Finite Group Databasebeta

← #49130791

Subgroups — #49130791

Order 36224.

458 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22583641C211yesmaximal, characteristic
2C22×#17985382C211yesmaximal, characteristic, complemented
3#31827041C211yesmaximal, characteristic
4#31826687C214yesmaximal, complemented
5#31826675C214yesmaximal, complemented
6#31826492C211yesmaximal, characteristic, complemented
7#31826473C211yesmaximal, characteristic, complemented
8#31826459C211yesmaximal, characteristic
9#519×C283C211yesmaximal, characteristic, complemented
10C2×#17985392C2211yescharacteristic
11C22×Dic566C2211yescharacteristic
12#22583641—24no—
13C2×#17985382—24no—
14C2×#17985382C2214yes—
15C2×#17985382C2212yes—
16C2×#17985379C2212yes—
17C2×#17985376C2211yescharacteristic
18C22×C283⋊C8C2211yescharacteristic
19#22583610C2212yes—
20#22583598C2212yes—
21#22583594—22no—
22#22583590—22no—
23C4⋊(C283⋊C8)C2214yes—
24#22583533C2212yes—
25#22583533C2214yes—
26#22583530C2212yes—
27C22×Q8×C283C2211yescharacteristic
28C4×Q8×C283—22no—
29C4×Q8×C283C2214yes—
30#117×C283—22no—
31#117×C283C2211yescharacteristic
32#117×C283C2211yescharacteristic
33#17985392—22no—
34#17985392—22no—
35C2×Dic566—21no—
36C2×Dic566—22no—
37C2×Dic566—22no—
38C2×Dic566C2312yes—
39C2×Dic566C2311yescharacteristic
40C2×D1132C2311yescharacteristic
41C2×C22⋊D283—21no—
42C22×Dic283—21no—
43C2×C4×D283—21no—
44#17985382—28no—
45#17985382—24no—
46#17985379—24no—
47#17985376—22no—
48C2×C283⋊C8—22no—
49C2×C283⋊C8C2312yes—
50C2×C283⋊C8C2312yes—
51C4⋊Dic283—24no—
52(C2×D283)⋊C4—24no—
53C2×Q8×C283—21no—
54C2×Q8×C283—22no—
55C2×Q8×C283D414yes—
56C2×Q8×C283C2312yes—
57C22×C4×C283—21no—
58C22×C4×C283C2311yescharacteristic
59C4⋊C4×C283—24no—
60C4⋊C4×C283D412yes—
61C4⋊C4×C283C2312yes—
62C22⋊C4×C283—21no—
63C22⋊C4×C283D412yes—
64C42×C283—24no—
65C42×C283—21no—
66C42×C283C2312yes—
67C22×D283—21no—
68Dic566—22no—
69Dic566—21no—
70Dic566—22no—
71Dic566—21no—
72Dic566—42no—
73D1132—21no—
74D1132—21no—
75C22⋊D283—42no—
76C2×Dic283—22no—
77C2×Dic283—21no—
78C2×Dic283—42no—
79C4×D283—42no—
80C283⋊C8—22no—
81C283⋊C8—22no—
82C23×C283C2×D411yescharacteristic
83Q8×C283—24no—
84Q8×C283—22no—
85Q8×C283C2×D414yes—
86C2×C4×C283—24no—
87C2×C4×C283—22no—
88C2×C4×C283—22no—
89C2×C4×C283C2×D414yes—
90C2×C4×C283C2×D411yescharacteristic
91C2×C4×C283C2×D412yes—
92C2×C4×C283#4112yes—
93C2×C4×C283C2411yescharacteristic
94C22×C283—22no—
95C22×C283#12112yes—
96C22×C283C22×D411yescharacteristic
97C2×D283—41no—
98C2×D283—42no—
99C4×C283—24no—
100C4×C283—24no—
101C4×C283—42no—
102C4×C283#12112yes—
103C4×C283C22×D411yescharacteristic
104C4×C283C2×#4111yescharacteristic
105Dic283—41no—
