Finite Group Databasebeta

← #1512×C283 #49116995

Subgroups — #1512×C283 #49116995

Order 36224.

222 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 88 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#529×C283C211yesmaximal, characteristic
2#432×C283C211yesmaximal, characteristic, complemented
3#382×C283C211yesmaximal, characteristic, complemented
4#328×C283C212yesmaximal, complemented
5#327×C283C212yesmaximal
6#126×C283—21no—
7#125×C283C411yescharacteristic, complemented
8#124×C283C411yescharacteristic, complemented
9#123×C283—21no—
10C22⋊Q8×C283C2211yescharacteristic
11#121×C283C2211yescharacteristic
12C4×Q8×C283C411yescharacteristic, complemented
13C4×D4×C283—21no—
14C4×D4×C283C411yescharacteristic, complemented
15#117×C283—21no—
16C2×C4⋊C4×C283—21no—
17C2×C42×C283C2211yescharacteristic
18C4⋊C8×C283—21no—
19C22⋊C8×C283C2212yes—
20#97×C283—21no—
21#95×C283—21no—
22#95×C283C2212yes—
23C2×Q8×C283C2×C411yescharacteristic
24C2×D4×C283—21no—
25C2×D4×C283C2×C411yescharacteristic
26C22×C4×C283—21no—
27C22×C4×C283—22no—
28C22×C4×C283D411yescharacteristic
29C22×C4×C283D411yescharacteristic
30C22×C4×C283C2311yescharacteristic
31C2×C8×C283—22no—
32C4⋊C4×C283—21no—
33C4⋊C4×C283—21no—
34C4⋊C4×C283—21no—
35C4⋊C4×C283—21no—
36C4⋊C4×C283—42no—
37C4⋊C4×C283C2×C411yescharacteristic
38C4⋊C4×C283C2×C411yescharacteristic
39C22⋊C4×C283—21no—
40C22⋊C4×C283—21no—
41C22⋊C4×C283—21no—
42C22⋊C4×C283—21no—
43C22⋊C4×C283—21no—
44C42×C283—21no—
45C42×C283C2×C411yescharacteristic
46C42×C283C2×C411yescharacteristic
47C42×C283D411yescharacteristic
48C42×C283D411yescharacteristic
49C23×C283—21no—
50C23×C283C2×D411yescharacteristic
51Q8×C283—41no—
52D4×C283—41no—
53D4×C283—41no—
54D4×C283—41no—
55C2×C4×C283—21no—
56C2×C4×C283—21no—
57C2×C4×C283—21no—
58C2×C4×C283—21no—
59C2×C4×C283—21no—
60C2×C4×C283—41no—
61C2×C4×C283—41no—
62C2×C4×C283—42no—
63C2×C4×C283—42no—
64C2×C4×C283—42no—
65C2×C4×C283—42no—
66C2×C4×C283C22⋊C411yescharacteristic
67C2×C4×C283C22⋊C411yescharacteristic
68C2×C4×C283C22⋊C411yescharacteristic
69C2×C4×C283C22⋊C411yescharacteristic
70C2×C4×C283C22×C411yescharacteristic
71C2×C4×C283C2×D411yescharacteristic
72C8×C283—42no—
73C22×C283—21no—
74C22×C283—21no—
75C22×C283—41no—
76C22×C283—41no—
77C22×C283—41no—
78C22×C283C2×C22⋊C411yescharacteristic
79C22×C283AGL(1,ℤ/8)11yescharacteristic
80C22×C283#13711yescharacteristic
81C4×C283—21no—
82C4×C283—21no—
83C4×C283—21no—
84C4×C283—21no—
85C4×C283—21no—
86C4×C283—21no—
87C4×C283—41no—
88C4×C283—41no—
89C4×C283—41no—
90C4×C283—82no—
91C2×C283—21no—
92C2×C283—21no—
93C2×C283—81no—
94C2×C283#41011yescharacteristic
95C2×C283#41711yescharacteristic
96C2×C283#42111yescharacteristic
97C283#151211yescharacteristic, direct product factor, Sylow
98#1512C28311yesmaximal, characteristic, direct product factor, Sylow
99#529C2×C28311yescharacteristic
