Finite Group Databasebeta

← #49119797

Subgroups — #49119797

Order 36224.

222 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 69 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#31826999C211yesmaximal, characteristic
2#31826522C211yesmaximal, characteristic, complemented
3#31826201C212yesmaximal, complemented
4#31826198C212yesmaximal
5#382×C283C211yesmaximal, characteristic, complemented
6#22583604—21no—
7#22583602C411yescharacteristic, complemented
8#22583598C411yescharacteristic, complemented
9#22583593—21no—
10#22583589C2211yescharacteristic
11#22583584C2211yescharacteristic
12C4×Dic566C411yescharacteristic, complemented
13C4×D1132C411yescharacteristic, complemented
14C4×C22⋊D283—21no—
15#22583567—21no—
16C4⋊(C283⋊C8)—21no—
17C22⋊(C283⋊C8)C2212yes—
18#22583521—21no—
19C2×C4⋊C4×C283—21no—
20C2×C42×C283C2211yescharacteristic
21#95×C283—21no—
22#95×C283C2212yes—
23C2×Dic566C2×C411yescharacteristic
24C2×D1132C2×C411yescharacteristic
25C2×C22⋊D283—21no—
26C2×C4×D283—21no—
27C2×C283⋊C8—22no—
28C4⋊Dic283C2×C411yescharacteristic
29C4⋊Dic283C2×C411yescharacteristic
30Dic283⋊C4—21no—
31Dic283⋊C4—21no—
32Dic283⋊C4—21no—
33Dic283⋊C4—21no—
34C22⋊Dic283—21no—
35(C2×D283)⋊C4—21no—
36(C2×D283)⋊C4—21no—
37(C2×D283)⋊C4—21no—
38(C2×D283)⋊C4—21no—
39C4×Dic283—21no—
40C22×C4×C283—22no—
41C22×C4×C283D411yescharacteristic
42C22×C4×C283D411yescharacteristic
43C22×C4×C283C2311yescharacteristic
44C4⋊C4×C283—42no—
45C42×C283C2×C411yescharacteristic
46C42×C283C2×C411yescharacteristic
47C42×C283D411yescharacteristic
48C42×C283D411yescharacteristic
49C22×D283—21no—
50Dic566—41no—
51D1132—41no—
52C22⋊D283—41no—
53C22⋊D283—41no—
54C2×Dic283—21no—
55C2×Dic283—21no—
56C2×Dic283—21no—
57C4×D283—42no—
58C283⋊C8—42no—
59C23×C283C2×D411yescharacteristic
60C2×C4×C283—21no—
61C2×C4×C283—21no—
62C2×C4×C283—41no—
63C2×C4×C283—41no—
64C2×C4×C283—42no—
65C2×C4×C283—42no—
66C2×C4×C283—42no—
67C2×C4×C283C22⋊C411yescharacteristic
68C2×C4×C283C22⋊C411yescharacteristic
69C2×C4×C283C22⋊C411yescharacteristic
70C2×C4×C283C22⋊C411yescharacteristic
71C2×C4×C283C22×C411yescharacteristic
72C2×C4×C283C2×D411yescharacteristic
73C22×C283—21no—
74C22×C283—21no—
75C22×C283C2×C22⋊C411yescharacteristic
76C22×C283AGL(1,ℤ/8)11yescharacteristic
77C22×C283#13711yescharacteristic
78C2×D283—41no—
79C2×D283—41no—
80C2×D283—41no—
81C4×C283—21no—
82C4×C283—21no—
83C4×C283—21no—
84C4×C283—21no—
85C4×C283—21no—
86C4×C283—21no—
87C4×C283—82no—
88Dic283—41no—
89Dic283—41no—
90Dic283—41no—
91C2×C283—21no—
92C2×C283—21no—
93C2×C283#41011yescharacteristic
94C2×C283#41711yescharacteristic
95C2×C283#42111yescharacteristic
96D283—81no—
97C283#151211yescharacteristic, complemented, Sylow
98#1512—2831nomaximal, Sylow
99#529—2831no—
100#432—2831no—
101#382D28311yescharacteristic, complemented
102#328—2832no—
103#327—2832no—
104#126—5661no—
105#125—2831no—
106#124—2831no—
107#123—5661no—
108C22⋊Q8—2831no—
109#121—2831no—
110C4×Q8—2831no—
111C4×D4—2831no—
112C4×D4—5661no—
113#117—5661no—
114C2×C4⋊C4—21no—
115C2×C42C2×D28311yescharacteristic
116C4⋊C8—5661no—
117C22⋊C8—2832no—
118#97—5661no—
119#95—21no—
120#95C2×D28312yes—
121C2×Q8—2831no—
122C2×D4—2831no—
123C2×D4—5661no—
124C22×C4—22no—
125C22×C4—5661no—
126C22×C4C22⋊D28311yescharacteristic
127C22×C4C22⋊D28311yescharacteristic
128C22×C4C22×D28311yescharacteristic
129C2×C8—5662no—
130C4⋊C4—42no—
131C4⋊C4—2831no—
132C4⋊C4—2831no—
133C4⋊C4—5661no—
134C4⋊C4—5661no—
135C4⋊C4—5661no—
136C4⋊C4—5661no—
137C22⋊C4—5661no—
138C22⋊C4—5661no—
139C22⋊C4—5661no—
140C22⋊C4—5661no—
141C22⋊C4—5661no—
142C42—5661no—
143C42C4×D28311yescharacteristic
144C42C4×D28311yescharacteristic
145C42D113211yescharacteristic
146C42D113211yescharacteristic
147C23—5661no—
148C23C2×C22⋊D28311yescharacteristic
149Q8—11321no—
150D4—11321no—
151D4—11321no—
152D4—11321no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—42no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—5661no—
161C2×C4—5661no—
162C2×C4—5661no—
163C2×C4—11322no—
164C2×C4(C2×D283)⋊C411yescharacteristic
165C2×C4(C2×D283)⋊C411yescharacteristic
166C2×C4(C2×D283)⋊C411yescharacteristic
167C2×C4(C2×D283)⋊C411yescharacteristic
168C2×C4C2×C4×D28311yescharacteristic
169C2×C4C2×D113211yescharacteristic
170C8—11322no—
171C22—21no—
172C22—21no—
173C22—11321no—
174C22—11321no—
175C22—11321no—
176C22C2×(C2×D283)⋊C411yescharacteristic
177C22#2258363611yescharacteristic
178C22#2258364111yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—82no—
186C4—11321no—
187C4—11321no—
188C4—11321no—
189C2—21no—
190C2—21no—
191C2—22641no—
192C2#3182643811yescharacteristic
193C2#3182646411yescharacteristic
194C2#3182648311yescharacteristic
subgroupG/H
centerC22C2×(C2×D283)⋊C4
commutatorC2×C4×C283C22×C4
FrattiniC22×C4C22×D283
Fitting#382×C283C2
socleC22×C283C2×C22⋊C4
prime radical#22583584C22
cosocleC22×C4×C283C23
hypercenter#382D283
hypocenterC283#1512
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #31826522C2semidirect
3. #31826201C2semidirect
5. #382×C283C2semidirect
7. #22583602C4semidirect
8. #22583598C4semidirect
12. C4×Dic566C4semidirect
13. C4×D1132C4semidirect
97. C283#1512semidirect
101. #382D283semidirect

Maximal subgroups

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

subgroupindex
#318269992
#318265222
#318262012
#318261982
#382×C2832
#1512283