Finite Group Databasebeta

← #49122087

Subgroups — #49122087

Order 36224.

360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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#31827011C211yesmaximal, characteristic
2#31826488C211yesmaximal, characteristic, complemented
3C2×#22583538C211yesmaximal, characteristic, complemented
4C2×#22583537C211yesmaximal, characteristic, complemented
5C2×#22583536C211yesmaximal, characteristic, complemented
6C42×Dic283C211yesmaximal, characteristic, complemented
7C2×#104×C283C211yesmaximal, characteristic, complemented
8C2×#17985392C2211yescharacteristic
9C2×#17985376C2211yescharacteristic
10#22583608C411yescharacteristic, complemented
11#22583606C411yescharacteristic, complemented
12#22583599C411yescharacteristic, complemented
13#22583597C411yescharacteristic, complemented
14#22583582—22no—
15C4×C22⋊D283—22no—
16C2×C4×Dic283—22no—
17C2×C4×Dic283C2211yescharacteristic
18C2×C4×Dic283C2211yescharacteristic
19Dic283⋊C8—22no—
20#22583538—22no—
21#22583537—22no—
22#22583536—22no—
23C2×#41×C283C2211yescharacteristic
24C2×M16×C283C2211yescharacteristic
25C2×C42×C283C2211yescharacteristic
26#104×C283—22no—
27#17985392—21no—
28#17985392—21no—
29#17985392—21no—
30#17985392—21no—
31C2×Dic566C2×C411yescharacteristic
32C2×D1132C2×C411yescharacteristic
33C2×C22⋊D283—22no—
34C2×C22⋊D283—21no—
35C22×Dic283—21no—
36C22×Dic283D412yes—
37C2×C4×D283—21no—
38#17985376—21no—
39#17985376—21no—
40C2×C283⋊C8—21no—
41Dic283⋊C4—22no—
42C22⋊Dic283—22no—
43(C2×D283)⋊C4—22no—
44C4×Dic283—28no—
45C4×Dic283—21no—
46C4×Dic283C2×C411yescharacteristic
47C4×Dic283C2×C411yescharacteristic
48C4×Dic283D412yes—
49C4×Dic283D412yescomplemented
50#41×C283—21no—
51#41×C283—21no—
52#41×C283—21no—
53#41×C283—21no—
54C2×Q8×C283C2×C411yescharacteristic
55C2×D4×C283—21no—
56C2×D4×C283C2×C411yescharacteristic
57C22×C4×C283—21no—
58C22×C4×C283—21no—
59C22×C4×C283C2311yescharacteristic
60M16×C283—21no—
61M16×C283—21no—
62C2×C8×C283—21no—
63C42×C283—21no—
64C42×C283D412yescomplemented
65C22×D283—21no—
66Dic566—21no—
67Dic566—21no—
68D1132—21no—
69D1132—21no—
70C22⋊D283—41no—
71C22⋊D283—41no—
72C22⋊D283—44no—
73C2×Dic283—24no—
74C2×Dic283—22no—
75C2×Dic283—24no—
76C2×Dic283—21no—
77C2×Dic283C22⋊C412yes—
78C2×Dic283C22⋊C412yes—
79C4×D283—41no—
80C4×D283—41no—
81C283⋊C8—41no—
82C23×C283—21no—
83C23×C283C2×D411yescharacteristic
84Q8×C283—21no—
85Q8×C283—21no—
86D4×C283—21no—
87D4×C283—21no—
88D4×C283—41no—
89D4×C283—41no—
90C2×C4×C283—24no—
91C2×C4×C283—22no—
92C2×C4×C283—21no—
93C2×C4×C283—41no—
94C2×C4×C283—41no—
95C2×C4×C283C22×C411yescharacteristic
96C2×C4×C283C2×D411yescharacteristic
97C2×C4×C283C2×D411yescharacteristic
98C2×C4×C283C2×D411yescharacteristic
99C2×C4×C283#4111yescharacteristic
100C2×C4×C283#4111yescharacteristic
101C8×C283—41no—
102C22×C283—22no—
103C22×C283—41no—
104C22×C283—42no—
105C22×C283C2×C22⋊C411yescharacteristic
106C22×C283#12111yescharacteristic
107C22×C283#12111yescharacteristic
108C2×D283—41no—
109C2×D283—42no—
110C4×C283—24no—
111C4×C283—41no—
112C4×C283C4×D411yescharacteristic
113C4×C283C4×D411yescharacteristic
114C4×C283#12411yescharacteristic
115C4×C283#12711yescharacteristic
116Dic283—24no—
117Dic283—22no—
118Dic283—41no—
119Dic283#10414yescomplemented
120C2×C283—21no—
121C2×C283—21no—
122C2×C283—81no—
123C2×C283#39011yescharacteristic
