Finite Group Databasebeta

← #49131552

Subgroups — #49131552

Order 36224.

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

normal subgroups only

This group has 382 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#31827070C211yesmaximal, characteristic
2#31826789C212yesmaximal, complemented
3#31826772C212yesmaximal, complemented
4#31826665C212yesmaximal, complemented
5#31826604C212yesmaximal, complemented
6#31826563C212yesmaximal, complemented
7C4×#17985379C212yesmaximal, complemented
8#31826526C211yesmaximal, characteristic, complemented
9#519×C283C211yesmaximal, characteristic, complemented
10C2×#17985379C2212yes—
11C2×#17985379C2212yes—
12#22583607C2211yescharacteristic
13#22583602C2211yescharacteristic
14#22583595—22no—
15#22583584C2212yes—
16#22583583—22no—
17C4×D1132C2212yes—
18#22583543C2212yes—
19#22583541C2212yes—
20C4⋊(C283⋊C8)C2212yes—
21#22583534C2212yes—
22#22583534C2212yes—
23#22583530C2212yes—
24#22583530C2212yes—
25C22⋊(C283⋊C8)C2212yes—
26#22583521C2211yescharacteristic
27C4×C283⋊C8C2211yescharacteristic
28C22×Q8×C283C2211yescharacteristic
29C4×Q8×C283—22no—
30C4×Q8×C283C2212yes—
31C4×Q8×C283C2212yes—
32#117×C283—22no—
33#117×C283C2211yescharacteristic
34#117×C283C2211yescharacteristic
35C2×D1132—22no—
36C2×D1132C2312yes—
37C2×C22⋊D283—22no—
38C2×C4×D283—22no—
39#17985379—24no—
40#17985379—24no—
41C2×C283⋊C8C2312yes—
42C2×C283⋊C8C2312yes—
43C4⋊Dic283C2312yes—
44Dic283⋊C4—22no—
45(C2×D283)⋊C4—22no—
46(C2×D283)⋊C4—22no—
47C2×Q8×C283—24no—
48C2×Q8×C283—21no—
49C2×Q8×C283C2312yes—
50C22×C4×C283—21no—
51C22×C4×C283C2311yescharacteristic
52C4⋊C4×C283—22no—
53C4⋊C4×C283—22no—
54C4⋊C4×C283D412yes—
55C4⋊C4×C283C2312yes—
56C22⋊C4×C283—21no—
57C22⋊C4×C283D412yes—
58C42×C283—22no—
59C42×C283—22no—
60C42×C283—21no—
61C42×C283C2311yescharacteristic
62C42×C283C2311yescharacteristic
63C22×D283—22no—
64D1132—22no—
65D1132—22no—
66D1132—82no—
67C22⋊D283—82no—
68C2×Dic283—22no—
69C4×D283—82no—
70C283⋊C8—22no—
71C283⋊C8—22no—
72C23×C283C2×D411yescharacteristic
73Q8×C283—24no—
74Q8×C283—22no—
75Q8×C283#4114yes—
76C2×C4×C283—24no—
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—42no—
88C2×D283—42no—
89C2×D283—42no—
90C4×C283—24no—
91C4×C283—21no—
92C4×C283—22no—
93C4×C283—22no—
94C4×C283—42no—
95C4×C283C2×#4112yes—
96Dic283—42no—
97C2×C283—41no—
98C2×C283#52511yescharacteristic
99C2×C283#57712yes—
100D283—82no—
101C283#312611yescharacteristic, complemented, Sylow
102#3126—2831nomaximal, Sylow
103#540—2831no—
104#519D28311yescharacteristic, complemented
105#482—2832no—
106#479—2832no—
107#460—2832no—
108#448—2832no—
109#440—2832no—
110C4×SD16—2832no—
111#433—2831no—
112C22×Q8C2×D28311yescharacteristic
113C2×SD16—2832no—
114C2×SD16—2832no—
115#127—2831no—
116#125—2831no—
117#123—5662no—
118#121—2832no—
119#121—5662no—
120C4×Q8—22no—
121C4×Q8C2×D28312yes—
122C4×Q8C2×D28312yes—
123C4×D4—2832no—
124#117—22no—
125#117C2×D28311yescharacteristic
126#117C2×D28311yescharacteristic
127#107—2832no—
128#106—2832no—
129C4⋊C8—2832no—
130#103—2832no—
131#103—2832no—
132#102—2832no—
133#102—2832no—
134C22⋊C8—2832no—
135#97—2831no—
136C4×C8—2831no—
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8C22×D28312yes—
140C2×D4—2832no—
141C2×D4—5662no—
142C2×D4—5662no—
143C22×C4—21no—
144C22×C4—5662no—
145C22×C4C22×D28311yescharacteristic
146SD16—5664no—
147SD16—5664no—
148C2×C8—2832no—
149C2×C8—2832no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—2832no—
153C4⋊C4—5662no—
154C4⋊C4C22⋊D28312yes—
155C4⋊C4C22×D28312yes—
156C22⋊C4—21no—
157C22⋊C4—5662no—
158C22⋊C4—5662no—
159C22⋊C4C22⋊D28312yes—
160C42—22no—
161C42—22no—
162C42—21no—
163C42C22×D28311yescharacteristic
164C42C22×D28311yescharacteristic
165C23—5662no—
166C23C2×C22⋊D28311yescharacteristic
167Q8—24no—
168Q8—22no—
169Q8#1798539214yes—
170D4—5662no—
171D4—5662no—
172D4—22642no—
173D4—22642no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—5662no—
179C2×C4—22642no—
180C2×C4C2×C22⋊D28312yes—
181C2×C4C2×C22⋊D28312yes—
182C2×C4C2×C22⋊D28311yescharacteristic
183C2×C4C23×D28311yescharacteristic
184C8—5662no—
185C8—5662no—
186C22—21no—
187C22—22no—
188C22—11322no—
189C22—11322no—
190C22—11322no—
191C22C22×C22⋊D28311yescharacteristic
192C4—24no—
193C4—21no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—11322no—
198C4C2×#1798539212yes—
199C2—41no—
200C2—22642no—
201C2#3182697611yescharacteristic
202C2#3182727312yes—
subgroupG/H
centerC22C22×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#519×C283C2
socleC22×C283C22×D4
prime radical#31827070C2
hypercenter#519D283
hypocenterC283#3126
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. #31826789C2semidirect
3. #31826772C2semidirect
4. #31826665C2semidirect
5. #31826604C2semidirect
6. #31826563C2semidirect
7. C4×#17985379C2semidirect
8. #31826526C2semidirect
9. #519×C283C2semidirect
101. C283#3126semidirect
104. #519D283semidirect

Maximal subgroups

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

subgroupindex
#318270702
#318267892
#318267722
#318266652
#318266042
#318265632
C4×#179853792
#318265262
#519×C2832
#3126283