Finite Group Databasebeta

← #49131645

Subgroups — #49131645

Order 36224.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#31827018C211yesmaximal, characteristic, complemented
2C2×#22583597C211yesmaximal, characteristic
3#31826823C214yesmaximal, complemented
4#31826818C214yesmaximal, complemented
5#31826475C211yesmaximal, characteristic, complemented
6#31826473C211yesmaximal, characteristic, complemented
7#31826470C211yesmaximal, characteristic
8M16×Dic283C211yesmaximal, characteristic, complemented
9#418×C283C211yesmaximal, characteristic
10C22×Dic566C2211yescharacteristic
11C2×#17985376C2211yescharacteristic
12#22583609C2212yescomplemented
13#22583601C2212yescomplemented
14#22583597—22no—
15#22583597C2212yes—
16#22583597C2212yes—
17#22583587—22no—
18C4×Dic566—22no—
19#22583569C2211yescharacteristic
20C2×C22⋊Dic283—22no—
21C2×C4×Dic283C2211yescharacteristic
22#22583535C2214yescomplemented
23#22583533C2214yescomplemented
24#22583531C2214yes—
25#22583520C2212yescomplemented
26C8×Dic283C2212yescomplemented
27C22×D4×C283C2211yescharacteristic
28C2×M16×C283C2211yescharacteristic
29#117×C283C2211yescharacteristic
30#102×C283C2214yes—
31C2×Dic566—22no—
32C2×Dic566—21no—
33C2×Dic566—22no—
34C2×Dic566—22no—
35C2×Dic566C2312yes—
36C22×Dic283—21no—
37C22×Dic283D412yes—
38#17985376—22no—
39C2×C283⋊C8C2312yes—
40C4⋊Dic283—22no—
41C4⋊Dic283C2312yes—
42Dic283⋊C4—22no—
43Dic283⋊C4—22no—
44C22⋊Dic283—24no—
45C22⋊Dic283—24no—
46C22⋊Dic283—21no—
47C4×Dic283—21no—
48C4×Dic283D412yes—
49C4×Dic283C2311yescharacteristic
50C4×Dic283C2311yescharacteristic
51C24×C283—21no—
52C2×D4×C283—21no—
53C2×D4×C283—22no—
54C2×D4×C283—22no—
55C2×D4×C283C2312yes—
56C22×C4×C283C2311yescharacteristic
57M16×C283—22no—
58C2×C8×C283C2312yes—
59C4⋊C4×C283C2312yes—
60C22⋊C4×C283—21no—
61C42×C283—21no—
62Dic566—22no—
63Dic566—22no—
64Dic566—44no—
65Dic566—42no—
66C2×Dic283—22no—
67C2×Dic283—22no—
68C2×Dic283—42no—
69C2×Dic283—42no—
70C2×Dic283C2×D412yes—
71C2×Dic283C2×D412yes—
72C283⋊C8—22no—
73C23×C283—22no—
74C23×C283—44no—
75C23×C283—42no—
76C23×C283C2×D411yescharacteristic
77D4×C283—22no—
78D4×C283—22no—
79D4×C283—42no—
80C2×C4×C283—22no—
81C2×C4×C283C2×D411yescharacteristic
82C2×C4×C283#4112yes—
83C2×C4×C283#4112yes—
84C2×C4×C283C2411yescharacteristic
85C8×C283—22no—
86C22×C283—22no—
87C22×C283—42no—
88C22×C283—44no—
89C22×C283—84no—
90C22×C283#12412yes—
91C22×C283C22×D411yescharacteristic
92C4×C283—42no—
93C4×C283#12412yes—
94C4×C283C2×#4111yescharacteristic
95C4×C283C2×#4111yescharacteristic
96Dic283—22no—
97Dic283—22no—
98Dic283—42no—
99Dic283—42no—
100C2×C283—22no—
101C2×C283—82no—
102C2×C283C2×#12411yescharacteristic
103C2×C283#57512yes—
104C283#314011yescharacteristic, complemented, Sylow
