Finite Group Databasebeta

← #49131508

Subgroups — #49131508

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#31826939C211yesmaximal, characteristic
2#31826803C212yesmaximal, complemented
3#31826762C212yesmaximal, complemented
4#31826667C212yesmaximal, complemented
5#31826615C212yesmaximal
6#31826563C212yesmaximal, complemented
7C4×#17985379C212yesmaximal, complemented
8#31826526C211yesmaximal, characteristic, complemented
9#541×C283C211yesmaximal, characteristic, complemented
10C22×D1132C2211yescharacteristic
11C2×#17985379C2212yes—
12C2×#17985379C2212yes—
13C4×D1132C2212yes—
14C4×D1132C2212yes—
15#22583572—22no—
16#22583569C2211yescharacteristic
17C22⋊C4×D283—22no—
18#22583543C2212yescomplemented
19#22583541C2212yescomplemented
20C4⋊(C283⋊C8)C2212yescomplemented
21#22583534C2212yescomplemented
22#22583534C2212yescomplemented
23#22583530C2212yes—
24#22583530C2212yes—
25C22⋊(C283⋊C8)C2212yes—
26#22583521C2211yescharacteristic, complemented
27C4×C283⋊C8C2211yescharacteristic, complemented
28C4⋊Q8×C283C2211yescharacteristic, complemented
29#126×C283—22no—
30#125×C283—22no—
31#125×C283C2211yescharacteristic, complemented
32C22⋊Q8×C283C2212yes—
33C4×Q8×C283C2212yescomplemented
34#117×C283C2211yescharacteristic
35C23×D283—21no—
36C2×D1132—24no—
37C2×D1132—21no—
38C2×D1132C2312yes—
39C2×C4×D283—22no—
40C2×C4×D283—22no—
41#17985379—24no—
42#17985379—24no—
43C2×C283⋊C8C2312yes—
44C2×C283⋊C8C2312yes—
45C4⋊Dic283C2312yes—
46C22⋊Dic283—21no—
47(C2×D283)⋊C4—22no—
48(C2×D283)⋊C4—22no—
49C4×Dic283—21no—
50C2×Q8×C283C2312yes—
51C22×C4×C283C2311yescharacteristic
52C4⋊C4×C283—22no—
53C4⋊C4×C283—22no—
54C4⋊C4×C283—22no—
55C4⋊C4×C283—22no—
56C4⋊C4×C283D412yes—
57C4⋊C4×C283C2312yes—
58C22⋊C4×C283—22no—
59C22⋊C4×C283D412yes—
60C42×C283—22no—
61C42×C283C2311yescharacteristic
62C42×C283C2311yescharacteristic
63C22×D283—22no—
64C22×D283—24no—
65C22×D283—82no—
66D1132—24no—
67D1132—22no—
68D1132#4114yes—
69C2×Dic283—22no—
70C4×D283—82no—
71C4×D283—82no—
72C283⋊C8—22no—
73C283⋊C8—22no—
74C23×C283C2×D411yescharacteristic
75Q8×C283—22no—
76Q8×C283—22no—
77C2×C4×C283—22no—
78C2×C4×C283—22no—
79C2×C4×C283—22no—
80C2×C4×C283C2×D412yes—
81C2×C4×C283C2×D412yes—
82C2×C4×C283C2×D411yescharacteristic
83C2×C4×C283C2411yescharacteristic
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×C283—42no—
95C4×C283—42no—
96C4×C283C2×#4112yes—
97Dic283—42no—
98C2×C283—41no—
99C2×C283#52511yescharacteristic
100C2×C283#57712yes—
101D283—44no—
102C283#312311yescharacteristic, complemented, Sylow
103#3123—2831nomaximal, Sylow
104#541D28311yescharacteristic, complemented
105#518—2831no—
106#485—2832no—
107#478—2832no—
108#461—2832no—
109#450—2832no—
110#440—2832no—
111C4×SD16—2832no—
112#433—2831no—
113C22×D4—2831no—
114C2×SD16—2832no—
115C2×SD16—2832no—
116C4⋊Q8C2×D28311yescharacteristic, complemented
117#126—22no—
118#125—22no—
119#125C2×D28311yescharacteristic, complemented
120C22⋊Q8C2×D28312yes—
121C4×Q8C2×D28312yescomplemented
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⋊C8—2832no—
131#103—2832no—
132#103—2832no—
133#102—2832no—
134#102—2832no—
135C22⋊C8—2832no—
136#97—2831no—
137C4×C8—2831no—
138C24—5661no—
139C2×Q8C22×D28312yes—
140C2×D4—2832no—
141C2×D4—5664no—
142C2×D4—5661no—
143C22×C4—5662no—
144C22×C4—5662no—
145C22×C4C22×D28311yescharacteristic
146SD16—5664no—
147SD16—5664no—
148C2×C8—2832no—
149C2×C8—2832no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—2832no—
155C4⋊C4C22⋊D28312yes—
156C4⋊C4C22×D28312yes—
157C22⋊C4—22no—
158C22⋊C4—5661no—
159C22⋊C4—5662no—
160C22⋊C4—5662no—
161C22⋊C4C22⋊D28312yes—
162C42—22no—
163C42—5661no—
164C42C22×D28311yescharacteristic
165C42C22×D28311yescharacteristic
166C23—5664no—
167C23—5662no—
168C23—22642no—
169C23C2×C22⋊D28311yescharacteristic
170Q8—22no—
171Q8—22no—
172D4—2834no—
173D4—5664no—
174D4—5662no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—5662no—
179C2×C4—22642no—
180C2×C4—22642no—
181C2×C4C2×C22⋊D28312yes—
182C2×C4C2×C22⋊D28311yescharacteristic
183C2×C4C2×C22⋊D28312yes—
184C2×C4C23×D28311yescharacteristic
185C8—5662no—
186C8—5662no—
187C22—21no—
188C22—22no—
189C22—5664no—
190C22—11322no—
191C22—11322no—
192C22—22644no—
193C22C22×C22⋊D28311yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—42no—
199C4—11322no—
200C4#41×D28312yes—
201C2—41no—
202C2—11324no—
203C2#3182697211yescharacteristic
204C2#3182727312yes—
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#541×C283C2
socleC22×C283C22×D4
prime radicalC22×D1132C22
hypercenter#541D283
hypocenterC283#3123
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #31826803C2semidirect
3. #31826762C2semidirect
4. #31826667C2semidirect
6. #31826563C2semidirect
7. C4×#17985379C2semidirect
8. #31826526C2semidirect
9. #541×C283C2semidirect
18. #22583543C22semidirect
19. #22583541C22semidirect
20. C4⋊(C283⋊C8)C22semidirect
21. #22583534C22semidirect
22. #22583534C22semidirect
26. #22583521C22semidirect
27. C4×C283⋊C8C22semidirect
28. C4⋊Q8×C283C22semidirect
31. #125×C283C22semidirect
33. C4×Q8×C283C22semidirect
102. C283#3123semidirect
104. #541D283semidirect
116. C4⋊Q8C2×D283semidirect
119. #125C2×D283semidirect
121. C4×Q8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318269392
#318268032
#318267622
#318266672
#318266152
#318265632
C4×#179853792
#318265262
#541×C2832
#3123283