Finite Group Databasebeta

← #49130792

Subgroups — #49130792

Order 36224.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#22583643C211yesmaximal, characteristic
2C22×Dic1132C211yesmaximal, characteristic, complemented
3#31827041C211yesmaximal, characteristic
4#31826942C211yesmaximal, characteristic, complemented
5#31826688C214yesmaximal, complemented
6#31826676C214yesmaximal, complemented
7#31826475C211yesmaximal, characteristic, complemented
8#31826462C211yesmaximal, characteristic
9#424×C283C211yesmaximal, characteristic, complemented
10C2×#17985392C2211yescharacteristic
11C22×Dic566C2211yescharacteristic
12C22×Dic566C2211yescharacteristic
13#22583643—24no—
14C2×Dic1132—24no—
15C2×Dic1132C2214yes—
16C2×Dic1132C2212yes—
17C2×#17985381C2212yes—
18#22583610C2212yes—
19#22583598C2212yes—
20#22583594—22no—
21#22583590—22no—
22C4×Dic566C2214yes—
23#22583575—22no—
24#22583569C2211yescharacteristic
25#22583566—22no—
26#22583535C2214yes—
27#22583535C2212yes—
28#22583532C2212yes—
29C2×M16×C283C2211yescharacteristic
30C22×C8×C283C2211yescharacteristic
31#117×C283C2211yescharacteristic
32C4⋊C8×C283C2214yes—
33#17985392—22no—
34#17985392—22no—
35C2×Dic566—21no—
36C2×Dic566—21no—
37C2×Dic566—22no—
38C2×Dic566—22no—
39C2×Dic566—22no—
40C2×Dic566D414yes—
41C2×Dic566C2312yes—
42C2×Dic566C2311yescharacteristic
43C2×Dic566C2312yes—
44C2×D1132C2311yescharacteristic
45C2×C22⋊D283—21no—
46C22×Dic283—21no—
47C22×Dic283—21no—
48C2×C4×D283—21no—
49Dic1132—28no—
50Dic1132—24no—
51#17985381—24no—
52C4⋊Dic283—24no—
53C4⋊Dic283C2312yes—
54Dic283⋊C4—24no—
55C22⋊Dic283—21no—
56(C2×D283)⋊C4—24no—
57C4×Dic283—24no—
58C4×Dic283—21no—
59C22×C4×C283C2311yescharacteristic
60M16×C283—22no—
61C2×C8×C283—22no—
62C2×C8×C283C2312yes—
63C2×C8×C283C2312yes—
64C4⋊C4×C283D412yes—
65C22⋊C4×C283D412yes—
66C42×C283C2312yes—
67C22×D283—21no—
68Dic566—24no—
69Dic566—22no—
70Dic566—22no—
71Dic566—21no—
72Dic566—22no—
73Dic566—21no—
74Dic566—42no—
75Dic566C2×D414yes—
76D1132—21no—
77D1132—21no—
78C22⋊D283—42no—
79C2×Dic283—24no—
80C2×Dic283—22no—
81C2×Dic283—22no—
82C2×Dic283—22no—
83C2×Dic283—21no—
84C2×Dic283—42no—
85C4×D283—42no—
86C23×C283C2×D411yescharacteristic
87C2×C4×C283C2×D412yes—
88C2×C4×C283C2×D414yes—
89C2×C4×C283C2×D411yescharacteristic
90C2×C4×C283#4112yes—
91C2×C4×C283C2411yescharacteristic
92C8×C283—22no—
93C8×C283—22no—
94C22×C283—22no—
95C22×C283#12112yes—
96C22×C283C22×D411yescharacteristic
97C2×D283—41no—
98C2×D283—42no—
99C4×C283—24no—
100C4×C283#12112yes—
101C4×C283C22×D411yescharacteristic
102C4×C283C2×#4111yescharacteristic
103Dic283—24no—
104Dic283—41no—
105Dic283—42no—
106Dic283—42no—
107C2×C283—22no—
108C2×C283C2×#12111yescharacteristic
109C2×C283#57812yes—
110D283—81no—
