Finite Group Databasebeta

← #49119894

Subgroups — #49119894

Order 36224.

238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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#31827014C211yesmaximal, characteristic
2#31826520C212yesmaximal, complemented
3#31826205C211yesmaximal, characteristic, complemented
4#31826204C212yesmaximal, complemented
5#329×C283C211yesmaximal, characteristic, complemented
6C2×#17985393C411yescharacteristic
7C2×#17985391C411yescharacteristic
8#22583608C411yescharacteristic
9#22583606C411yescharacteristic
10#22583598C2211yescharacteristic
11#22583583—22no—
12(C22⋊D283)⋊C4—22no—
13C42×D283C2211yescharacteristic
14Dic283⋊C8—22no—
15(C2×D283)⋊C8—22no—
16#22583521C2212yes—
17#124×C283C2211yescharacteristic
18#97×C283C2212yes—
19#17985393—42no—
20#17985391—42no—
21C2×Dic566C2×C411yescharacteristic
22C2×D1132—21no—
23C2×D1132C2×C411yescharacteristic
24C2×C22⋊D283—21no—
25C2×C22⋊D283—22no—
26C22×Dic283—21no—
27C2×C4×D283—21no—
28C2×C4×D283C2×C411yescharacteristic
29C2×C4×D283D412yes—
30C2×C283⋊C8—22no—
31Dic283⋊C4—22no—
32(C2×D283)⋊C4—22no—
33C4×Dic283C2×C411yescharacteristic
34C4×Dic283D412yes—
35C2×Q8×C283C2×C411yescharacteristic
36C2×D4×C283C2×C411yescharacteristic
37C2×C8×C283—22no—
38C22⋊C4×C283—22no—
39C42×C283C2311yescharacteristic
40C22×D283—21no—
41C22×D283C22⋊C411yescharacteristic
42Dic566—41no—
43D1132—41no—
44D1132—42no—
45C22⋊D283—44no—
46C22⋊D283—42no—
47C2×Dic283—21no—
48C2×Dic283—42no—
49C2×Dic283C22⋊C412yes—
50C2×Dic283C22⋊C411yescharacteristic
51C4×D283—22no—
52C4×D283—42no—
53C4×D283—42no—
54C283⋊C8—42no—
55C23×C283—21no—
56Q8×C283—41no—
57D4×C283—41no—
58C2×C4×C283—21no—
59C2×C4×C283C22×C411yescharacteristic
60C2×C4×C283C2×D412yes—
61C8×C283—42no—
62C22×C283—41no—
63C22×C283—42no—
64C22×C283C2×C22⋊C411yescharacteristic
65C2×D283—21no—
66C2×D283—22no—
67C2×D283—41no—
68C2×D283—42no—
69C4×C283—21no—
70C4×C283—22no—
71C4×C283—41no—
72Dic283—22no—
73Dic283—41no—
74Dic283#10012yes—
75C2×C283—81no—
76C2×C283C2×#10011yescharacteristic
77C2×C283#42112yes—
78D283—41no—
79D283—81no—
80C283#153611yescharacteristic, complemented, Sylow
81#1536—2831nomaximal, Sylow
82#532—2831no—
83#432—2832no—
84#329—2831no—
85#329—2832no—
86#329D28311yescharacteristic, complemented
87C2×#41—2831no—
88C2×#41—2831no—
89C4⋊Q8—2831no—
90#127—2831no—
91#124—2831no—
92#124C2×D28311yescharacteristic
93#121—5662no—
94C4×D4—5662no—
95C2×C42—2831no—
96C4⋊C8—5662no—
97C22⋊C8—5662no—
98#97—2832no—
99#97C2×D28312yes—
100#41—11322no—
101#41—11322no—
102C2×Q8—2831no—
103C2×Q8C4×D28311yescharacteristic
104C2×D4—2831no—
105C2×D4—5661no—
106C2×D4—5662no—
107C2×D4—5661no—
108C2×D4C4×D28311yescharacteristic
109C22×C4—2831no—
110C22×C4—2832no—
111C22×C4—5661no—
112C22×C4—5661no—
113C2×C8—22no—
114C2×C8—5662no—
115C4⋊C4—5662no—
116C22⋊C4—22no—
117C22⋊C4—5662no—
118C42—2831no—
119C42—2832no—
120C42C22×D28311yescharacteristic
121C23—21no—
122C23—2831no—
123C23—5661no—
124Q8—41no—
125Q8—11321no—
126D4—41no—
127D4—11321no—
128D4—11322no—
129D4—11324no—
130D4—11322no—
131C2×C4—21no—
132C2×C4—2831no—
133C2×C4—2832no—
134C2×C4—5662no—
135C2×C4—5661no—
136C2×C4—11322no—
137C2×C4—11322no—
138C2×C4—11322no—
139C2×C4C2×C4×D28311yescharacteristic
140C2×C4D4×D28312yes—
141C8—42no—
142C8—11322no—
143C22—41no—
144C22—42no—
145C22—5661no—
146C22—5662no—
147C22—11321no—
148C22—11322no—
149C22C22⋊C4×D28311yescharacteristic
150C4—21no—
151C4—22no—
152C4—41no—
153C4—2832no—
154C4—5662no—
155C4—11321no—
156C2—81no—
157C2—11321no—
158C2—22641no—
159C2#100×D28311yescharacteristic
160C2#3182648012yes—
subgroupG/H
centerC22C22⋊C4×D283
commutatorC2×C4×C283C22×C4
FrattiniC42C22×D283
Fitting#329×C283C2
socleC22×C283C2×C22⋊C4
prime radical#31827014C2
cosocleC42×C283C23
hypercenter#329D283
hypocenterC283#1536
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #31826520C2semidirect
3. #31826205C2semidirect
4. #31826204C2semidirect
5. #329×C283C2semidirect
80. C283#1536semidirect
86. #329D283semidirect

Maximal subgroups

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

subgroupindex
#318270142
#318265202
#318262052
#318262042
#329×C2832
#1536283