Finite Group Databasebeta

← #49122091

Subgroups — #49122091

Order 36224.

320 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 83 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
6#31826311C211yesmaximal, 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×Dic283C2211yescharacteristic
17C2×C4×Dic283C2211yescharacteristic
18Dic283⋊C8—22no—
19#22583538—22no—
20#22583537—22no—
21#22583536—22no—
22C283⋊#95—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—21no—
45C4×Dic283C2×C411yescharacteristic
46C4×Dic283C2×C411yescharacteristic
47C4×Dic283D412yes—
48C4×Dic283D412yescomplemented
49#41×C283—21no—
50#41×C283—21no—
51#41×C283—21no—
52#41×C283—21no—
53C2×Q8×C283C2×C411yescharacteristic
54C2×D4×C283—21no—
55C2×D4×C283C2×C411yescharacteristic
56C22×C4×C283—21no—
57C22×C4×C283—21no—
58C22×C4×C283C2311yescharacteristic
59M16×C283—21no—
60M16×C283—21no—
61C2×C8×C283—21no—
62C42×C283—21no—
63C42×C283D412yescomplemented
64C22×D283—21no—
65Dic566—21no—
66Dic566—21no—
67D1132—21no—
68D1132—21no—
69C22⋊D283—44no—
70C22⋊D283—41no—
71C22⋊D283—41no—
72C2×Dic283—21no—
73C2×Dic283—22no—
74C2×Dic283—42no—
75C2×Dic283—42no—
76C2×Dic283C22⋊C412yes—
77C2×Dic283C22⋊C412yes—
78C4×D283—41no—
79C4×D283—41no—
80C283⋊C8—41no—
81C23×C283—21no—
82C23×C283C2×D411yescharacteristic
83Q8×C283—21no—
84Q8×C283—21no—
85D4×C283—21no—
86D4×C283—21no—
87D4×C283—41no—
88D4×C283—41no—
89C2×C4×C283—21no—
90C2×C4×C283—22no—
91C2×C4×C283—42no—
92C2×C4×C283—41no—
93C2×C4×C283—41no—
94C2×C4×C283C22×C411yescharacteristic
95C2×C4×C283C2×D411yescharacteristic
96C2×C4×C283C2×D411yescharacteristic
97C2×C4×C283C2×D411yescharacteristic
98C2×C4×C283#4111yescharacteristic
99C2×C4×C283#4111yescharacteristic
100C8×C283—41no—
101C22×C283—22no—
102C22×C283—41no—
103C22×C283—42no—
104C22×C283C2×C22⋊C411yescharacteristic
105C22×C283#12111yescharacteristic
106C22×C283#12111yescharacteristic
107C2×D283—41no—
108C2×D283—42no—
109C4×C283—42no—
110C4×C283—41no—
111C4×C283C4×D411yescharacteristic
112C4×C283C4×D411yescharacteristic
113C4×C283#12411yescharacteristic
114C4×C283#12711yescharacteristic
115Dic283—22no—
116Dic283—22no—
117Dic283—42no—
118Dic283—41no—
119C2×C283—21no—
120C2×C283—21no—
121C2×C283—81no—
122C2×C283#39011yescharacteristic
123C2×C283#42112yes—
124D283—81no—
125C283#196311yescharacteristic, complemented, Sylow
126#1963—2831nomaximal, Sylow
127#532—2831no—
128#423—2831no—
129C2×#104—2831no—
130C2×#104—2831no—
131C2×#104—2831no—
132C2×#104D28311yescharacteristic, complemented
133#376—2831no—
134C2×#41—2831no—
135C2×#41C2×D28311yescharacteristic
136C2×M16—2831no—
137C2×M16C2×D28311yescharacteristic
138C4⋊Q8—2831no—
139#127—2831no—
140#124—2831no—
141#124—2831no—
142#121—5662no—
143C4×D4—5662no—
144C2×C42—2831no—
145C2×C42—2831no—
146C2×C42C2×D28311yescharacteristic
147C4⋊C8—5662no—
148#104—22no—
149#104—5662no—
150#104—5662no—
151#104—5662no—
152#95—5662no—
153#41—21no—
154#41—21no—
155#41—21no—
156#41—21no—
157#41—5661no—
158#41—5661no—
159#41—5661no—
160#41—5661no—
161C2×Q8—2831no—
162C2×Q8C4×D28311yescharacteristic
163C2×D4—21no—
164C2×D4—2831no—
165C2×D4—5662no—
166C2×D4—5661no—
167C2×D4C4×D28311yescharacteristic
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—2832no—
171C22×C4—5661no—
172C22×C4—5661no—
173C22×C4C22×D28311yescharacteristic
174M16—21no—
175M16—21no—
176M16—5661no—
177M16—5661no—
178C2×C8—21no—
179C2×C8—5661no—
180C4⋊C4—5662no—
181C22⋊C4—5662no—
182C22⋊C4—5662no—
183C42—21no—
184C42—2831no—
185C42—2831no—
186C42—2832no—
187C42—2832no—
188C42—5661no—
189C42C22⋊D28312yescomplemented
190C23—21no—
191C23—5661no—
192C23D4×D28311yescharacteristic
193Q8—21no—
194Q8—21no—
195Q8—5661no—
196Q8—5661no—
197D4—21no—
198D4—21no—
199D4—41no—
200D4—41no—
201D4—5661no—
202D4—5661no—
203D4—11324no—
204D4—11321no—
205D4—11321no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—2832no—
212C2×C4—2832no—
213C2×C4—5661no—
214C2×C4—5662no—
215C2×C4—11322no—
216C2×C4—11322no—
217C2×C4—11321no—
218C2×C4—11321no—
219C2×C4C2×C4×D28311yescharacteristic
220C2×C4D4×D28311yescharacteristic
221C2×C4D4×D28311yescharacteristic
222C2×C4C2×C22⋊D28311yescharacteristic
223C2×C4#1798539111yescharacteristic
224C2×C4#1798539211yescharacteristic
225C8—41no—
226C8—11321no—
227C22—22no—
228C22—42no—
229C22—41no—
230C22—11322no—
231C22—11321no—
232C22C22⋊C4×D28311yescharacteristic
233C22#2258358211yescharacteristic
234C22#2258358311yescharacteristic
235C4—42no—
236C4—41no—
237C4—5662no—
238C4—5662no—
239C4—11322no—
240C4—11321no—
241C4(C22⋊D283)⋊C411yescharacteristic
242C4C4×C22⋊D28311yescharacteristic
243C4#2258359611yescharacteristic
244C4#2258360611yescharacteristic
245C2—21no—
246C2—21no—
247C2—81no—
248C2—22641no—
249C2#3182636511yescharacteristic
250C2#3182648012yes—
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#1963
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. #31826311C2semidirect
7. C2×#104×C283C2semidirect
10. #22583608C4semidirect
11. #22583606C4semidirect
12. #22583599C4semidirect
13. #22583597C4semidirect
48. C4×Dic283D4semidirect
63. C42×C283D4semidirect
125. C283#1963semidirect
132. C2×#104D283semidirect
189. 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
#318263112
C2×#104×C2832
#1963283