Finite Group Databasebeta

← #49131384

Subgroups — #49131384

Order 36224.

424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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#31827015C211yesmaximal, characteristic
2C2×C4×Dic566C211yesmaximal, characteristic, complemented
3#31826779C212yesmaximal, complemented
4#31826761C212yesmaximal, complemented
5#31826666C212yesmaximal, complemented
6#31826606C212yesmaximal, complemented
7#31826567C214yesmaximal, complemented
8#432×C283C211yesmaximal, characteristic, complemented
9C2×#17985392—21no—
10C22×Dic566C2211yescharacteristic
11C2×#17985381C2214yes—
12#22583610C2211yescharacteristic
13#22583607C2211yescharacteristic
14#22583598—21no—
15#22583584—21no—
16#22583584C2212yes—
17C4×Dic566—21no—
18C4×Dic566—21no—
19C4×Dic566C2212yes—
20C4×Dic566C2212yes—
21C4×D1132—21no—
22C4×D1132C2212yes—
23C2×C4⋊Dic283C2211yescharacteristic
24C2×Dic283⋊C4—21no—
25C2×C4×Dic283—21no—
26#22583544C2214yes—
27#22583535C2214yes—
28#22583532C2214yes—
29C2×C42×C283C2211yescharacteristic
30C4⋊C8×C283C2212yes—
31C22⋊C8×C283C2212yes—
32#97×C283C2212yes—
33#17985392—44no—
34C2×Dic566—24no—
35C2×Dic566—21no—
36C2×Dic566—21no—
37C2×Dic566C2312yes—
38C2×D1132—21no—
39C2×D1132—21no—
40C2×D1132C2312yes—
41C2×C22⋊D283—22no—
42C22×Dic283—21no—
43C22×Dic283—21no—
44C2×C4×D283—22no—
45#17985381—28no—
46C4⋊Dic283—21no—
47C4⋊Dic283—21no—
48C4⋊Dic283C2312yes—
49C4⋊Dic283C2312yes—
50Dic283⋊C4—22no—
51Dic283⋊C4—22no—
52(C2×D283)⋊C4—22no—
53(C2×D283)⋊C4—22no—
54C4×Dic283—22no—
55C4×Dic283—22no—
56C22×C4×C283D411yescharacteristic
57C22×C4×C283D411yescharacteristic
58C22×C4×C283C2311yescharacteristic
59C2×C8×C283C2314yes—
60C42×C283D411yescharacteristic
61C42×C283D411yescharacteristic
62C42×C283C2311yescharacteristic
63C42×C283C2311yescharacteristic
64C22×D283—22no—
65Dic566—24no—
66Dic566—22no—
67Dic566—42no—
68Dic566#4114yescomplemented
69D1132—24no—
70D1132—42no—
71D1132—42no—
72C22⋊D283—44no—
73C2×Dic283—24no—
74C2×Dic283—22no—
75C2×Dic283—22no—
76C2×Dic283—22no—
77C2×Dic283—42no—
78C4×D283—44no—
79C23×C283C2×D411yescharacteristic
80C2×C4×C283—22no—
81C2×C4×C283—22no—
82C2×C4×C283—22no—
83C2×C4×C283C2×D411yescharacteristic
84C2×C4×C283C2×D411yescharacteristic
85C2×C4×C283C2×D411yescharacteristic
86C2×C4×C283C2×D411yescharacteristic
87C2×C4×C283C2×D411yescharacteristic
88C2×C4×C283C2411yescharacteristic
89C8×C283—24no—
90C22×C283—21no—
91C22×C283—21no—
92C22×C283AGL(1,ℤ/8)12yes—
93C22×C283C22×D411yescharacteristic
94C2×D283—42no—
95C2×D283—42no—
96C2×D283—42no—
97C4×C283—21no—
98C4×C283—21no—
99C4×C283—21no—
100C4×C283—21no—
101C4×C283#13712yes—
102C4×C283C2×#4112yes—
103Dic283—24no—
104Dic283—42no—
105Dic283—42no—
106C2×C283—22no—
107C2×C283#52511yescharacteristic
108C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
109C2×C283C2×#13711yescharacteristic
110D283—82no—
111C283#311211yescharacteristic, complemented, Sylow
