—22no—
87C2×C4×C283—21no—
88C2×C4×C283—21no—
89C2×C4×C283—41no—
90C2×C4×C283—41no—
91C2×C4×C283—41no—
92C2×C4×C283C22×C411yescharacteristic
93C2×C4×C283C2×D411yescharacteristic
94C8×C283—41no—
95C22×C283—21no—
96C22×C283—21no—
97C22×C283C2×C22⋊C411yescharacteristic
98C22×C283#13511yescharacteristic
99C22×C283#13511yescharacteristic
100C2×D283—21no—
101C2×D283—21no—
102C2×D283—21no—
103C2×D283—21no—
104C2×D283—21no—
105C2×D283—42no—
106C2×D283—42no—
107C2×D283—41no—
108C2×D283—41no—
109C2×D283—41no—
110C2×D283#10412yes—
111C4×C283—21no—
112C4×C283—21no—
113C4×C283—42no—
114C4×C283—41no—
115C4×C283—41no—
116Dic283—21no—
117Dic283—42no—
118Dic283—41no—
119Dic283#9912yes—
120C2×C283—21no—
121C2×C283—21no—
122C2×C283C2×#9911yescharacteristic
123C2×C283#41611yescharacteristic
124C2×C283C2×#10411yescharacteristic
125D283—22no—
126D283—41no—
127D283—81no—
128C283#150111yescharacteristic, complemented, Sylow
129#1501—2831nomaximal, Sylow
130#525—2831no—
131C2×C22⋊C8—2831no—
132C4×C22⋊C4—2831no—
133#328—2831no—
134#328D28311yescharacteristic, complemented
135#327—2831no—
136#327—2831no—
137C2×#41—2831no—
138C23×C4—2831no—
139C22×C8—5661no—
140#123—5661no—
141C22⋊Q8—2831no—
142C22⋊Q8C2×D28311yescharacteristic
143#121—2831no—
144#121—2831no—
145#120—5661no—
146C4×D4—5661no—
147C4×D4—5661no—
148#117—2831no—
149C2×C22⋊C4—5661no—
150C2×C42—5661no—
151C22⋊C8—2831no—
152C22⋊C8—5661no—
153C22⋊C8C2×D28311yescharacteristic
154#95—2831no—
155#95C2×D28311yescharacteristic
156C24—2831no—
157#41—11322no—
158C2×Q8C4×D28311yescharacteristic
159C2×D4—2831no—
160C2×D4—5661no—
161C2×D4—5661no—
162C2×D4—5661no—
163C22×C4—21no—
164C22×C4—2831no—
165C22×C4—2831no—
166C22×C4—2831no—
167C22×C4—2831no—
168C22×C4—2831no—
169C22×C4—5661no—
170C22×C4—5661no—
171C22×C4—11322no—
172C22×C4C22×D28311yescharacteristic
173C2×C8—21no—
174C2×C8—5661no—
175C2×C8—11322no—
176C4⋊C4—21no—
177C4⋊C4—2831no—
178C4⋊C4—5661no—
179C4⋊C4C4×D28311yescharacteristic
180C22⋊C4—21no—
181C22⋊C4—5661no—
182C22⋊C4—5661no—
183C22⋊C4—5661no—
184C22⋊C4—5664no—
185C22⋊C4—5661no—
186C42—5661no—
187C42—11322no—
188C23—2831no—
189C23—2831no—
190C23—5662no—
191C23—5661no—
192C23—5661no—
193C23—5661no—
194C23—11321no—
195C23D4×D28311yescharacteristic
196Q8—41no—
197D4—11321no—
198D4—11322no—
199D4—11322no—
200D4—11321no—
201D4—11321no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—2831no—
209C2×C4—2831no—
210C2×C4—5662no—
211C2×C4—5662no—
212C2×C4—5662no—
213C2×C4—5662no—
214C2×C4—5661no—
215C2×C4—11321no—
216C2×C4—11321no—
217C2×C4—11322no—
218C2×C4—11321no—
219C2×C4—11321no—
220C2×C4C2×C4×D28311yescharacteristic
221C2×C4D4×D28311yescharacteristic
222C8—41no—
223C8—11321no—
224C22—21no—
225C22—21no—
226C22—2832no—
227C22—5661no—
228C22—5661no—
229C22—5661no—
230C22—5661no—
231C22—5661no—
232C22—11322no—
233C22—11322no—
234C22—11321no—
235C22—11321no—
236C22—11321no—
237C22C22⋊C4×D28311yescharacteristic
238C22#2258363111yescharacteristic
239C22#2258363311yescharacteristic
240C4—21no—
241C4—21no—
242C4—42no—
243C4—41no—
244C4—41no—
245C4—2832no—
246C4—5661no—
247C4—11322no—
248C4—11321no—
249C2—21no—
250C2—21no—
251C2—5662no—
252C2—11321no—
253C2—22641no—
254C2#99×D28311yescharacteristic
255C2#3182646011yescharacteristic
256C2#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#1501
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. C22⋊C8×D283C2semidirect
3. #31826312C2semidirect
4. #31826202C2semidirect
5. #31826200C2semidirect
6. #31826198C2semidirect
7. #328×C283C2semidirect
8. C2×#17985393C4semidirect
12. #22583586C4semidirect
13. #22583585C4semidirect
18. #22583568C4semidirect
128. C283#1501semidirect
134. #328D283semidirect

Maximal subgroups

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

subgroupindex
#318269782
C22⋊C8×D2832
#318263122
#318262022
#318262002
#318261982
#328×C2832
#1501283