Finite Group Databasebeta

← #49119980

Subgroups — #49119980

Order 36224.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#31827013C211yesmaximal, characteristic
2#31826521C211yesmaximal, characteristic, complemented
3#31826487C211yesmaximal, characteristic, complemented
4#31826212C211yesmaximal, characteristic, complemented
5#31826210C211yesmaximal, characteristic, complemented
6#31826209C211yesmaximal, characteristic, complemented
7#331×C283C211yesmaximal, characteristic, complemented
8C2×#17985391—21no—
9C2×#17985375—21no—
10#22583610C2211yescharacteristic
11#22583597—21no—
12#22583581—21no—
13#22583581C412yes—
14D4×Dic283—21no—
15D4×Dic283C412yes—
16C42×D283C2211yescharacteristic
17C4⋊(C283⋊C8)C2211yescharacteristic
18C4⋊(C283⋊C8)C2211yescharacteristic
19Dic283⋊C8—21no—
20(C2×D283)⋊C8—21no—
21#22583520—21no—
22#127×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24C4⋊C8×C283C2211yescharacteristic
25#17985391—42no—
26#17985391—42no—
27C2×Dic566—21no—
28C2×C22⋊D283—22no—
29C22×Dic283—22no—
30C2×C4×D283C2×C411yescharacteristic
31C2×C4×D283D411yescharacteristic
32C2×C4×D283D411yescharacteristic
33#17985375—42no—
34C2×C283⋊C8—21no—
35C2×C283⋊C8—21no—
36C4⋊Dic283—21no—
37C4⋊Dic283C2×C412yes—
38C22⋊Dic283—22no—
39C22⋊Dic283—22no—
40C4×Dic283C2×C411yescharacteristic
41C4×Dic283D411yescharacteristic
42C4×Dic283D411yescharacteristic
43C2×D4×C283—21no—
44C2×D4×C283—21no—
45C2×D4×C283C2×C412yes—
46C2×C8×C283—21no—
47C2×C8×C283—21no—
48C42×C283C2311yescharacteristic
49C22×D283C22⋊C411yescharacteristic
50Dic566—41no—
51Dic566—41no—
52C22⋊D283—44no—
53C2×Dic283—22no—
54C2×Dic283—44no—
55C2×Dic283C22⋊C411yescharacteristic
56C2×Dic283C22⋊C411yescharacteristic
57C2×Dic283C22⋊C411yescharacteristic
58C4×D283—21no—
59C4×D283—21no—
60C4×D283—21no—
61C4×D283—21no—
62C4×D283—41no—
63C283⋊C8—41no—
64C283⋊C8—41no—
65C23×C283—22no—
66D4×C283—42no—
67D4×C283—41no—
68D4×C283—41no—
69D4×C283—41no—
70D4×C283—41no—
71C2×C4×C283C22×C411yescharacteristic
72C2×C4×C283C2×D411yescharacteristic
73C2×C4×C283C2×D411yescharacteristic
74C8×C283—41no—
75C8×C283—41no—
76C22×C283—42no—
77C22×C283—42no—
78C22×C283—42no—
79C22×C283C2×C22⋊C411yescharacteristic
80C2×D283—21no—
81C2×D283—21no—
82C2×D283—21no—
83C4×C283—21no—
84C4×C283AGL(1,ℤ/8)11yescharacteristic
85C4×C283AGL(1,ℤ/8)11yescharacteristic
86C4×C283AGL(1,ℤ/8)11yescharacteristic
87C4×C283#13711yescharacteristic
88Dic283—21no—
89Dic283—21no—
90Dic283—21no—
91Dic283—42no—
92C2×C283—82no—
93C2×C283#41311yescharacteristic
94C2×C283#41711yescharacteristic
95C2×C283#41811yescharacteristic
96D283—41no—
97C283#155711yescharacteristic, complemented, Sylow
98#1557—2831nomaximal, Sylow
99#532—2831no—
100#432—2831no—
101#423—2831no—
102#332—2831no—
103#332—2831no—
104#331—2831no—
105#331D28311yescharacteristic, complemented
106C2×#41—5661no—
107C2×M16—5661no—
108C4⋊Q8—2831no—
109#127C2×D28311yescharacteristic
110#124—5661no—
111#121—2832no—
112#121—5661no—
113C4×D4—2832no—
114C4×D4—5661no—
115C2×C42—2831no—
116C4⋊C8—2831no—
117C4⋊C8—2831no—
118C4⋊C8—5661no—
119C4⋊C8C2×D28311yescharacteristic
120C4⋊C8C2×D28311yescharacteristic
121C22⋊C8—5661no—
122#97—5661no—
123#41—11322no—
124#41—11322no—
125C2×Q8—5661no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—5662no—
129C2×D4C4×D28312yes—
130C22×C4—2831no—
131C22×C4—2831no—
132C22×C4—2831no—
133C22×C4—5662no—
134M16—11322no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—5661no—
138C2×C8—5661no—
139C4⋊C4—2832no—
140C4⋊C4—5661no—
141C22⋊C4—5662no—
142C22⋊C4—5662no—
143C42—2831no—
144C42—2831no—
145C42—2831no—
146C42C22×D28311yescharacteristic
147C23—22no—
148C23—2831no—
149Q8—11321no—
150Q8—11321no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—11324no—
157C2×C4—2831no—
158C2×C4—2831no—
159C2×C4—2831no—
160C2×C4—5661no—
161C2×C4—5661no—
162C2×C4—5661no—
163C2×C4—5661no—
164C2×C4—5662no—
165C2×C4—11321no—
166C2×C4—11324no—
167C2×C4C2×C4×D28311yescharacteristic
168C2×C4D4×D28311yescharacteristic
169C2×C4D4×D28311yescharacteristic
170C8—41no—
171C8—41no—
172C8—11321no—
173C8—11321no—
174C22—42no—
175C22—42no—
176C22—42no—
177C22—5661no—
178C22—5661no—
179C22—5661no—
180C22C22⋊C4×D28311yescharacteristic
181C4—21no—
182C4—5661no—
183C4—5661no—
184C4—5661no—
185C4—11322no—
186C4#2258363411yescharacteristic
187C4#2258363411yescharacteristic
188C4#2258363711yescharacteristic
189C4#2258363911yescharacteristic
190C2—82no—
191C2—11321no—
192C2#3182644611yescharacteristic
193C2#3182646311yescharacteristic
194C2#3182646811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D283
commutatorC2×C4×C283C22×C4
FrattiniC42C22×D283
Fitting#331×C283C2
socleC22×C283C2×C22⋊C4
prime radical#31827013C2
cosocleC42×C283C23
hypercenter#331D283
hypocenterC283#1557
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #31826521C2semidirect
3. #31826487C2semidirect
4. #31826212C2semidirect
5. #31826210C2semidirect
6. #31826209C2semidirect
7. #331×C283C2semidirect
97. C283#1557semidirect
105. #331D283semidirect

Maximal subgroups

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

subgroupindex
#318270132
#318265212
#318264872
#318262122
#318262102
#318262092
#331×C2832
#1557283