100#432C2×C28311yescharacteristic, complemented
101#382C2×C28311yescharacteristic, complemented
102#328C2×C28312yescomplemented
103#327C2×C28312yes—
104#126—21no—
105#125C4×C28311yescharacteristic, complemented
106#124C4×C28311yescharacteristic, complemented
107#123—21no—
108C22⋊Q8C22×C28311yescharacteristic
109#121C22×C28311yescharacteristic
110C4×Q8C4×C28311yescharacteristic, complemented
111C4×D4—21no—
112C4×D4C4×C28311yescharacteristic, complemented
113#117—21no—
114C2×C4⋊C4—21no—
115C2×C42C22×C28311yescharacteristic
116C4⋊C8—21no—
117C22⋊C8C22×C28312yes—
118#97—21no—
119#95—21no—
120#95C22×C28312yes—
121C2×Q8C2×C4×C28311yescharacteristic
122C2×D4—21no—
123C2×D4C2×C4×C28311yescharacteristic
124C22×C4—21no—
125C22×C4—22no—
126C22×C4D4×C28311yescharacteristic
127C22×C4D4×C28311yescharacteristic
128C22×C4C23×C28311yescharacteristic
129C2×C8—22no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—42no—
135C4⋊C4C2×C4×C28311yescharacteristic
136C4⋊C4C2×C4×C28311yescharacteristic
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—21no—
141C22⋊C4—21no—
142C42—21no—
143C42C2×C4×C28311yescharacteristic
144C42C2×C4×C28311yescharacteristic
145C42D4×C28311yescharacteristic
146C42D4×C28311yescharacteristic
147C23—21no—
148C23C2×D4×C28311yescharacteristic
149Q8—41no—
150D4—41no—
151D4—41no—
152D4—41no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4C22⋊C4×C28311yescharacteristic
165C2×C4C22⋊C4×C28311yescharacteristic
166C2×C4C22⋊C4×C28311yescharacteristic
167C2×C4C22⋊C4×C28311yescharacteristic
168C2×C4C22×C4×C28311yescharacteristic
169C2×C4C2×D4×C28311yescharacteristic
170C8—42no—
171C22—21no—
172C22—21no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22C2×C22⋊C4×C28311yescharacteristic
177C22AGL(1,ℤ/8)×C28311yescharacteristic
178C22#137×C28311yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—41no—
188C4—82no—
189C2—21no—
190C2—21no—
191C2—81no—
192C2#410×C28311yescharacteristic
193C2#417×C28311yescharacteristic
194C2#421×C28311yescharacteristic
subgroupG/H
center, socleC22×C283C2×C22⋊C4
commutatorC2×C4C22×C4×C283
Frattini, cosocleC22×C4C23×C283
prime radical#121×C283C22
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C283 ◁ C2×C42×C283 ◁ G

Complements

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

NH ≅ G/Ntype
2. #432×C283C2semidirect
3. #382×C283C2semidirect
4. #328×C283C2semidirect
7. #125×C283C4semidirect
8. #124×C283C4semidirect
12. C4×Q8×C283C4semidirect
14. C4×D4×C283C4semidirect
97. C283#1512direct (N × H)
98. #1512C283direct (N × H)
100. #432C2×C283semidirect
101. #382C2×C283semidirect
102. #328C2×C283semidirect
105. #125C4×C283semidirect
106. #124C4×C283semidirect
110. C4×Q8C4×C283semidirect
112. C4×D4C4×C283semidirect

Maximal subgroups

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

subgroupindex
#529×C2832
#432×C2832
#382×C2832
#328×C2832
#327×C2832
#1512283