Finite Group Databasebeta

← #487×D283 #49131569

Subgroups — #487×D283 #49131569

Order 36224.

424 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C4⋊Q8×D283C211yesmaximal, characteristic
2C4⋊Q8×D283C211yesmaximal, characteristic
3#31826817C211yesmaximal, characteristic, complemented
4#31826816C211yesmaximal, characteristic, complemented
5#31826815C211yesmaximal, characteristic, complemented
6#31826814C214yesmaximal, complemented
7#103×D283C214yesmaximal
8C4×C8×D283C211yesmaximal, characteristic
9#487×C283C211yesmaximal, characteristic, complemented
10C2×Q8×D283—21no—
11C2×Q8×D283C2212yes—
12C2×C8×D283C2212yes—
13#22583610C2211yescharacteristic
14#22583610C2211yescharacteristic
15#22583609—21no—
16#22583609—21no—
17#22583609—21no—
18#22583609C2212yes—
19#22583608—21no—
20#22583608C2212yes—
21C4⋊C4×D283—21no—
22C4⋊C4×D283—21no—
23C4⋊C4×D283—21no—
24C4⋊C4×D283C2212yes—
25C42×D283C2211yescharacteristic
26#22583535C2214yes—
27#22583534C2214yes—
28#22583533C2214yes—
29C4×C283⋊C8C2211yescharacteristic
30C8×Dic283C2212yes—
31C4⋊Q8×C283C2211yescharacteristic
32C4⋊Q8×C283C2211yescharacteristic
33#103×C283C2214yes—
34C4×C8×C283C2211yescharacteristic
35C2×Dic566—22no—
36C2×Dic566—22no—
37C2×Dic566—21no—
38C2×Dic566C2312yes—
39Q8×D283—28no—
40Q8×D283—44no—
41C2×C4×D283—22no—
42C2×C4×D283—22no—
43C2×C4×D283D411yescharacteristic
44C2×C4×D283D411yescharacteristic
45C2×C4×D283C2311yescharacteristic
46C2×C283⋊C8C2312yes—
47C8×D283—24no—
48C4⋊Dic283—21no—
49C4⋊Dic283—21no—
50C4⋊Dic283—21no—
51C4⋊Dic283C2312yes—
52Dic283⋊C4—22no—
53Dic283⋊C4—22no—
54Dic283⋊C4—22no—
55Dic283⋊C4—22no—
56C4×Dic283D411yescharacteristic
57C4×Dic283D411yescharacteristic
58C4×Dic283C2311yescharacteristic
59C2×Q8×C283—21no—
60C2×Q8×C283C2312yes—
61C2×C8×C283C2312yes—
62C4⋊C4×C283—21no—
63C4⋊C4×C283—21no—
64C4⋊C4×C283—21no—
65C4⋊C4×C283C2312yes—
66C42×C283C2311yescharacteristic
67C22×D283C2×D411yescharacteristic
68Dic566—24no—
69Dic566—42no—
70Dic566—44no—
71Dic566—44no—
72C2×Dic283—22no—
73C2×Dic283—22no—
74C2×Dic283C2×D411yescharacteristic
75C2×Dic283C2×D411yescharacteristic
76C2×Dic283C2×D411yescharacteristic
77C4×D283—44no—
78C4×D283—44no—
79C4×D283SD1614yes—
80C4×D283Q1614yes—
81C4×D283#4114yes—
82C283⋊C8—22no—
83Q8×C283—24no—
84Q8×C283—42no—
85C2×C4×C283—22no—
86C2×C4×C283—22no—
87C2×C4×C283C2×D411yescharacteristic
88C2×C4×C283C2×D411yescharacteristic
89C2×C4×C283C2411yescharacteristic
90C8×C283—22no—
91C22×C283C22×D411yescharacteristic
92C2×D283#12412yes—
93C2×D283C2×SD1612yes—
94C2×D283C2×Q1612yes—
95C4×C283—42no—
96C4×C283—42no—
97C4×C283C2×SD1612yes—
98C4×C283C2×Q1612yes—
99C4×C283C2×#4112yes—
100Dic283—42no—
101Dic283—42no—
102Dic283#12412yes—
103Dic283C2×SD1612yes—
104Dic283C2×Q1612yes—
105C2×C283C2×#12411yescharacteristic
106C2×C283C22×SD1611yescharacteristic