112#3112—2831nomaximal, Sylow
113#532—2831no—
114C2×C4×Q8—2831no—
115#480—2832no—
116#477—2832no—
117#460—2832no—
118#448—2832no—
119#440—2834no—
120#432D28311yescharacteristic, complemented
121C2×#41—5661no—
122C22×Q8—2831no—
123C2×SD16—2834no—
124C4⋊Q8—2831no—
125#127—2831no—
126#124—5661no—
127#121—2832no—
128#121—5661no—
129C4×Q8—2832no—
130C4×Q8—2832no—
131C4×Q8—5661no—
132C4×Q8—5661no—
133C4×D4—2832no—
134C4×D4—5661no—
135C2×C4⋊C4—2831no—
136C2×C4⋊C4—5661no—
137C2×C42—5661no—
138C2×C42C2×D28311yescharacteristic
139#107—2834no—
140C4⋊C8C2×D28312yes—
141#103—2834no—
142#102—2834no—
143C22⋊C8C2×D28312yes—
144#97C2×D28312yes—
145#41—11324no—
146C2×Q8—2832no—
147C2×Q8—5664no—
148C2×Q8—5661no—
149C2×Q8—5661no—
150C2×D4—2832no—
151C2×D4—5662no—
152C2×D4—5661no—
153C2×D4—5661no—
154C22×C4—5661no—
155C22×C4—5661no—
156C22×C4—5662no—
157C22×C4D113211yescharacteristic
158C22×C4D113211yescharacteristic
159C22×C4C22×D28311yescharacteristic
160SD16—5668no—
161C2×C8C22×D28314yes—
162C4⋊C4—2832no—
163C4⋊C4—2832no—
164C4⋊C4—5662no—
165C4⋊C4—5662no—
166C4⋊C4—5661no—
167C4⋊C4—5661no—
168C22⋊C4—5662no—
169C22⋊C4—5662no—
170C42—5662no—
171C42—5662no—
172C42D113211yescharacteristic
173C42D113211yescharacteristic
174C42C22×D28311yescharacteristic
175C42C22×D28311yescharacteristic
176C23—5662no—
177C23C2×D113211yescharacteristic
178Q8—2834no—
179Q8—5664no—
180Q8—5662no—
181Q8—11322no—
182D4—5664no—
183D4—11322no—
184D4—11324no—
185D4—11322no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—5664no—
190C2×C4—5662no—
191C2×C4—5662no—
192C2×C4—5662no—
193C2×C4—11324no—
194C2×C4—11322no—
195C2×C4C2×D113211yescharacteristic
196C2×C4C2×D113211yescharacteristic
197C2×C4C2×D113211yescharacteristic
198C2×C4C2×D113211yescharacteristic
199C2×C4C2×D113211yescharacteristic
200C2×C4C23×D28311yescharacteristic
201C8—24no—
202C22—21no—
203C22—21no—
204C22—11322no—
205C22—11322no—
206C22—11322no—
207C22#2258363812yes—
208C22C22×D113211yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—5664no—
214C4—11322no—
215C4—11322no—
216C4#2258364312yes—
217C4#41×D28312yes—
218C2—22no—
219C2—22642no—
220C2#3182697711yescharacteristic
221C2C2×#2258363811yescharacteristic
222C2C2×#2258364311yescharacteristic
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#432×C283C2
socleC22×C283C22×D4
prime radical#31827015C2
hypercenter#432D283
hypocenterC283#3112
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic566C2semidirect
3. #31826779C2semidirect
4. #31826761C2semidirect
5. #31826666C2semidirect
6. #31826606C2semidirect
7. #31826567C2semidirect
8. #432×C283C2semidirect
68. Dic566#41semidirect
111. C283#3112semidirect
120. #432D283semidirect

Maximal subgroups

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

subgroupindex
#318270152
C2×C4×Dic5662
#318267792
#318267612
#318266662
#318266062
#318265672
#432×C2832
#3112283