105#3140—2831nomaximal, Sylow
106#533—2831no—
107C2×#124—2831no—
108#489—2834no—
109#488—2834no—
110#419—2831no—
111#419—2831no—
112#418—2831no—
113#418D28311yescharacteristic
114C4×M16—2831no—
115C22×Q8—2831no—
116C22×D4C2×D28311yescharacteristic
117C2×M16—2831no—
118C2×M16C2×D28311yescharacteristic
119C4⋊Q8—2832no—
120#125—2832no—
121#124—2832no—
122#124—2832no—
123#124—5662no—
124C22⋊Q8—5662no—
125C4×Q8—5662no—
126#117—2831no—
127#117C2×D28311yescharacteristic
128C2×C22⋊C4—5662no—
129C2×C42—2831no—
130#103—2834no—
131#103—2834no—
132#102—2834no—
133#102C2×D28314yes—
134#97—2832no—
135C4×C8—2832no—
136C24—21no—
137C2×Q8—2832no—
138C2×Q8—5662no—
139C2×Q8—5661no—
140C2×Q8—5662no—
141C2×Q8—5662no—
142C2×D4—21no—
143C2×D4—22no—
144C2×D4—22no—
145C2×D4C22×D28312yes—
146C22×C4—2832no—
147C22×C4—5661no—
148C22×C4C22×D28311yescharacteristic
149M16—22no—
150M16—5662no—
151C2×C8—2832no—
152C2×C8C22×D28312yes—
153C4⋊C4—2832no—
154C4⋊C4—5662no—
155C4⋊C4—5662no—
156C4⋊C4—5662no—
157C4⋊C4C22×D28312yes—
158C22⋊C4—21no—
159C22⋊C4—5664no—
160C22⋊C4—5664no—
161C22⋊C4—5661no—
162C42—21no—
163C42—2832no—
164C42—2831no—
165C42—2831no—
166C42—5661no—
167C23—22no—
168C23—44no—
169C23—42no—
170C23D4×D28311yescharacteristic
171Q8—5662no—
172Q8—5662no—
173Q8—11324no—
174Q8—11322no—
175D4—22no—
176D4—22no—
177D4—42no—
178C2×C4—22no—
179C2×C4—2832no—
180C2×C4—2832no—
181C2×C4—5662no—
182C2×C4—5662no—
183C2×C4—11322no—
184C2×C4—11322no—
185C2×C4D4×D28311yescharacteristic
186C2×C4#1798539112yes—
187C2×C4#1798539212yes—
188C2×C4C23×D28311yescharacteristic
189C8—22no—
190C8—5662no—
191C22—22no—
192C22—42no—
193C22—44no—
194C22—84no—
195C22#2258359612yes—
196C22C2×D4×D28311yescharacteristic
197C4—42no—
198C4—5662no—
199C4—5662no—
200C4—11322no—
201C4—11322no—
202C4#2258359612yes—
203C4C2×#1798539111yescharacteristic
204C4C2×#1798539211yescharacteristic
205C2—22no—
206C2—82no—
207C2C2×#2258359611yescharacteristic
208C2#3182726112yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#418×C283C2
socleC22×C283C22×D4
prime radicalC22×D4×C283C22
hypercenter#418D283
hypocenterC283#3140
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #31827018C2semidirect
3. #31826823C2semidirect
4. #31826818C2semidirect
5. #31826475C2semidirect
6. #31826473C2semidirect
8. M16×Dic283C2semidirect
12. #22583609C22semidirect
13. #22583601C22semidirect
22. #22583535C22semidirect
23. #22583533C22semidirect
25. #22583520C22semidirect
26. C8×Dic283C22semidirect
104. C283#3140semidirect

Maximal subgroups

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

subgroupindex
#318270182
C2×#225835972
#318268232
#318268182
#318264752
#318264732
#318264702
M16×Dic2832
#418×C2832
#3140283