107C2×C283C22×Q1611yescharacteristic
108D283#48714yesdirect product factor
109C283C2×#48711yescharacteristic, complemented, Sylow
110C2×#487—2831nomaximal, Sylow
111C2×C4⋊Q8—2831no—
112C2×C4⋊Q8—2831no—
113#487—2831no—
114#487—2831no—
115#487—2834no—
116#487—2831no—
117#487D28311yescharacteristic, direct product factor
118C2×#103—2834no—
119C2×C4×C8—2831no—
120C22×Q8—2832no—
121C22×Q8—5661no—
122C22×C8—2832no—
123C4⋊Q8—2832no—
124C4⋊Q8—2832no—
125C4⋊Q8—2831no—
126C4⋊Q8—2831no—
127C4⋊Q8—5661no—
128C4⋊Q8—5661no—
129C4⋊Q8—5661no—
130C4⋊Q8—5661no—
131C4⋊Q8C2×D28311yescharacteristic
132C4⋊Q8C2×D28311yescharacteristic
133C2×C4⋊C4—2832no—
134C2×C4⋊C4—5661no—
135C2×C4⋊C4—5661no—
136C2×C4⋊C4—5661no—
137C2×C42—2831no—
138#103—2834no—
139#103—2834no—
140#103—2834no—
141#103C2×D28314yes—
142C4×C8—2832no—
143C4×C8—2831no—
144C4×C8C2×D28311yescharacteristic
145C2×Q8—21no—
146C2×Q8—2832no—
147C2×Q8—5662no—
148C2×Q8—5662no—
149C2×Q8—5668no—
150C2×Q8—5661no—
151C2×Q8—11324no—
152C2×Q8C22×D28312yes—
153C22×C4—2831no—
154C22×C4—2831no—
155C22×C4—2831no—
156C22×C4—5662no—
157C22×C4—5662no—
158C2×C8—2832no—
159C2×C8—5664no—
160C2×C8C22×D28312yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—2832no—
165C4⋊C4—5662no—
166C4⋊C4—5662no—
167C4⋊C4—5662no—
168C4⋊C4—5662no—
169C4⋊C4—5661no—
170C4⋊C4—5661no—
171C4⋊C4—5661no—
172C4⋊C4C22×D28312yes—
173C42—2831no—
174C42—2831no—
175C42—2831no—
176C42C22×D28311yescharacteristic
177C23—2831no—
178Q8—24no—
179Q8—42no—
180Q8—5664no—
181Q8—11324no—
182Q8—11324no—
183Q8—11322no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—2831no—
187C2×C4—2831no—
188C2×C4—2831no—
189C2×C4—2834no—
190C2×C4—2834no—
191C2×C4—2834no—
192C2×C4—5662no—
193C2×C4—5662no—
194C2×C4—11324no—
195C2×C4—11324no—
196C2×C4D4×D28311yescharacteristic
197C2×C4D4×D28311yescharacteristic
198C2×C4C23×D28311yescharacteristic
199C8—22no—
200C8—5662no—
201C22—2832no—
202C22—2832no—
203C22—2832no—
204C22C2×D4×D28311yescharacteristic
205C4—42no—
206C4—42no—
207C4—2832no—
208C4—2832no—
209C4—2832no—
210C4—11322no—
211C4—11322no—
212C4SD16×D28312yes—
213C4Q16×D28312yes—
214C4#41×D28312yes—
215C2—2834no—
216C2#124×D28311yescharacteristic
217C2C2×SD16×D28311yescharacteristic
218C2C2×Q16×D28311yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#487×C283C2
socleC22×C283C22×D4
prime radicalC22×D283C2×D4
hypercenter#487D283
hypocenterC283C2×#487
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #31826817C2semidirect
4. #31826816C2semidirect
5. #31826815C2semidirect
6. #31826814C2semidirect
9. #487×C283C2semidirect
108. D283#487direct (N × H)
109. C283C2×#487semidirect
117. #487D283direct (N × H)

Maximal subgroups

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

subgroupindex
C4⋊Q8×D2832
#318268172
#318268162
#318268152
#318268142
#103×D2832
C4×C8×D2832
#487×C2832
C2×#487283