124C2×C283C2×#10412yes—
125D283—81no—
126C283#196211yescharacteristic, complemented, Sylow
127#1962—2831nomaximal, Sylow
128#532—2831no—
129#423—2831no—
130C2×#104—2831no—
131C2×#104—2831no—
132C2×#104—2831no—
133C2×#104D28311yescharacteristic, complemented
134C43—2831no—
135C2×#41—2831no—
136C2×#41C2×D28311yescharacteristic
137C2×M16—2831no—
138C2×M16C2×D28311yescharacteristic
139C4⋊Q8—2831no—
140#127—2831no—
141#124—2831no—
142#124—2831no—
143#121—5662no—
144C4×D4—5662no—
145C2×C42—2831no—
146C2×C42—2831no—
147C2×C42—5662no—
148C2×C42C2×D28311yescharacteristic
149C4⋊C8—5662no—
150#104—22no—
151#104—5662no—
152#104—5662no—
153#104—5662no—
154#41—21no—
155#41—21no—
156#41—21no—
157#41—21no—
158#41—5661no—
159#41—5661no—
160#41—5661no—
161#41—5661no—
162C2×Q8—2831no—
163C2×Q8C4×D28311yescharacteristic
164C2×D4—21no—
165C2×D4—2831no—
166C2×D4—5662no—
167C2×D4—5661no—
168C2×D4C4×D28311yescharacteristic
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—2832no—
172C22×C4—5661no—
173C22×C4—5661no—
174C22×C4C22×D28311yescharacteristic
175M16—21no—
176M16—21no—
177M16—5661no—
178M16—5661no—
179C2×C8—21no—
180C2×C8—5661no—
181C4⋊C4—5662no—
182C22⋊C4—5662no—
183C22⋊C4—5662no—
184C42—21no—
185C42—2831no—
186C42—2831no—
187C42—2832no—
188C42—2832no—
189C42—5668no—
190C42—5661no—
191C42C22⋊D28312yescomplemented
192C23—21no—
193C23—5661no—
194C23D4×D28311yescharacteristic
195Q8—21no—
196Q8—21no—
197Q8—5661no—
198Q8—5661no—
199D4—21no—
200D4—21no—
201D4—41no—
202D4—41no—
203D4—5661no—
204D4—5661no—
205D4—11324no—
206D4—11321no—
207D4—11321no—
208C2×C4—24no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—2832no—
214C2×C4—2832no—
215C2×C4—5664no—
216C2×C4—5664no—
217C2×C4—5662no—
218C2×C4—5661no—
219C2×C4—11321no—
220C2×C4—11321no—
221C2×C4C2×C4×D28311yescharacteristic
222C2×C4D4×D28311yescharacteristic
223C2×C4D4×D28311yescharacteristic
224C2×C4C2×C22⋊D28311yescharacteristic
225C2×C4#1798539111yescharacteristic
226C2×C4#1798539211yescharacteristic
227C8—41no—
228C8—11321no—
229C22—22no—
230C22—42no—
231C22—41no—
232C22—11322no—
233C22—11321no—
234C22C22⋊C4×D28311yescharacteristic
235C22#2258358211yescharacteristic
236C22#2258358311yescharacteristic
237C4—24no—
238C4—41no—
239C4—2834no—
240C4—5664no—
241C4—5662no—
242C4—11321no—
243C4(C22⋊D283)⋊C411yescharacteristic
244C4C4×C22⋊D28311yescharacteristic
245C4#2258359611yescharacteristic
246C4#2258360611yescharacteristic
247C2—21no—
248C2—21no—
249C2—81no—
250C2—22641no—
251C2#3182636511yescharacteristic
252C2#104×D28312yes—
subgroupG/H
centerC2×C4D4×D283
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
FittingC2×#104×C283C2
socleC22×C283C2×C22⋊C4
prime radical#31827011C2
cosocleC22×C4×C283C23
hypercenterC2×#104D283
hypocenterC283#1962
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #31826488C2semidirect
3. C2×#22583538C2semidirect
4. C2×#22583537C2semidirect
5. C2×#22583536C2semidirect
6. C42×Dic283C2semidirect
7. C2×#104×C283C2semidirect
10. #22583608C4semidirect
11. #22583606C4semidirect
12. #22583599C4semidirect
13. #22583597C4semidirect
49. C4×Dic283D4semidirect
64. C42×C283D4semidirect
119. Dic283#104semidirect
126. C283#1962semidirect
133. C2×#104D283semidirect
191. C42C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
#318270112
#318264882
C2×#225835382
C2×#225835372
C2×#225835362
C42×Dic2832
C2×#104×C2832
#1962283