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#519D28311yescharacteristic, complemented
117#464—2834no—
118#462—2834no—
119#424—2831no—
120#419—2831no—
121#416—2831no—
122C2×#41—2831no—
123C22×Q8—2831no—
124C22×Q8C2×D28311yescharacteristic
125#137—5664no—
126C2×Q16—2834no—
127C2×Q16—2832no—
128C2×Q16—5664no—
129C2×SD16—2832no—
130C2×M16—2831no—
131C22×C8—2831no—
132C4⋊Q8—2832no—
133#124—2832no—
134#123—5662no—
135C22⋊Q8—5662no—
136C4×Q8—22no—
137C4×Q8C2×D28314yes—
138#117—22no—
139#117C2×D28311yescharacteristic
140#117C2×D28311yescharacteristic
141C4⋊C8—2834no—
142#103—2832no—
143#103—2834no—
144#102—2832no—
145#41—5662no—
146#41—5662no—
147C2×Q8—21no—
148C2×Q8—22no—
149C2×Q8—2832no—
150C2×Q8—2831no—
151C2×Q8—5661no—
152C2×Q8—5662no—
153C2×Q8—5662no—
154C2×Q8D113214yes—
155C2×Q8C22×D28312yes—
156C2×D4—2831no—
157C2×D4—5661no—
158C22×C4—21no—
159C22×C4—5661no—
160C22×C4—5661no—
161C22×C4C22×D28311yescharacteristic
162Q16—5668no—
163Q16—5664no—
164SD16—5664no—
165M16—5662no—
166C2×C8—2832no—
167C2×C8—2832no—
168C2×C8—5662no—
169C4⋊C4—24no—
170C4⋊C4—5664no—
171C4⋊C4C22⋊D28312yes—
172C4⋊C4C22×D28312yes—
173C22⋊C4—21no—
174C22⋊C4—5664no—
175C22⋊C4C22⋊D28312yes—
176C42—24no—
177C42—21no—
178C42C22×D28312yes—
179C23—5661no—
180C23C2×C22⋊D28311yescharacteristic
181Q8—24no—
182Q8—22no—
183Q8—5662no—
184Q8—5661no—
185Q8—5662no—
186Q8—5661no—
187Q8—11322no—
188Q8C2×D113214yes—
189D4—5661no—
190D4—5661no—
191D4—11322no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—5662no—
196C2×C4—5661no—
197C2×C4—11322no—
198C2×C4—11322no—
199C2×C4C2×C22⋊D28314yes—
200C2×C4C2×C22⋊D28311yescharacteristic
201C2×C4C2×D113212yes—
202C2×C4#1798539212yes—
203C2×C4C23×D28311yescharacteristic
204C8—5662no—
205C8—5662no—
206C22—22no—
207C22—11321no—
208C22—11322no—
209C22#2258358412yes—
210C22C22×C22⋊D28311yescharacteristic
211C4—24no—
212C4—24no—
213C4—42no—
214C4—11321no—
215C4—11322no—
216C4#2258358412yes—
217C4C22×D113211yescharacteristic
218C4C2×#1798539211yescharacteristic
219C2—22no—
220C2—22641no—
221C2C2×#2258358411yescharacteristic
222C2#3182728012yes—
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#519×C283C2
socleC22×C283C22×D4
prime radicalC2×#17985392C22
hypercenter#519D283
hypocenterC283#3044
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. C22×#17985382C2semidirect
4. #31826687C2semidirect
5. #31826675C2semidirect
6. #31826492C2semidirect
7. #31826473C2semidirect
9. #519×C283C2semidirect
111. C283#3044semidirect
116. #519D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836412
C22×#179853822
#318270412
#318266872
#318266752
#318264922
#318264732
#318264592
#519×C2832
#3044283