Finite Group Databasebeta

← #49131514

Subgroups — #49131514

Order 36224.

394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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#31827077C211yesmaximal, characteristic, complemented
2#31826939C211yesmaximal, characteristic
3#31826807C212yesmaximal, complemented
4#31826766C212yesmaximal, complemented
5#31826671C212yesmaximal, complemented
6#31826618C212yesmaximal
7#31826567C212yesmaximal, complemented
8C4×#17985381C212yesmaximal, complemented
9#433×C283C211yesmaximal, characteristic, complemented
10C22×D1132C2211yescharacteristic
11C2×#17985381C2212yes—
12C2×#17985381C2212yes—
13#22583610C2211yescharacteristic, complemented
14#22583603—22no—
15#22583602C2211yescharacteristic, complemented
16#22583600—22no—
17#22583589C2212yes—
18C4×Dic566C2212yescomplemented
19C4×D1132C2212yes—
20C4×D1132C2212yes—
21#22583572—22no—
22#22583569C2211yescharacteristic
23C22⋊C4×D283—22no—
24#22583544C2212yescomplemented
25#22583542C2212yescomplemented
26#22583535C2212yescomplemented
27#22583535C2212yescomplemented
28#22583532C2212yes—
29#22583532C2212yes—
30#117×C283C2211yescharacteristic
31C4⋊C8×C283C2212yescomplemented
32C22⋊C8×C283C2212yes—
33#97×C283C2211yescharacteristic, complemented
34C4×C8×C283C2211yescharacteristic, complemented
35C23×D283—21no—
36C2×Dic566C2312yes—
37C2×D1132—24no—
38C2×D1132—21no—
39C2×D1132C2312yes—
40C2×C4×D283—22no—
41C2×C4×D283—22no—
42#17985381—24no—
43#17985381—24no—
44C4⋊Dic283—22no—
45C4⋊Dic283C2312yes—
46C4⋊Dic283C2312yes—
47Dic283⋊C4—22no—
48Dic283⋊C4—22no—
49Dic283⋊C4—22no—
50C22⋊Dic283—21no—
51C22⋊Dic283—22no—
52(C2×D283)⋊C4—22no—
53(C2×D283)⋊C4—22no—
54C4×Dic283—21no—
55C4×Dic283—22no—
56C22×C4×C283C2311yescharacteristic
57C2×C8×C283C2312yes—
58C2×C8×C283C2312yes—
59C4⋊C4×C283D412yes—
60C22⋊C4×C283D412yes—
61C42×C283C2311yescharacteristic
62C42×C283C2311yescharacteristic
63C22×D283—22no—
64C22×D283—24no—
65C22×D283—82no—
66Dic566—22no—
67Dic566—22no—
68D1132—24no—
69D1132—22no—
70D1132#4114yes—
71C2×Dic283—22no—
72C2×Dic283—22no—
73C2×Dic283—22no—
74C4×D283—82no—
75C4×D283—82no—
76C23×C283C2×D411yescharacteristic
77C2×C4×C283—22no—
78C2×C4×C283C2×D412yes—
79C2×C4×C283C2×D412yes—
80C2×C4×C283C2×D411yescharacteristic
81C2×C4×C283C2411yescharacteristic
82C8×C283—22no—
83C8×C283—22no—
84C22×C283—21no—
85C22×C283—22no—
86C22×C283C22×D411yescharacteristic
87C2×D283—24no—
88C2×D283—42no—
89C2×D283—42no—
90C2×D283—84no—
91C4×C283—21no—
92C4×C283—22no—
93C4×C283—22no—
94C4×C283C2×#4112yes—
95Dic283—42no—
96Dic283—42no—
97Dic283—42no—
98C2×C283—41no—
99C2×C283#52511yescharacteristic
100C2×C283#57712yes—
101D283—44no—
102C283#312311yescharacteristic, complemented, Sylow
103#3123—2831nomaximal, Sylow
104#541—2831no—
105#518—2831no—
106#485—2832no—
107#478—2832no—
108#461—2832no—
109#450—2832no—