111C283#304411yescharacteristic, complemented, Sylow
112#3044—2831nomaximal, Sylow
113C2×#137—2831no—
114C22×Q16—2831no—
115#536—2831no—
116#519—2831no—
117#464—2834no—
118#462—2834no—
119#424D28311yescharacteristic, complemented
120#419—2831no—
121#416—2831no—
122C2×#41—2831no—
123C22×Q8—2831no—
124C22×Q8—2831no—
125#137—5664no—
126C2×Q16—2834no—
127C2×Q16—2832no—
128C2×Q16—5664no—
129C2×SD16—2832no—
130C2×M16C2×D28311yescharacteristic
131C22×C8C2×D28311yescharacteristic
132C4⋊Q8—2832no—
133#124—2832no—
134#123—5662no—
135C22⋊Q8—5662no—
136C4×Q8—2834no—
137C4×Q8—5662no—
138#117—2831no—
139#117—5662no—
140#117C2×D28311yescharacteristic
141C4⋊C8C2×D28314yes—
142#103—2832no—
143#103—2834no—
144#102—2832no—
145#41—5662no—
146#41—5662no—
147C2×Q8—2834no—
148C2×Q8—2832no—
149C2×Q8—2832no—
150C2×Q8—2831no—
151C2×Q8—5661no—
152C2×Q8—5661no—
153C2×Q8—5662no—
154C2×Q8—5662no—
155C2×Q8—5662no—
156C2×D4—2831no—
157C2×D4—5661no—
158C22×C4—5661no—
159C22×C4—5661no—
160C22×C4—5661no—
161C22×C4C22×D28311yescharacteristic
162Q16—5668no—
163Q16—5664no—
164SD16—5664no—
165M16—22no—
166C2×C8—22no—
167C2×C8C22×D28312yes—
168C2×C8C22×D28312yes—
169C4⋊C4—2832no—
170C4⋊C4—5664no—
171C4⋊C4—5664no—
172C4⋊C4D113212yes—
173C22⋊C4—5661no—
174C22⋊C4—5664no—
175C22⋊C4D113212yes—
176C42—5661no—
177C42—5664no—
178C42C22×D28312yes—
179C23—5661no—
180C23C2×D113211yescharacteristic
181Q8—2834no—
182Q8—5664no—
183Q8—5662no—
184Q8—5662no—
185Q8—5661no—
186Q8—5662no—
187Q8—5661no—
188Q8—11322no—
189D4—5661no—
190D4—5661no—
191D4—11322no—
192C2×C4—5664no—
193C2×C4—5662no—
194C2×C4—5662no—
195C2×C4—5662no—
196C2×C4—5661no—
197C2×C4—11322no—
198C2×C4—11322no—
199C2×C4D4×D28312yes—
200C2×C4C2×D113214yes—
201C2×C4C2×D113211yescharacteristic
202C2×C4#1798539312yes—
203C2×C4C23×D28311yescharacteristic
204C8—22no—
205C8—22no—
206C22—22no—
207C22—11321no—
208C22—11322no—
209C22#2258358512yes—
210C22C22×D113211yescharacteristic
211C4—24no—
212C4—5664no—
213C4—11321no—
214C4—11322no—
215C4—11322no—
216C4#2258358512yes—
217C4C2×D4×D28311yescharacteristic
218C4C2×#1798539311yescharacteristic
219C2—22no—
220C2—22641no—
221C2C2×#2258358511yescharacteristic
222C2#3182728212yes—
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#424×C283C2
socleC22×C283C22×D4
prime radicalC2×#17985392C22
hypercenter#424D283
hypocenterC283#3044
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
2. C22×Dic1132C2semidirect
4. #31826942C2semidirect
5. #31826688C2semidirect
6. #31826676C2semidirect
7. #31826475C2semidirect
9. #424×C283C2semidirect
111. C283#3044semidirect
119. #424D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836432
C22×Dic11322
#318270412
#318269422
#318266882
#318266762
#318264752
#318264622
#424×C2832
#3044283