110#440—2832no—
111C4×SD16—2832no—
112#433D28311yescharacteristic, complemented
113C22×D4—2831no—
114C2×SD16—2832no—
115C2×SD16—2832no—
116C4⋊Q8—2831no—
117#126—5662no—
118#125—2831no—
119#125—5662no—
120C22⋊Q8—2832no—
121C4×Q8—2832no—
122C4×D4—2832no—
123C4×D4—2832no—
124C4×D4—5662no—
125#117—2831no—
126#117C2×D28311yescharacteristic
127C2×C22⋊C4—5662no—
128#107—2832no—
129#106—2832no—
130C4⋊C8C2×D28312yescomplemented
131#103—2832no—
132#103—2832no—
133#102—2832no—
134#102—2832no—
135C22⋊C8C2×D28312yes—
136#97C2×D28311yescharacteristic, complemented
137C4×C8C2×D28311yescharacteristic, complemented
138C24—5661no—
139C2×Q8—2832no—
140C2×D4—2832no—
141C2×D4—5664no—
142C2×D4—5661no—
143C22×C4—5662no—
144C22×C4—5662no—
145C22×C4C22×D28311yescharacteristic
146SD16—5664no—
147SD16—5664no—
148C2×C8C22×D28312yes—
149C2×C8C22×D28312yes—
150C4⋊C4—2832no—
151C4⋊C4—2832no—
152C4⋊C4—5662no—
153C4⋊C4—5662no—
154C4⋊C4—5662no—
155C4⋊C4—5662no—
156C4⋊C4D113212yes—
157C22⋊C4—5661no—
158C22⋊C4—5662no—
159C22⋊C4—5662no—
160C22⋊C4—5662no—
161C22⋊C4D113212yes—
162C42—5661no—
163C42—5662no—
164C42C22×D28311yescharacteristic
165C42C22×D28311yescharacteristic
166C23—5664no—
167C23—5662no—
168C23—22642no—
169C23C2×D113211yescharacteristic
170Q8—5662no—
171Q8—5662no—
172D4—2834no—
173D4—5664no—
174D4—5662no—
175C2×C4—22no—
176C2×C4—5662no—
177C2×C4—5662no—
178C2×C4—5662no—
179C2×C4—22642no—
180C2×C4—22642no—
181C2×C4C2×D113212yes—
182C2×C4C2×D113211yescharacteristic
183C2×C4C2×D113212yes—
184C2×C4C23×D28311yescharacteristic
185C8—22no—
186C8—22no—
187C22—21no—
188C22—22no—
189C22—5664no—
190C22—11322no—
191C22—11322no—
192C22—22644no—
193C22C22×D113211yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—11322no—
198C4—11322no—
199C4—11322no—
200C4#41×D28312yes—
201C2—41no—
202C2—11324no—
203C2#3182697711yescharacteristic
204C2#3182727712yes—
subgroupG/H
centerC22C22×D1132
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#433×C283C2
socleC22×C283C22×D4
prime radicalC22×D1132C22
hypercenter#433D283
hypocenterC283#3123
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #31827077C2semidirect
3. #31826807C2semidirect
4. #31826766C2semidirect
5. #31826671C2semidirect
7. #31826567C2semidirect
8. C4×#17985381C2semidirect
9. #433×C283C2semidirect
13. #22583610C22semidirect
15. #22583602C22semidirect
18. C4×Dic566C22semidirect
24. #22583544C22semidirect
25. #22583542C22semidirect
26. #22583535C22semidirect
27. #22583535C22semidirect
31. C4⋊C8×C283C22semidirect
33. #97×C283C22semidirect
34. C4×C8×C283C22semidirect
102. C283#3123semidirect
112. #433D283semidirect
130. C4⋊C8C2×D283semidirect
136. #97C2×D283semidirect
137. C4×C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318270772
#318269392
#318268072
#318267662
#318266712
#318266182
#318265672
C4×#179853812
#433×C2832
#3123283